AGISTIN D6.3 Technical-Economic Sizing, Operation and Control Tools for Irrigation System Modernisation into Energy Storage Systems

HORIZON-CL5-2022-D3-01-11 Demonstration of innovative forms of storage and their successful operation and integration into innovative energy system and grid architectures D6.3 Technical-Economic Sizing, Operation and Control Tools for Irrigation System Modernisation into Energy Storage Systems Document properties FUNDING PROGRAM HORIZON EUROPE GRANT AGREEMENT NUMBER 101096197 PROJECT AGISTIN DELIVERABLE ID D6.3 TITLE Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems DISTRIBUTION LEVEL DUE DATE 30-06-2025 DATE SUBMITTED 30-06-2025 VERSION V1.0 WORK PACKAGE WP6 LEAD PARTICIPANT UPC TOTAL NUMBER OF PAGES 151 PU D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems All intellectual property rights are owned by the AGISTIN consortium members and are protected by the applicable laws. 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Version history VERSION DATE COMMENT V0.1 06-06-2025 FIRST DRAFT V1.0 30-06-2025 FINAL VERSION FOR SUBMISSION The Advanced Grid Interfaces for innovative STorage INtegration (AGISTIN) project has received funding from the European’s Union Horizon Europe research and innovation programme under grant agreement N°101096197 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Contents 1 Introduction 12 1.1 TheAGISTINProject.......................................... 12 1.2 Work package 6 and Objective of the Deliverable . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 StructureoftheDeliverable ..................................... 13 2 Irrigation communities 14 2.1 Currentsituation............................................ 14 2.2 Potential available energy estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Communitat de Regants Segrià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Othercommunities........................................... 18 2.5 CEDER-CIEMAT ............................................ 22 3 Optimisation and redesign for active role of irrigation systems as energy storage in the electrical grid 23 3.1 Introduction............................................... 23 3.1.1 Stateoftheart......................................... 24 3.1.2 Objective............................................ 25 3.2 Approach ................................................ 26 3.2.1 Other approaches / tested approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Optimisationtool............................................ 27 3.3.1 Devicemodels......................................... 27 3.3.2 Objectivefunction....................................... 39 3.3.3 Solvingtheproblem ..................................... 39 3.3.4 Scalability ........................................... 40 3.4 Studycases............................................... 44 3.4.1 Academiccase......................................... 45 3.4.2 Comunitat de Regants Les Planes i Aixalelles . . . . . . . . . . . . . . . . . . . . . . 47 3.4.3 Comunitat de Regants Segrià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.4 CEDER-CIEMAT........................................ 71 3.5 Conclusions............................................... 75 3.5.1 Futurework .......................................... 76 4 Energy storage sizing to prevent water hammer on PV pumping systems 77 4.1 Introduction............................................... 78 4.1.1 Water hammer in PV pumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.2 Contributions.......................................... 80 4.2 Problemdescription.......................................... 80 4.3 Methodology(Off-grid)........................................ 82 4.4 Studycase ............................................... 85 4.4.1 Clouds ............................................. 86 4.4.2 Results ............................................. 87 4.4.3 Feasibility and impact assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 4.4.4 Sensitivityanalysis ...................................... 90 4.5 Methodology(Gridconnected).................................... 93 4.5.1 PV disconnects, pump does not stop . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.5.2 PV disconnects, pump can stop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 4.5.3 PVdoesnotdisconnect ...................................100 4.6 AqueousECRbattery.........................................103 4.6.1 Results .............................................103 4.6.2 Results(Gridconnected)...................................103 4.7 Conclusion ...............................................104 4.7.1 Futurework ..........................................105 5 Potential grid services 106 5.1 Legislativecontext...........................................106 5.2 Applications in power system operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.2.1 Longtermstorage.......................................107 5.2.2 Shorttermstorage ......................................108 5.2.3 Comparison and requirements of long and short term storage . . . . . . . . . . . . 109 5.2.4 Services with revenue in Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 6 Real-time operation & control for innovative irrigation canal-based energy storage systems 113 6.1 Introduction...............................................113 6.2 Problemdefinition...........................................116 6.3 Methodology..............................................117 6.3.1 Development of OFO-based controller for pump-based irrigation plants . . . . . . 119 6.4 Performanceassessment.......................................121 6.4.1 Studycase...........................................121 6.4.2 Preliminaryresults ......................................122 6.5 Conclusions...............................................123 6.5.1 Futurework ..........................................124 7 Fundamental AGI topologies and control strategies 125 7.1 Introduction...............................................125 7.2 Comparing AC and DC microgrid approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.3 Control architectures for the converter connected to the primary grid . . . . . . . . . . . . . 128 7.3.1 Dual-Portcontrol .......................................129 7.4 Discussion on possible AGI configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.5 Models to study the connection to the primary grid . . . . . . . . . . . . . . . . . . . . . . . . 131 7.5.1 Steady-stateModel......................................132 7.5.2 LinearModel..........................................133 7.6 InitialResults..............................................135 7.6.1 Powerflowsolution .....................................136 7.6.2 Small-Signalanalysis ....................................137 7.6.3 PVstepchange........................................137 7.6.4 Gridanglestepchange....................................139 7.7 Futurework...............................................140 Bibliography 141 4 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems List of Figures 2.1 Evolution of the irrigated and dry crops extension in Spain between 2004 and 2023 . . . 15 2.2 Declared agricultural land in Catalonia, classified into irrigated and dry (year 2023) . . . . 15 2.3 Location of the reservoirs of the analysed irrigation communities next to the main participating rivers and tributaries. Colours correspond to different irrigation communities. . . . . 16 2.4 Facilities at the CR Segrià-Sud . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.5 Irrigation communities in the region considered for further analysis . . . . . . . . . . . . . . 19 2.6 Facilities at the CR de Les Planes i Aixalelles . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 CEDER-CIEMAT case schematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1 Location of the state of the art references. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Definition of the variables of a source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.3 Reservoirdefinition .......................................... 29 3.4 Definition of the flow direction in a pipe device . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5 Characteristiccurveofapipe..................................... 30 3.6 Definition of the flow and electric power direction in a pump device . . . . . . . . . . . . . . 31 3.7 Operating region of a variable speed pump. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.8 Operating region of linear approximation model . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.9 Definition of the flow and electric power direction in a new pump device . . . . . . . . . . . 34 3.10 Definition of the flow and electric power direction in a turbine device . . . . . . . . . . . . . 35 3.11 Comparison of different methods using equality, inequality, and linearized constraints. . . 42 3.12Studycasediagram........................................... 45 3.13 Maximum capacity, already installed and newly sized (dim.) magnitudes of the PV, battery andturbineelements.......................................... 46 3.14 Volume at the reservoirs (R0, R1) and flow of both pumps (P1, P2), irrigation at reservoir 1 (Irr)andturbine(T1)........................................... 47 3.15 Power balance of the system (defined positive if consumed by the element) and electricity cost. ................................................... 47 3.16 Battery state of charge and power (defined positive if absorbed). . . . . . . . . . . . . . . . 48 3.17 CR Les Planes i Aixalelles study case base system. . . . . . . . . . . . . . . . . . . . . . . . 48 3.18 Average daily irrigation demand on CR Les Planes i Aixalelles (S: Summer, W: Winter). Real data from 1 year and 90% confidence interval. . . . . . . . . . . . . . . . . . . . . . . . 48 3.19Variationsonthestudycase ..................................... 50 3.20Resultsofthebasecase........................................ 51 3.21ResultsofPaTcase(Case1)...................................... 51 3.22 Results of grid connected case (Case 2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.23 Results of grid connected + PaT case (Case 3). . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.24 CR Segrià-Sud Base case system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.25 CR Segrià-Sud water consumption for irrigation. . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.26 CR Segrià-Sud system division. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.27 CR Segrià-Sud lower and upper divisions and assumptions. . . . . . . . . . . . . . . . . . . 55 3.28 Grid equivalent GHG emission factor, cost of electricity and sell price for the defined typical days.................................................... 56 5 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3.29 CR Segrià-Sud upper results - Base case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.30 CR Segrià-Sud upper results - PaT case (Case 1). . . . . . . . . . . . . . . . . . . . . . . . . 61 3.31 CR Segrià-Sud upper results - grid connected case (Case 2). . . . . . . . . . . . . . . . . . . 62 3.32 CR Segrià-Sud upper results - PaT + grid connected case (Case 3). . . . . . . . . . . . . . . 63 3.33 CR Segrià-Sud upper results - emissions case (Case 3-em). . . . . . . . . . . . . . . . . . . 64 3.34 CR Segrià-Sud lower results - Base case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.35 CR Segrià-Sud lower results - grid connected case (Case 2). . . . . . . . . . . . . . . . . . . 68 3.36 CR Segrià-Sud lower results - PaT + grid connected case (Case 3). . . . . . . . . . . . . . . 69 3.37 CR Segrià-Sud lower results - emissions case (Case 3-em). . . . . . . . . . . . . . . . . . . 70 3.38 Spiderplots resulting from the sensitivity analysis. . . . . . . . . . . . . . . . . . . . . . . . . 71 3.39 CEDER case representation with Pyomo blocks. . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.40 CEDER results - Case 1 in summer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.41 CEDER results - Case 1 in winter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.42 CEDER results - Case 2 in summer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.43 CEDER results - Case 2 in winter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.44 CEDER results - Case 3 in summer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.45 CEDER results - Case 3 in winter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.46 CEDER costs results comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.1 Electrical scheme of a PV pumping system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2 Sketch representation of an irradiance drop event. . . . . . . . . . . . . . . . . . . . . . . . . 79 4.3 Irradiance drop event with ESS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.4 Data key points that define a cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.5 Location of the irradiance sensor and study case on the CR Segrià-Sud facilities. . . . . . . 85 4.6 Power generation and consumption of a PV pump system in the Segrià-Sud facilities, correspondingto25thJuly2022..................................... 86 4.7 Rank function plot of clouds’ duration and shaded radiant exposure. . . . . . . . . . . . . . 87 4.8 Number of pump stopping events shading a certain energy, from data and estimator . . . 87 4.9 Costs per year for different technologies and base case. . . . . . . . . . . . . . . . . . . . . . 88 4.10 Costs per year for different technologies and base case and sensitivity for interest rate 𝑖 and cost of energy 𝑐𝑔𝑟𝑖𝑑 ........................................ 90 4.11 Sensitivity of the costs per year for different technologies and base case for irradiance threshold 𝐺𝑡ℎ .............................................. 91 4.12 Cost function and minimum value for different irradiance thresholds between 100 and 600 W/m2. .................................................. 92 4.13 Sketch representation of the grid connected PV pumping system. . . . . . . . . . . . . . . . 93 4.14Strategy1................................................. 94 4.15 Costs per year for different technologies and grid connected case 1. . . . . . . . . . . . . . 96 4.16 Costs per year for different technologies and grid connected case 1 and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝.......................... 96 4.17Strategy2................................................. 97 4.18 Costs per year for different technologies and grid connected case 2. . . . . . . . . . . . . . 99 4.19 Costs per year for different technologies and grid connected case 2 and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝.......................... 99 4.20 Considered behaviour with grid and PV connected. . . . . . . . . . . . . . . . . . . . . . . . 100 4.21 Costs per year for different technologies and grid connected with PV. . . . . . . . . . . . . . 102 4.22 Costs per year for different technologies and grid connected case 1 and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝..........................102 4.23 Optimal sizing 𝐸(1) for the Geyser Aqueous ECR energy storage system for a range of capital cost and sensitivity for cost of energy 𝑐𝑔𝑟𝑖𝑑.........................104 5.1 ACER’s proposal on Requirements for generation in mixed-technology sites . . . . . . . . 107 6 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 5.2 Division of frequency regulation, frequency curve example (top) and power type responsibilities(bottom)............................................108 6.1 Online Feedback optimisation structure based on gradient flow. . . . . . . . . . . . . . . . . 117 6.2 Relationship between offline and online optimisation tools. . . . . . . . . . . . . . . . . . . . 120 6.3 Model of the simplest test case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 6.4 Testing of the plant with a good estimation of water consumption for irrigation. . . . . . . . 122 6.5 Testing of the plant with a wrong estimation of water consumption for irrigation. . . . . . . 123 7.1 Maximum Power Point Tracking. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.2 ACvsDCinterconnections.......................................128 7.3 Example of a DC voltage control architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 7.4 Example of an AC grid-forming control architecture with droop control. . . . . . . . . . . . 129 7.5 Dual-Port control architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.6 Schemes of the analysed AGI configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.7 VSCelectricschememodel. .....................................131 7.8 Controlled current source model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.9 Initialcasestudyscheme........................................136 7.10 Linear and non-linear models comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.11 Main converter active and reactive power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 7.12 Main converter dc voltage and angle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7.13 Main converter active and reactive power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7.14 Main converter voltage and current magnitudes. . . . . . . . . . . . . . . . . . . . . . . . . . 140 List of Tables 2.1 Potential available energy storage capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 CR Segrià-Sud legacy equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3 CR Segrià-Sud potential energy storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.4 CR Les Planes i Aixalelles legacy equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 CR Les Planes i Aixalelles potential energy storage . . . . . . . . . . . . . . . . . . . . . . . 19 2.6 CR Garrigues Sud legacy equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7 CR Garrigues Sud potential energy storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.8 CR Zona Oriental de la Terra Alta legacy equipment . . . . . . . . . . . . . . . . . . . . . . . 21 2.9 CR Zona Oriental de la Terra Alta potential energy storage (*: equipment planned or under construction) .............................................. 21 2.10 CEDER potential energy storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1 Results of time and final cost value and comparison between algorithms and methods. . . 43 3.2 Characteristics of the case’s elements (in p.u.) . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.3 Variableslinkedbyarcs........................................ 45 3.4 Costsin€/p.u............................................... 46 3.5 Characteristics of the case’s elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.6 Casessummary ............................................ 53 3.7 Characteristics of the CR Segria-Sud case’s devices . . . . . . . . . . . . . . . . . . . . . . . 54 3.8 Results(Upper)............................................. 57 7 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3.9 Results(Lower)............................................. 65 3.10 Sensitivity analysis total cost average . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.11 Objectives values and execution time per case and season. . . . . . . . . . . . . . . . . . . . 75 4.1 Irrigation communities with PV pumping systems in Catalunya. . . . . . . . . . . . . . . . . 78 4.2 Characteristics of the PV pumping system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.3 Capital and operation costs of the analysed energy storage systems . . . . . . . . . . . . . 86 4.4 Statistical description of the properties of the observed clouds. . . . . . . . . . . . . . . . . 86 4.5 Statistical description of the clouds dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.6 Sizingresults.............................................. 88 4.7 Properties of the ESS technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.8 PS3 sensitivity analysis results for cost of energy and real interest rate . . . . . . . . . . . . 91 4.9 PS3 sensitivity analysis results for irradiance threshold . . . . . . . . . . . . . . . . . . . . . 91 4.10 Grid connected base case characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.11 Grid connected sizing results (Strategy 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.12 PS3 sensitivity analysis results for cost of energy, real interest rate and excess power term 96 4.13 Grid connected sizing results (Strategy 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 4.14 Grid connected sizing results (without PV disconnection) . . . . . . . . . . . . . . . . . . . . 102 4.15 Maximum capital cost for 𝐸(1) ≤0,1 kWh for different cost of energy values . . . . . . . . . 103 4.16 Maximum capital cost for different excess power term (grid connected cases) . . . . . . . . 104 5.1 Comparison and requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 6.1 Parameters of the simple test case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 7.1 Mainconverterparameters.......................................136 7.2 Powerflowsolution...........................................136 7.3 System’seigenvalues..........................................138 8 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Acronyms AC alternating current ACATCOR Associació Catalana de Comunitats de Regants ACER Agency for Cooperation of Energy Regulators aFRR automatic frequency restoration reserve AGI advanced grid interface AGISTIN Advanced Grid Interfaces for innovative STorage INtegration CEDER Centro de Desarrollo de Energías Renovables CIEMAT Centro de Investigaciones Energéticas Medioambientales y Tecnológicas CR Comunitat de Regants DC direct current ECR electrochemical recuperator EMS energy management system ENTSO-E European Network of Transmission System Operators for Electricity ESS energy storage system FCR frequency containment reserve FENACORE Federación Nacional de Comunidades de Regantes Flow redox flow battery Fw flywheel GHG greenhouse gas IPOPT interior point optimiser LCOS levelised cost of storage Lead lead acid battery LIB lithium-ion battery mFRR manual frequency restoration reserve MINLP mixed integer non-linear programming MPPT maximum power point tracking NLP non-linear programming 9 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems as collected available data from public tenders [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Then, for each reservoir present in the systems we estimated the potential energy defined as: 𝐸=𝜌𝑔Δ𝐻𝑊, (2.1) where 𝜌is the density of the water assumed 1 000 kg/m3,𝑔the gravity acceleration constant near the surface of the Earth, assumed 9,81 m/s2,Δ𝐻(m) the average difference of heights between a reservoir and its direct source and 𝑊(m3) the volumetric capacity of the reservoir. The results are summarised in Table 2.1. We published the whole dataset, which is publicly available in [25]. The calculation does not consider the efficiency of the pumping systems and turbines or pump as turbine (PaT)s required to extract the energy. It does not examine either the operation of reservoirs in series, which will have an influence on the amount of energy that can be extracted on irrigation communities that have several reservoirs in series. Since not all of the required data could be gathered, some values were estimated as well as reservoirs were excluded from the analysis. Assuming a cost of 340 ±60 $/kWh [26] and a ratio of 1 $ = 0,86 €(as per June 2025), the capital investment required for an stationary energy storage system (ESS) of such characteristics would range in 643 ±114 M€. 0 30 60 km Figure 2.3 –Location of the reservoirs of the analysed irrigation communities next to the main participating rivers and tributaries. Colours correspond to different irrigation communities. 2.3 Communitat de Regants Segrià-Sud The Comunitat de Regants Segrià-Sud is located in the province of Lleida, at geographic coordinates N 41∘21’ 44” E 0∘27’ 14”, and has influence over the municipalities of Almatret, Llardecans, Maials, Seròs and Torrebesses. Its facilities consist of 4 pumping stations with 18,4 MW of installed power, 5 reservoirs with a total capacity of 980 000 m3and 3 solar photovoltaic (PV) plants totalling 1,3 MWp (Figure 2.4). Pumping stations PS0 and PS1 deliver water from the river Ebre to reservoir R1, from where it is distributed to reservoirs R2, R3 and R4 via pumping station PS2. Pumping station PS3 takes water from reservoir R4 to reservoir R5. Two of the PV plants are located at pumping station PS2 and the remaining one is projected to be installed at PS3 [21, 22, 27, 28, 29, 30]. Table 2.2 summarises the equipment present at the facilities of the Comunitat de Regants Segrià-Sud and Table 2.3 shows its potential energy storage as computed with (2.1). 16 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 2.1 –Potential available energy storage capacity (*: volume was estimated from reservoir surface). Data from [25]. Irrigation community Reservoirs E [MWh] Aigües del Montsant * 6 5,04 Albí 3 6.44 Algerri Balaguer 6 111,73 Ascó 2a zona * 2 4,76 Aubarrells 2 6,03 Bassanova 3 0,87 Benissanet 2 10,45 Garrigues Sud 15 158,30 Ginestar 2 11,46 Les Planes i Aixalelles 1 3,58 Monredons-Valls 1 18,64 Mora d’Ebre * 2 10,12 Mora la Nova * 1 3,83 Palma d’Ebre 3 47,84 Perelló 2 10,15 Pinell de Brai 1 16,48 Progrés * 1 1,60 Rasquera 2 34,13 Riu Rinet 2 7,10 Segarra Garrigues 38 1 186,21 Segrià Sud 5 255,01 Torre de l’Espanyol * 4 5,28 Torres de Segre 1 101,02 Vilosell 1 12,26 Vingalís 2 18,10 Xerta Sènia 3 23,57 Zona Oriental Terra Alta 8 183,54 TOTAL 2 223,52 Table 2.2 –CR Segrià-Sud legacy equipment. (*: equipment planned or under construction) Pumping station N. Pumps Power [kW] Flow [m3/h] Solar PV [kWp] PS0 3 3 x 950 11 520 - PS1 3 3 x 3 200 11 520 - PS2 9 3 x 250 3 x 315 3 x 1 250 3 154 2 010 6 570 - 523,00 527,50 PS3 3 3 x 160 2 778 274,68* Table 2.3 –CR Segrià-Sud potential energy storage Reservoir Volume [m3] Average altitude [m] Energy [MWh] Ebre River (Ribarroja) - 70 - Reservoir R1 142 869 331 101,73 Reservoir R2 297 042 359 22,62 Reservoir R3 85 268 419 20,38 Reservoir R4 269 485 426 69,27 Reservoir R5 185 814 447 10,97 17 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Figure 2.4 –Facilities at the CR Segrià-Sud. Ortophoto from Institut Cartogràfic i Geològic de Catalunya [31], World map from OpenStreetMap [32]. 2.4 Other communities Besides the CR Segrià-Sud being already in the project, we made a call for data to the irrigation communities involved with ACATCOR, the main Catalan association of irrigation communities. Several have answered and are depicted in Figure 2.5. Ebre and Segre, the two main rivers of the region which feed the communities reservoirs, are highlighted as well. Comunitat de Regants de Les Planes i Aixalelles The Comunitat de Regants de Les Planes i Aixalelles is located in the province of Tarragona, at geographic coordinates N 41∘12’ 39” E 0∘34’ 32”, and has influence over the municipalities of Ascó, Flix and Vinebre. Their facilities consist of a pumping station, a reservoir and a solar PV plant (Figure 2.6). The pumping station consists of 2 pumps of 110 kW powered by a three-phase motor with squirrel cage rotor. The reservoir can hold a volume of 13 000 m3and is located at an altitude of 138 m over sea level, 101 m above the pumping station. The solar PV plant, in service since march of 2023, is built of 468 PV panels for a total of 215,28 kWp. An anti-freezing system allows the facilities to work on colder conditions, extending the irrigation season on winter time [19, 33, 34]. Table 2.4 summarises the equipment present at the facilities of the Comunitat de Regants de Les Planes i Aixalelles and Table 2.5 shows its potential energy storage as computed with (2.1). 18 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Ebre Segre ARAGÓN LLEIDA TARRAGONA Segrià Sud Garrigues Sud Les Planes i Aixalelles Zona Oriental Terra Alta Figure 2.5 –Irrigation communities in the region considered for further analysis. World map from OpenStreetMap [32]. Data from [8]. Table 2.4 –CR Les Planes i Aixalelles legacy equipment Pumping station N. Pumps Power [kW] Flow [m3/h] Solar PV [kWp] PS1 1+1 (1+1) x 110 200 215,28 Table 2.5 –CR Les Planes i Aixalelles potential energy storage Reservoir Volume [m3] Average altitude [m] Energy [MWh] Ebre River (Ascó) - 37 - Reservoir R1 13 000 138 3,58 19 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Figure 2.6 –Facilities at the CR de Les Planes i Aixalelles. Ortophoto from Institut Cartogràfic i Geològic de Catalunya [31], World map from OpenStreetMap [32]. Comunitat de Regants del Garrigues Sud The Comunitat de Regants del Garrigues Sud is located in the province of Lleida, at geographic coordinates N 41∘22’ 16” E 0∘39’ 42”, and has influence over the county of Les Garrigues. Their facilities consist of 8 pumping stations, 15 reservoirs and 2 solar PV plants [18, 35, 36]. Table 2.6 summarises the equipment present at the facilities of the Comunitat de Regants del Garrigues Sud and Table 2.7 shows its potential energy storage as computed with (2.1). Table 2.6 –CR Garrigues Sud legacy equipment Pumping station N. Pumps Power [kW] Flow [m3/h] Solar PV [kWp] PS1 3+1 (3+1) x 450 1 537 601,88 PS2 3+1 (3+1) x 315 1 353 462,24 PS3 1+1 (1+1) x 400 800 - PS4 1+1 (1+1) x 75 118 - PS5 3+1 (3+1) x 355 1 080 - PS6 2+1 (2+1) x 110 608 - PS1-IV 3+1 7 500 6 109 - PS2-IV 3+1 8 400 6 109 - Comunitat de Regants de la Zona Oriental de la Terra Alta The Comunitat de Regants de la Zona Oriental de la Terra Alta is located in the province of Tarragona, at geographic coordinates N 41∘7’ 5” E 0∘22’ 23”, and has influence over the county of Terra Alta. Their facilities consist of 4 pumping stations and 7 reservoirs [24]. Table 2.8 summarises the equipment present at the facilities of the Comunitat de Regants de la Zona Oriental de la Terra Alta and Table 2.9 shows its potential energy storage as computed with (2.1). 20 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 2.7 –CR Garrigues Sud potential energy storage Reservoir Volume [m3] Average altitude [m] Energy [MWh] Ebre River (Flix) - 40,4 - Reservoir R0 3 600 203 1,60 Reservoir R1 14 688 198 0,25 Reservoir R2 74 870 323 25,50 Reservoir R3 280 418 0,07 Reservoir R4 40 470 0,02 Reservoir R5 54 000 518 28,77 Reservoir R6 54 000 580 9,05 Break 4 668 217 2,26 Break BT-0 1 000 328 0,78 Reservoir E1 92 000 619 16,49 Reservoir E2 35 500 545 18,60 Reservoir E3 82 900 662 18,52 Reservoir E4 91 000 685 5,88 Reservoir E5 65 800 637 12,08 Reservoir E6 56 600 781 18,43 Table 2.8 –CR Zona Oriental de la Terra Alta legacy equipment (*: equipment planned or under construction) Pumping station N. Pumps Power [kW] Flow [m3/h] Solar PV [kWp] PS0 3+1 (3+1) x 680 9 000 - PS1 3+1 (3+1) x 8 351 9 000 - PS2 12 (1+1) x 600 608 - (2+1) x 794 1 109 - (2+1) x 914 2 268 - (3+1) x 914 4 266 - PS3 2+1 (2+1) x 150 252 - PS4* 2+1 (2+1) x 178 1 620 - Table 2.9 –CR Zona Oriental de la Terra Alta potential energy storage (*: equipment planned or under construction) Reservoir Volume [m3] Average altitude [m] Energy [MWh] Ribarroja reservoir - 69 - Tank 3 600 88 0,19 Reservoir R1 50 000 359 36,86 Reservoir R2.1 150 000 445 35,15 Reservoir R2.2 270 000 457 72,47 Reservoir R2.3 33 000 465 9,53 Reservoir R2.4 41 000 521 18,10 Reservoir R3 30 800 551 2,56 Reservoir R4* 70 000 503 8,68 21 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 2.5 CEDER-CIEMAT Centro de Desarrollo de Energías Renovables (CEDER)-Centro de Investigaciones Energéticas MedioambientalesyTecnológicas(CIEMAT)islocatedinthe provinceofSoria atgeographic coordinates N41º36’22” E 2º27’37” is a center dedicated to the investigation in renewable energies and storage systems. Since the center is not dedicated to the supplying of water to fields and the facilities are fully dedicated to research finalities, the 3 reservoirs are relatively smaller than in irrigation communities. Table 2.10 shows the characteristics of these reservoirs. Table 2.10 –CEDER potential energy storage Reservoir Volume [m3] Average altitude [m] Energy [MWh] Reservoir R0 2 000 1 019 - Reservoir R1 1 500 1 086 0,27 Reservoir R2 500 1 096 0,09 The pumping station is composed of 4 pumps of 7,5 kW each connected to reservoir 1 and 2. The pumps are connected to a common bus with the grid and a 16 kW PV plant. Furthermore, a turbine of 40 kW is installed in the same pumping station. Note that the pumping station can pump to the reservoir 1 or 2 but only can turbine from the reservoir 1, and reservoir 1 and 2 are connected through a pipe with a valve. A 90 kW flow battery with 400 kWh capacity is also present in the system. The system is represented in Figure 2.7. Figure 2.7 –CEDER-CIEMAT case schematic. Figure provided by CEDER-CIEMAT. 22 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3 Optimisation and redesign for activeroleofirrigationsystemsasenergy storage in the electrical grid Currently, irrigation systems are viewed by the bulk power grid as energy demand points. Hence, the only form of interaction that occurs between these systems is limited to the unidirectional power flow from the grid to the pumping stations of the irrigation system. The demand profile of the pumping stations is correlated with the times when energy has a lower price (off-peak periods). However, the water stored in reservoirs at different heights can be regarded as a form of energy storage. In order to release the full potential of irrigation systems as grid-service providers, a redesign of the system components is required to increase it operational capacity. Therefore, within the framework of this project, we analyse the potential capacity of reservoir-based irrigation systems to adopt an active role in the electrical grid providing services such as energy storage. This chapter is structured as follows: i Section 3.1 introduces the topic and reviews the state of the art solutions. ii Section 3.2 introduces our approach. iii Section 3.3 describes the methodology and optimisation tool we developed to address the topic. iv Section 3.4 analyses several study cases applying the developed methodology. v Section 3.5 concludes the study and provides additional future research settled on the obtained results. 3.1 Introduction Irrigation communities’ water distribution systems may take many forms depending on whether they are pressurised or open canals and whether they use water storage in the form of reservoirs or deliver straight from the main water source. On this work, we focus on pump-fed reservoir-based irrigation systems. In such systems, a pumping station transfers water from the main source or an intermediate reservoir to a higher reservoir. From there, a series of canals or pipes deliver water to the users, usually by gravity. The energy requirements for the pumping stations of these systems are significant, ranging from hundreds of MWh to GWh. These requirements can account for more than 70 % of their operating costs. In the Languedoc-Roussillon Regional Hydraulic Network (France) 95 % of the annual 80 GWh stem from pumping stations [37]. However, energy demand is characterised by a seasonal nature, with the system remaining close to inactive during winter months, when irrigation demand drops. 23 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems In severalcases, irrigationcommunitiesdecide toinstall solarphotovoltaic (PV)pumping systems. On-site PVgenerationreducesenergyconsumptionfromthe electricalgridor replacesdieselpumping systems. Despite their potential, the role of irrigation systems as active players in the electricity grid has hardly been investigated or considered. As energy storage and demand response become increasingly relevant for grid stability [38], the unique characteristics of irrigation systems pose them as valuable providers of grid services. To provide grid services, it is essential to maintain enough water in reservoirs, enabling the flexibility to shift energy consumption or even supply power back to the grid. Achieving this will require precise long-term planning and, if necessary, the replacement of specific assets of pumping stations. 3.1.1 State of the art Previous works have addressed the matter of improving energy efficiency and reducing energy demand of irrigation systems. As noticed by [37], this can be achieved by optimising their design and operation and applying correcting measures, as well as using the existing infrastructure for energy production either from solar or hydraulic sources. Many different proposals can be found in the literature to exploit the potential that hydropower irrigation systems can provide. We classified these references according to whether they address reservoir-based energy storage, take advantage of the water flow running through open canals, or extract power from excess pressure on irrigation hydrants (Figure 3.1). Notice that several of them are located in Europe, which may suggest a localised raise of the interest on the topic but could also emerge from geographic research bias on funding, publication and recommendation [39] as well as our own bias. Legend Reservoirs Canals Hydrants Figure 3.1 –Location of the state of the art references. Reservoir-based energy storage On the Vidarbha region (India), [40] estimated the capacity of 19 projects involving micro-hydro power generation on irrigation dams, with results ranging from 150 kW to 2 200 kW. On Froyennes (Belgium), [41] selected and tested a 30 kW pump running in reverse, or pump as turbine (PaT), with a variable frequency driver for a micro pumped-storage hydropower (PSH) facility. The facility consisted of two 650 m3storm-water basins, a total of 110,2 kWp of PV peak power, four 2,4 kWp wind turbines and a centralised controller which integrated everything with a micro energy grid. On Perth (Australia), [42] developed and tested a two layer energy management system (EMS) for farmhouses to manage a PVPSH facility and the scheduling of the irrigation system. The methodology comprised the utilisation of neural network models for the prediction of weather and demand, in combination with a genetic algorithm for cost minimisation. The EMS was verified on a system consisting on a 3,0 kW pump and a 0,768 kW 24 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems turbine. Same authors modelled on [43] a PSH system which was validated on an experimental setup. On the Mount Lofty Ranges (Australia), [44] developed a combined 3,0 kW PaT with PV for household demand storing water in irrigation reservoirs. They compared the performance of the analysed system to a commercial battery energy storage system and estimated the former levelised cost of storage (LCOS) to be 30 % lower than the latter. On Catalonia (Spain), we preliminarily analysed a simple irrigation system consisting of a single 13 000 m3reservoir with a grid connected 110 kW pump and a 215,3 kWp PV pumping system and noticed it was feasible to run the system for energy storage in winter [45]. Flow on canals On Chia-Nan (Taiwan), [46] elaborated a preliminary location analysis for turbine placement on irrigation canals and installed a 1,5 kW water wheel in a canal on Yunlin (Taiwan) [47]. On the Piedmont (Italy), [48] analysed the combined use of irrigation and hydroelectric production and estimated between 3,5 MW and 9,0 MW of extra combined hydraulic power could be obtained through the introduction of small hydropower plants in irrigation systems. As reported by [49], on the Canal de Provence (France) an agreement between the public company responsible for the water management and the main irrigators union made it possible to invest in a hydropower plant which uses the flow of the canal to generate 5 GWh annually. On Calabria (Italy), [50] developed a methodology and evaluated the placement of micro hydropower plants on irrigation systems’ pipelines, calculating from 100 kW to 300 kW of feasible installed power on the analysed case study and noticing investment returns heavily depend on national subsidies for renewable energy. On Valencia (Spain), [51] analysed the deployment of Archimedes screw turbines to extract from 1 to 5 annual GWh from the canal. Excess pressure on hydrants On Andalusia (Spain), [52] validated, on a model, a methodology for PaT selection to extract the potential of excess pressure points and in [53] estimated a potential of 21,05 GWh per year on Sevilla and Córdoba (Spain) using the same power extraction method. On Vellore (India), [54] developed a pico hydropower generation system with a 0,74 kW induction motor to extract power directly from an irrigation hydrant to generate 150 W. On Córdoba (Spain), [55] analysed the environmental and economic impact of a 0,66 kWp PV with a 4 kW PaT system to recover energy from excess pressure and compared it to that of a 6 kVA diesel generator. The study concluded that the impacts are considerably lower for the novel system, even to that of a lone PV plant, but the corresponding battery highly contributes on the minerals and metals aspect of the environmental impact. On Alicante (Spain), [56] proposed an optimisation methodology and developed software to size and choose the best location of micro hydropower systems for irrigation systems, considering different configurations with floating PV, ground PV, PaT, battery energy storage and grid connection. 3.1.2 Objective To our best knowledge, there is no open source software that can accurately analyse and optimise irrigation systems for active participation on the grid, considering not only the energy flow but also the bounds and feasible operating points of the hydraulics equipment. The main novel contribution of this work is the development of a multi-physics open source optimisation tool based in Python and utilising the Pyomo libraries [57, 58]. The tool facilitates the efficient and clear formulation of optimisation problems, by linking pre-defined models. The tool then invokes a numerical solver algorithm to compute a solution to the problem. The intricacies of the solver are not addressed in this document 1. We presented an initial 1Readers interested in the subject are referred to [59]. 25 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems • Hydraulic power (3.14): 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡) • Electrical power (3.15): 𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡) • Flow limits (3.13): 𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖≤𝑄𝑖(𝑡)≤𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖 Pump (linear approximation) Quadratic expressions can increase the computational cost of the problem, as seen in the 𝐻-𝑄characteristic curve in the pump model. Therefore, relaxing this expression is an interesting approach. Previously, the relaxation of the same expression was achieved by substituting the equality constraint with an inequality constraint in the 𝐻-𝑄expression, allowing the elimination of the variable representing the pump speed, as suggested in [65]. Thanks to this improvement, it is now possible to construct a pump model where the quadratic expression is replaced with a linear approximation while maintaining the inequality constraint. For a better approximation of the original curve, the method divides the space between 𝑄𝑖and 𝑄𝑖into 𝑁𝐿,𝑖 intervals, fixing these points on the original curve. Then, a constraint is formulated for each line using an inequality, ensuring that the operating area lies below the approximation and, therefore, below the original curve—without requiring any binary variables. Figure 3.8 illustrates an example of this approximation using three equidistant intervals, along with the operating area for the optimisation problem. 𝑄 𝑄𝑖𝑄1,𝑖 𝑄2,𝑖 Δ𝑄=𝑄𝑖−𝑄𝑖 Δ𝑄/𝑁𝐿,𝑖 𝑄𝑖 𝐻 Figure 3.8 –Operating region of linear approximation model The constraints are built by using the following expressions: 𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖 𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...,𝑁𝐿(3.16) 𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖 𝑁𝐿,𝑖 𝑙=1,...,𝑁𝐿(3.17) 𝐻𝑙,𝑖 =( 𝑛𝑖 𝑛𝑁,𝑖)2𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖(𝑡))2𝑙=1,...,𝑁𝐿(3.18) Constraint (3.16) represents the line that approximates the curve, while (3.17) is used to calculate the key points that minimize the error. Finally, (3.18) projects the key flow points onto the original nominal curve of the pump. 32 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems With the modification the variables and parameters are: Linear Pump summary Variables: • Flow (inlet): Qin,i∈[−𝑄𝑖,0]. Connection: (3.3) • Flow (outlet): Qout,i∈[0,𝑄𝑖]. Connection: (3.3) • Head: Hi∈[0,𝐴𝑖]. Connection: (3.2) • Hydraulic power: ph,i∈[0,𝑝ℎ,𝑖] • Electric power: pe,i∈[0,𝑝𝑒,𝑖]. Connection: (3.3) • Pump ON: 𝛽ON,i∈{0,1} Constraints: • Pressure (3.16): 𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖 𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...,𝑁𝐿 • Flow key points (3.17): 𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖 𝑁𝐿,𝑖 𝑙=1,...,𝑁𝐿 • Flow points projection (3.18): 𝐻𝑙,𝑖 =( 𝑛𝑖 𝑛𝑁,𝑖)2𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖(𝑡))2𝑙=1,...,𝑁𝐿 • Flow coherence (3.12): 𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡) • Hydraulic power (3.14): 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡) • Electrical power (3.15): 𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡) • Flow limits (3.13): 𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖≤𝑄𝑖(𝑡)≤𝛽𝑂𝑁,𝑖(𝑡)𝑄𝑖 Pump (sizing) Sizes and sets up a new pump. Since new turbo-machinery are designed ad hoc, we consider their rated electrical power as the decision variable 𝑝𝑑𝑖𝑚,𝑖(W). The variables that define the 𝑖-th new pump are inlet an outlet flows Qin,i∈[−𝑄𝑖,0]and Qout,i∈[0,𝑄𝑖](m3/s), defined positive if exiting the pump, dynamic head Hi≥0(m), hydraulic power ph,i∈[0,𝑝ℎ,𝑖](W) and electric power pe,i∈[0,𝑝𝑒,𝑖](W). Flows and electric power connect with (3.3) while head connects with (3.2). We assume no further information on 33 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems the pump is available, then it is characterised just by its forecasted average efficiency 𝜂𝑖and formulated with (3.12), (3.14), (3.15) and (3.19). 𝑝𝑑𝑖𝑚,𝑖 ≥𝑝𝑒,𝑖(𝑡) (3.19) Qout Qin pe Figure 3.9 –Definition of the flow and electric power direction in a new pump device Pump (sizing) summary Variables: • Sized power: 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑑𝑖𝑚,𝑖] • Flow (inlet): Qin,i∈[−𝑄𝑖,0]. Connection: (3.3) • Flow (outlet): Qout,i∈[0,𝑄𝑖]. Connection: (3.3) • Head: Hi≥0. Connection: (3.2) • Hydraulic power: ph,i∈[0,𝑝ℎ,𝑖] • Electric power: pe,i∈[0,𝑝𝑒,𝑖]. Connection: (3.3) Constraints: • Sizing (3.19): 𝑝𝑑𝑖𝑚,𝑖 ≥𝑝𝑒,𝑖(𝑡) • Flow coherence (3.12): 𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡) • Hydraulic power (3.14): 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖(𝑡)𝐻𝑖(𝑡) • Electrical power (3.15): 𝑝𝑒,𝑖(𝑡)𝜂𝑖=𝑝ℎ,𝑖(𝑡) Turbine (sizing) Converts hydraulic power into rotational mechanical power and then to electric power through the use of mechanically coupled generators. Since no turbines are currently present in the system, we modelled them following a sizing approach as well. The variables that define the 𝑖-th new turbine are inlet an outlet flows Qin,i∈[−𝑄𝑖,0]and Qout,i∈[0,𝑄𝑖](m3/s), defined positive if exiting the turbine, dynamic head Hi≥0(m), hydraulic power ph,i∈[−𝑝ℎ,𝑖,0](W) and electric power pe,i∈[−𝑝𝑒,𝑖,0](W), defined positive if consumed. Flows and electric power connect with (3.3) while head connects with (3.2). We assume no further information on the turbine is available, then it is characterised just by its forecasted 34 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems average efficiency 𝜂𝑖and formulated with (3.12), (3.14), (3.20) and (3.21). The turbine is considered to be operated with adjustable speed, which allows for a greater range of operation and is specially convenient to extract power from irrigation reservoirs [66]. 𝑝𝑒,𝑖(𝑡)=𝑝ℎ,𝑖(𝑡)𝜂𝑖(3.20) 𝑝𝑑𝑖𝑚,𝑖 ≥−𝑝𝑒,𝑖(𝑡) (3.21) Constraint (3.14)involves aproduct of two variables. To reduce thecomplexityof theproblem we propose the following approximation: 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖𝑛,𝑖(𝑡)  𝐻𝑖,(3.22) where  𝐻(m) is the estimation of the dynamic head and can be determined, for instance, as  𝐻𝑖=Δ𝑧𝑖−( 𝑝ℎ,𝑖 𝜌𝑔Δ𝑧𝑖)2,(3.23) with Δ𝑧𝑖(m) the difference of heights between the reservoirs the turbine operates with. Qin Qout pe Figure 3.10 –Definition of the flow and electric power direction in a turbine device Turbine summary Variables: • Sized power: 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑑𝑖𝑚,𝑖] • Flow (inlet): Qin,i∈[−𝑄𝑖,0]. Connection: (3.3) • Flow (outlet): Qout,i∈[0,𝑄𝑖]. Connection: (3.3) • Head: Hi≥0. Connection: (3.2) • Hydraulic power: ph,i∈[−𝑝ℎ,𝑖,0] • Electric power: pe,i∈[−𝑝𝑒,𝑖,0]. Connection: (3.3) Constraints: • Sizing (3.21): 𝑝𝑑𝑖𝑚,𝑖 ≥−𝑝𝑒,𝑖(𝑡) • Flow coherence (3.12): 𝑄𝑖𝑛,𝑖(𝑡)=−𝑄𝑜𝑢𝑡,𝑖(𝑡) • Hydraulic power (3.14): 𝑝ℎ,𝑖(𝑡)=𝜌𝑔𝑄𝑖𝑛,𝑖(𝑡)𝐻𝑖(𝑡) • Electrical power (3.20): 𝑝𝑒,𝑖(𝑡)=𝑝ℎ,𝑖(𝑡)𝜂𝑖 35 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Pump as turbine (PaT) Pumps as turbines is a controversial topic on hydraulics and hydropower. Extracting power with the application of a pump instead of a turbine is an easily implementable and economical solution for small hydropower purposes [67]. Defining their characteristics is still a complex and complicated problem and requires data that is usually not available. However, other authors’ work analysing and reviewing pumps working as turbines proved useful to us when defining their behaviour in the optimisation model. In [68] the authors reviewed PaT performance prediction and stability literature and [41] implemented a 30 kW PaT with a variable frequency driver on their storm-water basin based micro energy grid. From this works we extracted that single stage centrifugal PaTs are the most recommended, pump geometry is a fundamentalparameter to predictthe performanceofit workingas aturbine, the performanceofPaTs may range from 50 to 80 %, and that operating the PaT with a variable frequency driver increases its operating range and may rise its efficiency to closely match that of working in pump mode. The optimisation tool does not consider an explicit device for a PaT, but its implementation can be achieved by defining a pump and a turbine properly connected in parallel, as exemplified in [45]. Energy balance node All equipment that consumes or delivers electrical power, 𝑝𝑒(W), are connected to energy balance nodes which aggregate and distribute the power among the connected devices. For a set of electrical devices 𝒳connected to the same energy balance node, the balance imposed is ∑ 𝑥∈𝒳𝑝𝑒,𝑥(𝑡)=0. (3.24) Energy balance node summary Variables: • None Constraints: • Power balance (3.24): ∑𝑥∈𝒳𝑝𝑒,𝑥(𝑡)=0 Electrical grid Delivers or accepts electrical power from connected devices. We modelled the grid as an ideal voltage source limited by the maximum power of the connection, which may be either a physical or a legal constraint. The variables that define the 𝑖-th grid are the total power pi∈[−𝑝𝑖,𝑝𝑖](W) and the powers flowing from and to the grid pfrom,i∈[0,𝑝𝑖]pto,i∈[0,𝑝𝑖](W), defined positive if consumed. Total electric power connects with (3.3). A grid device is governed by its own power balance (3.25) and, additionally, a boundary may be set on a specific timestamp 𝑡𝑐to represent a contractual restriction (3.26). 𝑝𝑖(𝑡)=𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡) (3.25) 𝑝𝑖(𝑡𝑐)≤𝑝𝑖,𝑡𝑐(3.26) Electrical grid summary Variables: 36 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems • Power (total): pi∈[−𝑝𝑖,𝑝𝑖]. Connection: (3.3) • Power (from): pfrom,i∈[0,𝑝𝑖] • Power (to): pto,i∈[0,𝑝𝑖] Constraints: • Power balance (3.25): 𝑝𝑖(𝑡)=𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡) Solar PV Converts irradiance into electrical power. The amount of power it can generate depends on the size of the plant 𝑝𝑖𝑛𝑠𝑡,𝑖(W), the efficiency of the converter 𝜂𝑖and the weather conditions, i.e. the irradiance level 𝐺𝑖(𝑡)(W/m2). We consider the size of the plant may be increased. The variables that define the 𝑖-th PV plant are the generated power pi∈[−𝑝𝑖,0](W), defined positive if consumed, and the new sized power 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖−𝑝𝑖𝑛𝑠𝑡,𝑖](W). Generated electric power connects with (3.3). The generated power is defined with (3.27) where the meteorological forecast 𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 values are expressed in per unit as (3.28). 𝑝𝑖(𝑡)≥−(𝑝𝑖𝑛𝑠𝑡,𝑖+𝑝𝑑𝑖𝑚,𝑖)𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡(𝑡)𝜂𝑖(3.27) 𝑚𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡(𝑡)=𝐺𝑖(𝑡) 1000 (3.28) Solar PV summary Variables: • Power: pi∈[−𝑝𝑖,0]. Connection: (3.3) • New sized power: 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖−𝑝𝑖𝑛𝑠𝑡,𝑖] Constraints: • Power balance (3.27): 𝑝𝑖(𝑡)≥𝑝𝑓𝑟𝑜𝑚,𝑖(𝑡)−𝑝𝑡𝑜,𝑖(𝑡) Battery (sizing) Stores energy from an electrical source. Our optimisation problem considers the sizing of new batteries. The variables that define the 𝑖-th battery are the total power transfer pi∈ [−𝑝𝑖,𝑝𝑖](W), defined positive if consumed, the charge and discharge power pch,i∈[0,𝑝𝑖]pdc,i∈[0,𝑝𝑖](W), the stored energy Ei∈ [0,𝐸𝑖𝑆𝑂𝐶𝑖](Wh) and the sized power 𝑝𝑑𝑖𝑚,𝑖 ∈ [0,𝑝𝑖](W) and capacity 𝐸𝑑𝑖𝑚,𝑖 ∈ [0,𝐸𝑖] (Wh). Electric power connects with (3.3). The sized power limits the charge, discharge and total power (3.29), (3.30), (3.31) and the sized capacity limits the energy stored through the state of charge bounds 𝑆𝑂𝐶𝑖∈[𝑆𝑂𝐶𝑖,𝑆𝑂𝐶𝑖](3.32), (3.33). Energy stored variation constraint is discretised using the backward Euler method considering the charge and discharge efficiencies 𝜂𝑐ℎ,𝑖𝜂𝑑𝑐,𝑖(3.34). 37 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 𝑝𝑖(𝑡)=𝑝𝑐ℎ,𝑖(𝑡)−𝑝𝑑𝑐,𝑖(𝑡) (3.29) 𝑝𝑐ℎ,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 (3.30) 𝑝𝑑𝑐,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 (3.31) 𝐸𝑖(𝑡)≤𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖(3.32) 𝐸𝑖(𝑡)≥𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖(3.33) {𝐸𝑖(𝑡)=𝐸𝑖(𝑡−Δ𝑡)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖) 𝑖𝑓𝑡>𝑡0 𝐸𝑖(𝑡)=𝐸𝑖(𝑡=𝑡𝑓)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖)otherwise (3.34) Battery summary Variables: • Power: pi∈[−𝑝𝑖,𝑝𝑖]. Connection: (3.3) • Charging power: pch,i∈[0,𝑝𝑖] • Discharging power: pdc,i∈[0,𝑝𝑖] • Energy stored: Ei∈[0,𝐸𝑖𝑆𝑂𝐶𝑖] • New sized power: 𝑝𝑑𝑖𝑚,𝑖∈[0,𝑝𝑖] • New sized capacity: 𝐸𝑑𝑖𝑚,𝑖∈[0,𝐸𝑖] Constraints: • Power balance (3.29): 𝑝𝑖(𝑡)≥𝑝𝑐ℎ,𝑖(𝑡)−𝑝𝑑𝑐,𝑖(𝑡) • Charging power limit (3.30): 𝑝𝑐ℎ,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 • Discharging power limit (3.31): 𝑝𝑑𝑐,𝑖(𝑡)≤𝑝𝑑𝑖𝑚,𝑖 • Maximum charge (3.32): 𝐸𝑖(𝑡)≤𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖 • Minimum charge (3.33): 𝐸𝑖(𝑡)≥𝐸𝑑𝑖𝑚,𝑖𝑆𝑂𝐶𝑖 • Stored energy (3.34): {𝐸𝑖(𝑡)=𝐸𝑖(𝑡−Δ𝑡)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖) 𝑖𝑓𝑡>𝑡0 𝐸𝑖(𝑡)=𝐸𝑖(𝑡=𝑡𝑓)+Δ𝑡(𝑝𝑐ℎ,𝑖(𝑡)𝜂𝑐ℎ,𝑖−𝑝𝑑𝑐,𝑖(𝑡)𝜂𝑑𝑐,𝑖)otherwise 38 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3.3.2 Objective function We are interested in two main objectives of this optimisation problem: an optimal average daily planing strategy to minimize the operational cost while providing storage services to the grid and satisfying the irrigation demand; and an optimal sizing of new elements (e.g batteries, pumps, turbines) or redesign of the already installed elements (e.g PV plants), to minimize the sum of the operating costs 𝐶𝑜𝑝 (€) and capital costs 𝐶𝑐𝑎𝑝(€) (3.35). Operating costs may consider the energy exchanges with the grid and other maintenance costs while capital costs account for the additional installed capacity of the new elements. 𝑓(⋅)=𝐶𝑜𝑝+𝐶𝑐𝑎𝑝 (3.35) The objective function is further detailed in the particular study cases along Section 3.4. We also defined an objective function from the perspective of the administration or a grid operator with the purpose of reducing the overall greenhouse gas (GHG) emissions of the grid. Instead of defining operation costs in monetary value we applied the emission factor of the grid to the energy exchanges with the grid. This objective function assumes an average behaviour of the grid and does not distinguish the technologies participating in the daily market. Further details are given in the particular study case in Section 3.4.3. 3.3.3 Solving the problem To solve the optimisation problem a suitable optimisation algorithm is required. We have achieved successful results with the following free open source software: • Couenne: branch and bound algorithm https://github.com/coin-or/Couenne. • Bonmin: Bonmin (Basic Open-source Nonlinear Mixed INteger programming) is an open-source solver for MINLP problems https://github.com/coin-or/Bonmin. It incorporates different algorithms to solve the models: Branch and bound (B-BB) is the simplest and default algorithm, based on solving a continuous non-linear program at each node of the search tree and branching on variables [69]. Outer approximation decomposition (B-OA), introduced first in [70] and [71], is implemented using Ipopt to solve the non-linear programming (NLP) problems and Cbc to solve the mixed-integer linear programming (MILP) problems. The Quesada and Grossman branch and cut (B-QG) algorithm, presented in [72], consists of an algorithm to solve convex MINLP problems based on LP and NLP sub-problems, by avoiding the sequential solution of NLP sub-problems and MILP master problems, that is required in the standard implementation of the generalized Benders decomposition (GBD) and B-OA algorithms, achieving up to an 84 % reduction of the number of nodes that need to be examined. The hybrid outer approximation based in branch-and-cut (B-Hyb) solves more NLPs to reduce the size of the tree, by reducing the algorithm to the classical NLP B-BB and the B-OA algorithm [70]. The outer-approximation based branch-and-cut with specific configuration (B-ECP) algorithm is based on the B-QG algorithm but implementing a linearizationbased algorithm [73]. Finally, the iterated feasibility pump algorithm (B-iPF) combines between solving NLP and MILP problems [70]. • Interior Point Optimizer (IPOPT): interior point algorithm to find local solutions to non-linear optimisation problems https://github.com/coin-or/Ipopt. It is a non-linear programming (NLP) solver so it is only suitable when no binary variables are present among the problem. 39 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3.3.4 Scalability This section details the performance and scalability issues thee methodology is and has been subject to, as well as some approaches we attempted to reduce their effect: • Binary and non-linear problem: the introduction of non-linearities and binary variables from hydraulics’ behaviour makes the analysis a MINLP problem. Non-linearities arise from the quadratic characteristic curvesofpipes andpumps (3.8)(3.11) andhydraulicpowercomputation (3.14), which is implicitly cubic. We required binary variables to model whether a pump is active (3.13). The linearised pump approach (3.16) and the approximation of the turbines’ dynamic head (3.22) address non-linearities regarding pumps and turbines. However, further work is required to reduce the remaining definitions. • Dynamics: We approached time dependency and dynamics of the reservoir and battery devices (3.6) (3.34) following an Euler discretisation methodology, such that the formulation preserves simplicity. • Time period: Even relatively small irrigation systems require considerable computational power and robust algorithms to be optimised for time periods considering 24 or 48 hours. Such a methodology does not have (yet) the capability to solve big systems for 8 760 hours to consider a full year. We have addressed this issue in the study cases by analysing two reference days, then extracting conclusions for the full year. • Large systems: systems with a large number of non-linear devices such as pumps, pipes or turbines, are demanding or even intractable for the solver’s algorithm. Although this issue has been dampened by linearising some hydraulic constraints, it is still a very present issue. • Initialisation: the ability to find global optimum or even find a solution is highly dependent on the initialisation values of the variables. This is specially relevant on large systems. Fixing the values of variables with prior knowledge does also help to reach global minimum solutions. Relaxation results In this section we show the results from testing three modelling strategies for the pump device: considering an equality quadratic characteristic curve constraint, inequality characteristic curve constraint (3.11) and linearizing the characteristic curve expression (3.16). Furthermore, we explore several Bonmin solver algorithms for the different optimisation problems: Quesada and Grossman (B-QG), Branch and Bound (B-BB), Extended Cutting Plane (B-ECP) and Outer Approximation (B-OA); which were the algorithms that performed the best in the analysed problems. Section 3.3.1 compresses all of the definitions and relaxations, however below follows a quick summary to introduce the results: The head expression of a variable speed pump is given by a quadratic constraint, both in terms of flow and rotational speed. For the 𝑖-th pump, at time 𝑡: 𝐻𝑖(𝑡)=(𝑛𝑖(𝑡))2𝐴𝑖−𝐵𝑖(𝑄𝑜𝑢𝑡,𝑖(𝑡))2. In [61] is proposed to transform the previous expression into an inequality. This modification sets the working area of the pump and allows for the removal of the rotational speed variable 𝑛𝑖(𝑡): 𝐻𝑖(𝑡)≤𝑛2 𝑖𝐴𝑖−𝐵𝑖(𝑄𝑜𝑢𝑡,𝑖(𝑡))2. 40 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems The previous relaxation supports a linear approximation. This can be achieved by generating a piecewise function of 𝑁𝐿linear functions that approximate the curve inside the working limit of the pump [𝑄𝑖,𝑄𝑖]. This approach does not only reduce the complexity of the dynamic head expression but of the hydraulic power as well. To reduce the impact of the approximation in the solution and ensure that the model returns inside the actual dynamic head curve we took a conservative approach by setting the linear approximation below it. A linear constraint is built per each segment that approximates the curve, each consisting in an inequality to avoid using binary variables as in a regular piecewise function: 𝐻𝑙,𝑖(𝑡)≤𝐻𝑙+1,𝑖−𝐻𝑙,𝑖 𝑄𝑙+1,𝑖−𝑄𝑙,𝑖 (𝑄𝑜𝑢𝑡,𝑖(𝑡)−𝑄𝑙,𝑖)+𝐻𝑙,𝑖 𝑙=1,...𝑁𝐿. Therefore, by incorporating the approximation we replace a quadratic constraint for 𝑁𝐿linear constraints and 2 extra variables per step time of optimisation. 𝑄𝑙,𝑖 =𝑄𝑖+𝑙𝑄𝑖−𝑄𝑖 𝑁𝐿,𝑖 𝑙=1,...𝑁𝐿 𝐻𝑙,𝑖 =𝑛2 𝑖𝐴𝑖−𝐵𝑖(𝑄𝑙,𝑖)2𝑙=1,...𝑁𝐿 Therefore, by applying this we do not use a quadratic expression but we add 𝑁𝐿constraints and 2 extra variables per time step to the problem. We tested 5 different systems with 6 different algorithms: Case C0 is explained in detail in Section 3.4.1 and the remaining 4 in Section 3.4.2. Case C0 considers 5 time steps and consists on a two reservoir system with two pumps, one turbine, a PV system connected to the grid and the sizing of a possible battery. The original execution time was 16.75 seconds. Cases C1, C2, C3 and C4 consist in two 24 hour typical averaged days (for a total of 48 time steps), one for summer and one for winter, over a system with two reservoirs, a grid connected pump and a PV pump which is not connected to the grid. Case C2 considers a pump as a turbine, in case C3 the PV plant is connected to the grid as well and case C4 optimises the operation of the system with both the PV plant connected to the grid and a pump running as a turbine. The source of the data used to analyse this system is a real case scenario near the Ebre river in the region of Catalunya (Spain). The original execution times were 9 minutes, 12 minutes, 65 minutes and 7 minutes respectively. We measured the performance of the computations in terms of execution time 𝑇𝑒(s) and final cost value 𝐺(€). The relaxation techniques must deliver lower execution times and not distance the solution from the real global optimum, which could derive from the relaxations defining a different problem. The study cases were solved using an Intel i5-8265U CPU @ 1.60 GHz laptop with 8 GB of RAM. We ran each case for a total of 10 experiences. However, in large execution time cases only 2 experiences were solved, which is the case of B-BB cases C2 and C3 with equality constraint, B-BB case C2 with 3 interval linear constraint and B-BB case C1 with 4 interval linear constraint. The box plots displayed in Figures 3.11a, 3.11b and 3.11c compare the execution times for each analysed technique and algorithm. B-OA is not presented since it resulted similar to B-QG. A star symbol (⋆) marks those cases that did not converge to a solution for a given method and algorithm. Figure 3.11a compares the equality (Eq) method with inequality (Ine), Figure 3.11b compares the equality with linearized approximation with 3 intervals (Lin3) and lastly Figure 3.11c compares equality and linearized with 4 intervals (Lin4). Table 3.1 summarises the results of B-BB, B-QG, B-OA and B-ECP for each method and case. Base values are highlighted with underline, while the other values express in percentage the relative difference to the base value. 41 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 01234 Time (u.t.) −1 0 1 SoC, Power (p.u.) SoC Power Figure 3.16 –Battery state of charge and power (defined positive if absorbed). Reservoir 1 Pumps Reservoir 0 Irrigation Pipe PV Battery Grid Hydro Power Figure 3.17 –CR Les Planes i Aixalelles study case base system. 0 6 12 18 23 0 100 200 Demand (m3/h) Time (h) S W Figure 3.18 –Average daily irrigation demand on CR Les Planes i Aixalelles (S: Summer, W: Winter). Real data from 1 year and 90% confidence interval. 48 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems PV plant is set for sizing. The upper reservoir has a capacity of 13 000 m3and is limited to a minimum volume of 9 000 m3, which corresponds to 3 days of autonomy during the irrigation season. This lower limit is arbitrary and set by the plant operator. To maintain operability, its initial and final volumes, 𝑊𝑅1(𝑡0) and 𝑊𝑅1(𝑡𝑓)respectively, are set to be within a ±5 % range (3.38). A sufficiently large reservoir models the river. Table 3.5 summarises the base case characteristics. 1,05𝑊𝑅1(𝑡0)≥𝑊𝑅1(𝑡𝑓)≥0,95𝑊𝑅1(𝑡0)(3.38) Table 3.5 –Characteristics of the case’s elements Device Characteristics Reservoir 1 Volume ∈[9 000, 13 000] m3 Height w.r.t. Reservoir 0 ∈[105, 111] m Pipe Quadratic losses coef. = 60 s2/m5 Pumps𝑎Power = 110 kW, 𝜂= 0,8, 𝜂𝑝𝑎𝑡= 0,5 Flow ∈[0,6, 1,9] p.u. Nominal flow = 0,056 m3/s A = 120 m, B = 3 865 s2/m5 PV Peak power = 215,3 kWp Converter efficiency = 0,98 Battery Max. size energy/power 200 kWh/200 kW Allowed state of charge ∈[0,2, 1,0] p.u. Charge/discharge efficiency = 0,8 𝑎𝜂efficiency and 𝜂𝑝𝑎𝑡efficiency as a turbine The objective function designed for this study considers the cost of buying 𝑐𝑏𝑢𝑦,𝑔and price of selling 𝑐𝑠𝑒𝑙𝑙,𝑔 electricity to the grid, as well as the capital expenditures of sizing a new battery 𝑐𝑝,𝑏𝑎𝑡,𝑐𝑒,𝑏𝑎𝑡. 𝑓(x)= 𝑇 ∑ 𝑡=0[𝑝𝑓,𝑔(𝑡)𝑐𝑏𝑢𝑦,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)𝑐𝑠𝑒𝑙𝑙,𝑔(𝑡)]Δ𝑡+ +𝑝𝑑𝑖𝑚,𝑏𝑎𝑡𝑐𝑝,𝑏𝑎𝑡+𝑒𝑑𝑖𝑚,𝑏𝑎𝑡𝑐𝑒,𝑏𝑎𝑡,(3.39) where xis the decision vector composed of 𝑝𝑓,𝑔 (kW), the power consumed from the grid and 𝑝𝑡,𝑔(kW) the power injected to the grid. Δ𝑡is the time step, which is equal to 1h in the study case. Based on irrigation demand (Figure 3.18), the case study considers, in parallel, two standard days which correspond to summer and winter and also determine the irradiance on the PV plant. 𝑝𝑑𝑖𝑚,𝑏𝑎𝑡(W) and 𝑒𝑑𝑖𝑚,𝑏𝑎𝑡(Wh) are the power and energy sized for the battery. The electricity prices are based on the market from the Iberian Peninsula, and the costs of sizing the battery energy 𝑐𝑒,𝑏𝑎𝑡 =0,2054 €/(Wh day) and power 𝑐𝑝,𝑏𝑎𝑡 =0,0410 €/(W day) are based on [74] for a Li-ion battery, normalised for 1 day and considering 20 years for the project lifetime. We considered the following modifications over the base case, which are detailed in Figure 3.19. 1. Pump as turbine: The pump connected to the grid can now be operated reversibly, i.e. pump as turbine (PaT), acting as a low efficiency Francis turbine. The other pump is kept connected to the PV and battery system. The PaT is modelled as a pump and a turbine operating in parallel, with the addition of (3.40) preventing them from operating simultaneously. 𝑄𝑜𝑢𝑡,𝑇𝑢𝑟𝑏𝑖𝑛𝑒(𝑡)𝑄𝑜𝑢𝑡,𝑃𝑢𝑚𝑝(𝑡)=0 ∀𝑡 (3.40) 49 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 2. Grid connected: Both pumps are connected to a common bus with the grid, PV panels and battery system. 3. PaT + Grid connected: Fusing both previous cases, electrical elements are connected to a common bus with the grid and one pump is allowed to run in reversible mode. Case 1 Case 2 Case 3 PAT PAT Figure 3.19 –Variations on the study case. Devices which present changes are highlighted. Overall, in this study case, we analyse whether the reversible use of pumps allows stored energy to be harnessed. In addition, we also consider the sizing of batteries to determine the effect of the price of energy on the decision to install such equipment. Results The results obtained from the base case (Figure 3.17) represent an optimal performance according to what is currently known. This means using the PV pumping system at its full potential and backing it up with the grid-connected pump during low-cost periods. No battery is found required or sized for any of the cases studied due to its high capital costs. The system works at full capacity in summer and is underutilised in winter, as can be observed on Figures 3.20a and 3.20b. Figure 3.20a displays the powers consumed (>0) by the PV plant 𝑃𝑃𝑉, PV pump 𝑃𝑝,𝑃𝑉, grid connected pump 𝑃𝑝,𝑔, the available PV power  𝑃𝑃𝑉 and the power exchanged with the grid 𝑃𝑔, as well as the cost and sell price of electrical energy. Figure 3.20b does the same for the flows delivered to reservoir 1 from both pumps 𝑄𝑝,𝑃𝑉 and 𝑄𝑝,𝑔and the irrigation demand 𝑄𝑖𝑟𝑟, along with the volume present at the reservoir and its bounds. This nomenclature is kept through the other cases. 1. Pump as turbine: Allowing the grid connected pump to operate as a turbine favors the usage of the pumping facility as a PV storage system, in which the PV pump transfers water to the highest reservoir during peak irradiance hours, then the PaT converts its potential energy into electricity to feed the grid during high sell price periods. This behaviour is illustrated in Figures 3.21a-3.21b in comparison to the underutilisation from the base case (Figures 3.20a-3.20b). Summer season presents no divergence from the base case and is therefore omitted from this discussion. 2. Grid connected: Connecting the whole facility to the grid allows for energy exchanges, which extract the full potential of the PV system. Pumps operation is rescheduled, as Figures 3.22a-3.22b portrays, and the available PV power fully exploited. 3. PaT + Grid connected: In such circumstances the optimisation must decide whether to inject the energy to the grid straight from the PV plant or store it in the form of potential energy in the reservoir and inject it during higher sell price periods. With the data fed and parameters set for the study case, the resulting operation (Figures 3.23a-3.23b) indicates that running the PaT during the highest sell price hours at winter is the optimal scheduling. Table 3.6 summarises the operation and sizing costs per day, after simulating each case for summer and winter conditions. It also displays the computation time in seconds on a 11th Gen Intel Core i7 @ 3.40 GHz laptop with 16,0 GB of RAM. From Table 3.6, it can be seen that the Base case is the most 50 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Time (h) 0 6 12 18 23 Price (€/MWh)Price (€/MWh) P (kW)P (kW) 300 200 100 300 200 200 100 0 -100 -200 200 100 0 -100 -200 100 Summer Winter (a) Resulting consumed power. Qp,PV Qp,g Qirr 10000 8000 0.1 0.0 13000 -0.1 0 6 12 18 23 Time (h) Q (m3/s)Volume (m3) Summer 0.1 0.0 -0.1 0 6 12 18 23 Time (h) Q (m3/s) Winter 10000 8000 13000 Volume (m3) (b) Flows and Reservoir 1 volume. Figure 3.20 –Results of the base case. Time (h) 0 6 12 18 23 Price (€/MWh)Price (€/MWh) P (kW)P (kW) 300 200 100 300 200 200 100 0 -100 -200 200 100 0 -100 -200 100 Summer Winter (a) Resulting consumed power. Qp,PV Qp,g Qirr 10000 8000 0.1 0.0 13000 -0.1 0 6 12 18 23 Time (h) Q (m3/s)Volume (m3) Summer 0.1 0.0 -0.1 0 6 12 18 23 Time (h) Q (m3/s) Winter 10000 8000 13000 Volume (m3) (b) Flows and Reservoir 1 volume. Figure 3.21 –Results of PaT case (Case 1). 51 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Time (h) 0 6 12 18 23 Price (€/MWh)Price (€/MWh) P (kW)P (kW) 300 200 100 300 200 200 100 0 -100 -200 200 100 0 -100 -200 100 Summer Winter (a) Resulting consumed power. Qp,PV Qp,g Qirr 10000 8000 0.1 0.0 13000 -0.1 0 6 12 18 23 Time (h) Q (m3/s)Volume (m3) Summer 0.1 0.0 -0.1 0 6 12 18 23 Time (h) Q (m3/s) Winter 10000 8000 13000 Volume (m3) (b) Flows and Reservoir 1 volume. Figure 3.22 –Results of grid connected case (Case 2). Time (h) 0 6 12 18 23 Price (€/MWh)Price (€/MWh) P (kW)P (kW) 300 200 100 300 200 200 100 0 -100 -200 200 100 0 -100 -200 100 Summer Winter (a) Resulting consumed power. Qp,PV Qp,g Qirr 10000 8000 0.1 0.0 13000 -0.1 0 6 12 18 23 Time (h) Q (m3/s)Volume (m3) Summer 0.1 0.0 -0.1 0 6 12 18 23 Time (h) Q (m3/s) Winter 10000 8000 13000 Volume (m3) (b) Flows and Reservoir 1 volume. Figure 3.23 –Results of grid connected + PaT case (Case 3). 52 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems expensive solution, whereas remodelling to the Case 3 topology (grid connected PV + PaT) results the most profitable option. Table 3.6 –Cases summary Case Base Case 1 Case 2 Case 3 Cost [€/day] 12,50 7,03 -12,05 -15,30 Exec. time [s] 4 10 5 12 3.4.3 Comunitat de Regants Segrià-Sud This study case, presented in [76], is based on the facility of the Comunitat de Regants (CR) Segrià-Sud (Section 2.4). The original irrigation system takes water from the river Ebre and raises it to a system of 5 reservoirs through 4 pumping stations composed of several kW to MW pumps. The vertical distance between the river and the highest reservoir is about 380 m. The electrical power that supplies the pumps comes from the power grid and from three PV plants with 523,00 kWp, 527,50 kWp and 274,68 kWp installed peak power. The PV plants are owned by the irrigation community and are not grid connected. Figure 3.24 shows a scheme of the CR Segrià-Sud facilities and Table 3.7 summarises the characteristics of its devices. Irr5 Pipe45 Pipe14 Pipe01 Pipe12 Pipe13 R4 R2 R3 R5 Grid Irr4 Irr3 Irr2 R1 R0 PS1 PS2 PS3 Irr1 (a) global P1g PS1 PV24 P23s P23gP22g P24s P24g PV23 PS2 P3g P3s PV3 PS3 (b) pumping stations Figure 3.24 –CR Segrià-Sud Base case system. The pumping stations currently operate between midnight and 8 a.m., when both the electrical power and energy term prices are the lowest. During the day, the energy produced by the PV plants is used to drive the PV pumps if enough solar power is available. Irrigation requirements are at their highest in summer, but in winter, the need for irrigation considerably reduces. Figure 3.25 displays the average daily irrigation demand for each reservoir stratified in winter and summer seasons, with a 95 % confidence interval2. Our scope is limited by the scalability issues the optimisation methodology presents (Section 3.3.4). To reduce the complexity of the problem we split the system in two sections upper and lower, as depicted in Figures 3.26-3.27. The subdivisions assume the following premises: •Lower section: Reservoir R0 (river Ebre) has infinite capacity, modelled as a large enough value, such that it can provide and absorb as much water as required without it having an effect on its manometric height. Irrigation from reservoirs R2 and R3 are directly aggregated to R1 and their pertinent hydraulic elements are not considered. Irrigation from reservoir R5 is directly aggregated to R4 and its pertinent hydraulic elements are not considered. 2We could not effectively obtain reliable data from Reservoir 4, thus we assumed the demand to be similar to Reservoir 5 since they are located next to each other and share similar altitudes and crop areas [22] 53 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 3.7 –Characteristics of the CR Segria-Sud case’s devices Device Characteristics Reservoirs R0: 𝑊∈[120, 240] 103m3,𝑧∈[129, 131] m R1: 𝑊∈[96, 143] 103m3,𝑧∈[336, 339] m R2: 𝑊∈[250, 297] 103m3,𝑧∈[355, 365] m R3: 𝑊∈[70, 86] 103m3,𝑧∈[418, 421] m R4: 𝑊∈[184, 270] 103m3,𝑧∈[427, 431] m R5: 𝑊∈[128, 186] 103m3,𝑧∈[448, 451] m Pipes Pipe01: 𝐾= 27,90 s2/m5 Pipe12: 𝐾= N/D Pipe13: 𝐾= 6,12 s2/m5 Pipe14: 𝐾= 27,81 s2/m5 Pipe45: 𝐾= 6,10 s2/m5 Pumps𝑎P1 (x3): 𝑃= 3 200 kW, 𝜂= 0,922, 𝜂𝑝𝑎𝑡= 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 1,06 m3/s, A = 300 m, B = 62,208 s2/m5 P22 (x1): 𝑃= 315 kW, N/D P23 (x2): 𝑃= 250 kW, 𝜂= 0,82, 𝜂𝑝𝑎𝑡= 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 0,285 m3/s, A = 105,81 m, B = 324 s2/m5 P24 (x2): 𝑃= 1 250 kW, 𝜂= 0,92, 𝜂𝑝𝑎𝑡 = 0,7, 𝑄∈[0,3, 1,1] p.u., 𝑄𝑛= 0,913 m3/s, A = 148 m, B = 103,7 s2/m5 P3 (x2): 𝑃= 160 kW, 𝜂= 0,86, 𝜂𝑝𝑎𝑡 = 0,7, 𝑄∈[0,6, 1,2] p.u., 𝑄𝑛= 0,469 m3/s, A = 37,8 m, B = 38,9 s2/m5 PV PV23: 𝑃𝑖𝑛𝑠𝑡= 523,0 kWp, 𝜂= 0,98 PV24: 𝑃𝑖𝑛𝑠𝑡= 527,5 kWp, 𝜂= 0,98 PV3: 𝑃𝑖𝑛𝑠𝑡= 274,7 kWp, 𝜂= 0,98 𝑎𝜂efficiency and 𝜂𝑝𝑎𝑡efficiency as a turbine 0 6 12 18 23 0 300 600 Demand (m3/h) Time (h) (a) Reservoir 1 0 6 12 18 23 0 300 600 Demand (m3/h) Time (h) (b) Reservoir 2 0 6 12 18 23 0 300 600 Demand (m3/h) Time (h) (c) Reservoir 3 0 6 12 18 23 0 300 600 Demand (m3/h) Time (h) (d) Reservoir 5 (same for Reservoir 4) Figure 3.25 –CR Segrià-Sud water consumption for irrigation. 54 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems •Upper section: Reservoir R0 will provide the required amount of water to reservoir R1, hence the latter has infinite capacity, modelled as a large enough value. Reservoirs R2 and R3 and their pertinent hydraulic elements are not considered. These assumptions entail the following constraints on the present analysis: • It is not possible to include reservoirs R2 and R3 and their pertinent hydraulic elements. • Reverse flow cannot be considered for Pipe01 on the lower section and for Pipe14 on the upper section. • The total operating cost obtained by the optimisation does not correspond to the total operating cost of the facility. • The total operating cost of the facility is not obtainable due to the removal of reservoirs R2 and R3. • An estimate total cost of operating the R0-R1-R4-R5 circuit can be obtained by adding the Base case operating costs of the left-out pumping station on either section (costs from pumping station PS1 on the upper section and costs from pumping station PS3 on the lower section). Irr5 Pipe45 Pipe14 Pipe01 Pipe12 Pipe13 R4 R2 R3 R5 Grid Irr4 Irr3 Irr2 R1 R0 PS1 PS2 PS3 Irr1 LOWER UPPER Figure 3.26 –CR Segrià-Sud system division. Pipe14 Pipe01 R4 Grid Irr4+5 Irr1+2+3 R1 R0 PS1 PS2 (a) lower Irr5 Pipe45 Pipe14 R4 R5 Grid Irr4 R1 PS2 PS3 (b) upper Figure 3.27 –CR Segrià-Sud lower and upper divisions and assumptions. For each division we considered analogous modifications over the Base case as for the CR Les Planes i Aixalelles analysis (see Section 3.4.2): 1. Pump as turbine: The grid connected pump can be operated reversibly (PaT), with a lower efficiency considered 𝜂𝑝𝑎𝑡 = 0,7 based on [41]. The other pump is kept connected to the PV system. The pumps selected for such function are Pump24g in lower section and Pump3g in upper section. The PaT is modelled as stated in Section 3.3.1, with a pump and a turbine operating in parallel and the addition of (3.40) preventing them from operating simultaneously. 2. Grid connected: All PV systems and pumps are connected to a common bus to the grid. The system is allowed to import and export electricity from the grid applying the corresponding costs and prices. 55 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 3. PaT + Grid connected: Combining both previous cases, all of the electrical elements are connected to a common bus with the grid and the originally grid connected pump is allowed to run in reversible mode (Pump24g in lower section and Pump3g in upper section). Notice that, due to imposing the condition of cycle by limiting the minimum volume value of the reservoirs at the end of the time period (see Section 3.3.1), the total volume of water that the system obtains from the river is strictly the irrigation demand on all of the cases. The objective of this study case is to analyse the behaviour of a multi-reservoir system and the effects of running a PaT at several locations. We defined two representative days for the electrical grid costs and GHG emission factor, depicted in Figure 3.28, which consist of the average daily evolution of the months of January (winter) and August (summer) of 2024 [77]. We also analyse the sensitivity of the solution to the fluctuation of parameters of relevance which present a significant uncertainty or are likely to evolve in the future: irrigation demand, price of exporting electricity to the grid and the efficiency of running PaTs. fGHG,g cbuy,g csell,g 0 6 12 18 23 0,12 300 200 100 Time (h) Price (€/MWh) Emission factor (tCO2-eq/MWh) 0,08 0,04 (a) winter fGHG,g cbuy,g csell,g 0 6 12 18 23 0,12 300 200 100 Time (h) Price (€/MWh) Emission factor (tCO2-eq/MWh) 0,08 0,04 (b) summer Figure 3.28 –Grid equivalent GHG emission factor, cost of electricity and sell price for the defined typical days. Data from [77]. We defined the objective function for the analysis of the CR Segrià-Sud system from the point of view of the community, which objective is to reduce the operating costs. The function considers the cost of buying 𝑐𝑏𝑢𝑦,𝑔 (€/MWh) and price of selling 𝑐𝑠𝑒𝑙𝑙,𝑔 (€/MWh) electricity to the grid and the energy imports 𝑝𝑓,𝑔(MW) and exports 𝑝𝑡,𝑔(MW): 𝑓(x)= 𝑇 ∑ 𝑡=0[𝑝𝑓,𝑔(𝑡)𝑐𝑏𝑢𝑦,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)𝑐𝑠𝑒𝑙𝑙,𝑔(𝑡)]Δ𝑡 (3.41) We also defined an objective function from the perspective of the administration or a grid operator with the purpose of reducing the overall GHG emissions of the grid, which we applied to Case 3 and named it Case 3-em: 𝑓(x)= 𝑇 ∑ 𝑡=0[𝑝𝑓,𝑔(𝑡)−𝑝𝑡,𝑔(𝑡)]𝑓𝐺𝐻𝐺,𝑔(𝑡)Δ𝑡 (3.42) with 𝑓𝐺𝐻𝐺,𝑔 (tCO2-eq/MWh) the GHG emission factor of the grid. This objective function assumes an averagebehaviourofthe gridand does notdistinguishthe technologiesparticipating inthe dailymarket. Results (Upper) This section presents the results obtained from the upper section of the irrigation system analysis, which are summarised on Table 3.8 and Figures 3.29-3.33. The computation time of each case, running the COIN-OR Bonmin algorithms [75] on a 11th Gen Intel Core i7 @3.40 GHz laptop with 16,0 GB of RAM, 56 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 3.8 –Results (Upper) Case Base Case 1 Case 2 Case 3 Case 3-em Computation time [s] 5,80 23,44 34,92 14,81 39,20 Energy imported average [kWh/d] 1 233,51 1 074,86 227,30 234,78 783,74 ” winter [kWh/d] 0,00 0,00 1,20 0,00 17,01 ” summer [kWh/d] 2 467,02 2 179,72 453,39 469,56 1 550,46 Energy exported average [kWh/d] - 202,17 1 067,50 1 051,99 1 376,02 ” winter [kWh/d] - 385,55 2 071,96 2 027,12 2 089,75 ” summer [kWh/d] - 18,78 63,04 76,86 662,29 Maximum imported power winter [kW] 0,00 0,00 1,20 0,00 17,01 ” summer [kW] 485,11 501,71 375,46 391,64 311,12 Maximum exported power winter [kW] - 112,00 480,50 480,50 480,50 ” summer [kW] - 18,78 57,84 57,84 219,69 GHG emissions average [kgCO2-eq/d] 119,17 94,60 -52,92 -51,96 - 68,43 ” winter [kgCO2-eq/d] 0,00 -34,68 -144,56 -143,20 -146,15 ” summer [kgCO2-eq/d] 238,35 223,89 38,71 39,28 9,29 Energy expense average [€/d] 166,85 144,89 31,19 32,17 118,87 ” winter [€/d] 0,00 0,00 0,15 0,00 3,11 ” summer [€/d] 333,70 289,77 62,23 64,33 243,62 Energy income average [€/d] - 26,24 87,30 88,41 119,61 ” winter [€/d] - 50,03 167,19 167,87 163,56 ” summer [€/d] - 2,45 7,40 8,95 75,65 Total cost average [€/d] 166,85 118,65 -56,10 -56,24 -0,74 ” winter [€/d] 0,00 -50,03 -167,04 -167,87 -160,45 ” summer [€/d] 333,70 287,32 54,83 55,34 158,67 57 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Winter Pumping station 3 Summer Pumping station 2 P (kW) 0,12 500 0 -500 0,08 0,04 Pumping station 2 Pumping station 3 PPV PPV Pp24s Pp24g PgPPV PPV Pp3s Pp3g Pg fGHG (tCO2-eq/MWh) P (kW) 300 0 -300 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) Time (h) 0 6 12 18 23 P (kW) 300 0 -300 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) Time (h) 0 6 12 18 23 P (kW) 500 0 -500 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) (a) Resulting consumed power 1 0 270 230 184 -1 Reservoir 5 Summer Reservoir 4 Reservoir 5 Winter Reservoir 4 Q (m3/s)WR4 (103m3/s) 1 0 186 160 128 -1 Q (m3/s)WR5 (103m3/s) 1 0 270 230 184 -1 Q (m3/s)WR4 (103m3/s) 1 0 186 160 128 -1 Q (m3/s)WR5 (103m3/s) Time (h) 0 6 12 18 23 Time (h) 0 6 12 18 23 (b) Flows and volume of reservoirs R4 and R5 Figure 3.33 –CR Segrià-Sud upper results - emissions case (Case 3-em). 64 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 3.9 –Results (Lower) Case Base Case 2 Case 3 Case 3-em Computation time [s] 12,36 399,11 1 273,53 15,44 Energy imported average [kWh/d] 13 571,40 13 061,10 13 567,10 15 251,30 ” winter [kWh/d] 5 371,68 5 107,54 5 695,48 4 680,16 ” summer [kWh/d] 21 771,20 21 014,60 21 438,70 25 822,40 Energy exported average [kWh/d] - 551,58 620,40 930,01 ” winter [kWh/d] - 1 000,09 971,06 390,21 ” summer [kWh/d] - 103,07 269,75 1 469,81 Maximum imported power winter [kW] 1 245,88 1 112,90 2 484,61 1 054,80 ” summer [kW] 2 315,78 2 272,36 3 853,23 3 448,49 Maximum exported power winter [kW] - 265,56 381,98 168,52 ” summer [kW] - 61,60 166,68 875,00 GHG emissions average [kgCO2-eq/d] 1 153,78 1 053,35 1 049,50 652,74 ” winter [kgCO2-eq/d] 464,23 361,76 414,46 275,01 ” summer [kgCO2-eq/d] 1 843,32 1 744,94 1 684,55 1 030,47 Energy expense average [€/d] 1 754,31 1 706,36 1 698,71 2 432,11 ” winter [€/d] 515,31 505,64 538,14 770,86 ” summer [€/d] 2 993,32 2 907,08 2 859,28 4 093,36 Energy income average [€/d] - 46,68 66,50 110,64 ” winter [€/d] - 81,57 105,69 34,75 ” summer [€/d] - 11,79 27,31 186,53 Total cost average [€/d] 1 754,31 1 659,68 1 632,21 2 321,47 ” winter [€/d] 515,31 424,06 432,44 736,10 ” summer [€/d] 2 993,32 2 895,30 2 831,97 3 906,83 65 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Environmental analysis From a GHG emissions point of view, considering the typical day grid’s equivalent CO2factor evolution in summer and winter (Figure 3.28) and null for the irrigation system, results in positive emissions for all cases. Case 3-em, as expected, derives the best for such a purpose and utilises its energy storage capabilities to maximise the energy delivered to the grid during high emission factor hours (mostly evening in summer). Fair compensations should however apply to the irrigation community since this operation strategy is not as economically beneficial as Case 3 solution with an average difference of 689,26 €/d for an average reduction of 396,76 kgCO2-eq/d in emissions. The daily water consumption is maintained for all the cases, as stated above, since a cycle condition is imposed in the reservoir device. In essence, the modelling of the system implicitly considers the extra daily impact on the water source and cancels it. Sensitivity analysis This section covers a sensitivity analysis on the most relevant parameters of the upper section of the Segrià-Sud irrigation system. The results of the sensitivity analysis are displayed in Table 3.10 and the spiderplots in Figure 3.38. Spiderplots plot a curve for each variable on a single 𝑥−𝑦plot showing the change in goal value over a relative change of the variable values from the base case. Their purpose is to display information about a certain number of variables including their limits, impact on the outcome and the amount of change required to reach a break even point [78]. We applied the following variations over the base case: • Irrigation demand 𝑄𝑖𝑟𝑟±20 %. As reviewed in Section 2.1, there is an interest from the administration to increase the share of irrigated land as well as a reduction of the water demand from these crops. We conceive two scenarios: an increase of the general irrigation demand due to a substitution of dry land to irrigated or a decrease of the general irrigation demand driven by water efficiency requirements. • Selling price of electricity 𝑐𝑠𝑒𝑙𝑙 ±20 % from 8:00 h to 16:00 h. The mass implementation of solar PV may drive market prices down during high intensity solar hours, as it has been noticed from selfconsumption surplus prices reaching negative values in Spain [77]. We also analyse the opposite scenario where the market prices increase instead, which would decrease the incentives to drive the facilities as an energy storage system. • Efficiency of PaT 𝜂𝑝𝑎𝑡 ∈(0,5, 0,8). As stated in Section 3.3.1, it is not a trivial task to define the characteristics and behaviour of a PaT, therefore we based the range of values of its performance in previous work and literature [41, 68]. Table 3.10 –Sensitivity analysis total cost average (€/d). (𝑡) marks the cases where the system makes use of the pump as a turbine. Case Base Case 1 Case 2 Case 3 base 166,85 (𝑡)118,65 -56,10 (𝑡) -56,24 -20% 𝑄𝑖𝑟𝑟 95,90 (𝑡) 45,12 -126,13 (𝑡)-126,52 +20% 𝑄𝑖𝑟𝑟 267,63 (𝑡)214,98 24,35 24,35 -20% 𝑐𝑠𝑒𝑙𝑙 166,85 (𝑡)119,00 -40,10 (𝑡) -41,50 +20% 𝑐𝑠𝑒𝑙𝑙 166,85 (𝑡)118,28 -71,77 -71,77 𝜂𝑝𝑎𝑡= 0,5 166,85 (𝑡)137,22 -56,10 -56,10 𝜂𝑝𝑎𝑡= 0,6 166,85 (𝑡)125,62 -56,10 (𝑡) -56,34 𝜂𝑝𝑎𝑡= 0,8 166,85 (𝑡)112,00 -56,10 (𝑡) -56,63 66 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Winter Pumping station 2 Summer Pumping station 1 Pumping station 1 Pumping station 2 Time (h) 0 6 12 18 23 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) Pp1g1 Pp1g2 Pg 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) 600 0 -600 300 200 100 P (kW) Price (€/MWh) PPV PPV Pp24s Pp24g Pg Time (h) 0 6 12 18 23 600 0 -600 300 200 100 P (kW) Price (€/MWh) (a) Resulting consumed power Reservoir 4 Summer Reservoir 1 Reservoir 4 Winter Reservoir 1 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,4+5 Qp24s Qp24g 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) (b) Flows and volume of reservoirs R1 and R4 Figure 3.34 –CR Segrià-Sud lower results - Base case. 67 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Winter Pumping station 2 Summer Pumping station 1 Pumping station 1 Pumping station 2 Time (h) 0 6 12 18 23 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) Pp1g1 Pp1g2 Pg 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) 600 0 -600 300 200 100 P (kW) Price (€/MWh) PPV PPV Pp24s Pp24g Pg Time (h) 0 6 12 18 23 600 0 -600 300 200 100 P (kW) Price (€/MWh) (a) Resulting consumed power Reservoir 4 Summer Reservoir 1 Reservoir 4 Winter Reservoir 1 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,4+5 Qp24s Qp24g 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) (b) Flows and volume of reservoirs R1 and R4 Figure 3.35 –CR Segrià-Sud lower results - grid connected case (Case 2). 68 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Winter Pumping station 2 Summer Pumping station 1 Pumping station 1 Pumping station 2 Time (h) 0 6 12 18 23 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) Pp1g1 Pp1g2 Pg 3000 0 -3000 300 200 100 P (kW) Price (€/MWh) 600 0 -600 300 200 100 P (kW) Price (€/MWh) PPV PPV Pp24s Pp24g Pg Time (h) 0 6 12 18 23 600 0 -600 300 200 100 P (kW) Price (€/MWh) (a) Resulting consumed power Reservoir 4 Summer Reservoir 1 Reservoir 4 Winter Reservoir 1 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2 0 2 -2 143 120 96 Q (m3/s) WR1 (103m3/s) 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,4+5 Qp24s Qp24g 0 2 -2 270 230 184 Q (m3/s) WR1 (103m3/s) (b) Flows and volume of reservoirs R1 and R4 Figure 3.36 –CR Segrià-Sud lower results - PaT + grid connected case (Case 3). 69 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Winter Pumping station 2 Summer Pumping station 1 Pumping station 1 Pumping station 2 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) Time (h) 0 6 12 18 23 3000 0 -3000 P (kW) Pp1g1 Pp1g2 PgPPV PPV Pp24s Pp24g Pg 3000 0 -3000 P (kW) 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) P (kW) 1000 0 -1000 0,12 0,08 0,04 fGHG (tCO2-eq/MWh) Time (h) 0 6 12 18 23 P (kW) 1000 0 -1000 (a) Resulting consumed power Reservoir 4 Summer Reservoir 1 Reservoir 4 Winter Reservoir 1 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,1+2+3 Qp24s Qp24g Qp1g1 Qp1g2 0 1 -1 143 120 96 Q (m3/s) WR1 (103m3/s) 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) Time (h) 0 6 12 18 23 Qirr,4+5 Qp24s Qp24g 0 1 -1 270 230 184 Q (m3/s) WR1 (103m3/s) (b) Flows and volume of reservoirs R1 and R4 Figure 3.37 –CR Segrià-Sud lower results - emissions case (Case 3-em). 70 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems C (€/d)C (€/d) Change from base (p.u.) 0 0,8 1,0 1,2 200 -200 0,8 1,0 1,2 0 200 -200 Base Grid connected Pump as turbine PaT + grid ηpat Qirr csell base Figure 3.38 –Spiderplots resulting from the sensitivity analysis. 3.4.4 CEDER-CIEMAT The study case of Centro de Desarrollo de Energías Renovables (CEDER)-Centro de Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT) is modelled as follows in Figure 3.39. The center contains 3 small reservoirs of 2 000 m3, 1 500 m3and 500 m3, a small 16 kW PV plant and a 40 kW turbine. There is a bank of pumps with a nominal power of 7,5 kW each, which can only operate at nominal power or be disconnected. Therefore, the DiscretePumps model used allows the activation of an integer number of pumps, ranging from 0 to the total number of installed pumps—in this case, 4 pumps. Initially, the pumps and turbines are connected to a common bus along with the PV plant and the grid, supplying the electrical loads of the center itself. In order to model the system in a Pyomo environment, it is necessary to introduce several blocks. For example, the electrical loads block is used to model the center’s demand, and the hydraulic switch block is used to supply either the upper (R2) or middle (R1) reservoir. Note that a source block is used between reservoir 1 and reservoir 2 to model a pipe with a controllable valve without losses. The Discrete Pump used in this case is modelled by adding to the Pump device the next constraint: 𝑃𝑒,𝑖(𝑡)=𝑃𝑛,𝑖𝑁𝑜𝑛,𝑖(𝑡) (3.44) Where 𝑃𝑛,𝑖 the nominal power of the pump and is introduced as a parameter into the model. On the other hand, 𝑁𝑜𝑛,𝑖(𝑡)is a integer variable that defines the number of working pumps, the variable have a minimum of 0 and a maximum of 𝑁𝑝𝑢𝑚𝑝𝑠that is the total number of installed pumps. Various cases are carried out to evaluate the tool and the CEDER system. Each case considers different initial conditions and assumptions: • Case 1: No battery nor PV sizing is considered. • Case 2: Possibility of sizing a new battery and extra PV power. • Case 3: Battery is already present and extra PV power can be sized. The model is constructed using data provided by CEDER, such as electrical demand and solar irradiation measurements. Additionally, another source is used to obtain voluntary price for the small consumer (PVPC) data. 71 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Pumps x4 Turbine R0 R2 R1 Pipe 10 Source21 Pipe 02 Switch PV Load Battery Grid CEDER System Figure 3.39 –CEDER case representation with Pyomo blocks. For each case, two simulations are performed: one considering typical summer data and another considering typical winter data. This approach allows the study of the tool’s potential in each season with different irradiance levels, electrical demand, and electricity prices. The initial conditions for a more accurate approach assume that reservoirs 1 and 2 are completely empty, while reservoir 0 is at maximum capacity. If a battery is considered, it is also assumed to be completely discharged. This approach ensures that no storage source has initial energy, whether electrical or gravitational. Results In each case, a plot is presented showing the balance of power consumed and generated, where power injected into the energy balance node is negative, while the remaining power is positive. Therefore, PV power will be shown as negative since it is generated and injected into the EB node. Additionally, a line plot represents the PVPC and the selling price per hour. Case 1 : In summer, the system takes advantage of high solar irradiation during the day and turbines at night to supply the electrical demand. On the other hand, in winter, the model takes advantage of low energy prices at night to activate the pumps and store water, which will be used during high price peaks to meet the demand. −40 −20 0 20 40 P (kW) T ime (h) P V L oad P umps Grid Turbine cbu y ,g cs el l ,g 100 200 300 Price (€ /MWh) 0 6 12 18 23 (a) Resulting consumed power. 0612 18 23 0.00 0.01 Flow (m³/s) T ime (h) Pipe01 Pipe02 Pipe10 0 50 Volume (%) 0612 18 23 T ime (h) R1 R0 R2 (b) Reservoirs level. Figure 3.40 –CEDER results - Case 1 in summer. 72 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems −40 −20 0 20 40 P (kW) T ime (h) P V L oad P umps Grid Turbine cbu y ,g cs el l ,g 100 200 300 Price (€ /MWh) 0 6 12 18 23 (a) Resulting consumed power. 0612 18 23 0612 18 23 0.00 0.02 Flow (m³/s) T ime (h) Pipe01 Pipe02 Pipe10 0 50 Volume (%) T ime (h) R1 R0 R2 (b) Reservoirs level. Figure 3.41 –CEDER results - Case 1 in winter. Case 2 : The problem determines the maximum PV power capacity, up to 66 kW. In summer, the system utilizes high solar irradiation to store water in the upper reservoirs and sells the excess energy. At night, the stored water is turbined to supply the load demand. In winter, the system takes advantage of the high installed PV power to sell electricity to the grid during periods of high prices and to store water in the upper reservoirs. Then, during the night and peak price periods, the stored water is used for turbining to generate energy and supply the electrical loads. No battery is sized in this optimisation case. 0612 18 23 −40 −20 0 20 40 P (kW) T ime (h) P V L oad P umps Grid Turbine cbu y ,g cs el l ,g 100 200 300 Price (€ /MWh) (a) Resulting consumed power. 0612 18 23 0. 0612 18 23 00 0.05 Flow (m³/s) T ime (h) Pipe01 Pipe02 Pipe10 0 100 Volume (%) T ime (h) R1 R0 R2 (b) Reservoirs level. Figure 3.42 –CEDER results - Case 2 in summer. Case 3 : In this case, the model considers an already installed battery. Since the battery’s efficiency is higher than that of the water storage system, the optimisation prioritizes charging and discharging the battery over using the water system. Therefore, in summer, the surplus PV power is used to charge the battery, supply the loads at night, and sell electricity when prices are high. On the other hand, in winter, the system takes advantage of low electricity prices at night to charge the batteries and discharge them during high-price periods. Again, no additional battery capacity is sized. Table 3.11 summarizes the operation and sizing costs per day after simulating each case under summer and winter conditions. It also displays the computation time in minutes on an 8th Gen Intel Core i5 @ 1,80 GHz laptop with 8,0 GB of RAM. From Table 3.11, it can be seen that Case 1 is the most expensive 73 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems tuning, the system could stand passing clouds of a few seconds. In turbines, appropriate gate and blade regulation manoeuvres would achieve the same results [104]. Hydraulic infrastructure Selecting pipes’ geometry and characteristics to increase the elasticity of the system help reduce the effective pressure wave velocity. Furthermore, the addition of air chambers, surge tanks and proper valving reduce the maximum pressure of such waves [92, Ch.10]. Some authors propose as well attaching a supplementary section of polymeric materials [94, 105, 106, 107]. 4.1.2 Contributions The main contribution of this work, as part of the Advanced Grid Interfaces for innovative STorage INtegration (AGISTIN) project, is the development of a sizing methodology of ESS to mitigate the negative water hammer effects derived from clouds shading over large PV pumping systems, which we found no previous work about. The methodology defines a cost function that considers capital and operation costs, including an statistical model of the clouds to consider their effect. The cost function can be solved analytically, requiring no iterative methods. We apply the methodology to a real study case using on-site data and analyse the feasibility and sensitivity of several ESS technologies, considering their environmental impact as well. The objective of this chapter is to develop a methodology to size an ESS for large PV pumping systems, while analysing several technologies to determine their feasibility in such application. The aim of such ESS is to improve the response of these PV pumping systems when clouds shade the PV plant. 4.2 Problem description Clouds shading over PV pumping systems derive in negative effects to the system such as water hammer. This work proposes the inclusion of an ESS to prevent water hammer by supplying the required energy to produce and sufficiently prolong a ramp of power when the pump stops. However, energy could also be supplied to maintain the pump running when the PV panels are shaded by a passing cloud, preventing the need to stop it. Therefore, the ESS is sized to accomplish two goals: (1) keep the pump running when a cloud shades the PV plant and (2) stop the pump smoothly, when required, following a ramp of power. Figure 4.3 portrays the energy supplied by the ESS, represented by the blue highlighted area. When a cloud event initiates, the ESS commences to provide the lack of energy resulting from the cloud shading to avoid stopping the pump ( 1in Figure 4.3). If the cloud continues for long enough, the ESS supplies the required energy to smoothly stop the pump ( 2 in Figure 4.3). This implies the ESS capacity is sized for the sum of the energy required for the ramp and that required for a certain assumed cloud: 𝐸𝐸𝑆𝑆 =𝐸(1)+𝐸(2),(4.1) with 𝐸(1) (kWh) the energy required to save a certain cloud event and 𝐸(2) (kWh) that required to shift from running power 𝑃𝑝𝑢𝑚𝑝(kW) to a complete stop 𝑃=0kW in the appropriate time Δ𝑡𝑟𝑎𝑚𝑝(s). To establish the energy 𝐸(1)it is essential to evaluate the actual weather circumstances and behaviour on the real site. By gathering and analysing relevant on-site data we can develop a probability model which will be applied to comprehend the scale and behaviour of the clouds and, subsequently, to size the ESS accordingly to that particular situation. 80 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 𝐺,𝑃 𝐺 𝑃𝑡 𝐺𝑡ℎ 𝑃𝑝𝑢𝑚𝑝 Save the cloud Cloud is too long Stop pump smoothly 12 Δ𝑡𝑟𝑎𝑚𝑝 Figure 4.3 –Irradiance drop event with ESS. The data required may be gathered by an irradiance sensor located in the PV system or its vicinities. This sensor measures the ambience irradiance and may be already installed to track and communicate the available power to the power converter. A threshold value 𝐺𝑡ℎ (W/m2) discerns in real time whether a cloud is shading the PV plant. A cloud is considered when the threshold value is reached and it stays until that value is not overcome (Figure 4.4), thus defining the duration of the cloud: Δ𝑡𝑐𝑙𝑜𝑢𝑑 =𝑡𝑛−𝑡0,(4.2) where 𝑡0(s) is the observation before intersecting the threshold value for the first time and 𝑡𝑛(s) the observation after intersecting it for the second (and last) time. Consequently we use the measures that result in the worst case-scenario, i.e. the longest duration. The maximum irradiance drop Δ𝐺𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑(W/m2) is also considered in order to size the maximum power that the ESS is required to supply: Δ𝐺𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑 =𝐺𝑡ℎ−𝐺𝑚𝑖𝑛.(4.3) The radiant exposure shaded by a cloud (J/m2) is expressed as the area compressed between the threshold value of irradiance and the measured irradiance and corresponds to the blue highlighted area in Figure 4.4. Since the data are discrete, the area between two observations 𝐴𝑖(J/m2) equals to that of a trapezoid 𝐴𝑖=𝐺𝑖−𝐺𝑡ℎ+𝐺𝑖+1−𝐺𝑡ℎ 2Δ𝑡𝑖,(4.4) where Δ𝑡𝑖(s) is the time elapsed between observations 𝐺𝑖and 𝐺𝑖+1(W/m2). The terminal areas, this is the ones between the threshold value and 𝐺0or 𝐺𝑛, are assumed to intersect in the midpoint between both observations. Accordingly for 𝐴0, and analogously 𝐴𝑛−1: 𝐴0=(𝐺1−𝐺𝑡ℎ)Δ𝑡0 2,(4.5) 𝐴𝑛−1 =(𝐺𝑛−1−𝐺𝑡ℎ)Δ𝑡𝑛−1 2.(4.6) The resulting radiant exposure shaded by a cloud 𝐴𝑐𝑙𝑜𝑢𝑑(J/m2) is the summation of the areas of the trapezoids: 𝐴𝑐𝑙𝑜𝑢𝑑 =𝑛−1 ∑ 𝑖=0𝐴𝑖.(4.7) The energy shaded by a cloud 𝐸𝑐𝑙𝑜𝑢𝑑 (kWh) is calculated with (4.8) and the maximum power drop 𝑃𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑(kW) with (4.9). These values are related to the specific PV system and refer to those required to achieve the same level of energy and power with an irradiance equal to 𝐺𝑡ℎ. 𝐸𝑐𝑙𝑜𝑢𝑑 =𝐴𝑐𝑙𝑜𝑢𝑑 1000 𝑃𝑃𝑉 𝜂𝑃𝑉 3600 ,(4.8) 81 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 𝐺𝐺0𝐴𝑖 𝐴0𝐴𝑛−1 𝐺𝑖 𝐺1 Δ𝑡𝑐𝑙𝑜𝑢𝑑 𝐺𝑚𝑖𝑛 𝐺𝑛 𝑡 𝑡𝑛 𝑡0 𝐺𝑡ℎ Figure 4.4 –Data key points that define a cloud. 𝑃𝑚𝑎𝑥,𝑐𝑙𝑜𝑢𝑑 =𝐺𝑚𝑖𝑛,𝑐𝑙𝑜𝑢𝑑 1000 𝑃𝑃𝑉 𝜂𝑃𝑉,(4.9) where 𝜂𝑃𝑉 is the efficiency of the PV and inverter system and 𝑃𝑃𝑉 the peak power of the PV system (kWp). Finally, it is crucial to disregard all instances of suspected cloud shading that are actually attributable to nighttime. These values are removed abiding by the following rule: if the date of the arrival of the cloud 𝑡0is different than that of its withdrawal 𝑡𝑛it is considered nighttime and the observation is removed. 4.3 Methodology (Off-grid) This section defines the methodology we developed to size an ESS for the PV pumping system to improve its performance and prevent the undesirable effects from clouds. As defined in Section 4.2, the ESS requires to be sized on its power 𝑃𝐸𝑆𝑆 and capacity 𝐸𝐸𝑆𝑆, which is split into 𝐸(1)and 𝐸(2)as defined in (4.1). Power 𝑃𝐸𝑆𝑆 Since the maximum power to be provided will not surpass the pump’s working power, the same is the power required by the energy storage system 𝑃𝐸𝑆𝑆: 𝑃𝐸𝑆𝑆 =𝑃𝑝𝑢𝑚𝑝.(4.10) The working power is determined by the operating point of the system and may not coincide with the nominal power of the pump. Capacity 𝐸(2) We can find the energy required for the ramp to be provided when stopping the pump 𝐸(2) with the resulting triangle from Figure 4.3: 𝐸(2) =𝑃𝑝𝑢𝑚𝑝Δ𝑡𝑟𝑎𝑚𝑝 2.(4.11) The appropriate stopping time Δ𝑡𝑟𝑎𝑚𝑝 (s) should be estimated, defined analytically, experimentally or given by the operators. Methods to obtain its value are out of the scope of this work. 82 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Number of clouds 𝑁 Data analysed on Section 4.4.1 suggest the number of clouds per day 𝑁shading more than a certain energy 𝐸follows a law of power with negative exponent 𝑁(𝐸)=𝐾𝐸𝛼,(4.12) with 𝐾>0and 𝛼<0. Applying properties of logarithms, it can also be expressed as a linear model: log(𝑁(𝐸))=log(𝐾)+𝛼log(𝐸). (4.13) Therefore, we can fit a linear regression model using the method of least squares to estimate its parameters. For readability purposes, in this case, we apply a change of variables such that 𝑦 =𝑙𝑜𝑔(𝑁(𝐸)), 𝛽=𝑙𝑜𝑔(𝐾)and 𝑥=𝑙𝑜𝑔(𝐸): 𝛼=∑𝒩 𝑖=1(𝑥𝑖−𝑥)(𝑦𝑖−𝑦) ∑𝒩 𝑖=1(𝑥𝑖−𝑥)2(4.14) 𝛽=𝑦−𝛼𝑥 (4.15) being 𝒩the total number of data points representing the curve. Total cost 𝐶 The total cost 𝐶(€) considers the capital and operating costs of the ESS itself and the costs associated to non-productive time, i.e. the pump stopping, during the lifetime of the ESS. We subdivided the total cost 𝐶into five conceptual parts, related to capital costs (4.17)-(4.18) and operation costs (4.19)-(4.20) of the ESS and operation costs of the facility (4.22). These subdivisions allow for a better subsequent understanding and analysis of the results: 𝐶=𝐶𝑐𝑎𝑝,𝐸+𝐶𝑐𝑎𝑝,𝑃 +𝐶𝑜𝑝,𝐸+𝐶𝑜𝑝,𝑃 +𝐶𝑜𝑝,𝑠,(4.16) where 𝐶𝑐𝑎𝑝,𝐸 (€) is the total capacity capital costs of the ESS, 𝐶𝑐𝑎𝑝,𝑃 (€) the total power capital costs of the ESS, 𝐶𝑜𝑝,𝐸 (€) the total variable operating costs of the ESS, 𝐶𝑜𝑝,𝑃 (€) the total fix operating costs of the ESS and 𝐶𝑜𝑝,𝑠(€) the total stop operating costs of the PV pumping facility. Capital costs Capital costs include the expenses of purchasing the ESS. For such an equipment capital costs can be subdivided in energy capacity capital costs 𝐶𝑐𝑎𝑝,𝐸(€) and power capital costs 𝐶𝑐𝑎𝑝,𝑃 (€). These costs are computed as the product of the unit price and its corresponding term: 𝐶𝑐𝑎𝑝,𝐸 =𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸(1)+𝐸(2)), (4.17) 𝐶𝑐𝑎𝑝,𝑃 =𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.18) with 𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 (€/kWh) the total cost per unit of energy of the ESS and 𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆 (€/kW) the total cost per unit of power of the ESS. Operation costs Operation costs include the maintenance expenses 𝐶𝑜𝑝,𝐸 (€) and 𝐶𝑜𝑝,𝑃 (€) of the ESS and the stopping costs, defined as the non-productive time that will have to be compensated with grid connected pumps 𝐶𝑜𝑝,𝑠(€). Variable operating costs consider the energy employed during both case 1 , where the ESS can provide enough energy to save the cloud, and 2 , where the pump is stopped (Figure 4.3). Otherwise, fixed operating costs relate to the installed power capacity: 𝐶𝑜𝑝,𝐸 =𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(1)(𝑁−  𝑁(𝐸(1)𝐷𝐸𝑆𝑆))+ +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸(1)+𝐸(2)) 𝑁(𝐸(1)𝐷𝐸𝑆𝑆), (4.19) 83 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems where 𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆 (€/kWh) is the variable operating costs of the ESS per utilised kWh, 𝑁is the average number of stops per day without ESS, 𝐿𝐸𝑆𝑆(days) is the average lifetime of the ESS and 𝐷𝐸𝑆𝑆 (p.u.) the depth of discharge of the ESS. Consider  𝑁as the particular estimator of 𝑁from (4.12), which is discussed further in Section 4.4.1; 𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.20) where 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆 (€/kW) is the fix operating costs of the ESS: 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆 =𝑇 ∑ 𝑡=1 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆,0 (1+𝑖)𝑡,(4.21) with 𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆,0(€/(kW⋅y)) the fix operating costs per year of the ESS at the year of investment, 𝑇is the 𝐿𝐸𝑆𝑆 expressed in years and 𝑖the real interest rate (p.u.); 𝐶𝑜𝑝,𝑠 =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆  𝑁(𝐸(1)𝐷𝐸𝑆𝑆), (4.22) where 𝑐𝑠𝑡𝑜𝑝 (€) is the cost per stop (4.23). In our study case cost per stop considers that the pumping system will have to operate grid connected during nighttime, however it should be adapted to the specific characteristics of each PV pumping facility. For instance, on a remote isolated area with no grid connection possibility other approaches would be considered such as just not pumping or utilising a diesel-driven pump. The former should contemplate losses due to lack of water for irrigation and the latter the price of fuel. 𝑐𝑠𝑡𝑜𝑝 =3600(𝑡𝑠𝑡𝑜𝑝 2+𝑡𝑛𝑤+𝑡𝑠𝑡𝑎𝑟𝑡 2)𝑃𝑝𝑢𝑚𝑝𝑐𝑔𝑟𝑖𝑑 (4.23) Substitute the terms into (4.16) and cost 𝐶can be expressed as a function of the capacity 𝐸(1): 𝐶(𝐸(1))=𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸(1)+𝐸(2))+ +𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆 + +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(1)(𝑁−  𝑁(𝐸(1)𝐷𝐸𝑆𝑆))+ +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸(1)+𝐸(2)) 𝑁(𝐸(1)𝐷𝐸𝑆𝑆)+ +𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆 + +𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆  𝑁(𝐸(1)𝐷𝐸𝑆𝑆), (4.24) Capacity 𝐸(1) Finally, by deriving 𝐶𝑑𝐶 𝑑𝐸(1) =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆𝐷𝛼 𝐸𝑆𝑆𝐾𝛼𝐸𝛼−1 (1) +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁+ +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝐸(2)𝐷𝛼 𝐸𝑆𝑆𝐾𝛼𝐸𝛼−1 (1) + +𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆, (4.25) we analytically obtain the expression for the capacity 𝐸(1)which minimises the cost (4.26): 𝑑𝐶 𝑑𝐸(1) =0 ⇒ 𝐸(1) =( −𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁−𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 𝐿𝐸𝑆𝑆𝐷𝛼 𝐸𝑆𝑆𝐾𝛼(𝑐𝑠𝑡𝑜𝑝+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐸(2)))1/(𝛼−1).(4.26) 84 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 4.4 Study case In this section, we apply the methodology developed in the previous section to a real scenario located in the region of Lleida (Catalonia, Spain), north-eastern Iberian Peninsula, and utilising the facilities of the irrigation community Comunitat de Regants Segrià-Sud. The facilities are located at geographical coordinates N 41∘21’ 40 E 0∘27’ 31. The whole system comprises 5 reservoirs and 3 pumping stations. Figure 4.5 shows an ortophoto of such system. There are currently two working PV pumping systems and further one under construction, which corresponds to that of the study case. Such system is described in Table 4.2. Reservoirs on the study case’s PV pumping system are 1 km apart and their difference of heights is 20 m. The irradiance sensor that provided the historic data is located on one of the PV plants. The PV plant utilises a North-South horizontal axis tracking system which increases the number of hours the system can pump per day, as demonstrated by [102]. Table 4.2 –Characteristics of the PV pumping system [28]. Concept Value Peak power 𝑃𝑃𝑉 275 kWp Inverter’s efficiency 𝜂𝑃𝑉 0,98 Irradiance threshold 𝐺𝑡ℎ 400 W/m2 Pump nominal power 𝑃𝑝𝑢𝑚𝑝,𝑁 160 kW Pump working power 𝑃𝑝𝑢𝑚𝑝 110 kW Stopping time 𝑡𝑠𝑡𝑜𝑝 30 s Startup time 𝑡𝑠𝑡𝑎𝑟𝑡 30 s Non-working time 𝑡𝑛𝑤 240 s Cost of energy 2𝑐𝑔𝑟𝑖𝑑 0,05 €/kWh Real interest rate 3𝑖4 % 0 2,5 5,0 km 1:220 000 sensor study case Figure 4.5 –Location of the irradiance sensor and study case on the CR Segrià-Sud facilities. Background maps obtained from Institut Cartogràfic i Geològic de Catalunya [31] and OpenStreetMap [32]. Figure elaborated in QGIS [110] We compared several technologies on this analysis, comprising lead acid batteries (Lead), lithium-ion batteries (LIB), redox flow batteries (Flow), ultracapacitors (Uc) and flywheels (Fw). Since many different sources exist for ESS costs with huge ranges of values, we decided to assume the characteristics from [111], which are listed on Table 4.3. 2Based on data from OMIE [108] 3Based on data from Banco de España [109] 85 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 4.3 –Capital and operation costs of the analysed energy storage systems [111] Technology 𝑐𝑐𝑎𝑝,𝐸 [€/kWh] 𝑐𝑐𝑎𝑝,𝑃 [€/kW] 𝑐𝑜𝑝,𝑣𝑎𝑟[€/MWh] 𝑐𝑜𝑝,𝑓𝑖𝑥,0[€/kW⋅y] 𝐷[p.u.] 𝐿[y] Lead acid 299,20 116,45 0,44 4,34 1,00 3 Lithium-ion 272,00 209,10 0,44 8,50 0,80 10 Redox flow 410,55 116,45 0,44 5,01 1,00 15 Ultracapacitor 63 308,00 0,00 25,5 0,85 1,00 16 Flywheel 9 792,00 0,00 25,5 4,76 1,00 20 4.4.1 Clouds Irradiance data comes from a solar irradiance sensor located besides one of the PV panels at the pumping station of the study case. This sensor feeds the control of the power converter. The dataset utilised was provided by the Comunitat de Regants Segrià-Sud and contains the sensor’s gathered data of 347 days since 28 March 2020 until 27 July 2023 with a 20 to 30 s sample time in daily spreadsheet files.Figure 4.6 plots the data regarding power generation of the PV system and power consumption of the pump of a PV pumping system in the CR Segrià-Sud facilities. The plotted PV pumping system is characterised by a 523 kWp PV system, an irradiance threshold set at 400 W/m2and a pump with a nominal power of 315 kW. Power (kW) Time (h) 0 0 200 100 300 500 400 6 12 18 23 Ppump Ppump,N PPV Gth PPV Figure 4.6 –Power generation and consumption of a PV pump system in the Segrià-Sud facilities, corresponding to 25th July 2022. We observed a total amount of 4 753 cloud events. The longest cloud lasted Δ𝑡𝑐𝑙𝑜𝑢𝑑 =269,50minutes and the largest shaded radiant exposure was 𝐴𝑐𝑙𝑜𝑢𝑑 =1 030,60 Wh/m2(Table 4.4). With an average of 14 clouds per day (Table 4.5), we did not detect any monthly or annual pattern that would be relevant for the study case. The standard deviation (SD) for both the number of clouds and the time cloudy is considerable. Table 4.4 –Statistical description of the properties of the observed clouds. Concept Mean (SD) Min. Median Max. Δ𝑡𝑐𝑙𝑜𝑢𝑑[min] 5,99 (15,5) 0,50 2,00 269,50 𝐴𝑐𝑙𝑜𝑢𝑑[Wh/m2] 14,59 (62,5) 0,01 1,24 1 030,60 𝐺𝑚𝑖𝑛[W/m2] 286,96 (86,3) 0,00 302,00 399,00 Figure 4.7 presents the rank distributions for the durations Δ𝑡𝑐𝑙𝑜𝑢𝑑and shaded radiant exposures 𝐴𝑐𝑙𝑜𝑢𝑑, defined in (4.2) and (4.7) respectively. Rank is defined as the complement of the cumulative distribution functionand serves asa visualisation foranalysingpower lawdistributionswith rareeventssuch as blackout sizes in electrical systems [112]. A succinct analysis on them suggests that a power law behaviour is present for both the radiant exposure and duration, therefore short and faint clouds are considerably more usual than long and thick ones, as expected from the dry continental Mediterranean climate of the region, with annual total precipitations of 350-550 mm [113]. 86 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 4.5 –Statistical description of the clouds dataset. Concept Per day (SD) Total in data Number of clouds 14 (14) 4 753 Time cloudy 1 h 22 m (1 h 30 m) 19 d 22 h 0 50 100 150 200 Duration ∆tcloud (min) 10−3 10−2 10−1 100 Rank ∆tcloud 0 200 400 600 800 Radiant exposure Acloud (Wh/m2) ∆tcloud Acloud Figure 4.7 –Rank function plot of clouds’ duration and shaded radiant exposure. Although data contains clouds shading up to 277 kWh from the PV plant, those are rare events and more than 90 % of the cases are found under 10 kWh, which encourages to set the range of the study case to 𝐸𝑐𝑙𝑜𝑢𝑑 ∈(0,1,10)kWh. Applying the methodology from Section 4.2, this is (4.14) and (4.15), the model that fits the study case (Figure 4.8), with an 𝑅2=0,9775, is  𝑁(𝐸)=3,746𝐸−0,51,(4.27) with  𝑁the number of estimated cloud events per day (day−1), analogous to (4.12), and 𝐸the shaded energy (kWh), which will also correspond to the energy supplied by the ESS. Alterations on the solar irradiance threshold 𝐺𝑡ℎinfluence this model. In our study case coefficient 𝐾linearly grows with the threshold while exponent 𝛼lightly fluctuates around -0,47 and -0,51. The influence on the resulting ESS sizing is analysed on Section 4.4.4. 10−1100101 Energy (kWh) 100 101 Count (day−1) R2= 0,9775 Figure 4.8 –Number of pump stopping events 𝑁shading a certain energy 𝐸, from data ( ) and estimator  𝑁 ( ) 4.4.2 Results The following section analyses the results obtained form applying the developed methodology (Section 4.3) to the study case system (Table 4.2) for the technologies listed in Table 4.3. We contemplate a base case as well. Base case considers no ESS either for stopping nor saving clouds and only serves as comparison for the cloud costs. It does not consider either the maintenance costs of the pumping system as a result of the effect of water hammer events, which is out of the scope of this 87 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems work. Its total cost 𝐶𝑏𝑎𝑠𝑒 (€) is computed as the stopping operating expenses considering an average number of cloud events per day: 𝐶𝑏𝑎𝑠𝑒 =𝑐𝑠𝑡𝑜𝑝𝐿𝑏𝑎𝑠𝑒𝑁. (4.28) To better compare the different ESS technologies, the total cost 𝐶is normalised by the lifetime 𝐿𝐸𝑆𝑆 for each of them, obtaining the total cost per year in €/y. Table 4.6 summarises the resulting optimal size and costs for each ESS technology. As depicted in Figure 4.9, the results of the optimisation show a clear preference for redox flow batteries and flywheels for the application and study case of this work. Since the application requires ESS with capacities that do not exceed 10 kWh but has to be able to deliver 𝑃𝑝𝑢𝑚𝑝 = 110 kW (Table 4.2), the optimisation favours those technologies with lowest power related costs, but is not influenced that much by capacity related costs. However, low capacity costs allow for larger storage, leading to less impact of clouds on the performance of the system and thus lower stopping related operating costs. One should notice that additional maintenance and replacement costs should be accounted for the base case, however, as stated previously further research is yet to be conducted on how to adequately reckon them. Table 4.6 –Sizing results Technology 𝐿[y] 𝐸(1)[kWh] 𝐸(2)[kWh] 𝑃[kW]  𝑁[day−1] Cost 𝐶[€] 𝐶/𝐿[€/y] Base case 10 0 0 0 14 21 093,19 2 109,32 Lead acid 3 1,99 0,46 110,00 2,64 16 126,88 5 375,63 Lithium-ion 10 4,88 ” ” 1,87 35 267,94 3 526,79 Redox flow 15 4,51 ” ” 1,74 25 296,67 1 686,44 Ultracapacitor 16 0,17 ” ” 9,18 64 184,49 4 011,53 Flywheel 20 0,60 ” ” 4,85 34 390,07 1 719,50 4 000 2 000 Cost per year (€/y) Base Lead LIB Flow Uc Fw 0 Ccap,E Ccap,P Cop,E Cop,P Cop,s Figure 4.9 –Costs per year for different technologies and base case. 4.4.3 Feasibility and impact assessment This section evaluates the feasibility of implementing the proposed solutions on the real site, considering its purpose and characteristics. The specific objectives are to study the physical feasibility of the application of different energy storage systems. It will be analysed that the volume and mass required for the installation of each ESS fit within the facilities, the required power (𝑃𝐸𝑆𝑆) is within the rated power, the response time is suitable for the operation, and the environmental impact and potential risks to health and environment of the ESS, taking into consideration where it will be located within the hydraulic installations and the fact that hydraulic installations are crucial to provide the water for the irrigation of large crop fields. 88 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Itis crucial tostudy the different spacesandweights that wouldbe dedicatedand requiredbythe ESS.The possible range of specific energy 𝑒and energy density 𝜌for each ESS from [114] are used. Considering both the sized capacity 𝐸𝐸𝑆𝑆 from Table 4.6, the possible range of mass 𝑚and volume 𝑣are found for each storage system. The results are presented in Table 4.7, which shows that vanadium redox flow batteriesrequirea rangeof166-497 kg and151-311 l, significantlyhighermass andvolumecomparedto other technologies. In addition, flywheels and ultracapacitors present relatively low volume requirements compared to other systems (around 70 l), but significantly higher mass requirements (106 and 252 kg). Lead-acid and lithium-ion batteries have similar volume and mass characteristics (less than 50 l and 80 kg), and lithium-ion batteries is the ESS technology that would require less space and mass. Table 4.7 –Properties of the ESS technologies [114] Technology 𝑒[Wh/kg] 𝜌[Wh/l] 𝑚[kg] 𝑣[l] Lead acid 30-50 50-80 49-82 31-49 Lithium-ion 75-200 200-500 27-71 11-27 Redox flow 10-30 16-33 166-497 151-311 Ultracapacitor 2,5-15 10-30 42-252 21-63 Flywheel 10-30 20-80 35-106 13-53 The ESS to be installed must be suited to deliver a specific amount of power, as calculated and presented previously in Table 4.6. Based on data from [115, 116], it is determined that since none of the evaluated ESS technologies have a rated power lower than the power of the pump (110 kW), all of them would be feasible in this regard. The response time of the ESS to an event is also critical in this application. A delayed response could result in power loss to the pump, potentially inducing water hammer. The required time for the study case is of a few seconds, therefore all technologies have the ability to respond in time for this application, since their response time is in the order of milliseconds [117]. The facilities are neighboured by 8 875 hm2of cropland and take part in their irrigation tasks [22]. In consequence, it is crucial to recognise and understand the hazards that the different ESS technologies entail for both health and the environment. There are different hazards regarding the use of each ESS. Lead acid and redox flow batteries may release hydrogen gases during normal operation, which can cause serious injury to humans [118]. Furthermore, lead acid batteries contain heavy metals that, in the event of damage or leakage [119], would release lead components into the soil, potentially contaminating water reservoirs or rivers, causing significant environmental damage. Likewise, lithium-ion battery cells may emit flammable gases such as hydrogen fluoride and hydrogen cyanide [118]. When exposed to water, air or high humidity, as is the case of the analysed application, they can undergo aggressive chemical reactions due to the corrosion of their components [118, 119], presenting a fire risk that could damage the equipments of the pumping station. It is important to consider these factors and choose a suitable location for the ESS to avoid personal, material and environmental damage. When deploying electrochemical batteries, it is essential to consider the use of a highly ventilated space and other infrastructures to prevent environmental risks, such as properly isolating the battery from the soil. The increase of the demand of electrochemical ESS might cause negative effects on the environment and social aspects of the countries involved in the chain of production [119]. These batteries are based on lithium, lead and vanadium, the three of which have relatively high abundance in the earth’s crust and are not considered rare elements. However, their extraction induces environmental and social issues, specially in economically unstable countries with a lack of regulation in the mining activity. Nevertheless, both lead acid and lithium-ion batteries can be recycled, specially in case of lead acid batteries with a recycling efficiency up to 95 % [119]. 89 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Base Lead LIB Flow Uc Fw 0 5000 10000 15000 Cost per year (€/y) Cc,E Cc,P Co,E Co,P CgCp Figure 4.15 –Costs per year for different technologies and grid connected case 1. Base Lead LIB Flow Uc Fw 0 10000 20000 Cost per year (€/y) i= 2-6 % cgrid = 2-10 c€/kWh tp= 5-15 c€/kWh Figure 4.16 –Costs per year for different technologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11 €/kW) and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝. Table 4.12 –PS3 sensitivity analysis results for cost of energy, real interest rate and excess power term 𝑐𝑔𝑟𝑖𝑑[€/kWh]: 0,05 0,05 0,05 0,05 0,02 0,10 𝑖[%]: 4 4 2 6 4 4 Technology 𝑡𝑝[€/kW]: 0,05 0,15 0,11 0,11 0,11 0,11 Base case 𝐸[kWh] 0 0 0 0 0 0 𝐶/𝐿[€/y] 10 112,74 24 722,74 18 878,74 18 878,74 17 194,10 21 686,48 Lead acid 𝐸[kWh] 10,98 10,98 10,98 10,98 10,98 10,98 𝐶/𝐿[€/y] 5 995,09 7 1446,81 6 694,15 6 678,49 6 689,12 6 686,12 Lithium-ion 𝐸[kWh] 10,98 10,98 10,98 10,98 10,98 10,98 𝐶/𝐿[€/y] 4 337,99 5 628,53 5 174,10 5 058,45 4 475,39 5 673,86 Redox flow 𝐸(1)[kWh] 10,98 10,98 10,98 10,98 10,98 10,98 𝐶/𝐿[€/y] 2 063,17 3 214,89 2 805,71 2 711,87 2 754,20 2 754,20 Ultracapacitor 𝐸[kWh] 0,41 0,85 0,69 0,69 0,67 0,72 𝐶/𝐿[€/y] 7 522,94 12 499,42 10 721,03 10 704,36 9 131,83 13 338,82 Flywheel 𝐸[kWh] 1,95 4,03 3,28 3,28 2,60 7,32 𝐶/𝐿[€/y] 5 244,96 7 492,88 6 745,97 6 638,39 5 447,04 8 305,19 96 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 4.5.2 PV disconnects, pump can stop This case considers that, in the event of a cloud, the converter will disconnect the PV from the system but the pump will be able to stop until the cloud has passed. Figure 4.17 shows the two stages the system may be found on during a cloud. Stage 1 comprises the span during which the ESS delivers power to the pump, limited by its own sized power 𝑃𝐸𝑆𝑆and capacity 𝐸𝐸𝑆𝑆. Stage 2, which may not be met, covers the stopping of the pump. 𝑡 𝑃 𝑃𝑝𝑢𝑚𝑝 Penalty 𝐸1𝐸2 Grid 𝑃𝑐𝑡𝑠𝑡𝑜𝑝 𝑡1 𝑃2 21 Figure 4.17 –Strategy 2. The optimisation problem is defined by a NLP consisting in a cost function to minimise (4.44) subject to constraints (4.45)-(4.52). Penalties must be considered just once per day, taking the highest value it achieves on each cloud, thus we consider only stage 1 on each cloud saved by the ESS (𝑁−  𝑁times) and stage 1 + stage 2 on each cloud that exceeds the capacity of the ESS (  𝑁times). Energy consumed from the grid corresponds to that the ESS could not deliver. To compute the penalty on stage 2 we require to know the value of the power 𝑃2(see Figure 4.17), which corresponds to the power that its left from the stopping ramp after utilising the whole capacity of the battery. Applying trivial trigonometry we can define such power as a function of the capacity 𝐸2,𝐸𝑆𝑆(4.48). Also, the penalty which applies to stage 2 should be the maximum between two possible circumstances (4.45) and (4.46). minimise 𝐸𝐸𝑆𝑆,𝑃𝐸𝑆𝑆 𝐶(𝐸𝐸𝑆𝑆,𝑃𝐸𝑆𝑆)=𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐)(1−  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆) 𝑁)+ +𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆𝑃𝑝𝑒𝑛,2( 𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆) 𝑁)+ +𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)+ +𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆𝑁𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝 𝑃𝐸𝑆𝑆 −1)+ +𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)(𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝 2−𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)+ +𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆𝑁+𝐸2,𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆))+ +𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆+𝐸2,𝐸𝑆𝑆)+ +𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆+𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆, subject to (4.44) 𝑃2−𝑃𝑐≤𝑃𝑝𝑒𝑛,2 (4.45) 𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐≤𝑃𝑝𝑒𝑛,2 (4.46) 97 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐≥0 (4.47) 𝑃2=√𝑃𝑝𝑢𝑚𝑝√𝑃𝑝𝑢𝑚𝑝−2𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆 𝑡𝑠𝑡𝑜𝑝 (4.48) 𝑃𝑝𝑒𝑛,2 ≥0 (4.49) 𝑃𝐸𝑆𝑆 >0 (4.50) 𝐸1,𝐸𝑆𝑆 ≥0 (4.51) 𝐸2,𝐸𝑆𝑆 ≥0 (4.52) Results We used the Pyomo library [62] to write the NLP and COIN-OR IPOPT [75] with a tolerance of 1e-4 to solve it. Below we analyse the results obtained form applying the developed methodology to the study case system for the technologies listed in Table 4.3. We subdivided the cost 𝐶(4.44) into six conceptual parts, related to capital costs (4.53)-(4.54) and operational costs (4.55)-(4.56) of the ESS, operational costs of the facility (4.57)-(4.58) and penalties (4.59). These subdivisions allow for a better understanding and analysis of the results: 𝐶𝑐𝑎𝑝,𝐸 =𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆+𝐸2,𝐸𝑆𝑆), (4.53) 𝐶𝑐𝑎𝑝,𝑃 =𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.54) 𝐶𝑜𝑝,𝐸 =𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆(𝐸1,𝐸𝑆𝑆𝑁+𝐸2,𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)), (4.55) 𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.56) 𝐶𝑜𝑝,𝑠 =𝑐𝑠𝑡𝑜𝑝𝐿𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆), (4.57) 𝐶𝑔=𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆𝐸1,𝐸𝑆𝑆𝑁(𝑃𝑝𝑢𝑚𝑝 𝑃𝐸𝑆𝑆 −1)+ +𝑐𝑔𝑟𝑖𝑑𝐿𝐸𝑆𝑆  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆)(𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝 2−𝐸2,𝐸𝑆𝑆𝐷𝐸𝑆𝑆), (4.58) 𝐶𝑝=𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆(𝑃𝑝𝑢𝑚𝑝−𝑃𝐸𝑆𝑆−𝑃𝑐)(1−  𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆) 𝑁)+ +𝑐𝑝𝑒𝑛𝐿𝐸𝑆𝑆𝑃𝑝𝑒𝑛,2( 𝑁(𝐸1,𝐸𝑆𝑆𝐷𝐸𝑆𝑆) 𝑁), (4.59) where 𝐶𝑐𝑎𝑝,𝐸 (€) is the total capacity capital costs of the ESS, 𝐶𝑐𝑎𝑝,𝑃 (€) the total power capital costs of the ESS, 𝐶𝑜𝑝,𝐸 (€) the total variable operational costs of the ESS, 𝐶𝑜𝑝,𝑃 (€) the total fix operational costs of the ESS, 𝐶𝑜𝑝,𝑠(€) the total stop operational costs of the PV pumping facility, 𝐶𝑔(€) the total cost of the energy acquired from the grid and 𝐶𝑝𝑒𝑛(€) the penalties for exceeding the contracted power 𝑃𝑐. We contemplate a base case as well. Base case considers no ESS and serves as comparison for the ESS technologies costs. Its total cost 𝐶𝑏𝑎𝑠𝑒(€) is computed as 𝐶𝑏𝑎𝑠𝑒 =𝑐𝑠𝑡𝑜𝑝𝐿𝑏𝑎𝑠𝑒𝑁+𝑐𝑔𝑟𝑖𝑑𝐿𝑏𝑎𝑠𝑒𝑁𝑃𝑝𝑢𝑚𝑝𝑡𝑠𝑡𝑜𝑝 2+𝑐𝑝𝑒𝑛𝐿𝑏𝑎𝑠𝑒(𝑃𝑝𝑢𝑚𝑝−𝑃𝑐). (4.60) 98 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems To better compare the different ESS technologies, the total cost 𝐶is normalised by the lifetime 𝐿𝐸𝑆𝑆 for each of them, obtaining the total cost per year in €/y. Table 4.13 summarises the resulting optimal size and costs for each ESS technology. As depicted in Figure 4.18, the results of the optimisation show a clear preference for redox flow batteries, ultracapacitors and flywheels for the application and study case of this work. The results show the best strategy in such context is to size an ESS to strictly stop the pump on every cloud without incurring in any excess power penalties. Table 4.13 –Grid connected sizing results (Strategy 2) Technology 𝐿[y] 𝐸1[kWh] 𝐸2[kWh] 𝑃[kW]  𝑁[day−1] Cost 𝐶[€] 𝐶/𝐿[€/y] Base case 10 0 0 0 14,0 182 975,03 18 287,50 Lead acid 3 0,00 0,46 100,00 14,0 19 366,73 6 455,58 Lithium-ion 10 ” 0,57 ” 14,0 49 341,82 4 934,18 Redox flow 15 ” 0,46 ” 14,0 49 277,34 3 285,16 Ultracapacitor 16 ” 0,45 ” 14,0 64 522,13 4 032,63 Flywheel 20 ”0,45 ”14,0 54 570,14 2 728,51 Base Lead LIB Flow Uc Fw 0 5000 10000 15000 Cost per year (€/y) Ccap,E Ccap,P Cop,E Cop,P Cop,s Cg Cpen Figure 4.18 –Costs per year for different technologies and grid connected case 2. The results for variations of interest rate, cost of energy and excess power term displayed in Figure 4.19 suggest that none of them have noticeable effects on the results. Base Lead LIB Flow Uc Fw 0 10000 20000 Cost per year (€/y) i= 2-6 % cgrid = 2-10 c€/kWh tp= 5-15 c€/kWh Figure 4.19 –Costs per year for different technologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11 €/kW) and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝. 99 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Transient excess of power In this scenario we could consider penalties only apply during stage 1, since stage 2 is a short lasting transient in comparison to the sampling rate of the registry, then 𝑃𝑝𝑒𝑛,2= 0 kW. The optimisation results reveal that the economically optimal solution should be not to size any ESS, since the operation costs of the excess power acquired from the grid do not surpass the capital costs an ESS would introduce. The cost per year would be 𝐶/𝐿= 2 205,09 €. 4.5.3 PV does not disconnect This case considers that, in the event of a cloud, the converter will keep the PV connected to the system. Figure 4.20 shows the two stages the system may be found on during a cloud. Stage 1 comprises the span during which the ESS delivers power to the pump, limited by its own sized power 𝑃𝐸𝑆𝑆and capacity 𝐸𝐸𝑆𝑆. Stage 2, which may not be met, covers the stopping of the pump. 𝑡 𝑃 𝑃𝑝𝑢𝑚𝑝 Penalty ESS PV Grid 𝑃𝑐𝑡𝑠𝑡𝑜𝑝 𝑡1 21 Figure 4.20 –Considered behaviour with grid and PV connected. This scenario contemplates both the energy and power lost on the PV plant due to a cloud event. Statistically considering these two variables resulted in a complex optimisation problem, therefore, we used a data driven approach to analyse this scenario. The total of 𝑁𝑐𝑙𝑜𝑢𝑑𝑠= 4 753 cloud data points during 𝑁𝑑𝑎𝑦𝑠 347 days were evaluated for each ESS technology to find the most economically suitable sizing following the subsequent methodology. First, a range of 𝐸𝐸𝑆𝑆 ∈(0,10) kWh in steps of 0,1 kWh, and 𝑃𝐸𝑆𝑆 ∈ (0,110) kW in steps of 1 kW, was defined as the possible sizing outcomes. In a combinatorial procedure, the final cost of each sizing was analysed, then the minimum was selected for each technology. The analysis methodology to find the final cost develops, for each cloud: • The amount of power required from the grid si computed as the difference of the power shaded by the cloud 𝑃𝑐𝑙𝑜𝑢𝑑(4.9) and the power that the ESS will provide: 𝑃𝑔=max(𝑃𝑐𝑙𝑜𝑢𝑑−𝑃𝐸𝑆𝑆,0) (4.61) • The power to be considered on the penalty computation (4.29) is the difference between the power required from the grid and the contracted power 𝑃𝑐. Penalties only apply for the considered time periods per day and not for each cloud, as defined in Section 4.5. 𝑃𝑝𝑒𝑛 =max(𝑃𝑔−𝑃𝑐,0) (4.62) A penalty will only apply if the the energy shaded by the cloud 𝐸𝑐𝑙𝑜𝑢𝑑 (4.8) is greater than the capacity of the ESS 𝐸𝐸𝑆𝑆, deducting the energy that will be saved to stop the pump in a ramp of power 𝐸(2)(4.11): 𝐸𝑐𝑙𝑜𝑢𝑑 >𝐸𝐸𝑆𝑆−𝐸(2) (4.63) 100 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems • The energy consumed from the grid results from the duration of the cloud Δ𝑡𝑐𝑙𝑜𝑢𝑑: 𝐸𝑔=𝑃𝑔Δ𝑡𝑐𝑙𝑜𝑢𝑑 (4.64) • The energy used from the ESS is equivalent to that of the cloud: 𝐸𝑢𝑠𝑒𝑑,𝐸𝑆𝑆 =min(𝐸𝑚𝑖𝑠𝑠𝑖𝑛𝑔,𝐸𝐸𝑆𝑆)(4.65) • Capital costs, for capacity 𝐶𝑐𝑎𝑝,𝐸 and power 𝐶𝑐𝑎𝑝,𝑃, are computed as: 𝐶𝑐𝑎𝑝,𝐸 =𝐸𝐸𝑆𝑆𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 (4.66) 𝐶𝑐𝑎𝑝,𝑃 =𝑃𝐸𝑆𝑆𝑐𝑐𝑎𝑝,𝑃,𝐸𝑆𝑆 (4.67) • Operating costs, for energy 𝐶𝑜𝑝,𝐸and power 𝐶𝑜𝑝,𝑃 usage, are computed as: 𝐶𝑜𝑝,𝐸 =𝐿𝐸𝑆𝑆 𝑁𝑑𝑎𝑦𝑠 ∑ 𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠𝐸𝑢𝑠𝑒𝑑,𝐸𝑆𝑆,𝑖 (4.68) 𝐶𝑜𝑝,𝑃 =𝑐𝑜𝑝,𝑓𝑖𝑥,𝐸𝑆𝑆𝑃𝐸𝑆𝑆,(4.69) • Grid costs are computed from the energy used from the grid: 𝐶𝑔=𝐿𝐸𝑆𝑆 𝑁𝑑𝑎𝑦𝑠 ∑ 𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠𝐸𝑔,𝑖𝑐𝑔𝑟𝑖𝑑 (4.70) • Operating costs of stopping the pump consider that non productive time should be compensated during nighttime with extra pumping operations, with 𝑁𝑐𝑙𝑜𝑢𝑑𝑠,𝑛𝑠 the number of clouds such that 𝐸𝐸𝑆𝑆 <𝐸𝑐𝑙𝑜𝑢𝑑(ns standing for not sufficient) and considering 𝑐𝑠𝑡𝑜𝑝defined in (4.23): 𝐶𝑜𝑝,𝑠 =𝐿𝐸𝑆𝑆 𝑁𝑑𝑎𝑦𝑠 ∑ 𝑖∈𝑁𝑐𝑙𝑜𝑢𝑑𝑠,𝑛𝑠𝑐𝑠𝑡𝑜𝑝 (4.71) • Finally, the total cost 𝐶is computed as the sum of the partial costs: 𝐶=𝐶𝑐𝑎𝑝,𝐸+𝐶𝑐𝑎𝑝,𝑃 +𝐶𝑜𝑝,𝐸+𝐶𝑜𝑝,𝑃 +𝐶𝑔+𝐶𝑝𝑒𝑛+𝐶𝑜𝑝,𝑠 (4.72) To better compare the different ESS technologies, the total cost 𝐶is normalised by the lifetime 𝐿𝐸𝑆𝑆 for each of them, obtaining the total cost per year in €/y. Table 4.14 summarises the resulting optimal size and costs for each ESS technology. As depicted in Figure 4.21, the results of the optimisation show a clear preference for redox flow batteries and flywheels for the application and study case of this work. It did not size a lead acid battery, which would be a more expensive solution than having no ESS. The results for variations of interest rate, cost of energy and excess power term displayed in Figure 4.22 suggest that, all of the parameters have little influence on the results. It is remarkable the effect of the cost of energy on the lead acid batteries technology, caused by not being sized and depending on the grid instead. Since lithium-ion batteries are sized to allow some penalties, the cost of penalty have a significant influence on it as well as the cost of energy. 101 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Table 4.14 –Grid connected sizing results (without PV disconnection) Technology 𝐿[y] 𝐸[kWh] 𝑃[kW] Cost 𝐶[€] 𝐶/𝐿[€/y] Base case 10 0 0 37 504,70 3 750,47 Lead acid 3 0,00 0,0 11 251,40 3 750,47 Lithium-ion 10 7,30 70,0 28 334,70 2 833,47 Redox flow 15 5,60 88,0 22 733,50 1 515,57 Ultracapacitor 16 0,10 104,0 45 213,80 2 825,86 Flywheel 20 1,30 97,0 36 795,80 1 839,79 Base LIB Flow Uc Fw 0 1000 2000 3000 Cost per year (€/y) Ccap,E Ccap,P Cop,E Cop,P Cop,s Cg Cpen Figure 4.21 –Costs per year for different technologies and grid connected with PV. Lead LIB Flow Uc Fw 0 1000 2000 3000 4000 Cost per year (€/y) i= 2-6 % cgrid = 2-10 c€/kWh tp= 5-15 c€/kWh Figure 4.22 –Costs per year for different technologies and base case (𝑖= 4 %, 𝑐𝑔𝑟𝑖𝑑 = 0,05 €/kWh and 𝑡𝑝= 0,11 €/kW) and sensitivity for interest rate 𝑖, cost of energy 𝑐𝑔𝑟𝑖𝑑and penalty 𝑡𝑝. 102 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 4.6 Aqueous ECR battery Although other storage technologies with higher readiness level may be suitable, as part of the AGISTIN4 project this chapter considers setting up an aqueous ECR. These low-energy storage batteries, currently in pre-commercial state (TRL-5), are supposed to supply high-power charge/discharge cycles with no significant degradation for 1 million cycles. Allegedly, in terms of energy stored and supplied power, this technology would fall in the mid ground of a LIB and an ultracapacitor. However, the aforementioned is to be tested and proven in the project on a demonstrator. Little to no actual information is available about aqueous ECR batteries but a white paper from the developer company [121], alleging the following characteristics: • Based in a solution of unspecified inorganic chemicals dissolved in pure water. • Specific energy up to 10,69 Wh/kg (tenths to hundreds of Wh per battery). • Specific power up to 5 kW/kg. • Projected life of more than 1 million cycles. • Deteriorates faster when charged, so it is advised to keep it discharged as much as possible and no overcharging it. • Suited for high power and high cyclability applications. 4.6.1 Results Applying the methodology from 4.3 we can obtain the capital costs at which an Aqueous ECR could be considered. Assuming a result of 𝐸(1) ≤0,10kWh, which is out of the analysed domain, implies that the sized ESS is not profitable, we can find the maximum capital cost to meet such condition. By solving (4.26) for 𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 𝑐𝑐𝑎𝑝,𝐸,𝐸𝑆𝑆 =−𝐿𝐸𝑆𝑆(𝑐𝑠𝑡𝑜𝑝+𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐸(2))𝐷𝛼 𝐸𝑆𝑆𝐾𝛼𝐸(𝛼−1) (1) −𝑐𝑜𝑝,𝑣𝑎𝑟,𝐸𝑆𝑆𝐿𝐸𝑆𝑆𝑁, (4.73) with 𝐸(1) =0,10kWh we find expression for the maximum capital prices for an Aqueous ECR battery on this application. Table 4.15 compiles the results for different costs of energy. For a range of 𝐸(1)see Figure 4.23. Table 4.15 –Maximum capital cost for 𝐸(1) ≤0,1 kWh for different cost of energy values Cost of energy (€/kWh) CAPEX (€/kWmin) 0,10 40,19 0,05 20,10 0,02 8,04 4.6.2 Results (Grid connected) Applying the methodology from 4.5 to a range of the ESS capital costs we can obtain those at which an Aqueous ECR could be considered. Table 4.16 summarises the results obtained for all of the considered strategies. 4https://www.agistin.eu/ 103 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 0 10 20 30 40 50 Capital cost (€/kW·min) 0,1 0,4 0,8 1,2 Energy E(1) (kWh) cgrid (€/kWh) 0,10 0,05 0,02 Figure 4.23 –Optimal sizing 𝐸(1) for the Geyser Aqueous ECR energy storage system for a range of capital cost and sensitivity for cost of energy 𝑐𝑔𝑟𝑖𝑑. Table 4.16 –Maximum capital cost for different excess power term (grid connected cases) Excess power term (€/kW) Strategy 1 CAPEX (€/kWmin) Strategy 2 CAPEX (€/kWmin) 0,05 11,00 12,00 0,11 24,00 26,00 0,15 33,00 36,00 4.7 Conclusion The application analysed in this work requires medium capacity (few kWh) but high power (hundreds of kW) energy storage. Our findings show that flywheels and redox flow batteries obtain the lower costs, benefiting from moderate storage capacity costs but low power related costs, as stated in the NREL literature. Ultracapacitor and lithium-ion prove to be solid technologies but are penalised by capacity capital costs and power capital costs respectively. Finally, lead acid batteries manifest low lifetime and high economic and environmental costs for such an application. However, such economic decisions are subject to the specific location and market conditions and should be analysed accordingly. It should be emphasized that the costs used in the study case are extrapolated from data provided by NREL, which originates from analysing higher capacity systems and could not be representative for this study case. This might be particularly relevant for the redox flow and lithium-ion batteries, as the results of the sizing methodology are allocated in the low-kWh range, forcing an important extrapolation of the cost range for them, typically in the 10-100 kWh range. This consideration challenges the optimal results obtained, as high-power, low-kWh redox flow and lithium-ion batteries might show a higher cost than the ones used for the analysis. Sensitivity analysis revealed that fluctuations of the cost of energy have a significant impact on the output of the optimisation, since low energy prices reduce the economical suitability for an ESS. This is especially relevant for energy storage technologies with higher capacity costs such as ultracapacitors and flywheels. Modifying the threshold value of irradiance that discerns clouds from having or not an effect on the system also considerably influences the final decision. Higher thresholds imply a greater number of considered clouds and energy to deliver, therefore storage capacity requirements are higher which benefits technologies with lower capacity costs. Flow batteries appear to be the most suitable option in terms of space requirements and installation mass, while still offering adequate response performance for the intended application. However, when considering environmental impact and lifetime, flywheel storage demonstrates advantages. 104 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 4.7.1 Future work This section discusses gaps we identified during our research to work on future analysis. Maintenance costs Start-stop cycles and consequent induced water hammer damage the infrastructure, which translates into increased maintenance and replacement costs. This costs are not reckoned in this study since we were not in possession of neither their financial worth nor any method of evaluation. Future analysis should be carried out in order to determine their value and account for them in further research on this topic. Control and management of the energy storage system Although, as mentioned in Section 4.1 other authors have worked in the implementation of a control strategy on the ESS and designing an energy management system (EMS), we did not find any that considered large reservoir-based PV pumping systems. Such systems carry their own challenges related to high power usage and large extensions of the PV systems. On-site implementation Implementing the ESS on the real site, after an energy management system is designed, will provide further insight on the behaviour and performance of the whole system that otherwise is not possible to appreciate. 105 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Secondary regulation Secondary regulation (aFRR) is a discretionary service aimed at maintaining the balance between generation and demand by automatically correcting deviations in grid frequency. The response time for this service ranges from 20 seconds to 15 minutes. Each day, the system operator publishes the reserve requirements for secondary regulation for each period of the corresponding program for the next day. The generation units eligible for the service submit their offers for the secondary regulation band. Once the service is assigned, it continues to cover the system’s needs according to a minimal cost rule [134]. The service is compensated through two market mechanisms: availability (regulation band) and utilization (the energy provided). Currently, this service is managed at a local level by the Spanish TSO. However, it is expected to be integrated and standardized with the European aFRR product and will be managed through the implementation of the European platform PICASSO. Tertiary regulation Tertiary regulation (mFRR) is a balancing service that activates active power reserves with the aim of maintaining network frequency and balance. The service is triggered manually, with a maximum activation time of 15 minutes, and it can be activated for at least 30 minutes. The energy provided by tertiary regulation is paid at the marginal price, following an allocation process that takes place 15 minutes before the scheduled period. Similar to secondary regulation, this process is currently managed at the local level by the TSO, but it is expected to be transferred to the European level through the implementation of the MARI platform [134]. Additionally, the P.O. 7.3 ”Regulación terciaria” mentions the potential of pumping stations to provide this service [135]. Replacement reserve The activation of the Replacement Reserve (RR) is a balancing service that activates active power reserves with the goal of resolving deviations between generation and demand that may be identified after the day-ahead market. It aims to restore or maintain the energy levels required for frequency recovery. Activation can be either manual or automatic (using secondary and tertiary regulation energies), depending on the need to prepare for imbalances or frequency deviations. The service must be activated within a maximum time of 30 minutes and is managed through the European platform LIBRA [134]. Service providers submit their RR offers to the local TSO, which, after a validation process, sends the offers to the European TSO. The European TSO then uses the LIBRA platform to optimise and determine activations at the local level, as well as the international energy exchanges [134]. 112 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 6 Real-time operation & control for innovativeirrigationcanal-basedenergy storage systems The proper operation of the irrigation facilities depends on the effective management of water resources. In the framework of this project, this involves to ensure that the necessary volumes of water for irrigation are available while providing grid services. Optimising the control of irrigation systems, particularly those involving reservoirs and pumps, presents a complex mathematical challenge. In addition to this challenge, incorporating uncertainties in water demand, availability, and meteorological and grid conditions represents a further complex aspect of the task. This chapter presents a mathematical description of the problem under consideration, including the classical elements of the irrigation system and the elements determined by the long-term optimisation tool described in 3. Furthermore, uncertainty sources are identified. The chapter then introduces the methodology employed in developing the plant controller capable of ensuring optimal operation, even in conditions that deviate from the expected operating scenario. Finally, the developed algorithm is tested in a simulation environment. The results are then presented and discussed. Specifically, this chapter is structured as follows: i Section 6.1 provides an overview of the current state of the art in the field, introducing the topic and reviewing the available solutions. ii Section 6.2 outlines the controller’s objectives and reviews the major challenges facing the irrigation system operation. It then introduces the mathematical formulation of the problem. iii Section 6.3 describes the methodology on which the optimal controller is based and develops the formulation for determining the proposed algorithm. iv Section 6.4 provides an analysis of the performance of the control algorithm developed on different case studies. v Section 6.5 concludes the chapter with the conclusions drawn. It also provides a description of the next steps to be taken in the project. 6.1 Introduction The irrigation system under consideration in this project is currently comprised of a series of reservoirs connected by pipes, with water flow facilitated by pumps organised in pumping stations. These reservoirs facilitate the storage and distribution of water to the fields. The plant operators then use heuristic rules to determine the demand for a certain amount of electrical power from the grid to maintain sufficient water in the upper reservoirs from the lower reservoirs. 113 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems The primary objective of this operational model is to reduce electricity costs. To this end, energy demand is scheduled to occur during periods of the day when, as stipulated in the contract, the price per kWh is lower, typically at night. In addition, off-grid photovoltaic panels are being installed to supply an isolated pump, so that when sufficient power is available, the pump associated with the PV installation will pump water. Within the framework of this project, the intention is to exploit the potential performance of the reservoirs as a store of electrical energy in the form of water. This will require the installation of new assets that allow for the bi-directional flow of water and the extraction of energy from water flows to be returned to the power grid. The introduction of new assets within the system will enable new functionalities, thereby increasing the complexity of plant operation. This will overrule the heuristic rules that operators have developed over the years. This new, larger and more complicated system will require more sophisticated control schemes to optimallybalancewaterdistribution, energyconsumption, andgridsupport. Traditionalrule-based orreactive control methods may no longer be sufficient as they lack the flexibility to anticipate future fluctuations in water availability, electricity prices and crop irrigation requirements. Instead, advanced optimisationbased approaches are needed to ensure real-time adaptability and long-term efficiency. The optimisation tool, which is explained in detail in Chapter 3, provides as output, in addition to the dimensioning of the plant elements, an optimal operating strategy for a specific scenario. However, from a control perspective, solving an offline optimisation problem (with all data known or estimated) and implementing its output as a set-point for a physical system is a feedforward approach. This approach can be considered adequate in cases where the plant model is perfectly known, both in terms of topology and parameters, and where the forecast of disturbances is estimated with high accuracy. In systems where uncertainty is a significant concern, such as the system under consideration in this project, however, achieving optimal control is complicated due to several interdependent factors: • Uncertainty in water demand: water requirements depend on soil conditions and external environmental conditions, creating variability in irrigation needs. • Accurate weather forecast: rainfall and evaporation rates are inherently unpredictable and have a significant impact on the availability of water in reservoirs. In addition, the production of photovoltaic energy is also dependent on climatic conditions. • Integration with the power grid: water storage in reservoirs serves as an energy reserve to support the electricity grid. However, the times when the grid is subject to disturbances are completely unpredictable. Given the stochastic nature of the system, robust and stochastic control techniques can help mitigate the effects of uncertainty by incorporating probabilistic models of rainfall, evaporation, and agricultural water demand. However, these methods can sometimes result in excessively conservative policies that may under-utilise available resources. In contrast, feedback optimisation structures offer a powerful framework for enhancing control robustness and adaptability. Unlike open-loop strategies that rely solely on forecasts and precomputed schedules, feedback-based methods continuously incorporate real-time measurements into the optimisation process. Such measurements can include reservoir levels, weather data and power grid signals, allowing the system to respond rapidly to unexpected disturbances. Embedding optimisation within a feedback loop enables the controller to adjust decisions as new information becomes available, thereby reducing the impact of modelling errors and forecast inaccuracies. Feedback optimisation provides a natural way to handle constraint violations and system nonlinearities, 114 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems ensuring safe and efficient operation even under highly variable conditions. When coupled with predictive strategies like Model Predictive Control (MPC), feedback optimisation enables anticipatory yet reactive decision-making, balancing long-term planning with short-term response - an essential feature of modern, multi-objective irrigation systems. MPC techniques provide an effective framework by explicitly considering future system dynamics within a receding horizon optimisation problem. MPC continuously updates its decisions based on new measurements and forecasts, optimising the operation of pumps and reservoirs. By leveraging predictive models and constraints, MPC can schedule water transfers and pumping operations in a way that minimises energy costs, prevents shortages, and strategically aligns water storage with periods of excess renewable energy generation. However, it should be noted that this methodology still relies on an accurate model of the existing plant to be optimised. In recent years, there has been a growing interest in the fact that many numerical optimisation algorithms, specially first order iterative algorithms, can be interpreted as dynamical systems. According to this interpretation, it is possible to construct an extended dynamical system consisting of plant dynamics and the dynamics of an algorithm for solving an optimisation problem. Therefore, this system will autonomously drive the plant to an optimal operating point. In the context of this notion, a technique known as Online Feedback Optimisation (OFO) has been introduced in the literature. The key idea of OFO is to implement optimisation algorithms as feedback controllers, which are connected with a physical plant to form a closed loop. Therefore, OFO-based controllers employs real-time measurements to adapt control actions as and when required. Moreover, OFO strategies demand minimal model information, making it particularly beneficial in situations where accurate models are challenging to acquire. The time evolution of the plant state converging to the solution of an optimisation problem follows the following structure: • The set of real-time measurements are collected in the central controller. • The controller updates the control actions by solving an iteration of the optimisation problem. • The new control actions are dispatched to the system by updating the set-points of the controllable devices. • After a waiting period during which the fastest transients disappear and the system measurements are taken again. Then, the process is repeated as the system converges to the solution of the optimisation problem. It is important to note that within the OFO framework, the plant is considered a constraint enforcer routine, i.e. given an input, the physical system will produce an output that satisfies the input-output relationship. As a consequence, there is no need to evaluate the (possibly nonlinear) functions describing the system’s behaviour, thereby reducing the computational cost. This feature provides OFO-based control structures with a high degree of scalability, making it an attractive option for large-scale and complex systems. Furthermore, feedback the measurement set, instead of being model dependent, inherently includes the effect of exogenous disturbances and the corresponding control actions are updated without the need to forecast them. Given these advantages, the application of OFO-based controller in combination with the developed classical optimisation tools on this irrigation system is a promising approach to achieving an optimal tradeoff between water availability, economic efficiency, and grid integration. 115 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 6.2 Problem definition Consider a non-linear dynamic system which is herein referred to as the plant. The behaviour of the system under consideration is determined by the following equations: 𝑑 𝑑𝑡𝜁=f(𝜁,u), y=g(𝜁)+d,(6.1) where 𝜁 ∈ℜ𝑛denotes the column vector comprising the 𝑛states of the system, u∈ℜ𝑝and y∈ℜ𝑞 are respectively the control actions and the measurable outputs of the plant. The vector field f(⋅)and the map g(⋅)describe the dynamic evolution of the plant and the output measurement process, respectively. In addition, in this plant, a set of disturbances is considered to be present which are represented by the column vector d∈ℜ𝑤. Note that these disturbances are considered to affect the system in an additive manner. One of the primary assumptions regarding this plant is that, given a constant input uand a constant disturbance d, the plant exhibits asymptotically stable behaviour. This implies that transients dissipate rapidly, leading to a fast convergence of the operating point towards a stationary state. Furthermore, it is assumed that a unique steady-state is reached for a given input: 𝜁𝑠𝑠 =h𝑠(u), which implies the following: 0=f(𝜁𝑠𝑠,u)=f(h𝑠(u),u). (6.2) It can be concluded that a direct consequence of this is the existence of a stationary mapping between disturbance-free measurements and control actions, as follows: y𝑠=h(u)∶=g(h𝑠(u)), (6.3) Here, it is necessary to consider that h(⋅)is continuously differentiable in u. In the system previously described, consider the problem of determining the values of the set-points, which are bounded by a feasible set, in order to minimise a given cost function while satisfying certain constraints on the set of output signals. This can be mathematically expressed as follows: minimise u𝜙(y,u) subject to h(u)+d−y=0 y∈𝒴 u∈𝒰, (6.4) where 𝜙(⋅)denotes a scalar function that encompasses the objective to be minimised. The objective in question may be dependent either on the inputs uor the outputs y, or indeed on both types of variable. 𝒴and 𝒰are used to denote, respectively, the sets of admissible steady-state values of the measured variables and the control actions. Finally, h(⋅)is the steady-state input-output (probably non-linear) map of the dynamic plant, and ddenotes the disturbance vector. The fundamental problem is therefore to steer the operating point of the plant to a state that satisfies all constraints while minimising the cost function value. 116 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Figure 6.1 –Online Feedback optimisation structure based on gradient flow. 6.3 Methodology This section outlines the procedure for obtaining the feedback control law that solves problem (6.4), described in the previous section. The objective of the algorithm is to drive the operating point of the plant to a point the minimises the function 𝜙(y,u)which is a function of the plant output yand input u. Considering that both the mathematical model of the stationary mapping and the disturbances are known, then the cost function can be reduced as follows:  𝜙(u)∶=𝜙(h(u)+d,u). (6.5) For a moment, assume that the minimisation problem 6.4 is unconstrained. In this case, the optimum can be reached by means of a simple gradient flow algorithm [136]: 𝑑 𝑑𝑡u=−∇𝑢 𝜙(u) =−∇𝑢h(u)⊤∇𝜙(h(u)+d,u)⊤,(6.6) where ∇𝑢h(u)is a consequence of the chain rule applied to 𝜙(h(u)+d,u). Note that ∇𝑢h(u)is the Jacobian matrix of the function h(⋅)at u. This matrix will be referred to as Hfrom here on in. This matrix matrix provides an indication of the sensitivity of the outputs to the inputs. Problem (6.6) can be solved in a closed loop without the need for additional information until an equilibrium point (𝜁⋆,u⋆)is reached. This stationary point of the plant satisfies ∇𝜙(h(u)+d,u)⊤=0, thus, it is a critical point of the cost function 𝜙(⋅). An alternative proposition is to recognise in (6.6) that the expression h(u)+dcorresponds to the set of measurements of the plant, i.e. y. In this case, the algorithm (6.6) is rewritten in an open loop form, as follows: 𝑑 𝑑𝑡u=−∇𝑢h(u)⊤∇𝜙(y,u)⊤.(6.7) The new algorithm (6.7) requires knowledge of the set of measurements y, but avoids the need to compute the plant model h(⋅)and thus avoids the need to know explicitly the disturbances d. The primary benefit of this approach is that it facilitates the construction of a closed-loop system, wherein the plant (6.1) is governed by algorithm (6.7) as the controller. The controller is referred to as Online Feedback Optimisation [137, 138]. The interconnection of these two systems is illustrated in Figure 6.1. 117 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems The integral control nature of (6.7) guarantees the convergence to a steady-state optimal point [139]. In order to avoid large excursions in control actions, a gain (𝜖) with a small positive value is added to the controller. Therefore, the whole interconnected system is expressed as follows: 𝑑 𝑑𝑡𝜁=f(𝜁,u) y=g(𝜁)+d 𝑑 𝑑𝑡u=−𝜖H⊤∇𝜙(y,u)⊤. (6.8) Due to its feedback nature, the OFO approach is robust to model inaccuracy and disturbance effects. Therefore, there is no need for a forecast of disturbance behaviour or comprehensive knowledge of the plant; only an estimation of sensitivity is required. Now that the unconstrained OFO operation has been reviewed, let’s return to the original problem and consider the constraints on the control actions and outputs of the plant. A variety of strategies can be employed to incorporate the constraints in the construction of the OFO-based control algorithm: 1. Gradient methods with penalty terms 2. Gradient methods with barrier functions 3. Projected gradient flows [140, 141] 4. Primal-Dual saddle points [142, 143] The first two methods have the disadvantage of modifying the objective function, so they can only converge to a value close to the optimum. Furthermore, it should be noted that the use of penalty-based methods does not ensure that the solution will satisfy the constraints. Primal-Dual saddle point methods have demonstrated excellent performance in converging to an optimal solution for convex-definite problems. Generally, these algorithms consist of a gradient descent in the primal problem and a gradient ascent in the dual problem. Controllers based on these algorithms have even been tested experimentally [142, 144]. However, if the objective function or constraints are nonconvex, convergence to a saddle point cannot be guaranteed. This requires the addition of regularisation terms to both the primal and dual problems. While this ensures convergence of the flow, the saddle points of the new problem will no longer correspond to those of the original problem. Finally, projected gradient flows enforce inequality constraints by utilising projection mechanisms. Classical projected gradient descent is based on the Euclidean minimum norm, which is used to project the result of each iteration onto the feasible region. In the interior of the feasible set, therefore, trajectories follow the gradient direction, whereas at the boundary they follow the steepest feasible direction. It should be noted that these methods are discontinuous systems by definition and therefore require non-smooth analysis techniques. For the purposes of this study, it was decided that an algorithm of the projected gradient flow type would be best suited to facilitating the integration of the problem’s inequality constraint. Specifically, the algorithm presented in [141] has been adopted, which functions by projecting the gradient iteration on a linearisation of the feasible set at the current point. The 𝑘-th iteration of the integral feedback controller, formulated in discrete time, can be expressed as follows: u[𝑘+1]=u[𝑘]+𝜖𝜎(u[𝑘],y[𝑘]), (6.9) 118 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems where 𝜖>0is a small fixed step-size, and 𝜎(u,y)is defined as: 𝜎(u,y)∶=arg min w‖w+G−H−∇𝜙(y[𝑘],u[𝑘])‖2 G subject to A(u[𝑘]+𝜖w)≤b C(y[𝑘]+𝜖Hw)≤d,(6.10) where Gis a continuous metric on the feasible set. The expression (6.10) determines the resulting vector from projecting the control action that reduces the objective function onto the linearisation of the feasible search region. Note that the constraints are evaluated at the point to which the system is expected to evolve in the linearised space, rather than at the current point. The remaining issue to be addressed in the implementation of the algorithm concerns the determination of the plant sensitivity matrix H. It is important to note that this matrix is not constant unless the plant can be characterised by a linear time-invariant (LTI) system, however, in realistic environments, the Jacobian matrix is state or time dependent. A salient feature of controllers that are based on OFO techniques is that, due to the feedback structure, they exhibit a high degree of robustness against inaccuracies in the values of the sensitivity matrix [145]. However, improved estimation of the values of this matrix lead to enhanced convergence of the system to the desired operating point. Therefore, it is highly desirable to have a good estimate of the input-output sensitivity. In cases where a model of the plant is available, the most direct approach is to evaluate the derivative at the desired operating point, thereby obtaining the sensitivity matrix analytically. A more direct approach, or online procedure, would be to perturb each of the control actions sequentially and determine their effect on the outputs. This would be equivalent to applying the finite difference method to the Jacobian matrix. In systems where such methods are not applicable, it is sufficient to determine a matrix with 0, 1 and -1, depending on whether the input has a zero effect on the output, whether it is directly proportional or inversely proportional. Each of these methods provides a value of the sensitivity at an operating point. It is therefore desirable that this matrix be updated online by comparing the expected variation with that obtained at each step. 6.3.1 Development of OFO-based controller for pump-based irrigation plants The first step in the OFO-based controller formulation is to identify the control variables and the measured variables. In pump-based irrigation systems, we consider that the control actions can be: 1. Electrical power supplied to the pump 𝑝𝑒, for pumping directly connected to the main grid. 2. Electrical power supplied to the pump 𝑝𝑒and mechanical speed of the motor 𝑛at those stations equipped with frequency regulating assets. In both cases, the electrical power shall remain in steady state within established operating limits: 𝑝𝑒≤𝑝𝑒≤𝑝𝑒,(6.11) where 𝑢denotes the minimum value that 𝑢can reach, whereas 𝑢is used to identify its maximum value. Where applicable, the rotational speed of the pump must also be forced to remain within the limits of steady state operation: 𝑛≤𝑛≤𝑛. (6.12) 119 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Turbine Pump Reservoir 1 Reservoir 0 Irrigation Pipe Hydro Power PV Battery Grid CP Figure 6.2 –Relationship between offline and online optimisation tools. The constraints defined in equations (6.11) and (6.12) are of the box-constraint type and can be formulated linearly in a compact form as follows: Au ≤b,(6.13) where the column vector ugroups the control actions. The matrix Acontains only 1 and -1 for the signs of the inequalities, and the column vector bcontains the previously defined upper and lower limits of operation. The disturbances that are considered unknown in this problem are the flows demanded for irrigation. With regard to the system’s outputs, it is essential to closely monitor the level of the reservoirs, 𝑧, (or the volume of water contained 𝑊), and the state of charge of the batteries 𝑆𝑂𝐶. It may also be advisable to considermeasuresofwaterflows. All these variables, alongwith theirrespectiveminimumand maximum limits, represent a set of box constraints that can be expressed as a linear inequality constraint, in the same way as equation (6.13). It is important to note that in this problem the objective is not exactly to reach an optimal operating point, but to determine an optimal water use planning. For that reason, the OFO-based controller is considered to interact with the long term offline optimiser presented in Section 3.3 through the objective function. Figure 6.2 details the interconnection between these two tools. Specifically, the system is considered to follow the optimal strategy coming from the offline optimiser. However, this optimisation depends on a weather forecast and a water demand forecast, which may be inaccurate. Therefore, the objective of the OFO-based controller will be to keep system operation as close as possible to the optimal strategy, while correcting any deviations caused by conditions that differ from those predicted during offline optimisation. 120 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Figure 6.3 –Model of the simplest test case. 6.4 Performance assessment Thissection presentsthe resultsofthe applicationof thecontrolalgorithmdevelopedusing themethodology described above on a case study. The objective of the present studies is to analyse the functionalities of the proposed controller. 6.4.1 Study case To date, only one case study has been analysed. This irrigation plant model is a simple system that allows for straightforward evaluation of the controller’s performance. The system consists of two reservoirs, one positioned at a higher level than the other, connected by a pipe. It is assumed that the irrigation system takes water from a river, so the volume of the modelled lower reservoir is much larger than the upper reservoir. The pumping station, which is connected to the main grid, is located adjacent to the lower reservoir. A schematic of the system is shown graphically in Figure 6.3 and Table 6.1 lists the main system parameters. Table 6.1 –Parameters of the simple test case. Parameter Value Maximum volume of the downstream reservoir 106m3 Minimum volume of the downstream reservoir 0m3 Maximum height of downstream reservoir 1m Minimum height of downstream reservoir 0m Maximum volume of the upstream reservoir 600m3 Minimum volume of the upstream reservoir 400m3 Maximum height of upstream reservoir 80m Minimum height of upstream reservoir 60m Linear pressure loss coefficient of the pipe 0.05 s2 m5 Pump coefficient A 120m Pump coefficient B 0,002 𝑠2 𝑚5 Pump efficiency 72% Pump maximum power 16kW The initial volume of the downstream reservoir is 105𝑚3, while the upstream reservoir 2 has a volume of 500𝑚3at the beginning of the simulation. Finally, it is considered that the pump is inactive. The irrigation water consumption profile has been randomly generated. The offline optimisationtool, which determines theoptimalconsumptionprofileofthe pump, is considered to update its references every hour. The OFO-based controller updates the control actions every minute, in this first study only the power consumed by the pump. 121 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Grid connection Grid connection PV system Pump system PV system Pump system AC grid DC grid Figure 7.2 –AC vs DC interconnections. pass through the primary grid. This also has implications on the flow of energy, and it is not possible to directly control which energy is delivered to the grid and which is fed to the pumping system. Based on these facts, it is interesting to consider connecting these two systems with DC. The difference between these two schemes is shown in Figure 7.2. The DC configuration maintains the two essential converters for the pumping and PV systems while interconnecting them using a DC microgrid. It includes an additional converter to interconnect this system to the principal AC grid. This configuration’s main advantage is the possibility of operating in islanded mode. The pumping system can be fed directly from the PV system without bypassing the electrical energy through the principal grid. Even if the grid is down, the system could still operate. The main disadvantage is its higher initial cost and its complexity. However, its higher price can eventually compensate for more hours of operation in islanded mode, i.e., without buying energy from the principal grid, and the possibility of offering grid services from the converter connecting this system to the principal grid. This configuration makes it easier to provide grid services from the main converter. It is suitable for operating in islanded mode and is considered a valid option for this application. 7.3 Control architectures for the converter connected to the primary grid On the DC grid interconnection strategy, there are at least three converters. The first one, the DC/DC converter of the PV system, performs the MPPT algorithm; the second one is the AC/DC converter of the pumping system, which regulates the frequency of the pumping shaft and its voltage. The control to be applied at the third converter must still be defined. This section’s main subject is an initial discussion on which possible control architectures can be applied to this converter. The literature contains control strategies and architectures to fulfil different requirements. Some of the most common state-of-the-art control architectures and functionalities are highlighted here. Specifically, three controllers are presented: PQ control, DC voltage control, and AC grid-forming control. PQ control, or AC grid-following control, relies on a Phase-Locked Loop (PLL) to synchronize with the grid voltage. This element reads the grid’s voltage and takes out the angle so the converter’s internal angle reference rotates at the same angle as the grid. It operates in the synchronous 𝑑𝑞0reference frame and regulates the output current to independently control the active (P) and reactive (Q) power delivered to the grid. This control strategy is typically used in systems where the strong grid provides a stable voltage reference. Thus, it depends on the presence of an external AC voltage source to function correctly. The same happens on the DC side; it relies on a stable DC grid voltage to be connected, as this controller cannot form the DC side voltage. 128 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems dc dc dc DC Voltage Loop AC Voltage support kV ac Figure 7.3 –Example of a DC voltage control architecture. + + + uq PI PIu + + C + + 1 s AC Voltage Loop _ _ u q d ω0 ac C ω0 ac uq* uqd u = 0 d* ω0 _ Syncrhonization Loop kP P ω 1 τs+1 Figure 7.4 –Example of an AC grid-forming control architecture with droop control. An alternative, that does not require a stable DC voltage to be connected with, is the DC voltage control scheme (see Figure 7.3), as this controller is used to regulate the voltage of the DC link by adjusting the active power exchange on the AC side of the converter. This control scheme is usually implemented in 𝑑𝑞0and requires a PLL to synchronize with the AC grid voltage. Thus, it also depends on the presence of an external AC voltage source to function correctly. An alternative control architecture that does not require an external AC voltage source is AC grid-forming control. AC grid-forming control, often implemented through virtual synchronous machine models, droop control, or power-angle regulation, replaces the PLL with an internal voltage and frequency reference (see Figure ?? for example). This allows the converter to regulate both voltage amplitude and frequency, making it suitable for operation in islanded systems, weak grids, or black-start conditions. Grid-forming control enables the VSC to act as the system’s voltage source. It can emulate inertia and damping, facilitating load sharing and system stability in inverter-dominated networks. It is essential to note that a stable DC voltage is required on the DC side, as this control strategy can form the AC voltage but not the DC. Different control architectures have been proposed in the literature [146, 147] to overcome this limitation, one of which is presented next. 7.3.1 Dual-Port control The previously discussed control architectures cannot provide grid-forming functionalities to both AC and DC sides. In the literature, several proposed control architectures [146, 147] exist that can provide this service on both sides. One proposed in [147] is the one depicted in Figure 7.5. The general scheme is very similar to a traditional AC grid-forming control, which includes an AC voltage vector control with a cascaded grid current control. The main difference comes in the synchronization loop, where a different scheme is used instead of a classical PLL. This scheme uses the DC voltage to synchronize the converter with the grid angle. 129 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems + + + uq PI PIu + + C k dp + + 1 s AC Voltage Loop _ _ u q d ω0 ac C ω0 ac uq* uqd u = 0 d* ω0 _dc dc Dual Port loop p k dp i Figure 7.5 –Dual-Port control architecture. Geyser storage Grid connection Grid connection Grid connection Geyser storage Grid connection PV system Pump system PV system PV system PV system Pump system Pump system Pump system Without storage With storage Without DC/DC converter With DC/DC converter Figure 7.6 –Schemes of the analysed AGI configurations. 7.4 Discussion on possible AGI configurations Four different configurations can be analysed based on previous discussions on the elements to be included in the system. This depends on whether to install storage and if the PV system consists of a DC/DC converter or is directly connected to the DC grid. Figure 7.6 represents these four configurations. These configurations are next analysed based on which control architecture is included in the converter interconnecting the system with the grid. Considering the configuration without the DC/DC converter complicates the option of operating the PV system following an MPPT. Depending on the control scheme configured in the main converter, some limited MPPT can be provided. It is limited in the sense that the DC voltage level on the DC grid cannot vary up and down without limits, as other converters are connected to this DC grid, such as the pump station converter. Moreover, very low or high levels on the DC side can cause underand over-modulation problems on the converter. The converter schemes that could provide limited MPPT are the DC voltage and Dual-Port control. The main limitation of the DC voltage control is that it can offer only limited grid service, i.e., only the ones requiring reactive power. The other control scheme, AC grid-forming, can not provide MPPT as it can not regulate the DC voltage. However, it will be possible to offer grid services. 130 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Ceq P ac + _ } %idc vdc AC side electric scheme DC side electric scheme Figure 7.7 –VSC electric scheme model. VVV } va,b,c PLL P Q * * τ s+1 1 θ vq calc. τ s+1 1 P τ s+1 1 Q i τ s+1 1 i ia,b,c iq id * * iq id P Q a b c qd0 abc qd0 abc vd Figure 7.8 –Controlled current source model. Including a DC/DC converter with the PV systems ensures the possibility of including MPPT. In this case, if the central controller is equipped with DC voltage control, similarly to the previous case, the grid services to provide are limited. A possibility is to include some battery storage. This can help to smooth transients and enhance the operation in stand-alone mode. When considering the different controls to apply to the main converter, a general, important consideration is to study how the perturbations propagate between the AC and DC systems. 7.5 Models to study the connection to the primary grid Different models have been implemented to properly study the connection to the primary grid, emulating the DC grid configuration. The main converter is modelled as a two-level VSC converter. The electric model includes the AC electrical side with its transformer/RL-filter, and the control inputs are applied via a controlled voltage source. The DC side is modelled as a controlled current source, ensuring the power balance between the AC and DC sides and including a capacitor. The model scheme used is depicted in Figure 7.7. The pumping system has been modelled with a two-level VSC converter and a controlled current source. The pumping system is connected to the DC side via a converter with the same scheme as the one used for the main converter (Figure 7.7). The controlled current source is modelled as in Figure 7.8. Finally, the storage has been modelled as a constant capacitor, and the PV system has been modelled as a current source. These elements are modelled in different ways. Three different types of models are included. These are described next. 131 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 7.5.1 Steady-state Model The steady-state model is used to calculate the power flow scenario. It can calculate steady-state performance indices, such as voltage droop between lines, power distribution inside the DC grid, etc. Moreover, it will be helpful to calculate the linear model’s linearization point and properly initialize the MATLABSimulink model. To solve the power flow in this case, it has to be considered that the algorithm used has to account for AC and DC grids. Generally, two different methods exist, categorized into sequential and unified approaches. Sequential methods involve solving AC and DC equations step-by-step, as seen in [148, 149, 150]. Unified methods simultaneously solve the AC and DC systems, as demonstrated in reference [151]. One advantage of the sequential method is its compatibility with existing AC-based power flow software, allowing for the integration of DC systems without requiring extensive program modifications, unlike the unified approach, which necessitates changing the entire implementation to solve both AC and DC systems simultaneously. An alternative approach, suitable for small-sized systems, is to include all non-linear equations conforming to the power flow scenario and solve them with a non-linear solver. This is badly scaled if the system needs to be increased, but it has the advantage that it can be fully configured. Considering that the system in this case is small, this approach is used to solve the power flow. To compute the steady-state solution of the system, we solve a non-linear constrained optimisation problem. The problem is formulated as: minimise xf(x) subject to g(x)=0.(7.1) Where: •x∈ℝ𝑛is the vector of system variables, initialized with x0, which includes voltages magnitudes, voltage angles and powers. •𝑓(x)is an auxiliary objective function used to regularize or select among multiple feasible solutions. The implementation may return zero or a minor norm-based penalty. •g(x)=0represents the nonlinear equality constraints imposed by the power flow equations and converter steady-state conditions. There are no other constraints imposed besides g(x)=0. • No linear inequality constraints (Ax ≤b), • No linear equality constraints (Aeqx=beq), • No explicit upper or lower bounds on variables (l𝑏=−∞,u𝑏=+∞). The problem is solved using MATLAB’s fmincon function with the interior-point algorithm: x∗=fmincon (𝑓,x0,A,b,Aeq,beq,l𝑏,u𝑏,g,options). The solution x∗contains the steady-state operating point of the system. 132 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 7.5.2 Linear Model Small-signal studies involve analysing the system around its operating point via a linear model. Generally, the models used are non-linear; these models need to be linearized around the operation point, which can be calculated based on the steady-state analysis, i.e., solving the AC/DC power-flow previously formulated. Small-signal studies provide valuable insights into the system’s dynamic stability and control performance. However, building these linear models is challenging, and some mistakes can be made during the process. Therefore, verifying the models by comparing the results obtained in the linear model with the non-linear one is essential. The steps followed with the linear model consider the following: 1. Computation of the system’s operation point via an AC/DC power flow. 2. Linearization point calculation. 3. Construction of all the linear models included in the AC/DC system. 4. Integrate all the linear models. 5. Linear model validation. 6. Linear model analysis. The computation of the complete linear model of the system can be divided into sub-linear models. Once all the sub-linear models are computed, they can be interconnected using linear algebra. One sub-linear model is connected to another if the output of this sub-linear model is the input of another one, and vice versa. Next, the most critical sub-linear models are included. rl-circuit The state-space model for an AC 𝑟𝑙-circuit connecting an AC node 𝑥to an AC node 𝑦can be represented as: • State vector: Δ𝑥(𝑡)=[Δ𝑖𝑞 𝑥𝑦,Δ𝑖𝑑 𝑥𝑦]𝑇 • Input vector: Δ𝑢(𝑡)=[Δ𝑣𝑞 𝑥,Δ𝑣𝑑 𝑥,Δ𝑣𝑞 𝑦,Δ𝑣𝑑 𝑦]𝑇 • Output vector: Δ𝑦(𝑡)=[Δ𝑖𝑞 𝑥𝑦,Δ𝑖𝑑 𝑥𝑦]𝑇 𝐴=[−𝑅 𝐿−𝜔0 𝜔0−𝑅 𝐿];𝐵=[1 𝐿0−1 𝐿0 01 𝐿0 −1 𝐿];𝐶=[ℐ2𝑥2];𝐷=[02𝑥4], (7.2) where 𝑣𝑞,𝑑 𝑥and 𝑣𝑞,𝑑 𝑦are the 𝑞𝑑voltages at the AC nodes 𝑥and 𝑦, respectively; 𝑖𝑞,𝑑 𝑥𝑦 is the current flowing from node 𝑥to node 𝑦and 𝑅and 𝐿are the 𝜋-section line resistance and inductance, respectively. This model can represent the converter’s AC side electrical scheme and a Thévenin equivalent model. 133 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems 𝑞𝑑-angle Rotation All the blocks linked to the AC system are represented in the converter local 𝑞𝑑-frame, which is given by its angle reference estimated by its PLL. To properly interconnect these subsystems, it is necessary to transform the inputs of the different blocks from the global frame (AC grid) to the local frame (converter local 𝑞𝑑-frame). This is done with a rotation matrix (7.4), which takes into account the PLL deviation (Δ𝑒𝜃) while it is estimating the grid frequency (𝜔𝑔). [Δ𝑥𝑞 𝑙 Δ𝑥𝑑 𝑙]=𝑇𝑔−𝑙⎡ ⎢ ⎣Δ𝑥𝑞 𝑔 Δ𝑥𝑑 𝑔 Δ𝑒𝜃⎤ ⎥ ⎦,(7.3) 𝑇𝑔−𝑙 =[cos(𝑒𝜃0) −sin(𝑒𝜃0) −sin(𝑒𝜃0)𝑥𝑞 0𝑔−cos(𝑒𝜃0)𝑥𝑑 0𝑔 sin(𝑒𝜃0)cos(𝑒𝜃0)cos(𝑒𝜃0)𝑥𝑞 0𝑔−sin(𝑒𝜃0)𝑥𝑑 0𝑔], (7.4) Δ𝑒𝜃=(Δ𝜔𝑃𝐿𝐿(𝑠)−Δ𝜔𝑔), (7.5) where 𝑇𝑔−𝑙 is the transformation matrix, Δ𝑥𝑞 𝑙and Δ𝑥𝑑 𝑙are the state transformed variables in the local frame, Δ𝑥𝑞 𝑔and Δ𝑥𝑑 𝑔are the state variables in the global frame, 𝑒𝜃0is the angle difference in the steadystate operation point between the global and the local frame and 𝑥𝑞 0𝑔and 𝑥𝑑 0𝑔are the variables to be transformed at the operation point expressed in the global frame. The outputs have to be transformed from the local frame to the global frame using (7.7), as: [Δ𝑥𝑞 𝑔 Δ𝑥𝑑 𝑔]=𝑇𝑙−𝑔⎡ ⎢ ⎣Δ𝑥𝑞 𝑙 Δ𝑥𝑑 𝑙 Δ𝑒𝜃⎤ ⎥ ⎦,(7.6) 𝑇𝑙−𝑔 =[cos(𝑒𝜃0)sin(𝑒𝜃0) −sin(𝑒𝜃0)𝑥𝑞 0𝑙+cos(𝑒𝜃0)𝑥𝑑 0𝑙 −sin(𝑒𝜃0)cos(𝑒𝜃0) −cos(𝑒𝜃0)𝑥𝑞 0𝑙−sin(𝑒𝜃0)𝑥𝑑 0𝑙], (7.7) where 𝑥𝑞 0𝑙and 𝑥𝑑 0𝑙are the variables to be transformed and expressed in the local frame at the steady-state linearization point. Phase-Locked Loop The PLL controller representation in state-space form is included next. • State vector: Δ𝑥(𝑡)=[Δ𝑥𝑝𝑙𝑙] • Input vector: Δ𝑢(𝑡)=[Δ𝑣𝑑 𝑔,𝑐] • Output vector: Δ𝑦(𝑡)=[Δ𝜔𝐼𝑃𝐶] 𝐴=[0];𝐵=[1];𝐶=[−𝑘𝑃𝐿𝐿 𝑖];𝐷=[−𝑘𝑃𝐿𝐿 𝑝], (7.8) where 𝑣𝑑 𝑔,𝑐 is the 𝑑component of the grid voltage seen by the converter, 𝜔𝐼𝑃𝐶 is the PLL’s estimated frequency. The proportional and integral PLL parameters are 𝑘𝑃𝐿𝐿 𝑝and 𝑘𝑃𝐿𝐿 𝑖. Note that all variables used in this block refer to the converter angle (𝑣𝑑 𝑔,𝑐). 134 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Converter angle difference From the obtained 𝜔𝑐frequency and the reference frequency 𝜔𝑔𝑟𝑖𝑑, the angle difference used to apply the reference change between global and local variables can be represented in state-space form as: • State vector: Δ𝑥(𝑡)=[Δ𝜃𝑒] • Input vector: Δ𝑢(𝑡)=[Δ𝜔𝑐,Δ𝜔𝑔𝑟𝑖𝑑]𝑇 • Output vector: Δ𝑦(𝑡)=[Δ𝜃𝑒] 𝐴=[0];𝐵=[1 −1];𝐶=[1];𝐷=[01𝑥2], (7.9) where Δ𝜔𝑐is the frequency estimated by the PLL, Δ𝜔𝑔𝑟𝑖𝑑 is the AC grid reference frequency, and 𝜃𝑒is the difference angle between the grid reference and the converter. Grid current control The state-space representation of this controller can be represented as: • State vector: Δ𝑥(𝑡)=[Δ𝑥𝑞,Δ𝑥𝑑]𝑇 • Input vector: Δ𝑢(𝑡)=[Δ𝑖𝑞 𝑠∗,Δ𝑖𝑑 𝑠∗,Δ𝑖𝑞,𝑐 𝑠,Δ𝑖𝑑,𝑐 𝑠]𝑇 • Output vector: Δ𝑦(𝑡)=[Δ𝑣𝑞,𝑐 𝑑𝑖𝑓𝑓,Δ𝑣𝑑,𝑐 𝑑𝑖𝑓𝑓]𝑇 𝐴=[02𝑥2];𝐵=[1 0 −1 0 0 0 0 1 0 −1 0 0]; 𝐶=[𝑘𝑖−𝑖𝑠0 0 𝑘𝑖−𝑖𝑠];𝐷=[𝑘𝑝−𝑖𝑠0 −𝑘𝑝−𝑖𝑠𝜔0𝐿𝑒𝑞 1 0 0 𝑘𝑝−𝑖𝑠−𝜔0𝐿𝑒𝑞 −𝑘𝑝−𝑖𝑠0 1](7.10) where 𝑖𝑞,𝑑 𝑠∗are the current references, 𝑖𝑞,𝑑,𝑐 𝑠are the diff circuit currents expressed in the converter local frame and, 𝑣𝑞,𝑑,𝑐 𝑑𝑖𝑓𝑓 are the voltages applied at the AC circuit in the converter local frame. The proportional and integral control parameters are 𝑘𝑝−𝑖𝑠and 𝑘𝑖−𝑖𝑠,𝜔0is the nominal grid frequency, and 𝐿𝑒𝑞is the equivalent inductance of the AC circuit. 7.6 Initial Results The previously discussed controls and models have been implemented in the case study shown in Figure 7.9. The main converter control selected for these initial results is the dual-port control depicted in Figure 7.5. The PV system is modelled as a current source where the injected current depends on the DC voltage. The Geyser storage is modelled as a supercap that includes an average DC/DC converter model controlling the supercap’s voltage level. The pump system is modelled as a voltage source converter imposing a voltage and frequency and a controlled load as depicted in Figure 7.8. The PV system power is 275 kW, the pump system power is 160 kW, and the Geyser storage is considered to give 100 kW for 1 minute. Thus, the supercap is dimensioned to 18,75 F. The main converter power is 320 kVA, and it is connected at 400 V. The connection to the main grid is done via a transformer 135 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Geyser storage Grid connection PV system Pump system V / θ1 1 Vdc 1 Vdc 2 Vdc 3 Vdc 4 Figure 7.9 –Initial case study scheme. Table 7.1 –Main converter parameters. Parameter Symbol Value Units Resistance filter R 0,01 pu Impedance filter X 0,1 pu DC side condenser C 1e-3 F Current control proportional gain 𝑘𝑐 𝑝0,16 V/A Current control integral gain 𝑘𝑐 𝑖5 V/A Voltage control integral gain 𝑘𝑐 𝑖2 A/V Voltage control proportional gain 𝑘𝑐 𝑝3 A/V Synchronization integral gain 𝑘𝑑𝑝 𝑖0,1 rad/(V·s) Synchronization proportional gain 𝑘𝑑𝑝 𝑝1 rad/V that elevates the voltage from 400 V to 25 kV. The grid’s SCR is considered to be 2. Thus, emulating a relatively weak grid. The DC voltage level of the DC grid is 800 V. The main converter’s parameters are given in Table 7.1 7.6.1 Power flow solution The case study presented considers the following scenario. The PV system injects full power to the DC grid, i.e., is injecting 275 kW, and the pump system is working at full power, i.e., absorbing 160 kW from the DC grid. The power flow is solved considering the main converter injects 0 var to the AC grid. The solution to the power flow is solved as explained in Section 7.5.1 and the results are given in Table 7.2. From the solution of the power flow, it can be seen that the scenario considered is well defined, as all voltages are set at a reasonable level. Moreover, it can be concluded that the algorithm to solve the power flow is well designed. The solution is reached in 3 iterations. Table 7.2 –Power flow solution. Parameter Value Units 𝑉1401,96 V 𝜃16,42 degree 𝑃𝑉𝑆𝐶 112,63 kW 𝑄𝑉𝑆𝐶 0 kvar 𝑉𝑑𝑐 1800 V 𝑉𝑑𝑐 2799,79 V 𝑉𝑑𝑐 3800,34 V 𝑉𝑑𝑐 4800 V 136 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems Figure 7.10 –Linear and non-linear models comparison. 7.6.2 Small-Signal analysis The linear model of the case study is computed. The linear model will give important information about the system stability and control performance. Firstly, to ensure the linear model’s validity, the linear model is compared with the non-linear model when a small perturbation is made. In this case, a 1% voltage change in the connection to the main grid is simulated. The comparison is shown in Figure 7.10. Next, the system’s eigenvalues are computed. These are shown in Tab. 7.3. All eigenvalues have a negative real part; therefore, the system is stable. Moreover, all the eigenvalues have a damping higher than 5 %, which indicates that, in general, the system dynamics will respond appropriately. 7.6.3 PV step change The system is checked when a sudden step change in the generated power in the PV system occurs. This can emulate a loss of generations due to an unexpected cloud that covers the PV panels. The generated power is changed from full (275 kW) to 0 kW. The main converter terminals’ active and reactive powers magnitudes are shown in Figure 7.11. The converter can adjust the new operation point by adjusting the amount of active and reactive power delivered to the grid. As shown, at the initial point, the converter injects approximately 100 kW, while after the disturbance, it absorbs around 200 kW. 137 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [40] S.P. Adhau, R.M. Moharil, and P.G. Adhau. Mini-hydro power generation on existing irrigation projects: Case study of indian sites. Renewable and Sustainable Energy Reviews, 16(7):4785– 4795, September 2012. [41] Alessandro Morabito and Patrick Hendrick. Pump as turbine applied to micro energy storage and smart water grids: A case study. Applied Energy, 241:567–579, May 2019. [42] Navid Mousavi, Ganesh Kothapalli, Daryoush Habibi, Choton K. Das, and Ali Baniasadi. A novel photovoltaic-pumped hydro storage microgrid applicable to rural areas. Applied Energy, 262:114284, March 2020. [43] Navid Mousavi, Ganesh Kothapalli, Daryoush Habibi, Mehdi Khiadani, and Choton K. Das. An improved mathematical model for a pumped hydro storage system considering electrical, mechanical, and hydraulic losses. Applied Energy, 247:228–236, August 2019. [44] Nicholas Gilmore, Thomas Britz, Erik Maartensson, Carlo Orbegoso-Jordan, Sebastian Schroder, and Martino Malerba. Continental-scale assessment of micro-pumped hydro energy storage using agricultural reservoirs. Applied Energy, 349:121715, November 2023. [45] Sergi Costa-Dilmé, J. Carlos Olives-Camps, Paula Muñoz-Peña, Pau García-Motilla, Oriol GomisBellmunt, and Eduardo Prieto-Araujo. Redesign of large-scale irrigation systems for flexible energy storage. In 2024 IEEE PES Innovative Smart Grid Technologies Europe (ISGT EUROPE), pages 1–5. IEEE, October 2024. [46] Li Wang, Dong-Jing Lee, Jian-Hong Liu, Zan-Zia Chen, Zone-Yuan Kuo, Jin-Shi Hsu, Cheng-Mei Chen, Shen-Syi Chiu, Ming-Hua Tsai, Wei-Taw Lin, and Yun-Chung Lee. Economic analysis of installing micro hydro power plants in chia-nan irrigation association of taiwan using water of irrigation canals. In 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, pages 1–5. IEEE, July 2008. [47] Li Wang, Dong-Jing Lee, Jian-Hong Liu, Zan-Zia Chen, Zone-Yuan Kuo, Huei-Yuan Jang, Jiunn-Ji You, Jin-Tsang Tsai, Ming-Hua Tsai, Wey-Tau Lin, and Yeun-Jong Lee. Installation and practical operation of the first micro hydro power system in taiwan using irrigation water in an agriculture canal. In 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, pages 1–6. IEEE, July 2008. [48] Ilaria Butera and Roberto Balestra. Estimation of the hydropower potential of irrigation networks. Renewable and Sustainable Energy Reviews, 48:140–151, August 2015. [49] François Prevost and G Guichard. Réalisation et exploitation d’une microcentrale: modalités d’un partenariat durable entre l’asco des irrigants de la crau et la société du canal de provence. In ICID Conference, Special Session ‘Irrigation and Energy’, Montpellier, France, 2015. [50] Demetrio Antonio Zema, Angelo Nicotra, Vincenzo Tamburino, and Santo Marcello Zimbone. A simple method to evaluate the technical and economic feasibility of micro hydro power plants in existing irrigation systems. Renewable Energy, 85:498–506, January 2016. [51] Tommaso Brazzini, Edgar Lorenzo-Saez, Vicent Sales Martínez, Esther López Pérez, Mar V. OrtegaReig, and Guillermo Palau-Salvador. Is small-scale hydropower energy recovery a viable alternative for climate change mitigation and adaptation? the case of the traditional irrigation system in valencia (spain). Energy Reports, 12:736–749, December 2024. [52] MiguelCrespo Chacón, JuanAntonio Rodríguez Díaz, Jorge García Morillo, and AonghusMcNabola. Hydropower energyrecovery inirrigation networks: Validationof amethodologyforflowprediction and pump as turbine selection. Renewable Energy, 147:1728–1738, March 2020. 144 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [53] MiguelCrespo Chacón, JuanAntonio Rodríguez Díaz, Jorge García Morillo, and AonghusMcNabola. Estimating regional potential for micro-hydropower energy recovery in irrigation networks on a large geographical scale. Renewable Energy, 155:396–406, August 2020. [54] Santoshkumar M. Hunachal, G. Arunkumar, Sushil Sirsat, P. R. Shankar, Rajat Shirgaonkar, and Bhushan Khandzode. Irrigation water as a renewable energy source in pico hydropower generation. In 2020 International Conference on Renewable Energy Integration into Smart Grids: A Multidisciplinary Approach to Technology Modelling and Simulation (ICREISG), pages 27–31. IEEE, February 2020. [55] A. Merida García, J. Gallagher, M. Crespo Chacón, and A. Mc Nabola. The environmental and economicbenefits of ahybridhydropower energyrecoveryand solarenergysystem(pat-pv), under varying energy demands in the agricultural sector. Journal of Cleaner Production, 303:127078, June 2021. [56] Angel V. Mercedes Garcia, Francisco Javier Sánchez-Romero, P. Amparo López-Jiménez, and Modesto Pérez-Sánchez. A new optimization approach for the use of hybrid renewable systems in the search of the zero net energy consumption in water irrigation systems. Renewable Energy, 195:853–871, August 2022. [57] William E. Hart, Jean-Paul Watson, and David L. Woodruff. Pyomo: modeling and solving mathematical programs in python. Mathematical Programming Computation, 3(3):219–260, August 2011. [58] Zev Friedman, Jack Ingalls, John D. Siirola, and Jean-Paul Watson. Block-oriented modeling of superstructure optimization problems. Computers & Chemical Engineering, 57:10–23, October 2013. [59] Jorge Nocedal and Stephen J. Wright. Numerical optimization, pages 1–664. Springer Series in Operations Research and Financial Engineering. Springer Nature, 2006. [60] Sergi Costa-Dilmé, J. Carlos Olives-Camps, Paula Muñoz-Peña, Pau García-Motilla, Oriol GomisBellmunt, and Eduardo Prieto-Araujo. Multi-physics operation and sizing optimisation in pyomo: Application to large irrigation systems. In 2024 Open Source Modelling and Simulation of Energy Systems (OSMSES), pages 1–6. IEEE, September 2024. [61] Dariush Fooladivanda and Joshua A. Taylor. Energy-optimal pump scheduling and water flow. IEEE Transactions on Control of Network Systems, 5(3):1016–1026, September 2018. [62] Michael L. Bynum, Gabriel A. Hackebeil, William E. Hart, Carl D. Laird, Bethany L. Nicholson, John D. Siirola, Jean-Paul Watson, and DavidL. Woodruff. Pyomo–optimization modeling in python, volume 67. Springer Science & Business Media, third edition, 2021. [63] The MathWorks Inc. Statistics and machine learning toolbox, 2023. [64] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 17:261– 272, 2020. [65] Ahmed S. Zamzam, Emiliano Dall’Anese, Changhong Zhao, Josh A. Taylor, and Nicholas D. Sidiropoulos. Optimal water–power flow-problem: Formulation and distributed optimal solution. IEEE Transactions on Control of Network Systems, 6(1):37–47, March 2019. 145 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [66] Juan I. Pérez, José R. Wilhelmi, and Luis Maroto. Adjustable speed operation of a hydropower plant associated to an irrigation reservoir. Energy Conversion and Management, 49(11):2973–2978, November 2008. [67] H. Ramos and A. Borga. Pumps as turbines: an unconventional solution to energy production. Urban Water, 1(3):261–263, September 1999. [68] Maxime Binama, Wen-Tao Su, Xiao-Bin Li, Feng-Chen Li, Xian-Zhu Wei, and Shi An. Investigation on pump as turbine (pat) technical aspects for micro hydropower schemes: A state-of-the-art review. Renewable and Sustainable Energy Reviews, 79:148–179, November 2017. [69] Omprakash K. Gupta and A. Ravindran. Branch and bound experiments in convex nonlinear integer programming. Management Science, 31(12):1533–1546, 1985. [70] Pierre Bonami, Lorenz T. Biegler, Andrew R. Conn, Gérard Cornuéjols, Ignacio E. Grossmann, Carl D. Laird, Jon Lee, Andrea Lodi, François Margot, Nicolas Sawaya, and Andreas Wächter. An algorithmic framework for convex mixed integer nonlinear programs. Discrete Optimization, 5(2):186–204, 2008. In Memory of George B. Dantzig. [71] Roger Fletcher and Sven Leyffer. Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming, 66:327–349, August 1994. [72] I. Quesada and I.E. Grossmann. An LP/NLP based branch and bound algorithm for convex MINLP optimization problems. Computers & Chemical Engineering, 16(10):937–947, 1992. An International Journal of Computer Applications in Chemical Engineering. [73] Kumar Abhishek, Sven Leyffer, and Jeff Linderoth. FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs. INFORMS Journal on Computing, 22(4):555–567, 2010. [74] Francisco Díaz-González, Andreas Sumper, and Oriol Gomis-Bellmunt. Energy Storage in Power Systems. Wiley, March 2016. [75] R. Lougee-Heimer. The common optimization interface for operations research: Promoting opensource software in the operations research community. IBM Journal of Research and Development, 47(1):57–66, January 2003. [76] Sergi Costa-Dilmé, J. Carlos Olives-Camps, Pau García-Motilla, Carla Cinto Campmany, Oriol Gomis-Bellmunt, and Eduardo Prieto-Araujo. Redesign of large-scale irrigation systems for flexible energy storage. unpublished, 2025. [77] REE. Reedata, 2025. https://www.ree.es/es/datos/aldia. [78] Ted G. Eschenbach. Spiderplots versus tornado diagrams for sensitivity analysis. Interfaces, 22(6):40–46, December 1992. [79] Sergi Costa-Dilmé, Pau García-Motilla, Oriol Gomis-Bellmunt, and Eduardo Prieto-Araujo. Energy storage sizing for clouds shading over solar photovoltaic pumping systems. unpublished, 2025. [80] Giuseppe Todde, Lelia Murgia, Paola Antonia Deligios, Rita Hogan, Isaac Carrelo, Madalena Moreira, Antonio Pazzona, Luigi Ledda, and Luis Narvarte. Energy and environmental performances of hybrid photovoltaic irrigation systems in Mediterranean intensive and super-intensive olive orchards. Science of The Total Environment, 651:2514–2523, February 2019. [81] Ramazan Senol. An analysis of solar energy and irrigation systems in turkey. Energy Policy, 47:478–486, August 2012. [82] P.C. Pande, A.K. Singh, S. Ansari, S.K. Vyas, and B.K. Dave. Design development and testing of a solar PV pump based drip system for orchards. Renewable Energy, 28(3):385–396, March 2003. 146 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [83] Ali A. Hamza and Azmi Z. Taha. Performance of submersible pv solar pumping systems under conditions in the sudan. Renewable Energy, 6(5–6):491–495, July 1995. [84] Olga V. Shepovalova, Alexander T. Belenov, and Sergei V. Chirkov. Review of photovoltaic water pumping system research. Energy Reports, 6:306–324, November 2020. [85] Olga V. Shepovalova and Alexander T. Belenov. Investigation of dc motors mechanical characteristics with powered by comparable capacity pv array. Energy Procedia, 119:990–994, July 2017. [86] Z.Abidin Firatoglu and Bulent Yesilata. New approaches on the optimization of directly coupled pv pumping systems. Solar Energy, 77(1):81–93, 2004. [87] Daniele Fiaschi, Roberto Graniglia, and Giampaolo Manfrida. Improving the effectiveness of solar pumping systems by using modular centrifugal pumps with variable rotational speed. Solar Energy, 79(3):234–244, September 2005. [88] R.H. Almeida, J.R. Ledesma, I.B. Carrêlo, L. Narvarte, G. Ferrara, and L. Antipodi. A new pump selection method for large-power pv irrigation systems at a variable frequency. Energy Conversion and Management, 174:874–885, October 2018. [89] Hicham Karmouni, Mohamed Chouiekh, Saad Motahhir, Hassan Qjidaa, Mohamed Ouazzani Jamil, and Mhamed Sayyouri. Optimization and implementation of a photovoltaic pumping system using the sine–cosine algorithm. Engineering Applications of Artificial Intelligence, 114:105104, September 2022. [90] Wissem Nemouchi, Youssouf Amrane, Hichem Nemouchi, and Najib Lakhdar Boucetta. Energy management for optimal design of pv/wind/diesel system for water pumping irrigation in semi-arid climate. Energy Conversion and Management, 304:118216, March 2024. [91] Victor L Streeter, E Benjamin Wylie, and Keith W Bedford. Fluid mechanics. Mc Graw Hill Education, Dec 1997. [92] E Benjamin Wylie and Victor Lyle Streeter. Fluid transients. Mc Graw Hill Inc., 1978. [93] Andrew F. Colombo and Bryan W. Karney. Energy and costs of leaky pipes: Toward comprehensive picture. Journal of Water Resources Planning and Management, 128(6):441–450, November 2002. [94] Jalil Emadi and Abbas Solemani. Maximum water hammer sensitivity analysis. World Acad. Sci. Eng. Technol, 73:416–419, 2011. [95] Josh A. Taylor, Richard Perryman, Aimy Bazylak, and Bryan Karney. Safely landing water networks during power outages with energy storage. In 2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 346–350. IEEE, October 2018. [96] Madhumita Das and Ratan Mandal. A comparative performance analysis of direct, with battery, supercapacitor, and battery-supercapacitor enabled photovoltaic water pumping systems using centrifugal pump. Solar Energy, 171:302–309, September 2018. [97] S. Orts-Grau, P. Gonzalez-Altozano, Francisco J. Gimeno-Sales, I. Balbastre-Peralta, C. I. Martinez Marquez, M. Gasque, and S. Segui-Chilet. Photovoltaic water pumping: Comparison between direct and lithium battery solutions. IEEE Access, 9:101147–101163, 2021. [98] Tehuan Chen, Zhigang Ren, Chao Xu, and Ryan Loxton. Optimal boundary control for water hammer suppression in fluid transmission pipelines. Computers & Mathematics with Applications, 69(4):275–290, February 2015. 147 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [99] J.K. Roy, P.K. Roy, and P. Basak. Waterhammerprotectionin watersupplysystem: A new approach with practical implementation. In 2011 International Conference on Communication and Industrial Application, pages 1–6. IEEE, December 2011. [100] Packiam Periasamy, N.K. Jain, and I.P. Singh. A review on development of photovoltaic water pumping system. Renewable and Sustainable Energy Reviews, 43:918–925, March 2015. [101] A. Mohammedi, N. Mezzai, D. Rekioua, and T. Rekioua. Impact of shadow on the performances of a domestic photovoltaic pumping system incorporating an mppt control: A case study in bejaia, north algeria. Energy Conversion and Management, 84:20–29, August 2014. [102] L. Narvarte, J. Fernández-Ramos, F. Martínez-Moreno, L.M. Carrasco, R.H. Almeida, and I.B. Carrêlo. Solutions for adapting photovoltaics to large power irrigation systems for agriculture. Sustainable Energy Technologies and Assessments, 29:119–130, October 2018. [103] Universidad Politécnica de Madrid. MASLOWATEN. Especificaciones Técnicas para Sistemas de Riego Fotovoltaico, 2018. Available online: https://maslowaten.eu (accessed on 30/01/2024). [104] Anton Bergant, Jernej Mazij, and Uroš Karadžić. Design of water hammer control strategies in hydropower plants. Applied Engineering Letters: Journal of Engineering and Applied Sciences, 3(1):27–33, 2018. [105] G. Remenieras. Dispositif simple pour réduire la célérité des ondes Élastiques dans les conduites en charge. La Houille Blanche, 38(sup1):172–196, January 1952. [106] Jinzhe Gong, Mark L. Stephens, Martin F. Lambert, Aaron C. Zecchin, and Angus R. Simpson. Pressure surge suppression using a metallic-plastic-metallic pipe configuration. Journal of Hydraulic Engineering, 144(6), June 2018. [107] Michał Kubrak. Water hammer mitigation by internal rubber hose. Archives of Civil Engineering, pages 275–288, March 2024. [108] OMIE: Operador del Mercado Ibérico de Energía - Polo Español. OMIEData Resultados del Mercado. www.omie.es/es, 2024. [109] Banco de España. Series: Statistical Bulletin. https://www.bde.es/wbe/en/publicaciones/in formacion-estadistica/boletin-estadistico/, 2024. [110] QGIS Development Team. QGIS Geographic Information System. QGIS Association, [111] Chad Augustine and Nathan Blair. Storage Futures Study: Storage Technology Modeling Input Data Report. NREL, May 2021. [112] Benjamin A. Carreras, Eder Batista Tchawou Tchuisseu, José M. Reynolds-Barredo, Damià Gomila, and Pere Colet. Effects of demand control on the complex dynamics of electric power system blackouts. Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(11), November 2020. [113] Javier Martín Vide. El Clima i el relleu. Geografia General dels Països Catalans. Enciclopèdia Catalana, Barcelona, 1992. [114] Haisheng Chen, Thang Ngoc Cong, Wei Yang, Chunqing Tan, Yongliang Li, and Yulong Ding. Progress in electrical energy storage system: A critical review. Progress in Natural Science, 19(3):291–312, March 2009. [115] Behnam Zakeri and Sanna Syri. Electrical energy storage systems: A comparative life cycle cost analysis. Renewable and Sustainable Energy Reviews, 42:569–596, February 2015. [116] Md Mustafizur Rahman, Abayomi Olufemi Oni, Eskinder Gemechu, and Amit Kumar. Assessment of energy storage technologies: A review. Energy Conversion and Management, 223:113295, November 2020. 148 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [117] Choton K. Das, Octavian Bass, Ganesh Kothapalli, Thair S. Mahmoud, and Daryoush Habibi. Overview of energy storage systems in distribution networks: Placement, sizing, operation, and power quality. Renewable and Sustainable Energy Reviews, 91:1205–1230, August 2018. [118] Ernest Moa and Yun Go. Large-scale energy storage system: safety and risk assessment. Sustainable Energy Research, 10, 09 2023. [119] A.R. Dehghani-Sanij, E. Tharumalingam, M.B. Dusseault, and R. Fraser. Study of energy storage systems and environmental challenges of batteries. Renewable and Sustainable Energy Reviews, 104:192–208, April 2019. [120] Circular 1/2025, de 28 de enero, de la Comisión Nacional de los Mercados y la Competencia, por la que se modifica la Circular 3/2020, de 15 de enero, por la que se establece la metodología para el cálculo de los peajes de transporte y distribución de electricidad. BOE-A-2025-2044, January 2025. [121] Geyser Batteries Oy. Geyser battery: Introduction to a power-dense battery for heavy-duty applications, 2021. [White paper]. Available online: https://www.geyserbatteries.com/technolo gy (accessed on 29/01/2024). [122] AGISTIN Project Consortium. D2.1: Energy Storage Integration Requirements, Incentives and Constraints: EU-wide Analyses. Technical Report D2.1, Horizon Europe Program, European Commission, December 2023. Grant Agreement Number: 101096197, Lead Participant: EPRI, Submitted: 25/12/2023. [123] EU ACER. ACER webinar on amendments to the European electricity grid connection network codes. Online, July 2023. Available onlien: https://www.youtube.com/watch?v=ptrP4qSX10&a b_channel=EUACER. [124] Xing Luo, Jihong Wang, Mark Dooner, and Jonathan Clarke. Overview of current development in electrical energy storage technologies and the application potential in power system operation. Applied Energy, 137:511–536, 2015. [125] Francisco Díaz-González, Andreas Sumper, Oriol Gomis-Bellmunt, and Roberto Villafáfila-Robles. A review of energy storage technologies for wind power applications. Renewable and Sustainable Energy Reviews, 16(4):2154–2171, 2012. [126] Enrique Lobato, Lukas Sigrist, and Luis Rouco. Use of energy storage systems for peak shaving in the spanish canary islands. In 2013 IEEE Power & Energy Society General Meeting, pages 1–5, 2013. [127] E.B. Prasasti, M. Aouad, M. Joseph, M. Zangeneh, and K. Terheiden. Optimization of pumped hydro energy storage design and operation for offshore low-head application and grid stabilization. Renewable and Sustainable Energy Reviews, 191:114122, 2024. [128] Jan Figgener, Benedikt Tepe, Fabian Rücker, Ilka Schoeneberger, Christopher Hecht, Andreas Jossen, and Dirk Uwe Sauer. The influence of frequency containment reserve flexibilization on the economics of electric vehicle fleet operation. Journal of Energy Storage, 53:105138, 2022. [129] Krishnakumar R. Vasudevan, Vigna K. Ramachandaramurthy, Gomathi Venugopal, J.B. Ekanayake, and S.K. Tiong. Variable speed pumped hydro storage: A review of converters, controls and energy management strategies. Renewable and Sustainable Energy Reviews, 135:110156, 2021. [130] C Nicolet, O Braun, N Ruchonnet, J. Hell, A Béguin, and F Avellan. Simulation of pump-turbine prototype fast mode transition for grid stability support. Journal of Physics: Conference Series, 813(1):012040, mar 2017. 149 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [131] Anto Joseph, Raghu Selvaraj, Thanga Raj Chelliah, and S. V. Appa Sarma. Starting and braking of a large variable speed hydrogenerating unit subjected to converter and sensor faults. IEEE Transactions on Industry Applications, 54(4):3372–3382, July 2018. [132] Eduardo Sánchez-Díez, Edgar Ventosa, Massimo Guarnieri, Andrea Trovò, Cristina Flox, Rebeca Marcilla, Francesca Soavi, Petr Mazur, Estibaliz Aranzabe, and Raquel Ferret. Redox flow batteries: Status and perspective towards sustainable stationary energy storage. Journal of Power Sources, 481:228804, 2021. [133] Andrea Trovò, Vito Di Noto, Joseph Epoupa Mengou, Chiara Gamabaro, and Massimo Guarnieri. Fast response of kw-class vanadium redox flow batteries. IEEE Transactions on Sustainable Energy, 12(4):2413–2422, 2021. [134] Red Eléctrica de España. Guía descriptiva: Ser proveedor de servicios de balance, January 2024. Accessed: 2025-01-29. [135] Comisión Nacional de los Mercados y la Competencia. Resolución de 3 de octubre de 2024, de la Comisión Nacional de los Mercados y la Competencia, por la que se modifican los procedimientos de operación eléctricos 14.1 y 14.4 para la adaptación de la liquidación al ISP cuarto-horario. Boletín Oficial del Estado, 248:131410–131478, October 2024. Reference: BOE-A-2024-20995, Accessed: 2025-01-29. [136] David G. Luenberger and Yinyu Ye. Linear and Nonlinear Programming. Springer Publishing Company, Incorporated, 2015. [137] Adrian Hauswirth, Alessandro Zanardi, Saverio Bolognani, Florian Dörfler, and Gabriela Hug. Online optimization in closed loop on the power flow manifold. In 2017 IEEE Manchester PowerTech, pages 1–6, 2017. [138] Miguel Picallo, Dominic Liao-McPherson, Saverio Bolognani, and Florian Dörfler. Cross-layer design for real-time grid operation: Estimation, optimization and power flow. Electric Power Systems Research, 212:108378, 2022. [139] Marcello Colombino, Emiliano Dall’Anese, and AndreyBernstein. Online optimizationasa feedback controller: Stability and tracking. IEEE Transactions on Control of Network Systems, 7(1):422–432, 2020. [140] Adrian Hauswirth, Saverio Bolognani, Gabriela Hug, and Florian Dörfler. Projected gradient descent on riemannian manifolds with applications to online power system optimization. In 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 225–232, 2016. [141] V. Häberle, A. Hauswirth, L. Ortmann, S. Bolognani, and F. Dörfler. Non-convex feedback optimization with input and output constraints. IEEE Control Systems Letters, 5(1):343–348, 2020. [142] Lukas Ortmann, Adrian Hauswirth, Ivo Caduff, Florian Dörfler, and Saverio Bolognani. Experimental validation of feedback optimization in power distribution grids. Electric Power Systems Research, 189:106782, 2020. [143] J. C. Olives-Camps, A. Rodríguez del Nozal, J. M. Mauricio, and J. M. Maza-Ortega. A model-less control algorithm of dc microgrids based on feedback optimization. International Journal of Electrical Power & Energy Systems, 141:108087, 2022. [144] E.A. Rodríguez-Gonzalez, J.C. Olives-Camps, F.P. García-Lopez, A. Rodríguez Del Nozal, J.M. Mauricio, and J.M. Maza-Ortega. Experimental validation of a real-time distributed model-less control for dc microgrids. In 2022 International Conference on Smart Energy Systems and Technologies (SEST), pages 1–6, 2022. 150 D6.3 Technical-economic sizing, operation and control tools for irrigation system modernisation into energy storage systems [145] Marcello Colombino, John W. Simpson-Porco, and Andrey Bernstein. Towards robustness guarantees for feedback-based optimization. In 2019 IEEE 58th Conference on Decision and Control (CDC), pages 6207–6214, 2019. [146] Jaume Girona-Badia, Vinícius Albernaz Lacerda, Daniel Westerman Spier, Eduardo Prieto-Araujo, and Oriol Gomis-Bellmunt. Resource-aware grid-forming synchronization control: Design, analysis and validation. IEEE Transactions on Energy Conversion, pages 1–12, 2024. [147] Irina Subotić and Dominic Groß. Universal dual-port grid-forming control: Bridging the gap between grid-forming and grid-following control. IEEE Transactions on Power Systems, 39(6):6861– 6875, 2024. [148] M.E. El-Hawary and S.T. Ibrahim. A new approach to AC-DC load flow analysis. Electric Power Systems Research, 33(3):193–200, 1995. [149] Ugur Arifoglu. The power flow algorithm for balanced and unbalanced bipolar multiterminalACDC systems. Electric Power Systems Research, 64(3):239–246, 2003. [150] Jef Beerten, Stijn Cole, and Ronnie Belmans. A sequential AC/DC power flow algorithm for networks containing multi-terminal VSC HVDC systems. In IEEE PES General Meeting, pages 1–7, 2010. [151] M. M. El-marsafawy and R. M. Mathur. A new, fast technique for load-flow solution of integrated multi-terminal DC/AC systems. IEEE Transactions on Power Apparatus and Systems, PAS99(1):246–255, 1980. [152] Fnn guideline: Grid forming behaviour of hvdc systems and dc-connected ppms. Technical guideline, Forum Netztechnik/Netzbetrieb (FNN), VDE, 2023. 151