Using hybrid distributed energy resources as non-wire alternatives to minimise investment costs

Contents lists available at ScienceDirect Sustainable Energy, Grids and Networks journal homepage: www.elsevier.com/locate/segan Using hybrid distributed energy resources as non-wire alternatives to minimise investment costs Carlos García-Santacruz∗, Alejandro Marano-Marcolini, José L. Martínez-Ramos Department of Electrical Engineering, Universidad de Sevilla, Sevilla, Spain ARTICLE INFO Keywords: Distributed energy resources Non-wires alternatives Renewable integration methods Optimal DER location Energy storage systems ABSTRACT The trend of increasing electricity demand and policies promoting clean energy generation are leading to an increase in the use of distributed energy resources (DERs). These distributed resources can be used as nonwire alternatives (NWA) to eliminate overload and voltage problems in the grid, instead of relying on network reinforcements. To accomplish this, it is essential to determine the optimal location and type of energy resource. This paper presents a mixed-integer nonlinear optimisation problem for determining the optimal location, selection, and sizing of distributed energy resources. The formulation includes the possibility of associating generation resources with energy storage systems to form hybrid plants that can solve network problems. The proposed method is tested on the CIGRE European Medium Voltage Distribution System using two load scenarios that lead to different grid problems. The results indicate that the use of hybrid systems reduces the total investment cost of the solution compared to the use of generators alone. Additionally, results allow inferring the importance of properly sizing the energy storage in terms of power and energy to match the type and duration of the problems. 1. Introduction During the last few years, renewable energy sources have significantly increased their presence in the energy mix [1]. This, together with the trend in the growth of electricity consumption [2], implies that the network operator has to deal with possible problems such as overloads in lines or transformers, as well as voltages outside the feasible limits (undervoltage or overvoltage) [3]. To solve these problems, investments have traditionally been made to modify the network, improving elements such as lines, substations or replacing elements [4]. This problem has been extensively addressed in several studies. The study developed in [5] jointly addresses the planning of transmission and distribution systems, considering the necessary investments in the network and generation capacity. In [6], a planning model is defined in which, in addition to the replacement and need of new lines, storage is considered to improve reliability. Another expansion planning model [7], includes electric vehicle charging stations, which will become very important in the future. These actions may require high investment, specially in the case of underground equipment, they may have to overcome administrative barriers, or even face the impossibility of carrying out reinforcements in areas of high population density. The so called non-wire alternatives (NWA) [8], are another increasingly widespread option to address these problems. The potential of ∗Corresponding author. E-mail addresses: [email protected] (C. García-Santacruz), [email protected] (A. Marano-Marcolini), [email protected] (J.L. Martínez-Ramos). these solutions becomes apparent in the projects that have been carried out in recent years [9]. These NWAs involve the use of distributed resources [10], or demand side management (DSM) techniques [11,12], to solve problems in the grid and defer, reduce or avoid the need for conventional investments. This option is very interesting due to technological advances, decreasing costs of renewable energy generation, and policies that encourage the use of clean energy [13]. In addition, the uncertainty associated with financial costs makes it attractive to defer investment in the grid, reducing the risk that the expected load will not materialise. Focusing on the use of assets, when a DER is strategically located in the grid and its power injections contribute to solving problems, these resources can be considered as an NWA. Note that DERs can have a certain value to the grid depending on the time and location [14] of the generation. It is therefore important to find this value for the group of DERs that contribute to solving grid problems. Regarding optimal DER location methods, works such as [15,16] locate generation giving value to the technical aspect, such as minimising losses and voltage deviations respectively, more than to the economic criteria. Similarly, in [17], losses and voltage deviations are jointly minimised. In [18], the location is done by reducing investment in photovoltaic (PV) generation. The work developed in [19] carries out https://doi.org/10.1016/j.segan.2024.101422 Received 10 February 2024; Received in revised form 14 April 2024; Accepted 17 May 2024 Sustainable Energy, Grids and Networks 39 (2024) 101422 Available online 22 May 2024 2352-4677/© 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/bync-nd/4.0/ ). C. García-Santacruz et al. Nomenclature Sets Set of 𝑇periods, 𝑡∈. Set of 𝐷DERs, 𝑑∈. Set of 𝑁nodes, 𝑖, 𝑗 ∈. Set of 𝐾lines with edges (𝑖, 𝑗),𝑘∈. Parameters 𝐶𝑖𝑛𝑠 𝑑,𝑗 Specific installation cost for resource 𝑑at node 𝑗(e/MW). 𝐶𝑝 𝑑,𝑗 Specific power cost for the storage associated to the resource 𝑑at node 𝑗 (e/MW). 𝐶𝑒 𝑑,𝑗 Specific energy cost for the storage associated to the resource 𝑑at node 𝑗 (e/MWh). 𝑀𝑑,𝑡 Generation profile for resource 𝑑during period 𝑡(pu). 𝑉𝑚𝑎𝑥 𝑖Maximum voltage magnitude allowed at node i. 𝑉𝑚𝑖𝑛 𝑖Minimum voltage magnitude allowed at node i. 𝑅𝑖𝑗 Resistance of line (𝑖, 𝑗). 𝑋𝑖𝑗 Reactance of line (𝑖, 𝑗). 𝑃𝑙𝑜𝑎𝑑 𝑗,𝑡 Net active power consumption at node 𝑗 during interval 𝑡. 𝑄𝑙𝑜𝑎𝑑 𝑗,𝑡 Net reactive power consumption at node 𝑗 during interval 𝑡. 𝐼𝑚𝑎𝑥 𝑖𝑗 Maximum value of current magnitude for line (𝑖, 𝑗). 𝑃𝑚𝑎𝑥 𝑑,𝑗 Maximum installed capacity for generation resource 𝑑at node 𝑗(MW). 𝑃𝑚𝑖𝑛 𝑑,𝑗 Minimum installed capacity for generation resource 𝑑at node 𝑗(MW). 𝑆𝑚𝑎𝑥 𝑑,𝑗 Maximum installed power capacity for storage associated to resource 𝑑at node 𝑗 (MW). 𝑆𝑚𝑖𝑛 𝑑,𝑗 Minimum installed power capacity for storage associated to resource 𝑑at node 𝑗 (MW). 𝐸𝑚𝑎𝑥 𝑑,𝑗 Maximum installed energy capacity for storage associated to resource 𝑑at node 𝑗 (MWh). 𝐸𝑚𝑖𝑛 𝑑,𝑗 Minimum installed energy capacity for storage associated to resource 𝑑at node 𝑗 (MWh). 𝜂𝑐ℎ Storage charge efficiency. 𝜂𝑑𝑖𝑠 Storage discharge efficiency. 𝑆𝑂𝐶𝑚𝑖𝑛 𝑑,𝑗 Minimum state of charge of storage associated to resource 𝑑at node 𝑗. 𝑆𝑂𝐶𝑚𝑎𝑥 𝑑,𝑗 Maximum state of charge of storage associated to resource 𝑑at node 𝑗. Variables 𝑝𝑖𝑛𝑠 𝑑,𝑗 Installed capacity for generation resource 𝑑 at node 𝑗(MW). 𝑠𝑖𝑛𝑠 𝑑,𝑗 Installed power capacity for storage associated to resource 𝑑at node 𝑗(MW). 𝑒𝑖𝑛𝑠 𝑑,𝑗 Installed energy capacity for storage associated to resource 𝑑at node 𝑗(MWh). 𝑝𝑑,𝑗,𝑡 Active power injection by generation resource 𝑑at node 𝑗in interval 𝑡. 𝑞𝑑,𝑗,𝑡 Reactive power injection by resource 𝑑at node 𝑗in interval 𝑡. 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 Net active power injection of hybrid plant formed by resource 𝑑and storage at node 𝑗 in interval 𝑡. 𝑞𝑠𝑦𝑠 𝑑,𝑗,𝑡 Reactive power injection of hybrid plant formed by resource 𝑑and storage at node 𝑗in interval 𝑡. 𝑝𝑐ℎ 𝑑,𝑗,𝑡 Power charged by storage associated to resource 𝑑at node 𝑗in interval 𝑡. 𝑝𝑑𝑖𝑠 𝑑,𝑗,𝑡 Power discharged by storage associated to resource 𝑑at node 𝑗in interval 𝑡. 𝐸𝑏𝑎𝑡 𝑑,𝑗,𝑡 State of charge of the storage associated to resource 𝑑at node 𝑗in interval 𝑡. 𝑝𝑖𝑗,𝑡 Active power flow through line (𝑖, 𝑗)in interval 𝑡. 𝑞𝑖𝑗,𝑡 Reactive power flow through line (𝑖, 𝑗)in interval 𝑡. 𝑧1Objective value. 𝑖𝑖𝑗,𝑡 Current magnitude squared through line (𝑖, 𝑗)in interval 𝑡. 𝑣𝑗,𝑡 Voltage magnitude squared in node 𝑗in interval 𝑡. 𝑢𝑑,𝑗 Binary variable to indicate the installation of generation resource 𝑑at node 𝑗. 𝑏𝑢𝑑,𝑗 Binary variable to indicate the installation of storage associated to resource 𝑑at node 𝑗. 𝑏𝑢𝑑𝑖𝑠 𝑑,𝑗,𝑡 Binary variable to indicate the discharge of storage associated to resource 𝑑at node 𝑗in interval 𝑡. 𝑏𝑢𝑐ℎ 𝑑,𝑗,𝑡 Binary variable to indicate the charge of storage associated to resource 𝑑at node 𝑗 in interval 𝑡. the sizing and location, trying to unite the criteria of maximum use and minimum investment of different generation technologies to integrate the DER that solve the problems. The concept of Locational Marginal Value (LMV) [20] can be used to quantify the value of DERs to the grid. This value can be calculated through the locational marginal prices (LMPs), which are used in [21] to identify the necessary injections and their location to solve network problems. In [22], LMPs are used to prioritise where to locate DERs that help solve problems. Despite the advantage of being invariant, and evaluate the congestion solution from the operator’s point of view, this approach does not provide a way to compare different technologies as NWA. Energy storage systems (ESS) are another type of NWAs [23,24] that can be considered. The consideration of energy storage is a key aspect, as it significantly increases the flexibility of DER management and integration. Problems on the network can be solved by injecting or absorbing power as required by the circumstances. In [25], ESSs are used as the only distributed resource. In [26], ESSs are used to integrate PV generation without creating new problems. The work developed in [27] presents a model of ESS placement to reduce power losses, and going a little further, [28] attempts to find the optimal configuration of ESSs to avoid voltage problems. Furthermore, the research in [29] proposes a model for locating and sizing batteries Sustainable Energy, Grids and Networks 39 (2024) 101422 2 C. García-Santacruz et al. to reduce grid losses and voltage problems at the same time. In [30], the location of hybrid generation plants with fixed power/energy ratio storage is proposed to solve congestion and voltage problems. The consideration of a fixed ratio in the ESS is a disadvantage, as it does not permit the selection of the power and energy configuration adapted to the characteristics of the problems (duration) that occur in the network. This research aims to evaluate hybrid systems, which are defined as renewable generation systems with ESSs, as NWA solutions. Hybrid plants have the potential to decrease the size of installed power, reducing investment costs and increasing versatility through ESSs. This can improve their deployment as effective and practical NWA solutions. To achieve this, it is essential to select the best type of generation technology and combining it with the optimal power and energy configuration of the ESS to address the grid issues. This work proposes a Mixed-Integer Nonlinear Programming (MINLP) optimisation model for the location and sizing of hybrid systems. The objective is to determine whether it is better to install only renewable generation or whether it is more beneficial to complement it with energy storage capability, taking into account the availability of the primary energy resource and the installation costs. The main contributions can be summarised as follows: •The proposed methodology considers the DSO’s point of view and evaluates the use of different energy resources to solve grid problems at minimum cost. •The optimal location and size of new DERs are determined considering the type of technology and the availability of the primary energy resource. •The convenience of installing stand-alone generators or hybrid systems at the nodes, from a technical and economic perspective, is determined. •The power and energy configuration of the energy storage system is independently sized to address the expected problems in the network. The rest of the paper is organised as follows. Section 2presents a description of the proposed methodology. Section 3describes the data used to test the model presented. Section 4shows the main results obtained, and finally, the main conclusions are shown in Section 5. 2. Methodology To make a NWA solution based on generation plus storage effective, it is necessary to know the best installation locations, where the hybrid plant has the most potential. This paper presents a model for optimal hybrid plant location, sizing and operation to solve voltage and current problems in the grid. This approach is based on the DSO’s vision. Fig. 1 shows an overview of the proposed methodology, indicating required input data, main objectives and outputs obtained. The main input data to the model are: network data (𝑅𝑖,𝑗 ,𝑋𝑖,𝑗 and admissible values of current and voltage), consumption at the nodes (𝑃𝑙𝑜𝑎𝑑 𝑗,𝑡 ), availability profiles of the renewable resource at each node (𝑀𝑑,𝑡) and installation costs of generation and storage (𝐶𝑖𝑛𝑠 𝑑,𝑗 ,𝐶𝑝 𝑑,𝑗 , 𝐶𝑒 𝑑,𝑗 ). Based on this data, the optimisation model selects the optimal location, technologies and sizes of DERs needed to solve grid problems with their power injections. This is achieved by minimising the total cost of installation, according to resource availability, cost technologies and the problems to be solved. The method can associate storage, sized in terms of energy and power, with a generation source. Thus, a hybrid plant is located at nodes if it is the best economic and technical solution. As outputs of the method, the location, type and installed power of the generation source are obtained (𝑢𝑑,𝑗 ,𝑝𝑖𝑛𝑠 𝑑,𝑗 ). If it is considered that a hybrid plant is more advantageous, the ESS configuration (𝑠𝑖𝑛𝑠 𝑑,𝑗 ,𝑒𝑖𝑛𝑠 𝑑,𝑗 ) associated with the generation source (through 𝑏𝑢𝑑,𝑗 ) is also determined. These DERs will supply the required power, 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 and 𝑞𝑠𝑦𝑠 𝑑,𝑗,𝑡, to address grid issues. Fig. 1. Outline of the proposed methodology indicating objectives, input data and results obtained. 2.1. Objective function The objective function of this problem, which seeks to solve grid problems using renewable generation resources together with storage and minimising investment costs, is defined as: min 𝑧1=∑ 𝑗∑ 𝑑[𝐶𝑖𝑛𝑠 𝑑,𝑗 ⋅𝑝𝑖𝑛𝑠 𝑑,𝑗 + (𝐶𝑝 𝑑,𝑗 ⋅𝑠𝑖𝑛𝑠 𝑑,𝑗 +𝐶𝑒 𝑑,𝑗 ⋅𝑒𝑖𝑛𝑠 𝑑,𝑗 )](1) where the main decision variables are the type, size and location (𝑝𝑖𝑛𝑠 𝑑,𝑗 ) of the generation resources, and the size and configuration of the storage system associated with the resource (𝑠𝑖𝑛𝑠 𝑑,𝑗 ,𝑒𝑖𝑛𝑠 𝑑,𝑗 ) in the hybrid plant. 2.2. Problem constraints The optimisation problem is subject to network constraints, behaviour of generators and storage, as well as the relationships for the composition of the hybrid plant. Eqs. (2) and (3) define active and reactive power balance for each bus of the network (AC power flow). This formulation is valid for radial and balanced networks. The variables 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 represent the active power contribution of distributed resources (generators and storage systems). In (4) and (5) the voltage at the nodes and the currents through the lines are defined, respectively. The admissible limits of the voltage and current are defined in (6) and (7). 𝑝𝑖𝑗,𝑡 −𝑖𝑖𝑗,𝑡 ⋅𝑅𝑖𝑗 −∑ 𝑘∶𝑗−𝑘 𝑝𝑗𝑘,𝑡 −𝑃𝑙𝑜𝑎𝑑 𝑗,𝑡 + ∑ 𝑑 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 = 0,∀𝑗∈∖{0},∀𝑡∈(2) 𝑞𝑖𝑗,𝑡 −𝑖𝑖𝑗,𝑡 ⋅𝑋𝑖𝑗 −∑ 𝑘∶𝑗−𝑘 𝑄𝑗𝑘,𝑡 −𝑄𝑙𝑜𝑎𝑑 𝑗,𝑡 +∑ 𝑑 𝑞𝑠𝑦𝑠 𝑑,𝑗,𝑡 = 0, ∀𝑗∈∖{0},∀𝑡∈ (3) 𝑣𝑗,𝑡 =𝑣𝑖,𝑡 − 2 ⋅(𝑝𝑖𝑗,𝑡𝑅𝑖𝑗 +𝑞𝑖𝑗,𝑡𝑋𝑖𝑗 )+ (𝑅2 𝑖𝑗 +𝑋2 𝑖𝑗 )𝑖𝑖𝑗,𝑡,∀𝑗∈,∀𝑡∈(4) 𝑣𝑖,𝑡 ⋅𝑖𝑖𝑗,𝑡 ≥𝑝2 𝑖𝑗,𝑡 +𝑞2 𝑖𝑗,𝑡,∀𝑘∈,∀𝑡∈(5) 𝑖𝑖𝑗,𝑡 ≤(𝐼𝑚𝑎𝑥 𝑖𝑗 )2,∀𝑘∈,∀𝑡∈(6) (𝑉𝑚𝑖𝑛 𝑖)2≤𝑣𝑖,𝑡 ≤(𝑉𝑚𝑎𝑥 𝑖)2,∀𝑖∈,∀𝑡∈(7) The minimum and maximum size of the generation is defined in (8). Eqs. (9) and (10) define the limits of active and reactive power Sustainable Energy, Grids and Networks 39 (2024) 101422 3 C. García-Santacruz et al. injections, conditioned by the availability of the renewable resource in each time interval. 𝑃𝑚𝑖𝑛 𝑑,𝑗 ⋅𝑢𝑑,𝑗 ≤𝑝𝑖𝑛𝑠 𝑑,𝑗 ≤𝑃𝑚𝑎𝑥 𝑑,𝑗 ⋅𝑢𝑑,𝑗 ,∀𝑑∈,∀𝑗∈(8) 𝑝𝑑,𝑗,𝑡 ≤𝑀𝑑,𝑡 𝑝𝑖𝑛𝑠 𝑑,𝑗 ,∀𝑑∈,∀𝑗∈,∀𝑡∈(9) −𝑝𝑑,𝑗,𝑡 ⋅tan 𝜑≤𝑞𝑠𝑦𝑠 𝑑,𝑗,𝑡 ≤𝑝𝑑,𝑗,𝑡 ⋅tan 𝜑, ∀𝑑∈,∀𝑗∈,∀𝑡∈(10) To associate storage with a renewable generator, Eq. (11) is included, where the installation of the storage system is possible only if a generator is previously installed (determined by the binary variable 𝑏𝑢𝑑,𝑗 ). This allows the installation of a hybrid plant only when it is really necessary and convenient. 𝑢𝑑,𝑗 ≥𝑏𝑢𝑑,𝑗 ,∀𝑑∈,∀𝑗∈(11) At the point of interconnection of the plant to the grid, either generator only or hybrid plant, the following balance must be complied: 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 =𝑝𝑑,𝑗,𝑡 +𝑝𝑑𝑖𝑠 𝑑,𝑗,𝑡 −𝑝𝑐ℎ 𝑑,𝑗,𝑡,(12) ∀𝑑∈,∀𝑗∈,∀𝑡∈ where the total power injected into the grid, 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡, is the sum of the available generation and the battery discharge. The battery can only be charged using energy from the associated distributed generator. This is achieved by forcing the variable 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 to be non-negative. The Eq. (13) is defined to relate the battery charge to the associated resource. 𝑝𝑑,𝑗,𝑡 ≥𝑝𝑐ℎ 𝑑,𝑗,𝑡,∀𝑑∈,∀𝑗∈,∀𝑡∈(13) The size of the storage systems is constrained by Eqs. (14) and (15). 𝑆𝑚𝑖𝑛 𝑑,𝑗 ⋅𝑏𝑢𝑑,𝑗 ≤𝑠𝑖𝑛𝑠 𝑑,𝑗 ≤𝑆𝑚𝑎𝑥 𝑑,𝑗 ⋅𝑏𝑢𝑑,𝑗 , ∀𝑑∈,∀𝑗∈(14) 𝐸𝑚𝑖𝑛 𝑑,𝑗 ⋅𝑏𝑢𝑑,𝑗 ≤𝑒𝑒𝑠𝑠 𝑑,𝑗 ≤𝐸𝑚𝑎𝑥 𝑑,𝑗 ⋅𝑏𝑢𝑑,𝑗 , ∀𝑑∈,∀𝑗∈(15) Constraints (16),(17),(18),(19) and (20) model the storage system behaviour. The maximum charging and discharging power is defined, avoiding simultaneous charging and discharging, the state of charge update and the maximum and minimum state of charge for safe operation. 𝑝𝑐ℎ 𝑑,𝑗,𝑡 ≤𝑠𝑖𝑛𝑠 𝑑,𝑗 ⋅𝑏𝑢𝑐ℎ 𝑑,𝑗,𝑡,∀𝑑∈,∀𝑗∈,∀𝑡∈(16) 𝑝𝑑𝑖𝑠 𝑑,𝑗,𝑡 ≤𝑠𝑖𝑛𝑠 𝑑,𝑗 ⋅𝑏𝑢𝑑𝑖𝑠 𝑑,𝑗,𝑡,∀𝑑∈,∀𝑗∈,∀𝑡∈(17) 𝑏𝑢𝑐ℎ 𝑑,𝑗,𝑡 +𝑏𝑢𝑑𝑖𝑠 𝑑,𝑗,𝑡 ≤1,∀𝑑∈,∀𝑗∈,∀𝑡∈(18) 𝐸𝐵𝑎𝑡 𝑑,𝑗,𝑡 =𝐸𝐵𝑎𝑡 𝑑,𝑗,𝑡−1 +𝑝𝑐ℎ 𝑑,𝑗,𝑡 ⋅𝜂𝑐ℎ −𝑝𝑑𝑖𝑠 𝑑,𝑗,𝑡 ⋅ 1 𝜂𝑑𝑖𝑠 , ∀𝑑∈,∀𝑗∈,∀𝑡∈ (19) 𝑆𝑂𝐶𝑚𝑖𝑛 ⋅𝑒𝑒𝑠𝑠 𝑑,𝑗 ≤𝐸𝐵𝑎𝑡 𝑑,𝑗,𝑡 ≤𝑆𝑂𝐶𝑚𝑎𝑥 ⋅𝑒𝑒𝑠𝑠 𝑑,𝑗 , ∀𝑑∈,∀𝑗∈,∀𝑡∈. (20) Finally, the size of the storage systems is restricted, installing at most the power of the associated generation resource: 𝑠𝑖𝑛𝑠 𝑑,𝑗 ≤𝑝𝑖𝑛𝑠 𝑑,𝑗 ,∀𝑑∈,∀𝑗∈.(21) Fig. 2. European CIGRE MV distribution system with the problems identified in the two load scenarios (in both scenarios the problems occur in the same nodes and lines). Table 1 Line ampacity ratings. Line A Line A Line A Line A 0–1 730 3–4 145 8–7 145 12–13 195 0–12 730 4–5 145 8–9 145 13–14 195 1–2 130 5–6 145 9–10 145 2–3 130 3–8 145 10–11 145 3. Grid data The proposed method will be tested on the European CIGRE medium-voltage (MV) distribution system, shown in Fig. 2 in two scenarios. This network has a nominal voltage of 20 kV, with minimum voltage limits of 0.95 and a maximum of 1.05 pu. The base power is 10 MVA, and the base current 288.6 A. Table 1 shows the ampacity ratings of the lines. The resistance and reactance values of the lines are given in [31]. The cases analysed cover five days, divided into 120 hourly intervals. This is indicated by defining the set of periods as = {𝑡0,…, 𝑡119}. The load profiles of these days are based on the consumption profiles of typical winter days as described in [32]. A sequence of two weekdays, with the second having higher consumption, followed by Saturday, Sunday, and then another weekday is selected. To use these consumption profiles in the MV CIGRE network, they must first be disaggregated into unit profiles of commercial and residential types. These profiles will then be scaled by the rated power at each node, as provided in [31]. The method used to generate the disaggregated profiles from the total consumption data is described in an open repository [33], where all the data and network parameters used in the scenarios are also available. The profiles obtained for each type of load are detailed in Fig. 3(a). Fig. 3(b) shows the availability profile of primary energy resources, specifically solar and wind, for the RES that are being considered for installation. Initially, there are no distributed generation resources on the grid. There are no problems with the original power ratings and specified profiles. It is necessary to increase the load on the nodes to generate problem scenarios. Two scenarios with different characteristics Sustainable Energy, Grids and Networks 39 (2024) 101422 4 C. García-Santacruz et al. Fig. 3. (a) Evolution profiles for each type of load, (b) availability of primary energy resources. Table 2 Capital costs. Technology Cost PV 995 ke/MW Wind 1473 ke/MW ESS power 388 ke/MW ESS energy 372 ke/MWh have been synthesised to analyse the results obtained by applying the proposed method in two different situations. In terms of economic data, the capital costs for the different technologies under consideration as NWAs are shown in Table 2 [34, 35]. 3.1. Scenario A In this scenario, the aim is to analyse occasional problems lasting a maximum of two hours. To create these issues, the overall load connected to node 1 is increased by 60%, and the total load of node 12 is increased by 70% for all periods. Thus, occasional overloads occur on lines 0-1 and 0-12, which are the two lines closest to the primary substation. These issues arise during the time frame of 7 pm to 8 pm on day 2 (𝑡43 and 𝑡44 of the analysis period). On day 4, which corresponds to Sunday, there are occasional issues between 12 pm and 1 pm (𝑡84 and 𝑡85 of the total period) and between 7 pm and 8 pm (𝑡91 and 𝑡92 of the total period). At specific hours, the voltage levels at the nodes furthest away from the primary substation fall below the permissible operating limits. Table 3 displays the hours during which specific lines exceed their capacity, indicating the extent of overload beyond the permitted limit. The values range from 6.8 A to 128.3 A, meaning that at certain hours, the current values are between 736.7 A and 858.3 A. Table 3 Overloaded lines in scenario A: value of currents above the limit for each hour (A). Line 𝑡43 𝑡44 𝑡84 𝑡85 𝑡91 𝑡92 0–1 88.1 75.9 128.9 64.0 99.3 65.5 0–12 27.1 16.2 74.2 17.7 37.1 6.8 Table 4 Overloaded lines in scenario B: value of currents above the limit for each hour (A). Line 𝑡43 𝑡44 𝑡84 𝑡85 𝑡86 𝑡87 0–1 88.1 75.9 128.9 128.9 65.5 128.9 0–12 27.1 16.2 74.2 74.2 6.8 74.2 Line 𝑡88 𝑡89 𝑡90 𝑡91 𝑡92 0–1 99.3 128.9 99.3 99.3 65.5 0–12 37.1 74.2 37.1 37.1 6.8 3.2. Scenario B This scenario aims to analyse problems that persist for longer periods than in Scenario A. Therefore, it maintains the same issues for the second day and includes a 9-hour overload on day 4, between 1 pm and 9 pm (𝑡84 and 𝑡92), increasing the consumption at nodes 1 and 12 during this period. Table 4 displays all the overload problems in scenario B. A full description of both scenarios can be found in [33]. 4. Results This section presents the main results obtained from applying the proposed model to the CIGRE network, correcting the overload and voltage problems that appear in the grid in the two scenarios presented above. The simulations were carried out using GAMS with the KNITRO solver [36] for MINLP problems, in a computer with Intel [email protected] GHz processor with 8 GB of RAM running Windows 10. The implemented optimisation procedure for Scenario A took 58.48 s to solve. To test the scalability of the proposed method, simulations were performed by duplicating the network (29 nodes) with the data from scenario A, resulting in an execution time of 195.11 s. The most time-consuming optimisation corresponds to Scenario B with a longer period of overload, which took 593.23 s. The application of a MINLP optimisation model may increase the solution time when applied to large networks or complex scenarios. However, it is important to note that while NWAs are included in the set of planning problems, the time required to solve the optimisation problem is typically not a critical issue. The following paragraphs detail the results obtained for each scenario. In both cases, the minimum size considered for the installation of RES is 0.1 MW. 4.1. Scenario A The scenario A involves current overloads lasting up to two consecutive hours and voltage levels outside the feasible range in certain buses. Using power injections from the proposed DERs located and sized after executing the problem (1)–(20), the voltage and current problems can be addressed. Fig. 4 compares the current evolution on lines 0-1 and 0-12 before and after using DER power injections resulting from the optimisation problem. The first overloads occur during the second day, specifically during the 𝑡43–𝑡44 period (which corresponds to hours 7 pm and 8 pm of the second day). On the fourth day, problems occur again, in hours with solar generation, at hours 12 pm and 1 pm (𝑡84–𝑡85), and 7 pm and 8 pm (𝑡91–𝑡92). In all of these periods, it is observed that by locating DERs that inject power, the overload problems on the lines are solved, and the current values remain within the permissible limits. Sustainable Energy, Grids and Networks 39 (2024) 101422 5 C. García-Santacruz et al. Fig. 4. Current evolution in scenario A when the proposed method is applied: (a) line 0-1, (b) line 0-12. Fig. 5. Results for scenario A: comparison of maximum and minimum voltages in the grid under initial conditions and when the proposed DER powers are injected. Following the installation of new resources, all voltages remained above the lower operating limit of 0.95 pu. The initial voltages were below this limit, as illustrated in Fig. 5. It is worth noting that low voltage issues arise at the nodes farthest from the primary substation. Thus, the installation of DERs at nodes far from the feeder head and overloaded lines is necessary to address the low voltage problems. At nodes where originally all voltages remain in the feasible range, such as the 12-13-14 branch, DERs are only installed to solve the overload on the 0-12 line. The proposed location and size for the new distributed resources (generation and associated energy storage) obtained as a solution are depicted in Fig. 6. The proposed solution suggests using PV generation as the main energy source, with wind generation installed in only two nodes. In most cases, associating generation with ESS is the optimal solution compared to locating pure generation. If pure generation is the best option, ESS is excluded, which is the case for some nodes. This method has the advantage of locating and sizing ESS only at the nodes where they are needed. The overload on line 0-12, is addressed by installing at node 12 a hybrid plant consisting of a 1.14 MW PV generator and an ESS with a capacity of approximately 1 MW/1 MWh. Another PV generator with 0.29 MW is proposed at node 14, with less storage capacity: 0.26 MW/0.9 MWh. At node 5, which has the largest total installed capacity in this part of the grid, a 0.1 MW Wind generator and a 0.85 MW PV plant with a storage capacity of 0.85 MW/1.80 MWh are proposed to solve the overload in line 0-1. At node 10, a hybrid plant of 0.73MW PV and 0.73MW/1.5MWh ESS is installed. The location at this node, in addition to solving the overload in line 0-1, helps to correct voltage Fig. 6. Location and size results obtained with the proposed approach for scenario A: (a) size of generation resources for each bus, (b) power capacity for each ESS, (c) energy capacity for each ESS. Fig. 7. Analysis of overloads in scenario A after the application of the proposed approach: total power injections for each hour by type of resource. deviations below 0.95 pu at the nodes located furthest from the feeder head (11-10-9). Table 5 displays the numerical results (values of optimisation variables 𝑝𝑖𝑛𝑠 𝑑,𝑗 ,𝑠𝑖𝑛𝑠 𝑑,𝑗 and 𝑒𝑖𝑛𝑠 𝑑,𝑗 ) for the location and sizing of the new devices, and reveals two noteworthy findings. On the one hand, PV is the main generation technology to be installed, although wind generation is also needed. In addition, while some stand-alone generators are installed, hybrid plants appear to play a significant role as NWA. The behaviour of the generators and hybrid plants during periods of overload is analysed in Fig. 7, where numeric values of 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡 are represented. The ESS associated with PV are the assets that contribute the most to solving the overload problems. Thanks to their flexibility, ESSs charge energy from photovoltaic generation and discharge it during problematic hours. Wind generation (associated also with ESS) makes only small contributions. It is more advantageous to use Sustainable Energy, Grids and Networks 39 (2024) 101422 6 C. García-Santacruz et al. Table 5 Results of sizing DERs and ESSs for scenario A using the proposed approach. Node Resource Capacity ESS power ESS energy (MW) (MW) (MWh) 1PV 0.10 – – Wind – – – 3PV 0.22 0.22 0.22 Wind – – – 4PV 0.10 – – Wind – – – 5PV 0.85 0.85 1.80 Wind 0.10 – – 6PV 0.10 – – Wind 0.37 0.37 0.39 8PV 0.54 0.54 1.00 Wind – – – 9PV 0.28 0.28 0.58 Wind – – – 10 PV 0.73 0.73 1.51 Wind – – – 11 PV 0.10 – – Wind – – – 12 PV 1.14 1.02 1.07 Wind – – – 14 PV 0.29 0.26 0.91 Wind – – – Table 6 Investment and total sizing results obtained for scenario A with the proposed method. Investment Power installed Energy capacity (Me) (MW) (MWh) PV generation 4.43 4.45 – Wind generation 0.69 0.47 – ESS assoc. to PV 4.15 3.90 7.09 ESS assoc. to Wind 0.29 0.37 0.39 Total 9.56 9.19 7.48 PV+ESS during the night hours, as wind resources would have to be sized ad-hoc according to the availability for these concrete hours, requiring a higher investment. During periods 𝑡84 and 𝑡85, solar energy is the most efficient and economical solution to the existing problems. Hybrid power plants that combine optimally PV generation with ESS are therefore crucial to overcoming grid problems both day and night. Table 6 displays the total installed sizes and required investment for the installation of each technology. The total energy needed to solve problems is 23.92 MWh, with a total investment of 9.56Me. Hybrid plants formed by PV generation and ESS associated with this technology represent the largest investment, accounting for 85.6% of the investment in generation. This is due to the lower installation costs of PV generation, 995 ke/MW compared to 1473 ke/MW for wind generation. By combining storage with PV, the energy produced can be stored and injected during problematic hours at night. This combination is a better alternative than wind generation, with higher cost and greater variability of production between hours. Fig. 8 shows the proportion of investment allocated to each type of plant out of the total investment. Table 7 illustrates the disparity in capacity size and investment costs between two alternative cases, the first considering only the option of installing generator units (forcing the variable 𝑏𝑢𝑑,𝑗 in the optimisation problem to be 0) and the second considering hybrid units as NWA resources (𝑏𝑢𝑑,𝑗 can take the value 1). When hybrid plants are considered, the installed generation power is reduced by 65% thanks to the associated energy storage. When land availability is limited or it is not possible to install a large amount of generation, ESS can significantly reduce investment costs. The use of energy storage enhances the capability and economic efficiency of PV plants to act as NWA, resulting in Fig. 8. Solution obtained for scenario A: proportion of the total investment for each type of asset. Fig. 9. Location of resources for Scenario A comparing two cases: when only generation resources can be installed, and applying the proposed method when hybrid plants are considered. Table 7 Size and installation costs results for scenario A in two cases: one considering only generators and the other allowing hybrid plants. Case PV Wind Total generation ESS Cost (MW) (MW) (MW) (MW) (Me) Only generation 3.31 11.02 14.33 – 19.5 Hybrid plants 4.45 0.47 4.92 4.27 9.6 a reduction of approximately 50% in investment costs. Without energy storage, wind power would be the most installed resource, despite being the most expensive, due to its availability during problematic hours (at the night). In this scenario, wind generation would account for approximately 77% of the total investment. Fig. 9 illustrates the changes in location and capacity size when only generators are installed compared to when hybrid plants are considered as NWAs. It is observed that when ESSs are considered, the location of PV associated with ESS increases, being a better option, reducing the presence of wind generation at the nodes. Sustainable Energy, Grids and Networks 39 (2024) 101422 7 C. García-Santacruz et al. Fig. 10. Current evolution in scenario B when the proposed method is applied:: (a) line 0-1, (b) line 0-12. Fig. 11. Comparison of the maximum and minimum voltages with the proposed DER injections and in the initial condition of scenario B. These results demonstrate the potential benefits of considering hybrid plants with storage as NWAs. This approach can reduce the size of installed generation and investment costs required to solve the same problems. In addition, ESSs allow the use of energy from renewable generators that do not adjust their generation pattern to the occurrence of grid problems, which can be injected at appropriate times. 4.2. Scenario B In this scenario, the aim is to resolve longer-lasting overloads, such as the one that occurs between periods 𝑡84 and 𝑡92. The installation of the resources obtained as solution, shown in Fig. 12, avoids problems related to both overloads and voltage limit violations in this scenario B. Using DER injections as NWA, the current values for previously overloaded lines 0-1 and 0-12 are below the admissible limits (see Fig. 10), and the voltage values remain within the normal operating range of 0.95 - 1.05 pu, as illustrated in Fig. 11. The results demonstrate how the set of DERs and sizes obtained is effective in solving long-running problems. Fig. 12 displays the location and size of the installed generation, as well as the associated ESS configuration if applicable. It should be noted that in the proposed solution, there is no wind generation installed and that all the generation is from PV sources. To provide sufficient power during extended periods of overload, it would be necessary to install large wind generation capacities, due to the changing availability of the wind resource throughout the problematic hours. All of the plants Table 8 Results of sizing DERs and ESSs for scenario B using the proposed approach. Node Resource Capacity ESS power ESS energy (MW) (MW) (MWh) 1 PV 0.76 0.76 1.42 3 PV 0.36 0.36 1.50 4 PV 0.33 0.33 1.82 5 PV 0.60 0.60 3.71 6 PV 0.45 0.45 3.07 7 PV 0.10 – – 8 PV 0.51 0.51 2.92 9 PV 0.43 0.43 2.97 10 PV 0.43 0.43 3.08 11 PV 0.27 0.27 1.91 12 PV 2.31 2.00 6.90 14 PV 0.56 0.56 2.38 proposed by the method solution are hybrid plants, with the exception of the PV generator proposed at node 7. In comparison to Scenario A, and analysing the data collected in Table 8, corresponding to the values of 𝑝𝑖𝑛𝑠 𝑑,𝑗 ,𝑠𝑖𝑛𝑠 𝑑,𝑗 and 𝑒𝑖𝑛𝑠 𝑑,𝑗 , ESSs are installed at more nodes and are larger in terms of both power and energy in Scenario B. This is because overloads last longer in this scenario, requiring more hours of energy storage. For instance, at node 12, the energy storage capacity increases from 1 MWh in Scenario A to 6.9 MWh in Scenario B. The same trend is observed at node 5, where the storage capacity also increases from 1.80 MWh to 3.71 MWh. These differences between the scenarios demonstrate that the proposed method can adapt to different situations, optimally sizing the complete ESS configuration according to the type of problem to be solved. Fig. 13 shows the contributions made (values of variables 𝑝𝑠𝑦𝑠 𝑑,𝑗,𝑡) by the resources over nine consecutive problem hours. As time progresses, the contribution of PV generation decreases due to its limited availability, with the batteries providing all the power during the night hours. The total energy needed to solve the problems is 44.7 MWh. To address the issues in both scenarios, the proposed solution suggests installing a minimal amount of wind generation, or none at all. This is because, in addition to a higher installation cost, the availability of wind power fluctuates significantly from hour to hour. This makes it challenging to have the required power accessible when issues arise. Although wind availability may be sufficient for brief periods, it is not economically feasible to install enough wind capacity to safely provide power over extended periods of time. For instance, to generate the required power to address the issues in hour 𝑡88, it would be necessary to install 21.59 MW of wind capacity to effectively inject 4.13 MW, due to the low availability of the resource at this hour (see Fig. 3). This solution would require an investment of about 31 million euros. On the other hand, the hybrid plant approach makes use of the flexibility of the ESSs, which are sized based on the issues they need to address, without depending on the variability of the resource during those hours. Table 9 shows the total required investment obtained for scenario B. The investment in ESSs increases compared to scenario A due to the duration of the problems that need to be solved, which require batteries with higher energy capacity. This leads to an investment in ESS of 14.4 Me(67% of the total), more than twice the amount invested in PV generation. The installed power is very similar between ESSs and generation plants, due to Eq. (21), which relates the maximum power of the ESS to the associated generation. To highlight the importance of accurately sizing the ESS in terms of power and energy capacity as proposed in this work, the results are compared in two cases in which the ESSs are sized based on a fixed power-to-energy ratio. In one case, a storage duration of 1 h is selected, resulting in a power-to-energy ratio of 1:1, which is consistent with the ratio observed in previous results [30]. In the other case, a duration of two hours is defined (ratio 1:2). The economic comparison of these cases is summarised in Table 10. The use of hybrid systems, even with a fixed ratio, significantly reduces Sustainable Energy, Grids and Networks 39 (2024) 101422 8 C. García-Santacruz et al. Fig. 12. Location and size results obtained with the proposed method for scenario B: (a) size of generation resources for each bus, (b) power capacity for each ESS, (c) energy capacity for each ESS. Fig. 13. Analysis of overloads in scenario B after the application of the proposed method: total power injections for each hour by type of resource. Table 9 Investment and total sizing results obtained for scenario B. Investment Power installed Energy capacity (Me) (MW) (MWh) PV generation 7.1 7.1 – ESS assoc. to PV 14.4 6.7 31.68 Total 21.5 13.8 31.68 investment costs. ESS with a higher power-to-energy ratio reduce the amount of wind power required, resulting in lower investment costs. For instance, a ratio of 1:2 requires only 10.1 Mein wind generation, compared to 16.2 Mefor a ratio of 1:1. Using independent sizing for the ESS in each case can reduce investment by approximately 15% compared to using a fixed ratio of 1:2. When using a ratio of Fig. 14. Total investment results when considering independent energy-to-power ratio sizing, and when considering fixed energy-to-power ratios for the hybrid plants in scenario B. Table 10 Comparison of capital costs for ESS sizing in scenario B: Independent power and energy vs. Fixed ratios. Case PV (Me) Wind (Me) ESS (Me) Total (Me) Indep. sizing 7.1 – 14.4 21.5 Fixed ratio 1:2 4.9 10.1 10.5 25.5 Fixed ratio 1:1 6.3 16.2 11.0 35.6 Only generation 23.4 35.7 – 59.1 1:1, independent sizing can achieve a reduction of almost 40%. The proposed method offers the advantage of full sizing, allowing for the optimal configuration of ESS at each node as required. The fixed energy to power ratio sizing is inadequate to cover all energy needs, particularly when problems arise at night. Therefore, additional installation of wind power would be required. The battery placement at node 12 highlights a clear difference between the use of a free energy-to-power ratio sizing and a fixed ratio approach. According to our analysis, an ESS with a configuration of 2MW and 6.9MWh is the optimal solution to address the problems. Fig. 14 illustrates the disparity in total investment costs between the proposed method (which allows free energy-to-power ratio sizing) and scenarios using fixed ratios for 1 and 2 h of energy storage. From an investment standpoint, hybrid plants emerge as a more cost-effective solution compared to pure generation. The results presented in this section show that the proposed approach exploits the optimal energy generation technology, location and capacity with the optimal ESS configuration, leading to reduced investment costs. 5. Conclusions Emission reductions and the promotion of clean energy are favouring the use of DERs as NWAs to solve grid problems and defer investments in increasingly congested networks. This paper proposes a method for the optimal location and sizing of DERs to be used as NWA, considering the option of locating hybrid plants (generation and energy storage), minimising the total investment costs. The proposed solution takes into account the temporal availability of each kind of primary energy resource. The sizing of ESS is performed in terms of power and energy to fully utilise the flexibility offered by storage systems. The results show that the proposed method can adapt to the types of congestion, select the best locations and adequately size all distributed resources for an efficient solution. Additionally, it is demonstrated that creating a hybrid plant by combining distributed generation with ESS reduces the required installed power and total investment needed to address overloads and voltage issues in the grid. A significant conclusion that can be drawn is that appropriately sizing energy storage in terms of power and energy to match anticipated Sustainable Energy, Grids and Networks 39 (2024) 101422 9