Optimal operation of battery storage systems in standalone and grid-connected DC microgrids using parallel metaheuristics optimization algorithms.

Optimal operation of battery storage systems in standalone and grid-connected DC microgrids using parallel metaheuristics optimization algorithms. Luis Fernando Grisales-Nore˜ naa,∗, Jauder Alexander Ocampo-Torob,c, Oscar Danilo Montoya-Giraldod,e, Jhon Montanof, J.C Hernand´ ezg aDepartment of Electrical Engineering, Faculty of Engineering, Universidad de Talca, Curic´o 3340000, Chile bFacultad de Ingenier´ıa, Instituci´on Universitaria Pascual Bravo, Medell´ın, Colombia. cEstudiante de Doctorado en Ingenier´ıa, Instituto Tecnol´ogico Metropolitano, Medell´ın, Colombia dFacultad de Ingenier´ıa, Universidad Distrital Francisco Jos´e de Caldas, Bogot´a D.C., Colombia. eLaboratorio Inteligente de Energ´ıa, Universidad Tecnol´ogica de Bol´ıvar, Cartagena, Colombia. fFacultad de Ingenier´ıas, Instituto Tecnol´ogico Metropolitano, Medell´ın, Colombia gDepartment of Electrical Engineering, Universidad de Ja´en, Ja´en, 23071, Spain Abstract In this paper is proposed a battery energy management system for standalone and grid-connected Direct Current (DC) Microgrids (MGs) by considering distributed generation based on photovoltaic solar energy (PV) operating in maximum power point, aiming at improving their technical, economical and environmental indicators. To this end, a mathematical model was formulated that to propose the optimization of a DC MG with three different objective functions. The first objective function corresponds to the minimization of the operational costs including the energy purchasing cost of the conventional generators and maintenance costs of the PV systems and Battery Storage Systems (BSS) integrated into the grid. The second objective function is the reduction of energy losses associated to the energy transport on DC MG, and the third objective function is associate with the minimization of the total emissions of CO2to the atmosphere by the conventional generators. This model also considers the set of constraints involved in the operation of a DC MG in an environment with distributed energy resources (PV generators +BSS). These objective functions are minimized using a single-objective optimization approach through the application of parallel version of metaheuristic methods: Particle Swarm Optimization (PPSO), Vortex Search Algorithm (PVSA) and Ant-Lion optimizer (PALO). Two test systems composed of 27 and 33 nodes set for standalone and grid-connected grids located in Colombia regions are used in the numerical validations. The standalone grid corresponds to an adaptation of the PV power generation and demand curves, as well as the energy purchasing cost and CO2emissions related to the convectional generators based on Diesel used in Capurgan´ a-Choc´ o. While, the grid-connected system using the same operating conditions of the metropolitan area of Medell´ ın-Antioquia, by considering for this particular case variable and fixed costs purchasing energy cost to the grid. The integration of three PV Distributed Generators (DGs) and three lithium-ion batteries of different types into the DC MG was considered. With the purpose to validate the effectiveness of the proposed energy management system in terms of solution, repeatability, and processing times each solution methodology was executed 100 times in each test system. Based in the simulations return obtained, it was possible established that for standalone grids in Colombia the methodology with the best performance is the PVSA, while for the grid-connected network the methodology that achieved the best results is the PALO. Keywords: Energy management system; Batteries; DC microgrids; Parallel processing; metaheuristic methods; Variable power demand; Variable renewable generation; Particle swarm optimization, Vortex search algorithm ; Ant-Lion optimizer. 1. Introduction 1.1. General context World energy consumption has grown exponentially due to economic development and population growth in recent years [1]. This increase in energy demand has generated the need ∗Corresponding author Email addresses: [email protected] (Luis Fernando Grisales-Nore˜ na ), [email protected] (Jauder Alexander Ocampo-Toro), [email protected] (Oscar Danilo Montoya-Giraldo), [email protected] (Jhon Montano), [email protected] (J.C Hernand´ ez) to increase the infrastructure of conventional electric power systems. This change has generated different problems such as the increase of: energy price, energy losses associated with electricity transport and environmental impact related to the emission of polluting gases associated with electricity generation processes base on fossil fuels, among others [2]. The interest and use of Renewable Energy Sources (RES) for electric power generation has experienced strong growth as an alternative to reduce the high dependence on conventional generators based on fossil fuels, and different problematic described above. RES represent more than 60% of the gross capacity additions expected by 2040 in almost all regions of the world (about 9500 GW) [3]. Being the Photovoltaic solar (PV) Preprint submitted to RI December 28, 2022 energy projected to be second after hydro generation installed capacity renewable by 2040, this accounts for almost 60% of the expected growth [4], demonstrating the importance of these energy resource in generation systems worldwide. The use of RES in electric power generation processes is currently done under the concept of distributed generation [1]. The main characteristic of this concept is the location of generators close to the load, reducing or eliminating the need for a large-scale power system to transport energy [5]. Distributed generators and their integration into power systems represents an economical, flexible and low environmental impact solution to expand energy coverage worldwide, since it allows to exploit to the maximum the generation capacities coming from RES, and at the same time reduce the environmental impact associated with power generation systems [5]. Due to the high variability and intermittency of the main RES, energy storage (ES), batteries mainly, are also used. Which to help to manage the energy in the electrical grid by storing and injecting excess power, while promoting the quality and continuity of the electrical service supplied to the user [6]. In this paper, it is considered the implementation of batteries as ES, due to this energy storage system is the most developed and installed ES technology currently around the world [7]. The distributed energy resources (DER), RES+ES, are widely installed in conventional power distribution systems and microgrids (MG) [8], with the aim management the energy by improving the technical, economical an environmental conditions of the electrical network. Due to development of DER technologies, the electrical systems have been migrating towards a new operating paradigm known as smart grid [9] [10], where the structure of the conventional grid is changing from passive to active [11], by presenting the ability to control itself trough smart energy systems, with the aim to improve the quality and reliability of service for users [9], as well as the technical and economical benefits for the owners and operator of electrical network. Furthermore, in the last years the electrical Microgrid (MG) have been widely studied and used, due to allow to small number of users management their energy resources in a smart way, by reducing the complexity and investment cost in relation to the conventional power systems. The MG can be grid-connected or isolated (standalone). Grid-connected MG are implemented to support the integration of RES-based DG into the main grid [12], and the MG adjusts the generation and demand balance by buying or selling power to the main grid to maximize operational benefits. In the standalone mode, the MG cannot take advantage of the main grid support and aims to maintain reliable power supply for customers using offers from DG [13]. These MG are very useful in remote areas where grid extension is technically and/or economically unfeasible [12], by using in both kinds of electrical networks the implementation of ES for guarantying the global power balance, reduce the effects associate the variability of the renewable energy resources and potentiality the technical, economical and environmental benefits obtained by the energy management systems used [6]. The integration of DER into existing alternating current (AC) grids represents technical challenges that are difficult and/or costly to solve, because the most important and developed DER (PV generators and batteries) operating in direct current (DC) [13], by requiring the installation and operation of multiples electronic converters devices for the AC/DC conversion. In this way, the DC is the best option to MG, due to this present multiple advantages over AC networks, such as a major power line capacity due to the absence of reactive power, reduced power losses and voltage drop in the system, minor investment costs, and reduced complexity of mathematical models and control strategies, since reactive power and frequency fluctuation are not a concern within the system [14–16]. However, without doubt, one of the most attractive advantages of DC networks is the possibility of integrating DER that operate directly with DC, for wich the implementation of DC MGs has grown around the world in the last years [17]. It is important highlight that, the multiples benefits that cab be obtain by the DC MG that considering the installation of PV DGs, ES and other DER, it is related to the operation of DER within power grids: The operating points or power references of these devices modifying the behavior of the DC network, generating positive or negative impacts on the technical, economical and environmental conditions of the electrical system. The could be positive or negative depending on the quality of the energy management systems proposed for controlling all devices that make up the MG [8]. From this point of view, an adequate operation of DG and ES within the DC microgrid allows obtaining different benefits from the technical, economic and environmental conditions, such as the reduction of power losses and operating costs, the improvement of voltage profiles, the reduction of the environmental impact associated with the operation of the system, among others. Energy management strategies in DC MG seek to identify the optimal power levels to be injected or stored by the different DER installed within the DC MG. At the same time, these strategies must take control decisions for improving the efficiency and reliability of the system [18]. Furthermore, the control scheme for energy management have to considering into account: whether the DC MG is standalone or grid-connected (voltage levels and limitations of power to be demanded and injected), the variations in generation and power demand, the technical characteristics of the DG and ES used, among others [19]. For include this information inside the problem here studied, mathematical models have been proposed to represent the operation of a MG, by considering all variables and parameters that affect it. Then, the mathematical model must be solved using optimization strategies and intelligent control methods, to operate the DC MG within permitted technical operating conditions and to meet technical, economical or environmental objectives imposed by the grid operator [20]. The present work study the problem of battery energy management in DC MG by considering PV DGs operating at its maximum power point (MPPT), as traditionally occurs in the real life [21]. Batteries are responsible for balancing the energy in the DC MG, storing the excess generation, or injecting energy into the grid when the generation does not meet the demand of the users [22]. The usefulness of batteries 2 is greater in standalone grids, since they allow supplying the stored energy in times of low generation, avoiding the use of fossil energies of high cost and environmental impact, and total absence of electricity service. In the grid-connected mode, due to the variable energy prices, it is not always convenient to use the renewable energy, being better in some scenarios to store it and use it hours of high energy price[23]. Battery energy management problem in DC MG can be solved by dividing the problem into two stages. The first one proposes an optimal power flow problem (OPF) in the network, which seeks to identify the power levels to be injected or stored by each DG and ES installed within the DC MG, so that it fulfills an objective function to improve operational aspects of the grid (technical, economical or environmental). The other stage proposes a hourly power flow (HPF), which is essential to analyze the impact of each possible power configuration proposed by the OPF (first stage). The OPF in DC MG is a complex mathematical problem to solve, because it corresponds to non-linear and non-convex formulations, related to the equations that represented the DC grid operation, which implies high mathematical and computational efforts for its solution [15]. Additionally, it is necessary that the processing times required to solve the OPF and HPF problem be short, since in the energy management systems, it is necessary to evaluate multiple scenarios in short times, for obtaining the operating points of all devices that composing the DC MG each time that the power generation and demand conditions changes [24]. 1.2. State of the art Among the methods reported in the literature for solving the power flow problem in DC MG, the most efficient method is the successive approximations (SA) method [25], due to it presents an excellent convergence with reduce times. For solving the power flow in each hour, the SA has been adapted by obtaining an hourly power flow method (HPF), highly used in literature and selected in thus paper as solution to this problem [6, 26]. This is explained in Section 3 of this paper. In the solution of the OPF, exact methods have been reported that stand out for their accuracy in terms of convergence [2]. An example of this is the work presented by Gil et al. [24], where it was proposed a convex optimization method based on semidefinite programming to operate batteries and renewable energy DG in DC MG, with the aim to reduce the operational cost and energy losses. This method presents excellent results when it is compared with other methodologies, however, the processing times required by the methodology are not analyzed. Furthermore, the maintenance costs of the DER were not included inside the mathematical model proposed. The same problematic occurs in [27], where the authors proposing a convex mathematical model based on second-order cone programming for DC MG with the aim to operate multiples batteries located into the grid with the presence of renewable generation, by using the reduction of operational costs and energy losses as objective function. Among these methods, linear programming [20], mixed linear [28], quadratic [29], and the sweep method [30] stand out. These solution methodologies increasing the complexity and costs of energy management systems, related to the implementation and acquisition [6]. In recent years, solutions based on sequential programming methods, such as metaheuristic optimizations methods, have been employed in literature to provide a solution to OPF in MGs, by considering PV DG and batteries as ES. Being highly used optimization methods in the specialized literature the genetic algorithm (GA) [30], particle swarm optimization (PSO) [31], ant colony, bee colony [32], among others. It is important to mention that, hybrid methods are used to potentiate the mentioned techniques, by combining two or more of these optimization techniques [2] [15]. Specifically, for the OPF problem in DC MG that to include batteries as ES system, the following works stand out: Wang, Wang and Xu [33] using a PSO algorithm to solve the OPF in DC networks, considering DG and batteries located in the network. By using as objective function the reduction of the energy costs, satisfying all technical constraints that represents the DC grids under an scenario of PV DGs and ES. In this work, different test cases are considered, but comparison methodologies and processing times analysis were not considered, which do not allow an adequate performance analysis. In [34], a non-linear optimization model for optimal operation of PV DGs, wind DGs and batteries considering constant power loads was presented. However, the uncertainties of the primary sources were not considered for wind and solar power generation. This make that the solutions obtained do not represent a real scenario, for which the results obtained are not representative for the regions considered under the study. Others researches have considered the optimal operation of batteries in MGs, by using solutions methods as such as multi-agent optimization based on market decisions, multi-objective PSO, bee colony optimization and GA [35, 36]. In [6] it was proposed a master-slave methodology, that using in the master stage a continuous version of the genetic algorithm, the Montecarlo method and a parallel version of the particle swarm optimization algorithm; for solving the operation of multiples batteries located in a DC microgrid by considering PV DGs operating in MPPT conditions. In slave stage, it was used the HPF method based on SA for evaluating the objective functions and constraints that represent the problem, being the objective function used a function compose by the energy purchasing costs and energy losses. The results obtained demonstrating the effectiveness of the parallel particle swarm optimization method for solving the problem addressed, evaluation the average solution, standard deviation and processing time. However the mathematical model used do not consider the maintenance cost related to the DER, for which the solutions obtained are not representatives in the real life. For improvement the environmental conditions of the electrical networks trough the optimal operation of DER that compose it, the number of works reported are reduced in comparison with the energy management systems proposed for improving technical and economical conditions. In relation to the improvements of environmental conditions of DC grids, the work reported in [37] proposing a strategy for reducing the gas 3 emission related to the fuel consumption in a DC grid. In this study it is proposed a control strategy for speed reduction in generators installed in the network. The authors of [38] used the algorithm theta-crow search for solving the problem of optimal operation of ES in AC/DC grids, by considering the reduction of operational cost and CO2emissions as objective functions. The excellent performance of the proposed methodology is demonstrated by employing an electrical test system, without using comparison methods, as well as average solution analysis and processing time. Currently, exist few works related to the improvement of the environmental conditions reported on the DC grids, the reported works focused on the reduction of CO2 emissions. Although the works reviewed in the state of the art demonstrating a good performance of the methods used, the number of comparison scenarios is small, and average solution and processing time required by the algorithms is not analyzed in the major of the cases. Being important to obtain energy management with solution highly efficient in terms of solution, repeatability and processing times; by considering the improvement of the must used technical, economical an environmental conditions: reduction of energy costs, power losses and CO2emissions [10, 28, 39–41]. From the review of the specialized literature, it was found that the exploration and progress in energy management strategies in DC MG has not been as remarkable as in AC grids [6]. Specifically, for battery energy management in DC MG considering RES installed on the grid (PV Distributed generators mainly). Furthermore, currently it is necessary to propose mathematical models and optimization strategies that considering variable power generation and demand, as well as all constraints that describe the operation of DC MGs under a DER scenario. Moreover, these energy management systems should provide a solution to the mathematical model proposed in short processing times, with the objective of analyzing the largest possible number of scenarios in the times that compose the variation of generation and demand power within the electric grids [42]. Furthermore, the new solution methodologies proposed must be compared with works reported in literature for validating its effectiveness from the point of view of the average solution and standard deviation. With the aim to guarantee that each time that the solution method is executed, the solution obtained will be of good quality as reported by the authors. With the aim to solve the problems previously described, this paper proposes an energy management system based on parallel version of the metaheuristic techniques: Particle swarm optimization method, vortex search algorithm and Ant-Lion optimizer, for solving the problem of optimal operation of battery storage systems in DC MG, considering PV DGs located on the grids, and operating in maximum power point. The selection of this solution methodologies was based on the excellent results reported by the authors for solving optimal power flow problem in literature, while the parallel processing added to the traditional methods searches to reduce the processing times. The mathematical model used considered the reduction of the operational cost, the power losses and the CO2emissions, by considering all technical and operatives constraints that represent the operation of a DC MG under a scenario of DER (PV DGs +Batteries). As test scenarios were used a stand-alone and grid-connected DC MG, that using the power generation, power demand, energy cost and emission data of the Medell´ ın-Antioquia City (grid-connected MG) and Capurgan´ a-Choco town (Standalone MG) from Colombia. With the aim to evaluate the effectiveness and robustness of the solution methodologies proposed, each optimization methods was executed 100 times with the aim of evaluating and analyzing the best solution, average solution, standard deviation and processing time required. The main contributions of this paper are presented below: •A mathematical model that represents the problem of optimal operation of batteries in DC grids for improving the technical, economical and environmental conditions of the grid by considering all technical and operatives constraints that represent the problem. •Three parallel version of metaheuristic algorithms for solving the problem of optimal power dispatch of batteries in DC grids. •The adaptation of two DC MG that considering the energy cost, factor emissions, power demand and PV generation from a grid-connected and a standalone systems located in different regions of Colombia. •A methodology based on average results and standard deviation values for selecting the strategy with the best performance for solving the problem of optimal operation of batteries in DC grids by considering the improvement of the technical, economical and environmental conditions. Finally, this paper is organized as follow: in Section 2 it is present the mathematical formulation proposed. Section 3 presents the solution methodologies proposed for solving the problem formulated in section 2. In Section 4 are describe the electrical parameters and operating conditions of grid-connected and standalone microgrids used as test scenarios. Section 5 describes and analyzes the simulations results obtained by the solution methodologies proposed in the test scenarios used. At last, Section 6 presents the conclusions and future works related to this research work. 2. Mathematical Formulation To solve the problem of optimal energy management of batteries in DC MGs, in this section a mathematical model was formulated. By using three different objective functions for improving the economical, technical and environmental conditions, integrating all set of constraints that represent the DC grids under an scenario of DER [43] [44]. The mathematical model proposed takes into account variable PV generation and demand related to the users, by considering an operation that compose by 24 hours whit periods of one hour. 4 The different indices considered inside the objective functions are described below: •Reduction of energy purchasing cost associated to the conventional generator and maintenance costs of the PV DGs: Reduction of operational costs (Ecost) •Reduction of power losses associated to the energy transport on DC MG: Reduction of power losses (Eloss). •Reduction of CO2emissions related to the generation of conventional generators: Reduction of CO2emissions (Emissions). The mathematical set of equations developed for the optimal operation of battery systems in a DC MG are presented below. 2.1. Operating cost reduction Equation (1) describes the expression used to calculate the energy purchasing costs to the conventional generators (CG) installed in the DC MG in each period of time t(CEE (t)). In this equation, the purchasing energy cost to the conventional generators located in the bus i(CCGi (t)), it can takes two different values that depending of the kind of electrical grid considered. In MGs operating in grid-connected, this cost is related to the energy purchasing to the electrical grid, which supply energy to the MG in the bus i. This cost is reported by the local electrical distribution company, and it could be fix or variable. While, in MGs that operate in standalone mode, the energy purchasing cost is related to the production of energy by using the Diesel generator located in the bus i, being this fixed energy cost due to the Diesel cost is the same the whole operation day. In this equation, PCGi (t)is the variable used for representing the power produce by the conventional generator located in the bus iat the period of time t, and Ndenotes the set that contains of the buses of the DC MG. Equation (2) presents the expression used for calculating the maintenance costs of PV DGs and batteries installed on the DC grids (CM(t)). In this equation CMDGi (t)and CMBi (t)represent the maintenance cost associated to the PV DGs and batteries storage systems installed within the DC MG. Due to the maintenance costs is in function of the power management by the DERs, in this equation it is necessary to considering the variables PDGi (t)and PMBi (t), that describing the power generate and storage by the PV DGs and batteries located in the bus iat the period of time t. The total operating costs of the DC MG, C(t), are obtained from the sum of the electric power and maintenance costs of the MG (see Equation (3)) in each period of time considered. The operating cost minimization objective function for the 24-hour mathematical model, FO1, is expressed by unsin Equation (4). CEE (t)=X i∈N (CCGi (t)∗PCGi (t)) (1) CM(t)=X i∈N (CMDGi ∗PDGi (t)+CMBi ∗PBi (t)) (2) C(t)=CEE (t)+CM(t)(3) FO1=min         24 X t=1 C(t)        (4) 2.2. Energy losses reduction Equation (5) is used to calculate the power losses (Ploss (t)) in the DC MG at each time period t. Where, Pdi (t)represents the power demanded by the load connected at bus iin the period of time t.Vi(t)and Vj(t)are the voltages buses iand jat the period of time t, respectively. Gi j denote the component of the conductance matrix of the lines that interconnected the buses iand j. Finally, Gi0represent the constant resistance loads included in the conductance matrix, which do not produce power losses associated with energy transport [32]. The energy losses minimization by considering 24-hour used as objective function in the mathematical model proposed, FO2, is expressed by Equation 6. Ploss (t)=X i∈N (PCGi (t)+PDGi (t)±PBi (t)−Pdi (t)) =X i∈N       X j∈N Gi j ∗Vi(t)∗Vj(t)−Gi0∗V2 i(t)        (5) FO2=min         24 X t=1 Ploss (t)        (6) 2.3. Reduction of CO2emissions In this objective function is considering the reduction of CO2emissions related to the operation of conventional generators in each period of time t,E(t)[45]. In this equation did not consider CO2emissions by the PV DGs, due to this energy resources it is considered a free emission technology, by generating some environmental impacts it is construction but no in its energy production process [46]. γCGi denotes the CO2factor emission related to the conventional generators, this parameter takes different values depending the kind of energy resources installed at the bus i. In the particular case of this manuscript, it is used the CO2emission values associated to the energy generation in the grid and using Diesel fuel. Equation (7) is used to calculate the CO2emissions of the system in each period of time considered under the horizon time analyzed. E(t)= n X i=1 (γCGi ∗PCGi (t)) (7) The CO2emissions minimization objective function, FO3, is expressed by Equation (8). FO3=min         24 X t=1 E(t)        (8) 2.4. Set of constraints The problem of optimal energy management of batteries in a DC MG is limited by the fulfillment of the technical and operative conditions (constraints) represented in Equations 9 to 21. 5 The first constraint corresponding to the power balance, see Equation (9). This equation must be satisfy for all set of buses and hours contains in Nand H. PCGi (t)+PDGi (t)±PBi (t)−Pdi (t) =Vi(t)∗X j∈N Gi j ∗Vj(t)∀i,j∈N,∀t∈H(9) The minimum (Pmin CGi) and maximum (Pmax CGi) power generation capacity allowed in the different conventional generators located on the buses that composing the DC MG is fixed by Equation (10). Pmin CGi ≤PCGi (t)≤Pmax CGi ∀i∈N,∀t∈H(10) The maximum (Pmax DGi (t)) and minimum (Pmin DGi (t)) power limits to be the supply for the PV distributed generators installed in the DC grid at the period of time t, is established by Equation (11). Pmin DGi (t)≤PDGi (t)≤Pmax DGi (t)∀i∈N,∀t∈H(11) The battery storage and supply capacity for the battery located in the bus iat the hour tis fixed by Equation (12). In this equation Pchar max Bi and Pdisch max Bi corresponding to the maximum charging and discharging power allowed for the kind of battery located at the bus i. Pchar max Bi ≤PBi (t)≤Pdisch max Bi ∀i∈N,∀t∈H(12) Being the power charging and discharging limits of battery located in the bus icalculate by using the Equation (13) and (14). Where, CBi is the nominal capacity of a battery at the node i.tcBi ytdBi are the charging and discharging times of a battery installed the bus i. Pchar min Bi =−CBi tcBi ∀i∈N(13) Pdisch max Bi =CBi tdBi ∀i∈N(14) Equation (15) represent the state of charge (SOC) of battery installed in the bus iat the period of time t. In this equation, S OCBi (t)denotes the SOC of a battery at the bus iand time t,ϕBi is the Charge/discharge factor of the battery installed in the bus i, and ∆tis the duration of the period of time t. The Equation (16) allows to calculate ϕBi. S OCBi (t)=S OCBi (t−1)−(ϕBi ∗PBi (t)) ∗∆t ∀i∈N,∀t∈H(15) ϕBi =1 tcBi ∗Pchar min Bi =1 tdBi ∗Pdisch max Bi ∀i∈N,∀t∈H (16) With the aim to improve the technical, economical and environmental impacts of the energy management systems proposed for the problem here studied, in the literature have been fixed initial (S OC0i) and final (S OC f i) state of charge for the batteries installed in the DC grid, see Equations (17) and (18). In this work all batteries start and finish in the 50% of the state of charge following the suggestion made in [6]. Furthermore, Equation (19) established the SOC limits for the batteries installed in the bus i. Being S OCmin iand S OCmax ithe maximum and minimum SOC allowed for the kind of battery used. As in this work were considering Lithium-ion batteries, this parameters take a value of 0.1 and 0.9, respectively [27]. S OCBi (1)=S OC0i∀i∈N(17) S OCBi (24)=S OC f i ∀i∈N(18) S OCmin i≤S OCBi (t)≤S OCmax i∀i∈N,∀t∈H(19) Finally, with the aim to guarantee the voltage profiles and current limits of the DC grid were used the Equation (20) and (21). Where, Vmin iyVmax irepresent the minimum and maximum allowable voltages at the bus i,Ri j is the electrical resistance of the connection line between buses iand j,Ii j (t) denoted the electric current that flow by the line that connect the buses iand j, at time t, and at last, Imax i j is the maximum electric current allowed for line between buses iand j. Vmin i≤Vi(t)≤Vmax i∀i∈N,∀t∈H(20) Ii j (t)=Vi(t)−Vj(t) Ri j ≤Imax i j ∀i,j∈N,∀t∈H(21) 2.5. Fitness function For satisfying all constraints that represent the problem of operation of DC MGs previously described, in this work is used the fitness function (FF) presents in Equation (22). This equation in composed by the objective function analyzed (FOi), a normalize factor for regulated the penalization (β), and the Penalize Factor (PF) that penalizing the objective function in the particular case that one solution proposed violates some constraints in the different period of time analyzed. The value of βin this work was calculated in a heuristic way by obtaining a value of 1000. This value guarantee that all solution obtained by the optimization methodologies proposed were feasible at the final of the iterative process, by allowing to these exploring non-feasible regions. This kind of exploration of the solution space reducing the processing times required by the solution methods [46]. FF =FOi +β∗PF ∀i∈1,2,3.(22) 6 PF = 24 X t=1                                                                      max (0,P i∈N (PBi (t)−Pchar max Bi )) + min (0,P i∈N PBi (t)−Pdisch max Bi )) max (0,P i∈N (S OCBi (t)−S OCmax i)) + min (0,P i∈N (S OCBi (t)−S OCmin i)) +max (0,P i∈N (Vi(t)−Vmax i)) + min (0,P i∈N (Vi(t)−Vmin i)) +max (0,P i∈N P j∈N (Ii j (t)−Imax i j ))                                                                      (23) 3. Proposed solution methodologies For solving the problem of optimal operation of batteries in DC MGs for improving the economical, technical and environmental conditions. In this work was proposed the implementation of three master-slave methodologies composed in the master stage for the Parallel versions of the Ant-Lion Optimizer (PALO), Vortex Search Algorithm (PVSA) and the Particle Swarm Optimization (PPSO). The selection of this optimization methodologies was based in the excellent results achieved for these for solving optimal power flow problems in DC grids in terms of solution, repeatability and processing times [33, 46, 47]. Being the parallel processing used for reducing the processing time required for these, due to in the operation of DER it is necessary to obtain fast solution with the best solution quality [6]. For all methodologies in the slave stage was used the Hourly Power Flow method based on SA (HPFSA), due to the excellent results reported for this method in literature in terms of convergence and processing times [6]. For understanding the master-slave methodologies proposed in this paper, to below are described the main characteristic of the codification problem used, the optimization methods employed, the parallel process added to these, and the HPFSA. 3.1. Problem codification The problem of optimal operation of batteries in electrical networks requiring a continuous codification that allows to establish the power to be supply or storage by batteries in each period of time considered inside the horizon time analyzed. For carrying out this labor, in this paper it was used a continuous codification that using a vector of size 1x(NB ∗ |H|), where NB represents the number of batteries installed on the DC MG and |H|the number of periods of time considered inside the horizon time. The codification used is presented in Figure 1, where for each battery located in the grid it is proposed the state of the charge associated to each period of time, starting and finishing in 50% of SOC for the batteries to follow the suggestion described in the last section. In an example mode, Battery 1 starts in 50% of SOC, then discharging the battery in the hour 2 until 40%; in hour 23 the battery has a SOC of 40% and finally this is charging to finish in the 50% of SOC. Following the same methodology, this codification suggests the SOC behavior hour at hour for the Battery 2 and k. This methodology allows proposing a solution for the operation of batteries located in the DC MG in function of the SOC. It is important to highlight that, when the optimization methodologies proposing a new solution inside their iterative process, it is necessary to guarantee that the SOC proposed for each battery satisfy all constraints presented in section 2 of this document. 3.2. Master stage The master stage is responsible to solve the problem of operation of batteries in DC grids, by proposing solutions to this problem by using the codification previously described, and evaluating its impact in the objective function studied through the slave stage. Due to the problem here analyzed is a continuous problem non-lineal and non-convex, in this work were selected three metaheuristic methods. Selected by the excellent performance reported in literature fol solving optimal power flow problems in DC grids [33, 46, 47]: ALO, VSA and PSO. Being all these optimization algorithm based on population, which make possible to use parallel processing for evaluating the objective function of each one of the individuals that composing the population, with the aim to reduce the processing time required [6]. In this way, in this paper are generating the Parallel versions of the Ant-Lion Optimizer (PALO), Vortex Search Algorithm (PVSA) and the Particle Swarm Optimization (PPSO), respectively. With the aim to control the exploration of all solution methods proposed, in this work were considered two stopping criteria: a maximum number of iteration (itermax) and a maximum number of non-improvement iterations (iterN maxI); both stopping criteria finishing the iterative process of the algorithm when are achieving. The main characteristic of each solution method and the adaptation of the parallel processing is presented to below. Being important highlight that if the reader of this paper need more information of the optimization algorithm could search in the references used. 3.2.1. Parallel Ant-Lion Optimizer This optimization algorithm take advantage of the hunting strategies of the Ant-Lions for obtaining food, which creating cone-shaped trap on the ground to hunt other ants, moving by using randoms walks within the area where it is located to improve the possibility of obtaining food [46]. This optimization algorithm was formulated with the aim to explore the solution space by using randoms walks of the ants, that represents individuals that composing the population. By updating the position in the solution space of the Antlion with the aim to obtain solution of good quality, the parallel version of the Ant-lion optimizer is shown in the Algorithm 1 and described below. The iterative process of the PALO start reading the data of electrical systems that including lines parameter, number of 7 Figure 1: Continuous codification proposed for operating batteries in DC grids Data: Load electrical data of DC MG and PALO optimization parameters Generate the initial population in aleatory way; Evaluate the fitness function of the population with the Slave stage by using parallel processing; Select best solution as the Antlioniter (incumbent); for iter =0 : itermax do Generate the new population by using the last population and Antlion information; Evaluate the fitness function of the population with the Slave stage by using parallel processing; Update the Antlioniter+1(incumbent); if Antlioniter≤Antlioniter+1then iterNI =iterNI +1; if iterNI =iterNI max then Solution achieved; Result: Print the Antlioniter as solution to the problem ; break; end else iterNI =0; end if iter =itermax then Solution achieved; Result: Print the Antlioniter+1as solution to the problem break; end end Algorithm 1: PALO iterative process. buses, conventional generators, PV DGs, batteries, generation and demand curves, energy costs, factor emission, among others. Furthermore, in the first step of the algorithm is reading the parameters of the PALO, for this and the other optimization algorithms used in this paper were tuned by using a discrete-continuous genetic algorithm [48, 49], with the aim to offering the best performance for each solution methods used. This information is described in Section 5 of this manuscript. Then, in the second step of the iterative process, the PALO generating the initial population of Ants in a random way by using the codification presented in Figure 1. In the third step is evaluating the fitness function of the individuals that composing the initial population, for carrying out this labor, it is necessary that the fitness function of each individual be evaluated by using the slave stage. By requiring for this task Nslave stage process, where Nis equal to the number of individuals. With the aim to take advantage of the parallel processing, the fitness function of the whole population it is evaluated by using the Wnumber of workers of the computer, by allowing to reduce the number of process as it is describing in the Equation (24). In this equation, NP represents the number of process required for evaluating the FF of Nindividuals that composing the population. Being the processing time required for the iterative process describe by the Equation (25), where MPT is the maximum processing time required in the NP iterative process make by the parallel processing, and PT is the total processing time required for evaluation of the whole population. It is important to highlight that, as the Wand the performance of the computer increase, the processing time of the optimization methods is lower. After to evaluate the fitness function of the initial population, it is selected the individual with the best objective function as the Antlion in the current iteration (Antlioniter). NP =N/W(24) PT =MPT ∗NP (25) Then, the iterative process of the PALO starts after to obtain the initial values of the algorithm. With the values of the initial population, randoms and constant values and Antlioniter, the population is updates. Then, by using parallel processing and the slave stage, it is evaluate the fitness function of all individual that composing the new population. Subsequently, it is updates the Antlioniter+1. With the aim to validate if the stopping criterion have been met, first is validate if the current Antlioniter+1is better than the previous Antlioniter. In the case that this is affirmative, the counter of iteration of non-improvement (iterNI ) takes a value of zero, in otherwise add 1 to the counter. If iterNI max has been met the algorithm finishing and print Antlioniter as the solution to the problem, else the iterative process of the algorithm continue. Then, it is verify if the itermax has been met, if it is true the algorithm stop and print Antlioniter+1as the solution to the problem, else the iterative process continue. 8 3.2.2. Parallel vortex search algorithm The vortex search algorithm works by using the behavior of the of vortexes created in stirred fluids [50]. This optimization algorithm generating non-concentric hyper-spheres that reducing the radius and relocated the center in each iteration, being the center of the concentric hyper-spheres updates with the information of the best solution obtained in each iteration. In this paper this algorithm using the same stopping criteria that the PALO, and it is iterative process is described in the Algorithm 2. Data: Load electrical data and PVSA optimization parameters Define (riter) and (µiter) of the hyper-sphere; Generate the initial population by using the µiter,riter and a Gaussian distribution; Evaluate the fitness function of the population with the Slave stage by using parallel processing; Select the best solution of the population as the Incumbentiter for iter =0 : itermax do Select position associated to the best solution of the population as the new center of the hyper-sphere µiter+1; Updates the radius of the hyper-sphere riter+1; Generate the new population by using the µiter+1, riter+1and a Gaussian distribution; Evaluate the fitness function of the population with the Slave stage by using parallel processing; Select the best solution of the population as the Incumbentiter+1; if Incumbentiter≤Incumbentiter+1then iterNI =iterNI +1; if iterNI =iterNI max then Solution achieved; Result: Print the µiter and Incumbentiter as solution to the problem ; break; end else iterNI =0; end if iter =itermax then Solution achieved; Result: Print the µiter+1and Incumbentiter+1as solution to the problem break; end end Algorithm 2: PVSA iterative process. Similar to the PALO, the PVSA starts the iterative process reading the data of the electrical system and PVSA parameters, the last one are reported in Table 6. Then, with the maximum and minimum values assigned to the variables that composing the problem are generating the initial radius (riter) and center (µiter) of the hyper-sphere. Subsequently, it is obtaining the initial population by using the values aforementioned and a Gaussian distribution, that spread the individuals on the solution space guaranteeing a symmetric exploration. After that, it is used the parallel processing described for the PALO for evaluating the fitness function of the population by using the slave stage. Finally, for obtaining the initial conditions of the PVSA is selecting the best solution of the population as the current incumbent (Incumbentiter), from the results obtained previously. With the initial values of the PVSA starts the iterative process, selecting the individual associate to the best solution as the new center of the hyper-sphere (µiter+1). After that, it is updated the radius for the current iteration (riter+1), and it is obtained the new population with these data and the Gaussian distribution. Then, it is calculated the fitness function of population by using the slave stage. Afterwards, the best solution found is selected as the incumbent of the problem in the current iteration (Incumbentiter+1). With the current and last value of the incumbent is evaluation the stopping criteria, in the particular case that some of two criteria have been met the PVSA stop and print the current center and incumbent as the solution of the problem, in otherwise, the optimization algorithm continues its iterative process. 3.2.3. Parallel particle swarm optimization algorithm The PSO uses the hunting behavior of birds and flock of fishes for obtaining food, by employing the cognitive and social knowledge of swarm for exploring the solution space and obtaining the best possible food. By converging all the individuals that composing the population in the best point of the solution space to eat [6]. In this paper is used the parallel version of the PSO (PPSO), which it is described in the algorithm 3. The iterative process of the PPSO starts reading the data related to the electrical systems and PPSO parameters, see Table 6 for the last one. Then, the algorithm generates the initial population randomly, by using the codification presented in Figure 1 and the maximum and minimum values fixed for the continuous variables. Subsequently, the fitness function of each of the particles that composing the swarms is evaluated by using the same parallel process described for the PALO. Finally, the best particle and swarm solution are identified, selecting the last one as the incumbent of the problem in the current iteration (Incumbeniter). After to fix the initial conditions of the PPSO, the iterative process starts updating the position of the particles in the solution space. For carrying out this labor, it is used the best position achieved for the particle and the swarm, as well as some random values and cognitive, social and inertia constants that controlling the exploration and convergence of the algorithm. Afterwards, it is evaluated the fitness function of the particles by using parallel processing. With the results obtained are update, the best solution for each particle and the swarm, being the last one the new incumbent of the problem (Incumbeniter+1). Then, it is verified is the stopping criteria 9 0.0524 1.3212 7.804 0.1811 0.0489 1.3039 7.4846 0.1721 0.0724 1.3016 7.6457 0.176 0.063 1.2314 7.4812 0.1718 0.0468 1.3026 7.5573 0.1692 2.7487 7.7446 6.6678 2.553 Fixed Ecost Var Ecost Eloss Emissions Fixed Ecost Var Ecost Eloss Emissions (a) Minimum reductions (b) Average reductions 10-1 100 101 102 Reductions obtained with respect to the base case [%] PALO PVSA PPSO Figure 8: Minimum and average reductions obtained by optimization methods in economical, technical and environmental used in the grid-connected DC MG. Table 8: Simulations results obtained by the optimization methodologies in grid-connected DC MG. Minimum objective function Method FixedEcost (USD) VarEcost (USD) Eloss (kWh) Emissions (kgCO2) Base case 7712.3561 6865.0130 1357.8724 9702.2009 PALO 7708.3160 6774.3110 1251.9038 9684.6295 PVSA 7706.7759 6775.6568 1254.0538 9685.1205 PPSO 7708.7433 6775.5870 1255.2538 9685.7857 Mean objective function Method FixedEcost (USD) VarEcost (USD) Eloss (kWh) Emissions (kgCO2) PALO 7708.9983 6775.5008 1256.2415 9685.5077 PVSA 7708.0344 6780.4781 1256.2878 9685.5355 PPSO 7901.0559 7396.6830 1448.4129 9949.9013 Standard deviation [%] Method FixedEcost VarEcost Eloss Emissions PALO 0.3229 1.5115 1.0933 0.1835 PVSA 0.5197 2.0896 3.9290 0.6933 PPSO 6.8675 21.3403 33.8851 10.9089 Average processing time [s] Method FixedEcost VarEcost Eloss Emissions PALO 107.5622 108.4697 107.6267 110.2476 PVSA 82.6331 82.3462 83.1082 87.0673 PPSO 54.3801 50.2689 66.0224 58.6334 the methodologies in relation to the base case are presented in Figure 8. By analyzing this figure, it is possible to calculate an average minimum reduction of FixedEcots of 0.0572%, VarEcost of 1.3085%, Eloss of 7.6690% and Emissions of 0.1754%. By observing the average reductions of the objective functions after 1000 executions of each optimization methodology, it is possible to identify an average reduction of 0.9535%, 3.4266%, 7.2112% and 0.9656% when are analyzed the FixedEcots,VarEcost,Eloss and Emissions in relation to the base case. These results demonstrating that all solutions methodologies used improving the economical, technical and environmental conditions of the grid-connected DC MG, being the PALO the optimization methodology with the best performance from the point of view of the solution. Furthermore, observing the results presented in Table 8 and illustrate in Figure 8, it is possible to observe that the optimization algorithms increase the impact in Ecost when it is considering variable costs. In this way, a reduction of 3.36 USD$ was obtained in an operation day when fixed energy purchasing cost it is considered, while in the case that is used variable energy purchasing cost it is possible to obtain a reduction of the energy purchasing cost of 89.51 USD$, which generates an increase in the reduction of daily energy purchase costs, going from saving in the year of fixed cost 1226.40 USD$ to 32671.15 USD$ in variable cost; by obtaining an annual reduction in energy purchasing cost of 96.24% when a variable cost is considered. This situation shows the importance and need to use variable costs of energy within energy management systems that considering the operation of batteries. On the other hand, for Eloss and Emissions, average daily reductions of 101.63 kW and 16.69 KgCO2are achieved, presenting in an average year of operation around 37.095 GW and 6.093 TonCO2. Demonstrating that using methodologies that promote adequate operation of batteries within an grid-connected DC MG allow to improvement the technical, economical and environmental conditions. Figure 9 illustrates the reductions obtained by the PALO with respect to the other solution methods used. Figure 9(a) presents the average reduction obtained by the PALO in minimum reductions of the objective functions, by obtaining an average reduction of -0.0072%, 0.0193%, 0.2192%, and 0.0085% when it is compared with the PVSA and PPSO, in relation to the FixedEcots,VarEcost,Eloss and Emissions, respectively. Being important highlighting that, although the PALO loses against the PVSA in Fixedcost the difference is minimal, but in Varcost,Eloss and Emissions the PALO obtains better results than the other solution methods employed. This behavior is similar where the average reductions obtained by the optimization methodologies are analyzed, see Figure 9(b), where the PALO obtains an average reduction of 1.2091%, 4.2358%, 6.6357% and 1.3288% when is compared with the PVSA and PPSO in relation to the FixedEcots,VarEcost, Eloss and Emissions, respectively. The last results allow identifying the PALO as the 16 0.02 0.0199 0.1714 0.0051 0.0125 0.0734 0.0037 0.0003 0.0055 0.0188 0.2669 0.0119 2.4308 8.3981 13.2677 2.6572 0.02 0.0125 Fixed Ecost Var Ecost Eloss Emissions Fixed Ecost Var Ecost Eloss Emissions (a) Minimum objective functions reductions (b) Average objective functions reductions 10-2 100 102 Minimum and average reductions in objective functions [%] PVSA PPSO 37.8736 27.6671 72.1733 73.5327 30.1684 31.724 29.5019 26.6234 95.2981 92.9172 96.7372 98.3179 97.7972 115.779 63.0153 88.0285 30.1684 31.724 29.5019 26.6234 97.7972 115.779 63.0153 88.0285 Fixed Ecost Var Ecost Eloss Emissions Fixed Ecost Var Ecost Eloss Emissions (c) STD reductions (d) Time reductions 102 103 Reductions in STD and average time [%] PVSA PPSO Figure 9: Reductions obtained by the PALO with respect to the comparison methods in grid-connected DC MG. best methodology in terms of minimum and average results for improving the technical, economical and environmental conditions of the grid-connected DC MG, by considering fixed and variable energy purchasing cost to the CGs. For the standard deviations, as in the standalone DC MG case, the solution algorithms were executed 1000 times, in order to observe the behavior of the methodologies based in terms of standard deviation, see Figure 9(c). For standard deviation values reported for the FixedEcost,VarEcost,Eloss and Emissions, the PALO obtained a reduction of 66.5859%, 60.2921%, 84.4552% and 86.9253%, respectively, in relation to the PPSO and PVSA, cataloging the PALO to be used in grid-connected DC networks, since it allows obtaining the best results in solution quality with reduced standard deviations in terms of the magnitudes used. Being the PALO the optimization methodology with the best performance in terms of minimum reductions, averages and standard deviations for improving the technical, economical and environmental conditions of standalone and grid-connected DC MGs. Furthermore, it is necessary to determine the average computing processing times required by the proposed methodologies in grid-connected DC MGs, see 9(d), where PALO ranks third, presenting improvements in the average times in FixedEcost of 30.1684%, VarEcost of 31.7240%, Eloss 29.5019% and Emissions of 26.6234%, with respect to the solution times required by the PVSA. The first place is obtained by the PPSO, presenting average reductions in times of 97.7972%, 115.7790%, 63.0153% and 88.0285% respectively to the solutions required by the PALO when it is analyzed the FixedEcost,VarEcost,Eloss and Emissions. Being important to highlight that the average processing times required for the PALO for improving the economical, technical and environmental conditions of the grid is equal to 108.75 seconds, which it is considered a shorter time when it is analyzed the operation of a whole day in an electric system. Furthermore, as in the standalone case, the PPSO is the faster method with the worst result in terms of objective function for the grid-connected DC MG, for which it is considered a not suitable solution for the problem here studied. Through the results analyzed in this document and under consideration of the processing times of the optimization techniques, the methodology with the best performance to solve the problem of optimal operation of batteries in grid-connected DC MGs, by considering energetic and emission data from Colombia, it is the PALO, while for the standalone DC MG is the PVSA. Since, under the results obtained, these methodologies deliver an excellent performance based on the reductions that improve the technical, economical and environmental conditions of the DC grids studied with a reduced processing times. 6. Conclusions and Future Work In this document, three different optimization methodology based on master-slave strategy were proposed by using parallel versions of the PSO, ALO, VSA and a hourly power flow based on successive approximations to solve the problem of energy management of batteries in grid-connected and standalone DC MGs, that considering PV DGs operating in the maximum power point. As objective functions were considered the reduction of the operational costs including fixed and variable energy purchasing cost to the conventional generators located in the network, and the reductions of energy losses and levels of CO2emissions. These scenarios were validated under operation profiles of an average day of typical electricity generation and demand of a standalone DC MG located in Capurgan´ a, Choc´ o, and a grid-connected DC MG located in Medell´ ın, Antioquia; both Colombian regions. All methodologies were validated in the test systems proposed by evaluating each one 1000 times, whit the aim to evaluate the effectiveness in terms of minimum solution, average solution, standard deviation and average processing times. 17 Based on the results obtained for both test scenarios, it was shown that for the standalone DC MG, in terms of reductions in operational costs with fixed energy purchasing costs, reductions of energy losses and reduction of CO2emissions, the solution methodology with the best performance in terms of solution and repeatability was the PVSA, since it obtained the best results in terms of minimum and average solutions after performing 1000 executions. By obtaining standard deviation values lower of 1.12% with reduced processing times (lower than 18.29 seconds on average). For other hand, the PALO obtained the best results for the grid-connected DC MG. By presenting the best results in terms of minimum and average reduction of the objective functions used, with average standard deviation levels of 0.78%, by presenting reduce processing times, lower than 108.75 seconds on average. Based on the simulation results obtained in this work, it is possible to notice that for grid-connected DC MGs it is necessary to consider variable energy purchasing cost, since this allow to reduce the operational cost in comparison to the scenario that using fixed cost in a 96.24%. For which, in the Colombian case, it is necessary to promote laws and regulation that integrating the variable costs in all kind of user: regulate and non regulate. Due to the current regulation only offering this possibility to the non regulate users, that are composing by big commerce and industrial users. Furthermore, this energy regulation must be implemented in the standalone networks with the aim to increase the economical impact of the energy management systems in this kind of electrical networks; by including economical penalties for this type of DC MGs that promoting to use renewable energy resources. As future works of this research, it could be possible to consider new optimization methodologies that allow obtaining better solutions in terms of effectiveness and processing times, that considering the technical, economical and environmental aspects of electrical networks in standalone and grid-connected MGs. Furthermore, inside the mathematical formulation could be to integrate the optimal operation of the PV generators and other renewable energy resources, with the aim to improved the operative conditions of the DC MG. 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