BEOA optimization algorithm-based high-proportion wind and light system energy storage site selection method

Abstract

The invention relates to a BEOA optimization algorithm-based high-proportion wind and light system energy storage site selection method, which comprises the following steps of: constructing a high-proportion wind and light system energy storage site selection optimization model by taking minimization of a multi-objective optimization function consisting of system voltage deviation, active power loss and energy storage system demand capacity as an objective function, and solving through a particle empire optimization algorithm. The particle empire optimization algorithm is used for solving the energy storage site selection optimization model of the high-proportion wind and light system, the energy storage site selection scheme is used as particles in the particle empire optimization algorithm, the excellent particle swarms are ensured to be further optimized through fitness comparison and combination among the particle swarms, the overall optimization efficiency and quality are improved, and meanwhile the convergence characteristic is better. According to the method, multiple optimization targets can be comprehensively considered, balanced optimization among the targets is realized, the energy storage site selection optimization effect is effectively improved, multi-target optimization can be carried out through the particle empire optimization algorithm, and the overall optimization efficiency and quality are effectively improved.

Description

Technical Field

[0001] The present invention relates to a method for selecting an energy storage site for a high-ratio wind-solar system based on a BEOA optimization algorithm, and in particular to a method for selecting an energy storage site for a high-ratio wind-solar system based on a BEOA optimization algorithm. Background Art

[0002] Energy storage systems are crucial in the power distribution network. They are the key to balancing power supply and demand and improving system stability. In the face of load fluctuations and the intermittent nature of renewable energy, energy storage systems can store energy when there is excess power and release energy when demand peaks or renewable energy is insufficient, effectively alleviating grid pressure and improving power supply reliability and the utilization rate of renewable energy. In addition, energy storage systems can also reduce the phenomenon of wind and solar power abandonment caused by load fluctuations and unstable power generation, and optimize the power business environment. In the process of building a new power system, energy storage systems, as flexible regulation resources, have unique advantages in improving system flexibility and ensuring the safety and stability of the power grid, and are a key support for the construction of new power systems.

[0003] The site selection of energy storage in the distribution network power system is directly related to the reliability and stability of power supply. As a flexible regulation resource, the energy storage system can better play its peak and frequency regulation capabilities, improve the flexibility and resilience of the power system, and respond to emergencies and load fluctuations through optimized site selection. In the early stage of load growth, the optimization of energy storage site selection can balance the supply and demand of electricity, reduce the burden on the power grid, delay the upgrade of the power grid, reduce construction costs, and improve service life and economic benefits. Therefore, the optimization of energy storage site selection is an important link to ensure the stable operation of the power system, improve economic benefits, promote the use of renewable energy and enhance the flexibility of the system, and it must be given great attention during the construction of the energy storage system. Traditional energy storage site selection optimization methods mainly include cost analysis method, grid access condition assessment method, and environmental factor consideration method.

[0004] Although these methods can all obtain energy storage site selection, they still have the following defects:

[0005] 1. Cost data in the cost analysis method may be difficult to obtain accurately, especially in the early stages of a project, which may lead to inaccurate site selection decisions.

[0006] 2. The grid access condition assessment method limits the flexibility of site selection.

[0007] 3. Environmental factors consideration Environmental assessment may be affected by data availability and the subjectivity of the assessment method.

[0008] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of the application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0009] The purpose of the present invention is to overcome the shortcomings of the prior art that both accuracy and flexibility cannot be met at the same time, and to provide a high-ratio wind-solar system energy storage site selection method based on the BEOA optimization algorithm that can meet both accuracy and flexibility.

[0010] To achieve the above objectives, the technical solution of the present invention is:

[0011] In a first aspect, the present invention proposes a method for selecting a high-ratio wind-solar system energy storage site based on a BEOA optimization algorithm, comprising:

[0012] The optimization method comprises:

[0013] S1. Construct a high-ratio wind-solar system energy storage site selection model, which aims to minimize the multi-objective optimization function consisting of system voltage deviation, active network loss and energy storage system demand capacity, and considers the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network;

[0014] S2. Solve the energy storage site selection model for high-ratio wind-solar systems, establish the BEOA optimization algorithm through the objective function and constraints set in S1, and obtain the optimal energy storage site selection plan.

[0015] The high-ratio wind-solar system energy storage site selection model includes:

[0016] minF = {f1,f2,f3};

[0017]

[0018] In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

[0019] The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints;

[0020] The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes:

[0021]

[0022] In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i;

[0023] The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes:

[0024] V min ≤V ik ≤V max ;

[0025] In the above formula, V ik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively;

[0026] The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include:

[0027]

[0028] In the above formula, is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

[0029] The feasibility constraints include state of charge constraints and charge and discharge power constraints;

[0030] The state of charge constraints include:

[0031]

[0032] In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS respectively;

[0033] The charge and discharge power constraints include:

[0034]

[0035] The S2 includes:

[0036] S2.1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best.

[0037] S2.2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated.

[0038] S2.3, set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, the competition begins. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows:

[0039]

[0040] In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function;

[0041] The position update formula after the clusters are competitively merged is:

[0042] x new =x old +f rand ×(F upper -F lower );

[0043] In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively;

[0044] S2.4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. According to the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows:

[0045] x i+1 =x i +s×d dir ×f sign (F right -F left );

[0046] In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction;

[0047] S2.5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship.best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection plan.

[0048] In a second aspect, the present invention proposes a high-ratio wind-solar system energy storage site selection system based on a BEOA optimization algorithm, the system comprising a model building module and a model solving module;

[0049] The model building module is used to build a high-proportion wind-solar system energy storage site selection model with the minimization of a multi-objective optimization function consisting of system voltage deviation, active network loss and energy storage system required capacity as the objective function, and consider the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network;

[0050] The model solving module is used to solve the energy storage site selection model of a high-ratio wind-solar system, and establish a BEOA optimization algorithm through the objective function and constraint conditions set in the model building module to obtain the optimal energy storage site selection plan.

[0051] The high-ratio wind-solar system energy storage site selection model includes:

[0052] minF = {f1,f2,f3};

[0053]

[0054] In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

[0055] The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints;

[0056] The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes:

[0057]

[0058] In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i;

[0059] The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes:

[0060] V min ≤V ik ≤V max ;

[0061] In the above formula, V ik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively;

[0062] The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include:

[0063]

[0064] In the above formula, is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

[0065] The feasibility constraints include state of charge constraints and charge and discharge power constraints;

[0066] The state of charge constraints include:

[0067]

[0068] In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS respectively;

[0069] The charge and discharge power constraints include:

[0070]

[0071] The solution process of the model solution module includes:

[0072] S2.1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best.

[0073] S2.2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated.

[0074] S2.3, set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, the competition begins. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows:

[0075]

[0076] In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function;

[0077] The position update formula after the clusters are competitively merged is:

[0078] x new =x old +f rand ×(F upper -F lower );

[0079] In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively;

[0080] S2.4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. According to the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows:

[0081] x i+1 =x i +s×d dir ×f sign (F right -F left );

[0082] In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction;

[0083] S2.5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship.best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection plan.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] 1. In the method for selecting energy storage sites for high-ratio wind-solar systems based on the BEOA optimization algorithm, a high-ratio wind-solar system energy storage site selection optimization model is constructed with the multi-objective optimization function minimization consisting of system voltage deviation, active network loss and energy storage system demand capacity as the objective function, and solved by the BEOA optimization algorithm. The model and algorithm comprehensively consider multiple optimization objectives to achieve balanced optimization between objectives. Therefore, this design can comprehensively consider multiple optimization objectives, achieve balanced optimization between objectives, and effectively improve the optimization effect of energy storage site selection.

[0086] 2. In the high-ratio wind-solar system energy storage site selection method based on the BEOA optimization algorithm of the present invention, the high-ratio wind-solar system energy storage site selection optimization model is solved by the BEOA optimization algorithm. The energy storage site selection scheme is used as a particle in the BEOA optimization algorithm. By comparing and merging the fitness between particle groups, it is ensured that the excellent particle group is further optimized, the overall optimization efficiency and quality are improved, and the convergence characteristics are better. Therefore, this design can perform multi-objective optimization through the BEOA optimization algorithm, effectively improving the overall optimization efficiency and quality.

[0087] 3. In the high-ratio wind-solar system energy storage site selection method based on the BEOA optimization algorithm of the present invention, the multi-objective functions of system voltage deviation, active network loss and energy storage system demand capacity are combined into a comprehensive goal, and the constraints such as system power balance, node voltage, and energy storage operation are incorporated. At the same time, by tuning the algorithm parameters and improving the cluster competition and merging mechanism, the algorithm's search ability and convergence speed are significantly enhanced. Therefore, this design can effectively improve the optimization effect and overall optimization efficiency by setting a comprehensive goal and improving the cluster competition algorithm at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a flow chart of the method of the present invention.

[0089] Figure 2 It is a structural diagram of the system described in the present invention.

[0090] Figure 3 The schematic diagram of the operation of the method of the present invention is shown in FIG.

[0091] Figure 4 This is a flow chart of the energy storage site selection optimization model for a high-ratio wind-solar system in the present invention.

[0092] Figure 5 This is a structural diagram of the IEEE-33 node power distribution system in Example 1 of the present invention.

[0093] Figure 6 This is a system voltage deviation convergence curve diagram in Example 1 of the present invention.

[0094] Figure 7 This is a daily active network loss convergence curve diagram in Example 1 of the present invention.

[0095] Figure 8 It is a schematic diagram of the equipment structure in Example 3. DETAILED DESCRIPTION

[0096] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0097] Embodiment 1:

[0098] See also Figure 1 , Figure 3 and Figure 4 , a high-ratio wind-solar system energy storage site selection method based on BEOA optimization algorithm, the optimization method comprising:

[0099] S1. Construct a high-ratio wind-solar system energy storage site selection model, which aims to minimize the multi-objective optimization function consisting of system voltage deviation, active network loss and energy storage system demand capacity, and considers the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network;

[0100] S2. Solve the energy storage site selection model for high-ratio wind-solar systems, establish the BEOA optimization algorithm through the objective function and constraints set in S1, and obtain the optimal energy storage site selection plan.

[0101] The high-ratio wind-solar system energy storage site selection model includes:

[0102] minF = {f1,f2,f3};

[0103]

[0104]

[0105] In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

[0106] The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints;

[0107] The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes:

[0108]

[0109] In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i;

[0110] The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes:

[0111] V min ≤V ik ≤V max ;

[0112] In the above formula, Vik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively;

[0113] The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include:

[0114]

[0115] In the above formula, is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

[0116] The feasibility constraints include state of charge constraints and charge and discharge power constraints;

[0117] The state of charge constraints include:

[0118]

[0119] In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS respectively;

[0120] The charge and discharge power constraints include:

[0121]

[0122] The S2 includes:

[0123] S2.1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best.

[0124] S2.2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated.

[0125] S2.3, set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, the competition begins. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows:

[0126]

[0127] In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function;

[0128] The position update formula after the clusters are competitively merged is:

[0129] x new =x old +f rand ×(F upper -F lower );

[0130] In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively;

[0131] S2.4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. According to the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows:

[0132] x i+1 =x i +s×d dir ×f sign (F right -F left );

[0133] In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction;

[0134] S2.5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship. best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection scheme;

[0135] See also Figures 1 to 7 , a distribution system model was established in the simulation software, and typical wind power and load data were combined for simulation. The energy storage optimization configuration model under different algorithms was simulated and analyzed and the results were compared. The steps include:

[0136] The IEEE-33 node distribution network system is selected as an example to simulate and analyze the energy storage optimization configuration model under different algorithms and compare the results. Figure 5The system voltage level of the simulation example is 10kV, the per unit value is 1.0pu, and when no other loads are initially connected, the active load is 3.715MW and the reactive load is 2.3Mvar. The simulation process is calculated according to the following steps:

[0137] (1) Collect data such as system node voltage, load, wind power and photovoltaic output power, and perform necessary preprocessing.

[0138] (2) Initialize the BEOA optimization algorithm and other algorithms according to the set initial conditions and algorithm parameters.

[0139] (3) In each iterative step, the objective function value is calculated based on the selected key indicators (system voltage deviation, active network loss, and energy storage system rated capacity).

[0140] (4) Ensure that the optimal energy storage site selection plan meets the constraints of system power balance, node voltage, energy storage operation, charge state, and charge and discharge power.

[0141] (5) Update the particle position according to the algorithm strategy and calculate the new fitness value.

[0142] (6) Check whether the number of iterations reaches the maximum or whether the fitness value meets the convergence condition. If so, stop the iteration.

[0143] (7) Output the optimal energy storage site selection plan and the corresponding objective function value.

[0144] The simulation models under the BEOA optimization algorithm and the comparison algorithm are run independently. The comparison algorithm selects the genetic algorithm (GA) to analyze the system voltage deviation and active network loss, two objective functions that measure the safe and stable operation of the distribution network system. The corresponding objective function values ​​of the two algorithms are shown in the following table:

[0145] Table 1. Comparison of objective function values ​​under different algorithms

[0146]

[0147] The comparison of the objective function convergence curves of BEOA optimization algorithm and genetic algorithm is shown in the figure below: Figure 6 , Figure 7 As shown in the results, it can be seen that the BEOA algorithm has higher search accuracy than the genetic algorithm, the two indicators solved are smaller, and the convergence characteristics are better, making it easier to find the optimal solution to the energy storage optimization configuration problem.

[0148] Embodiment 2:

[0149] See also Figure 2 , a high-ratio wind-solar system energy storage site selection system based on BEOA optimization algorithm, the system comprising a model building module and a model solving module;

[0150] The model building module is used to build a high-proportion wind-solar system energy storage site selection model with the minimization of a multi-objective optimization function consisting of system voltage deviation, active network loss and energy storage system required capacity as the objective function, and consider the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network;

[0151] The model solving module is used to solve the energy storage site selection model of a high-ratio wind-solar system, and establish a BEOA optimization algorithm through the objective function and constraint conditions set in the model building module to obtain the optimal energy storage site selection plan.

[0152] The high-ratio wind-solar system energy storage site selection model includes:

[0153] minF = {f1,f2,f3};

[0154]

[0155] In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

[0156] The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints;

[0157] The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes:

[0158]

[0159] In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i;

[0160] The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes:

[0161] V min ≤V ik ≤V max ;

[0162] In the above formula, V ik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively;

[0163] The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include:

[0164]

[0165] In the above formula, is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

[0166] The feasibility constraints include state of charge constraints and charge and discharge power constraints;

[0167] The state of charge constraints include:

[0168]

[0169] In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS respectively;

[0170] The charge and discharge power constraints include:

[0171]

[0172] The solution process of the model solution module includes:

[0173] S2.1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best.

[0174] S2.2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated.

[0175] S2.3, set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, the competition begins. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows:

[0176]

[0177] In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function;

[0178] The position update formula after the clusters are competitively merged is:

[0179] x new =x old +f rand ×(F upper -F lower );

[0180] In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively;

[0181] S2.4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. According to the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows:

[0182] x i+1 =x i +s×d dir ×f sign (F right -F left );

[0183] In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction;

[0184] S2.5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship. best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection plan.

[0185] Embodiment 3:

[0186] A high-ratio wind-solar system energy storage site selection device based on a BEOA optimization algorithm, the device comprising a processor and a memory;

[0187] The memory is used to store computer program code and transmit the computer program code to the processor;

[0188] The processor is used to execute the high-ratio wind-solar system energy storage site selection method based on the BEOA optimization algorithm described in Example 1 according to the instructions in the computer program code.

[0189] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for selecting a site for energy storage in a high-ratio wind-solar system based on a BEOA optimization algorithm as described in Example 1.

[0190] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.

Claims

1. A method for selecting a high-ratio wind-solar system energy storage site based on a BEOA optimization algorithm, characterized in that: The optimization method comprises: S1. Construct a high-ratio wind-solar system energy storage site selection model, which aims to minimize the multi-objective optimization function consisting of system voltage deviation, active network loss and energy storage system demand capacity, and considers the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network; S2. Solve the energy storage site selection model for high-ratio wind-solar systems, establish the BEOA optimization algorithm through the objective function and constraints set in S1, and obtain the optimal energy storage site selection plan.

2. According to claim 1, a method for selecting a high-ratio wind-solar system energy storage site based on a BEOA optimization algorithm, characterized in that: The high-ratio wind-solar system energy storage site selection model includes: minF = {f1,f2,f3}; In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

3. The method for selecting a site for high-ratio wind-solar system energy storage based on BEOA optimization algorithm according to claim 2, characterized in that: The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints; The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes: In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i; The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes: In min ≤V ik ≤V max ; In the above formula, V ik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively; The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include: In the above formula, P c BESS (t) is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

4. The method for selecting a site for high-ratio wind-solar system energy storage based on BEOA optimization algorithm according to claim 2, characterized in that: The feasibility constraints include state of charge constraints and charge and discharge power constraints; The state of charge constraints include: In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS, respectively; The charge and discharge power constraints include:

5. A method for selecting a site for high-ratio wind-solar system energy storage based on BEOA optimization algorithm according to any one of claims 1 to 4, characterized in that: The S2 includes: S2.

1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best. S2.

2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated. S2.3, set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, the competition begins. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows: In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function; The position update formula after the clusters are competitively merged is: x new =x old +f rand ×(F upper -F lower ); In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively; S2.

4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. Based on the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows: x i+1 =x i +s×d dir ×f sign (F right -F left ); In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction; S2.

5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship. best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection plan.

6. A high-ratio wind-solar system energy storage site selection system based on BEOA optimization algorithm, characterized by: The system includes a model building module and a model solving module; The model building module is used to build a high-ratio wind-solar system energy storage site selection model with the minimization of a multi-objective optimization function consisting of system voltage deviation, daily active network loss and energy storage system demand capacity as the objective function, and consider the safety constraints and feasibility constraints of the energy storage optimization site selection scheme in the actual distribution network; The model solving module is used to solve the energy storage site selection model of a high-ratio wind-solar system, and establish a BEOA optimization algorithm through the objective function and constraint conditions set in the model building module to obtain the optimal energy storage site selection plan.

7. The battery replacement optimization configuration and guidance system considering the automatic driving of electric vehicles according to claim 6 is characterized by: The high-ratio wind-solar system energy storage site selection model includes: minF = {f1,f2,f3}; In the above formula, f1 is the sum of the squares of the voltage deviations of all nodes in the system; f2 is the total active network loss of the distribution network in a dispatching cycle; f3 is the required capacity of the energy storage system, which is the maximum charge and discharge energy value in a dispatching cycle; V b is the actual voltage value at the end of branch b; V N is the rated voltage at the end of the line; P b,t With Q b,t are respectively the active load and reactive load at the end of branch b at time t; V b,t is the voltage at the end of branch b at time t; R b is the impedance of branch b; m is the scheduling period, n is the number of branches; N BESS is the total number of BESSs allowed to access the system; t0 is the initial time of operation; t0+nΔt is n charging / discharging periods; is the charging / discharging power of the BESS connected to node i at time t; Δt is the duration of BESS charging / discharging.

8. The battery replacement optimization configuration and guidance system considering the automatic driving of electric vehicles according to claim 7 is characterized in that: The safety constraints include system power balance constraints, node voltage constraints and energy storage operation constraints; The system power balance constraint is used to ensure that the power injection and power outflow of each node in the distribution network are balanced. The system power balance constraint includes: In the above formula, are the active power and reactive power input by DWG at node i at time t respectively; is the charging / discharging power value of the BESS configured at node i at time t; are the active load and reactive load of node i at time t respectively; U i,t , U j,t are the actual voltage values ​​of nodes i and j at time t; G i,j , B i,j are the real and imaginary parts of the mutual admittance between nodes i and j respectively; δ ij,t is the phase angle difference between nodes i and j at time t; N i is the number of nodes connected to node i; The node voltage constraint is used to keep the node voltage within a certain allowable range to ensure the safe and stable operation of the power grid. The node voltage constraint includes: In min ≤V ik ≤V max ; In the above formula, V ik is the actual voltage amplitude of node i at time k; V min 、V max are the lower and upper limits of the actual node voltage amplitude of the system respectively; The energy storage operation constraints are used to limit the charging and discharging power of the energy storage system within a certain limit range to prevent equipment damage and ensure the stable operation of the power grid. The energy storage operation constraints include: In the above formula, P c BESS (t) is the charge / discharge power of the cth BESS at time t; are the upper and lower limits of the charging / discharging power of the cth BESS respectively; is the remaining capacity of the cth BESS at time t; η ch , η dis are BESS charging and discharging efficiency respectively.

9. The battery replacement optimization configuration and guidance system considering automatic driving of electric vehicles according to claim 8, characterized in that: The feasibility constraints include state of charge constraints and charge and discharge power constraints; The state of charge constraints include: In the above formula, is the charge state of the cth BESS at time t; are the upper and lower limits of the state of charge of the cth BESS, respectively; The charge and discharge power constraints include:

10. The battery replacement optimization configuration and guidance system considering automatic driving of electric vehicles according to claim 9, characterized in that: The solution process of the model solution module includes: S2.

1. Initialize the particle swarm. Set the particle position, particle velocity and population size in the particle swarm. The particle position is a multidimensional vector. Each dimension of the multidimensional vector represents the node number that an energy storage system may be connected to in the distribution network. The particle velocity represents the direction and step length of the particle moving in the search space. The population size is used to clarify the solution space range of the problem. The population size includes the possible locations of the energy storage site selection and the upper and lower limits of the fixed capacity. Each particle represents a scheme for energy storage site selection. The particle swarm is divided into several clusters, and a part of the better particles are selected as the leaders of the clusters. For each particle, the fitness value is calculated using the collected data and the defined objective function. The smaller the fitness value, the better the particle. The better particle is to arrange all particles in order from small to large in fitness value, take the set of particles with the proportion set before, set the individual best Pbest and the global best Gbest. For each particle, record the best position encountered during the iteration, that is, the position corresponding to the minimum fitness value as the individual best of the particle. Among the individual best of all particles, select the position with the smallest fitness value as the global best. S2.

2. Use the collected data and the defined objective function to calculate the objective function value of each particle in the particle swarm. For each particle, calculate the fitness value according to its objective function value and assign the fitness value to the particle. During the algorithm iteration process, all particles are compared and sorted according to the fitness value. Particles with smaller fitness values ​​are considered better, and the individual optimum and global optimum are updated. S2.

3. Set the relevant parameters of BEOA optimization for each particle, including the step factor, the number of search directions, and the search range. According to the fitness value of the leader of each cluster, evaluate and sort all clusters. According to the overall fitness value, let the clusters compete. Each cluster searches. When the clusters come into contact, they start competing. The winning cluster will have the opportunity to expand its territory and attract particles from the losing cluster to ensure that the better cluster has more resources for further search and optimization. The cluster fitness calculation formula is as follows: In the above formula, Nemp is the total number of clusters; F(xi) is the fitness function; The position update formula after the clusters are competitively merged is: x new =x old +f rand ×(F upper -F lower ); In the above formula, f rand is a random number function; F upper and F lower They are the upper and lower bounds of the search space respectively; S2.

4. Calculate the left and right fitness values ​​of the particles. For each particle direction, calculate the fitness value of the new position in that direction. Based on the selected optimal direction, calculate and update the particle position variable x. i and the particle velocity variable v i , in order to increase the diversity of the search and approach the optimum, the particle position update formula is as follows: x i+1 =x i +s×d dir ×f sign (F right -F left ); In the above formula, F right and F left are the left and right fitness functions of the particle respectively; x i represents the spatial coordinates of the particle mass center; s is the step length; f sign is the symbol function; d dir is the search direction; S2.

5. After updating the particle position, re-evaluate the particle fitness and update the particle P according to the dominance relationship. best With G best , select the global optimal solution G of the population by sorting by crowding distance best , and judge whether the iteration termination condition is met. The iteration termination condition is that in multiple consecutive iterations, the change value of the objective function value of the global optimal solution is lower than the set value or the number of iterations reaches the maximum. When the iteration termination condition is not met, S2.2 to S2.4 are repeated. When the iteration termination condition is met, the position with the smallest fitness value is selected as the global optimal G best The output is the optimal particle position, i.e., the optimal energy storage site selection plan.

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