Locating and sizing method and system for battery energy storage system of power distribution network

Abstract

The invention discloses a power distribution network battery energy storage system locating and sizing method and system, and relates to the technical field of power system planning and operation, and the method comprises the steps: carrying out the preprocessing and chaotic mapping initialization through the multi-dimensional data of a power distribution network battery energy storage system, and obtaining an initial population; based on the initial population, using a mixed integer linear programming model and an improved dual adaptive evolution reverse learning Pedal optimization algorithm to perform dual-stage optimization, and obtaining a battery energy storage system site selection and constant volume scheme; and verification and evaluation are carried out according to the battery energy storage system site selection and sizing scheme, and a power distribution network battery energy storage system site selection and sizing result is obtained. According to the method, the global optimization capacity of battery energy storage configuration is remarkably improved while the calculation efficiency is guaranteed, the voltage quality improvement level is effectively improved, the line loss is reduced, and the safety, stability and economical efficiency of a power distribution network under the high-proportion distributed photovoltaic access condition can be better supported.

Description

Technical Field

[0001] This invention relates to the field of power system planning and operation technology, and in particular to a method and system for site selection and capacity determination of a battery energy storage system for a distribution network. Background Technology

[0002] Renewable energy sources (such as photovoltaics and wind power) are increasingly used in new power systems due to their significant environmental benefits. However, their intermittent nature can lead to power output fluctuations, potentially causing issues such as voltage spikes and bidirectional power flow in the distribution network. Battery energy storage systems (BESS), with their flexible charge and discharge control capabilities, can manage and smooth out these fluctuations, improve voltage distribution, and reduce network losses. However, BESS has high investment costs, and its effectiveness is highly dependent on its installation location in the grid, its capacity, and its daily charge and discharge strategies. Therefore, optimal site selection and capacity determination for BESS are crucial for maximizing its techno-economic benefits.

[0003] Meanwhile, existing research focuses only on a single optimization objective or static configuration strategy, ignoring the impact of dynamic charging and discharging strategies on real-time power grid operation. Furthermore, when dealing with high-dimensional, complex, nonlinear, large-scale distribution network optimization problems, traditional precise algorithms based on mathematical programming and metaheuristic algorithms based on biomimetic intelligence are prone to getting trapped in local optima, leading to premature convergence of the algorithms.

[0004] Therefore, there is an urgent need for a method and system for site selection and capacity determination of battery energy storage systems in power distribution networks to address the shortcomings of existing technologies. Summary of the Invention

[0005] The purpose of this invention is to propose a method and system for site selection and capacity determination of battery energy storage systems in power distribution networks, so as to overcome the technical defects of traditional Gazelle Optimization (MGO) algorithm, which is prone to getting trapped in local optima and premature convergence when dealing with high-dimensional problems.

[0006] On the one hand, to achieve the above objectives, the present invention provides a method for site selection and capacity determination of a distribution network battery energy storage system, comprising:

[0007] S1. Use multi-dimensional data from the distribution network battery energy storage system for preprocessing and chaotic mapping initialization to obtain the initial population;

[0008] S2. Based on the initial population, a two-stage optimization is performed using a mixed integer linear programming model and an improved dual adaptive evolutionary back-learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme.

[0009] S3. Verify and evaluate the battery energy storage system location and capacity determination scheme to obtain the location and capacity determination results of the distribution network battery energy storage system.

[0010] Optionally, S1, preprocess and initialize the chaotic mapping using multi-dimensional data from the distribution network battery energy storage system to obtain an initial population, including:

[0011] Collect multi-dimensional data from the battery energy storage system of the power distribution network;

[0012] The multi-dimensional data of the power distribution network battery energy storage system is purified to obtain purified multi-dimensional data.

[0013] The purified multi-dimensional data is mapped using a normalization method to obtain standardized multi-dimensional data.

[0014] Feature extraction is performed based on the standardized multi-dimensional data to obtain the core features of the distribution network battery energy storage system configuration.

[0015] Chaotic mapping initialization is performed based on the core features of the power distribution network battery energy storage system configuration to obtain the initial population.

[0016] Optionally, based on the core features of the distribution network battery energy storage system configuration, chaotic mapping initialization is performed to obtain an initial population, including:

[0017] The chaotic sequence is obtained by using the Logistic chaotic mapping.

[0018] Based on the core characteristics of the configuration of the distribution network battery energy storage system, the search space of decision variables is obtained, including the installation location of the battery energy storage system and the rated capacity / power of the BESS.

[0019] The chaotic sequence is mapped to the search space of the decision variables, and an initial value is assigned to each individual in the population to obtain the initial population.

[0020] Optionally, S2, based on the initial population, a two-stage optimization is performed using a mixed-integer linear programming model and an improved dual adaptive evolutionary back-learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme, including:

[0021] Based on the initial population and the constraints of the mixed-integer linear programming model, a mixed-integer linear programming model is constructed.

[0022] Solve the mixed-integer linear programming model to obtain the initial installation location set and initial capacity configuration scheme of the battery energy storage system;

[0023] Based on the initial installation location set and initial capacity configuration scheme of the battery energy storage system, an improved dual adaptive evolutionary back-learning gazelle optimization algorithm is used to obtain the battery energy storage system site selection and capacity determination scheme.

[0024] Optionally, the constraints of the mixed-integer linear programming model are:

[0025]

[0026] Among them, P Subs,t Let N be the active power of the substation during time period t, and P be the number of loads. Load,i,t Let N be the active power of the load at node i during time period t. PV P represents the number of photovoltaic power plants. PV,i,t Let N be the active power of the photovoltaic power station at node i during time period t. RES P represents the amount of energy stored in the battery. BES,i,t Let P be the active power of battery storage at node i during time period t. loss,t R is the active power loss during time period t. Subs,t R represents the reactive power of the substation during time period t. Load,i,t R represents the load reactive power of node i during time period t. PV,i,t Let R be the reactive power of the photovoltaic power station at node i during time period t. BES,i,t Let R be the reactive power of battery storage at node i during time period t. loss,t V represents the reactive power loss during time period t. min V is the minimum allowable node voltage. i,t Let V be the node voltage of node i during time period t. max Where B is the maximum allowable node voltage, and I is the number of nodes in the system. i,t Let I be the current of the i-th line at time t. max H represents the maximum allowable line current, and H is the number of lines in the system.

[0027] Optionally, based on the initial installation location set and initial capacity configuration scheme of the battery energy storage system, an improved dual adaptive evolutionary back-learning gazelle optimization algorithm is used to obtain a battery energy storage system site selection and capacity determination scheme, including:

[0028] The initial installation location set and initial capacity configuration scheme of the battery energy storage system are obtained as the initial population of the improved dual adaptive evolutionary reverse learning gazelle optimization algorithm.

[0029] The mathematical model of gazelle social behavior is used to update the position of each individual in the initial population of the improved dual adaptive evolutionary back-learning gazelle optimization algorithm using the standard gazelle optimization algorithm, thereby obtaining the population updated by the standard gazelle optimization algorithm. The mathematical model of gazelle social behavior includes mathematical models of territorial solitary male behavior, matrilineal group behavior, single male group behavior, and migratory foraging behavior.

[0030] The inverse solution is obtained by performing a reverse learning operation based on a dual adaptive evolution strategy on the population updated by the standard gazelle optimization algorithm.

[0031] The inverse solution is used for elite selection and population update to obtain the site selection and capacity determination scheme for the battery energy storage system.

[0032] Optionally, the reverse solution is obtained by performing a reverse learning operation based on a dual adaptive evolution strategy on the population updated according to the standard gazelle optimization algorithm, including:

[0033] Based on the population update using the standard gazelle optimization algorithm, and combined with the population's iterative process, an adaptive jump probability is obtained.

[0034] Using the adaptive jump probability, the population individuals that perform the reverse operation are obtained;

[0035] The inverse solution is obtained by combining the population individuals that perform the inverse operation with the dynamic search boundary.

[0036] Optionally, the inverse solution is used for elite selection and population update to obtain a battery energy storage system site selection and capacity determination scheme, including:

[0037] The fitness variance of the current population is obtained as a quantitative detection index by calculating the fitness degree of the population updated based on the standard gazelle optimization algorithm and the reverse solution.

[0038] If the quantitative detection index is lower than the quantitative detection index threshold, the globally optimal individual is retained, and chaotic restart and directed Gaussian mutation are performed on the remaining individuals. The population is reshaped and updated by combining the optimal solution of the reverse solution to obtain the target population. Otherwise, the fitness values ​​of the population updated by the standard gazelle optimization algorithm and the reverse solution are compared. The optimal solution that satisfies the constraints is retained, the population is updated, and the target population is obtained.

[0039] The target population is used to check whether the stopping criterion has been met. If so, the battery energy storage system site selection and capacity determination scheme is obtained based on the target population. Otherwise, the operation is returned to the first operation.

[0040] The first operation is as follows: based on the mathematical model of gazelle social behavior, the position of each individual in the initial population of the improved dual adaptive evolutionary back-learning gazelle optimization algorithm is updated using the standard gazelle optimization algorithm to obtain the population updated by the standard gazelle optimization algorithm.

[0041] Optionally, S3, verify and evaluate the battery energy storage system location and capacity determination scheme to obtain the location and capacity determination results of the distribution network battery energy storage system, including:

[0042] Based on the battery energy storage system location and capacity setting scheme, load the energy storage configuration scheme parameters and construct a time-series power flow simulation model;

[0043] Based on the time-series power flow simulation model, the time-series power flow simulation results are obtained by performing time-series power flow simulation on the battery energy storage system's location and capacity setting scheme.

[0044] Using the aforementioned time-series power flow simulation results, key evaluation indicators are obtained;

[0045] Determine whether the key evaluation indicators meet the preset optimization stopping criteria. If yes, obtain the site selection and capacity determination results of the distribution network battery energy storage system; otherwise, return to step S2.

[0046] On the other hand, to achieve the above objectives, the present invention provides a distribution network battery energy storage system location and capacity determination system, including: a preprocessing module, an intelligent optimization module and a verification and evaluation module;

[0047] The preprocessing module is used to preprocess and initialize chaotic mapping using multi-dimensional data from the distribution network battery energy storage system to obtain an initial population.

[0048] The intelligent optimization module is used to perform two-stage optimization based on the initial population using a mixed integer linear programming model and an improved dual adaptive evolutionary back learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme.

[0049] The verification and evaluation module is used to perform verification and evaluation based on the battery energy storage system location and capacity determination scheme, and obtain the location and capacity determination results of the distribution network battery energy storage system.

[0050] Compared with the closest existing technology, the present invention has the following advantages:

[0051] This invention deeply integrates deterministic mathematical programming with an adaptively reinforced metaheuristic algorithm, achieving rapid acquisition of high-quality initial solutions and efficient approximation of the global optimum. The improved DA-EOBMGO algorithm, through the synergistic effect of adaptive jump probabilities, dynamic search boundaries, and evolutionary back-learning mechanisms, significantly enhances population diversity and the algorithm's ability to escape local optima, while effectively suppressing premature convergence. Combined with time-series power flow verification, it achieves coordinated optimization of site selection, capacity determination, and grid operation feasibility. Compared with traditional single optimization methods, this invention significantly improves the global optimization capability of battery energy storage configuration while ensuring computational efficiency, effectively enhancing voltage quality and reducing line losses, thus better supporting the safety, stability, and economy of distribution networks under conditions of high-proportion distributed photovoltaic access. Attached Figure Description

[0052] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0053] Figure 1 This is a flowchart illustrating a method for site selection and capacity determination of a battery energy storage system in a power distribution network, according to an embodiment of the present invention.

[0054] Figure 2 This is a flowchart of the overall process of the improved evolutionary backward learning gazelle optimization algorithm based on a dual adaptive hybrid strategy proposed in this embodiment of the invention.

[0055] Figure 3 This is a flowchart of the evolutionary reverse learning operation based on a dual adaptive hybrid strategy proposed in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of the structure of a distribution network battery energy storage system location and capacity determination system according to an embodiment of the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0058] The terminology used in the embodiments section of this invention is for the purpose of explaining specific embodiments of the invention only, and is not intended to limit the invention.

[0059] The core of this invention is a two-stage optimization framework that deeply integrates a deterministic mixed-integer linear programming (MILP) model capable of rapidly obtaining high-quality feasible solutions with an improved evolutionary inverse learning mountain gazelle optimization algorithm based on a dual adaptive hybrid strategy. This achieves optimization throughout the entire process, from "rapid coarse screening" to "precise optimization." Specifically, in the initial stage, the aim is to quickly obtain a high-quality initial feasible solution using the MILP model. In the secondary stage, the solution obtained by MILP is used as the initial population or an important component of the improved dual adaptive evolutionary inverse learning mountain gazelle optimization algorithm (DA-EOBMGO), and a dual adaptive evolutionary inverse learning operation is performed to dynamically generate and evaluate inverse solutions, enabling the algorithm to effectively escape local optima. In the secondary optimization stage, the DA-EOBMGO algorithm is introduced. By embedding an evolutionary back-learning mechanism into the Mountain Gazelle Optimization (MGO) algorithm, the global search capability and efficiency in escaping local extrema are fundamentally enhanced. The dual adaptive hybrid strategy is manifested in adaptive jump probability and dynamic search boundary. These two mechanisms are dynamically adjusted according to the iteration process, enabling the algorithm to autonomously adapt to the search state. This invention aims to improve the voltage level of the distribution network, reduce system network losses, and enhance the grid's capacity to absorb renewable energy.

[0060] like Figure 1 As shown, this embodiment of the invention provides a method for site selection and capacity determination of a distribution network battery energy storage system, including:

[0061] S1. Use multi-dimensional data from the distribution network battery energy storage system for preprocessing and chaotic mapping initialization to obtain the initial population;

[0062] The system collects multi-dimensional data such as distribution network topology parameters, load, and photovoltaic output. After cleaning processes such as outlier removal, missing value completion, and normalization, core features such as voltage sensitivity and key nodes are extracted. Then, a chaotic sequence with ergodicity and pseudo-randomness is generated using Logistic chaotic mapping. This sequence is mapped to the search space of BESS installation location and capacity / power. Combined with preset population parameters, an initial population with uniform distribution and sufficient diversity is generated, laying the foundation for subsequent optimization.

[0063] S2. Based on the initial population, a two-stage optimization is performed using a mixed integer linear programming model and an improved dual adaptive evolutionary back-learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme.

[0064] Starting with the initial population, a two-stage optimization is initiated: In the first stage, a MILP model is constructed with the goal of minimizing voltage deviation and active power loss, incorporating power balance, voltage, and line current constraints, and a high-quality initial configuration scheme is quickly output through the GUROBI solver; In the second stage, this scheme is used as the initial population for the DA-EOBMGO algorithm, and standard MGO behavior updates, dual adaptive back learning (dynamic jump probability + dynamic search boundary), and elite selection are iteratively executed. At the same time, premature convergence is detected through fitness variance and elite retention, chaotic restart, and Gaussian mutation are executed. After the termination condition is met, a series of battery energy storage system configuration schemes are output.

[0065] S3. Verify and evaluate the battery energy storage system location and capacity determination scheme to obtain the location and capacity determination results of the distribution network battery energy storage system.

[0066] Using tools such as OpenDSS, load and photovoltaic forecast data and charge / discharge curves of configuration schemes are loaded to conduct time-series power flow simulation; constraints such as node voltage, line current carrying capacity, and BESS operating status are verified to evaluate the network loss improvement and renewable energy consumption effect; finally, the scheme with the best fitness and that meets all constraints is selected, and the final site selection and capacity determination results including installation nodes, rated capacity and power, and operating strategies are output to ensure the safe, stable and economical operation of the distribution network.

[0067] like Figure 2 As shown, the flowchart fully presents the core operation process of BESS (Best Safe Energy System) location and capacity optimization in a distribution network: Starting from "Start," the optimization foundation is first laid through diversified population initialization based on chaotic mapping. Then, a primary optimization model (MILP) and a secondary optimization model based on the improved DA-EOBMGO algorithm are constructed simultaneously. The process sequentially executes MGO standard behavior updates, reverse learning operations using a dual adaptive evolution strategy, elite selection, and population updates. Finally, the feasibility of the current configuration scheme is verified through time-series power flow simulation. If the termination condition is not met after verification, the process returns to rebuilding the primary optimization model and enters a loop iteration. If the termination condition is met, the optimal BESS location and capacity scheme is output, and the process ends. This flowchart clearly demonstrates the closed-loop logic of "dual-model optimization - algorithm iteration - simulation verification - loop tuning," ensuring the accuracy and feasibility of the configuration scheme.

[0068] In summary, this invention constructs a two-stage optimization framework consisting of MILP and DA-EOBMGO. The first stage utilizes the MILP model to minimize the overall network voltage deviation and line active power loss, rapidly determining the initial installation location and capacity configuration of the battery energy storage system while satisfying the physical constraints of the distribution network and the operational constraints of energy storage. The second stage uses the optimal initial solution from the first stage as the population basis for evolutionary optimization, introducing a dual adaptive hybrid strategy. This strategy generates a reverse solution through adaptive jump probability, dynamic search boundary, and evolutionary back-learning mechanism, and combines an elite retention strategy to achieve in-depth exploration of the solution space. Simultaneously, time-series power flow simulation is used to verify the grid operation feasibility and evaluate the fitness of each candidate scheme. This process significantly improves global optimization capabilities while ensuring computational efficiency, effectively overcoming the shortcomings of traditional MGO, such as being prone to local optima and premature convergence. It achieves high-precision site selection and capacity optimization configuration of the battery energy storage system, improving the voltage quality and operational economy of the distribution network under high-proportion renewable energy access.

[0069] As one possible implementation, in the above embodiments, step S1 may specifically include the following steps:

[0070] S1-1. Collect multi-dimensional data from the battery energy storage system of the power distribution network;

[0071] Comprehensive collection of multi-dimensional core data supports BESS site selection and capacity determination, specifically including: static topology parameters of the distribution network (such as line parameters, node connection relationships, etc.), historical and predicted load data (reflecting the temporal changes in user electricity demand), and photovoltaic output curves (reflecting the intermittent output characteristics of distributed photovoltaics). The core purpose of collecting this data is to provide comprehensive and realistic basic inputs for subsequent data processing, model building, and optimization calculations, ensuring that the optimization process closely matches the actual operating scenario of the distribution network.

[0072] S1-2. The multi-dimensional data of the power distribution network battery energy storage system is purified to obtain the purified multi-dimensional data.

[0073] The core of the data purification process is data cleaning, which aims to remove outliers, missing values, duplicates, and other interfering information from the original data. Since the original collected data may be distorted due to monitoring equipment errors, transmission failures, etc., purification can correct these biases and ensure the accuracy and reliability of the data. The processed data can accurately reflect the operating status of the distribution network, load variation patterns, and photovoltaic output characteristics, avoiding the negative impact of poor-quality data on the subsequent optimization model's solution results, and laying a solid foundation for subsequent standardization processing and feature extraction.

[0074] S1-3. The purified multi-dimensional data is mapped using a normalization method to obtain standardized multi-dimensional data.

[0075] The core purpose of normalization is to eliminate the differences in units and numerical scales between data of different dimensions. For example, the units and numerical ranges of distribution network topology parameters, load data, and photovoltaic output data are different. Directly substituting them into the model can lead to the over-amplification or under-amplification of some feature weights, affecting the convergence efficiency and solution accuracy of the optimization algorithm. By normalizing the purified data to a unified numerical range, such as [0,1], the data scale is standardized, making the data of different dimensions comparable. This ensures that the subsequent mixed-integer linear programming model and improved optimization algorithm can fairly and efficiently utilize the data features for optimization.

[0076] S1-4. Based on the standardized multi-dimensional data, feature extraction is performed to obtain the core features of the distribution network battery energy storage system configuration.

[0077] Feature extraction involves filtering key information from standardized data that significantly impacts energy storage site selection and capacity determination, simplifying the optimization process. Combining distribution network operating characteristics with energy storage configuration requirements, core extracted features include voltage sensitivity (reflecting the degree of response of node voltage to power changes, helping to identify nodes with significant voltage improvement potential) and key node identification (screening out core nodes that dominate grid power flow distribution and voltage stability). These core features accurately focus on key influencing factors for energy storage configuration, reduce redundant information interference, provide targeted input for subsequent optimization models, and improve the relevance and effectiveness of site selection and capacity determination.

[0078] S1-5. Based on the core features of the configuration of the power grid battery energy storage system, perform chaotic mapping initialization to obtain the initial population;

[0079] To avoid the uneven population distribution and insufficient diversity caused by conventional random initialization, this step uses a chaotic mapping method based on core features to generate an initial population with inherent ergodicity and pseudo-randomness, laying the foundation for global optimization. Simultaneously, the chaotic sequence is mapped to the search space of decision variables, and initial values ​​are assigned to each individual, including parameters such as population size, maximum number of iterations, and maximum dynamic jump rate. This method leverages the inherent randomness and ergodicity of chaotic systems to ensure a more uniform distribution of the initial population within the search space, avoiding structural biases in the initialization phase and laying a diversity foundation for subsequent deep searches.

[0080] In summary, steps S1-1 to S1-5 not only ensured the accuracy and comparability of the input data through data purification and standardization, but also focused on key influencing factors and simplified the optimization complexity by extracting core features. At the same time, the chaotic mapping initialization avoided the structural bias of traditional random initialization, providing a high-quality foundation for the subsequent two-stage optimization of mixed-integer linear programming and improved evolutionary back-learning gazelle optimization algorithm. This effectively supports the algorithm in improving its global optimization ability and avoiding local optima and premature convergence problems, laying a solid foundation for high-precision site selection and capacity determination of distribution network battery energy storage systems.

[0081] As one possible implementation, in the above embodiments, steps S1-5 may specifically include the following steps:

[0082] S1-5-1. Use the Logistic chaotic mapping to obtain the chaotic sequence;

[0083] Using the classic Logistic chaotic mapping, its dynamic equation is as follows:

[0084] x n+1 =μ∙x n ∙(1-x n (1)

[0085] Where n is the iteration number or iteration index of the chaotic mapping, used to represent the nth iteration in the chaotic sequence generation process, x n ∈(0,1), x n Let x be the chaotic state variable at the nth iteration, representing the values ​​of the chaotic sequence within the interval (0,1). n+1 Let μ be the chaotic state variable for the next moment calculated by the nth iteration, representing the next value in the chaotic sequence. μ is a control parameter, typically set to 4.0, at which point the system is in a completely chaotic state. The chaotic sequence generated by iteratively using this dynamic equation has a value range limited to the (0,1) interval. Its randomness and global coverage characteristics avoid the distribution limitations of traditional random sequences, providing diverse and uniform basic data support for subsequent population initialization.

[0086] S1-5-2. Based on the core characteristics of the configuration of the distribution network battery energy storage system, obtain the search space of decision variables;

[0087] The search space for decision variables is directly defined by the core features of the distribution network BESS configuration, including voltage sensitivity and key node identification results. The decision variables in the search space are divided into two categories: first, discrete variables, namely the installation location of the BESS. Based on the key node identification results, a set of candidate nodes that play a crucial role in improving grid voltage and reducing grid losses is selected, constituting the search range for installation locations; second, continuous variables, namely the rated capacity / power of the BESS. Combining voltage sensitivity, load data, and photovoltaic output characteristics, upper and lower limits for capacity and power are set that conform to grid operation constraints and the physical characteristics of the energy storage device. The resulting search space not only fits the actual operational needs of the distribution network but also clearly defines the legal value boundaries of each decision variable, providing a clear framework for subsequent mapping operations.

[0088] S1-5-3. Map the chaotic sequence to the search space of the decision variables, and assign initial values ​​to each individual in the population to obtain the initial population;

[0089] Mapping the chaotic sequence to the search space of actual decision variables, for the j-th dimension variable of the i-th individual in the population, its initial value X i,j (0) Determined by the following formula:

[0090] X i,j (0)=LB j +x i,j ∙(UB j -LB j (2)

[0091] Among them, LB j Let x be the lower bound of the j-th dimension decision variable. i,j UB represents the chaotic values ​​in the interval (0,1) generated by the Logistic mapping. j Let be the upper bound of the j-th dimension decision variable.

[0092] Initial values ​​are assigned to each individual in the population, including population size, maximum number of iterations, and maximum dynamic jump rate, so that each individual in the population corresponds to a complete BESS initial configuration scheme. This mapping method makes full use of the ergodicity of chaotic sequences, ensuring that the initial population is evenly distributed in the search space, and effectively avoiding the structural bias that may exist in traditional random initialization.

[0093] In summary, steps S1-5-1 to S1-5-3 fully utilize the excellent characteristics of the Logistic chaotic mapping, effectively avoiding problems such as uneven population distribution and insufficient diversity caused by traditional random initialization. This ensures that the initial population is evenly distributed in the search space without structural bias, providing a high-quality data foundation for the rapid coarse screening of subsequent mixed-integer linear programming. It also lays a solid foundation of population diversity for the accurate optimization of the improved evolutionary back-learning gazelle optimization algorithm, thereby helping the algorithm improve its global optimization ability and effectively overcome the technical defects of local optima and premature convergence.

[0094] As one possible implementation, in the above embodiments, step S2 may specifically include the following steps:

[0095] S2-1. Based on the initial population and the constraints of the mixed-integer linear programming model, construct a mixed-integer linear programming model;

[0096] This step uses a uniform and diverse initial population generated by chaotic mapping as the basis of the solution space to establish a mixed-integer linear programming model with the objectives of minimizing the overall voltage deviation and total active power loss of the distribution network system. This model fully considers the physical constraints of grid operation and the operational constraints of the BESS (Battery Energy Storage System). Its decision variables include the installation location of the battery energy storage devices (binary integer variables) and the rated capacity and power of each installation location (continuous variables).

[0097] The problem of optimizing the allocation and scale determination of battery energy storage systems in power distribution networks is formulated as a MILP model. With the objective of minimizing the voltage deviation and active power loss of the entire network, a linear approximate model that can be solved quickly is established, with the following objective function:

[0098] (3)

[0099] Where f1 is the comprehensive objective function value of the distribution network battery energy storage system site selection and capacity optimization problem, used to measure the comprehensive performance index of distribution network voltage operation quality and line active power loss level throughout the entire optimization period. It is composed of two weighted parts: the sum of squares of voltage deviations of all network nodes and the sum of active power losses of all network lines; ω1 and ω2 are weighting coefficients for balancing different optimization objectives, ω1 is the weighting coefficient of the voltage deviation objective, and ω2 is the weighting coefficient of the active power loss objective, which satisfy ω1+ω2=1 to reflect the preference for different optimization objectives; T is the total number of optimization periods, such as 24 hours; N bus V represents the number of nodes in a battery energy storage system. i,t V represents the voltage amplitude of node i during time period t. REF The rated reference voltage is typically taken as 1.0 pu; N line P represents the number of branches in the battery energy storage system. loss,k,tLet be the active power loss of branch k during time period t.

[0100] The constraints involved in this MILP model mainly relate to various constraints concerning the physical operation of the distribution network. This set of constraints, from top to bottom, includes: active power balance constraints and reactive power balance constraints (collectively referred to as power flow constraints) for each bus in the network at each time period; and the allowable voltage range and current limits stipulated by regulatory agencies for the operation of the distribution network. The constraints of the mixed-integer linear programming model are:

[0101] (4)

[0102] Among them, P Subs,t Let N be the active power of the substation during time period t, and P be the number of loads. Load,i,t Let N be the active power of the load at node i during time period t. PV P represents the number of photovoltaic power plants. PV,i,t Let N be the active power of the photovoltaic power station at node i during time period t. RES P represents the amount of energy stored in the battery. BES,i,t Let P be the active power of battery storage at node i during time period t. loss,t R is the active power loss during time period t. Subs,t R represents the reactive power of the substation during time period t. Load,i,t R represents the load reactive power of node i during time period t. PV,i,t Let R be the reactive power of the photovoltaic power station at node i during time period t. BES,i,t Let R be the reactive power of battery storage at node i during time period t. loss,t V represents the reactive power loss during time period t. min V is the minimum allowable node voltage. i,t Let V be the node voltage of node i during time period t. max Where B is the maximum allowable node voltage, and I is the number of nodes in the system. i,t Let I be the current of the i-th line at time t. max H represents the maximum allowable line current, and H is the number of lines in the system.

[0103] S2-2. Solve the mixed integer linear programming model to obtain the initial installation location set and initial capacity configuration scheme of the battery energy storage system.

[0104] The constructed MILP model is efficiently solved using commercial solvers such as GUROBI. Leveraging the convexity of the MILP model and the mature algorithms of the solvers, high-quality initial feasible solutions are quickly output. The optimal solution obtained is then used as an elite individual and directly input into the initial population of the subsequent improved DA-EOBMGO algorithm. The solution results clearly contain two core pieces of information: first, the initial set of BESS installation locations, i.e., the candidate nodes with the highest potential for voltage improvement and network loss reduction; second, the initial capacity and power configuration schemes corresponding to each installation location, whose values ​​strictly satisfy the model constraints and distribution network operation requirements. The core value of this initial scheme lies in providing "elite seeds" for subsequent secondary optimizations, directly serving as the initial population or an important component of the improved algorithm, avoiding the algorithm from getting bogged down in invalid searches, and significantly improving the overall optimization efficiency and stability. Furthermore, through the convexity of the MILP model and the efficiency of commercial solvers, high-quality initial solutions can be obtained in a short time, further improving the overall optimization efficiency and stability of the algorithm.

[0105] S2-3. Based on the initial installation location set and initial capacity configuration scheme of the battery energy storage system, the improved dual adaptive evolutionary back learning gazelle optimization algorithm is used to obtain the battery energy storage system site selection and capacity determination scheme.

[0106] The secondary optimization main loop of the improved DA-EOBMGO algorithm uses the initial solution generated by MILP as the population basis for iterative optimization. First, based on the mathematical model of four social behaviors of gazelles—territorial solitary males, matrilineal groups, single male groups, and migratory foraging—the position of individuals in the population is updated to achieve a dynamic balance between global exploration and local development. Next, the dual adaptive evolutionary backward learning (DA-EOBL) operation is executed, dynamically adjusting the jump probability according to the iteration process (broad exploration in the early stage and fine development in the later stage), and generating backward solutions based on the current dynamic boundary of the population to expand the search space. Then, through an elite strategy, the fitness values ​​of the backward solutions and the individuals in the original population are compared, and the best individuals are retained to complete the population update. Finally, it is determined whether the termination condition is met. If the maximum number of iterations or the convergence threshold is not reached, the loop is returned to repeat; otherwise, the iteration ends, laying a solid foundation for subsequent scheme verification and optimal solution output.

[0107] In summary, the process from steps S2-1 to S2-3, through a two-stage integrated design of "rapid coarse screening + precise optimization," not only ensures the high quality and efficiency of the initial solution by leveraging the MILP model, but also significantly enhances the global optimization capability through the improved algorithm. This effectively overcomes the shortcomings of traditional algorithms, such as being prone to getting trapped in local optima and premature convergence, and achieves high-precision optimization configuration of BESS. As a result, it improves the voltage quality of the distribution network, reduces line losses, and provides strong support for the safe, stable, and economical operation of the distribution network under high-proportion distributed photovoltaic access.

[0108] Based on the optimal initial solution provided by the MILP model, the secondary optimization process of the improved DA-EOBMGO algorithm is executed. In the main loop of the improved DA-EOBMGO algorithm, each iteration sequentially executes the secondary optimization main loop of the improved DA-EOBMGO algorithm, i.e., steps S2-3, to systematically guide the population to evolve towards the optimal solution domain.

[0109] As one possible implementation, in the above embodiments, step S2-3 may specifically include the following steps:

[0110] S2-3-1. Obtain the initial installation location set and initial capacity configuration scheme of the battery energy storage system as the initial population of the improved dual adaptive evolutionary reverse learning gazelle optimization algorithm.

[0111] The core of this step is to transform the high-quality results of the primary optimization stage into the starting point for secondary optimization, laying the foundation for accurate optimization. After solving the problem using the MILP model, the output set of initial BESS installation locations and initial capacity and power configuration schemes will directly serve as the core component of the initial population of the improved DA-EOBMGO algorithm. Because the MILP model fully considers the physical constraints of the distribution network and the operational constraints of the BESS, and efficiently obtains the optimal initial solution using commercial solvers such as GUROBI, this initial population naturally possesses "elite attributes," ensuring both the feasibility and quality of the initial solution while preventing the algorithm from getting trapped in invalid search regions, significantly improving the efficiency and stability of subsequent optimizations.

[0112] S2-3-2. Based on the mathematical model of gazelle social behavior, the position of each individual in the initial population of the improved dual adaptive evolutionary back learning gazelle optimization algorithm is updated using the standard gazelle optimization algorithm to obtain the population updated by the standard gazelle optimization algorithm.

[0113] Drawing inspiration from the social and group behaviors of gazelles in the wild, mathematical formulas were used to simulate four core behaviors of gazelle populations in nature: territorial solitary male behavior, matrilineal group behavior, solitary male group behavior, and migratory foraging behavior, in order to conduct basic evolution of the population.

[0114] (1) Territorial solitary male behavior: This is used to simulate how male gazelles establish separate territories after reaching adulthood and gaining strength. Adult male gazelles fiercely defend these territories and fight for them or to possess female gazelles.

[0115] This behavior describes the process by which adult male antelopes approach their dominant territory. Through a "confrontational-approach" mechanism with the global optimum, they rapidly explore potentially high-quality areas, thereby enhancing the algorithm's global optimization ability. The mathematical model for the territorial solitary male behavior is as follows:

[0116] (5)

[0117] in, Let X be the position of the i-th individual in the (t+1)-th iteration. best V represents the position of the current globally optimal individual, where α1 and α2 are random integers within the range {1,2}. i This is a coefficient vector generated based on the random positions of young male antelopes. Let G(t) be the position of the i-th individual in the t-th iteration, and G(t) be an adjustment factor that decreases with each iteration to control the search intensity. r These are enhancement coefficients that are updated randomly.

[0118] (2) Maternal group behavior: This is used to simulate the behavior of female groups gathering around a dominant male. This behavior reflects the coordinated movement characteristics of female groups under the guidance of the dominant male, which helps increase the diversity of search directions and enables the population to explore a wider range of feasible areas. The mathematical model of maternal group behavior is as follows:

[0119] (6)

[0120] Among them, C 1,r C 2,r Let X be a random coefficient vector, where α3 and α4 are random integers within the range {1,2}. rand Individuals in the population are randomly selected.

[0121] (3) Behavior of single males: This model simulates the territorial competition between young and adult males. A competition function is constructed to simulate the conflict and displacement processes during territorial struggles. Nonlinear perturbations are introduced to enable the algorithm to transition when the population is trapped in a local optimum. The mathematical model for the behavior of single males is as follows:

[0122] (7)

[0123] Among them, F i Let F be a competition function, where α5 and α6 are random numbers within the range {0,1}. i The definition is as follows:

[0124] (8)

[0125] (4) Migratory foraging behavior: This is used to simulate the long-distance migration of gazelles in search of food resources. This behavior is essentially a global random migration, used to quickly escape local areas. When the algorithm shows signs of premature convergence, it can effectively restore population dispersion and enhance global search capabilities. The mathematical model of migratory foraging behavior is as follows:

[0126] (9)

[0127] Where lb is the global lower bound of the variable, ub is the global upper bound of the variable, and α7 is a randomly generated number within {0,1}.

[0128] Through the alternation and fusion of these four types of behaviors, MGO achieves a dynamic balance between global exploration and local development, thereby improving the search space coverage and the ability to avoid premature convergence, and providing a stable and diverse population foundation for subsequent embedding evolution reverse learning mechanisms.

[0129] S2-3-3. Obtain the reverse solution by performing a reverse learning operation based on a dual adaptive evolution strategy on the population updated according to the standard gazelle optimization algorithm.

[0130] For the population updated using the standard gazelle optimization algorithm, a reverse solution for each individual is generated through a dual adaptive evolutionary backward learning (DA-EOBL) mechanism to expand the search space. The DA-EOBL mechanism works as follows: first, the dynamic jump probability value for the current iteration is calculated. At the beginning of the optimization process, this probability remains high to drive extensive exploration of the entire search space; as iterations progress, the probability value decays exponentially, making the algorithm more inclined to refine the exploration of promising regions.

[0131] S2-3-4. Use the reverse solution to perform elite selection and population update to obtain the battery energy storage system site selection and capacity determination scheme;

[0132] This step, through optimal selection, dynamic verification, and iterative control, ultimately locks in the globally optimal solution and monitors the algorithm's iteration status in real time. If a sharp decline in population diversity or signs of getting stuck in a local optimum are detected, an intervention mechanism is immediately activated. First, the fitness values ​​of all reverse solutions are calculated based on the objective function. The fitness values ​​of the reverse solutions are compared with those of the individuals in the original population, and individuals with better fitness (i.e., the elite strategy) are retained, thus updating the population. Then, it is determined whether the termination condition is met. If the maximum number of iterations or the convergence threshold has not been reached (e.g., the fitness value no longer changes significantly), the process returns to step S2-3-2 to continue the loop; otherwise, the iteration ends, and the population update is completed. The population updated by the standard gazelle optimization algorithm retains the high-quality solutions discovered in the early search process and incorporates potential optimal solutions generated by reverse learning, effectively maintaining population diversity while strengthening the trend towards the globally optimal solution domain, providing a high-quality population foundation for subsequent iterative optimization.

[0133] In summary, the process from steps S2-3-1 to S2-3-4, through a collaborative design of "high-quality initial population + standard MGO update + dual adaptive reverse learning + elite retention," not only improves the optimization starting point and efficiency by leveraging the initial solution of MILP, but also significantly enhances population diversity and the ability to escape local optima through the improved algorithm, effectively suppressing premature convergence defects. While ensuring computational efficiency, it achieves high-precision optimization configuration of BESS, which can significantly improve the voltage quality of the distribution network under high-proportion distributed photovoltaic access, reduce line active power loss, and provide strong support for the safe, stable, and economical operation of the power grid.

[0134] The evolutionary back-learning mechanism based on a dual adaptive hybrid strategy introduces two adaptive strategies—adaptive jump probability and dynamic search boundary—to enhance the algorithm's ability to escape local optima, building upon traditional evolutionary back-learning. For example... Figure 3 As shown, the core back-learning execution step in the improved dual adaptive evolutionary back-learning gazelle optimization algorithm operates as follows: First, the current iteration number and the current population X updated by the standard gazelle optimization algorithm are input. Then, the jump probability is dynamically adjusted with the iteration process, i.e., the early stage of the iteration is adapted to global exploration, and the later stage is biased towards local development, so as to balance the search strategy. Next, a random number in the interval [0,1] is generated and compared with the jump probability to determine whether the evolutionary back-learning mechanism is triggered. If it is not triggered, the optimization loop process is directly returned. If it is triggered, a back solution is generated based on the dynamic boundary of each decision variable dimension of the current population. Then, the fitness value of the back solution is calculated based on the objective function of distribution network voltage deviation and active power loss. Then, the fitness of the back solution is compared with that of the individuals in the original population. Through greedy selection, better individuals are retained and an elite retention operation is performed. Finally, the optimized population is returned to the subsequent optimization loop process. This process achieves flexible triggering of reverse operations through dynamic jump probabilities, improves the accuracy of reverse solutions with the help of dynamic boundaries, and maintains the quality and diversity of the population through greedy selection and elite preservation. This effectively helps the algorithm balance global exploration and local development, and avoids local optima and premature convergence problems.

[0135] As one possible implementation, in the above embodiments, step S2-3-3 may specifically include the following steps:

[0136] S2-3-3-1. Based on the standard gazelle optimization algorithm, the population updated and combined with the population's iterative process are used to obtain the adaptive jump probability.

[0137] The core of this step is to dynamically adjust the trigger probability of the back-learning operation based on the algorithm's iteration progress, achieving intelligent matching between the search strategy and the convergence state. The trigger probability of the back-learning operation, i.e., the adaptive jump probability, is not a fixed value but is dynamically adjusted according to the algorithm's convergence progress. Its calculation formula is as follows:

[0138] (10)

[0139] Among them, J P Max is the transition probability. jP Max represents the maximum transition probability in the early and late stages. jP ∈[0.6,0.8], Min jP Min represents the minimum transition probability in the early stage. jP ∈[0.01,0.05], t is the current iteration number, and T is the maximum iteration number.

[0140] The calculation uses the population updated by the standard MGO as a reference background and dynamically adjusts it according to the current iteration stage: early iteration stage ( In the later stages of iteration, the jump probability is set to a lower value to encourage the algorithm to explore the entire search space extensively and avoid prematurely limiting itself to a local region; When the jump probability decreases exponentially and then tends to a higher value, the algorithm focuses on existing potential areas for fine development, thereby balancing the efficiency of global exploration and local development.

[0141] S2-3-3-2. Using the adaptive jump probability, obtain the population individuals that perform the reverse operation;

[0142] By using adaptive jump probabilities to select individuals in the population that require reverse learning operations, the reverse operation is triggered in a targeted manner. For each individual in the population updated by the standard MGO, a random number in the interval [0,1] is generated. This random number is compared with the calculated adaptive jump probability: if the random number is greater than the jump probability, the individual is selected to perform the reverse learning operation; if the random number is less than or equal to the jump probability, the individual remains in its original state and does not participate in this reverse operation, returning directly to the loop process. This selection method ensures that some individuals in the population can expand the search space through reverse learning, while avoiding excessive reverse operations that could damage the structure of existing high-quality solutions, thus maintaining the stability and diversity of the population.

[0143] S2-3-3-3: Obtain the reverse solution based on the population individuals that performed the reverse operation and the dynamic search boundary;

[0144] If the evolutionary reverse learning mechanism is triggered, the reverse solution for that individual is first generated based on the dynamic boundaries of each decision variable dimension of the current population X, i.e., the current minimum and maximum values ​​of the population in the corresponding dimensions. For the individual that needs to perform reverse learning, its reverse solution ox j The calculation does not depend on a fixed global boundary, but is based on the dynamic boundary of the current population in this dimension [min(X j ),max(X jThis prompts the search to focus on potentially promising regions, at which point the inverse solution becomes:

[0145] ox j =min(X j )+max(X j )-x j (11)

[0146] This computational method ensures that the reverse solution always focuses on the active region of the current population, effectively expanding the local coverage of the solution space while avoiding the generation of invalid solutions that deviate from the actual search direction. This significantly improves the efficiency and quality of local searches in later iterations. Furthermore, this newly generated dynamic reverse solution is compared with the original solution, and the best solution is selected for the next generation of population evolution. By dynamically shrinking the search boundary to the actual activity range of the current population, the search focus can continuously narrow as the population aggregates, significantly improving the efficiency and accuracy of local searches in later iterations.

[0147] In summary, steps S2-3-3-1 to S2-3-3-3 abandon the rigid mode of fixed probability and fixed boundary in traditional reverse learning. By using adaptive jump probability, the search strategy and iterative process are precisely matched, which effectively avoids getting trapped in local optima too early in the early stage of iteration and improves the fineness of local development in the later stage of iteration. Targeted selection of reverse operation individuals not only retains the high-quality solutions already explored in the population but also introduces new search directions, significantly improving population diversity. The dynamic search boundary greatly reduces the generation of invalid reverse solutions, improves the effectiveness of reverse learning, and effectively enhances the algorithm's global optimization ability, suppresses premature convergence defects, and provides high-quality candidate solutions for subsequent elite selection and population update. This helps the battery energy storage system site selection and capacity setting scheme achieve better global optima and engineering adaptability.

[0148] As one possible implementation, in the above embodiments, step S2-3-4 may specifically include the following steps:

[0149] S2-3-4-1. Based on the standard gazelle optimization algorithm, the population updated by the standard gazelle optimization algorithm and the reverse solution are used to calculate the fitness variance of the current population as a quantitative detection index.

[0150] The core of this step is to accurately identify whether the population has fallen into premature convergence through fitness quantification and variance analysis, providing a basis for dynamic adjustment of the subsequent population update strategy. First, the original population updated by the standard MGO and the generated inverse solution are integrated into the current complete population. Based on the dual-objective optimization function of the distribution network (minimizing total active power loss + minimizing node voltage deviation), the fitness value of each individual in the population (corresponding to a BESS configuration scheme) is calculated. The fitness value is strictly correlated with the objective function value (the smaller the objective function value, the better the fitness), and it is necessary to simultaneously verify whether the individual meets the basic constraints such as distribution network power balance and voltage / current limits (individuals that do not meet the constraints are assigned extremely low fitness values ​​and are considered invalid solutions). Then, at the end of each iteration, the fitness variance of all individuals in the current generation is calculated as the core basis for judging whether the population has prematurely converged. The calculation formula is:

[0151] (12)

[0152] in, Let f be the variance of fitness of all individuals in the current population, N be the population size, and f be the variance of fitness of all individuals in the current population. i Let i be the fitness value of individual i. This represents the average fitness value of the population. The variance is used as a quantitative indicator; a smaller variance indicates a more concentrated individual fitness level, suggesting premature convergence. A larger variance indicates sufficient population diversity, suggesting the population is still in a normal evolutionary state.

[0153] S2-3-4-2. Determine whether the quantitative detection index is lower than the quantitative detection index threshold. If so, retain the globally optimal individual and perform chaotic restart and directed Gaussian mutation on the remaining individuals. Combine the optimal solution of the reverse solution to complete the population reshaping and update, and obtain the target population. Otherwise, compare the fitness value of the population updated by the standard gazelle optimization algorithm with the fitness value of the reverse solution, retain the optimal solution that satisfies the constraints, complete the population update, and obtain the target population.

[0154] This step achieves adaptive regulation of population renewal through branch decision-making, ensuring that high-quality solutions are not lost while effectively preventing premature convergence and maintaining population diversity and evolutionary vitality. A very small positive threshold δ is set as a reference. min When satisfied When the fitness of the vast majority of individuals becomes consistent, the algorithm has lost its direction and is judged as premature convergence.

[0155] If the quantitative detection index is below a preset threshold: the population is determined to have entered premature convergence. In this case, the elite preservation strategy is prioritized, that is, the current globally best individual Xbest is unconditionally retained to ensure that existing optimization results are not lost, and chaotic restart and directed Gaussian mutation fusion operations are performed on the remaining individuals. Specifically:

[0156] Chaotic restart: For all individuals in the population except Xbest, perform the chaos mapping initialization process, as follows:

[0157] (13)

[0158] in, These are diverse individuals resulting from chaotic mapping. These are individuals in the population other than Xbest. Chaotic restart is designed to leverage the ergodicity of chaos to reintroduce highly diverse individuals into the search space, breaking the deadlock.

[0159] Directed Gaussian Mutation: To further enhance the ability to escape local optima, Gaussian mutation is applied to a subset of individuals (e.g., the first 30%) after chaotic restart, introducing controllable random noise. The mutation formula is as follows:

[0160] (14)

[0161] Where i is the individual index, used to identify the i-th candidate solution in the population; j is the decision variable index, used to identify the j-th optimization variable in the i-th individual; The mutated variable value of the i-th individual in the j-th dimension is used to construct new candidate solutions and participate in subsequent fitness evaluation and screening; Let be the pre-mutation variable value of the i-th individual in the j-th dimension, typically the individual's position component after chaotic restart or directed update. η is a variable-asynchronous long factor that adaptively decreases with the iteration process, for example... N(0,1) is a random number distributed according to a standard normal distribution; η0 is the initial variable asynchronous length coefficient, used to determine the intensity of random disturbance in the early stage of the algorithm; t is the current iteration number; T is the maximum number of iterations set by the algorithm.

[0162] Specifically, a uniformly distributed chaotic sequence is generated through Logistic chaotic mapping, and the decision variables of individuals (BESS installation location, capacity, etc.) are chaotically restarted, breaking the original clustering state and expanding the search space. At the same time, a directed Gaussian mutation is applied around the variable range of the globally optimal individual (the mutation intensity dynamically decays with the iteration process), realizing a local fine search. Finally, individuals with better fitness in the reverse solution are merged to complete the population reshaping and update, and the target population is output, thereby quickly escaping local optima.

[0163] If the quantitative detection index is not lower than the preset threshold, the population is determined to have no premature convergence and is in a normal evolutionary state. At this point, the fitness values ​​of the original population after the standard MGO update and the reverse solution are directly compared. Individuals with better fitness that satisfy all constraints of the distribution network are selected, and high-quality individuals are retained according to the preset population size to complete the population update, outputting the target population. This method preserves the high-quality evolutionary results of the original population while incorporating the new search direction brought by the reverse solution, balancing population stability and diversity.

[0164] S2-3-4-3: Check whether the stopping criterion has been met based on the target population and the convergence judgment criterion. If yes, obtain the battery energy storage system site selection and capacity setting scheme based on the target population. Otherwise, return to step S2-3-2.

[0165] The convergence of the algorithm is theoretically demonstrated, and reasonable termination conditions are set in practice. The convergence proof is as follows: the state transition process of the algorithm is analyzed by constructing a Markov chain-based model, the state space of the algorithm is defined, and its state transition probability matrix Q=[q ij The condition P{X(k+1)=j|X(k)=i}=q is satisfied. ij Then it is proved that the algorithm converges to the global optimal solution set with probability 1. Here, i and j are state indices in the state space, i is the current state in the current iteration, j is the state that the next iteration may transition to, and q... ij Let P{∙} be the state transition probability from state i to j, and let P{∙} be the probability operator used to characterize the probability of a certain state transition event occurring under given conditions. Let X(k+1) be the system state random variable of the algorithm in the (k+1)th iteration, that is, the new generation population state formed after undergoing the actions of operators such as selection, update, and mutation. Let X(k) be the system state random variable of the algorithm in the kth iteration, which is composed of the decision variable values ​​of all individuals in the current population (i.e., the site selection location and capacity configuration scheme of the battery energy storage system).

[0166] This step is the closed-loop control link of the algorithm iteration. Convergence verification clarifies the optimization process, ensuring the global optimality and engineering feasibility of the final output solution. First, the preset convergence judgment criterion, i.e., the stopping criterion, is defined: In practical engineering applications, iteration can stop when any one of the following conditions is met: reaching the preset maximum number of iterations T. max Alternatively, within K consecutive generations (e.g., K = 50), the improvement in the global optimal solution is less than a minimum tolerance value (e.g., 10). -4 Then, based on the target population, it is verified whether the stopping criteria are met:

[0167] If the stopping criterion is met: extract the individual with the best fitness in the target population, and the decision variables corresponding to this individual (BESS installation node set, rated energy storage capacity and power of each node) are the final battery energy storage system site selection and capacity setting scheme.

[0168] If the stopping criterion is not met: return to step S2-3-2, which is to perform standard MGO updates on the position of each individual in the current target population (replacing the initial population to achieve iterative evolution) based on the mathematical model of gazelle social behavior, generate a new generation of standard MGO updated population, and enter the next round of iterative process of "reverse learning-fitness detection-population update-convergence verification" until the stopping criterion is met.

[0169] In summary, steps S2-3-4-1 to S2-3-4-3 accurately identify the premature convergence state of the population through fitness variance, and adopt a differentiated population update strategy. When premature convergence occurs, chaotic restart is used to break local clustering and directional Gaussian mutation is used to enhance fine search. Elite retention and reverse optimization are combined to achieve efficient population reshaping. During normal evolution, optimal updates are selected to ensure the quality of the population. The optimization process is controlled by closed-loop iteration and convergence verification. This effectively suppresses the premature convergence problem that is prone to occur in traditional algorithms, and continuously maintains population diversity and evolutionary vitality. It significantly improves the global optimization ability and optimization accuracy of the algorithm. The final output battery energy storage system site selection and capacity setting scheme has both global optimality and engineering constraint compliance. It can effectively reduce the total active power loss of the distribution network, improve the voltage quality of nodes, and provide reliable support for the safe, economical and stable operation of the distribution network.

[0170] As one possible implementation, in the above embodiments, step S3 may specifically include the following steps:

[0171] S3-1. Based on the battery energy storage system location and capacity setting scheme, load the energy storage configuration scheme parameters and construct a time-series power flow simulation model;

[0172] The core parameters corresponding to the BESS site selection and capacity setting scheme are extracted, including the installation node location, capacity, power, and charging and discharging strategy. At the same time, the corresponding 24-hour load data, photovoltaic power generation forecast data, and charging and discharging scheduling curves matching the scheme are loaded. Finally, professional power system simulation tools such as OpenDSS and PSCAD are called to build an accurate AC power flow model. This enables the construction of a time-series power flow simulation model that covers the distribution network topology, dynamic boundary conditions, and BESS configuration, ensuring that the model can realistically reproduce the full-time operating characteristics of the distribution network.

[0173] S3-2. Based on the time-series power flow simulation model, perform time-series power flow simulation on the battery energy storage system location and capacity setting scheme, and obtain the time-series power flow simulation results.

[0174] By launching the established time-series power flow simulation model, the operation of the distribution network under the BESS configuration scheme is simulated. This involves substituting the optimized BESS configuration scheme (location, capacity, charging and discharging strategy) into a precise AC power flow model for year-round or typical day simulation calculations, enabling dynamic extrapolation of the scheme's actual operational effects. During the simulation, the model automatically follows the fundamental laws of power system power flow calculation, combining the BESS charging and discharging scheduling logic (such as peak load discharge and peak PV output charging), to calculate and output detailed operational data for the entire 24-hour period, namely the time-series power flow simulation results. These results cover core operating parameters: voltage amplitude at each node, active power loss in each branch, hourly charging and discharging power and remaining capacity of the BESS, and hourly load and PV output matching at each node, providing comprehensive data support for subsequent indicator evaluation.

[0175] S3-3. Using the aforementioned time-series power flow simulation results, obtain key evaluation indicators;

[0176] Using the results of time-series power flow simulation, we calculate the relevant indicators of the core optimization objectives, including the total voltage deviation of the entire network and the total active power loss of the system, to quantify the effect of the scheme on voltage quality improvement and network loss reduction. On the other hand, we extract the key technical constraint verification indicators, including whether the voltage of all nodes meets the upper and lower voltage limits in all time periods; whether the power or current of all branches does not exceed their thermal stability limits; calculate the network loss changes before and after configuring BESS; and check the BESS's own operating constraints, such as whether the state-of-charge trajectory is reasonable and whether the cycle life is within an acceptable range.

[0177] S3-4. Determine whether the key evaluation indicators have reached the preset optimization stopping criteria. If yes, obtain the location and capacity determination results of the distribution network battery energy storage system; otherwise, return to step S2.

[0178] This step is the closed-loop decision-making stage for verification and evaluation. It determines whether the solution meets engineering requirements by comparing indicator thresholds, ensuring the reliability of the output results. First, the preset optimization stopping criteria are defined, specifically: all key evaluation indicators must reach preset thresholds, such as total active power loss ≤ preset economic threshold, voltage deviation rate ≤ 3%, voltage over-limit duration = 0, BESS utilization rate ≥ 60%, line current carrying capacity over-limit times = 0, etc., and the improvement in the optimal value of the indicator in two consecutive iterations ≤ 10. -3Subsequently, the key evaluation indicators are compared with the above criteria one by one: if all are satisfied, the solution is deemed to meet the criteria, the algorithm ends the iteration, and the optimal solution in the entire optimization process is output, that is, the individual with the best fitness value. The BESS installation location and capacity configuration scheme represented by this individual includes the specific installation nodes, recommended capacity and power, and expected operating strategy, which is the final optimal configuration scheme; if any indicator fails to meet the criteria, the solution is deemed not to meet the requirements, and the algorithm returns to step S2 to continue the next round of iteration calculation until the optimal solution that meets the optimization stopping criteria is output.

[0179] In summary, steps S3-1 to S3-4 employ a closed-loop verification logic of "modeling and simulation - index calculation - criterion judgment." This process not only relies on time-series simulation to recreate the dynamic operating characteristics of the distribution network throughout all time periods, ensuring the authenticity and accuracy of the assessment, but also ensures that the final output energy storage site selection and capacity determination scheme fully meets the requirements for safe, stable, and economical operation of the distribution network through multi-dimensional verification of key indicators and closed-loop iterative optimization. This effectively reduces overall network losses, improves voltage quality, and enhances energy storage utilization efficiency, providing a solid guarantee for the reliable operation of a high proportion of distributed power sources connected to the distribution network.

[0180] Further reference Figure 4 As an implementation of the methods shown in the above figures, this disclosure provides an embodiment of a location and capacity determination system for a distribution network battery energy storage system. This system embodiment is similar to... Figure 1 Corresponding to the method embodiments shown, this device can be specifically applied to various electronic devices.

[0181] This invention employs a "two-layer optimization, step-by-step progression" approach to construct a multi-module collaborative system. For example... Figure 4 As shown, the site selection and capacity determination system for a distribution network battery energy storage system in this embodiment includes a preprocessing module, an intelligent optimization module, and a verification and evaluation module. The functions of each module are as follows:

[0182] The preprocessing module is used to preprocess and initialize chaotic mapping using multi-dimensional data from the distribution network battery energy storage system to obtain an initial population.

[0183] This module is the fundamental support unit of the entire site selection and capacity determination system, with its core revolving around multi-dimensional data processing and the construction of a high-quality initial population. On the one hand, this module comprehensively collects key information such as distribution network topology parameters, historical and predicted load data, and photovoltaic output curves. Through data cleaning, normalization to remove outliers, and standardization of data scale, it extracts core features such as voltage sensitivity and key nodes, providing reliable data input for subsequent optimization models. On the other hand, it employs a chaotic mapping method with inherent randomness and ergodicity to map the chaotic sequence to the search space of solutions, assigning initial values ​​(including parameters such as population size and maximum number of iterations) to each individual, ensuring that the initial population is evenly distributed in the search space, avoiding structural biases in the initialization stage, and laying the foundation for population diversity for subsequent deep optimization.

[0184] The intelligent optimization module is used to perform two-stage optimization based on the initial population using a mixed integer linear programming model and an improved dual adaptive evolutionary back learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme.

[0185] This module is the core optimization engine of the system. It is responsible for integrating the MILP pre-selection optimizer and the improved evolutionary back-learning gazelle optimization algorithm based on a dual adaptive hybrid strategy, forming a dual-core driven system optimization engine. It achieves efficient optimization through a two-stage architecture of "rapid coarse screening + precise optimization". The first stage constructs a MILP model with the objectives of minimizing the overall voltage deviation and total active power loss of the distribution network. It fully considers the physical constraints of the distribution network and the operational constraints of the BESS, using the BESS installation location (binary integer variable), rated capacity, and power (continuous variables) as decision variables. It uses commercial solvers such as GUROBI to quickly output a high-quality initial configuration scheme. The second stage uses the optimal solution of MILP as the initial population and starts the improved DA-EOBMGO algorithm. It sequentially executes the four behaviors of standard MGO, dual adaptive evolutionary back learning (dynamically adjusting the jump probability and search boundary to generate back solutions), elite selection, and population update. At the same time, it embeds premature convergence detection and elite reshaping mechanisms (judging by fitness variance, triggering chaotic restart and directed Gaussian mutation), combined with iterative termination control (maximum number of iterations or convergence threshold), and finally outputs a BESS configuration scheme that takes into account both global optimality and convergence efficiency.

[0186] The verification and evaluation module is used to perform verification and evaluation based on the battery energy storage system location and capacity determination scheme, and obtain the location and capacity determination results of the distribution network battery energy storage system.

[0187] This module is crucial for ensuring the feasibility and effectiveness of the configuration scheme. Through precise simulation and multi-dimensional verification, it rigorously checks the electrical safety and economic viability of the optimized output scheme, achieving a closed-loop solution. Based on tools such as OpenDSS and MATLAB / Power Systems Toolbox, this module performs time-series power flow simulations, loading 24-hour load data, photovoltaic power generation forecast data, and BESS charge / discharge scheduling curves to simulate the grid's annual or typical daily operation under the configuration scheme. Subsequently, it verifies key indicators across multiple dimensions, including whether the voltage at all nodes meets upper and lower limits at each time period, whether branch power / current does not exceed thermal stability limits, whether distribution network losses change as expected, and whether the BESS's state-of-charge trajectory, cycle life, and other operational constraints are reasonable. After comprehensive verification confirms that the scheme meets safety and economic requirements, it outputs the final site selection and capacity determination report, specifying the specific installation nodes, recommended capacity and power, and expected operating strategies.

[0188] In summary, the site selection and capacity determination system for the distribution network battery energy storage system is composed of a preprocessing module, an intelligent optimization module, and a verification and evaluation module working together. The preprocessing module collects multi-dimensional data such as distribution network topology parameters, load, and photovoltaic output, and after preprocessing, uses chaotic mapping to initialize and generate an initial population with uniform distribution and sufficient diversity. Based on this initial population, the intelligent optimization module quickly obtains a high-quality initial solution through the MILP model, and then performs secondary precise optimization by combining the improved DA-EOBMGO algorithm to form a battery energy storage system configuration scheme. The verification and evaluation module evaluates the feasibility of the configuration scheme through time-series power flow simulation and verification of multi-dimensional key indicators, and outputs the final site selection and capacity determination results. This system deeply integrates deterministic mathematical programming with adaptive reinforced metaheuristic algorithms, effectively overcoming the shortcomings of traditional algorithms that are prone to getting trapped in local optima and premature convergence. While ensuring computational efficiency, it significantly improves the global optimization capability, enabling precise site selection and capacity determination of battery energy storage systems. This, in turn, improves the voltage quality of the distribution network, reduces active power losses in the lines, and enhances the grid's capacity to absorb renewable energy, providing strong support for the safe, stable, and economical operation of the distribution network under high-proportion distributed photovoltaic access.

[0189] In this embodiment, the specific processing of a distribution network battery energy storage system location and capacity determination system and the resulting technical effects can be referred to respectively. Figure 1 The relevant descriptions of steps S1, S2 and S3 in the corresponding embodiments will not be repeated here.

[0190] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0191] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0192] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0193] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0194] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for site selection and capacity determination of a battery energy storage system in a power distribution network, characterized in that, include: S1. Use multi-dimensional data from the distribution network battery energy storage system for preprocessing and chaotic mapping initialization to obtain the initial population; S2. Based on the initial population, a two-stage optimization is performed using a mixed integer linear programming model and an improved dual adaptive evolutionary back-learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme. S3. Verify and evaluate the battery energy storage system location and capacity determination scheme to obtain the location and capacity determination results of the distribution network battery energy storage system.

2. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 1, characterized in that, S1. Preprocess and initialize the chaotic mapping using multi-dimensional data from the distribution network battery energy storage system to obtain the initial population, including: Collect multi-dimensional data from the battery energy storage system of the power distribution network; The multi-dimensional data of the power distribution network battery energy storage system is purified to obtain purified multi-dimensional data. The purified multi-dimensional data is mapped using a normalization method to obtain standardized multi-dimensional data. Feature extraction is performed based on the standardized multi-dimensional data to obtain the core features of the distribution network battery energy storage system configuration. Chaotic mapping initialization is performed based on the core features of the power distribution network battery energy storage system configuration to obtain the initial population.

3. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 2, characterized in that, Chaotic mapping initialization is performed based on the core features of the power distribution network battery energy storage system configuration to obtain an initial population, including: The chaotic sequence is obtained by using the Logistic chaotic mapping. Based on the core characteristics of the configuration of the distribution network battery energy storage system, the search space of decision variables is obtained, including the installation location of the battery energy storage system and the rated capacity / power of the BESS. The chaotic sequence is mapped to the search space of the decision variables, and an initial value is assigned to each individual in the population to obtain the initial population.

4. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 1, characterized in that, S2. Based on the initial population, a two-stage optimization is performed using a mixed-integer linear programming model and an improved dual adaptive evolutionary back-learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme, including: Based on the initial population and the constraints of the mixed-integer linear programming model, a mixed-integer linear programming model is constructed. Solve the mixed-integer linear programming model to obtain the initial installation location set and initial capacity configuration scheme of the battery energy storage system; Based on the initial installation location set and initial capacity configuration scheme of the battery energy storage system, an improved dual adaptive evolutionary back-learning gazelle optimization algorithm is used to obtain the battery energy storage system site selection and capacity determination scheme.

5. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 4, characterized in that, The constraints of the mixed-integer linear programming model are: Among them, P Subs,t Let N be the active power of the substation during time period t, and P be the number of loads. Load,i,t Let N be the active power of the load at node i during time period t. PV P represents the number of photovoltaic power plants. PV,i,t Let N be the active power of the photovoltaic power station at node i during time period t. RES P represents the amount of energy stored in the battery. BES,i,t Let P be the active power of battery storage at node i during time period t. loss,t R is the active power loss during time period t. Subs,t R represents the reactive power of the substation during time period t. Load,i,t R represents the load reactive power of node i during time period t. PV,i,t Let R be the reactive power of the photovoltaic power station at node i during time period t. BES,i,t Let R be the reactive power of battery storage at node i during time period t. loss,t V represents the reactive power loss during time period t. min V is the minimum allowable node voltage. i,t Let V be the node voltage of node i during time period t. max Where B is the maximum allowable node voltage, and I is the number of nodes in the system. i,t Let I be the current of the i-th line at time t. max H represents the maximum allowable line current, and H is the number of lines in the system.

6. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 4, characterized in that, Based on the initial installation location set and initial capacity configuration scheme of the battery energy storage system, an improved dual adaptive evolutionary back-learning gazelle optimization algorithm is used to obtain the battery energy storage system site selection and capacity determination scheme, including: The initial installation location set and initial capacity configuration scheme of the battery energy storage system are obtained as the initial population of the improved dual adaptive evolutionary reverse learning gazelle optimization algorithm. The mathematical model of gazelle social behavior is used to update the position of each individual in the initial population of the improved dual adaptive evolutionary back-learning gazelle optimization algorithm using the standard gazelle optimization algorithm, thereby obtaining the population updated by the standard gazelle optimization algorithm. The mathematical model of gazelle social behavior includes mathematical models of territorial solitary male behavior, matrilineal group behavior, single male group behavior, and migratory foraging behavior. The inverse solution is obtained by performing a reverse learning operation based on a dual adaptive evolution strategy on the population updated by the standard gazelle optimization algorithm. The inverse solution is used for elite selection and population update to obtain the site selection and capacity determination scheme for the battery energy storage system.

7. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 6, characterized in that, Based on the population updated using the standard gazelle optimization algorithm, a reverse solution is obtained through a reverse learning operation using a dual adaptive evolution strategy, including: Based on the population update using the standard gazelle optimization algorithm, and combined with the population's iterative process, an adaptive jump probability is obtained. Using the adaptive jump probability, the population individuals that perform the reverse operation are obtained; The inverse solution is obtained by combining the population individuals that perform the inverse operation with the dynamic search boundary.

8. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 6, characterized in that, Using the inverse solution for elite selection and population update, a site selection and capacity determination scheme for the battery energy storage system is obtained, including: The fitness variance of the current population is obtained as a quantitative detection index by calculating the fitness degree of the population updated based on the standard gazelle optimization algorithm and the reverse solution. If the quantitative detection index is lower than the quantitative detection index threshold, the globally optimal individual is retained, and chaotic restart and directed Gaussian mutation are performed on the remaining individuals. The population is reshaped and updated by combining the optimal solution of the reverse solution to obtain the target population. Otherwise, the fitness values ​​of the population updated by the standard gazelle optimization algorithm and the reverse solution are compared. The optimal solution that satisfies the constraints is retained, the population is updated, and the target population is obtained. The target population is used to check whether the stopping criterion has been met. If so, the battery energy storage system site selection and capacity determination scheme is obtained based on the target population. Otherwise, the operation is returned to the first operation. The first operation is as follows: based on the mathematical model of gazelle social behavior, the position of each individual in the initial population of the improved dual adaptive evolutionary back-learning gazelle optimization algorithm is updated using the standard gazelle optimization algorithm to obtain the population updated by the standard gazelle optimization algorithm.

9. The method for site selection and capacity determination of a distribution network battery energy storage system according to claim 1, characterized in that, S3. Verify and evaluate the battery energy storage system location and capacity determination scheme to obtain the location and capacity determination results of the distribution network battery energy storage system, including: Based on the battery energy storage system location and capacity setting scheme, load the energy storage configuration scheme parameters and construct a time-series power flow simulation model; Based on the time-series power flow simulation model, the time-series power flow simulation results are obtained by performing time-series power flow simulation on the battery energy storage system's location and capacity setting scheme. Using the aforementioned time-series power flow simulation results, key evaluation indicators are obtained; Determine whether the key evaluation indicators meet the preset optimization stopping criteria. If yes, obtain the site selection and capacity determination results of the distribution network battery energy storage system; otherwise, return to step S2.

10. A site selection and capacity determination system for a distribution network battery energy storage system, implementing the method described in any one of claims 1-9, characterized in that, include: Preprocessing module, intelligent optimization module, and verification and evaluation module; The preprocessing module is used to preprocess and initialize chaotic mapping using multi-dimensional data from the distribution network battery energy storage system to obtain an initial population. The intelligent optimization module is used to perform two-stage optimization based on the initial population using a mixed integer linear programming model and an improved dual adaptive evolutionary back learning gazelle optimization algorithm to obtain a battery energy storage system site selection and capacity determination scheme. The verification and evaluation module is used to perform verification and evaluation based on the battery energy storage system location and capacity determination scheme, and obtain the location and capacity determination results of the distribution network battery energy storage system.

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