A collaborative planning approach for photovoltaic and long-duration energy storage considering the economics and security of distribution networks.
Patent Information
- Application Number
- CN202610391805.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-27
- Publication Date
- 2026-06-30
AI Technical Summary
Existing photovoltaic energy storage system capacity configuration methods suffer from unsystematic grid security assessments, rudimentary handling of source-load uncertainties, and difficulty in coordinating planning and operational decisions, resulting in insufficient adaptability of configuration schemes under diverse operating conditions.
An improved spectral clustering algorithm is used to generate power curves and their probabilities for typical scenarios. A two-layer collaborative optimization configuration model for photovoltaic and long-term energy storage systems is constructed and solved using an improved Harris Eagle algorithm based on a surrogate model, achieving safe, reliable, and economically optimal configuration in multiple scenarios.
It significantly improves the reliability, adaptability, and robustness of configuration schemes, ensures economic optimization throughout the entire life cycle, and provides a practical decision-making tool for complex power distribution network scenarios.
Smart Images
Figure CN122315745A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system planning, specifically relating to a collaborative planning method for photovoltaic and long-term energy storage that considers the economics and security of distribution networks. Background Technology
[0002] As the global energy structure evolves towards cleaner and lower-carbon energy sources, the scale of distributed renewable energy, represented by photovoltaic (PV) power generation, in distribution networks continues to expand, and its penetration level continues to increase. However, the intermittent and random characteristics of PV output have also placed significant pressure on the power balance, voltage stability, and economic operation of distribution networks. Against this backdrop, energy storage systems with both energy time-shifting and power regulation capabilities, especially long-duration electrochemical energy storage, have become an important solution for improving PV absorption capacity and enhancing the flexibility and resilience of grid operation. Through the coordinated planning and optimized operation of PV and energy storage devices, it is possible to effectively smooth fluctuations in renewable energy output, improve network power flow distribution, and participate in market ancillary services, thereby achieving a holistic optimization of system safety operation and overall economic benefits.
[0003] Currently, numerous studies have addressed the capacity planning problem of photovoltaic-energy storage systems in distribution networks. Existing technical solutions often focus on economic indicators such as return on investment and operating costs as single optimization objectives, or introduce traditional safety constraints such as voltage deviation and current overruns as boundary conditions in the configuration model. Although some studies have attempted to incorporate safety-related factors, they typically fail to construct a complete and quantitative safety assessment index system, making it difficult to comprehensively evaluate the combined impact of renewable energy access on the static and dynamic safety levels of the distribution network. Furthermore, when facing the uncertainty of photovoltaic output and load demand, existing methods often rely on extreme scenarios or single typical daily curves, lacking refined modeling of the interaction between system safety and economic performance under various operating scenarios. The single-layer optimization frameworks adopted by most fail to clearly distinguish between capacity location decisions in the planning stage and real-time power scheduling in the operation stage, which may lead to insufficient adaptability of the planning scheme under diverse actual operating conditions.
[0004] Therefore, the existing technology has the following main shortcomings: First, the characterization of grid security in the capacity configuration model is often not systematic and in-depth enough, and there is a lack of effective collaborative optimization mechanism between security objectives and economic objectives; second, the handling of uncertainties in new energy sources and loads is relatively rough, and the robustness of the configuration scheme to multiple time scales and multiple operating scenarios needs to be improved; finally, the decision-making coupling relationship between planning and operation is not fully decoupled in the model structure, which affects the engineering practicality and global optimality of the scheme.
[0005] To address the aforementioned issues, there is an urgent need to propose a capacity optimization configuration method for long-term electrochemical energy storage systems that can synergistically consider grid operation security and project lifecycle economics, adapt to multi-scenario analysis needs, and achieve hierarchical coordination of planning and operation strategies. Summary of the Invention
[0006] Objective: To address the technical problems in existing photovoltaic energy storage system capacity configuration methods, such as unsystematic assessment of grid security, rudimentary handling of source-load uncertainties, and difficulty in coordinating planning and operational decisions, this invention provides a multi-scenario long-term energy storage capacity optimization configuration method that considers both grid security and economy. This method aims to establish a comprehensive security assessment index system, achieve refined modeling across multiple scenarios, and, through a two-layer planning-operation optimization framework, ultimately output a safe, reliable, economically optimal energy storage system configuration scheme and operation strategy applicable to various operating scenarios.
[0007] This invention provides a method for coordinated planning of photovoltaic and long-duration energy storage that considers the economics and security of distribution networks, comprising:
[0008] S1 selects the safety and economic evaluation indicators for the power distribution network;
[0009] S2 uses an improved spectral clustering algorithm to obtain power curves for typical scenarios and their occurrence probabilities;
[0010] S3 constructs a two-layer collaborative optimization configuration model for photovoltaic and long-term energy storage systems;
[0011] S4 is solved using an improved Harris Eagle algorithm based on a surrogate model.
[0012] Specifically, S1 selects power distribution network safety and economic evaluation indicators, including:
[0013] Four types of indicators are selected to measure the safety assessment level of the distribution network: node operation status safety, node balance safety, line operation status safety, and line balance safety.
[0014]
[0015]
[0016]
[0017]
[0018] in, These are the safe operating values for power grid nodes. It is the structural safety value of the power grid node. These are safety indicator values for the line's operational status. It is the line balance vulnerability index value;
[0019] and These represent the total number of nodes and the total number of branches in the distribution network, respectively. It is a node exist The per-unit safety value at any given time. and It is a node before standardization. The maximum and minimum safe values; It is a node exist The actual voltage value at that moment. It is a node The nominal voltage value, It is the maximum voltage offset; and These are the actual load and the maximum load, respectively. It is the number of scheduling cycles.
[0020] Specifically, S2 employs an improved spectral clustering algorithm to obtain power curves for typical scenarios and their occurrence probabilities, including:
[0021] Using historical operating data of the distribution network as the original scenario, an improved spectral clustering algorithm is employed to reduce the scenario. The original scenario power curve set is clustered and reduced to obtain typical scenario power curves and their occurrence probabilities. Let the time series to be clustered be... and .
[0022] Specifically, it includes:
[0023] S2.1 Calculate the adaptive similarity index of time series sequences ;
[0024] S2.2 Constructing the Time Series Laplace Matrix ;
[0025] S2.3 Solve the generalized characteristic problem and normalize the numerical values;
[0026] S2.4 performs K-means clustering on the normalized values to obtain cluster centers and thus typical scenarios and their probabilities of occurrence.
[0027] More specifically, S2.1 calculates the adaptive similarity index of time series sequences.
[0028]
[0029] in, It is a dynamic time-warped distance. yes and Pearson's first relation coefficient, and For the corresponding weights, It is the first difference of the time series;
[0030] More specifically, S2.2 constructs the time-series Laplace matrix.
[0031]
[0032] in, , To propagate regularization parameters for features, For regularization matrix
[0033]
[0034] in, It is a time series Time neighbor set, These are time series labels. It is a time decay parameter;
[0035] More specifically, S2.3 solves the generalized characteristic problem and performs numerical normalization;
[0036]
[0037] in, For time smoothing regularization parameters,
[0038]
[0039] in ;right Normalization of specificity
[0040]
[0041] Finally, for Perform K-means clustering to obtain cluster centers and thus typical scenarios and their probabilities of occurrence.
[0042] Specifically, S3 constructs a two-layer collaborative optimization configuration model for photovoltaic and long-duration energy storage systems, including:
[0043] S3.1 Construct a lower-level operation model considering indicators such as network security, network line loss, and operating costs;
[0044] The upper-level planning model S3.2 is used to determine the installation location and capacity of photovoltaic and energy storage systems, providing a basis for lower-level optimization scheduling.
[0045] More specifically, S3.1 considers network security, network line loss, and operating cost indicators to construct the lower-level operating model:
[0046]
[0047]
[0048]
[0049] in, It is a cybersecurity index. It's network line loss. It is the system operating cost; , , , It is the target weight; This represents the probability of the scenario occurring. For the line electrical conductivity, For the line susceptivity, This is the phase angle difference; and For nodes and nodes The phase angle difference, For nodes The operation and maintenance costs of photovoltaic systems For electricity purchase price, For electricity sales price, For the cost of curtailing electricity, For nodes The operation and maintenance costs of energy storage systems For the power output of the photovoltaic system, Purchase electricity for the system. For the system's electricity sales volume, For energy storage charging and discharging power, This is the available output curve for photovoltaic power generation.
[0050] Furthermore, in S3.1, the physical model of distribution network and equipment operation is further considered in the lower-level operation model, specifically including the following constraints:
[0051] (1) Power balance constraints;
[0052] (2) Voltage over-limit constraint;
[0053] (3) Energy storage charging and discharging constraints;
[0054] (4) Electricity purchase and sale constraints.
[0055] The specific constraints are as follows:
[0056] (1) Power balance constraint
[0057]
[0058]
[0059] in, and For nodes The active and reactive power injected.
[0060] (2) Voltage over-limit constraint
[0061]
[0062] in, , These are the upper and lower limits of the node voltage.
[0063] (3) Energy storage charging and discharging constraints
[0064]
[0065] in, and It is a node Energy storage The 0-1 variable representing the charging and discharging state at any given time. and It is a node Energy storage Constant charging and discharging power, This is the current charge level of the energy storage. , It refers to the charging and discharging efficiency of energy storage. and These are the upper and lower limits of the charge level. , It represents the upper and lower limits of the energy storage charging and discharging power.
[0066] (4) Electricity purchase and sale constraints
[0067] .
[0068] More specifically, the upper-level planning model S3.2 is used to determine the installation location and capacity of photovoltaic and energy storage systems, providing a basis for lower-level optimization scheduling, including setting objective functions and planning constraints.
[0069] (1) Objective function
[0070]
[0071] in, It takes into account the total investment cost discounted to present value. , These are the discount rates for photovoltaics and energy storage, respectively. , The planning lifespan for photovoltaic and energy storage, , It is the unit capacity investment cost of photovoltaics and energy storage. , It is the first The capacity of a photovoltaic or energy storage system.
[0072] (2) Planning constraints:
[0073] Planning constraints include both photovoltaic installation capacity constraints and energy storage installation capacity constraints, namely
[0074]
[0075]
[0076] In addition, to achieve the characteristics of long-term energy storage, the following constraints are further considered.
[0077]
[0078] in, This represents the number of hours that the energy storage can discharge at its maximum discharge power, typically taken as 4.
[0079] Specifically, S4 is solved using the improved Harris Hawk algorithm based on the surrogate model as follows:
[0080] The optimized representation of the two-layer collaborative optimization configuration model of photovoltaic and long-term energy storage systems in S3 is as follows:
[0081]
[0082] in, It is an abstract form of constraint formula (20)-formula (22). It is an abstract form of the constraint formulas (11)-(19).
[0083] The improved Harris Eagle algorithm solution method includes:
[0084] (1) Lower-level optimization problem: Equivalent method for multi-objective optimization problem based on surrogate model;
[0085] (2) Upper-level optimization problem: Upper-level optimization solution method based on improved Harris Eagle intelligent algorithm.
[0086] More specifically, the equivalent method for the lower-level optimization problem (1) described in S4, which is based on the surrogate model for multi-objective optimization problems, is as follows:
[0087] Let the upper-level parameter vector be , and generate it in the upper-level parameter space. Group parameter samples For each set of parameter samples, the corresponding lower-level mixed-integer nonlinear multi-objective optimization problem is solved offline to obtain its multi-objective optimization result, and then a performance index vector is extracted to characterize the optimization result:
[0088]
[0089] The performance indicators are continuous scalar indicators, including but not limited to hypervolume indicators of multi-objective Pareto fronts and objective function values corresponding to representative optimal solutions.
[0090] Therefore, a training sample set is constructed:
[0091]
[0092] To improve training stability, both input parameters and output metrics are linearly normalized.
[0093] The surrogate model employs a multi-layer feedforward neural network, whose forward propagation form is expressed as:
[0094]
[0095] in, For the input layer, , The first The weight matrix and bias vector of the layer, The activation function is the Modified Linear Unit Function (ReLU). In this embodiment, the activation function for the hidden layer is the Modified Linear Unit Function (ReLU):
[0096]
[0097] The output layer uses a linear activation function to predict continuous performance metrics.
[0098]
[0099] This allows for the construction of a nonlinear mapping model from parameters to the features of the lower-level optimization results.
[0100] The training objective of the surrogate model is to minimize the error between the predicted output and the true performance metric. In this implementation, the mean squared error loss function (MSE) is used as the training objective function, and its mathematical expression is:
[0101]
[0102] in, For the proxy model to the first The prediction results of the group parameter samples are calculated. The gradient of the loss function with respect to the network parameters is calculated by the backpropagation algorithm, and the network parameters are iteratively updated by the gradient-based optimization algorithm (such as the Adam adaptive moment estimation algorithm) until the loss function converges or the preset number of training rounds is reached.
[0103] The training sample set is divided into a training set and a validation set. After the model is trained, the validation set is used to evaluate the error of the surrogate model's prediction results. When the validation error is lower than a preset threshold, the surrogate model is considered to have the prediction accuracy to replace the lower-level optimization problem.
[0104] More specifically, the upper-level optimization problem (2) described in S4: the upper-level optimization solution method based on the improved Harris Eagle intelligent algorithm is as follows:
[0105] The upper-level optimization problem is solved using an improved Harris Eagle intelligent algorithm, and a trained deep learning agent model is used as a replacement model for the lower-level optimization problem, thereby achieving efficient hierarchical optimization.
[0106] Let the upper-level optimization decision variables be a vector.
[0107]
[0108] The upper-level optimization objective function, based on the surrogate model's prediction results, is expressed as:
[0109]
[0110] in, The performance metrics for predicting lower-level optimizations in deep learning agent models; Operators are constructed for the objective function that combines or scalarizes the performance indicators. Therefore, the upper-level optimization problem does not need to directly call the lower-level mixed-integer nonlinear multi-objective optimization model during the solution process, but can be quickly evaluated only through a surrogate model.
[0111] At the start of the upper-level optimization, initialize the Harris Eagle population, setting the population size to be... Each Harris Eagle corresponds to a set of candidate parameter solutions:
[0112]
[0113] The initial population is generated randomly or quasi-randomly, and satisfies the range constraints of the upper-level parameters. The surrogate model is used to evaluate the objective function of each candidate solution in the initial population, and the current optimal solution is selected as the prey position.
[0114] During the iteration process, the search behavior in the exploration and development phases is dynamically adjusted based on the improved Harris Eagle intelligent algorithm. This is achieved by introducing an energy factor. The ability of prey to escape is described and calculated as follows:
[0115]
[0116] in: The initial energy is a random value. This represents the current iteration number. This represents the maximum number of iterations. When... At this point, the algorithm is in the global exploration phase, and the Harris Eagle expands the search range within the parameter space using a random search strategy; when At this point, the algorithm enters the local exploration phase, performing a refined search around the current optimal solution. By introducing a nonlinear control factor to adaptively adjust the search step size, the algorithm's ability to escape local optima is improved, and its search stability in complex nonconvex parameter spaces is enhanced.
[0117] During the algorithm iteration process, a nonlinear control factor related to the number of iterations is introduced. It is used to dynamically adjust the search step size, and its expression is:
[0118]
[0119] in, and These are the minimum and maximum step size control coefficients, respectively. This is a nonlinear adjustment index used to control the rate of decline of the search step size. Through this nonlinear control factor, the algorithm maintains a larger search step size in the early stages of iteration to enhance global search capability, and gradually decreases the search step size in the later stages of iteration to improve local search accuracy.
[0120] In the improved Harris Eagle intelligent algorithm, the individual position update formula is modified from the original:
[0121]
[0122] Indicates the first Only Harris Eagle in the first The position at the next iteration; This indicates the direction of position change calculated based on the original trapping or exploration mechanism of the Harris Eagle intelligent algorithm. Through this method, the search step size is adaptively adjusted with the iteration process, and random perturbations are introduced at key stages, thereby improving global search capability while maintaining algorithm convergence.
[0123] After each position update, a deep learning proxy model is used to quickly predict the updated parameter solution, obtain the corresponding lower-level optimization performance index, and calculate the fitness function value accordingly.
[0124]
[0125] The iterative process of improving the Harris Eagle intelligent algorithm will terminate when any of the following conditions are met:
[0126] 1. Reach the maximum number of iterations;
[0127] 2. The optimal fitness function value changes below a preset threshold in several consecutive iterations.
[0128] After termination, output the currently obtained optimal upper-level parameter solution:
[0129]
[0130] After completing the upper-level optimization solution, the final result is output as follows:
[0131] 1. Output the optimal upper-level parameter configuration , as the optimal decision parameter of the system;
[0132] 2. Based on the surrogate model, output the predicted values of the lower-level optimization performance indicators corresponding to the optimal parameters;
[0133] 3. Optionally, the optimal parameters are solved by calling a lower-level mixed-integer nonlinear multi-objective optimization model to verify the prediction results of the surrogate model;
[0134] 4. Output the optimal parameters and corresponding performance indicators in the form of data files, control commands, or system configuration parameters for subsequent system operation or decision-making modules to call.
[0135] Beneficial Effects: Compared with existing technologies, the significant advantages of this invention are: by introducing a comprehensive safety assessment index system and an improved spectral clustering scenario generation method, it can systematically assess power grid safety risks and finely characterize source-load uncertainties, thereby significantly improving the reliability, adaptability, and robustness of configuration schemes during the planning stage; simultaneously, by utilizing a planning-operation two-layer collaborative optimization framework, capacity configuration and operation strategies are jointly iteratively solved, effectively addressing the problem of decision-making disconnect in traditional phased optimization, and achieving significant optimization of the entire life cycle economy while ensuring safety constraints; furthermore, this method employs an improved Harris Eagle algorithm based on a surrogate model for efficient solution, reducing complex simulation calls through the surrogate model, and significantly improving computational efficiency while ensuring solution accuracy, providing a practical decision-making tool for the collaborative planning of photovoltaics and long-term energy storage in complex distribution network scenarios. Attached Figure Description
[0136] Figure 1 This is a computational example diagram of the IEEE-33 node in an embodiment of the present invention.
[0137] Figure 2 This is a photovoltaic power output scenario diagram according to an embodiment of the present invention.
[0138] Figure 3 This is a load output scenario diagram of an embodiment of the present invention.
[0139] Figure 4 This is a flowchart illustrating the implementation of the present invention. Detailed Implementation
[0140] See attached document Figure 1-4 This embodiment provides a method for coordinated planning of photovoltaic and long-duration energy storage that considers the economics and security of distribution networks. The method includes:
[0141] (1) Selection of distribution network safety and economic evaluation indicators: Typical distribution network safety and economic evaluation indicators include node operating status safety ( ), node balance security ( ), Line operation status safety ( ) and line balance safety ( The four categories of indicators, including ( ), are used to measure the safety assessment level of the power distribution network.
[0142]
[0143]
[0144]
[0145]
[0146] in, These are the safe operating values for power grid nodes. It is the structural safety value of the power grid node. These are safety indicator values for the line's operational status. It is the line balance vulnerability index value. and These represent the total number of nodes and the total number of branches in the distribution network, respectively. It is a node exist The per-unit safety value at any given time. and It is a node before standardization. The maximum and minimum safe values. It is a node exist The actual voltage value at that moment. It is a node The nominal voltage value, It is the maximum voltage offset. and These are the actual load and the maximum load, respectively. It is the number of scheduling cycles.
[0147] (2) An improved spectral clustering algorithm is used to obtain the power curves of typical scenarios and their occurrence probabilities, namely:
[0148] Using historical operational data of the power distribution network as the original scenario, an improved spectral clustering algorithm is employed to reduce the scenario. This process clusters and reduces the power curve set of the original scenario to obtain typical scenario power curves and their occurrence probabilities. Let the time series to be clustered be... and First, calculate the adaptive similarity index of time series sequences.
[0149]
[0150] in, It is a dynamic time-warped distance. yes and Pearson's first relation coefficient, and For the corresponding weights, It is the first difference of a time series.
[0151] Secondly, construct the time-series Laplace matrix.
[0152]
[0153] in, , To propagate regularization parameters for features, For regularization matrix
[0154]
[0155] in, It is a time series Time neighbor set, These are time series labels. It is a time decay parameter.
[0156] Then, solve the generalized feature problem.
[0157]
[0158] in, For time smoothing regularization parameters,
[0159]
[0160] in .right Normalization of specificity
[0161]
[0162] Finally, for Perform K-means clustering to obtain cluster centers and thus typical scenarios and their probabilities of occurrence.
[0163] (3) Construct a two-layer collaborative optimization configuration model for photovoltaic and long-term energy storage systems, including:
[0164] The lower-level operation model is constructed by considering key indicators such as network security, network line loss, and operating costs.
[0165]
[0166]
[0167]
[0168] in, It is a cybersecurity index. It's network line loss. It is the system operating cost. , , , It is the target weight. This represents the probability of the scenario occurring. For the line electrical conductivity, For the line susceptivity, This is the phase angle difference. and For nodes and nodes The phase angle difference, For nodes The operation and maintenance costs of photovoltaic systems For electricity purchase price, For electricity sales price, For the cost of curtailing electricity, For nodes The operation and maintenance costs of energy storage systems For the power output of the photovoltaic system, Purchase electricity for the system. For the system's electricity sales volume, For energy storage charging and discharging power, This is the available output curve for photovoltaic power generation.
[0169] The physical model of distribution network and equipment operation is further considered in the lower-level operation model:
[0170] Power balance constraints
[0171]
[0172]
[0173] in, and For nodes The active and reactive power injected.
[0174] Voltage over-limit constraint:
[0175]
[0176] in, , These are the upper and lower limits of the node voltage.
[0177] Energy storage charge and discharge constraints:
[0178]
[0179] in, and It is a node Energy storage The 0-1 variable representing the charging and discharging state at any given time. and It is a node Energy storage Constant charging and discharging power, This is the current charge level of the energy storage. , It refers to the charging and discharging efficiency of energy storage. and These are the upper and lower limits of the charge level. , It represents the upper and lower limits of the energy storage charging and discharging power.
[0180] Electricity purchase and sale constraints:
[0181]
[0182] The upper-level planning model is used to determine the installation location and capacity of photovoltaic and energy storage systems, providing a basis for lower-level optimization scheduling.
[0183] Objective function:
[0184]
[0185] in, It takes into account the total investment cost discounted to present value. , These are the discount rates for photovoltaics and energy storage, respectively. , The planning lifespan for photovoltaic and energy storage, , It is the unit capacity investment cost of photovoltaics and energy storage. , It is the first The capacity of a photovoltaic or energy storage system.
[0186] constraint:
[0187] Planning constraints include both photovoltaic installation capacity constraints and energy storage installation capacity constraints, namely
[0188]
[0189]
[0190] In addition, to achieve the characteristics of long-term energy storage, the following constraints are further considered.
[0191]
[0192] in, This represents the number of hours that the energy storage can discharge at its maximum discharge power, typically taken as 4.
[0193] (4) Solve using the improved Harris Hawk algorithm based on the surrogate model:
[0194] The general form of the above optimization problem is:
[0195]
[0196] This is a two-level optimization problem, where the lower-level optimization problem is a mixed-integer nonlinear multi-objective optimization problem, and the upper-level optimization problem is a linear programming problem. To solve this problem, this invention proposes an improved Harris Hawk algorithm based on a surrogate model.
[0197] Lower-level optimization problem: Equivalent method for multi-objective optimization problem based on surrogate model
[0198] Let the upper-level parameter vector be Generate in the upper parameter space Group parameter samples For each set of parameter samples, the corresponding lower-level mixed-integer nonlinear multi-objective optimization problem is solved offline to obtain its multi-objective optimization result, and then a performance index vector is extracted to characterize the optimization result:
[0199]
[0200] The performance indicators are continuous scalar indicators, including but not limited to hypervolume indicators of multi-objective Pareto fronts and objective function values corresponding to representative optimal solutions.
[0201] Therefore, a training sample set is constructed:
[0202]
[0203] To improve training stability, both input parameters and output metrics are linearly normalized.
[0204] The surrogate model employs a multi-layer feedforward neural network, whose forward propagation form is expressed as:
[0205]
[0206] in, For the input layer, , The first The weight matrix and bias vector of the layer, The activation function is the Modified Linear Unit Function (ReLU). In this embodiment, the activation function for the hidden layer is the Modified Linear Unit Function (ReLU):
[0207]
[0208] The output layer uses a linear activation function to predict continuous performance metrics.
[0209]
[0210] This allows for the construction of a nonlinear mapping model from parameters to the features of the lower-level optimization results.
[0211] The training objective of the surrogate model is to minimize the error between the predicted output and the true performance metric. In this implementation, the mean squared error loss function (MSE) is used as the training objective function, and its mathematical expression is:
[0212]
[0213] in, For the proxy model to the first The prediction results of the group parameter samples are calculated. The gradient of the loss function with respect to the network parameters is calculated by the backpropagation algorithm, and the network parameters are iteratively updated by the gradient-based optimization algorithm (such as the Adam adaptive moment estimation algorithm) until the loss function converges or the preset number of training rounds is reached.
[0214] The training sample set is divided into a training set and a validation set. After the model is trained, the validation set is used to evaluate the error of the surrogate model's prediction results. When the validation error is lower than a preset threshold, the surrogate model is considered to have the prediction accuracy to replace the lower-level optimization problem.
[0215] Upper-level optimization problem: A solution method for upper-level optimization based on an improved Harris Eagle intelligent algorithm
[0216] The upper-level optimization problem is solved using an improved Harris Eagle intelligent algorithm, and a trained deep learning agent model is used as a replacement model for the lower-level optimization problem, thereby achieving efficient hierarchical optimization.
[0217] Let the upper-level optimization decision variables be a vector.
[0218]
[0219] The upper-level optimization objective function, based on the surrogate model's prediction results, is expressed as:
[0220]
[0221] in, The performance metrics for predicting lower-level optimizations in deep learning agent models; Operators are constructed for the objective function that combines or scalarizes the performance indicators. Therefore, the upper-level optimization problem does not need to directly call the lower-level mixed-integer nonlinear multi-objective optimization model during the solution process, but can be quickly evaluated only through a surrogate model.
[0222] At the start of the upper-level optimization, initialize the Harris Eagle population, setting the population size to be... Each Harris Eagle corresponds to a set of candidate parameter solutions:
[0223]
[0224] The initial population is generated randomly or quasi-randomly, and satisfies the range constraints of the upper-level parameters. The surrogate model is used to evaluate the objective function of each candidate solution in the initial population, and the current optimal solution is selected as the prey position.
[0225] During the iteration process, the search behavior in the exploration and development phases is dynamically adjusted based on the improved Harris Eagle intelligent algorithm. This is achieved by introducing an energy factor. The ability of prey to escape is described and calculated as follows:
[0226]
[0227] in: The initial energy is a random value. This represents the current iteration number. This represents the maximum number of iterations. When... At this point, the algorithm is in the global exploration phase, and the Harris Eagle expands the search range within the parameter space using a random search strategy; when At this point, the algorithm enters the local exploration phase, performing a refined search around the current optimal solution. By introducing a nonlinear control factor to adaptively adjust the search step size, the algorithm's ability to escape local optima is improved, and its search stability in complex nonconvex parameter spaces is enhanced.
[0228] During the algorithm iteration process, a nonlinear control factor related to the number of iterations is introduced. It is used to dynamically adjust the search step size, and its expression is:
[0229]
[0230] in, and These are the minimum and maximum step size control coefficients, respectively. This is a nonlinear adjustment index used to control the rate of decline of the search step size. Through this nonlinear control factor, the algorithm maintains a larger search step size in the early stages of iteration to enhance global search capability, and gradually decreases the search step size in the later stages of iteration to improve local search accuracy.
[0231] In the improved Harris Eagle intelligent algorithm, the individual position update formula is modified from the original:
[0232]
[0233] Indicates the first Only Harris Eagle in the first The position at the next iteration; This indicates the direction of position change calculated based on the original trapping or exploration mechanism of the Harris Eagle intelligent algorithm. Through this method, the search step size is adaptively adjusted with the iteration process, and random perturbations are introduced at key stages, thereby improving global search capability while maintaining algorithm convergence.
[0234] After each position update, a deep learning proxy model is used to quickly predict the updated parameter solution, obtain the corresponding lower-level optimization performance index, and calculate the fitness function value accordingly.
[0235]
[0236] The iterative process of improving the Harris Eagle intelligent algorithm will terminate when any of the following conditions are met:
[0237] 1. Reach the maximum number of iterations;
[0238] 2. The optimal fitness function value changes below a preset threshold in several consecutive iterations.
[0239] After termination, output the currently obtained optimal upper-level parameter solution:
[0240]
[0241] After completing the upper-level optimization solution, this invention outputs the final result in the following manner:
[0242] 1. Output the optimal upper-level parameter configuration , as the optimal decision parameter of the system;
[0243] 2. Based on the surrogate model, output the predicted values of the lower-level optimization performance indicators corresponding to the optimal parameters;
[0244] 3. Optionally, the optimal parameters are solved by calling a lower-level mixed-integer nonlinear multi-objective optimization model to verify the prediction results of the surrogate model;
[0245] 4. Output the optimal parameters and corresponding performance indicators in the form of data files, control commands, or system configuration parameters for subsequent system operation or decision-making modules to call.
[0246] (5) Based on the proposed planning method, calculate the capacity of the distribution network photovoltaic and long-term energy storage configurations. The specific steps are as follows:
[0247] Step 1: Obtain historical operation data of the distribution network and construct calculation formulas for multi-dimensional safety assessment indicators of nodes and lines;
[0248] Step 2: Use an improved spectral clustering algorithm to perform cluster analysis on historical data to generate typical operating scenarios and their probability of occurrence;
[0249] Step 3: For each typical scenario, establish a multi-objective optimization model with safety, line loss, and operating cost as objectives, and solve the operating strategy;
[0250] Step 4: Based on the solution results of the lower-level model, train a neural network surrogate model to establish a fast mapping relationship between "planning parameters and runtime performance".
[0251] Step 5: With the goal of minimizing the total life cycle cost, the improved Harris Eagle algorithm combined with the surrogate model is used to optimize the site selection and capacity determination scheme of photovoltaic and energy storage.
[0252] Step 6: Output the optimal capacity configuration, energy storage scheduling strategies for typical scenarios, and provide an executable system deployment plan.
[0253] Example explanation:
[0254] This patented method was fully validated using a complete computational example in an extended IEEE 33-node distribution system. The system pre-set photovoltaic access points at nodes 6, 18, 22, and 30, and constructed 35,040 time-series scenarios with one-hour intervals using actual annual solar irradiance and load data for a specific region. First, based on the four types of safety indicators defined in the patent, the quantitative safety values for each node and line were calculated, and weights were assigned to form a comprehensive safety evaluation target. Then, an improved spectral clustering algorithm integrating dynamic time warping and Pearson correlation coefficients was used to cluster the massive time-series curves, reducing them to five typical scenarios and their probabilities of occurrence, providing refined uncertainty modeling for subsequent optimization.
[0255] At the optimization solution level, a two-layer planning-running model was constructed. The lower layer is a multi-objective mixed-integer nonlinear running model with constraints including power balance, voltage, and energy storage dynamics. To overcome the challenges of computational complexity and difficulty in embedding it into the upper-layer planning, a surrogate model employs a three-layer feedforward neural network: the input layer is 2-dimensional (the planned capacity of photovoltaic and energy storage), the hidden layer has 16 neurons using the ReLU activation function, and the output layer has linear activation, outputting a 1-dimensional lower-layer performance index (i.e., the normalized value of the Pareto front hypervolume). Training was performed using 200 sets of random samples, and the mean square error was minimized using the Adam optimizer. The validation set error was less than 1%, successfully establishing a fast and accurate mapping from planning parameters to system performance. The upper-layer planning aims to minimize the total lifecycle cost and is optimized using an improved Harris Eagle algorithm. This algorithm introduces a nonlinear adaptive step size control factor, dynamically balancing global exploration and local development during iteration, and replacing expensive inner-layer simulations with the trained surrogate model to efficiently solve for the optimal configuration scheme.
[0256] The final planning result is as follows: 523kW, 312kW, 406kW, and 653kW of photovoltaic power will be configured at nodes 6, 18, 22, and 30, respectively, along with 2234kWh, 1564kWh, 1829kWh, and 2501kWh of supporting long-term energy storage. The total lifecycle cost is RMB 12.4723 million, which is approximately 18% lower than the traditional single-stage planning method. Simulation verification under a typical high photovoltaic and high-load scenario shows that the system's photovoltaic absorption rate reaches 96.2%, the voltage of each node is maintained between 0.95 and 1.03 pu throughout the day, and the energy storage system achieves intelligent scheduling based on electricity price and output curves (such as charging at noon and discharging in the evening). The annual operating cost is 31% lower than the baseline scenario without energy storage, fully demonstrating the synergistic optimization capability of this method in improving economic efficiency, ensuring safety, and promoting absorption.
Claims
1. A method for coordinated planning of photovoltaic and long-duration energy storage considering the economics and security of distribution networks, characterized in that, include: S1 selects the safety and economic evaluation indicators for the power distribution network; S2 uses an improved spectral clustering algorithm to obtain power curves for typical scenarios and their occurrence probabilities; S3 constructs a two-layer collaborative optimization configuration model for photovoltaic and long-term energy storage systems; S4 is solved using an improved Harris Eagle algorithm based on a surrogate model.
2. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 1, characterized in that, S1 selects power distribution network safety and economic evaluation indicators, including: Four types of indicators are selected to measure the safety assessment level of the distribution network: node operation status safety, node balance safety, line operation status safety, and line balance safety. in, These are the safe operating values for power grid nodes. It is the structural safety value of the power grid node. These are safety indicator values for the line's operational status. It is the line balance vulnerability index value; and These represent the total number of nodes and the total number of branches in the distribution network, respectively. It is a node exist The per-unit safety value at any given time. and It is a node before standardization. The maximum and minimum safe values; It is a node exist The actual voltage value at that moment. It is a node The nominal voltage value, It is the maximum voltage offset; and These are the actual load and the maximum load, respectively. It is the number of scheduling cycles.
3. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 1, characterized in that, S2 employs an improved spectral clustering algorithm to obtain power curves for typical scenarios and their occurrence probabilities, including: Using historical operating data of the distribution network as the original scenario, an improved spectral clustering algorithm is employed to reduce the scenario. The original scenario power curve set is clustered and reduced to obtain typical scenario power curves and their occurrence probabilities. Let the time series to be clustered be... and ; Specifically, it includes: S2.1 Calculate the adaptive similarity index of time series sequences ; S2.2 Constructing the Time Series Laplace Matrix ; S2.3 Solve the generalized characteristic problem and normalize the numerical values; S2.4 performs K-means clustering on the normalized values to obtain cluster centers and thus typical scenarios and their probabilities of occurrence.
4. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 3, characterized in that, S2.1 Calculate the adaptive similarity index of time series sequences in, It is a dynamic time-warped distance. yes and Pearson's first relation coefficient, and For the corresponding weights, It is the first difference of a time series.
5. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 3, characterized in that, S2.2 Constructing the Time Series Laplace Matrix in, , To propagate regularization parameters for features, For regularization matrix in, It is a time series Time neighbor set, These are time series labels. It is a time decay parameter.
6. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 3, characterized in that, S2.3 Solve the generalized characteristic problem and normalize the numerical values; in, For time smoothing regularization parameters, in ;right Normalization of specificity Finally, for Perform K-means clustering to obtain cluster centers and thus typical scenarios and their probabilities of occurrence.
7. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security according to claim 1, characterized in that, S3 constructs a two-layer collaborative optimization configuration model for photovoltaic and long-duration energy storage systems, including: S3.1 Construct a lower-level operation model considering indicators such as network security, network line loss, and operating costs; The upper-level planning model S3.2 is used to determine the installation location and capacity of photovoltaic and energy storage systems, providing a basis for lower-level optimization scheduling.
8. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 7, characterized in that, S3.1 Construct a lower-level operational model considering indicators such as network security, network line loss, and operating costs: in, It is a cybersecurity index. It's network line loss. It is the system operating cost; , , , It is the target weight; This represents the probability of the scenario occurring. For the line electrical conductivity, For the line susceptivity, This is the phase angle difference; and For nodes and nodes The phase angle difference, For nodes The operation and maintenance costs of photovoltaic systems For electricity purchase price, For electricity sales price, For the cost of curtailing electricity, For nodes The operation and maintenance costs of energy storage systems For the power output of the photovoltaic system, Purchase electricity for the system. For the system's electricity sales volume, For energy storage charging and discharging power, This is the available output curve for photovoltaic power generation.
9. A method for coordinated planning of photovoltaic and long-duration energy storage considering the economics and security of distribution networks, as described in claim 7, is characterized in that... In S3.1, the physical model of distribution network and equipment operation is further considered in the lower-level operation model, specifically including the following constraints: (1) Power balance constraints; (2) Voltage over-limit constraint; (3) Energy storage charging and discharging constraints; (4) Electricity purchase and sale constraints.
10. A method for coordinated planning of photovoltaic and long-duration energy storage considering the economy and security of distribution networks, as described in claim 9, is characterized in that... The specific constraints are as follows: (1) Power balance constraint in, and For nodes Active and reactive power injection power; (2) Voltage over-limit constraint in, , These are the upper and lower limits of the node voltage; (3) Energy storage charging and discharging constraints in, and It is a node Energy storage The 0-1 variable representing the charging and discharging state at any given time. and It is a node Energy storage Constant charging and discharging power, This represents the current charge level of the energy storage system; , It refers to the charging and discharging efficiency of energy storage; and These are the upper and lower limits of the charge level; , These are the upper and lower limits of the energy storage charging and discharging power; (4) Electricity purchase and sale constraints 。 11. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 7, characterized in that, The upper-level planning model S3.2 is used to determine the installation location and capacity of photovoltaic and energy storage systems, providing a basis for lower-level optimization scheduling, including setting objective functions and planning constraints; (1) Objective function in, It takes into account the total investment cost discounted to present value; , These are the discount rates for photovoltaics and energy storage, respectively. , The planning lifespan for photovoltaic and energy storage, , It is the unit capacity investment cost of photovoltaics and energy storage; , It is the first The capacity of a photovoltaic or energy storage unit; (2) Planning constraints: Planning constraints include both photovoltaic installation capacity constraints and energy storage installation capacity constraints, namely In addition, to achieve the characteristics of long-term energy storage, the following constraints are further considered. in, This represents the number of hours that the energy storage can discharge at its maximum discharge power.
12. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 1, characterized in that, The solution in S4 is obtained using the improved Harris Hawk algorithm based on the surrogate model: The optimized representation of the two-layer collaborative optimization configuration model of photovoltaic and long-term energy storage systems in S3 is as follows: in, It is an abstract form of constraint formula (20)-formula (22). It is an abstract form of the constraint formulas (11)-(19).
13. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 12, characterized in that, The improved Harris Eagle algorithm solution method includes: (1) Lower-level optimization problem: Equivalent method for multi-objective optimization problem based on surrogate model; (2) Upper-level optimization problem: Upper-level optimization solution method based on improved Harris Eagle intelligent algorithm.
14. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 13, characterized in that, The equivalent method for the lower-level optimization problem (1) described in S4, based on the surrogate model, is as follows: Let the upper-level parameter vector be , and generate it in the upper-level parameter space. Group parameter samples For each set of parameter samples, the corresponding lower-level mixed-integer nonlinear multi-objective optimization problem is solved offline to obtain its multi-objective optimization result, and then a performance index vector is extracted to characterize the optimization result: The performance index is a continuous scalar index, including but not limited to the hypervolume index of the multi-objective Pareto front and the objective function value corresponding to the representative optimal solution; Therefore, a training sample set is constructed: To improve training stability, both input parameters and output metrics are linearly normalized. The surrogate model employs a multi-layer feedforward neural network, whose forward propagation form is expressed as: in, For the input layer, , The first Layer weight matrix and bias vector, The activation function is the modified linear unit function (ReLU) used in this embodiment. The output layer uses a linear activation function to predict continuous performance metrics. This allows for the construction of a nonlinear mapping model from parameters to the features of the lower-level optimization results; The training objective of the surrogate model is to minimize the error between the predicted output and the true performance metric; the mean squared error loss function (MSE) is used as the training objective function, and its mathematical expression is: in, For the proxy model to the first The prediction results of the group parameter samples; the gradient of the loss function with respect to the network parameters is calculated by the backpropagation algorithm, and the network parameters are iteratively updated by the gradient-based optimization algorithm until the loss function converges or the preset training rounds are reached; The training sample set is divided into a training set and a validation set. After the model is trained, the validation set is used to evaluate the error of the surrogate model's prediction results. When the validation error is lower than a preset threshold, the surrogate model is considered to have the prediction accuracy to replace the lower-level optimization problem.
15. The photovoltaic and long-duration energy storage coordinated planning method considering distribution network economy and security as described in claim 13, characterized in that, The upper-level optimization problem (2) described in S4: The upper-level optimization solution method based on the improved Harris Eagle intelligent algorithm is as follows: The upper-level optimization problem is solved using an improved Harris Eagle intelligent algorithm, and a trained deep learning agent model is used as a replacement model for the lower-level optimization problem, thereby achieving efficient hierarchical optimization solution. Let the upper-level optimization decision variables be a vector. The upper-level optimization objective function, based on the surrogate model's prediction results, is expressed as: in, The performance metrics for predicting lower-level optimizations in deep learning agent models; Operators are constructed for the objective function that combines or scalarizes the performance indicators; thus, the upper-level optimization problem does not need to directly call the lower-level mixed-integer nonlinear multi-objective optimization model during the solution process, but only performs fast evaluation through the surrogate model; At the start of the upper-level optimization, initialize the Harris Eagle population, setting the population size to be... Each Harris Eagle corresponds to a set of candidate parameter solutions: The initial population is generated randomly or quasi-randomly and satisfies the range constraints of the upper-level parameters; the surrogate model is used to evaluate the objective function of each candidate solution in the initial population, and the current optimal solution is selected as the prey position; During the iteration process, the search behavior in the exploration and development phases is dynamically adjusted based on the improved Harris Eagle intelligent algorithm; and an energy factor is introduced. The ability of prey to escape is described and calculated as follows: in: The initial energy is a random value. This represents the current iteration number. The maximum number of iterations; when At this point, the algorithm is in the global exploration phase, and the Harris Eagle expands the search range within the parameter space using a random search strategy; when At this point, the algorithm enters the local development stage, where it performs a fine search around the current optimal solution. By introducing a nonlinear control factor to adaptively adjust the search step size, the algorithm's ability to escape local optima is improved, and the search stability in complex non-convex parameter spaces is enhanced. During the algorithm iteration process, a nonlinear control factor related to the number of iterations is introduced. It is used to dynamically adjust the search step size, and its expression is: in, and These are the minimum and maximum step size control coefficients, respectively; The nonlinear adjustment index is used to control the rate of decay of the search step size. Through the above nonlinear control factor, the algorithm maintains a large search step size in the early stage of iteration to enhance the global search capability, and gradually reduces the search step size in the later stage of iteration to improve the local search accuracy. In the improved Harris Eagle intelligent algorithm, the individual position update formula is modified from the original: Indicates the first Only Harris Eagle in the 1st The position at the next iteration; This indicates the direction of position change calculated based on the original trapping or exploration mechanism of the Harris Eagle intelligent algorithm. Through the above method, the search step size is adaptively adjusted with the iteration process, and random perturbations are introduced at key stages, thereby improving the global search capability while maintaining the convergence of the algorithm. After each position update, a deep learning proxy model is used to quickly predict the updated parameter solution, obtain the corresponding lower-level optimization performance index, and calculate the fitness function value accordingly. The iterative process of improving the Harris Eagle intelligent algorithm will terminate when any of the following conditions are met: (1) Reach the maximum number of iterations; (2). The value of the optimal fitness function changes below a preset threshold in several consecutive iterations; After termination, output the currently obtained optimal upper-level parameter solution: After completing the upper-level optimization solution, the final result is output as follows: (1) Output the optimal upper-level parameter configuration , as the optimal decision parameter of the system; (2). Based on the surrogate model, output the predicted value of the lower-level optimization performance index corresponding to the optimal parameters; (3). Optionally, the optimal parameters are solved by calling the lower-level mixed integer nonlinear multi-objective optimization model to verify the prediction results of the proxy model; (4) Output the optimal parameters and corresponding performance indicators in the form of data files, control instructions or system configuration parameters for subsequent system operation or decision-making modules to call.