Robust planning method and system for power distribution system network storage based on coupling of light time-space randomness

Abstract

This invention discloses a robust planning method and system for grid-storage distribution systems with spatiotemporal stochastic coupling of photovoltaic (PV) and electric vehicle (EV) charging loads. The main contents include: constructing a joint source-load probability distribution model using a multivariate Student's t-Copula function to capture the symmetric tail correlation between PV output and load under extremely unfavorable scenarios; introducing relevant structure injection and equal probability mapping into the t-Copula latent variable space, reconstructing the net load probability distribution using Gram-Charlier series expansion, and constructing a box-shaped uncertainty set consistent with the probability coverage level by calibrating the global uncertainty budget parameter Γ through Monte Carlo sampling of the t-Copula joint distribution; embedding the demand price elasticity response mechanism into the second-stage node net load injection constraint to establish a two-stage robust optimization configuration model. This method accurately characterizes the spatiotemporal coupling stochasticity of distributed PV and EV charging loads while achieving synergistic hedging of passive uncertainty bearing and active demand-side response, effectively improving the economy and robustness of the planning scheme.

Description

Technical Field

[0001] This invention belongs to the field of distribution network planning and is applicable to the optimization planning problem of distribution networks with distributed photovoltaic and electric vehicle charging load access. It involves a robust planning method for distribution system grid-storage based on the spatiotemporal random coupling of photovoltaic and charging. Background Technology

[0002] Guided by the "dual carbon" goal, distributed renewable energy, represented by photovoltaics, and new loads, represented by electric vehicles, are being massively integrated into the distribution network, profoundly changing its source-load characteristics and operation. On the source side, distributed photovoltaic output is significantly affected by factors such as solar radiation intensity and meteorological conditions, exhibiting uncertainty and volatility far exceeding traditional power generation methods. With a large number of photovoltaic systems connected to the grid, the randomness of power distribution in the distribution network increases dramatically, leading to problems such as heavy overloads, high or low voltage at the end of lines in some areas, and consequently, curtailment of solar power. On the load side, the number of electric vehicles continues to grow rapidly, and the randomness and temporal aggregation of charging loads place new pressure on the distribution network, with some areas already experiencing significant absorption pressure. On the energy storage side, the cost of new energy storage technologies continues to decline while performance significantly improves. Distribution network energy storage has been proven in practice to effectively mitigate the impact of photovoltaic grid connection and charging load fluctuations, serving as an important means to address these challenges.

[0003] To address the aforementioned issues, scholars both domestically and internationally have conducted extensive research on distribution network planning, energy storage configuration, and retrofitting technologies. Some studies focus on distribution network expansion planning under distributed generation integration, proposing planning methods based on transmission capacity or reliability indicators; others address the coordinated configuration of photovoltaics and energy storage, proposing site selection and capacity determination methods based on cluster partitioning or robust optimization; still others explore retrofitting strategies to enhance the carrying capacity of distribution networks from the perspectives of flexible load shaping and demand response.

[0004] However, the above studies have the following shortcomings: First, most existing photovoltaic (PV) distribution network plans are based on a single section or a few typical output levels, neglecting the comprehensive impact of the combined fluctuations of PV output and charging load on the distribution network. This leads to significant deviations between the planning results and actual operating scenarios, easily resulting in problems such as localized heavy overloads, high and low voltage at the end of lines, and curtailment of solar power, or excessively high investment costs due to overly conservative scenarios. Second, existing methods generally fail to comprehensively consider the synergistic impact of distributed PV and electric vehicle (EV) charging loads on distribution network planning, making it difficult to simultaneously alleviate the two core problems of limited EV charging load capacity and bottlenecks in distributed PV access. Therefore, it is necessary to study robust planning methods for distribution systems with spatiotemporal stochastic coupling of PV and charging, in order to improve the economy and robustness of planning schemes while ensuring the safe and reliable operation of the system. Summary of the Invention

[0005] This invention provides a robust planning method and system for power distribution systems with spatiotemporal random coupling of photovoltaic charging, specifically including: (1) A source-load joint probability distribution model was constructed using the multivariate Student's t-Copula function to capture the symmetric tail correlation between photovoltaic output and load under extreme adverse scenarios. This solves the problem that existing methods usually treat photovoltaic and load as independent random variables and ignore the joint probability of both deteriorating simultaneously under extreme scenarios. (2) Introduce relevant structure injection and equal probability mapping in the t-Copula latent variable space, use the three-point estimation method of dependency preservation to estimate the net load in a reduced moment, and combine Gram-Charlier series expansion to reconstruct the net load probability distribution; then, by performing Monte Carlo sampling on the above t-Copula joint distribution, take the quantile of the scenario total normalization deviation to calibrate the global uncertainty budget parameter Γ, and construct a box uncertainty set consistent with the probability coverage level; (3) Based on the above uncertainty set, a two-stage robust optimization configuration model is established, and the demand price elasticity response mechanism is embedded into the node net load injection constraint to form a flexible hedging mechanism that combines passive bearing of uncertainty and active response of demand side. The improved C&CG algorithm is used to solve the problem, and the worst scenario is pre-screened for each iteration subproblem using the Monte Carlo sampling scenario library in step (2) to guide the search direction and accelerate convergence.

[0006] The specific steps for constructing the source-load joint probability distribution model based on t-Copula in step (1) are as follows: Step i: Probabilistic modeling of distributed photovoltaic power output, providing two methods: Method 1: Photovoltaic probability model based on β distribution. When historical data is sufficient and the assumption that irradiance follows a β distribution holds, the probability density function of photovoltaic output is: (1) In the formula, the shape parameter and Determined by the statistical characteristics of historical data, This refers to the installed capacity of photovoltaic power.

[0007] Method 2: A real-time photovoltaic probabilistic model based on the superposition of the HDKR model and normal error. When the irradiance does not follow a β distribution, the HDKR model is used to obtain the real-time irradiance sequence, and the predicted photovoltaic output is calculated by combining it with a piecewise output model. : (2) In the formula, This refers to the rated power of the photovoltaic system. Rated irradiance; The critical irradiation intensity at which the output characteristics change from nonlinear to linear. For the first t Real-time irradiance intensity per hour. (Based on predicted values) The base values ​​are superimposed with a mean of 0 and a standard deviation of 0. The normal distribution error, proportional to the predicted value, characterizes the prediction uncertainty. The probability density function of the prediction error is: (3) (4) In the formula, For prediction error, Let be the standard deviation of its normal distribution. The real-time photovoltaic output, considering prediction errors, is: (5) Step ii: Electric vehicle charging load modeling, the specific process is as follows: a) The k-means clustering algorithm was used to segment historical daily charging load data into different scenarios. Each sample represents a time-series vector of the charging load over a single day (24 hours). The clustering objective function is: (6) In the formula, K To preset the number of clusters, It is the first k Clusters, It is the cluster center.

[0008] b) Using the contour coefficient method in K The optimal number of clusters is determined from 2 to 10. (Sample) The contour coefficient is: (7) In the formula, The average distance between a sample and its cluster members. This represents the average distance between the sample and the nearest heterogeneous cluster. The sample is selected when the average silhouette coefficient is maximized. K The value is used as the optimal cluster number to obtain K Typical daily load scenario curves and the probability of occurrence of each scenario.

[0009] c) For each typical scenario, load data at each time period are modeled using GMM for detailed analysis. Parameters are estimated iteratively using the EM algorithm. k A typical scenario t The probability density function of the preload response for the time period is: (8) In this formula, M is the number of Gaussian components; , , These are the weights, mean, and variance of the m-th Gaussian component, respectively.

[0010] d) Introduce a demand price elasticity matrix, using the self-elasticity coefficient. (Usually negative) Characterizes the effect of electricity price changes on its own charging load during this period, using the cross-elasticity coefficient. (Usually a positive value) Characterizing the load time shift effect, the charging load after the response is expressed as: (9) (10) In the formula, In response to the previous baseline charging load, The benchmark electricity price, This represents the real-time electricity price for each time period.

[0011] Step iii: Conventional load probability modeling, with both active and reactive power modeled using normal distribution: (11) (12) Considering the temporal correlation and drift phenomenon of the load, the probability box theory is used for modeling. The upper and lower bounds of the mean and variance drift intervals are combined to obtain four sets of normal distribution parameters, which are then discretized with equal confidence to form a probability box of the load active power.

[0012] Step iv: Constructing the source-load joint probability distribution using the t-Copula function: Kendall's rank correlation coefficient is used to quantify the nonlinear correlation between random variables; the multivariate Student's t-Copula function is selected, which can effectively capture the symmetric tail correlation when extreme adverse scenarios such as extremely low photovoltaic output and extremely high load occur simultaneously. Compared with Gaussian Copula, it does not underestimate the joint occurrence probability in extreme scenarios, providing more accurate joint probability information for subsequent robust optimization to find the worst-case scenario. According to Sklar's theorem, the three-variable joint probability density function is expressed as: (13) In the formula, c (⋅) is the probability density function of t-Copula, and the correlation coefficient matrix is... sum and degree of freedom parameters The maximum likelihood estimation method is calibrated based on historical data.

[0013] The specific steps for constructing the box-type uncertain set in step (2) are as follows: Step i: Construction of representative points for the three-point estimation of t-Copula dependency preservation, the specific process is as follows: a) Construct 2n+1 representative points in the independent standard space. (n=3 is the dimension of the random variable) and corresponding weights : (13) (14) b) The t-Copula correlation matrix Perform Cholesky decomposition Introducing the t-distribution covariance coefficient Mapping the representative points to the t-Copula related space: (15) This operation ensures that the subsequent moment estimation reflects the source-load related structure in the sense of the t-Copula joint distribution, rather than the edge independent superposition; c) For each representative point First, perform a CDF mapping on the t-distribution to obtain a uniform variable: (16) Then, the representative points are mapped to the physical quantity space through the inverse CDF of each edge distribution to obtain the source-charge sample matrix, and the elements of the sample matrix are defined. : (17) (18) (19) In the formula, Given by the β distribution; Given by the GMM model; The CDF follows a normal distribution. These are the midpoints of each edge distribution.

[0014] And calculate the net load sample matrix and moment information for each representative point. k Calculate the net load sample: (20) Using weights Calculate the first and second moments (nominal values ​​and variance) of the net load: (twenty one) (twenty two) To support Gram–Charlier expansion, the third and fourth central moments are further calculated: (twenty three) And define skewness and kurtosis: (twenty four) Step ii: Gram-Charlier expansion to obtain the net load probability distribution: Based on the moments obtained in step ii, let the standardized variables... (25) , These are the standard normal PDF and CDF, respectively. Given a probability-theoretic Hermite polynomial, the net load probability density function is obtained using a Gram-Charlier A-series expansion. With cumulative distribution function This reduces the high-dimensional t-Copula joint distribution information to a one-dimensional net load distribution: (26) (27) Step iii: Determining the net load fluctuation range and maximum fluctuation deviation: Take the average net load as the nominal value. (28) Based on a confidence level α (e.g., 95%), the quantile method is used to... Determine the upper and lower bounds of the net load fluctuation range and the maximum fluctuation deviation: (29) (30) Therefore, the interval can be written as: (31) Step iv: Calibration of the uncertainty budget parameter Γ based on the t-Copula joint distribution: Based on the t-Copula joint distribution, generate S daily net load scenarios, and generate each scenario s according to the “t-space → uniform → edge inverse transformation” process of equations (15)–(18). ,get And calculate the total normalized deviation: (32) In the formula, where For the set of nodes in the transformer area; This is a time period set. It includes all scenes. The α quantile is used as the global uncertainty budget parameter Γ to ensure that the planning scheme covers the intraday overall fluctuation with a probability of about α, while eliminating low-probability extreme combinations through budget constraints to avoid over-conservatism.

[0015] Step v: Constructing the box-type uncertainty set: Introducing a normalized bias variable Then the node net load is expressed as: (33) Constructing a box-type uncertain set: (34) Γ is determined by step iv based on the t-Copula joint distribution, ensuring the consistency of the probabilistic meaning of the uncertainty set and the source-load joint probability model, which is different from the traditional empirical setting method.

[0016] The specific process of step (3) is as follows: 1) Establish a two-stage robust optimization configuration model, embed box-type uncertainty set into the model constraints, and introduce the demand price elasticity response mechanism into the second-stage node net load injection constraint, so that the electric vehicle charging load can achieve cross-time transfer through time-of-use pricing in the worst scenario, forming a synergistic optimization of uncertainty hedging and demand-side response; The objective function and constraints of the two-stage robust optimization configuration model are as follows: (35) (36) (37) In the formula, , These are investment costs and operating costs, respectively. For the construction of the railway line, use 0-1 decision variables; Construction cost per unit length of the line; This refers to the line length; A collection of lines in a single-feeder distribution network; Configure 0-1 decision variables for energy storage; , These are the investment costs per unit power and energy capacity of energy storage, respectively. , These are the rated power and energy capacity of the energy storage, respectively. For the set of nodes in the transformer area; The electricity purchase price; express Purchase power from the main grid at all times; Operation and maintenance cost per unit power of energy storage; Cost of per unit of abandoned light penalty; This refers to the power of discarded light. To optimize the cycle.

[0017] The first phase of constraints includes constraints on the number and budget of power lines to be built, constraints on the number of energy storage configurations, upper and lower limits on energy storage power and energy capacity, constraints on the energy-to-power ratio of energy storage, and constraints on grid connectivity. The second stage of constraints includes branch power flow balance constraints, node net load injection constraints with dynamic adjustment of demand price elasticity, energy storage charging and discharging operation constraints, reactive power compensation device operation constraints, distributed photovoltaic power output constraints, grid interconnection power constraints, node voltage constraints, line capacity constraints, and N-1 reliability constraints. Among these, the branch power flow balance constraints, after second-order cone relaxation treatment, transform the original nonlinear non-convex constraints into rotated second-order cone constraints. (38) (39) (40) (41) In the formula, Represented by node It is the set of the first nodes of the terminal nodes; Represented by node It is the set of end nodes of the first node; , Representing time respectively branch road Branch roads The active power; , Representing time respectively branch road Branch roads reactive power; This represents the square of the node voltage magnitude. Represents the square of the branch current amplitude; , Representing branches The resistance and reactance.

[0018] Including node net load injection constraints with dynamic adjustment of demand price elasticity, nodes j At any moment t The injected active power is: (42) In the formula, To provide photovoltaic power with uncertainties; For routine loads containing uncertainties; This represents the base EV charging load before the response, which includes uncertainties; the item in parentheses represents the adjustment amount based on the demand price elasticity response. Given time-of-use pricing strategy parameters. Uncertain parameters. Simultaneously acting on three components—photovoltaics, conventional loads, and EV base charging loads—the elastic response term provides the ability to actively adjust the EV component, enabling the second phase to still have the ability to flexibly offset demand even in the worst-case scenario.

[0019] 2) An improved C&CG algorithm is used to solve the above three-layer optimization problem. Based on the scenario library obtained by Monte Carlo sampling, the worst scenario is pre-screened for sub-problems before each iteration, guiding the search of sub-problems to concentrate on high-risk areas. This is different from the blind search of the standard C&CG algorithm, and accelerates the convergence of the algorithm while ensuring global optimality.

[0020] The specific steps of the two-stage robust optimization model solution method are as follows: Step i: Initialization Set the number of iterations Lower bound of the objective function Upper Realm Convergence accuracy ; and the Monte Carlo sampling of the t-Copula joint distribution S Daily net load scenario Initialize as a candidate scene library S This is for subsequent pre-screening.

[0021] Step ii: Solve the main problem Solve for the case of the preceding part The secondary problem returns to the primary problem with scenario constraints, yielding the first-stage decision variables. and the upper bound variable of operating costs Update the Nether ; Step iii: Pre-screening of the worst-case scenarios based on the scenario library Before formally solving the subproblems, utilize the candidate scenario library. S Regarding the current planning scheme Perform rapid evaluation: for each candidate scenario Calculate its value in a given context Approximate operating cost Select the highest-cost scenarios to form the guidance set. This pre-screening mechanism uses a concentrated scenario as the initial solution for the subproblem, guiding the subproblem to search in a concentrated area of ​​high-risk scenarios, thus reducing ineffective iterations. This pre-screening mechanism shares the same Monte Carlo scenario library with the calibration of the uncertainty budget parameter Γ, ensuring that the high-risk direction guided by the pre-screening is consistent with the source-load joint probability model in a probabilistic sense. This differs from the blind search of subproblems starting from arbitrary initial points in the standard C&CG algorithm.

[0022] Step iv: Solve the subproblems Will Substituting the subproblem into the strong duality theory, the max-min bilevel problem is transformed into a single-level max problem. By introducing 0-1 variables and auxiliary variables, the Big M method is used to eliminate bilinear terms, transforming the subproblem into MILP form. The MILP subproblem is solved using the scenario of the guiding set in step iii as the initial solution, yielding the worst-case scenario. Second-stage decision variables Calculate operating costs Update the upper boundary ; Step v: Convergence judgment and constraint update like If the algorithm converges, it outputs the optimal planning solution; otherwise, it changes the scenario. and Add the corresponding constraints to the main problem; Included in the candidate scenario library S The library's coverage is continuously expanded through iterative identification of the most severe real-world scenarios; Return to step ii.

[0023] Based on the above method embodiments, the present invention provides corresponding system embodiments.

[0024] One embodiment of the present invention provides a robust planning system for power distribution network and energy storage with spatiotemporal random coupling of optical charging, including: a source-load probability modeling module, an uncertainty set construction module, a robust optimization model construction module, and a model solving module; The source-load probability modeling module is used to construct marginal probability distribution models for distributed photovoltaic power output (β distribution or HDKR + normal error), electric vehicle charging load (k-means scenario partitioning + GMM modeling + demand-price elasticity response) and conventional load (normal distribution + probability box), and to establish a joint probability distribution model that captures the tail correlation of extreme scenarios and describes the spatiotemporal coupling randomness of source and load using a multivariate t-Copula function. The uncertainty set construction module, based on the t-Copula related structure of the source load probability modeling module, introduces related structure injection and equal probability mapping into the t-Copula latent variable space, uses the dependency-preserving three-point estimation method and Gram-Charlier series expansion method to obtain the net load probability characteristics, determines the net load fluctuation range through the quantile method, calibrates the uncertainty budget parameter Γ through t-Copula joint distribution Monte Carlo sampling, constructs a box uncertainty set consistent with the probability model, and outputs the sampling scenario library for use by the model solution module; The robust optimization model construction module embeds the box-type uncertainty set into a two-stage robust optimization configuration model. The first stage determines the line construction and energy storage configuration scheme. The second stage embeds the demand price elasticity response into the node net load injection constraint under the uncertainty set constraint, so as to achieve the synergy of passively bearing uncertainty and actively responding to demand. The model solving module uses an improved C&CG algorithm to decompose the three-layer optimization model into a main problem and sub-problems. It uses the Monte Carlo scenario library output by the uncertainty set construction module to pre-screen the worst-case scenarios for the sub-problems. Combining strong duality theory and Big M linearization, the sub-problems are transformed into MILP form. The main problem and sub-problems are iteratively alternated and converged to the global optimal planning scheme. Attached Figure Description

[0025] Appendix Figure 1 This is a flowchart illustrating the robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging in this invention. Appendix Figure 2 This invention uses the three-point estimation method to reduce the dimensionality of the net load solution. W A flowchart illustrating the probability distribution function; Appendix Figure 3 This is a schematic diagram of the iterative solution process of the robust optimization model C&CG algorithm in this invention; Appendix Figure 4 This is a schematic diagram of the grid and energy storage planning results obtained by the robust planning method for power distribution system grid and energy storage based on the spatiotemporal random coupling of light and charge in this invention. Detailed Implementation

[0026] As attached Figure 1 As shown, a robust planning method for power distribution system grid-storage under spatiotemporal random coupling of optical-charging technology is presented. This method includes the following steps: Step 1: Collect historical data on distributed photovoltaic power output, electric vehicle charging load, and conventional load within the distribution network area. After preprocessing, establish marginal probability distribution models for each random variable: Distributed photovoltaic power output is modeled using a β distribution when the irradiance intensity conforms to the β distribution assumption; otherwise, an HDKR model combined with normal distribution error is used to construct a real-time photovoltaic probability model. For electric vehicle charging load, k-means clustering algorithm is used to extract K typical daily scenarios. Within each typical scenario, a Gaussian mixture model (GMM) is used to describe randomness, and a demand price elasticity matrix is ​​introduced to establish a response model of charging load to time-of-use electricity prices. For conventional load, both active and reactive power are modeled using a normal distribution, and the time-series drift uncertainty of the mean and variance is handled using probability box theory.

[0027] Step 2: Kendall's rank correlation coefficient is used to quantify the nonlinear correlation among three types of random variables: photovoltaic power output, electric vehicle charging load, and conventional load. A three-variable joint probability distribution model is established using the multivariate Student's t-Copula function. Compared to Gaussian Copula, t-Copula can effectively capture the symmetric tail correlation of source and load under extremely unfavorable scenarios, without underestimating the probability of joint occurrence in extreme scenarios. The correlation coefficient matrix R and the degree of freedom parameter ν are calibrated based on historical data using the maximum likelihood estimation method.

[0028] Step 3: Introduce relevant structural injections and equal probability mappings into the t-Copula latent variable space, and use the dependency-preserving three-point estimation method to perform dimensionality-reduced moment estimation of the net load (see appendix for details). Figure 2 The net load probability density function and cumulative distribution function are reconstructed using Gram-Charlier series expansion; the net load fluctuation range and maximum fluctuation deviation for each node in each time period are determined by quantiles based on a given confidence level; Monte Carlo sampling is further performed on the t-Copula joint distribution to calculate the total normalized deviation for each scenario and calibrate the global uncertainty budget parameter Γ using its quantiles; a normalized deviation variable is introduced. We construct a box-type uncertainty set consistent with the probability coverage level, and output the scene library obtained by Monte Carlo sampling for subsequent solution.

[0029] Step 4: Establish a two-stage robust optimization configuration model with the objective of minimizing the sum of investment costs and operating costs under the worst-case scenario. The first stage determines the line construction plan and the energy storage configuration plan for the transformer substations. The second stage finds the worst-case scenario and optimizes the system operation strategy under the constraints of the box-type uncertainty set. The demand price elasticity response mechanism is embedded into the node net load injection constraint, so that the electric vehicle charging load can still be transferred across time periods through time-of-use pricing under the worst-case scenario, forming a flexible hedging mechanism that combines passive uncertainty bearing with active demand-side response. The power flow balance constraint in the second stage is transformed into a rotating second-order cone constraint through second-order cone relaxation treatment, which also includes operating constraints such as energy storage charging and discharging, node voltage, line capacity, and N-1 reliability.

[0030] Step 5: Use the improved C&CG algorithm to decompose the three-level optimization model into a main problem and sub-problems, and solve them iteratively (see appendix for details). Figure 3Before each iteration, the Monte Carlo scenario library obtained in Step 3 is used to quickly evaluate the current planning scheme, and several scenarios with the highest approximate operating costs are selected to form a guiding set. The scenarios in the guiding set are used as the initial solutions to subproblems, guiding the subproblems to search in high-risk areas, which is different from the blind search of the standard C&CG algorithm. The subproblems are transformed into MILP form and solved by strong duality theory and the Big M method. The worst scenario identified each time is used to supplement the scenario library. The main subproblems are iterated alternately until the difference between the upper and lower bounds meets the convergence accuracy requirements, and the optimal network line construction scheme and transformer area energy storage configuration scheme are output.

[0031] Based on the embodiments, and in conjunction with the aforementioned solution method and process, the planning results can be obtained as shown in the appendix. Figure 4 As shown.

[0032] This application also provides an electronic device, which may include at least one processor and at least one memory.

[0033] The processor may include one or more processing cores. The processor connects to various parts of the server using various interfaces and lines, and performs various server functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory, and by accessing data stored in memory.

[0034] This application also provides a computer-readable storage medium storing instructions. When executed by one or more processors, these instructions cause an electronic device to perform one or more of the methods described in the above embodiments.

[0035] Furthermore, the functional units in this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0036] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0037] The flowcharts and block diagrams in the accompanying drawings illustrate possible architectures, functions, and operations according to the invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0038] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical-charging technology, characterized by: (1) A multivariate Student's t-Copula function was used to construct a source-load joint probability distribution model in order to capture the symmetrical tail correlation between photovoltaic output and load under extreme adverse scenarios; (2) Introduce relevant structure injection and equal probability mapping in the t-Copula latent variable space, use the dependency-preserving three-point estimation method to estimate the net load in a reduced moment, and combine Gram-Charlier series expansion to reconstruct the net load probability distribution; then, by performing Monte Carlo sampling on the joint distribution of the above multivariate Student's t-Copula function, take the quantile of the scenario total normalization deviation to calibrate the global uncertainty budget parameter Γ, and construct a box uncertainty set consistent with the probability coverage level; (3) Based on the above box uncertainty set, a two-stage robust optimization configuration model is established, and the demand price elasticity response mechanism is embedded into the node net load injection constraint to form a flexible hedging mechanism that combines passive uncertainty bearing with active demand response. The improved C&CG algorithm is used to solve the problem, and the worst scenario is pre-screened for each iteration subproblem using the scenario library sampled in step (2) Monte Carlo sampling to guide the search direction and accelerate convergence.

2. The robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging as described in claim 1, characterized in that, The specific steps for constructing the source-load joint probability distribution model in step (1) are as follows: Step i: Probabilistic modeling of distributed photovoltaic power output, providing two methods: Method 1: When the irradiance intensity conforms to the β distribution assumption, directly use the β distribution to establish the photovoltaic power output probability density function: （1）， In the formula, the shape parameter , Determined by statistical characteristics of historical data; For photovoltaic installed capacity; Method 2: When the irradiance does not follow a β distribution, the HDKR model is used to obtain the real-time irradiance sequence, and the photovoltaic predicted value is calculated in combination with the piecewise power output model. The prediction uncertainty is characterized by superimposing a normal error with a mean of 0 and a standard deviation proportional to the predicted value. Step ii: Electric vehicle charging load modeling, the specific process is as follows: a) The k-means clustering algorithm was used to divide the historical daily charging load data into scenarios, and the silhouette coefficient method was used to determine the optimal number of clusters. K ,get K A typical daily load scenario and the probability of occurrence of each scenario; b) For each typical scenario, the load data at each time period are modeled using a Gaussian mixture model, and the parameters are estimated iteratively using the EM algorithm. k A typical scenario t The probability density function of the preload response for the time period is: （2）， In the formula, M It is the number of Gaussian components; , , The first m The weights, mean, and variance of each Gaussian component; c) Introduce a demand price elasticity matrix, using the self-elasticity coefficient. To characterize the effect of electricity price changes on its own charging load during this period, the cross-elasticity coefficient is used. To characterize the load shifting effect, a linear mapping relationship is established between the charging load after the response and the base load before the response: （3） （4） In the formula, In response to the underlying charging load; This is the overall response coefficient; The benchmark electricity price; This refers to the real-time electricity price for each time period; Step iii: Conventional load probability modeling, both active and reactive power are modeled using normal distribution, and the time series uncertainty caused by mean and variance drift is characterized by probability box theory; Step iv: Constructing the source-load joint probability distribution using the t-Copula function: Kendall's rank correlation coefficient is used to quantify the nonlinear correlation between the random variables; the multivariate Student's t-Copula function is selected, which can effectively capture the symmetric tail correlation when extreme adverse scenarios such as extremely low photovoltaic output and extremely high load occur simultaneously. Compared with Gaussian Copula, it does not underestimate the joint occurrence probability in extreme scenarios, providing more accurate joint probability information for subsequent robust optimization to find the worst-case scenario. According to Sklar's theorem, the three-variable joint probability density function is expressed as: （5） In the formula, c (⋅) is the probability density function of t-Copula, and the correlation coefficient matrix is... With degrees of freedom parameters The maximum likelihood estimation method is calibrated based on historical data.

3. The robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging as described in claim 1, characterized in that, The specific steps for constructing the box-type uncertain set in step (2) are as follows: Step i: Construction of representative points for the three-point estimation of t-Copula dependency preservation, the specific process is as follows: a) Construct 2n+1 representative points in the independent standard space. and corresponding weights n=3 is the dimension of the random variable; b) The t-Copula correlation matrix Perform Cholesky decomposition Introducing the t-distribution covariance coefficient Map the representative points to the t-Copula related space: （6） This operation ensures that the subsequent moment estimation reflects the source-load related structure in the sense of the t-Copula joint distribution, rather than the edge independent superposition; c) First, perform a t-distribution CDF mapping on the representative points to obtain uniform variables. Then, map the representative points to the physical quantity space through the inverse CDF of each marginal distribution to obtain the source load sample matrix, which is defined by the net load: （7） Using weights Calculate the mean net load. ,variance and higher-order moments (skewness, kurtosis); Step ii: Obtain the net load probability distribution using Gram-Charlier expansion: Based on the moments obtained in step ii, the net load probability density function is obtained using Gram-Charlier A-series expansion. With cumulative distribution function This reduces the high-dimensional t-Copula joint distribution information to a one-dimensional net load distribution. Step iii: Determination of net load fluctuation range and maximum fluctuation deviation: Based on confidence level α, the quantile method is used to determine... Determine the upper and lower bounds of the net load fluctuation range and the maximum fluctuation deviation: （8） （9） Step iv: Calibration of the uncertainty budget parameter Γ based on the t-Copula joint distribution: Generating the t-Copula joint distribution S For each daily net load scenario, s Calculate the total normalized deviation: （10） In the formula, where For the set of nodes in the transformer area; For time periods, take all scenes. The α quantile is used as the global uncertainty budget parameter Γ to ensure that the planning scheme covers the intraday overall fluctuation with a probability of about α. At the same time, the budget constraint excludes low-probability extreme combinations to avoid excessive conservatism. Step v: Constructing the box-type uncertainty set: Introducing a normalized bias variable Then the node net load is expressed as: （11） Constructing a box-type uncertain set: （12） Γ is determined by step iv based on the t-Copula joint distribution, ensuring the consistency of the probabilistic meaning of the uncertainty set and the source-load joint probability model, which is different from the traditional empirical setting method.

4. The robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging as described in claim 1, characterized in that, Step (3) is performed in the following two steps: 1) Establish a two-stage robust optimization configuration model, embed box-type uncertainty set into the model constraints, and introduce the demand price elasticity response mechanism into the second-stage node net load injection constraint, so that the electric vehicle charging load can achieve cross-time transfer through time-of-use pricing in the worst scenario, forming a synergistic optimization of uncertainty hedging and demand-side response; 2) An improved C&CG algorithm is used to solve the above three-layer optimization problem. Based on the scenario library obtained by Monte Carlo sampling, the worst scenario is pre-screened for sub-problems before each iteration, guiding the search of sub-problems to concentrate on high-risk areas. This is different from the blind search of the standard C&CG algorithm, and accelerates the convergence of the algorithm while ensuring global optimality.

5. The robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging as described in claim 4, characterized in that, The objective function and constraints of the two-stage robust optimization configuration model described in step 1) are as follows: （13） （14） （15） In the formula, , These are investment costs and operating costs, respectively. For the construction of the railway line, use 0-1 decision variables; Construction cost per unit length of the line; This refers to the line length; A collection of lines in a single-feeder distribution network; Configure 0-1 decision variables for energy storage; , These are the investment costs per unit power and energy capacity of energy storage, respectively. , These are the rated power and energy capacity of the energy storage, respectively. For the set of nodes in the transformer area; The electricity purchase price; express Purchase power from the main grid at all times; Operation and maintenance cost per unit power of energy storage; Cost of per unit of abandoned light penalty; This refers to the power of discarded light. To optimize the cycle; The first phase of constraints includes constraints on the number and budget of power lines to be built, constraints on the number of energy storage configurations, upper and lower limits on energy storage power and energy capacity, constraints on the energy-to-power ratio of energy storage, and constraints on grid connectivity. The second stage of constraints includes branch power flow balance constraints, node net load injection constraints with dynamic adjustment of demand price elasticity, energy storage charging and discharging operation constraints, reactive power compensation device operation constraints, distributed photovoltaic power output constraints, grid interconnection power constraints, node voltage constraints, line capacity constraints, and N-1 reliability constraints. Among these, the branch power flow balance constraints are transformed into rotated second-order cone constraints through second-order cone relaxation treatment. （16） （17） （18） （19） In the formula, Represented by node It is the set of the first nodes of the terminal nodes; Represented by node It is the set of end nodes of the first node; , Representing time respectively branch road Branch roads The active power; , Representing time respectively branch road Branch roads reactive power; This represents the square of the node voltage magnitude. Represents the square of the branch current amplitude; , Representing branches Resistance and reactance; Including node net load injection constraints with dynamic adjustment of demand price elasticity, nodes j At any moment t The injected active power is: （20） In the formula, To provide photovoltaic power with uncertainties; For routine loads containing uncertainties; This represents the base EV charging load before the response, which includes uncertainties; the item in parentheses represents the adjustment amount based on the demand price elasticity response. Given time-of-use pricing strategy parameters, and unknown parameters. Simultaneously acting on three components—photovoltaics, conventional loads, and EV base charging loads—the elastic response term provides the ability to actively adjust the EV component, enabling the second phase to still have the ability to flexibly offset demand even in the worst-case scenario.

6. The robust planning method for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging as described in claim 4, characterized in that, Step 2) The specific steps of the two-stage robust optimization model solution method are as follows: Step i: Initialization Set the number of iterations Lower bound of the objective function Upper Realm Convergence accuracy ; and the Monte Carlo sampling of the t-Copula joint distribution S Daily net load scenario Initialize as a candidate scene library S For subsequent pre-screening; Step ii: Solve the main problem Solve for the case of the preceding part The secondary problem returns to the primary problem with scenario constraints, yielding the first-stage decision variables. and the upper bound variable of operating costs Update the Nether ; Step iii: Pre-screening of the worst-case scenarios based on the scenario library Before formally solving the subproblems, utilize the candidate scenario library. S Regarding the current planning scheme Perform rapid evaluation: for each candidate scenario Calculate its value in a given context Approximate operating cost Select the highest-cost scenarios to form the guidance set. The pre-screening mechanism uses the guided concentrated scene as the initial solution of the sub-problem, guiding the sub-problem to search in a concentrated high-risk scene area, reducing invalid iterations. This pre-screening mechanism shares the same Monte Carlo scene library with the calibration of the uncertainty budget parameter Γ, which ensures that the high-risk direction guided by the pre-screening is consistent with the source-load joint probability model in a probabilistic sense, which is different from the blind search of the sub-problem starting from an arbitrary initial point in the standard C&CG algorithm. Step iv: Solve the subproblems Will By substituting the subproblem, the max-min bilevel problem is transformed into a single-level max problem using strong duality theory. By introducing 0-1 variables and auxiliary variables, and using the Big M method to eliminate bilinear terms, the subproblem is transformed into a MILP form. The MILP subproblem is then solved using the scenario in step iii as the initial solution, yielding the worst-case scenario. Second-stage decision variables Calculate operating costs Update the upper boundary ; Step v: Convergence judgment and constraint update like The algorithm converges and outputs the optimal planning solution; Otherwise: the scene and Add the corresponding constraints to the main problem; Included in the candidate scenario library S The library's coverage is continuously expanded through iterative identification of the most severe real-world scenarios; Return to step ii.

7. A robust planning system for power distribution network and energy storage with spatiotemporal random coupling of optical and charging technologies, characterized in that: include: The module includes a source load probability modeling module, an uncertainty set construction module, a robust optimization model construction module, and a model solving module. The source-load probability modeling module is used to construct the marginal probability distribution model of distributed photovoltaic power output, electric vehicle charging load and conventional load, and to establish a joint probability distribution model that captures the tail correlation of extreme scenarios and describes the spatiotemporal coupling randomness of source and load using a multivariate t-Copula function. The uncertainty set construction module, based on the t-Copula related structure of the source load probability modeling module, introduces related structure injection and equal probability mapping into the t-Copula latent variable space, uses the dependency-preserving three-point estimation method and Gram-Charlier series expansion method to obtain the net load probability characteristics, determines the net load fluctuation range through the quantile method, calibrates the uncertainty budget parameter Γ through t-Copula joint distribution Monte Carlo sampling, constructs a box uncertainty set consistent with the probability model, and outputs the sampling scenario library for use by the model solution module; The robust optimization model construction module embeds the box-type uncertainty set into a two-stage robust optimization configuration model. The first stage determines the line construction and energy storage configuration scheme. The second stage embeds the demand price elasticity response into the node net load injection constraint under the uncertainty set constraint, so as to achieve the synergy of passively bearing uncertainty and actively responding to demand. The model solving module uses an improved C&CG algorithm to decompose the three-layer optimization model into a main problem and sub-problems. It uses the Monte Carlo scenario library output by the uncertainty set construction module to pre-screen the worst-case scenarios for the sub-problems. Combining strong duality theory and Big M linearization, the sub-problems are transformed into MILP form. The main problem and sub-problems are iteratively alternated and converged to the global optimal planning scheme.

8. A robust planning device for power distribution system grid-storage based on the spatiotemporal random coupling of optical charging, characterized in that, It includes a memory and a processor, the memory storing a program that runs on the processor, and the processor executing the steps of the robust planning method for power distribution system grid-storage with spatiotemporal random coupling of optical charging as described in any one of claims 1 to 6 when running the program.

9. An electronic device, characterized in that, It includes one or more processors, which execute the robust planning method for power distribution system grid-storage with spatiotemporal random coupling of optical charging as described in any one of claims 1 to 6.

10. A computer storage medium, characterized in that the computer-readable storage medium stores computer instructions for causing a computer to execute the robust planning method for power distribution system grid-storage with spatiotemporal random coupling of optical charging as described in any one of claims 1 to 6.

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