Game theory-based power system stochastic programming scene generation method and system

Abstract

The invention discloses a game theory-based power system stochastic programming scene generation method, which comprises the following steps of: 1) expressing historical data of an uncertain parameter set, constructing a statistical moment of uncertain parameters, and performing distribution fitting; 2) simulating single-variable probability distribution of each uncertain parameter according to a statistical moment, generating a multivariable joint original scene set, and performing cluster division on the generated scene set; 3) constructing an MILP model generated by a typical scene based on a game theory; and 4) solving the MILP model, and outputting a final scene set. The method has the beneficial effects that statistical indexes are constructed through concepts such as statistical moments and distribution fitting, key index parameters are extracted to serve as target functions, the target functions are regarded as game participants, multiple items in the target functions are balanced through Nash bargaining solutions, and the representativeness and robustness of typical scene sets generated under different subject definition parameter sets are improved.

Description

Technical Field

[0001] The present invention relates to the field of power system data mining and analysis, and in particular to a method and system for generating random planning scenarios of a power system based on game theory. Background Art

[0002] In the research on new power systems, optimization problems considering uncertainty have received increasing attention. Traditional deterministic optimization methods mainly build models based on preset fixed parameters and conditions. However, in the operation and management of actual power systems, many key parameters often show uncertainty characteristics, which leads to significant limitations in the application of deterministic optimization methods. To solve this problem, stochastic programming methods have emerged and have shown their unique advantages in power system optimization. This method allows a variety of potential scenarios to be considered comprehensively under the premise that the probability distribution of parameters is known, thereby optimizing the expected value of the problem. This method of considering uncertainty can provide power systems with more robust and adaptable decision-making solutions, which helps to improve the stability and economy of power systems in the face of uncertain factors.

[0003] One of the core issues of stochastic programming is representative scenario generation, which is to create a small and representative set of scenarios to effectively handle computationally challenging random programs. The quality of the scenario generation method is directly related to the stability and quality of the stochastic programming solution. Existing scenario generation methods include sampling-based methods, prediction-based methods, and optimization-based methods. Among them, optimization-based methods have received special attention because they can ensure that the statistical properties of the generated scenario set are consistent with the original data through mathematical programming techniques.

[0004] However, existing optimization-based scene generation methods, such as the moment matching problem and the distributed moment matching problem (DMP), have improved performance and statistical matching, but they are usually nonlinear and non-convex optimization problems, which may lead to difficulties in solving and are sensitive to user-defined parameters, which affects the stability and effectiveness of the model. In addition, most of the existing techniques will have numerical problems when dealing with multiple objective function terms, so a new optimization framework is needed to improve the stability and robustness of scene generation. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art, and to provide a method and system for generating random planning scenarios for power systems based on game theory. The multi-objective optimization problem for typical scenarios is processed by statistical indicators and Nash game theory methods, and the problem is converted into a linear programming problem that is easier to solve by a separable planning method, so as to obtain a more stable and universal set of typical scenarios. The present invention aims to solve the problem that the prior art is difficult to ensure stability and universality when generating typical scenarios, and is specifically implemented by the following technical solutions:

[0006] The method for generating random planning scenarios for a power system based on game theory comprises the following steps:

[0007] Step 1) expressing the historical data of the uncertain parameter set, constructing the statistical moments of the uncertain parameters, and performing distribution fitting;

[0008] Step 2) simulate the univariate probability distribution of each uncertain parameter according to the statistical moment, generate a multivariate joint original scene set by the Copula method, and use the K-means method to cluster the generated scene set; Step 3) construct a MILP model for typical scene generation based on game theory;

[0009] Step 4) Solve the MILP model and output the final scenario set and corresponding probabilities for subsequent power system stochastic programming problems.

[0010] The further design of the random planning scenario generation method for the power system based on game theory is that the historical data of the uncertain parameter set in step 1) is specifically expressed as follows: for each uncertain parameter i∈I, four statistical moments in its original scenario set are calculated, including mean, variance, skewness and kurtosis, specifically: the mean μ is calculated according to formula (1): i ,

[0011]

[0012] In formula (1), x in represents the value of parameter i in the original scene n, p n is the probability of the original scene n occurring; the variance is calculated according to formula (2)

[0013]

[0014] Calculate the skewness S according to formula (3): i ,

[0015]

[0016] Calculate the kurtosis K according to formula (4): i ,

[0017]

[0018] The further design of the method for generating random planning scenarios of power systems based on game theory is that the distribution fitting in step 1) is specifically as follows:

[0019] According to formula (5), the empirical cumulative distribution function ECDF is constructed, and the historical data of each parameter is fitted according to the empirical cumulative distribution function to determine the type of parameter probability distribution.

[0020]

[0021] In formula (5), z i represents the random parameter, t is the independent variable of the function, 1{z i ≤t} is the indicator function, when z i When it is less than or equal to t, the value is 1, and n is the sample size.

[0022] The further design of the random planning scenario generation method for the power system based on game theory is that when the K-means method is used in step 2) to cluster the generated scenario set, a dynamic set CL is introduced kn , CL kn Use cluster labels to map each scene to a pre-specified cluster so that the number of clusters is the same as the number of typical scenes after simplification. kn Contains two decision variables:

[0023] Binary selection variable y kn : If the original scene n is selected as the scene k of the final scene set, then y kn =1, otherwise y kn =0; probability variable p kn : When scenario n is selected as the final scenario k, the probability of its occurrence is p kn .

[0024] The further design of the power system random planning scenario generation method based on game theory is that when constructing the objective function of the MILP model, the matching errors of statistical moments, covariance and ECDF are regarded as participants in the game through the Nash game theory method, and the Nash product maximization objective function is constructed according to formula (6):

[0025]

[0026] Among them, T is the set of game participants, N is the set of all original scenarios, is the maximum error allowed in scene generation by the tth participant, represents the optimization result of the tth participant in scenario g, λ tg is the linearized weight, which is used to construct a piecewise linear function to approximate the original nonlinear Nash product, p kn represents the probability that a certain scene n is selected as the final scene k, y kn Used to record whether scene n is selected as scene k in the final scene set.

[0027] The further design of the game theory-based power system stochastic planning scenario generation method is to construct the constraints of the MILP model, including:

[0028] Weight normalization constraint: Target item optimization results: Scene selection constraints: Where K represents the final scene set;

[0029] Probability assignment constraints: Where P min , P max Assign the minimum and maximum values ​​of the occurrence probability to all scenarios respectively;

[0030] Probability normalization constraint: Statistical moment matching error: ECDF matching error: Covariance matching error: Where W is the weight of different error terms, and are the positive and negative deviation variables of the statistical moments and covariances, e i is the maximum deviation of the ECDF.

[0031] The further design of the method for generating random planning scenarios for power systems based on game theory is that, in step 3), the Nash product is piecewise approximated by using logarithmic transformation coupled with SOS2 variables, specifically: first, the Nash product is convexified by performing logarithmic transformation; then, the Nash product is linearized by a piecewise linear function of a pre-specified scenario.

[0032] The further design of the random programming scenario generation method for power systems based on game theory is that the process of solving the MILP model is specifically as follows: constructing a data-driven scenario generation algorithm framework, using a mixed integer linear programming solver to solve the previously constructed MILP model; according to the solution of the MILP model, determining the scenarios selected as the final scenario set in each cluster and the corresponding probabilities, and combining them to form a final typical scenario set. The present invention also provides a random programming scenario generation system for power systems based on game theory, including: a historical data statistical analysis module, which expresses the historical data of an uncertain parameter set from the perspective of statistical indicators, constructs statistical moments of uncertain parameters, and performs distribution fitting on the historical data of each parameter to construct an empirical cumulative distribution function;

[0033] The original scene generation and clustering module uses the results of statistical analysis to simulate the univariate probability distribution of each uncertain parameter, generates a multivariate joint original scene set based on the Copula method, and clusters the generated scene set using the K-means method. Each scene is mapped to a pre-specified cluster by introducing a dynamic set;

[0034] The typical scenario generation model building module uses the Nash game theory method to establish a game model with statistical moments, covariance and ECDF matching errors as participants, construct the Nash product maximization objective function, and introduce the set constraints to build a MILP model for generating typical scenarios of random planning of power systems;

[0035] The typical scenario output module builds a data-driven scenario generation algorithm framework, uses a mixed integer linear programming solver to solve the MILP model, and determines the scenes selected as the final scenario set in each cluster and the corresponding probabilities according to the solution of the MILP model, and combines them to form the final typical scenario set.

[0036] The present invention also provides a computer-readable storage medium, wherein the storage medium stores a computer program, and the computer program is executed by a processor to implement the game theory-based method for generating random planning scenarios for a power system.

[0037] The advantages of the present invention are as follows:

[0038] Compared with similar random planning scenario generation methods, the method of the present invention constructs statistical indicators through concepts such as statistical moments and distribution fitting, extracts key indicator parameters as the objective function, and regards them as participants in the game. It balances multiple items in the objective function through Nash bargaining solutions, thereby improving the representativeness and robustness of the typical scenario set generated under different subject-defined parameter sets. Therefore, the method of the present invention can effectively provide more accurate and reliable decision support for random planning problems with uncertainty, and is particularly suitable for power system operation planning problems. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flowchart of a power grid diagnosis method based on discrete median filter and mathematical morphology provided in an embodiment of the present invention.

[0040] Figure 2 A clustering diagram.

[0041] Figure 3 A schematic diagram of a power grid diagnosis system based on discrete median filter and mathematical morphology provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is described in detail below.

[0043] Embodiment 1

[0044] Reference Figure 1 , which is the first embodiment of the present invention, provides a method for generating random planning scenarios for a power system based on game theory, comprising the following steps:

[0045] Step 1) From the perspective of statistical indicators, the historical data of the uncertain parameter set is expressed, the statistical moments of the uncertain parameters are constructed, and distribution fitting is performed;

[0046] Statistical analysis of raw data: For each uncertainty parameter i∈I, there are four statistical moments in the raw scene set to be calculated, including mean, variance, skewness and kurtosis. Among them, skewness adds information about risk asymmetry, and kurtosis describes the thickness of the tail and points out the importance of the extreme cases of the distribution. By definition, skewness and kurtosis are normalized properties, but here they are used in a non-normalized form to avoid nonlinearity caused by scaling. The specific calculation method is:

[0047] Calculate the mean μ i , where x in represents the value of parameter i in the original scene n, p n is the probability of the original scenario n occurring;

[0048] Calculating variance

[0049] Calculate the skewness S i ,

[0050] Calculate the kurtosis K i ,

[0051] Distribution fitting: Perform distribution fitting on the historical data of each parameter to determine the type and parameters of its probability distribution, specifically:

[0052] Construct the empirical cumulative distribution function (ECDF), where 1{z i ≤t} is the indicator function, when z i The value is 1 when it is less than or equal to t.

[0053] Step 2) Simulate the univariate probability distribution of each uncertain parameter according to the statistical moment, and then use the Copula method to generate a multivariate joint original scene set, and use the K-means method to cluster the generated scene set;

[0054] Original scene generation and clustering: After the statistical characteristics of moments, correlations and Copulas are preliminarily estimated / constructed, the statistical analysis results are used to simulate the univariate distribution and generate the original scene based on the Copula method, which is then divided into as many clusters as possible using the K-means method, such as Figure 2 shown.

[0055] Define decision variables: In order to make the number of clusters divided equal to the number of typical scenes after simplification, a dynamic set CL is introduced kn It maps each scene into a pre-specified cluster using a cluster label and contains two decision variables:

[0056] Binary selection variable y kn : If the original scene n is selected as the scene k of the final scene set, then y kn =1, otherwise y kn =0;

[0057] Probability variable p kn : When scenario n is selected as the final scenario k, the probability of its occurrence is p kn .

[0058] Step 3) Construct a MILP model for typical scenario generation based on game theory, including the process of constructing the objective function and introducing constraints.

[0059] Objective function construction: Using the Nash game theory method, the different terms of the objective function (statistical moments, covariance, and ECDF matching errors) are regarded as participants in the game, and the Nash product maximization objective function is constructed, which can be specifically expressed as: Where T is the set of target items (statistical characteristics), N is the set of all original scenes, is the maximum error allowed for the t-th optimization objective in scene generation, represents the optimization result of the tth target item in scene g, λ tg is the linearized weight, which is used to construct a piecewise linear function to approximate the original nonlinear Nash product, p kn represents the probability that a certain scene n is selected as the final scene k, y kn Used to record whether scene n is selected as scene k in the final scene set.

[0060] Objective function linearization: The linearization of the Nash product objective function is based on the separable programming method. First, the Nash product is convexified by logarithmic transformation. Then the Nash product is linearized by a piecewise linear function of a pre-specified scenario.

[0061] Introducing constraints: The constraints specifically include:

[0062] Weight normalization constraint: Make sure the sum of all scene weights is 1;

[0063] Target item optimization results: Scene selection constraints: Ensure that only one representative scene is selected in each cluster, where K represents the final set of scenes;

[0064] Probability assignment constraints: Assign a probability of occurrence to the selected scenario, where P min , P max Assign the minimum and maximum values ​​of the occurrence probability to all scenarios respectively;

[0065] Probability normalization constraint: Make sure the sum of the probabilities of all final scenarios is 1;

[0066] Statistical moment matching error: ECDF matching error: Covariance matching error: Where W is the weight of different error terms, and are the positive and negative deviation variables of the statistical moments and covariances, e i is the maximum deviation of the ECDF.

[0067] Step 4) Build a data-driven scenario generation algorithm framework, solve the MILP model, obtain the selected scenarios and corresponding probabilities, and output the final scenario set and its probabilities.

[0068] The constructed algorithm framework is a data-driven scenario generation framework, including statistical analysis, univariate distribution simulation, Copula-based scenario generation, clustering, and MILP model solving. After solving with a mixed integer linear programming solver (such as Gurobi, CPLEX, etc.), the scenarios selected as the final scenario set in each cluster and their probabilities are determined according to the solution of the MILP model, and they are combined to form the final typical scenario set for subsequent power system stochastic programming problems. The algorithm flow can be described by Algorithm 1 in the following table.

[0069]

[0070] Embodiment 2

[0071] Reference Figure 3 , which is the second embodiment of the present invention, and this embodiment provides a random planning scenario generation system for power systems based on game theory. The system constructs a series of key indicator parameters with the help of statistical methods such as statistical moments and distribution fitting, and uses them as the core components of the objective function. These objective functions are regarded as participants in the game, and the balance of multiple competitive objectives in the objective function is achieved through the Nash bargaining solution method. The system significantly improves the representativeness and robustness of the typical scenario set generated under different parameter sets, can better cope with the uncertainty factors in the power system, and provides strong technical support for the stable operation and optimization planning of the power system. The system includes 4 modules, namely: historical data statistical analysis module, original scenario generation and clustering module, typical scenario generation model building module and typical scenario output module.

[0072] Historical data statistical analysis module: This module describes the historical data of the uncertain parameter set from the perspective of statistical indicators, constructs the statistical moments of the uncertain parameters, and performs distribution fitting on the historical data of each parameter to construct an empirical cumulative distribution function.

[0073] Original scene generation and clustering module: This module uses the results of statistical analysis to simulate the univariate probability distribution of each uncertain parameter, generates a multivariate joint original scene set based on the Copula method, and uses the K-means method to cluster the generated scene set. By introducing a dynamic set, each scene is mapped to a pre-specified cluster class.

[0074] Typical scenario generation model building module: This module uses the Nash game theory method to establish a game model with statistical moments, covariance and ECDF matching errors as participants, constructs the Nash product maximization objective function, and introduces corresponding constraints to build a MILP model for generating typical scenarios of random planning of power systems.

[0075] Typical scenario output module: This module builds a data-driven scenario generation algorithm framework and uses a mixed integer linear programming solver to solve the previously constructed MILP model. Based on the solution of the MILP model, it determines the scenarios in each cluster that are selected as the final scenario set and their probabilities, and combines them to form the final typical scenario set.

[0076] Embodiment 3

[0077] This embodiment provides a computer-readable storage medium, which stores a computer program. The computer program is executed by a processor to implement a method for generating random planning scenarios for a power system based on game theory.

[0078] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for generating random planning scenarios for power systems based on game theory, characterized in that: The steps include: Step 1) expressing the historical data of the uncertain parameter set, constructing the statistical moments of the uncertain parameters, and performing distribution fitting; Step 2) simulate the univariate probability distribution of each uncertain parameter according to the statistical moment, generate a multivariate joint original scene set by the Copula method, and use the K-means method to cluster the generated scene set; Step 3) construct a MILP model for typical scene generation based on game theory; Step 4) Solve the MILP model and output the final scenario set and corresponding probabilities for subsequent power system stochastic programming problems.

2. The method for generating random planning scenarios for power systems based on game theory according to claim 1, characterized in that: In step 1), the historical data of the uncertain parameter set is expressed by calculating the four statistical moments of the original scene set for each uncertainty parameter i∈I, including mean, variance, skewness and kurtosis, specifically: According to formula (1), the mean μ is calculated i , In formula (1), x in represents the value of parameter i in the original scene n, p n is the probability of the original scene n occurring; the variance is calculated according to formula (2) Calculate the skewness S according to formula (3): i , Calculate the kurtosis K according to formula (4): i , 3. The method for generating random planning scenarios for power systems based on game theory according to claim 1, characterized in that: The distribution fitting in step 1) is specifically as follows: According to formula (5), the empirical cumulative distribution function ECDF is constructed, and the historical data of each parameter is fitted according to the empirical cumulative distribution function to determine the type of parameter probability distribution. In formula (5), z i represents the random parameter, t is the independent variable of the function, 1{z i ≤t} is the indicator function, when z i When it is less than or equal to t, the value is 1, and n is the sample size.

4. The method for generating random planning scenarios for power systems based on game theory according to claim 1, characterized in that: When the K-means method is used in step 2 to cluster the generated scene set, a dynamic set CL is introduced. kn , CL kn Use cluster labels to map each scene to a pre-specified cluster so that the number of clusters is the same as the number of typical scenes after simplification. kn Contains two decision variables: Binary selection variable y kn : If the original scene n is selected as the scene k of the final scene set, then y kn =1, otherwise y kn =0; probability variable p kn : When scenario n is selected as the final scenario k, the probability of its occurrence is p kn .

5. The method for generating random planning scenarios for power systems based on game theory according to claim 1, characterized in that: When constructing the objective function of the MILP model, the Nash game theory method is used to regard the statistical moment, covariance and ECDF matching error as game participants, and the Nash product maximization objective function is constructed according to formula (6): Among them, T is the set of game participants, N is the set of all original scenarios, is the maximum error allowed in scene generation by the tth participant, represents the optimization result of the tth participant in scenario g, λ tg is the linearized weight, which is used to construct a piecewise linear function to approximate the original nonlinear Nash product, p kn represents the probability that a certain scene n is selected as the final scene k, y kn Used to record whether scene n is selected as scene k in the final scene set.

6. The method for generating random planning scenarios for power systems based on game theory according to claim 5, characterized in that: The constraints for constructing the MILP model include: Weight normalization constraint: Target item optimization results: Scene selection constraints: Where K represents the final scene set; Probability assignment constraint: P min ·y kn ≤p kn ≤P max ·y kn Where P min , P max Assign the minimum and maximum values ​​of the occurrence probability to all scenarios respectively; Probability normalization constraint: Statistical moment matching error: ECDF matching error: Covariance matching error: Where W is the weight of different error terms, and are the positive and negative deviation variables of the statistical moments and covariances, e i is the maximum deviation of the ECDF.

7. The method for generating random planning scenarios for power systems based on game theory according to claim 5, characterized in that: In step 3), the Nash product is piecewise approximated by coupling the logarithmic transformation of the SOS2 variables. Specifically, first, the Nash product is convexified by performing a logarithmic transformation; then, the Nash product is linearized by a piecewise linear function of a pre-specified scenario.

8. The method for generating random planning scenarios for power systems based on game theory according to claim 1, characterized in that: The specific process of solving the MILP model is as follows: construct a data-driven scenario generation algorithm framework, and use a mixed integer linear programming solver to solve the previously constructed MILP model; based on the solution of the MILP model, determine the scenarios selected as the final scenario set in each cluster and the corresponding probabilities, and combine them to form the final typical scenario set.

9. A random planning scenario generation system for power systems based on game theory, characterized in that: include: Historical data statistical analysis module, which describes the historical data of the uncertain parameter set from the perspective of statistical indicators, constructs the statistical moments of the uncertain parameters, and performs distribution fitting on the historical data of each parameter to construct the empirical cumulative distribution function; The original scene generation and clustering module uses the results of statistical analysis to simulate the univariate probability distribution of each uncertain parameter, generates a multivariate joint original scene set based on the Copula method, and clusters the generated scene set using the K-means method. Each scene is mapped to a pre-specified cluster by introducing a dynamic set; The typical scenario generation model building module uses the Nash game theory method to establish a game model with statistical moments, covariance and ECDF matching errors as participants, construct the Nash product maximization objective function, and introduce the set constraints to build a MILP model for generating typical scenarios of random planning of power systems; The typical scenario output module builds a data-driven scenario generation algorithm framework, uses a mixed integer linear programming solver to solve the MILP model, and determines the scenes selected as the final scenario set in each cluster and the corresponding probabilities according to the solution of the MILP model, and combines them to form the final typical scenario set.

10. A computer-readable storage medium, characterized in that The storage medium stores a computer program, and the computer program is executed by a processor to implement the game theory-based method for generating random planning scenarios for a power system as described in any one of claims 1 to 8.

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