Power system optimization planning method and device considering supply and demand probability balance

Abstract

The invention belongs to the technical field of power system optimization, and particularly relates to a power system optimization planning method and device considering supply and demand probability balance, and the method comprises the steps: defining edge distribution for a random variable of each geographic position; a hierarchical Copula model is constructed; estimating parameters in the joint Copula model by using a maximum likelihood estimation method; a sample is extracted from the joint Copula function through a Monte Carlo method, and a joint scene is generated; based on the power loss risk and the resource waste risk, setting a comprehensive risk index under the joint scene; establishing a power system planning model, and setting an objective function and constraint conditions; and solving the power system planning model by using a Benders decomposition method to obtain a power system optimization planning scheme. According to the method, the space-time uncertainty of the new energy power system can be accurately quantified, the planning model considering the investment cost and the operation risk is constructed, and the reliability and the economical efficiency of the system are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system optimization, and in particular relates to a power system optimization planning method and device considering the probabilistic balance of supply and demand. Background Art

[0002] In power systems with high penetration of renewable energy, the uncertainties of wind power, photovoltaic power generation, and loads pose significant challenges to the planning and operation of these systems. Traditional approaches to planning these systems are typically based on deterministic scenarios or simple probabilistic models. For example, these approaches simulate uncertainty by generating multiple typical scenarios or describe the stochastic nature of wind power and photovoltaic power generation using probability distributions. These approaches attempt to plan power systems based on fixed or predictable generation capacity and electricity demand to accommodate fluctuations in renewable energy output and load demand.

[0003] However, existing technologies have many defects and deficiencies when dealing with new power system planning problems under high penetration of renewable energy. First, most traditional methods do not fully consider spatial correlation and ignore the spatial correlation between wind power, photovoltaic power and loads in different geographical locations, resulting in a large deviation between scenario generation and actual conditions. In addition, existing methods usually only focus on a single type of risk, such as power outage risk, and fail to comprehensively consider power outage risk and resource waste risk. There is a lack of effective risk quantification indicators, which makes it difficult for planning results to balance economy and reliability. At the same time, existing planning models are usually complex nonlinear problems with large computational complexity and low efficiency when solving. There is a lack of effective decomposition algorithms, which makes large-scale new power system planning problems difficult to solve.

[0004] In recent years, Copula functions have been used to describe the correlations between multiple variables. However, traditional Copula methods often ignore spatial characteristics. Therefore, how to comprehensively consider the randomness and spatial correlation of wind power, photovoltaic power, and load in the planning of new power systems has become an urgent problem. Summary of the Invention

[0005] In view of the above shortcomings in the existing technology, the purpose of the present invention is to provide a power system optimization planning method and device that considers the probabilistic balance of supply and demand. It integrates the hierarchical Copula model and CVaR risk assessment, can accurately quantify the spatiotemporal uncertainty of the new energy power system, and constructs a planning model that takes into account both investment costs and operational risks. It is efficiently solved through the Benders decomposition method, significantly improving the system reliability and economy.

[0006] To achieve the above objectives, the present invention provides a power system optimization planning method considering the probabilistic balance of supply and demand, comprising the following steps: S1. Define marginal distributions for random variables at each geographic location, including photovoltaic, wind power, and load; S2. Construct a hierarchical Copula model, including a first-layer Copula based on Gaussian Copula and a second-layer Copula based on Clayton Copula, and combine them into a joint Copula model to describe the joint distribution of photovoltaic, wind power, and load; S3. Use the maximum likelihood estimation method to estimate the parameters in the joint copula model and obtain the optimal parameter estimates; S4, extracting samples from the joint Copula function through the Monte Carlo method to generate a joint scene; S5. Based on the risk of power outage and resource waste, set comprehensive risk indicators for the combined scenario; S6. Based on the comprehensive risk indicators, establish a power system planning model and set its objective function and constraints; S7. Use the Benders decomposition method to solve the power system planning model and obtain the power system optimization planning solution.

[0007] As a preferred solution of the present invention, in S1, for geographical location i, the photovoltaic edge distribution is expressed as: (1); Where, represents probability; is the cumulative distribution function of photovoltaic output at geographical location i, express The probability of x is an arbitrary real number, which represents the possible value of photovoltaic output; is the photovoltaic output at geographical location i; The wind power marginal distribution is expressed as: (2); Where, is the cumulative distribution function of wind power output at the geographical location i of the wind farm, express The probability of , y is an arbitrary real number, representing the possible value of wind power output; The wind power output at geographical location i; The load marginal distribution is expressed as: (3); (4); Where, is the electricity demand at geographical location i; represents a normal distribution, is the average load value at geographical location i, is the load fluctuation amplitude at geographical location i; is the cumulative distribution function of load at geographical location i, express The probability of z is an arbitrary real number, which represents the possible value of the load; Represents the cumulative distribution function of the standard normal distribution.

[0008] As a preferred embodiment of the present invention, , the output of the photovoltaic power source at a certain moment is related to the radiation intensity and temperature at that moment, which is expressed by formula (5). The actual light intensity is calculated using formula (6): (5); (6); Where, represents the photovoltaic output at geographical location i at time t; Standard light intensity 1000W / m 2 and the photovoltaic output at a standard temperature of 25°C; F is the actual light intensity received by the photovoltaic power source; is the power temperature coefficient; T is the actual temperature of the photovoltaic power source; Beta distribution is used to simulate the reduction factor of photovoltaic power output due to weather changes such as shadows and clouds; This is the standard illumination without considering the obstruction of clouds; It reflects the power generation capacity of the wind farm at a certain moment, which is affected by the wind speed. According to the power curve of the wind turbine, The relationship with wind speed is a piecewise function: (7); Where, represents the wind power output at geographical location i at time t; is the wind speed at time t; is the cut-in wind speed of the wind turbine; is the wind energy utilization coefficient; is the swept area of ​​the wind turbine rotor; is the air density; is the rated wind speed of the wind turbine; is the cut-out wind speed of the wind turbine; is the rated power of the wind turbine.

[0009] As a preferred embodiment of the present invention, in S2, the process of constructing the hierarchical Copula model is as follows: S2.1. After defining the marginal distribution, different types of physical variables are standardized into uniformly distributed variables through probability integral transformation. The heterogeneous distributions of photovoltaic, wind power, and load are converted into uniformly distributed variables in the interval [0, 1]. This eliminates the differences in variable distribution types so that the correlation between multiple variables can be processed in the Copula framework. This is expressed as: (8); (9); (10); (11); Where, is a uniformly distributed variable in the range [0, 1], representing the standardized probability value of geographic location i; is the marginal distribution function of geographic location i, representing 、 or ; is the original random variable of geographical location i; 、 、 are standardized uniformly distributed variables, representing the standardized variables of photovoltaic power, wind power and load at geographical location i; 、 、 The raw PV, wind power and load variables of geographical location i respectively; S2.2. For the first-level Copula, assuming that there is local correlation between wind power, photovoltaic power, and load, Gaussian Copula is used to describe data with symmetric correlation: (12); Where, Represents the first layer Copula function, Used to capture local correlation between wind power and photovoltaic power; is the correlation coefficient between wind power and photovoltaic power; 、 are the standard deviations of wind power and photovoltaic power, respectively; is the inverse cumulative distribution function of the standard normal distribution; S2.3. The second-level Copula describes the long-term dependence between wind power, photovoltaic power, and load. Clayton Copula is used, which is suitable for describing variables with asymmetric dependence: (13); Where, 、 、 are the dependency parameters in Clayton Copula, which determine the strength of the correlation between wind power and photovoltaic power; Represents the second-layer Copula function, Used to describe the long-range dependency between wind power, photovoltaic power and load; S2.3. Combine the two layers of Copula functions into a joint Copula model: (14); Where, is the joint Copula function, Used to describe the joint distribution of wind power, photovoltaic power and load.

[0010] As a preferred solution of the present invention, in S3, the process of obtaining the optimal parameter estimation is: S3.1. Given sample data , the maximum likelihood function for: (15); Where n is the total number of geographical locations; is the density function of the joint copula; is the parameter to be estimated; S3.2. For the first-layer Copula function, its density function is: Based on the joint Copula function, sampling from the joint distribution generates uniform variables for multiple scenarios: (16); Where, Represents the density function of the first layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 ; S3.3. For the second-layer Copula function, its density function is: (17); Where, Represents the density function of the second layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 .

[0011] As a preferred solution of the present invention, in S4, the process of generating the joint scene is: S4.1. Using the estimated joint Copula model, sample K scenarios from the joint Copula function, each scenario corresponding to a set of uniform variables 、 、 : (18); Where, 、 、 is the standardized uniformly distributed variable of the kth scenario, k = 1, 2, …, K; S4.2. Extract K groups of samples from the joint copula function using the Monte Carlo method. Each group of samples represents a possible supply and demand combination. The samples reflect the interaction between geographical locations through the spatial correlation matrix R. The sampled uniform variables are back-transformed into actual physical quantities to form scenario data that can be used for planning: (19); Where, is the physical quantity of geographical location i in the kth scenario; is the inverse function of the marginal distribution of geographical location i; is the uniformly distributed variable of geographical location i in the kth scenario; S4.3. Finally, K joint scenarios are generated: (20); Where, 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location 1 under the kth scenario; 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location i under the kth scenario.

[0012] As a preferred embodiment of the present invention, in S5, the process of setting the comprehensive risk index under the joint scenario is as follows: S5.1. Construct a power failure loss function based on power failure risk: Based on planning decision a, the loss of each scenario is calculated. The power outage loss reflects the amount of loss when the sum of wind power and photovoltaic output of the power system cannot meet the total load demand in the kth scenario. Specifically, the power outage loss function calculates the difference between the sum of the load demand at all locations and the sum of wind power and photovoltaic output. If the difference is positive, the difference is the power outage loss; if the difference is negative or zero, the loss is 0. The power-off loss function is expressed as: (twenty one); Where, is the power failure loss function of the kth scenario; Output power for the generator at geographical location i in the kth scenario; Contribute to the external network of geographic location i in the kth scenario; S5.2. Based on the risk of resource waste, the resource waste loss function is expressed as: (twenty two); Where, is the resource waste loss function for the kth scene; When the sum of wind power and photovoltaic power output is greater than the sum of load demands at all locations, the excess is wasted resources; if the supply is insufficient, the waste is zero; S5.3. Calculate the power loss function and resource waste loss function of the generated K joint scenarios, arrange the loss values ​​in ascending order, and determine For the Values: (twenty three); Where, Is the confidence level Value at risk under For the Calculate the power loss risk and resource waste risk CVaR by the sorted power loss loss values: (twenty four); (25); Where, is the power outage risk CvaR; CvaR is the risk of wasted resources; Indicates filtering out Scene k, Similarly; S5.4. Obtain comprehensive risk indicators through weighted integration: (26); Where, 、 They are 、 The weight of .

[0013] As a preferred embodiment of the present invention, in S6, the objective function of the power system planning model is: (27); (28); Where, represents the investment cost; is the risk factor; is the unit capacity cost of wind power; is the installed wind power capacity at geographical location i; is the unit capacity cost of photovoltaics; is the installed photovoltaic capacity at geographical location i; is the unit capacity cost of traditional power generation; is the installed capacity of traditional power plants at geographical location i; is the unit capacity cost of the transmission line from geographic location i to geographic location j; is the capacity of the transmission line from geographic location i to geographic location j; Constraints include: Capacity constraints: (29); Where, Output for the traditional power plant at geographical location i in the kth scenario; is the power flow in the transmission line from geographical location i to geographical location j in the kth scenario; Supply and demand probability balance constraint: (30); Where, is the permissible probability of power failure; The supply and demand probability balance constraint is converted into a computable form through the sample average approximation: (31); Transmission constraints: At any geographic location i and scenario k, the sum of local generation, externally imported power, outflow power, and any unmet demand must equal the load demand at that node: (32); Where, The total power of all types of power generation at location i under scenario k, where types represents different types of power generation methods; is the power flow in the transmission line from geographic location j to geographic location i in the kth scenario; is the power loss at geographical location i under scenario k.

[0014] As a preferred embodiment of the present invention, in S7, the solution process is: S7.1. Collect historical data on wind power, photovoltaic output, and load demand, and determine their probability distribution; S7.2. Use spatial copula functions to capture dependencies between geographic locations and calculate the spatial correlation matrix , is the distance between geographical locations i and j; S7.3. Define planning stage decision variables and operational phase decision variables , A binary variable indicating whether scene k is selected or activated, 、 They represent the power loss and resource waste under scenario k respectively, and linearize the power system planning model; S7.4. Solve the power system planning model using the Benders decomposition method: S7.4.1. Set initial planning variables , initial risk Estimated to be 0; S7.4.2. Solve the Main Problem ; S7.4.3, bring in Calculate the scenario loss function and evaluate CVaR and probability constraints; S7.4.4. If the subproblem is infeasible, add a feasibility cut; if feasible, add an optimality cut and update the risk value ; S7.4.5. Repeat the main question and sub-questions until convergence.

[0015] The device for optimizing and planning a power system considering the probabilistic balance of supply and demand includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The above method is implemented by executing the computer program by the processor.

[0016] The beneficial effects of the present invention are: This paper adopts a hierarchical Copula model to divide the correlation between wind power, photovoltaics and load into two levels: local and long-range for modeling. It generates multiple joint scenarios through the Monte Carlo method, which significantly improves the ability to characterize the spatial correlation of multi-source uncertain factors such as wind power, photovoltaics and load. It provides more accurate and reliable input scenario data for the planning of new power systems and lays a solid foundation for subsequent supply and demand probability balance constraints.

[0017] The power system planning model constructed in this paper comprehensively considers investment costs and operational risks. The objective function aims to minimize the sum of the two, and specifically considers the supply-demand probabilistic balance constraint to ensure system reliability at a given confidence level. Furthermore, the Benders decomposition method is used to improve model solution efficiency. Simulation results show that, while this model requires a slightly higher initial investment than traditional methods, it offers significant advantages in key metrics such as operating costs, curtailment rate, and the frequency of supply-demand imbalances. This effectively reduces system operational risks and resource waste, while improving the robustness and cost-effectiveness of the planning scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 This is a comparison chart of correlation metrics of different methods in the verification process of the present invention; Figure 3 This is a comparison chart of squared Euclidean distances of different methods in the verification process of the present invention; Figure 4 It is a planning result diagram in the verification process of the present invention. DETAILED DESCRIPTION

[0019] The embodiments of the present invention are further described below with reference to the accompanying drawings: Example 1: Figure 1 As shown in Figure 2, the power system optimization planning method considering the probabilistic balance of supply and demand includes the following steps: S1. Define marginal distributions for random variables at each geographic location, including photovoltaic, wind power, and load; S2. Construct a hierarchical Copula model, including a first-layer Copula based on Gaussian Copula and a second-layer Copula based on Clayton Copula, and combine them into a joint Copula model to describe the joint distribution of photovoltaic, wind power, and load; S3. Use the maximum likelihood estimation method to estimate the parameters in the joint copula model and obtain the optimal parameter estimates; S4, extracting samples from the joint Copula function through the Monte Carlo method to generate a joint scene; S5. Based on the risk of power outage and resource waste, set comprehensive risk indicators for the combined scenario; S6. Based on the comprehensive risk indicators, establish a power system planning model and set its objective function and constraints; S7. Use the Benders decomposition method to solve the power system planning model and obtain the power system optimization planning solution.

[0020] In S1, for geographical location i, the photovoltaic edge distribution is expressed as: (1); Where, represents probability; is the cumulative distribution function of photovoltaic output at geographical location i (node ​​i), express The probability of PV output is , where x is an arbitrary real number, representing the possible value of PV output. In planning, x can be used to set output thresholds and analyze the performance of the system at different output levels. The same is true for y. is the photovoltaic output at geographical location i; The wind power marginal distribution is expressed as: (2); Where, is the cumulative distribution function of wind power output at the geographical location i of the wind farm, express The probability of , y is an arbitrary real number, representing the possible value of wind power output; is the wind power output at geographical location i (the power output of the wind turbine); In actual power system operation, power load demand is influenced by a variety of factors, including seasonal variations, weather conditions, industrial production activities, and people's lifestyles. These factors lead to significant load volatility. Actual load data often exhibits symmetrical fluctuations around the mean. Therefore, in new power system planning, load is often modeled as a random variable following a normal distribution.

[0021] The load marginal distribution is expressed as: (3); (4); Where, is the electricity demand at geographical location i; represents a normal distribution, is the average load value at geographical location i, is the load fluctuation amplitude at geographical location i; is the cumulative distribution function of load at geographical location i, express The probability of z is an arbitrary real number, which represents the possible value of the load; Represents the cumulative distribution function of the standard normal distribution.

[0022] for , the output of the photovoltaic power source at a certain moment is related to the radiation intensity and temperature at that moment, which is expressed by formula (5). The actual light intensity is calculated using formula (6): (5); (6); Where, represents the photovoltaic output at geographical location i at time t; Standard light intensity 1000W / m 2 and the photovoltaic output at a standard temperature of 25°C; F is the actual light intensity received by the photovoltaic power source; is the power temperature coefficient; T is the actual temperature of the photovoltaic power source; Beta distribution is used to simulate the reduction factor of photovoltaic power output due to weather changes such as shadows and clouds; This is the standard illumination without considering cloud cover, determined by the local geographical location; It reflects the power generation capacity of the wind farm at a certain moment, which is affected by the wind speed. According to the power curve of the wind turbine, The relationship with wind speed is a piecewise function: (7); Where, represents the wind power output at geographical location i at time t; is the wind speed at time t; The cut-in wind speed of the wind turbine. When the wind speed reaches the cut-in wind speed, the wind turbine output meets the grid connection conditions and can be used for grid connection. is the wind energy utilization coefficient; is the swept area of ​​the wind turbine rotor; is the air density; is the rated wind speed of the wind turbine, which is the minimum wind speed at which the wind turbine can output rated power; The cut-out wind speed of the wind turbine. When the wind speed is greater than the cut-out wind speed, the environment is not suitable for the wind turbine to operate and the wind turbine will shut down. is the rated power of the wind turbine.

[0023] wind speed The model usually follows a Weibull distribution. This approach ensures that the model can reflect the actual fluctuation characteristics of wind power output, such as zero output at low wind speeds and saturation effects at rated wind speeds.

[0024] In S2, the process of building a hierarchical Copula model is as follows: S2.1. After defining the marginal distribution, different types of physical variables are standardized into uniformly distributed variables through probability integral transformation. The heterogeneous distributions of photovoltaic, wind power, and load are converted into uniformly distributed variables in the interval [0, 1]. This eliminates the differences in variable distribution types so that the correlation between multiple variables can be processed in the Copula framework. This is expressed as: (8); (9); (10); (11); Where, is a uniformly distributed variable in the range [0, 1], representing the standardized probability value of geographic location i; is the marginal distribution function of geographic location i, representing 、 or ; is the original random variable of geographical location i; 、 、 are standardized uniformly distributed variables, representing the standardized variables of photovoltaic power, wind power and load at geographical location i; 、 、 The raw PV, wind power and load variables of geographical location i respectively; A copula is a mathematical tool that connects multiple marginal distributions and can be used to describe the correlation between variables. In a multivariate distribution, the copula function unites the variables in the marginal distributions to capture the dependencies between them. To address the complex temporal and spatial relationships between wind power, photovoltaic power generation, and load, a hierarchical copula model is used.

[0025] The main idea of ​​the hierarchical Copula model is to divide the correlation in the system into multiple levels for modeling, and the Copula function of each level reflects the dependency between variables at different levels.

[0026] In this model, we separate the correlations between multiple variables (e.g., wind power, PV, and load) into local correlations (spatial scale) and long-range correlations (temporal scale). First-level copula: Neighboring wind farms are highly correlated, and a Gaussian copula is used to describe this level of dependency. A Gaussian copula is used to capture the spatial correlation between adjacent wind farms.

[0027] S2.2. For the first-level Copula, it is assumed that there is local correlation between wind power, photovoltaic power, and load. In order to model this correlation, Gaussian Copula is used to describe data with symmetric correlation: (12); Where, Represents the first layer Copula function, Used to capture local correlation between wind power and photovoltaic power; is the correlation coefficient between wind power and photovoltaic power; 、 are the standard deviations of wind power and photovoltaic power, respectively; is the inverse cumulative distribution function of the standard normal distribution; S2.3. The second-level Copula is used to describe dependencies on a longer time scale, such as the long-term dependencies between wind power, photovoltaic power, and load. To capture this correlation, the Clayton Copula is used, which is suitable for describing variables with asymmetric dependencies: (13); Where, 、 、 are the dependency parameters in Clayton Copula, which determine the strength of the correlation between wind power and photovoltaic power; Represents the second-layer Copula function, Used to describe the long-range dependency between wind power, photovoltaic power and load; S2.3. Combine the two layers of Copula functions into a joint Copula model: (14); Where, is the joint Copula function, Used to describe the joint distribution of wind power, photovoltaic power and load.

[0028] In S3, the process of obtaining the optimal parameter estimation is: S3.1. Given sample data , the maximum likelihood function for: (15); Where n is the total number of geographical locations, which represents the total number of nodes considered in the system; is the density function of the joint copula; is the parameter to be estimated; S3.2. For the first-layer Copula function, its density function is: Based on the joint Copula function, sampling from the joint distribution generates uniform variables for multiple scenarios: (16); Where, Represents the density function of the first layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 ; S3.3. For the second-layer Copula function, its density function is: (17); Where, Represents the density function of the second layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 .

[0029] In S4, the process of generating a joint scene is as follows: S4.1. By combining the joint Copula model and maximum likelihood estimation, multiple scenarios can be generated from the joint distribution for risk assessment and system optimization. Using the estimated joint Copula model, K scenarios are sampled from the joint Copula function. Each scenario corresponds to a set of uniform variables. 、 、 : (18); Where, 、 、 is the standardized uniformly distributed variable of the kth scenario, k = 1, 2, …, K; S4.2. K groups of samples are extracted from the joint Copula function using the Monte Carlo method. Each group of samples represents a possible supply and demand combination. These samples not only reflect the marginal distribution characteristics of each location, but also reflect the interaction between geographical locations through the spatial correlation matrix R. In the planning of new power systems, this sampling method can generate a variety of scenarios, including extreme situations (such as low wind speed or high load across the entire network), thereby providing comprehensive data support for risk assessment and optimization. The randomness of the Monte Carlo method ensures the statistical representativeness of the samples, while the spatial characteristics of R enhance the physical reality of the samples. The sampled uniform variables are back-transformed into actual physical quantities to form scenario data that can be used for planning: (19); Where, is the physical quantity of geographical location i in the kth scenario; is the inverse function of the marginal distribution of geographical location i; is the uniformly distributed variable of geographical location i in the kth scenario; S4.3. Finally, K joint scenarios are generated: (20); Where, 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location 1 under the kth scenario; 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location i under the kth scenario.

[0030] In S5, the process of setting the comprehensive risk indicator under the joint scenario is as follows: S5.1. Construct a power failure loss function based on power failure risk: In power system risk assessment, power outage risk and resource waste risk are core dimensions for measuring uncertainty on both the supply and demand sides. They characterize system operational risks from the perspectives of power supply reliability and resource utilization efficiency, respectively. Power system risks primarily stem from insufficient power supply (power outage losses) and inefficient resource utilization (resource waste losses). This example quantifies these two types of losses using explicit mathematical formulas and performs calculations based on scenarios generated by a hierarchical copula.

[0031] Based on planning decision a, the loss for each scenario is calculated. The power outage loss reflects the amount of loss in the power system when the sum of wind power and photovoltaic output cannot meet the total load demand in the kth scenario. Specifically, the power outage loss function calculates the difference between the sum of the load demand at all locations and the sum of wind power and photovoltaic output. If the difference is positive (i.e., demand exceeds supply), the difference is the power outage loss; if the difference is negative or zero (sufficient supply), the loss is zero. The power-off loss function is expressed as: (twenty one); Where, is the power failure loss function of the kth scenario; Output power for the generator at geographical location i in the kth scenario; Contribute to the external network of geographic location i in the kth scenario; S5.2. Based on the risk of resource waste, the resource waste loss function is expressed as: (twenty two); Where, is the resource waste loss function of the kth scenario, which measures the amount of waste when the total supply of the power system exceeds the total load demand in the kth scenario; When the sum of wind power and photovoltaic power output is greater than the sum of load demands at all locations, the excess is wasted resources; if the supply is insufficient, the waste is zero; S5.3. Calculate the power loss function and resource waste loss function of the generated K joint scenarios, arrange the loss values ​​in ascending order, and determine For the Values: (twenty three); Where, Is the confidence level Value at risk under For the Calculate the power loss risk and resource waste risk CVaR by the sorted power loss loss values: (twenty four); (25); Where, is the power outage risk CvaR; CvaR is the risk of wasted resources; Indicates filtering out Scene k, Similarly; S5.4. Obtain comprehensive risk indicators through weighted integration: (26); Where, 、 They are 、 The weight of .

[0032] In S6, the objective function of the power system planning model is: (27); (28); Where, represents the investment cost; is the risk factor, which is used to adjust the trade-off between cost and risk; is the unit capacity cost of wind power; is the installed wind power capacity at geographical location i; is the unit capacity cost of photovoltaics; is the installed photovoltaic capacity at geographical location i; is the unit capacity cost of traditional power generation; is the installed capacity of traditional power plants at geographical location i; is the unit capacity cost of the transmission line from geographic location i to geographic location j; is the capacity of the transmission line from geographic location i to geographic location j; Constraints include: Capacity constraints: (29); Where, Output for the traditional power plant at geographical location i in the kth scenario; is the power flow in the transmission line from geographical location i to geographical location j in the kth scenario; Traditional deterministic supply and demand balance constraints require that power generation must equal load demand at any given moment. However, in scenarios with a high proportion of renewable energy, due to the randomness and volatility of its output, a completely deterministic supply and demand balance becomes difficult to achieve. Therefore, this embodiment adopts a probabilistic supply and demand balance constraint, which allows the supply and demand balance to be met at a certain probability level, rather than a strict deterministic balance. The probabilistic supply and demand balance constraint is expressed as: (30); Where, is the permissible probability of power failure; The supply and demand probability balance constraint is converted into a computable form through the sample average approximation: (31); Transmission constraints: At any geographic location i and scenario k, the sum of local generation, externally imported power, outgoing power, and any unmet demand (power losses) must equal the load demand at that node: (32); Where, The total power of all types of power generation at location i under scenario k, where types represents different types of power generation methods; is the power flow in the transmission line from geographic location j to geographic location i in the kth scenario; is the power loss at geographical location i under scenario k.

[0033] In S7, the solution process is: S7.1. Collect historical data on wind power, photovoltaic output, and load demand, and determine their probability distribution; S7.2. Use spatial copula functions to capture dependencies between geographic locations and calculate the spatial correlation matrix , is the distance between geographical locations i and j; S7.3. Define planning stage decision variables and operational phase decision variables , A binary variable indicating whether scene k is selected or activated, 、 They represent the power loss and resource waste under scenario k respectively, and linearize the power system planning model; S7.4. Solve the power system planning model using the Benders decomposition method: S7.4.1. Set initial planning variables , initial risk Estimated to be 0; S7.4.2. Solve the Main Problem ; S7.4.3, bring in Calculate scenario loss functions (power failure loss function and resource waste loss function) and evaluate CVaR and probability constraints; S7.4.4. If the subproblem is infeasible, add a feasibility cut; if feasible, add an optimality cut and update the risk value ; S7.4.5. Repeat the main question and sub-questions until convergence.

[0034] The verification process is: Scenario Generation Simulation: The hierarchical Copula function proposed in this embodiment is used to capture the correlation between variables in different geographical locations, and multiple joint scenarios are generated through the Monte Carlo method. The generated scenarios are compared with the traditional scenario generation method based on time series to analyze its advantages in capturing spatial correlation. The historical data of wind power, photovoltaic power and load in the area where a certain park is located are obtained. In order to quantify the performance of different scenario generation methods in capturing spatial correlation, the Spearman correlation coefficient is selected to measure the correlation between the generated scenarios and the actual historical data. The Kendall rank correlation coefficient is used to evaluate the degree of matching between the generated scenarios and the actual data in terms of rank correlation. The squared Euclidean distance measures the difference between the generated scenarios and the actual data distribution. The results are as follows Figure 2 and Figure 3 shown.

[0035] The simulation results show that the scenario generation method based on the hierarchical Copula model outperforms traditional methods in terms of measurement indicators such as the Spearman correlation coefficient (0.91), Kendall rank correlation coefficient (0.84), and squared Euclidean distance (12.3), significantly improving the ability to characterize the spatial correlation of multi-source uncertainties such as wind power, photovoltaics, and load.

[0036] This fully demonstrates the innovation and effectiveness of the method proposed in this example in the key step of "constructing a spatial correlation probability model." It can provide more accurate and reliable input scenario data for the "supply and demand probability balance constraint" in subsequent new power system planning models, thereby improving the robustness and cost-effectiveness of the overall planning scheme. Compared with traditional methods, the hierarchical Copula model not only better preserves the spatial dependency structure between variables, but also demonstrates greater adaptability and versatility in the coordinated planning of multi-regional and multi-type energy resources, providing key support for the safe, efficient, and low-carbon operation of large-scale new power systems.

[0037] Planning model simulation: In order to improve the planning robustness and risk perception ability of large new power systems in scenarios with a high proportion of new energy access, simulation experiments are conducted to verify the effectiveness and superiority of the power system planning method proposed in this embodiment in scenarios with high penetration of new energy, and in medium- and long-term planning scenarios when the power system has a new energy penetration rate of 30%. Among them, the model of the present invention considers 1,000 load and renewable output joint scenarios generated by the hierarchical Copula method, and introduces supply and demand probability balance constraints at a confidence level of 95%, aiming to improve the system's ability to respond to risks under uncertain conditions. The simulation results of the installed capacity distribution of each node in the power system and the capacity configuration of the transmission line are shown in the figure below. Figure 4 shown.

[0038] At the same time, the advantages of the power system planning model in this embodiment are compared with the traditional deterministic load planning model. The comparison model uses the traditional deterministic planning method, which is based only on typical load days and the average output of renewable energy. It does not consider the spatial correlation and probabilistic differences of the scenarios, nor does it include risk confidence constraints. The comparison results are shown in Table 1: Table 1 Model comparison parameters and results

[0039] Comparison results show that while the model in this embodiment requires a slightly higher initial investment (5-10%), operating costs are significantly reduced, demonstrating improved resource utilization and system scheduling flexibility. By introducing probabilistic supply and demand balance constraints, the model in this embodiment effectively reduces the system's curtailment rate and the frequency of supply and demand imbalances, enhancing its resilience to extreme scenarios. The frequency of supply and demand imbalances dropped from 29 times per year to 3 times per year, demonstrating system stability at a 95% confidence level. While ensuring power supply security, a more reasonable redundancy rate provides a risk buffer, making it more practical than the traditional model's blind compression of planned capacity. Furthermore, the risk exposure level is kept below 5%, far superior to traditional methods.

[0040] Example 2: A power system optimization planning device considering the probabilistic balance of supply and demand includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The method in Example 1 is implemented by executing the computer program by the processor.

Claims

1. A power system optimization planning method considering the probabilistic balance of supply and demand, characterized by The following steps are involved: S1. Define marginal distributions for random variables at each geographic location, including photovoltaic, wind power, and load; S2. Construct a hierarchical Copula model, including a first-layer Copula based on Gaussian Copula and a second-layer Copula based on Clayton Copula, and combine them into a joint Copula model to describe the joint distribution of photovoltaic, wind power, and load; S3. Use the maximum likelihood estimation method to estimate the parameters in the joint copula model and obtain the optimal parameter estimates; S4, extracting samples from the joint Copula function through the Monte Carlo method to generate a joint scene; S5. Based on the risk of power outage and resource waste, set comprehensive risk indicators for the combined scenario; S6. Based on the comprehensive risk indicators, establish a power system planning model and set its objective function and constraints; S7. Use the Benders decomposition method to solve the power system planning model and obtain the power system optimization planning solution.

2. The power system optimization planning method considering the supply and demand probability balance according to claim 1 is characterized in that: In S1, for geographical location i, the photovoltaic edge distribution is expressed as: （1）； Where, represents probability; is the cumulative distribution function of photovoltaic output at geographical location i, express The probability of x is an arbitrary real number, which represents the possible value of photovoltaic output; is the photovoltaic output at geographical location i; The wind power marginal distribution is expressed as: （2）； Where, is the cumulative distribution function of wind power output at the geographical location i of the wind farm, express The probability of , y is an arbitrary real number, representing the possible value of wind power output; The wind power output at geographical location i; The load marginal distribution is expressed as: （3）； （4）； Where, is the electricity demand at geographical location i; represents a normal distribution, is the average load value at geographical location i, is the load fluctuation amplitude at geographical location i; is the cumulative distribution function of load at geographical location i, express The probability of z is an arbitrary real number, which represents the possible value of the load; Represents the cumulative distribution function of the standard normal distribution.

3. The power system optimization planning method considering the supply and demand probability balance according to claim 2 is characterized in that: for , the output of the photovoltaic power source at a certain moment is related to the radiation intensity and temperature at that moment, which is expressed by formula (5). The actual light intensity is calculated using formula (6): （5）； （6）； Where, represents the photovoltaic output at geographical location i at time t; Standard light intensity 1000W / m 2 and the photovoltaic output at a standard temperature of 25°C; F is the actual light intensity received by the photovoltaic power source; is the power temperature coefficient; T is the actual temperature of the photovoltaic power source; Beta distribution is used to simulate the reduction factor of photovoltaic power output due to weather changes such as shadows and clouds; This is the standard illumination without considering the obstruction of clouds; It reflects the power generation capacity of the wind farm at a certain moment, which is affected by the wind speed. According to the power curve of the wind turbine, The relationship with wind speed is a piecewise function: （7）； Where, represents the wind power output at geographical location i at time t; is the wind speed at time t; is the cut-in wind speed of the wind turbine; is the wind energy utilization coefficient; is the swept area of ​​the wind turbine rotor; is the air density; is the rated wind speed of the wind turbine; is the cut-out wind speed of the wind turbine; is the rated power of the wind turbine.

4. The power system optimization planning method considering the supply and demand probability balance according to claim 2 is characterized in that: In S2, the process of constructing the hierarchical Copula model is as follows: S2.

1. After defining the marginal distribution, different types of physical variables are standardized into uniformly distributed variables through probability integral transformation. The heterogeneous distributions of photovoltaic, wind power, and load are converted into uniformly distributed variables in the interval [0, 1]. This eliminates the differences in variable distribution types so that the correlation between multiple variables can be processed in the Copula framework. This is expressed as: （8）； （9）； （10）； （11）； Where, is a uniformly distributed variable in the range [0, 1], representing the standardized probability value of geographic location i; is the marginal distribution function of geographic location i, representing 、 or ; is the original random variable of geographical location i; 、 、 are standardized uniformly distributed variables, representing the standardized variables of photovoltaic power, wind power and load at geographical location i; 、 、 The raw PV, wind power and load variables of geographical location i respectively; S2.

2. For the first-level Copula, assuming that there is local correlation between wind power, photovoltaic power, and load, Gaussian Copula is used to describe data with symmetric correlation: （12）； Where, Represents the first layer Copula function, Used to capture local correlation between wind power and photovoltaic power; is the correlation coefficient between wind power and photovoltaic power; 、 are the standard deviations of wind power and photovoltaic power, respectively; is the inverse cumulative distribution function of the standard normal distribution; S2.

3. The second-level Copula describes the long-term dependence between wind power, photovoltaic power, and load. Clayton Copula is used, which is suitable for describing variables with asymmetric dependence: （13）； Where, 、 、 are the dependency parameters in Clayton Copula, which determine the strength of the correlation between wind power and photovoltaic power; Represents the second-layer Copula function, Used to describe the long-range dependency between wind power, photovoltaic power and load; S2.

3. Combine the two layers of Copula functions into a joint Copula model: （14）； Where, is the joint Copula function, Used to describe the joint distribution of wind power, photovoltaic power and load.

5. The power system optimization planning method considering the supply and demand probability balance according to claim 4 is characterized in that: In S3, the process of obtaining the optimal parameter estimation is: S3.

1. Given sample data , the maximum likelihood function for: （15）； Where n is the total number of geographical locations; is the density function of the joint copula; is the parameter to be estimated; S3.

2. For the first-layer Copula function, its density function is: Based on the joint Copula function, sampling from the joint distribution generates uniform variables for multiple scenarios: （16）； Where, Represents the density function of the first layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 ; S3.

3. For the second-layer Copula function, its density function is: （17）； Where, Represents the density function of the second layer Copula function; By maximizing the log-likelihood function, we can get the estimated parameters 、 、 .

6. The power system optimization planning method considering the supply and demand probability balance according to claim 5 is characterized in that: In the aforementioned S4, the process of generating the joint scene is as follows: S4.

1. Using the estimated joint Copula model, sample K scenarios from the joint Copula function, each scenario corresponding to a set of uniform variables 、 、 : （18）； Where, 、 、 is the standardized uniformly distributed variable of the kth scenario, k = 1, 2, …, K; S4.

2. Extract K groups of samples from the joint copula function using the Monte Carlo method. Each group of samples represents a possible supply and demand combination. The samples reflect the interaction between geographical locations through the spatial correlation matrix R. The sampled uniform variables are back-transformed into actual physical quantities to form scenario data that can be used for planning: （19）； Where, is the physical quantity of geographical location i in the kth scenario; is the inverse function of the marginal distribution of geographical location i; is the uniformly distributed variable of geographical location i in the kth scenario; S4.

3. Finally, K joint scenarios are generated: （20）； Where, 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location 1 under the kth scenario; 、 、 are the wind power output, photovoltaic output, and electricity demand of geographical location i under the kth scenario.

7. The power system optimization planning method considering the supply and demand probability balance according to claim 6 is characterized in that: In S5, the process of setting the comprehensive risk indicator under the joint scenario is as follows: S5.

1. Construct a power failure loss function based on power failure risk: Based on planning decision a, the loss of each scenario is calculated. The power outage loss reflects the amount of loss when the sum of wind power and photovoltaic output of the power system cannot meet the total load demand in the kth scenario. Specifically, the power outage loss function calculates the difference between the sum of the load demand at all locations and the sum of wind power and photovoltaic output. If the difference is positive, the difference is the power outage loss; if the difference is negative or zero, the loss is 0. The power-off loss function is expressed as: （21）； Where, is the power failure loss function of the kth scenario; Output power for the generator at geographical location i in the kth scenario; Contribute to the external network of geographic location i in the kth scenario; S5.

2. Based on the risk of resource waste, the resource waste loss function is expressed as: （22）； Where, is the resource waste loss function for the kth scene; When the sum of wind power and photovoltaic power output is greater than the sum of load demands at all locations, the excess is wasted resources; if the supply is insufficient, the waste is zero; S5.

3. Calculate the power loss function and resource waste loss function of the K joint scenarios generated, arrange the loss values ​​in ascending order, and determine For the Values: （23）； Where, Is the confidence level Value at risk under For the Calculate the power loss risk and resource waste risk CVaR by the sorted power loss values: （24）； （25）； Where, is the power outage risk CvaR; CvaR is the risk of wasted resources; Indicates filtering out Scene k, Similarly; S5.

4. Obtain comprehensive risk indicators through weighted integration: （26）； Where, 、 They are 、 The weight of .

8. The power system optimization planning method considering the supply and demand probability balance according to claim 7 is characterized in that: In S6, the objective function of the power system planning model is: （27）； （28）； Where, represents the investment cost; is the risk factor; is the unit capacity cost of wind power; is the installed wind power capacity at geographical location i; is the unit capacity cost of photovoltaic; is the installed photovoltaic capacity at geographical location i; is the unit capacity cost of traditional power generation; is the installed capacity of traditional power plants at geographical location i; is the unit capacity cost of the transmission line from geographic location i to geographic location j; is the capacity of the transmission line from geographic location i to geographic location j; Constraints include: Capacity constraints: （29）； Where, Output for the traditional power plant at geographical location i in the kth scenario; is the power flow in the transmission line from geographical location i to geographical location j in the kth scenario; Supply and demand probability balance constraint: （30）； Where, is the permissible probability of power failure; The supply and demand probability balance constraint is converted into a computable form through the sample average approximation: （31）； Transmission constraints: At any geographic location i and scenario k, the sum of local generation, externally imported power, outflow power, and any unmet demand must equal the load demand at that node: （32）； Where, The total power of all types of power generation at location i under scenario k, where types represents different types of power generation methods; is the power flow in the transmission line from geographic location j to geographic location i in the kth scenario; is the power loss at geographical location i under scenario k.

9. The power system optimization planning method considering the supply and demand probability balance according to claim 8 is characterized in that: In the above-mentioned S7, the solution process is as follows: S7.

1. Collect historical data on wind power, photovoltaic output, and load demand, and determine their probability distribution; S7.

2. Use spatial copula functions to capture dependencies between geographic locations and calculate the spatial correlation matrix , is the distance between geographical locations i and j; S7.

3. Define planning stage decision variables and operational phase decision variables , A binary variable indicating whether scene k is selected or activated, 、 They represent the power loss and resource waste under scenario k respectively, and linearize the power system planning model; S7.

4. Solve the power system planning model using the Benders decomposition method: S7.4.

1. Set initial planning variables , initial risk Estimated to be 0; S7.4.

2. Solve the Main Problem ; S7.4.3, bring in Calculate the scenario loss function and evaluate CVaR and probability constraints; S7.4.

4. If the subproblem is infeasible, add a feasibility cut; if feasible, add an optimality cut to update the risk value ; S7.4.

5. Repeat the main question and sub-questions until convergence.

10. A power system optimization planning device considering the probabilistic balance of supply and demand, characterized by: The method comprises a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the method according to any one of claims 1 to 9 is implemented by executing the computer program by the processor.

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