A deep peak regulation risk decision method based on generalized conditional value at risk evaluation

Abstract

A deep peak regulation risk decision method based on generalized conditional value at risk evaluation, first establishes a deep peak regulation model for dynamic division of thermal power peak regulation partition boundaries; second, classifies wind power and photovoltaic output correlation scenarios and constructs a representative scenario set; based on the representative new energy output scenario, a peak regulation risk evaluation model is constructed, and the generalized conditional value at risk GCVaR is used to uniformly quantify the peak regulation loss under different risk levels; finally, a comprehensive objective function is constructed based on the system expected operation cost and the generalized conditional value at risk, and combined with power balance constraints, new energy output constraints, thermal power unit output constraints and other constraints, a deep peak regulation optimization scheduling model is established; the method is suitable for peak regulation risk evaluation and optimization scheduling scenario under high proportion of new energy access to power grid, and can improve the wind and light uncertainty scenario representation ability and enhance the system's ability to depict extreme and sub-extreme risks.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to the field of power system operation optimization and deep peak shaving risk control technology. Specifically, it relates to a deep peak shaving risk decision-making technology based on generalized conditional risk value assessment, which is applicable to power system peak shaving risk assessment, scenario modeling and optimization scheduling model construction under conditions of high proportion of renewable energy access. Background Technology

[0002] With the continuous growth of installed capacity of renewable energy sources such as wind power and photovoltaics, the randomness, volatility and time-series coupling characteristics of power system source-side output are becoming increasingly prominent. The high proportion of new energy access has changed the traditional peak-shaving operation mode dominated by conventional thermal power units, making the system face more complex peak-shaving pressure and operation constraints in scenarios such as load troughs, high output of new energy and rapid power fluctuations.

[0003] Currently, thermal power units remain a crucial regulatory resource for peak shaving in the power system. When fluctuations in renewable energy output intensify, thermal power units frequently need to undertake tasks such as ramp-up, valley-level regulation, and low-load operation, easily entering deep peak-shaving operating ranges. Under deep peak-shaving conditions, the unit's minimum stable combustion boundary, ramp-up capability, start-up and shutdown constraints, and characteristics of different operating sections all change significantly, increasing the complexity of system peak-shaving modeling and operation control. Especially under conditions of high renewable energy integration, if the deep peak-shaving boundary and operating characteristics of thermal power units cannot be accurately characterized, it will be difficult to effectively support the safe and stable operation of the system.

[0004] To address the peak-shaving problem caused by the uncertainty of new energy sources, existing research typically employs risk quantification methods to assess system operational deviations under disturbance scenarios. Among these, Value at Risk (VaR) and Conditional Value at Risk (CVaR) can characterize the risk boundary and tail loss level at a given confidence level. Compared to VaR, CVaR can further reflect the average loss intensity after exceeding the risk threshold, and therefore has been used in power system uncertainty dispatch and operational risk analysis. However, existing CVaR methods are mostly based on models built on a single confidence level, making it difficult to simultaneously cover multiple levels of risk, including extreme disturbances, sub-extreme disturbances, and routine fluctuations, resulting in insufficient completeness in risk characterization.

[0005] Furthermore, wind power and photovoltaic output typically exhibit significant temporal correlation and coupling characteristics. If renewable energy output is simplified to independent random variables during scenario modeling, or if their joint distribution structure is not fully considered, the representative scenario set's ability to characterize real disturbances will be reduced, thus affecting the accuracy of subsequent risk assessment and peak-shaving model construction. In scenarios with a high proportion of renewable energy integration, how to balance the joint fluctuation characteristics of renewable energy, the need to characterize multiple levels of risk, and the deep peak-shaving operation boundaries of thermal power units has become a key technical issue in power system peak-shaving risk assessment and optimal scheduling modeling. Summary of the Invention

[0006] To address the technical shortcomings of existing technologies, such as inaccurate characterization of deep peak-shaving operation boundaries for thermal power units, insufficient ability to represent joint fluctuation scenarios of new energy sources, and the inability of single-confidence risk assessment models to comprehensively cover multi-level peak-shaving risks, this invention provides a deep peak-shaving risk decision-making technology based on generalized conditional value of risk assessment. This invention aims to solve the technical problem of how to accurately coordinate the segmented operation characteristics and demand response resources of thermal power units under high-proportion new energy access, and to balance system operating costs and peak-shaving risks through multi-confidence risk quantification indicators.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A deep peak-shaving risk decision-making method based on generalized conditional value-at-risk assessment includes the following steps: Step 1: Based on the operating characteristics of thermal power units, such as minimum output, ramping capability, and start-up and shutdown costs, a deep peak-shaving model is established by constructing a segmented operating cost model for thermal power units and performing peak-shaving capability difference clustering. This model is used to determine the basis for the composition of the expected operating cost of the system. Step 2: Propose a clustering method for power output scenarios based on the improved ISODATA algorithm to classify the power output correlation scenarios of wind power and photovoltaic power and construct a representative set of new energy power output scenarios; Step 3: Construct a dynamic time-of-use pricing mechanism based on the predicted distribution of system net load, and establish a corresponding user demand response model to achieve dynamic linkage between time-of-use pricing, user load, and supply and demand fluctuations; Step 4: Construct a peak-shaving risk assessment model based on the representative new energy output scenarios obtained in Step 2, and use the Generalized Conditional Value at Risk (GCVaR) to uniformly measure the peak-shaving loss under different risk levels. The GCVaR is composed of a weighted average of the Conditional Value at Risk (CVaR) at multiple confidence levels. Step 5: Construct a comprehensive objective function using the expected operating cost of the system established in Step 1 and the generalized conditional risk value measured in Step 4. Combine the power balance constraints, renewable energy output constraints, thermal power unit output constraints, deep peak shaving zoning constraints determined in Step 1, thermal power unit ramping constraints, line transmission capacity constraints, and the response capability constraints and user electricity price constraints involved in Step 3 to establish a deep peak shaving optimization scheduling model. Based on the model solution, realize the optimal risk decision for deep peak shaving under a high proportion of renewable energy access. Through the above steps, peak-shaving risk modeling for uncertain scenarios is achieved, and optimal risk decision-making for deep peak-shaving under high-proportion renewable energy access is realized based on model solution.

[0008] Step 1 includes the following sub-steps: Sub-step 1-1) Construct a segmented operation cost model for thermal power units; Sub-steps 1-2) Perform peak-shaving capacity difference clustering.

[0009] In sub-step 1-1), the peak shaving operation depth is divided into the conventional peak shaving stage, the non-oil-injection stable combustion deep peak shaving stage, and the oil-injection combustion-supporting deep peak shaving stage. The peak shaving zone boundaries are delineated accordingly, and corresponding stage function models and start-stop cost models are established respectively. include: 1) Description of the regular peak-shaving phase: (1); In equation (1), For the first The coal consumption cost corresponding to each thermal power unit; , and Represented as the first Coal consumption cost coefficient corresponding to a thermal power unit; For the first Taiwan thermal power units Efforts made at all times; Based on the current coal price, Numbering of thermal power units t This is the scheduling time period number.

[0010] 2) Description of the deep peak-shaving stage without oil injection: (2); (3); In equations (2) and (3): For the first Taiwan thermal power units at time Additional wear and tear costs when the fuel supply is not in the deep peak shaving stage of stable fuel injection; This represents the loss coefficient during the operation of thermal power units; For the first The cost of purchasing a thermal power unit; The rotor cracking cycle number determined by the rotor low-cycle fatigue curve is related to the unit output. related.

[0011] 3) Description of the deep peak-shaving stage of oil injection for combustion assistance: (4); In equation (4): For the first Taiwan thermal power units at time Oil injection costs during the deep peak shaving phase; Based on the current oil price; For the first Taiwan thermal power units at time Oil input during the deep peak shaving phase.

[0012] Based on the cost analysis of the above three-stage model, the comprehensive operating cost of thermal power units can be represented in segments as follows: (5); In formula (5): The overall operating cost of thermal power units, To achieve the minimum output for fuel-assisted combustion, To achieve the minimum output without adding oil for stable combustion, This is the lower limit of normal peak-shaving output. This is the upper limit of normal peak-shaving output.

[0013] Start-up and shutdown costs for thermal power units: (6); In formula (6): This indicates the start-up and shutdown costs for thermal power units. For the first Start-up costs for a thermal power unit; For the first The cost of shutting down a thermal power unit; and Indicates the operating status of the thermal power unit; This represents the total number of thermal power units participating in peak shaving within the system.

[0014] In sub-steps 1-2), to distinguish units with different peak-shaving capabilities from those participating in deep peak shaving and to determine the boundaries of the peak-shaving zones, rated capacity, maximum peak-shaving rate, and ramp-up rate are selected as indicators. The K-means clustering method is used to divide the participating units into groups, including: Description of peak shaving rate of deep peak shaving units: (7); In equation (7) This represents the maximum output of the i-th unit. Let t be the output of the i-th generating unit at time t. This refers to the peak shaving rate.

[0015] Maximum peak shaving rate of deep peak shaving units (8); Equation (8) For the first Maximum peak load rate of the unit. For the unit The lowest stable fuel output that can be achieved without fuel injection under peak-shaving conditions.

[0016] Relative index of ramp rate of deep peak shaving units for: (9); In equation (9): For the first The ramp-up rate of the deep peak-shaving unit. For the first The maximum ramp rate of the deep peak shaving unit.

[0017] Evaluation indicators of the comprehensive peak-shaving capacity of deep peak-shaving units : (10); (11); In equation (11): For the system The workload of the moment; The system's scheduling period is based on day-ahead scheduling, with a time period of 24. The percentage of the maximum load fluctuation in the system relative to the maximum load peak-to-valley difference represents the degree of influence of the ramp rate on peak-shaving capacity.

[0018] K-means clustering algorithm process: (1) Randomly and uniformly select from the data Each sample serves as a cluster center.

[0019] (2) For each data point in the dataset Calculate its relationship with the selected cluster centers. Shortest Euclidean distance The samples were then assigned to clusters corresponding to each type of center according to the principle of proximity. Clusters.

[0020] (12); In equation (12): The dimension of the space; and They are and The Each attribute.

[0021] (3) Recalculate the cluster center using the distance metric so that it equals the mean of all samples in the cluster.

[0022] (4) Convergence judgment: Repeat steps (2) to (3) until the error meets the preset threshold and the iteration process is terminated.

[0023] Peak shaving standard classification: (13); (14); In equation (13): The cluster centers of each type of unit; This is the adjustment coefficient for the peak shaving limit; For the standard peak shaving law; in equation (14): The peak shaving rate of the units included in each category; The classification of peak-shaving standards to characterize the differences in peak-shaving capacity of generating units.

[0024] In step 2, a representative set of new energy power output scenarios is constructed, including the following sub-steps: Sub-step 2-1) Constructing a probability distribution model for new energy power output: Using a non-parametric estimation method, kernel density estimation is employed to generate the probability density function of historical wind and solar power output. (15); In equation (15): It is the probability density function; and They are respectively Fitted values ​​of wind and solar power at any given time; The total number of samples; The window width represents the length of each interval; For kernel functions; and They are respectively Wind, light and electricity fields The per-unit values ​​of wind and solar power for each sample.

[0025] Sub-step 2-2) Analyze the correlation between wind and solar power output: The Copula function is used to describe the correlation between wind and solar power output. Candidate functions are jointly evaluated by the rank correlation coefficient and the squared Euclidean distance. The Frank Copula function is selected to construct a joint wind and solar power distribution model. (16); In the formula The joint distribution function; , It is the marginal distribution function; For Copula connection functions; , For wind power and solar power output, use random variables.

[0026] Inverting the marginal distribution function yields the Copula function, as shown in the following formula: (17); Taking its partial derivative yields the joint probability density function: (18); In equation (18): Let be the probability density function of the Copula function; , For random variables , The probability density function.

[0027] The selection of the Copula function is based on the correlation index and the goodness-of-fit index. The candidate functions are jointly evaluated to determine the optimal function suitable for the joint distribution of wind power and photovoltaic power output.

[0028] (1) Correlation index (Kendall rank correlation coefficient) Spearman rank correlation coefficient ) To evaluate the correlation fit performance of the Copula function in modeling the joint distribution of wind and solar power output, Kendall's rank correlation coefficient and Spearman's rank correlation coefficient were used as rank correlation discriminant indicators. The rank correlation coefficients calculated by various Copula functions were compared with the actual rank correlation coefficients of the sample data. The smaller the difference, the better the function fit performance, thus determining the optimal Copula function. The formulas for calculating the correlation indicators are as follows: (19); (20); In equation (20): , Consistent logarithm and inconsistent logarithm in the joint contribution of wind and solar power; The number of sampling points; For any output sample observation value in wind power output exist rank in; For any sample observation value of photovoltaic power generation output exist The rank and have , .

[0029] (2) Goodness-of-fit index (squared Euclidean distance) ) To measure the fitting accuracy between candidate Copula functions and sample empirical Copula functions, the squared Euclidean distance is used as a goodness-of-fit evaluation index. This index quantifies the distance between the theoretical joint distribution and the empirical distribution; the smaller the distance, the better the fitting performance. The calculation formula is as follows: (twenty one); In equation (21): The empirical distribution of the sample; This is the joint distribution of the Copula function.

[0030] Considering the characteristics of Frank Copula, such as distribution symmetry, asymptotic independence of the tails, and compatibility with positive and negative correlations, this study ultimately chose the Frank Copula function to construct the joint wind-solar distribution model, whose joint probability density function is as follows: (twenty two); In equation (22): Based on the relevant parameters and the joint probability density function of wind and solar power output, the hourly wind and solar power output can be obtained through sampling and inverse transformation.

[0031] Sub-steps 2-3) Execution of scenario clustering and reduction: An improved ISODATA clustering algorithm is used, employing particle swarm optimization (PSO) to find initial cluster centers, and Mahalanobis distance is used instead of Euclidean distance as the metric to generate the representative new energy power output scenario set. (1) Input the dataset to be clustered Output the cluster centers based on the number of clusters and the maximum number of iterations. Given a clustering partition, input the particle swarm optimization algorithm parameters and initialize the initial position of each particle. and initial velocity ; (2) Evaluate the applicability value of each particle using the following formula: (twenty three); In the formula For particle applicable values, This represents the distance between the sample and the cluster center.

[0032] (3) If the particle's applicable value is better than the individual optimal solution Then that position is the current particle. Position; if the particle's applicable value is better than the overall optimal solution of the population. Then that position is the current particle. Location; (4) Update the particle position according to equations (24)-(25). and speed ; (twenty four); (25); In equation (24): It represents the number of times the particles are renewed; a constant. and For learning factors; and for Random numbers within a range; For the first The particle in the first The position at the next iteration; For the first Individual particles Speed ​​during the next iteration; Let i be the optimal position for the i-th particle. This represents the global optimal position of the particle swarm.

[0033] (5) Repeat step (2) until the stopping condition is met. Once the condition is met, terminate the particle swarm iteration and update the corresponding... Cluster centers are used as initial values ​​for the ISODATA algorithm to perform clustering; (6) Calculate each data point arrive Mahalanobis distance of the initial cluster centers Each sample is assigned to the nearest cluster center. In the corresponding clusters, the result of the cluster partitioning is: Determine the minimum number of samples for each category. If the number of samples in a cluster is less than this parameter, then that class is discarded. The sample is then reassigned to the class with the closest remaining class center distance; otherwise, the recalculation is performed. ; (26); (27); In equation (26): This is the weight matrix; For the first 100 sample vectors to be clustered For the first There are several clusters.

[0034] (7) Judgment If the number of iterations is odd, a split operation is performed, splitting the center into new clusters. and The formula is: (28); In the formula, and These are the new cluster centers generated after the split; The largest component in the standard deviation vector of this type of sample; (8) Judgment If the number of iterations is even, a merging operation is performed, calculating the Mahalanobis distance. Two classes with a distance less than a threshold are merged, and the new cluster centers are: (29); In the formula, and These represent the number of samples in the two clusters being merged. and The cluster centers before the merger; (9) Each time a split operation instruction is performed, then If merged once The iteration stops when the maximum number of iterations is reached. Step 3 involves constructing the electricity pricing mechanism and demand response model, using the following sub-steps: Sub-step 3-1) Constructing a dynamic time-of-use (TOU) electricity pricing model: Dividing the system into peak, flat, and valley intervals according to the net load power distribution, using equal division of power values ​​as the dividing line, and implementing a sorting-rearrangement strategy to map power to time series, including: Constructing a dynamic TOU partitioning mathematical model and judgment formula: Dynamic TOU partitioning mathematical model: (30); In equation (30): The power is divided equally into power values; and These are the maximum and minimum net load power of the system, respectively. and These are the dividing lines for the system's net load power curve.

[0035] Formula for determining the division of electricity price periods: (31); In equation (31): , and For the newly defined peak, flat, and valley electricity prices; The symbolic function indicates that if the condition in parentheses is met, the electricity price at that moment is divided into the electricity price period on the right side of the equation. For a moment Net load power; Sub-step 3-2) Constructing multi-type user demand response models: Based on differentiated response characteristics, load response behavior is divided into Type I (easily transferable), Type II (easily replaceable), and Type III (rigid) loads. Corresponding response quantification models are established using the logistic function and the price elasticity of demand matrix, including: Based on the differentiated response characteristics of load users to changes in electricity prices, under the TOU mechanism, load response behavior at different times is divided into three categories: (32); In equation (32): for Type I load at any given time, i.e., easily transferable load; for Type II load at any given time, i.e., easily replaceable load; for Type III load at any given time, i.e., rigid load; (1) For Type I load, active user participation response prediction curves and passive user participation response prediction curves were constructed based on the logistic function. The area enclosed by these curves represents the actual user participation demand response: (33); In equation (33): Load shift rate is the ratio of the amount of load shifted from a high-electricity-price area to a low-electricity-price area to the total load in the high-electricity-price area. This refers to the price difference between peak and off-peak hours. It is a variable that controls the up and down movement of the curve; Indicates the range of function values. for The x-coordinate corresponding to the function value. represents the steep slope parameter of the function.

[0036] Type I user responses are divided into three response ranges, with... and The two electricity price differences are used as the basis for the division: (34); (35); In equation (34): The membership degree of the optimistic response; in equation (35) This represents the actual peak-valley load transfer rate. The load transfer rate corresponding to the response prediction curve for active user participation; This represents the load transfer rate corresponding to the passive participation response prediction curve.

[0037] The load changes under demand response are as follows: (36); (37); In equation (36): This refers to the change in load after Type I users participate in demand response; and These are the average load values ​​for peak hours and normal hours, respectively; The equivalent load after Type I users participate in demand response.

[0038] (2) Users of Type II loads typically respond to electricity prices by saving on electricity consumption and increasing their electricity usage. Their electricity consumption pattern is suitable for electricity demand elasticity matrix modeling. The elasticity coefficients in the price elasticity matrix... : (38); In equation (38): This indicates the initial load amount of a Type II load. This indicates the change in power of the load response and demand response of Type II users; Original time-of-use electricity price Price elasticity of demand matrix: (39); In equation (39): , and The initial load values ​​for Type II loads in three time periods; , and This represents the load changes over three time periods following the demand response. It is the self-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the load during that period; , , , , , It is the cross-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the transfer of load during other periods.

[0039] Type II load user response load under time-of-use pricing (40); In equation (40): The equivalent load after Type II users participate in demand response; For Type II users at any time The original load; This represents the load change of Type II users under demand response.

[0040] (3) Type III load response modeling: Type III load users are extremely insensitive to electricity price changes, and their load demand has a weak responsiveness to TOU (Time to Operate). It is assumed that the load demand of this type of user is basically unaffected by TOU, and the responsive load under the current electricity price is... (41); Step 4, constructing the peak-shaving risk assessment model, includes the following sub-steps: Sub-step 4-1) Define Generalized Conditional Value at Risk (GCVaR): GCVaR is defined as a weighted combination of conditional values ​​at different confidence levels, used to simultaneously characterize the expected value of peak-shaving losses in extreme, sub-extreme, and conventional risk scenarios. Its mathematical expression is as follows: (42); (43); In the formula Indicates the confidence level stratum; …represents the weighting coefficients of each layer of CvaR. Sub-step 4-2) Constructing an auxiliary optimization function: Each CVaR term in the GCVaR index is transformed into an auxiliary optimization function for solution, establishing the multi-confidence sequence and its corresponding value at risk; each of the GCVaR indicators... The term is solved using an auxiliary optimization function, the objective function of which is: (44); In equation (44): , For decision variables; For random variables After discretization, the first One sample data; In the first In a random scenario, the decision variables The corresponding system loss cost function; The total number of samples; For the first The probability corresponding to each sample data; This is a multi-confidence sequence. Generally, a confidence level of 3 is selected, that is, focusing on high confidence for extremely low probability extreme scenarios, medium confidence for sub-extreme scenarios, and low confidence for relatively high probability normal scenarios; The value at risk corresponding to each confidence level, i.e. : (45); In equation (45): , These are decision variables and random variables, respectively. For loss cost function; It is a random variable The probability density function; The confidence level reflects the decision-maker's level of risk aversion; Value at risk at this confidence level; Let be the set of real numbers.

[0041] Step 5 involves establishing and solving the deep peak shaving optimization scheduling model, including the following steps: Sub-step 5-1) Constructing the system's comprehensive objective function: The Generalized Conditional Value at Risk (GCVaR) is used as the risk metric, and a linearly weighted combination is performed with the expected operating cost of the system described in step 1. The balance between economic efficiency and safety is adjusted through preference weight coefficients. The objective function is as follows: (46); (47); In the formula: The overall system cost based on GCVaR; The expected operating cost of the system is composed of the operating cost and start-up and shutdown costs of the thermal power unit in step 1; The risk preference coefficient, with a value of [0,1], indicates whether decision-makers are more inclined to ensure the economy or the security of the system when making decisions. For the cost of operating thermal power units, Cost of starting and stopping thermal power units , These represent the system's penalties for wind and solar power curtailment. Compensation costs for responding to user requests via system calls.

[0042] Sub-step 5-2) Establish model constraints: Integrate various boundary conditions for system operation and optimization, specifically including: (1) Ignore power balance constraints for network losses: (48); in, For the first Each wind farm at any time Those who have made contributions For the first A photovoltaic field at any time Those who have made contributions For the first Taiwan thermal power units at time Those who have made contributions For a moment The system load, For the number of wind farms, For the number of photovoltaic fields, This refers to the number of thermal power units. (2) Output constraints of new energy units: (49); (50); In equation (49): For the first Typhoon power plant units The maximum active power output at a given time; in equation (50): For the first Photovoltaic fields in Maximum active power output at any given time (3) Output constraints of conventional thermal power units: (51); (4) Depth peaking partitioning constraints determined based on the partitioning boundaries described in sub-step 1-1): (52); (5) Climbing constraint: (53); (6) Line transmission capacity constraints: (54); In the formula: and Represented as nodes and nodes The voltage phase angle; Represents a node and nodes The susceptance between them; Represents a node and nodes The per-unit value of the maximum transmission power that the line can achieve; (7) Response capability constraints established based on sub-step 3-2): (55); In equation (55): This is the allowable fluctuation percentage of the load, generally taken as around 10%. Post-demand response time The equivalent load; (8) User electricity price constraints established based on sub-step 3-2): (56); (9) CVaR constraints used to calculate auxiliary variables: (57); (58); In the formula: It is an auxiliary variable for the CVaR value corresponding to the k-th scene. It serves as an auxiliary variable for Value at Risk.

[0043] Sub-step 5-3) Model Solving and Decision Output: After establishing the above deep peak shaving optimization scheduling model, the mixed integer linear programming solver (CPLEX) is used to solve the model to obtain the optimal output plan, oil injection and combustion assistance status, and demand response load call amount of each thermal power unit at different time periods, thereby finally generating a deep peak shaving optimal decision scheme that takes into account both economy and safety.

[0044] In the "wind power + photovoltaic" scenario, Euclidean distance differs from traditional independent distances across dimensions, exhibiting a strong correlation between the two. Therefore, this invention also proposes an ISODATA scene clustering method based on PSO optimization and Mahalanobis distance improvement. This method aims to address the technical problems of traditional clustering algorithms in extracting high-dimensional correlated features and reducing representative scenes, such as sensitivity to initial values, susceptibility to local optima, and inability to accurately measure the correlation between variables. Specifically, this method includes: Step 1: Obtain the original dataset to be clustered, and initialize the parameters of the Particle Swarm Optimization (PSO) algorithm and the expected clustering parameters of the ISODATA algorithm according to the characteristics of the dataset; Step 2: Execute the Particle Swarm Optimization (PSO) algorithm to perform global optimization and obtain the optimal initial cluster centers of the ISODATA algorithm to overcome the clustering instability problem caused by randomly selecting initial values; Step 3: Using Mahalanobis distance as a similarity criterion, assign the samples in the original dataset to the nearest cluster centers to construct the initial cluster partition; Step 4: Based on the preset category splitting and merging criteria, the initial clusters are dynamically adjusted to achieve adaptive optimization of the number of cluster centers; Step 5: Through multiple iterations and updates, when the termination condition is met, output the final representative scene set and its corresponding scene probability distribution.

[0045] In step 2, the optimal initial cluster centers are obtained using the following sub-steps: Sub-step 2-1: Initialize the position and velocity of each particle, where the particle's position represents a set of potential ISODATA initial cluster centers; Sub-step 2-2: Evaluate the quality of each particle using a fitness function, which is constructed based on the tightness between the sample and its cluster center; Sub-steps 2-3: Update the individual historical optimal solution and the overall optimal solution of the group through the information exchange mechanism, and update the position and velocity of the particles according to the following formula: (twenty four); (25); In the formula: It represents the number of times the particles are renewed; a constant. and For learning factors; and for Random numbers within a range; This represents the globally optimal solution for the entire particle swarm. This is the globally optimal solution for the entire particle swarm; For the first The current position of each particle; Sub-steps 2-4: After the maximum number of iterations is reached, the position coordinates corresponding to the globally optimal particle are used as the initial cluster center output of the ISODATA algorithm.

[0046] In step 3, sample allocation is performed using the following sub-steps: Sub-step 3-1: Calculate the Mahalanobis distance from each sample in the dataset to each initial cluster center. The Mahalanobis distance takes into account the covariance relationship between variables, and the formula is as follows: (26); After the initial sample allocation is completed, the center of each cluster is updated using the following formula: (27) In the formula, Indicates the first A cluster, Indicates the first The number of samples in each cluster This represents the cluster center updated based on the current mean of samples within the cluster.

[0047] Sub-step 3-2: Based on the principle of minimum Mahalanobis distance, assign each sample to the nearest cluster. If the number of samples in a cluster is less than the preset minimum number of samples, discard that cluster and reallocate the samples.

[0048] In step 4, dynamic adjustments are performed using the following sub-steps: (28); In the formula, and These are the new cluster centers generated after the split; The largest component in the standard deviation vector of this type of sample; Sub-step 4-1: Split operation. When the number of iterations is odd or the current number of clusters is too small, calculate the standard deviation of each category of samples. If the standard deviation of a certain category is greater than the preset splitting threshold and the sample size meets the condition, then split the center into two new cluster centers. Sub-step 4-2: Merge operation; when the number of iterations is even, calculate the Mahalanobis distance between each cluster center. If the distance between two clusters is less than a preset merging threshold, merge the two clusters to generate new cluster centers. (29); In the formula, and These represent the number of samples in the two clusters being merged. and These are the cluster centers before the merger.

[0049] The proposed ISODATA scene clustering method based on PSO optimization and Mahalanobis distance improvement overcomes the shortcomings of traditional clustering algorithms that are prone to getting trapped in local optima, significantly improving the global stability of clustering results; it accurately characterizes the coupling features between high-dimensional variables, effectively eliminating the interference of dimensionality and correlation of multi-source data; it achieves adaptive dynamic optimization of the number of clusters, avoiding subjective bias caused by manually preset parameters; and it effectively improves the quality and representativeness of scene reduction, providing high-fidelity input for downstream stochastic optimization and risk decision-making.

[0050] Compared with the prior art, the present invention has the following technical effects: 1) This invention proposes a deep peak-shaving risk decision-making method based on generalized conditional value of risk assessment. This method constructs typical wind and solar power combined output samples through an improved new energy scenario clustering algorithm, and introduces the GCVaR index as a quantitative measurement tool for multi-level peak-shaving loss risk on this basis. It is linearly combined with the expected operating cost to form an optimized objective function, thereby realizing a dynamic trade-off between operating cost and risk. 2) This invention constructs a comprehensive optimization scheduling framework that integrates thermal power unit peak-shaving capacity modeling, improved ISODATA new energy scenario clustering, and generalized conditional risk value assessment mechanism. Through multi-factor segmented modeling, it accurately characterizes unit operating characteristics and, combined with new energy-related output scenarios, significantly improves the reliability and representativeness of system scheduling inputs. 3) This invention introduces Generalized Conditional Value at Risk (GCVaR) as a multi-level risk indicator, breaking through the limitations of traditional single-confidence-level CVaR models and achieving synergistic assessment of extreme, sub-extreme, and normal volatility risks. This indicator constructs an objective function through a weighted combination of multiple confidence-level CVaRs, enabling the model to possess higher risk robustness and adjustment flexibility while ensuring operational economy. 4) This invention models GCVaR and expected system operating costs in a linear combination and introduces an adjustable preference weight mechanism to achieve dynamic balance between risk loss and operating costs. Numerical simulations verify that this method can effectively reduce the proportion of wind and solar power curtailment and the cost of deep regulation of thermal power, improve the renewable energy absorption rate, and is suitable for power system operation optimization and risk decision-making in scenarios with a high proportion of renewable energy access. 5) This invention can accurately characterize the differentiated operating costs and capacity boundaries of thermal power units at different depths of peak shaving, such as conventional peak shaving, stable combustion without oil injection, and oil injection for combustion assistance; considering the high-dimensional correlation between wind and solar power, this invention can efficiently and accurately extract a set of highly representative wind and solar power combined output scenarios; this invention breaks through the limitations of a single risk threshold and uses a unified measurement mechanism (i.e., generalized conditional value of risk GCVaR) to simultaneously capture peak shaving losses caused by extreme, sub-extreme, and conventional fluctuations, and dynamically integrates them with economic costs for optimization. Attached Figure Description

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a diagram of the IEEE 30-node system; Figure 3 It is a histogram of wind power output frequency; Figure 4 It is a photovoltaic frequency histogram; Figure 5 This is a schematic diagram of the relevant scene generation; Figure 6 This is a simplified diagram of the relevant scenario. Detailed Implementation

[0052] like Figure 1 As shown, a deep peak-shaving risk decision-making method based on generalized conditional value-at-risk assessment includes the following steps: Step 1: Based on the operating characteristics of thermal power units, such as minimum output, ramping capability, and start-up and shutdown costs, a deep peak-shaving model is established by constructing a segmented operating cost model for thermal power units and performing peak-shaving capability difference clustering. This model is used to determine the basis for the composition of the expected operating cost of the system. Step 2: Propose a clustering method for power output scenarios based on the improved ISODATA algorithm to classify the power output correlation scenarios of wind power and photovoltaic power and construct a representative set of new energy power output scenarios; Step 3: Construct a dynamic time-of-use pricing mechanism based on the predicted distribution of system net load, and establish a corresponding user demand response model to achieve dynamic linkage between time-of-use pricing, user load, and supply and demand fluctuations; Step 4: Construct a peak-shaving risk assessment model based on the representative new energy output scenarios obtained in Step 2, and use the generalized conditional value of risk (GCVaR) to uniformly measure the peak-shaving loss under different risk levels. The GCVaR is composed of a weighted average of conditional values ​​of risk (CVaR) at multiple confidence levels. Step 5: Construct a comprehensive objective function using the expected operating cost of the system established in Step 1 and the generalized conditional value of risk measured in Step 4. Combine this with power balance constraints, renewable energy output constraints, thermal power unit output constraints, deep peak shaving zoning constraints determined in Step 1, thermal power unit ramping constraints, line transmission capacity constraints, and response capability constraints and user electricity price constraints involved in Step 3. Establish a deep peak shaving optimization scheduling model and solve it based on the model to achieve the optimal risk decision for deep peak shaving under a high proportion of renewable energy access.

[0053] Through the above steps, peak-shaving risk modeling for uncertain scenarios is achieved, and optimal risk decision-making for deep peak-shaving under high-proportion renewable energy access is realized based on model solution.

[0054] Step 1 includes the following sub-steps: Sub-step 1-1) Construct a segmented operation cost model for thermal power units; Sub-steps 1-2) Perform peak-shaving capacity difference clustering.

[0055] In sub-step 1-1), the peak shaving operation depth is divided into the conventional peak shaving stage, the non-oil-injection stable combustion deep peak shaving stage, and the oil-injection combustion-supporting deep peak shaving stage. The peak shaving zone boundaries are delineated accordingly, and corresponding stage function models and start-stop cost models are established respectively. include: 1) Description of the regular peak-shaving phase: (1); In equation (1), For the first The coal consumption cost corresponding to each thermal power unit; , and Represented as the first Coal consumption cost coefficient corresponding to a thermal power unit; For the first Taiwan thermal power units Efforts made at all times; Based on the current coal price, Numbering of thermal power units t This is the scheduling time period number.

[0056] 2) Description of the deep peak-shaving stage without oil injection: (2); (3); In equations (2) and (3): For the first Taiwan thermal power units at time Additional wear and tear costs when the fuel supply is not in the deep peak shaving stage of stable fuel injection; This represents the loss coefficient during the operation of thermal power units; For the first The cost of purchasing a thermal power unit; The rotor cracking cycle number determined by the rotor low-cycle fatigue curve is related to the unit output. related.

[0057] 3) Description of the deep peak-shaving stage of oil injection for combustion assistance: (4); In equation (4): For the first Taiwan thermal power units at time Oil injection costs during the deep peak shaving phase; Based on the current oil price; For the first Taiwan thermal power units at time Oil input during the deep peak shaving phase.

[0058] Based on the cost analysis of the above three-stage model, the comprehensive operating cost of thermal power units can be represented in segments as follows: (5); In formula (5): The overall operating cost of thermal power units, To achieve the minimum output for fuel-assisted combustion, To achieve the minimum output without adding oil for stable combustion, This is the lower limit of normal peak-shaving output. This is the upper limit of normal peak-shaving output.

[0059] Start-up and shutdown costs for thermal power units: (6); In formula (6): This indicates the start-up and shutdown costs for thermal power units. For the first Start-up costs for a thermal power unit; For the first The cost of shutting down a thermal power unit; and Indicates the operating status of the thermal power unit; This represents the total number of thermal power units participating in peak shaving within the system.

[0060] In sub-steps 1-2), to distinguish units with different peak-shaving capabilities from those participating in deep peak shaving and to determine the boundaries of the peak-shaving zones, rated capacity, maximum peak-shaving rate, and ramp-up rate are selected as indicators. The K-means clustering method is used to divide the participating units into groups, including: Description of peak shaving rate of deep peak shaving units: (7); In equation (7) This represents the maximum output of the i-th unit. Let t be the output of the i-th generating unit at time t. This refers to the peak shaving rate.

[0061] Maximum peak shaving rate of deep peak shaving units (8); Equation (8) For the first Maximum peak load rate of the unit. For the unit The lowest stable fuel output that can be achieved without fuel injection under peak-shaving conditions.

[0062] Relative index of ramp rate of deep peak shaving units for: (9); In equation (9): For the first The ramp-up rate of the deep peak-shaving unit. For the first The maximum ramp rate of the deep peak shaving unit.

[0063] Evaluation indicators of the comprehensive peak-shaving capacity of deep peak-shaving units : (10); (11); In equation (11): For the system The workload of the moment; The system's scheduling period is based on day-ahead scheduling, with a time period of 24. The percentage of the maximum load fluctuation in the system relative to the maximum load peak-to-valley difference represents the degree of influence of the ramp rate on peak-shaving capacity.

[0064] K-means clustering algorithm process: (1) Randomly and uniformly select from the data Each sample serves as a cluster center.

[0065] (2) For each data point in the dataset Calculate its relationship with the selected cluster centers. Shortest Euclidean distance The samples were then assigned to clusters corresponding to each type of center according to the principle of proximity. Clusters.

[0066] (12); In equation (12): The dimension of the space; and They are and The Each attribute.

[0067] (3) Recalculate the cluster center using the distance metric so that it equals the mean of all samples in the cluster.

[0068] (4) Convergence judgment: Repeat steps (2) to (3) until the error meets the preset threshold and the iteration process is terminated.

[0069] Peak shaving standard classification: (13); (14); In equation (13): The cluster centers of each type of unit; This is the adjustment coefficient for the peak shaving limit; For the standard peak shaving law; in equation (14): The peak shaving rate of the units included in each category; The classification of peak-shaving standards to characterize the differences in peak-shaving capacity of generating units.

[0070] In step 2, a representative set of new energy power output scenarios is constructed, including the following sub-steps: Sub-step 2-1) Constructing a probability distribution model for new energy power output: Using a non-parametric estimation method, kernel density estimation is employed to generate the probability density function of historical wind and solar power output. (15); In equation (15): It is the probability density function; and They are respectively Fitted values ​​of wind and solar power at any given time; The total number of samples; The window width represents the length of each interval; For kernel functions; and They are respectively Wind, light and electricity fields The per-unit values ​​of wind and solar power for each sample.

[0071] Sub-step 2-2) Analyze the correlation between wind and solar power output: The Copula function is used to describe the correlation between wind and solar power output. Candidate functions are jointly evaluated by the rank correlation coefficient and the squared Euclidean distance. The Frank Copula function is selected to construct a joint wind and solar power distribution model. (16); In the formula The joint distribution function; , It is the marginal distribution function; For Copula connection functions; , For wind power and solar power output, use random variables.

[0072] Inverting the marginal distribution function yields the Copula function, as shown in the following formula: (17); Taking its partial derivative yields the joint probability density function: (18); In equation (18): Let be the probability density function of the Copula function; , For random variables , The probability density function.

[0073] The selection of the Copula function is based on the correlation index and the goodness-of-fit index. The candidate functions are jointly evaluated to determine the optimal function suitable for the joint distribution of wind power and photovoltaic power output.

[0074] (1) Correlation index (Kendall rank correlation coefficient) Spearman rank correlation coefficient ) To evaluate the correlation fit performance of the Copula function in modeling the joint distribution of wind and solar power output, Kendall's rank correlation coefficient and Spearman's rank correlation coefficient were used as rank correlation discriminant indicators. The rank correlation coefficients calculated by various Copula functions were compared with the actual rank correlation coefficients of the sample data. The smaller the difference, the better the function fit performance, thus determining the optimal Copula function. The formulas for calculating the correlation indicators are as follows: (19); (20); In equation (20): , Consistent logarithm and inconsistent logarithm in the joint contribution of wind and solar power; The number of sampling points; For any output sample observation value in wind power output exist rank in; For any sample observation value of photovoltaic power generation output exist The rank and have , .

[0075] (2) Goodness-of-fit index (squared Euclidean distance) ) To measure the fitting accuracy between candidate Copula functions and sample empirical Copula functions, the squared Euclidean distance is used as a goodness-of-fit evaluation index. This index quantifies the distance between the theoretical joint distribution and the empirical distribution; the smaller the distance, the better the fitting performance. The calculation formula is as follows: (twenty one); In equation (21): The empirical distribution of the sample; This is the joint distribution of the Copula function.

[0076] Considering the characteristics of Frank Copula, such as distribution symmetry, asymptotic independence of the tails, and compatibility with positive and negative correlations, this study ultimately chose the Frank Copula function to construct the joint wind-solar distribution model, whose joint probability density function is as follows: (twenty two); In equation (22): Based on the relevant parameters and the joint probability density function of wind and solar power output, the hourly wind and solar power output can be obtained through sampling and inverse transformation.

[0077] Sub-steps 2-3) Execution of scenario clustering and reduction: An improved ISODATA clustering algorithm is used, employing particle swarm optimization (PSO) to find initial cluster centers, and Mahalanobis distance is used instead of Euclidean distance as the metric to generate the representative new energy power output scenario set. (1) Input the dataset to be clustered Output the cluster centers based on the number of clusters and the maximum number of iterations. Given a clustering partition, input the particle swarm optimization algorithm parameters and initialize the initial position of each particle. and initial velocity ; (2) Evaluate the applicability value of each particle using the following formula: (twenty three); In the formula For particle applicable values, This represents the distance between the sample and the cluster center.

[0078] (3) If the particle's applicable value is better than the individual optimal solution Then that position is the current particle. Position; if the particle's applicable value is better than the overall optimal solution of the population. Then that position is the current particle. Location; (4) Update the particle position according to equations (24)-(25). and speed ; (twenty four); (25); In equation (24): It represents the number of times the particles are renewed; a constant. and For learning factors; and for Random numbers within a range; For the first The particle in the first The position at the next iteration; For the first Individual particles Speed ​​during the next iteration; Let i be the optimal position for the i-th particle. This represents the global optimal position of the particle swarm.

[0079] (5) Repeat step (2) until the stopping condition is met. Once the condition is met, terminate the particle swarm iteration and update the corresponding... Cluster centers are used as initial values ​​for the ISODATA algorithm to perform clustering; (6) Calculate each data point arrive Mahalanobis distance of the initial cluster centers Each sample is assigned to the nearest cluster center. In the corresponding clusters, the result of the cluster partitioning is: Determine the minimum number of samples for each category. If the number of samples in a cluster is less than this parameter, then that class is discarded. The sample is then reassigned to the class with the closest remaining class center distance; otherwise, the recalculation is performed. ; (26); (27); In equation (26): This is the weight matrix; For the first 100 sample vectors to be clustered For the first There are several clusters.

[0080] (7) Judgment If the number of iterations is odd, a split operation is performed, splitting the center into new clusters. and The formula is: (28); In the formula, and These are the new cluster centers generated after the split; The largest component in the standard deviation vector of this type of sample; (8) Judgment If the number of iterations is even, a merging operation is performed, calculating the Mahalanobis distance. Two classes with a distance less than a threshold are merged, and the new cluster centers are: (29); In the formula, and These represent the number of samples in the two clusters being merged. and The cluster centers before the merger; (9) Each time a split operation instruction is performed, then If merged once The iteration stops when the maximum number of iterations is reached. Step 3 involves constructing the electricity pricing mechanism and demand response model, using the following sub-steps: Sub-step 3-1) Constructing a dynamic time-of-use (TOU) electricity pricing model: Dividing the system into peak, flat, and valley intervals according to the net load power distribution, using equal division of power values ​​as the dividing line, and implementing a sorting-rearrangement strategy to map power to time series, including: Constructing a dynamic TOU partitioning mathematical model and judgment formula: Dynamic TOU partitioning mathematical model: (30); In equation (30): The power is divided equally into power values; and These are the maximum and minimum net load power of the system, respectively. and These are the dividing lines for the system's net load power curve.

[0081] Formula for determining the division of electricity price periods: (31); In equation (31): , and For the newly defined peak, flat, and valley electricity prices; The symbolic function indicates that if the condition in parentheses is met, the electricity price at that moment is divided into the electricity price period on the right side of the equation. For a moment Net load power; Sub-step 3-2) Constructing multi-type user demand response models: Based on differentiated response characteristics, load response behavior is divided into Type I (easily transferable), Type II (easily replaceable), and Type III (rigid) loads. Corresponding response quantification models are established using the logistic function and the price elasticity of demand matrix, including: Based on the differentiated response characteristics of load users to changes in electricity prices, under the TOU mechanism, load response behavior at different times is divided into three categories: (32); In equation (32): for Type I load at any given time, i.e., easily transferable load; for Type II load at any given time, i.e., easily replaceable load; for Type III load at any given time, i.e., rigid load; (1) For Type I load, active user participation response prediction curves and passive user participation response prediction curves were constructed based on the logistic function. The area enclosed by these curves represents the actual user participation demand response: (33); In equation (33): Load shift rate is the ratio of the amount of load shifted from a high-electricity-price area to a low-electricity-price area to the total load in the high-electricity-price area. This refers to the price difference between peak and off-peak hours. It is a variable that controls the up and down movement of the curve; Indicates the range of function values. for The x-coordinate corresponding to the function value. represents the steep slope parameter of the function.

[0082] Type I user responses are divided into three response ranges, with... and The two electricity price differences are used as the basis for the division: (34); (35); In equation (34): The membership degree of the optimistic response; in equation (35) This represents the actual peak-valley load transfer rate. The load transfer rate corresponding to the response prediction curve for active user participation; This represents the load transfer rate corresponding to the passive participation response prediction curve.

[0083] The load changes under demand response are as follows: (36); (37); In equation (36): This refers to the change in load after Type I users participate in demand response; and These are the average load values ​​for peak hours and normal hours, respectively; The equivalent load after Type I users participate in demand response.

[0084] (2) Users of Type II loads typically respond to electricity prices by saving on electricity consumption and increasing their electricity usage. Their electricity consumption pattern is suitable for electricity demand elasticity matrix modeling. The elasticity coefficients in the price elasticity matrix... : (38); In equation (38): This indicates the initial load amount of a Type II load. This indicates the change in power of the load response and demand response of Type II users; Original time-of-use electricity price Price elasticity of demand matrix: (39); In equation (39): , and The initial load values ​​for Type II loads in three time periods; , and This represents the load changes over three time periods following the demand response. It is the self-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the load during that period; , , , , , It is the cross-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the transfer of load during other periods.

[0085] Type II load user response load under time-of-use pricing (40); In equation (40): The equivalent load after Type II users participate in demand response; For Type II users at any time The original load; This represents the load change of Type II users under demand response.

[0086] (3) Type III load response modeling: Type III load users are extremely insensitive to electricity price changes, and their load demand has a weak responsiveness to TOU (Time to Operate). It is assumed that the load demand of this type of user is basically unaffected by TOU, and the responsive load under the current electricity price is... (41); Step 4, constructing the peak-shaving risk assessment model, includes the following sub-steps: Sub-step 4-1) Define Generalized Conditional Value at Risk (GCVaR): GCVaR is defined as a weighted combination of conditional values ​​at different confidence levels, used to simultaneously characterize the expected value of peak-shaving losses in extreme, sub-extreme, and conventional risk scenarios. Its mathematical expression is as follows: (42); (43); In the formula Indicates the confidence level stratum; …represents the weighting coefficients of each layer of CvaR. Sub-step 4-2) Constructing an auxiliary optimization function: Each CVaR term in the GCVaR index is transformed into an auxiliary optimization function for solution, establishing the multi-confidence sequence and its corresponding value at risk; each of the GCVaR indicators... The term is solved using an auxiliary optimization function, the objective function of which is: (44); In equation (44): , For decision variables; For random variables After discretization, the first One sample data; In the first In a random scenario, the decision variables The corresponding system loss cost function; The total number of samples; For the first The probability corresponding to each sample data; This is a multi-confidence sequence. Generally, a confidence level of 3 is selected, that is, focusing on high confidence for extremely low probability extreme scenarios, medium confidence for sub-extreme scenarios, and low confidence for relatively high probability normal scenarios; The value at risk corresponding to each confidence level, i.e. : (45); In equation (45): , These are decision variables and random variables, respectively. For loss cost function; It is a random variable The probability density function; The confidence level reflects the decision-maker's level of risk aversion; Value at risk at this confidence level; Let be the set of real numbers.

[0087] Step 5 involves establishing and solving the deep peak shaving optimization scheduling model, including the following steps: Sub-step 5-1) Constructing the system's comprehensive objective function: The Generalized Conditional Value at Risk (GCVaR) is used as the risk metric, and a linearly weighted combination is performed with the expected operating cost of the system described in step 1. The balance between economic efficiency and safety is adjusted through preference weight coefficients. The objective function is as follows: (46); (47); In the formula: The overall system cost based on GCVaR; The expected operating cost of the system is composed of the operating cost and start-up and shutdown costs of the thermal power unit in step 1; The risk preference coefficient, with a value of [0,1], indicates whether decision-makers are more inclined to ensure the economy or the security of the system when making decisions. For the cost of operating thermal power units, Cost of starting and stopping thermal power units , These represent the system's penalties for wind and solar power curtailment. Compensation costs for responding to user requests via system calls.

[0088] Sub-step 5-2) Establish model constraints: Integrate various boundary conditions for system operation and optimization, specifically including: (1) Ignore power balance constraints for network losses: (48); in, For the first Each wind farm at any time Those who have made contributions For the first A photovoltaic field at any time Those who have made contributions For the first Taiwan thermal power units at time Those who have made contributions For a moment The system load, For the number of wind farms, For the number of photovoltaic fields, This refers to the number of thermal power units. (2) Output constraints of new energy units: (49); (50); In equation (49): For the first Typhoon power plant units The maximum active power output at a given time; in equation (50): For the first Photovoltaic fields in Maximum active power output at any given time (3) Output constraints of conventional thermal power units: (51); (4) Depth peaking partitioning constraints determined based on the partitioning boundaries described in sub-step 1-1): (52); (5) Climbing constraint: (53); (6) Line transmission capacity constraints: (54); In the formula: and Represented as nodes and nodes The voltage phase angle; Represents a node and nodes The susceptance between them; Represents a node and nodes The per-unit value of the maximum transmission power that the line can achieve; (7) Response capability constraints established based on sub-step 3-2): (55); In equation (55): This is the allowable fluctuation percentage of the load, generally taken as around 10%. Post-demand response time The equivalent load; (8) User electricity price constraints established based on sub-step 3-2): (56); (9) CVaR constraints used to calculate auxiliary variables: (57); (58); In the formula: It is an auxiliary variable for the CVaR value corresponding to the k-th scene. It serves as an auxiliary variable for Value at Risk.

[0089] Sub-step 5-3) Model Solving and Decision Output: After establishing the above deep peak shaving optimization scheduling model, the mixed integer linear programming solver (CPLEX) is used to solve the model to obtain the optimal output plan, oil injection and combustion assistance status, and demand response load call amount of each thermal power unit at different time periods, thereby finally generating a deep peak shaving optimal decision scheme that takes into account both economy and safety.

[0090] In the "wind power + photovoltaic" scenario, Euclidean distance differs from traditional independent distances across dimensions, exhibiting a strong correlation between the two. Therefore, this invention also proposes an ISODATA scene clustering method based on PSO optimization and Mahalanobis distance improvement. This method aims to address the technical problems of traditional clustering algorithms in extracting high-dimensional correlated features and reducing representative scenes, such as sensitivity to initial values, susceptibility to local optima, and inability to accurately measure the correlation between variables. Specifically, this method includes: Step 1: Obtain the original dataset to be clustered, and initialize the parameters of the Particle Swarm Optimization (PSO) algorithm and the expected clustering parameters of the ISODATA algorithm according to the characteristics of the dataset; Step 2: Execute the Particle Swarm Optimization (PSO) algorithm to perform global optimization and obtain the optimal initial cluster centers of the ISODATA algorithm to overcome the clustering instability problem caused by randomly selecting initial values; Step 3: Using Mahalanobis distance as a similarity criterion, assign the samples in the original dataset to the nearest cluster centers to construct the initial cluster partition; Step 4: Based on the preset category splitting and merging criteria, the initial clusters are dynamically adjusted to achieve adaptive optimization of the number of cluster centers; Step 5: Through multiple iterations and updates, when the termination condition is met, output the final representative scene set and its corresponding scene probability distribution.

[0091] In step 2, the optimal initial cluster centers are obtained using the following sub-steps: Sub-step 2-1: Initialize the position and velocity of each particle, where the particle's position represents a set of potential ISODATA initial cluster centers; Sub-step 2-2: Evaluate the quality of each particle using a fitness function, which is constructed based on the tightness between the sample and its cluster center; Sub-steps 2-3: Update the individual historical optimal solution and the overall optimal solution of the group through the information exchange mechanism, and update the position and velocity of the particles according to the following formula: (twenty four); (25); In the formula: It represents the number of times the particles are renewed; a constant. and For learning factors; and for Random numbers within a range; This represents the globally optimal solution for the entire particle swarm. This is the globally optimal solution for the entire particle swarm; For the first The current position of each particle; Sub-steps 2-4: After the maximum number of iterations is reached, the position coordinates corresponding to the globally optimal particle are used as the initial cluster center output of the ISODATA algorithm.

[0092] In step 3, sample allocation is performed using the following sub-steps: Sub-step 3-1: Calculate the Mahalanobis distance from each sample in the dataset to each initial cluster center. The Mahalanobis distance takes into account the covariance relationship between variables, and the formula is as follows: (26); After the initial sample allocation is completed, the center of each cluster is updated using the following formula: (27) In the formula, Indicates the first A cluster, Indicates the first The number of samples in each cluster This represents the cluster center updated based on the current mean of samples within the cluster.

[0093] Sub-step 3-2: Based on the principle of minimum Mahalanobis distance, assign each sample to the nearest cluster. If the number of samples in a cluster is less than the preset minimum number of samples, discard that cluster and reallocate the samples.

[0094] In step 4, dynamic adjustments are performed using the following sub-steps: (28); In the formula, and These are the new cluster centers generated after the split; The largest component in the standard deviation vector of this type of sample; Sub-step 4-1: Split operation. When the number of iterations is odd or the current number of clusters is too small, calculate the standard deviation of each category of samples. If the standard deviation of a certain category is greater than the preset splitting threshold and the sample size meets the condition, then split the center into two new cluster centers. Sub-step 4-2: Merge operation; when the number of iterations is even, calculate the Mahalanobis distance between each cluster center. If the distance between two clusters is less than a preset merging threshold, merge the two clusters to generate new cluster centers. (29); In the formula, and These represent the number of samples in the two clusters being merged. and These are the cluster centers before the merger.

[0095] The proposed ISODATA scene clustering method based on PSO optimization and Mahalanobis distance improvement overcomes the shortcomings of traditional clustering algorithms that are prone to getting trapped in local optima, significantly improving the global stability of clustering results; it accurately characterizes the coupling features between high-dimensional variables, effectively eliminating the interference of dimensionality and correlation of multi-source data; it achieves adaptive dynamic optimization of the number of clusters, avoiding subjective bias caused by manually preset parameters; and it effectively improves the quality and representativeness of scene reduction, providing high-fidelity input for downstream stochastic optimization and risk decision-making.

[0096] Example: This embodiment focuses on segmented modeling of thermal power unit output, proposing a cost modeling method covering the entire process of conventional peak shaving, stable combustion without oil injection, and combustion-assisted combustion with oil injection. The model constructs peak shaving segment boundaries based on physical parameters such as the unit's minimum technical output, maximum ramp rate, start-up and shutdown costs, and stable operation boundaries, and assigns differentiated cost functions to each operating stage, thereby forming a thermal power peak shaving capability model with cost-technology-response capability linkage characteristics.

[0097] To more realistically depict the uncertainties in the combined output of wind and solar power, an improved ISODATA clustering algorithm is employed to process a large amount of historical output data. First, a particle swarm optimization (PSO) algorithm is introduced to search for optimal initial cluster centers, enhancing the algorithm's global search capability and overcoming the tendency of traditional ISODATA to get trapped in local optima. Second, to more effectively handle the correlations between high-dimensional feature samples, Mahalanobis distance is used instead of Euclidean distance as the similarity metric. Finally, a representative, evenly distributed set of typical wind and solar power output scenarios with joint correlation structures is formed, serving as the input dataset for subsequent risk modeling.

[0098] To address the need for measuring peak-shaving risk, Generalized Conditional Value at Risk (GCVaR) is introduced as a risk quantification indicator in the peak-shaving optimization objective function. The GCVaR model comprehensively considers the expected system peak-shaving loss under extreme, sub-extreme, and normal disturbance scenarios by weighted combining CVaR values ​​at multiple confidence levels. This method solves the problem of insufficient risk coverage in traditional CVaR at a single confidence level, enhancing the granularity of risk identification and the flexibility of regulatory response.

[0099] A scheduling optimization function with dual objectives of risk and cost is constructed by linearly combining the GCVaR index with the expected system operating cost. By setting preference weight coefficients, the model is guided to achieve a dynamic balance between peak-shaving economy and risk control. Finally, the sample average approximation method is used to solve the optimization problem in multiple scenarios, outputting the optimal peak-shaving strategy for each thermal power unit under each typical scenario.

[0100] The IEEE 30-node example was used for simulation, with only the access positions of each main component adjusted, such as... Figure 1 As shown in Table 1, the system comprises five thermal power units, with parameters for each unit listed below. Spinning reserve is 10% of the load. It connects to a 1000MW wind farm and a 1500MW photovoltaic power station. The on-grid tariff for thermal power is 375 yuan / (MWh), the benchmark on-grid tariff for wind power is 570 yuan / (MWh), and the on-grid tariff for photovoltaic power is 921 yuan / (MWh). The first and second tier compensation tariffs for deep peak shaving of thermal power are 200 yuan / (MWh) and 500 yuan / (MWh), respectively, and the renewable energy penalty coefficient is 536 yuan / (MWh). The optimal Copula function for the combined wind and solar power distribution is constructed using measured data from a region in Northwest China from July 1, 2024 to September 1, 2024, with a sampling time interval of 1 hour. The simulation example uses MATLAB / YALMIP to build a deep peak shaving model and the CPLEX solver to solve it.

[0101] Table 1 Operating parameters of thermal power units

[0102] Taking the 50% output limit stipulated in the Hubei peak-shaving ancillary service market as an example (i.e.) =0.5), using the clustering index of unit peak-shaving difference as the cluster center for K-means clustering, units of different capacities are divided into two groups, and the average of the highest peak-shaving rates of the two groups are approximately 66.5% and 58.1%, respectively. According to equation (13), it can be calculated that the peak-shaving capacity of units is 0.5%. The percentages of various boundaries are shown in the table.

[0103] Table 2 Unit Classification Results and Peak Shaving Critical Values

[0104] To analyze the impact of this method on the operation of deep peak-shaving units, this section sets up the following two scenarios for comparison.

[0105] Scenario 1: Traditional deep peak shaving unit model.

[0106] Scenario 2: Dynamically partitioning the unit model based on peak-shaving compensation boundaries considering differences in peak-shaving capabilities.

[0107] Table 3 Peak Shaving Benefits and Operating Costs for Each Scenario

[0108] The peak-shaving results obtained from the two schemes are shown in Table 3. It can be seen that the total operating cost of the unit in Scheme 1 is 5,041,300 yuan, while the total operating cost of the unit in Scheme 2 is 5,026,800 yuan, which is about 0.3% lower than that in Scheme 1. The unit revenue increased from 9,759,800 yuan to 10,256,000 yuan, and the peak-shaving revenue increased by about 5.1%, thus improving the overall economic efficiency.

[0109] Figure 2 and Figure 3 The output probability density distribution characteristics of wind farms and photovoltaic power plants are shown separately, where the horizontal axis represents the per-unit output value and the vertical axis f(x) represents the probability density. After fitting with the Frank-Copula function, 1000 wind-solar related scenarios were generated using Monte Carlo sampling. Then, K-means, ISODATA, and the proposed improved ISODATA were used to reduce the number of generated scenarios, respectively. The population size was set to 50, the maximum number of iterations to 100, and the learning factors were 2.1 and 2.1, respectively. The inertia weight was linearly adjusted. The comparison of different clustering algorithms is shown in Table 4.

[0110] Table 4 Comparison of clustering performance of different algorithms

[0111] Analyzing from the perspective of clustering evaluation metrics DBI and DI, the traditional ISODATA and K-means algorithms did not show significant differences in clustering quality, with ISODATA performing slightly better. This is mainly because the two algorithms are essentially similar, with the core difference lying in the cluster splitting and merging operations during the iteration process, leading to high similarity in their clustering results. The improved ISODATA algorithm integrates the PSO optimization strategy and the Mahalanobis distance metric, effectively increasing the probability of convergence to the global optimum by optimizing the initial cluster center selection mechanism, thus achieving optimal clustering performance. From the perspective of clustering computational efficiency, the K-means algorithm has the best time efficiency, followed by the ISODATA algorithm, and finally the improved ISODATA method. The main reason for this difference in computational time is that the ISODATA algorithm requires additional cluster splitting and merging operations, involving complex operations such as calculating the distance between samples and cluster centers, calculating the distance between cluster centers, and calculating sample standard deviations, all of which significantly increase computational complexity. Meanwhile, the improved algorithm improves clustering accuracy by optimizing the initial center selection strategy, but the corresponding optimization process adds additional computation, resulting in a decrease in computational efficiency. The Copula joint scene generation improves the PSO-ISODATA scene reduction results, such as... Figure 4 and Figure 5 As shown in Table 5, each scenario and its corresponding probability are presented.

[0112] Table 5. Probability Distribution of Wind-Solar Combined Power Generation Scenarios

[0113] To illustrate the superiority of the generalized CVaR optimization method proposed in this patent, this section presents three comparative analysis scenarios: Scenario 1: Random optimization method, without considering CVaR.

[0114] Scenario 2: Stochastic optimization method, while using CVaR model to optimize risk losses caused by uncertainties in wind power and photovoltaic power.

[0115] Scenario 3: Stochastic optimization method, which simultaneously utilizes a generalized CVaR model to optimize risk losses arising from uncertainties in wind power and photovoltaic power.

[0116] CVaR confidence level The confidence level is set to 0.99; the number of confidence sequence layers in the generalized CVaR is set to 3, and the confidence level of each layer decreases by 0.1; the weights of each layer are set to 0.1, 0.2, and 0.7. The system operating costs under different optimization models are shown in Table 6.

[0117] Table 6. Optimization results under different optimization models

[0118] Scenario 1 only considers the expected cost of typical scenarios, ignoring the tail risk of extreme scenarios, which may lead to an underestimation of actual risk. Scenario 2, however, uses the CVaR theoretical model to quantify system operational risk. It not only focuses on the expected cost of typical scenarios but also considers the potential risks arising from the uncertainty of wind and solar power output. This leads to a more conservative scheduling strategy, mobilizing more equipment to address potential risks and thus increasing operating costs. This approach balances the economic robustness of system operation to some extent, with a total operating cost of 970,250 yuan, demonstrating the effectiveness of considering the CVaR model. However, this risk value considers the risk at a confidence level of 0.99, reflecting only the average cost under extreme risk scenarios. The result is overly conservative and cannot comprehensively cover different risk levels. The confidence level reflects the decision-maker's risk aversion preference and risk tolerance boundary; an increase in the confidence level indicates a higher level of risk aversion. As the confidence level increases in a fixed stepwise manner from 0.79 to 0.99, the cost exhibits a non-linear upward trend, indicating that the enhanced risk aversion strategy leads to increased risk losses due to unbalanced power in the system. The cost of the method proposed in this chapter falls between that of Scenario 1 and Scenario 2. This is because, in addition to considering the losses in extreme risk scenarios exceeding the risk value threshold, it also appropriately optimizes the losses in sub-extreme scenarios that are close to but not exceeded the risk value threshold. This flexibly integrates different levels of risk, providing an overall risk assessment index that balances extreme and sub-extreme risks, and achieves a good balance between economy and safety.

Claims

1. A deep peak-shaving risk decision-making method based on generalized conditional value-at-risk assessment, characterized in that, Includes the following steps: Step 1: Based on the operating characteristics of thermal power units, such as minimum output, ramping capability, and start-up and shutdown costs, a deep peak-shaving model is established by constructing a segmented operating cost model for thermal power units and performing peak-shaving capability difference clustering. This model is used to determine the basis for the composition of the expected operating cost of the system. Step 2: Classify the scenarios related to wind power and photovoltaic output and construct a representative set of new energy output scenarios; Step 3: Construct a dynamic time-of-use pricing mechanism based on the predicted distribution of system net load, and establish a corresponding user demand response model; Step 4: Based on the representative new energy output scenarios obtained in Step 2, construct a peak-shaving risk assessment model, and use the generalized conditional value at risk (GCVaR) to uniformly measure peak-shaving losses under different risk levels. Step 5: Construct a comprehensive objective function using the expected operating cost of the system established in Step 1 and the generalized conditional risk value measured in Step 4. Combine the power balance constraints, renewable energy output constraints, thermal power unit output constraints, deep peak shaving zoning constraints determined in Step 1, thermal power unit ramping constraints, line transmission capacity constraints, and the response capability constraints and user electricity price constraints involved in Step 3 to establish a deep peak shaving optimization scheduling model. Based on the model solution, realize the optimal risk decision for deep peak shaving under a high proportion of renewable energy access. Through the above steps, peak-shaving risk modeling for uncertain scenarios is achieved, and optimal risk decision-making for deep peak-shaving under high-proportion renewable energy access is realized based on model solution.

2. The method according to claim 1, characterized in that, Step 1 includes the following sub-steps: Sub-step 1-1) Construct a segmented operation cost model for thermal power units; Sub-steps 1-2) Perform peak-shaving capability difference clustering; In sub-step 1-1), the peak shaving operation depth is divided into the conventional peak shaving stage, the non-oil-injection stable combustion deep peak shaving stage, and the oil-injection combustion-supporting deep peak shaving stage. The peak shaving zone boundaries are delineated accordingly, and corresponding stage function models and start-stop cost models are established respectively. In sub-steps 1-2), in order to distinguish the participation of units with different peak-shaving capabilities in deep peak shaving and to determine the boundary of the peak-shaving zone, rated capacity, maximum peak-shaving rate and ramp rate are selected as indicators, and K-means clustering method is used to divide the units participating in peak shaving.

3. The method according to claim 2, characterized in that, In sub-step 1-1), the constructed model includes: 1) Description of the regular peak-shaving phase: （1）； In equation (1), For the first The coal consumption cost corresponding to each thermal power unit; , and Represented as the first Coal consumption cost coefficient corresponding to a thermal power unit; For the first Taiwan thermal power units Efforts made at all times; Based on the current coal price, Numbering of thermal power units t Number the scheduling period; 2) Description of the deep peak-shaving stage without oil injection: （2）； （3）； In equations (2) and (3): For the first Taiwan thermal power units at time Additional wear and tear costs when the fuel supply is not in the deep peak shaving stage; This represents the loss coefficient during the operation of thermal power units; For the first The cost of purchasing a thermal power unit; The rotor cracking cycle number determined by the rotor low-cycle fatigue curve is related to the unit output. related; 3) Description of the deep peak-shaving stage of oil injection for combustion assistance: （4）； In equation (4): For the first Taiwan thermal power units at time Oil injection costs during the deep peak shaving phase; Based on the current oil price; For the first Taiwan thermal power units at time Oil input during the deep peak shaving phase; Based on the cost analysis of the above three-stage model, the comprehensive operating cost of thermal power units can be represented in segments as follows: （5）； In equation (5): The overall operating cost of thermal power units, To achieve the minimum output for fuel-assisted combustion, To achieve the minimum output without adding oil for stable combustion, This is the lower limit of normal peak-shaving output. This is the upper limit of normal peak-shaving output; Start-up and shutdown costs for thermal power units: （6）； In formula (6): This indicates the start-up and shutdown costs for thermal power units. For the first Start-up costs for a thermal power unit; For the first The shutdown costs of a thermal power unit; and Indicates the operating status of the thermal power unit; This represents the total number of thermal power units participating in peak shaving within the system.

4. The method according to claim 2, characterized in that, Sub-steps 1-2) specifically include: Description of peak shaving rate of deep peak shaving units: （7）； In equation (7) This represents the maximum output of the i-th unit. Let t be the output of the i-th generating unit at time t. Peak shaving rate; Maximum peak shaving rate of deep peak shaving units （8）； Equation (8) For the first Maximum peak load rate of the unit. For the unit The lowest stable fuel output that can be achieved without fuel injection under peak fuel injection conditions; Relative index of ramp rate of deep peak shaving units for: （9）； In equation (9): For the first The ramp-up rate of the deep peak-shaving unit. For the first The maximum ramp rate of the deep peak-shaving unit; Evaluation indicators of the comprehensive peak-shaving capacity of deep peak-shaving units : （10）； （11）； In equation (11): For the system The workload of the moment; The system's scheduling period is based on day-ahead scheduling, with a time period of 24. The percentage of the maximum load fluctuation in the system relative to the maximum load peak-to-valley difference represents the degree of influence of the ramp rate on peak-shaving capacity.

5. The method according to any one of claims 1 to 4, characterized in that, In step 2, a representative set of new energy power output scenarios is constructed, including the following sub-steps: Sub-step 2-1) Constructing a probability distribution model for new energy output: Using a non-parametric estimation method, the probability density function of historical wind and solar power output is generated using kernel density estimation; Sub-step 2-2) Analyze the correlation between wind and solar power output: The Copula function is used to describe the correlation between wind and solar power output. The candidate functions are jointly evaluated by the rank correlation coefficient and the squared Euclidean distance. The Frank Copula function is selected to construct a joint wind and solar power distribution model. Sub-steps 2-3) Execution of scenario clustering and reduction: An improved ISODATA clustering algorithm is adopted, using the particle swarm optimization (PSO) algorithm to find the initial cluster centers, and Mahalanobis distance is used instead of Euclidean distance as the measure to generate the representative new energy power output scenario set.

6. The method according to claim 5, characterized in that, In sub-step 2-1, the probability density function is: （15）； In equation (15): It is the probability density function; and They are respectively Fitted values ​​of wind and solar power at any given time; The total number of samples; The window width represents the length of each interval; For kernel functions; and They are respectively Wind, light and electricity fields The per-unit values ​​of wind and solar power for each sample.

7. The method according to claim 6, characterized in that, In sub-step 2-2, a joint wind-solar distribution model is established: （16）； In the formula The joint distribution function; , It is the marginal distribution function; For Copula connection functions; , For wind power and solar power output, random variables are used. Inverting the marginal distribution function yields the Copula function, as shown in the following formula: （17）； Taking its partial derivative yields the joint probability density function: （18）； In formula (18): Let be the probability density function of the Copula function; , For random variables , The probability density function.

8. The method according to claim 7, characterized in that, In sub-steps 2-3, the specific steps are as follows: (1) Input the dataset to be clustered Output the cluster centers based on the number of clusters and the maximum number of iterations. Given a clustering partition, input the particle swarm optimization algorithm parameters and initialize the initial position of each particle. and initial velocity ; (2) Evaluate the applicability value of each particle using the following formula: （23）； In the formula For particle applicable values, The distance between the sample and the cluster center; (3) If the particle's applicable value is better than the individual optimal solution Then that position is the current particle. Position; if the particle's applicable value is better than the overall optimal solution of the population. Then that position is the current particle. Location; (4) Update the particle position according to equations (24)-(25). and speed ; （24）； （25）； In equation (24): It represents the number of times the particles are renewed; a constant. and For learning factors; and for Random numbers within a range; For the first The particle in the first The position at the next iteration; For the first Individual particles Speed ​​during the next iteration; Let i be the optimal position for the i-th particle. This represents the global optimal position of the particle swarm. (5) Repeat step (2) until the stopping condition is met; after the condition is met, terminate the iteration of the particle swarm and set the corresponding... Cluster centers are used as initial values ​​for the ISODATA algorithm to perform clustering; (6) Calculate each data point arrive Mahalanobis distance of the initial cluster centers Each sample is assigned to the nearest cluster center. In the corresponding clusters, the result of the cluster partitioning is: Determine the minimum number of samples for each category. If the number of samples in a cluster is less than this parameter, then that class is discarded. The sample is then reassigned to the class with the closest remaining class center distance; otherwise, the recalculation is performed. ; （26）； （27）； In equation (26): This is the weight matrix; For the first 100 sample vectors to be clustered For the first One cluster; (7) Judgment If the number of iterations is odd, a split operation is performed, splitting the center into new clusters. and The formula is: （28）； In the formula, and These are the new cluster centers generated after the split; The largest component in the standard deviation vector of this type of sample; (8) Judgment If the number of iterations is even, a merging operation is performed, calculating the Mahalanobis distance. Two classes with a distance less than a threshold are merged, and the new cluster centers are: （29）； In the formula, and These represent the number of samples in the two clusters being merged. and The cluster centers before the merger; (9) Each time a split operation instruction is performed, then If merged once The iteration stops when the maximum number of iterations is reached.

9. The method according to claim 1, 2, 3, 4, 6, 7, or 8, characterized in that, In step 3, the electricity pricing mechanism and demand response model are constructed, using the following sub-steps: Sub-step 3-1) Construct a dynamic time-of-use (TOU) electricity price allocation model: Divide the system net load power distribution into peak, flat, and valley intervals, use power values ​​to divide the baseline, and realize the mapping between power and time series through sorting-rearrangement strategy; Sub-step 3-2) Constructing multi-type user demand response models: Based on differentiated response characteristics, load response behavior is divided into Type I - easily transferable load, Type II - easily replaceable load, and Type III - rigid load. Corresponding response quantification models are established using the logistic function and the price demand elasticity matrix, respectively.

10. The method according to claim 9, characterized in that, Sub-step 3-1) specifically includes constructing a dynamic TOU partitioning mathematical model and a judgment formula: Dynamic TOU partitioning mathematical model: （30）； In equation (30): The power is divided equally into power values; and These are the maximum and minimum net load power of the system, respectively. and These are the dividing lines for the system's net load power curve; Formula for determining the time period division of each motor: （31）； In equation (31): , and For the newly defined peak, flat, and valley electricity prices; The symbolic function indicates that if the condition in parentheses is met, the electricity price at that moment is divided into the electricity price period on the right side of the equation. For a moment Net load power; In sub-step 3-2), the specific steps include: based on the differentiated response characteristics of load users to electricity price changes, under the TOU mechanism, the load response behavior at different times is divided into three categories: （32）； In equation (32): for Type I load at any given time, i.e., easily transferable load; for Type II load at any given time, i.e., easily replaceable load; for Type III load at any given time, i.e., rigid load; (1) For Type I load, active user participation response prediction curves and passive user participation response prediction curves were constructed based on the logistic function. The area enclosed by these curves represents the actual user participation demand response: （33）； In equation (33): Load shift rate is the ratio of the amount of load shifted from a high-electricity-price area to a low-electricity-price area to the total load in the high-electricity-price area. This refers to the price difference between peak and off-peak hours. It is a variable that controls the up and down movement of the curve; Indicates the range of function values. for The x-coordinate corresponding to the function value. represents the slope parameter of the function; Type I user responses are divided into three response ranges, with... and The two electricity price differences are used as the basis for the division: （34）； （35）； In equation (34): The membership degree of the optimistic response; in equation (35) This represents the actual peak-valley load transfer rate. The load transfer rate corresponding to the response prediction curve for active user participation; The load transfer rate corresponding to the passive participation response forecast curve; The load changes under demand response are as follows: （36）； （37）； In equation (36): This refers to the change in load after Type I users participate in demand response; and These are the average load values ​​for peak hours and normal hours, respectively; The equivalent load after Type I users participate in demand response; (2) Users of type II load typically respond to electricity prices by saving on electricity consumption and increasing electricity usage for that type of load. Their electricity consumption pattern is suitable for electricity demand elasticity matrix modeling; the elasticity coefficients in the price elasticity matrix : （38）； In equation (38): This indicates the initial load amount of a Type II load. This indicates the change in power of the load response and demand response of Type II users; Original time-of-use electricity price Price elasticity of demand matrix: （39）； In equation (39): , and The initial load values ​​for Type II loads in three time periods; , and This represents the load changes over three time periods following the demand response. It is the self-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the load during that period; , , , , , It is the cross-elasticity coefficient, which represents the impact of changes in electricity prices during a certain period on the transfer of load during other periods; Type II load user response load under time-of-use pricing （40）； In equation (40): The equivalent load after Type II users participate in demand response; For Type II users at any time The original load; For Type II users, this represents the load change under demand response. (3) Type III load response modeling: Type III load users are extremely insensitive to electricity price changes, and their load demand has a weak responsiveness to TOU (Time to Operate). It is assumed that the load demand of this type of user is basically unaffected by TOU, and the responsive load under the current electricity price is... （41）。

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