Load control methods based on game theory and optimal user-side benefits

Abstract

This invention provides a load regulation method based on game theory and user-side benefit optimization, comprising the following steps: 1) establishing a load model and a load benefit model; 2) establishing a grid-side benefit model and formulating a time-of-use pricing strategy; 3) using a Cplex solver to optimize the user-side objective function; 4) determining the game convergence condition to obtain the optimal time-of-use price and load allocation. With grid demand response as the core and a price regulation strategy that changes real-time electricity prices as the means, this invention adjusts load changes by solving for future electricity prices. Combining game theory, this invention constructs load models, load benefit models, and grid-side benefit models with the user side and grid side as the game subjects, respectively. Load constraints and price constraints are set, and a Cplex solver is used to calculate the load user benefit results and grid load regulation results. The proposed method can effectively regulate the grid load during peak and valley periods while ensuring optimal user-side benefits.

Description

Technical Field

[0001] This invention relates to the field of power system load regulation technology, and in particular to a load regulation method based on game theory and user-side optimal benefits. Background Technology

[0002] With the development of electricity market reform, the policy decisions on deepening electricity price reform and improving the electricity price formation mechanism, and fully leveraging the signaling role of time-of-use pricing, have gradually become one of the main research contents of smart grids. During the operation of the power system, electricity prices are affected by multiple factors, including market characteristics, generation capacity, and overcapacity or undercapacity, resulting in highly sensitive and volatile electricity prices. This poses a significant challenge to the formulation of time-of-use pricing. Therefore, considering the correlation between various factors and electricity prices and selecting appropriate methods for formulating time-of-use pricing is of great importance.

[0003] To achieve load regulation, the obtained electricity price should continuously change with the daily load to incentivize load. However, in most cases, the power grid still charges users a fixed price, and the corresponding economic losses caused by load fluctuations are borne by the power grid. Meanwhile, since users are not bound by electricity prices, the daily load curve currently exhibits distinct peak and valley periods. Based on foreseeable developments, the load connected to the grid will continue to increase in the future, and this situation will continue to worsen. It is precisely because of the peak-valley difference in the power grid that generating units constantly adjust their load to maintain power balance, causing economic losses on both the power source and grid sides and posing a significant obstacle to the safe and stable operation of the power grid. However, current research on time-of-use pricing at home and abroad is mainly based on optimization theory, elasticity matrices, and game theory. But the elasticity matrix method usually requires establishing a linear relationship model between user electricity consumption and the retail electricity price, without considering the difference in the elasticity matrix when the retail electricity price changes are small and large. To address these problems, this invention focuses on power grid demand response and uses a price regulation strategy that changes the real-time electricity price as a means to adjust load changes by obtaining the future electricity price. This invention, incorporating game theory principles, proposes a game-theoretic method based on optimizing user-side benefits. It constructs load models, load benefit models, and grid benefit models with the user side and grid side as the game subjects, respectively. Load constraints and electricity price constraints are set, and the Cplex solver is used to calculate the load user revenue results and grid load regulation results. The proposed load regulation method effectively regulates grid load during peak and off-peak periods while ensuring optimal user-side benefits. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, this invention provides an effective load regulation method that balances the benefits of the grid and load sides and incorporates game theory. This method effectively predicts electricity prices while ensuring stable grid operation and economic efficiency.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] The load control method based on game theory and user-side optimal benefits includes the following steps:

[0007] 1) Establish a load model and a load benefit model;

[0008] 2) Establish a grid-side benefit model and formulate time-of-use pricing control strategies;

[0009] 3) Use the Cplex solver to optimize the user-side objective function;

[0010] 4) Determine the game convergence conditions to obtain the optimal time-of-use electricity price and load allocation.

[0011] Furthermore, step 1) of establishing the load model and the load benefit model includes the following:

[0012] I. Establishing a load model

[0013] Assuming all game participants are rational, from the perspective of load-side benefits, the ultimate goal of all load users is to minimize their electricity costs. Therefore, the interests of the load side are aligned. Let's take one day as the electricity consumption cycle and divide the cycle into m time periods. Then, the electricity consumption time can be represented as:

[0014] K = [k1, k2, k3, ... k m-1 ,k m (1)

[0015] Where K is the set of electricity usage times, k1 to k m This represents the m time periods that have been divided into; the power grid side changes the original electricity consumption habits of electricity users by implementing electricity price control strategies.

[0016] When electricity prices change, different types of loads respond differently. To differentiate the response effects of various load types and to reasonably calculate the revenue of each load during the regulation process, the load model is divided into two categories: controllable load model and uncontrollable load model. The controllable load is set as users sensitive to electricity prices, but in reality, it depends on the user's choice, and not all controllable loads will change due to changes in electricity prices. To simplify the model, the controllable load is set as the part that can be regulated. During the process of regulating electricity prices, these users will change their electricity consumption strategies according to changes in electricity prices, thereby reducing the total electricity expenditure of these users. Therefore, according to formula (1), the electricity load of each time period is expressed as:

[0017] q υ =[q υ1 ,q υ2 ,q υ3 ,…q υm-1 ,q υm (2)

[0018] In the formula, q υ q represents the set of controllable load electricity consumption. υ,1 to q υ,m This represents the electricity load at different time periods. Therefore, the total electricity consumption of the controllable load and the constraints on the change in controllable load during the adjustment process can be expressed as:

[0019]

[0020] Among them, Q υ The total load of the controllable load, q υt,σ Let represent the controllable load at time t (t∈m). When the controllable load spans multiple time periods, it satisfies the condition from the start time period K of the load. start Time period K until load ends end . q υt,σmax With q υt,σmin These represent the maximum and minimum values ​​of the load transfer in and out at time t during the controllable load regulation process.

[0021] Uncontrollable loads are classified as public utility loads, and their usage time remains unchanged regardless of electricity price fluctuations. Similarly, the electricity consumption of uncontrollable loads in each time period and the total electricity consumption can be expressed as follows:

[0022] q b =[q b1 ,q b2 ,q b3 ,…q bm-1 ,q bm (4)

[0023]

[0024] Where, q b q represents the set of uncontrollable load electricity consumption. b1 to q bm This represents the uncontrollable load at different times. Q b This represents the total load of uncontrollable loads. q bt,σ This represents the uncontrollable load at time t. When the uncontrollable load spans multiple time periods, it satisfies the condition from the start time period K. start Time period K until load ends end . q bt,σmax With q bt,σmin These represent the maximum and minimum values ​​of the uncontrollable load at time t during the controllable load regulation process, respectively.

[0025] II. Establishing a load benefit model

[0026] The objective function for total load expenditure and the electricity expenditure of each component can be expressed as:

[0027]

[0028] In the formula, C represents the total electricity expenditure on the load side. υ , C b Let g represent the electricity expenditure for controllable and uncontrollable loads, respectively; κ represent the total number of games; i represent the number of game rounds (i∈κ); and g t,i Let g represent the electricity price at time t in the i-th round of the game. t,i ∈g i g i It is expressed as follows:

[0029] g i =[g 1,i ,g 2,i ,g 3,i ,…g m-1,i ,g m,i (7)

[0030] Furthermore, step 2) of establishing a grid-side benefit model and formulating a time-of-use pricing strategy includes the following:

[0031] The electricity price control strategy is set as follows:

[0032]

[0033] Among them, g i g i-1 F, Q i-1 All are m-dimensional vectors (i = 1, 2, ..., κ), g1, g2, ..., g κ This represents the electricity price in each round of the game, from round 1 to round κ. F represents the electricity generation in each time period, and Q represents the electricity price in each time period. i-1F and Q represent the electricity consumption for each time period in the previous cycle. i-1 The representation method is as follows:

[0034] F = [F1, F2, F3, ..., F m (9)

[0035] Q i-1 =Q iυ-1 +Q ib-1 (10)

[0036] In the formula, F1, F2, F3, ..., F m This refers to the amount of electricity generated from time period 1 to time period m. Q iυ-1 Q ib-1 These represent the total load of the controllable and uncontrollable loads in the previous cycle, respectively.

[0037] Therefore, the cost per load-side operation is:

[0038] min C i =min(C iυ +C ib (11)

[0039] Among them, C i Let C represent the expenditure in round i. iυ and C ib Let $i$ represent the controllable load expenditure and the uncontrollable load expenditure in the $i$ round, respectively.

[0040] In reality, loads will only actively adjust their load if they increase their revenue under the new electricity price control policy. Therefore, this invention also sets the following constraints regarding the electricity price change strategy:

[0041]

[0042] In the formula, θ represents the peak-to-valley difference, which is determined by the maximum electricity consumption Q in the i-th round. imax The minimum power consumption Q in the i-th round imin Subtracting them gives us g. i,μ Let g represent the average electricity price in the i-th round. i,α g i,γ Let w represent the peak-hour electricity price and the off-hour electricity price in the i-th round, and w represent the peak-to-off-hour price ratio. When setting the peak-to-off-hour price ratio, a large ratio will disrupt the electricity consumption order on the load side and harm the interests of the power grid; a small ratio will not achieve the effect of peak-to-off-hour pricing. Therefore, the value of the peak-to-off-hour price ratio is limited to around 4.

[0043] Furthermore, the grid-side cost is set by considering only the variables that affect the grid-side cost during the regulation process, and the grid-side cost is minimized, which means the grid efficiency is maximized.

[0044] The evaluation formulas for the load curve and power generation curve in the power grid are used as conditions for grid-side revenue to approximate the effect of peak shaving and valley filling, and the following formula replaces the evaluation of grid-side revenue:

[0045]

[0046] ψ i An assessment formula representing the load and power generation for each cycle.

[0047] Furthermore, step 3) of calling the Cplex solver to optimize the user-side objective function specifically includes the following:

[0048] After determining the objective function and optimization variables, the user-side load allocation model was modeled and optimized using the Cplex solver and yalmip modeling tool in Matlab. The specific steps are as follows.

[0049] 1. Using the yalmip modeling toolkit, define the controllable load change in each time period as variables, and define the controllable load change threshold in each time period as constraints;

[0050] 2. Based on maximizing the objective function profit, write a program considering the time-of-use electricity price adjustment plan given by the grid side in the current round;

[0051] 3. Use the Cplex solver to optimize the objective function and obtain the controllable load allocation results for the user side in each time period;

[0052] Furthermore, step 4) of determining the game convergence condition to obtain the optimal time-of-use electricity price and load allocation specifically includes the following:

[0053] According to the definition of Nash equilibrium, each player in a game achieves optimal performance, i.e., Nash equilibrium, given the strategies of the other players. After each round of the game and obtaining the load curve after electricity price regulation, the grid-side benefit ψ is calculated. i and load-side benefits C i If the benefits of this round on the grid side and the user side are the same as the benefits of the previous round, ψ i-1 , C i-1 If the absolute value of the difference is less than the set precision range ε, that is, if the optimized decision satisfies the formula written below, then the game reaches equilibrium; if it does not meet the precision range, then the next round of adjustment continues until the equilibrium point is reached.

[0054]

[0055] Considering that electricity prices are affected by factors such as load fluctuations and power imbalances, predicting electricity prices is very difficult. Therefore, we first need to overcome the power imbalance between the grid and the load side by formulating a reasonable electricity price regulation strategy, and obtain the predicted electricity price after dynamic adjustment. Then, the predicted electricity price in each round is used for grid load dispatch, and the revenue of the load side and the grid side in each round is calculated. Since factors such as grid losses, peak shaving, and load regulation costs continuously change the revenue of the grid side and the user side through each round of regulation, in order to optimize the user side benefits, after each round of electricity price regulation and load dispatch, we need to determine whether the revenue of the grid side and the load side has reached the optimal user benefit (i.e., dynamic equilibrium). Otherwise, the electricity price will continue to be regulated according to the strategy, and finally, the optimal electricity price prediction result is obtained when dynamic equilibrium is satisfied.

[0056] Compared with the prior art, the present invention has the following beneficial effects:

[0057] This invention focuses on grid demand response and employs a price control strategy that modifies real-time electricity prices to adjust load changes. It incorporates game theory principles, constructing load, load benefit, and grid benefit models with the user side and grid side as the main players in the game. Load and price constraints are set, and a Cplex solver is used to calculate the user's revenue and the grid load control results. The proposed price prediction method effectively controls grid load during peak and off-peak periods while ensuring optimal user-side benefits. Attached Figure Description

[0058] Figure 1 This is a flowchart of the dynamic game theory process of the present invention;

[0059] Figure 2 This is the initial power generation and load curve of the present invention;

[0060] Figure 3 The electricity price curves before and after the game theory in this invention;

[0061] Figure 4 The figures show the electricity price change curves after each round of the game in this invention.

[0062] Figure 5 These are the load variation curves for each wheel in this invention;

[0063] Figure 6 The load optimization results and initial curves of this invention are shown below;

[0064] Figure 7 The comparison curves are for load optimization examples of the present invention. Detailed Implementation

[0065] The specific embodiments provided by the present invention will be described in detail below with reference to the accompanying drawings.

[0066] like Figure 1 As shown, the load control method based on game theory and optimal user-side benefits of the present invention includes the following steps:

[0067] 1) Establish a load model and a load benefit model;

[0068] 2) Establish a grid-side benefit model and formulate time-of-use pricing control strategies;

[0069] 3) Use the Cplex solver to optimize the user-side objective function;

[0070] 4) Determine the game convergence conditions to obtain the optimal time-of-use electricity price and load allocation.

[0071] The specific implementation process is as follows:

[0072] Step 1) involves establishing a load model and a load benefit model, which includes the following:

[0073] (I) Establishing a load model

[0074] Assuming all game participants are rational, from the perspective of load-side benefits, the ultimate goal of all load users is to minimize their electricity costs. Therefore, the interests of the load side are aligned. Let's take one day as the electricity consumption cycle and divide the cycle into m time periods. Then, the electricity consumption time can be represented as:

[0075] K = [k1, k2, k3, ... k m-1 ,k m (1)

[0076] Where K is the set of electricity usage times, k1 to k m This represents the m time periods that have been divided into; the power grid side changes the original electricity consumption habits of electricity users by implementing electricity price control strategies.

[0077] When electricity prices change, different types of loads respond differently. To differentiate the response effects of various load types and to reasonably calculate the revenue of each load during the regulation process, the load model is divided into two categories: controllable load model and uncontrollable load model. The controllable load is set as users sensitive to electricity prices, but in reality, it depends on the user's choice, and not all controllable loads will change due to changes in electricity prices. To simplify the model, the controllable load is set as the part that can be regulated. During the process of regulating electricity prices, these users will change their electricity consumption strategies according to changes in electricity prices, thereby reducing the total electricity expenditure of these users. Therefore, according to formula (1), the electricity load of each time period is expressed as:

[0078] q υ =[q υ1 ,qυ2 ,q υ3 ,…q υm-1 ,q υm (2)

[0079] In the formula, q υ q represents the set of controllable load electricity consumption. υ,1 to q υ,m This represents the electricity load at different time periods. Therefore, the total electricity consumption of the controllable load and the constraints on the change in controllable load during the adjustment process can be expressed as:

[0080]

[0081] Among them, Q υ The total load of the controllable load, q υt,σ Let represent the controllable load at time t (t∈m). When the controllable load spans multiple time periods, it satisfies the condition from the start time period K of the load. start Time period K until load ends end . q υt,σmax With q υt,σmin These represent the maximum and minimum values ​​of the load transfer in and out at time t during the controllable load regulation process.

[0082] Uncontrollable loads are classified as public utility loads, and their usage time remains unchanged regardless of electricity price fluctuations. Similarly, the electricity consumption of uncontrollable loads in each time period and the total electricity consumption can be expressed as follows:

[0083] q b =[q b1 ,q b2 ,q b3 ,…q bm-1 ,q bm (4)

[0084]

[0085] Where, q b q represents the set of uncontrollable load electricity consumption. b1 to q bm This represents the uncontrollable load at different times. Q b This represents the total load of uncontrollable loads. q bt,σ This represents the uncontrollable load at time t. When the uncontrollable load spans multiple time periods, it satisfies the condition from the start time period K. start Time period K until load ends end . q bt,σmax With q bt,σmin These represent the maximum and minimum values ​​of the uncontrollable load at time t during the controllable load regulation process, respectively.

[0086] (II) Establishing a load benefit model

[0087] The objective function for total load expenditure and the electricity expenditure of each component can be expressed as:

[0088]

[0089] In the formula, C represents the total electricity expenditure on the load side. υ , C b Let g represent the electricity expenditure for controllable and uncontrollable loads, respectively; κ represent the total number of games; i represent the number of game rounds (i∈κ); and g t,i Let g represent the electricity price at time t in the i-th round of the game. t,i ∈g i g i It is expressed as follows:

[0090] g i =[g 1,i ,g 2,i ,g 3,i ,…g m-1,i ,g m,i (7)

[0091] II. Step 2) Establishing a grid-side benefit model and formulating a time-of-use pricing strategy includes the following:

[0092] The electricity price control strategy is set as follows:

[0093]

[0094] Among them, g i g i-1 F, Q i-1 All are m-dimensional vectors (i = 1, 2, ..., κ), g1, g2, ..., g κ This represents the electricity price in each round of the game, from round 1 to round κ. F represents the electricity generation in each time period, and Q represents the electricity price in each time period. i-1 F and Q represent the electricity consumption for each time period in the previous cycle. i-1 The representation method is as follows:

[0095] F = [F1, F2, F3, ..., F m (9)

[0096] Q i-1 =Q iυ-1 +Q ib-1 (10)

[0097] In the formula, F1, F2, F3, ..., F m This refers to the amount of electricity generated from time period 1 to time period m. Q iυ-1 Q ib-1 These represent the total load of the controllable and uncontrollable loads in the previous cycle, respectively.

[0098] Therefore, the cost per load-side operation is:

[0099] min C i =min(C iυ +C ib (11)

[0100] Among them, C i Let C represent the expenditure in round i. iυ and C ib Let $i$ represent the controllable load expenditure and the uncontrollable load expenditure in the $i$ round, respectively.

[0101] In reality, loads will only actively adjust their load if they increase their revenue under the new electricity price control policy. Therefore, this invention also sets the following constraints regarding the electricity price change strategy:

[0102]

[0103] In the formula, θ represents the peak-to-valley difference, which is determined by the maximum electricity consumption Q in the i-th round. imax The minimum power consumption Q in the i-th round imin Subtracting them gives us g. i,μ Let g represent the average electricity price in the i-th round. i,α g i,γ Let w represent the peak-hour electricity price and the off-hour electricity price in the i-th round, and w represent the peak-to-off-hour price ratio. When setting the peak-to-off-hour price ratio, a large ratio will disrupt the electricity consumption order on the load side and harm the interests of the power grid; a small ratio will not achieve the effect of peak-to-off-hour pricing. Therefore, the value of the peak-to-off-hour price ratio is limited to around 4.

[0104] Due to the complexity and variability of actual economic indicators for network losses, generation costs, and storage costs, the evaluation formulas for load curves and generation curves in each round are used as conditions for grid-side revenue to approximate the effect of peak shaving and valley filling. The following formula replaces (20) in evaluating grid-side revenue:

[0105]

[0106] ψ i An assessment formula representing the load and power generation for each cycle.

[0107] III. Step 3) Optimizing the user-side objective function using the Cplex solver specifically includes the following:

[0108] After determining the objective function and optimization variables, the user-side load allocation model was modeled and optimized using the Cplex solver and yalmip modeling tool in Matlab. The specific steps are as follows.

[0109] 1. Using the yalmip modeling toolkit, define the controllable load change in each time period as variables, and define the controllable load change threshold in each time period as constraints.

[0110] 2. Based on maximizing the objective function profit, write a program considering the time-of-use electricity price adjustment plan given by the grid side in the current round;

[0111] 3. Use the Cplex solver to optimize the objective function and obtain the controllable load allocation results for the user side in each time period;

[0112] 4) Determine the game convergence conditions to obtain the optimal time-of-use electricity price and load allocation;

[0113] According to the definition of Nash equilibrium, each player in a game achieves optimal performance, i.e., Nash equilibrium, given the strategies of the other players. After each round of the game and obtaining the load curve after electricity price regulation, the grid-side benefit ψ is calculated. i and load-side benefits C i If the benefits of this round on the grid side and the user side are the same as the benefits of the previous round, ψ i-1 , C i-1 If the absolute value of the difference is less than the set precision range ε, that is, if the optimized decision satisfies the formula written below, then the game reaches equilibrium; if it does not meet the precision range, then the next round of adjustment continues until the equilibrium point is reached.

[0114]

[0115] Considering that electricity prices are affected by factors such as load fluctuations and power imbalances, predicting electricity prices is very difficult. Therefore, a reasonable electricity price regulation strategy is first formulated to overcome the power imbalance between the grid and the load side. After dynamic adjustment, the predicted electricity price is obtained. Then, the electricity price regulated in each round is used for load dispatching of the grid, and the revenue of the load side and the grid side in each round is calculated. Since factors such as grid losses, peak shaving, and load regulation costs continuously change the revenue of the grid side and the user side through each round of regulation, in order to optimize the user side's benefits, after each round of electricity price regulation and load dispatching, it is determined whether the revenue of the grid side and the load side has reached the optimal user benefit, i.e., dynamic equilibrium. Otherwise, the electricity price will continue to be regulated according to the strategy, and the optimal result will be obtained when dynamic equilibrium is met.

[0116] This invention uses a combination of game theory and Cplex solver to predict electricity prices and apply them to load regulation. First, a load model is established based on the load response, and then a load benefit model is established based on the load model. At the same time, a method for evaluating the benefits on the grid side is determined. The game reaches an equilibrium point based on the convergence condition, and the benefit value is obtained by comparing the electricity price result obtained in the last round with the optimized load response curve. This achieves the goal of regulating grid load and optimizing user-side benefits.

[0117] The daily load is divided into 1-hour time periods, and the daily load is set to 24 time periods, i.e., m = 24. Therefore, the electricity usage time can be expressed as K = [1, 2, 3, ..., 23, 24]. The maximum and minimum values ​​of the load transfer in and out at time t during the controllable load regulation process are set to q. υt,σmax =150 and q υt,σmin =-100, uncontrollable load is set to a fixed value. Initial electricity price g0 is set to 1. Peak-valley price ratio w = 4, accuracy range ε ​​= 50. Initial power generation F and initial load Q are set as shown in the attached figure. Figure 2 As shown.

[0118] Appendix Figure 3 As can be seen, there is a certain power imbalance between the initial power generation and consumption at different times. Based on the actual situation, peak and valley periods are set on the load side. (Appendix) Figure 3 3(a) represents the initial electricity price, set to 1. From 3(b) to... Figure 3 (f) shows the electricity price generated after each round of regulation in the five-round game. As can be seen from 3(a), after the first round of the game, the electricity price has changed from the initial price to the real-time price. During off-peak hours, the electricity price is lower than the initial price, with the lowest price being 0.57. Similarly, during peak hours, the electricity price is higher than the initial price, with the highest price being 1.04. It can be seen that the effect of the price change after the first round of the game is not significant during peak hours. The electricity price results obtained after each round of regulation are shown in Table 1:

[0119] Table 1: Results of Electricity Price Rounds

[0120]

[0121] As shown in Figure 3(f), the lowest electricity price in the final round of the game was 0.49, and the highest was 1.54, demonstrating a significant effect of price fluctuations at the peak. Compared to the lowest price in the initial round, the lowest price in the final round decreased by 50.172%. Compared to the highest price in the initial round, the highest price in the final round increased by 55.36%. To better illustrate the comparison between each round of the game, see Appendix... Figure 4 The graph shows the electricity price changes after each round of the game.

[0122] The electricity price change curves after each round of the game clearly show the changes in electricity prices. The grid side guides the load side to adjust its load through changes in electricity prices. Specifically, some loads respond to the grid's pricing strategy, reducing their electricity expenditure. A comparison between the original load curve and the fifth round load response curve is shown in Table 2.

[0123] Table 2: Comparison of Electricity Consumption

[0124]

[0125] Based on the resulting electricity prices, the results of each round of load dispatch are attached. Figure 5 View in the middle.

[0126] During the regulation process, the load is further regulated in accordance with each round of electricity price changes. Figure 5 (a) It is evident that the initial load curve exhibits distinct peak and trough electricity consumption, and the curve is not smooth. After incorporating the predicted electricity prices for each round into load regulation, the load is incentivized by the price changes to alter its electricity consumption behavior. With each round of load regulation, the load-side electricity consumption gradually flattens out; the electricity consumption that was initially in trough gradually increases after regulation, while the load during peak hours decreases after regulation. The final curve is then compared with the initial generation and consumption data. Figure 6 As can be seen, the optimized load is closer to the power generation than the original load, thus achieving the goal of peak shaving and valley filling on the grid side.

[0127] In each round of the game, the revenue generated by the grid side and the load side is calculated based on the regulated electricity price and the transferred load as follows:

[0128] Table 3: Comparison of Payoffs on Both Sides in the Game Theory

[0129]

[0130] As shown in Table 3, according to formula (13), the grid-side benefits are reflected in the closer approximation of power generation and consumption, decreasing from the initial 164.21 to 64.31. Load-side expenditure decreased by 3.46%, from the initial 2253.50 to the final 2175.44. Although load expenditure was higher in the fourth round of regulation than in the fifth round, it could be mitigated through supplementary measures. Figure 5 As shown in the diagram, the power imbalance in this round of regulation has increased the imbalance in the power grid, and the benefits have not met the convergence condition. Therefore, the optimal benefits are achieved after the fifth round of the game.

[0131] To better verify the effectiveness of the proposed method in load regulation, this paper compares it with an improved particle swarm optimization algorithm with linearly decreasing weights. In the improved PSO algorithm, the inertia weight is linearly reduced from 1.4 to 0.4, the learning factor c1 = c2 = 2, the population size is set to 40, and the maximum number of iterations is set to 100. Under the same data conditions, load regulation was performed using particle swarm optimization, and the results are shown in the appendix. Figure 7 As shown.

[0132] The improved particle swarm optimization algorithm exhibits greater fluctuations in load regulation compared to the method proposed in this paper. Specific comparative data are shown in the table below:

[0133] Table 4: Comparison of Case Study Data

[0134]

[0135] Meanwhile, the response curve remains relatively stable during the game adjustment process. Compared with the particle swarm optimization algorithm, the load-side expenditure of the response curve is reduced by 0.95%, and the network-side expenditure is reduced by 6.14%, which verifies the effectiveness of the proposed method.

[0136] The above embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the above embodiments. Unless otherwise specified, the methods used in the above embodiments are conventional methods.

Claims

1. A load control method based on game theory and optimal user-side benefits, characterized by: Includes the following steps: 1) Establish a load model and a load benefit model; 2) Establish a grid-side benefit model and formulate time-of-use pricing control strategies; 3) Use the Cplex solver to optimize the user-side objective function; 4) Determine the game convergence conditions to obtain the optimal time-of-use electricity price and load allocation; Step 1) involves establishing a load model and a load benefit model, which includes the following: I. Establishing a load model Assuming all game participants are rational, from the perspective of load-side benefits, the ultimate goal of all load users is to minimize their electricity costs. Therefore, the interests of the load side are aligned. Let's take one day as the electricity consumption cycle and divide the cycle into m time periods. Then, the electricity consumption time can be represented as: K=[k1,k2,k3,…k m-1 ,k m ] (1) Where K is the set of electricity usage times, k1 to k m This represents the m time periods that have been divided into; the power grid side changes the original electricity consumption habits of electricity users by implementing electricity price control strategies. When electricity prices change, different types of loads respond differently. To differentiate the response effects of various load types and to reasonably calculate the revenue of each load during the regulation process, the load model is divided into two categories: controllable load model and uncontrollable load model. The controllable load is set as users sensitive to electricity prices, but in reality, it depends on the user's choice, and not all controllable loads will change due to changes in electricity prices. To simplify the model, the controllable load is set as the part that can be regulated. During the process of regulating electricity prices, these users will change their electricity consumption strategies according to changes in electricity prices, thereby reducing the total electricity expenditure of these users. Therefore, according to formula (1), the electricity load of each time period is expressed as: q υ =[q υ1 ,q υ2 ,q υ3 ,…q υm-1 ,q υm ] (2) In the formula, q υ q represents the set of controllable load electricity consumption. υ,1 to q υ,m This represents the electricity load at different time periods; therefore, the total electricity consumption of the controllable load and the constraints on the change in controllable load during the adjustment process are expressed as: Among them, Q υ The total load of the controllable load, q υt , σ This represents the controllable load at time t (t∈m). When the controllable load spans multiple time periods, it satisfies the condition from the start time period K. start Time period K until load ends end q υt,σmax With q υt,σmin These represent the maximum and minimum values ​​of the load transfer-in and transfer-out amounts at time t during the controllable load regulation process; Uncontrollable loads are classified as public utility loads, and their usage time remains unchanged regardless of electricity price fluctuations. Similarly, the electricity consumption of uncontrollable loads in each time period is expressed as follows: q b =[q b1 ,q b2 ,q b3 ,…q bm-1 ,q bm ] (4) Where, q b q represents the set of uncontrollable load electricity consumption. b1 to q bm Represents uncontrollable load at different times; Q b The total load of uncontrollable loads; q bt,σ This represents the uncontrollable load at time t. When the uncontrollable load spans multiple time periods, it satisfies the condition from the start time period K. start Time period K until load ends end ;q bt,σmax With q bt,σmin These represent the maximum and minimum values ​​of the uncontrollable load at time t during the controllable load regulation process, respectively. II. Establishing a load benefit model The objective function for total load expenditure and the electricity expenditure of each component are expressed as follows: In the formula, C represents the total electricity expenditure on the load side. υ C b Let g represent the electricity expenditure for controllable and uncontrollable loads, respectively; κ represent the total number of games; i represent the number of game rounds (i∈κ); and g t,i Let g represent the electricity price at time t in the i-th round of the game. t,i ∈g i g i It is expressed as follows: g i =[g 1,i ,g 2,i ,g 3,i ,…g m-1,i ,g m,i ] (7)。 2. The load regulation method based on game theory and optimal user-side benefits according to claim 1, characterized in that: Step 2) involves establishing a grid-side benefit model and formulating a time-of-use pricing strategy, which includes the following: The electricity price control strategy is set as follows: Among them, g i g i-1 F, Q i-1 All are m-dimensional vectors (i = 1, 2, ..., κ), g1, g2, ..., g κ This represents the electricity price in each round of the game from round 1 to round κ, where F represents the electricity generation in each time period, and Q represents the electricity price in each time period. i-1 F and Q represent the electricity consumption for each time period in the previous cycle. i-1 The representation method is as follows: F=[F1,F2,F3…,F m (9) Q i-1 =Q iυ-1 +Q ib-1 (10) In the formula, F1, F2, F3, ..., F m This refers to the amount of electricity generated from time period 1 to time period m, Q iυ-1 Q ib-1 These represent the total load of the controllable and uncontrollable loads in the previous cycle, respectively. Therefore, the cost per load-side operation is: my C i =min(C iυ +C ib ) (11) Among them, C i C represents the expenditure in round i; iυ and C ib Let $i$ represent the controllable load expenditure and the uncontrollable load expenditure in the i-th round, respectively. In reality, loads will only actively adjust their load if they increase their revenue under the new electricity price control policy. Therefore, this invention also sets the following constraints regarding the electricity price change strategy: In the formula, θ represents the peak-to-valley difference, which is determined by the maximum electricity consumption Q in the i-th round. imax The minimum power consumption Q in the i-th round imin Subtracting them gives g i,μ Let g represent the average electricity price in the i-th round. i,α g i,γ Let w represent the peak-hour electricity price and the off-hour electricity price in the i-th round, and w represent the peak-to-off-hour electricity price ratio.

3. The load regulation method based on game theory and optimal user-side benefits according to claim 1, characterized in that: Due to the complexity and differences in the actual economic indicators of network losses, power generation costs and storage costs, the evaluation formulas of load curves and power generation curves in each round are used as conditions for grid-side revenue to approximate the effect of peak shaving and valley filling, and the following formula replaces (20) to evaluate grid-side revenue. Its expression is as follows: ψ i An assessment formula representing the load and power generation for each cycle.

4. The load control method based on game theory and optimal user-side benefits according to claim 1, characterized in that: Step 3) involves calling the Cplex solver to optimize the user-side objective function, specifically including the following: After determining the objective function and optimization variables, the user-side load allocation model was modeled and optimized using the Cplex solver and yalmip modeling tool in Matlab. The specific steps are as follows. 1) Using the yalmip modeling toolkit, define the controllable load change in each time period as variables, and define the controllable load change threshold in each time period as constraints. 2) Based on maximizing the objective function profit, write a program considering the time-of-use electricity price adjustment plan given by the grid side in the current round; 3) Call the Cplex solver to optimize the objective function and obtain the controllable load allocation results for the user side in each time period.

5. The load control method based on game theory and optimal user-side benefits according to claim 1, characterized in that: Step 4) involves determining the game convergence condition to obtain the optimal time-of-use electricity price and load allocation, specifically including the following: According to the definition of Nash equilibrium, each player in a game achieves optimal performance, i.e., Nash equilibrium, given the strategies of the other players. After each round of the game and obtaining the load curve regulated by electricity prices, the grid-side benefits ψ are calculated. i and load-side benefits C i If the benefits of this round on the grid side and the user side are the same as the benefits of the previous round, ψ i-1 C i-1 If the absolute value of the difference is less than the set precision range ε, that is, if the optimization decision satisfies the formula written below, then the game reaches equilibrium; if it does not meet the precision range, then continue to make the next round of adjustments until the equilibrium point is reached. Considering that electricity prices are affected by factors such as load fluctuations and power imbalances, predicting electricity prices is very difficult. Therefore, a reasonable electricity price regulation strategy is first formulated to overcome the power imbalance between the grid and the load side. After dynamic adjustment, the predicted electricity price is obtained. Then, the electricity price regulated in each round is used for load dispatching of the grid, and the revenue of the load side and the grid side in each round is calculated. Since factors such as grid losses, peak shaving, and load regulation costs continuously change the revenue of the grid side and the user side through each round of regulation, in order to optimize the user side's benefits, after each round of electricity price regulation and load dispatching, it is determined whether the revenue of the grid side and the load side has reached the optimal user benefit, i.e., dynamic equilibrium. Otherwise, the electricity price will continue to be regulated according to the strategy, and the optimal result will be obtained when dynamic equilibrium is met.

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