Improved ying optimization algorithm is used to optimize load peak valley period division and peak valley electricity price method

Abstract

The application discloses a method for improving the optimization of load peak-valley period division and peak-valley electricity price by using the improved hawk optimization algorithm, and the method comprises the following steps: 1) a fuzzy half trapezoidal membership function is used to calculate the large-biased and small-biased half gradient membership of each time point; 2) the large-biased and small-biased half gradient membership of each time point is taken as a statistical index, and a basic period division scheme is obtained based on a fuzzy clustering analysis method; 3) a threshold index is calculated according to the basic period division scheme, the optimal threshold of the large-biased and small-biased half trapezoidal membership function is further determined, and a final peak-valley period division scheme is obtained through a correction strategy; 4) a demand response model of user load is established, and a combined model considering the peak load cutting and valley load filling effect and user satisfaction is established; and 5) the improved hawk optimization algorithm is used to find the optimal peak-valley electricity price under the combined model. The method can make the user's comprehensive satisfaction higher, better achieve the purpose of peak load cutting and valley load filling, and realize the win-win of the power supply company and the user.

Description

Technical Field

[0001] This invention belongs to the field of electricity market, specifically relating to a method for optimizing peak-valley time period division and peak-valley electricity price. Background Technology

[0002] Demand-side management (DSM) is a means of guiding electricity consumers to adopt reasonable electricity consumption structures and methods through price signals, and it has achieved certain results in some countries. Time-of-use pricing is one of the important approaches to DSM, with peak-valley time-of-use pricing being its most important component. Its basic idea is to reflect the value of electricity as a scarce commodity during peak load periods, using price levers to guide end-user electricity consumption behavior, improve grid security and load factor levels, and encourage users to change their electricity consumption patterns based on the adjustability and interests of their own production methods, thereby affecting system load. The division of peak and valley periods and the determination of the peak-valley price ratio are the foundation for formulating peak-valley time-of-use pricing.

[0003] Based on the theory of peak-valley time period division, the currently implemented methods mainly include the following two: ① Analysis based on power supply cost changes. This method combines the unit operating conditions to establish a power generation cost-load function, and uses the abrupt change characteristics of this function at the load point to divide the peak-valley time period intervals. This method is relatively complex and difficult to implement in practice. ② Analysis based on load curve distribution. This method generally uses the fuzzy semi-trapezoidal membership function method, dividing the peak-valley time period intervals according to the probability that each point on the load curve is in a peak or valley period. This method is highly operable, but it is difficult to reasonably define the boundary time points of each time period interval based on the membership function threshold.

[0004] Peak-valley pricing (TOU pricing) is a price-based demand-side management measure. A reasonable peak-valley pricing level can achieve peak shaving and valley filling, resulting in a win-win situation for both power companies and users. However, if the peak-valley price ratio is too high, users will over-respond to the price, leading to significant peak-valley time-of-use shifts and even peak-valley inversion, resulting in peak shaving failure and economic losses for the power grid. Conversely, if the peak-valley price ratio is too low, users will under-respond, failing to achieve the intended effect of peak-valley pricing. Therefore, effectively measuring and quantifying user response to peak-valley time-of-use pricing is essential. Existing peak-valley pricing fails to fully tap the benefits of demand response, and the division of peak-valley time periods is not entirely reasonable. Furthermore, the formulation of peak-valley time-of-use pricing has not adequately considered user satisfaction with the policy, nor has it sought a balance between economic benefits, user satisfaction, and other system objectives. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes an improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing. It utilizes the fuzzy membership function method and fuzzy clustering combination method, based on a constructed threshold index function λ. tif This invention proposes a modified scheme to address the difficulty of defining the decomposition points between peak and valley intervals using the fuzzy membership function method. Simultaneously, an improved Tianying optimization algorithm is employed to optimize peak-valley electricity pricing. The established objective function comprehensively considers the effects of peak shaving and valley filling, as well as overall user satisfaction. Compared with the original peak-valley electricity pricing scheme in a certain region, the proposed method's peak-valley time period division better conforms to the load curve characteristics. The optimized peak-valley pricing effectively reduces the maximum load and the load peak-valley difference. A comparison of the improved Tianying optimization algorithm with the optimization results of the traditional particle swarm optimization algorithm reveals that the latter is prone to getting trapped in local optima and has a slow convergence speed.

[0006] The present invention adopts the following technical solution:

[0007] An improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing includes the following steps:

[0008] Step 1: Based on the power system load data, divide the day into 24 time points, with 1 hour as the unit, forming a time point set T = {t1, t2, ..., t...} 24 The set of load values ​​corresponding to each time point is Q = {q1, q2, ..., q}. 24 Using the fuzzy semi-trapezoidal membership function method, and employing both skewed large and skewed small semi-gradient membership functions, t is initially determined. i Peak and trough membership degree x at any given time i1 and x i2 ;

[0009] Step two: Use fuzzy clustering analysis to determine the peak and valley membership degrees x at each time point. i1 and x i2 As a statistical indicator, after calibration and clustering, the cluster set T for peak, flat, and trough periods is obtained. f T p and T g ;

[0010] Step 3: Using the concept of set classification, and based on the basic time period segmentation results obtained from fuzzy clustering analysis, calculate the constructed threshold index function λ. tif Further determine the optimal thresholds λ1 and λ2 for the semi-trapezoidal membership functions of the larger and smaller sizes;

[0011] Step four: Based on the optimal thresholds λ1 and λ2 of the semi-trapezoidal membership functions for the larger and smaller sizes, compare them with t. i Peak and trough membership degree x at any given time i1 and x i2The peak and valley time period division results were compared. In view of the problem that the membership function threshold is difficult to reasonably define the boundary time point of each time period interval, the final peak and valley time period division scheme was obtained by referring to the characteristics of the basic scheme and the implemented time period division scheme after modification strategy.

[0012] Step 5: Based on the final peak-valley time period division scheme, establish a user elastic response matrix and a user load demand response model;

[0013] Step 6: Construct user satisfaction models for electricity usage patterns and electricity cost expenditures. A comprehensive user satisfaction model is derived through linear weighting. A peak-valley time-of-use pricing and load optimization model is then constructed with the objective functions of maximizing system valley load, minimizing the peak-valley load difference, and achieving the highest comprehensive user satisfaction. The constraints are: unchanged total electricity load demand before and after price adjustments, peak and valley price boundary constraints, and revenue constraints for users and the power supply company. The improved Tianying optimization algorithm is used to obtain the optimized time-of-use pricing and the demand response load curve under this pricing.

[0014] Furthermore, in step one, t i Peak and trough membership degree x at any given time i1 and x i2 It is calculated using the following method:

[0015]

[0016] For t i The load values ​​at each time point are a and b, which are the minimum and maximum load values ​​at each time point, respectively.

[0017] Furthermore, in step two, the fuzzy clustering analysis method includes the following steps:

[0018] (1) Taking the load at each time point as the classification object, and using the peak and valley membership degree x at each time point as the classification object. i1 and x i2 As a statistical indicator, at this time: x i =(x i1 x i2 In the formula: i = 1, 2, ..., 24

[0019] The characteristic index matrix X is obtained as follows:

[0020]

[0021] (2) Perform a standardization transformation on the feature index matrix X, and establish the fuzzy similarity matrix R(r) based on the absolute value subtraction method. 24×24 ;where R(x) i1 x i2 ) = r ij r ijCalculated by the following formula:

[0022]

[0023] In the formula: i, j = 1, 2, ..., 24; m = 1, 2; σ is an appropriately selected parameter that makes r ij ∈[0,1],

[0024] |x im -x jm | represents x i With x j The distance between them;

[0025] (3) For similar matrices R(r) 24×24 Find the square, i.e., R→R 2 →…→R 2k Until the first appearance of R k ×R k =R k R k This is the transitive closure of the substitution, denoted as t(R) = (t ij ) 24×24 ;

[0026] (4) Find the cut matrix R of the transitive closure. δ R δ =(δγ ij ) 24×24 ,δγ ij Calculated by the following formula:

[0027]

[0028] In the formula: i, j = 1, 2, ..., 24; δ ∈ [0, 1], let δ gradually decrease from 1, according to R δ Dynamic clustering with a cluster size of 3 yields the cluster aggregation T for peak, flat, and valley periods. f T p and T g .

[0029] Furthermore, in step three, the concept of set classification is applied, based on the cluster sets T of peak, flat, and valley periods obtained by fuzzy cluster analysis. f T p and T g Threshold index function λ tif It is calculated using the following method:

[0030]

[0031] P fl P pu P pl and P gu T respectivelyf The minimum load value in the load corresponding to the collection time point, T p The maximum load value in the load corresponding to the collection time point, T p The minimum load value and T at the time of collection correspond to the load. g The maximum load value P corresponds to the point in time of collection. i P j For T f The set point corresponds to any two different load values ​​in the load, β i β j For T p The set point corresponds to any two distinct load values ​​in the load, α i α j For T g The set time point corresponds to any two different load values ​​in the load; the threshold index function λ tif The numerator represents the minimum distance between samples in adjacent sets, and the denominator represents the maximum difference between samples within a set. Based on the concept of set classification, this makes the differences between samples in different sets explicit, while blurring the differences between samples within the same set. Therefore, λ tif The larger the value, the better the division of peak, flat, and valley periods.

[0032] Furthermore, in step four, to address the issue that the membership function threshold is difficult to define the boundary time points of each time interval, the following correction scheme is proposed:

[0033] ① The number of time points within the three time periods (peak, normal, and off-peak) should be controlled between 6 and 10; the division scheme should conform to the characteristics of a typical daily load curve, such as a typical bimodal distribution, with peak electricity consumption typically occurring once in the morning and once in the afternoon, and off-peak periods usually occurring at night. Specifically, this can be achieved by adjusting the membership function threshold and then comparing the threshold index function λ. tif To reasonably regulate the size of the peak, flat, and valley time periods;

[0034] ② The time periods should be feasible and easy to implement. Therefore, each time period in the peak, normal, and low-peak set should not be less than 2 hours. If a certain time point is isolated, it should be adjusted according to the basic scheme obtained by the fuzzy clustering analysis method and the relative magnitude of the load values ​​corresponding to the isolated point and its neighboring points.

[0035] Furthermore, in step five, based on the final peak-valley time period division scheme, the user elastic response matrix is ​​determined, and the user load demand response model is established as follows:

[0036] The user elastic response matrix M is as follows:

[0037]

[0038] In the formula, the subscripts f, p, and g represent the three time periods of peak, flat, and trough, respectively. The elements on the diagonal represent the self-elasticity coefficient, and the elements off the diagonal represent the cross-elasticity coefficient.

[0039] The electricity consumption after the user load demand response is the sum of the original electricity consumption and the change in electricity consumption in each time period, as shown in the following model:

[0040]

[0041] In the formula, E TOU =[e f e p e g ] T This represents the electricity consumption during each time period after the implementation of peak-valley time-of-use pricing; E0 = [e 0f e 0p e 0g ] T This represents the original electricity consumption for each time period; p 0f p 0p p 0g These represent the electricity prices for each time period before the implementation of time-of-use pricing; Δp f Δp p Δp g These are the changes in electricity prices for each time period before and after the implementation of time-of-use pricing. Based on this, the total change in electricity consumption for each peak, flat, and valley period is allocated to each hour using the proportional coefficient corresponding to the original hourly electricity consumption in each time period. This allows us to obtain the change in electricity consumption for each hour after the implementation of time-of-use pricing, and thus the load value at each time point after implementation.

[0042] Furthermore, in step six, the established models for user satisfaction with electricity usage patterns and user satisfaction with electricity expenditure are as follows:

[0043] Satisfaction with electricity usage methods, μ, is represented by:

[0044]

[0045] in, S represents the sum of changes in electricity consumption at various points in time after the implementation of peak-valley time-of-use pricing, where S TOU,t (P f ,P p ,P g P represents the electricity load during time period t after the implementation of time-of-use pricing. f P p P g Electricity prices for peak, off-peak, and valley periods, respectively, S t (P t This represents the electricity load during a time period when peak-valley time-of-use pricing is not implemented; it is the electricity price P during time period t. t The function.

[0046] μ reflects the user's comfort level after adjusting the electricity usage time. μ∈[0,1], that is, the user's satisfaction with the electricity usage method is the highest when the electricity consumption at each time point does not change.

[0047] Satisfaction with electricity expenditure Represented as:

[0048]

[0049] Among them, C TOU C0 represents the total electricity cost for users after the implementation of peak-valley time-of-use pricing, while C0 represents the total electricity cost for users before implementation.

[0050] Overall user satisfaction is calculated as a weighted average of satisfaction with electricity usage methods and satisfaction with electricity costs. The specific model is as follows:

[0051]

[0052] Among them, ε1+ε2=1, ε1 and ε2 are flexibly selected according to the user's emphasis on electricity consumption and electricity expenditure, and can be selected according to the assignment method of fuzzy description based on user type;

[0053] Based on the objective function of maximizing system valley load, minimizing peak-valley load difference, and maximizing overall user satisfaction in step six, the peak-valley time-of-use pricing and load optimization model is constructed as follows:

[0054]

[0055] Where ω1+ω2=1; ω1 and ω2 represent the user's weights on peak shaving and valley filling and overall satisfaction, minQ and maxQ-minQ represent the minimum load and peak-valley difference before the implementation of time-of-use pricing, respectively, minQ TOU and maxQ TOU -minQ TOU These represent the minimum load and the peak-valley difference after the implementation of peak-valley time-of-use pricing, respectively. The ratio between the two is calculated to set its value range to around 1, so that it can be compared with the overall user satisfaction Ψ at the same level.

[0056] The improved Skyhawk Optimization Algorithm (IAO) includes the following steps:

[0057] Step 1, Algorithm Initialization:

[0058] Step 1.1: During population initialization, a chaotic mapping is introduced to embed positional information between particles, thus broadening the search range. The population size is set to N, the solution space dimension to Dim, and the maximum number of iterations to Miter. Two counters are set: C1 = 0 and C2 = 0. N sets of position vectors are initialized, the first set being X1 = [x...]. 11 ,x12 ,…,x 1Dim Randomly generated, the remaining N-1 groups are derived from the formula: X n+1 =θX n (1-X n Calculations show that θ is a variation factor, and different chaotic states can be generated according to the change of θ; initialize t = 0;

[0059] Step 1.2, during the initialization process using chaotic mapping, the condition cos(X) needs to be satisfied. i ,X j )≤ε, i, j=1,2,…,N, i≠j; where cos(X) i ,X j This represents the distance between position vectors. The smaller the value, the farther apart the two particles are. The calculation method is as follows:

[0060]

[0061] ε∈[0,1] is the threshold, which can be given based on experience and statistical experiments.

[0062] Step 1.3, initialize the N sets of position vectors in the solution space [X min ,X max Mapping is performed in ];

[0063] Step 2: Calculate the fitness value of the population and sort these position vectors to preliminarily determine the global optimal solution;

[0064] Step 3, during each iteration, the position update of the Skyhawk is described as follows:

[0065] Step 3.1, Expand the search At this point, the eagle identifies the prey area and selects the best hunting ground by flying vertically with its back bent. To increase population diversity and address the "precocious" problem, a cosine variation factor can be added to the position update process. The mathematical model is as follows:

[0066]

[0067] Where X1(t+1) is the solution generated by the first search method in the (t+1)th iteration; X best (t) represents the best solution obtained before the t-th iteration, which reflects the approximate position of the prey; rand is a random value between 0 and 1; X M (t) represents the average value of the current solution at the t-th iteration, calculated as follows:

[0068]

[0069] Step 3.2, narrow down the search In the second method, when the eagle spots the prey area from high altitude, it hovers above the target prey, preparing to land and then attack. This method is called short-gliding attack contour flight. Here, the AO narrowly explores a selected area of ​​the target prey in preparation for the attack; the mathematical model of this behavior is shown in the following formula:

[0070] X2(t+1)=X best (t)×Levy(Dim)+X R (t)+(yx)×rand

[0071] In the formula, X2(t+1) is the solution of the (t+1)th iteration generated by the second search method; Levy(Dim) is the Levy flight distribution function, X R (t) is a random solution obtained in the range [1,N] during the t-th iteration;

[0072]

[0073] In the formula, s = 0.01, u and v are random numbers between 0 and 1, β = 1.5, and σ is calculated as follows:

[0074]

[0075] x and y represent the spiral shape in the search, where x = r × cos(θ); y = r × sin(θ); r = r1 + U × D1; r1 takes a value between 1 and 20 to fix the number of search cycles, U = 0.00565, D1 is an integer from 1 to the dimension Dim of the search space, ω = 0.005;

[0076] Step 3.3, Extended Development In the third method, when the eagle has accurately identified the prey area and is ready to land and attack, it descends vertically and launches an initial attack to probe the prey's reaction; this method is called a low-altitude descent attack. Here, the AO uses the selected area of ​​the target to approach the prey and launch an attack, and the mathematical model of this behavior is shown in the following formula:

[0077] X3(t+1)=(X best (t)-X M (t))×α-rand+((UB-LB)×rand+LB)×δ

[0078] In the formula, X3(t+1) is the solution of the (t+1)th iteration generated by the third search method; α and δ are development adjustment parameters fixed at a small value (0.1); UB and LB are the upper and lower bounds of the position vector.

[0079] Step 3.4, narrow down the development In the fourth method, as the eagle approaches its prey, it attacks the prey on land based on its random movement; this method is called "walking and seizing the prey." Finally, the AO attacks the prey from the last position. The mathematical model of this behavior is shown in the following formula:

[0080] X4(t+1)=QF(t)×X best (t)-(G1×X(t)×rand)-G2×Levy(D)+Rand×G1

[0081] In the formula, X4(t+1) is the solution of the (t+1)th iteration generated by the fourth search method; QF(t) represents the quality function used to balance the search strategy at the tth iteration; G1 represents the various movements used to track the prey during the search; G2 represents the flight speed of the eagle tracking the prey; Levy(D) is the Levy flight function; and X(t) is the position at the tth iteration.

[0082] The formula for calculating the mass function is: G1 = 2 × rand - 1; the flight speed was changed from linearly decreasing to:

[0083] Step 4: Calculate the updated fitness value and update the population extreme value X. best If X in this iteration best If no update is performed, then let C1 = C1 + 1;

[0084] Step 5: Evaluate whether the algorithm exhibits premature convergence and make corrections accordingly;

[0085] Step 5.1: If C1≥2, then C2=C2+1, and at the same time let C1=0;

[0086] Step 5.2, if C2≥γ, γ∈[5,10], then let the population extremum X best The update is performed along its negative gradient direction, calculated as follows:

[0087]

[0088] In the formula, For X best The value before the most recent update;

[0089] Step 6: Determine if the termination condition is met. If it is, output the optimal solution and end the program; otherwise, repeat the above Tianying optimization algorithm process to continue the optimization iteration.

[0090] The beneficial effects of this invention are:

[0091] Compared with the original peak-valley electricity pricing scheme in a certain region, the peak-valley time period division proposed in this invention is more in line with the characteristics of the load curve. The peak-valley pricing optimized by the improved Tianying algorithm effectively reduces the maximum load and the load peak-valley difference, while the overall user satisfaction is high. Attached Figure Description

[0092] Figure 1 This is a flowchart of the IAO algorithm optimization method for load peak-valley time period division and peak-valley electricity pricing in this invention;

[0093] Figure 2 Load data and optimized tiered electricity pricing chart;

[0094] Figure 3 Optimize the iteration curve of the PSO algorithm;

[0095] Figure 4 Optimize the iteration curve of the IAO algorithm;

[0096] Figure 5 Comparison of the original load curve and the load curve after user response under the original peak-valley electricity price;

[0097] Figure 6 A comparison chart of the original load curve and the load curve after user response under the optimized peak-valley electricity price. Detailed Implementation

[0098] Figure 1 This document presents a flowchart of the IAO algorithm for optimizing load peak-valley time periods and peak-valley pricing in this invention. A specific example illustrates the implementation process, validating the method's effectiveness using actual load data from a user. Before implementing peak-valley pricing, the system electricity price was 0.49 yuan / (kW·h). After implementing peak-valley pricing, the peak, flat, and valley prices are 0.658 yuan / (kW·h), 0.49 yuan / (kW·h), and 0.358 yuan / (kW·h), respectively. The original peak-valley time period division was as follows: 24:00–7:00 was the valley period; 8:00–11:00 and 18:00–24:00 were the peak periods; and 7:00–8:00 and 11:00–18:00 were the flat periods.

[0099] First, fuzzy clustering analysis is used, with the peak and valley membership degrees x at each time point as the basis. i1 and x i2 As a statistical indicator, after calibration and clustering, the cluster set T for peak, flat, and trough periods is obtained. f T p and T g Then, using the concept of set classification and based on the basic time period segmentation results obtained from fuzzy clustering analysis, the constructed threshold index function λ is calculated. tifThe optimal thresholds λ1 and λ2 for the semi-trapezoidal membership functions of the larger and smaller segments were further determined. Finally, the final peak-valley time period division scheme was obtained after adjusting the strategy, as shown in Table 1.

[0100] Table 1 Time Period Division Scheme

[0101]

[0102] After obtaining the final peak-valley time period division results, using the electricity price elasticity matrix and the established user demand response model, with the objective function of maximizing system valley load, minimizing the peak-valley load difference, and maximizing overall user satisfaction, the improved Tianying optimization algorithm was used to obtain the optimized peak-valley electricity price results, as shown in Table 2:

[0103] Table 2 Results of Peak-Valley Electricity Pricing

[0104]

[0105] Figure 2 This is a diagram showing load data and optimized tiered electricity pricing.

[0106] Based on the optimization results of peak-valley electricity pricing, the rationality and advantages of the model are further analyzed. Tables 3 and 4 below show the comparison data of the optimized peak-valley electricity pricing and the original peak-valley electricity pricing.

[0107] Table 3 Comparison of satisfaction results before and after peak-valley electricity pricing optimization

[0108]

[0109] Table 4 Comparison of Peak Shaving and Valley Filling Effects Before and After Peak-Valley Electricity Pricing Optimization

[0110]

[0111] The algorithm parameters in this implementation example are taken as follows:

[0112] PSO algorithm: Particle swarm size N = 100; dimension Dim = 2; maximum number of iterations Miter = 200.

[0113] IAO Algorithm: Eagle population size N = 100, dimension Dim = 2, maximum number of iterations Miter = 200

[0114] This example user is an industrial user. Because they operate on a three-shift production system, process adjustments are relatively easy, and the product output has high power consumption. Therefore, the overall user satisfaction level is taken as: Meanwhile, since this user is located relatively early in the power rationing meter, we take ω1 = 0.7 and ω2 = 0.3.

[0115] This invention employs the improved Skyhawk Optimization Algorithm (IAO) proposed in this paper to optimize the load peak-valley time period division and peak-valley electricity pricing method, and compares the optimization results with those of the Particle Swarm Optimization Algorithm (PSO). Figures 3-6 The results show that, compared with the traditional PSO algorithm optimization, the present invention has a faster convergence speed and higher optimization accuracy. As shown in Tables 3 and 4, the optimized time-of-use electricity price has a better peak shaving and valley filling effect than the original peak-hour electricity price, and the user satisfaction is higher.

[0116] Finally, it should be noted that the above description is only for specific embodiments of the present invention. However, the present invention is not limited to the specific embodiments described above. Equivalent modifications and substitutions made to the present invention by those skilled in the art are also within the scope of the present invention. Therefore, all equivalent changes and modifications made without departing from the spirit and scope of the present invention are covered within the scope of the present invention.

Claims

1. An improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing, characterized in that, Includes the following steps: Step 1: Based on the power system load data, divide the day into 24 time points, using 1 hour as the unit, forming a time point set T={ , , , The set of load values ​​corresponding to each time point is Q={ , , , Using the fuzzy semi-trapezoidal membership function method, and employing both skewed large and skewed small semi-gradient membership functions, the membership degree of the members was initially determined. Peak and trough membership degree at any given time and ; Step two: Use fuzzy clustering analysis to determine the membership degrees of peaks and troughs at each time point. and As a statistical indicator, after calibration and clustering steps, cluster sets of peak, flat, and trough periods are obtained. , and ; Step 3: Using the concept of set classification, and based on the basic time period segmentation results obtained from fuzzy clustering analysis, calculate the constructed threshold index function. Further determine the optimal thresholds for the semi-trapezoidal membership functions of skewed large and skewed small sizes. and ; Step 4: Based on the optimal threshold of the semi-trapezoidal membership functions for skewed large and skewed small sizes. and , and Peak and trough membership degree at any given time and The peak and valley time period division results were compared. In view of the problem that the membership function threshold is difficult to reasonably define the boundary time point of each time period interval, the final peak and valley time period division scheme was obtained by referring to the characteristics of the basic scheme and the implemented time period division scheme after modification strategy. Step 5: Based on the final peak-valley time period division scheme, establish a user elastic response matrix and a user load demand response model; Step 6: Construct user satisfaction models for electricity usage patterns and electricity cost expenditures. Through linear weighting, derive a comprehensive user satisfaction model. Construct a peak-valley time-of-use pricing and load optimization model with the objective functions of maximizing system valley load, minimizing the peak-valley load difference, and maximizing comprehensive user satisfaction. The constraints are: unchanged total electricity demand before and after price adjustments, peak and valley price boundary constraints, and revenue constraints for users and the power company. Use the improved Tianying optimization algorithm to obtain the optimized time-of-use pricing and the demand response load curve under that pricing. In step two, the fuzzy clustering analysis method includes the following steps: The classification is based on the load at each time point, and the membership degree of the peak and trough at each time point is used as the classification object. and As a statistical indicator, at this time: , In the formula: i = 1, 2, ..., 24 Obtain the feature index matrix for: ， Feature index matrix Perform a standardization transformation and establish a fuzzy similarity matrix based on the absolute value subtraction method. ;in , Calculated by the following formula: ， In the formula: i, j = 1, 2, ..., 24; m = 1, 2; For appropriately selected parameters, so that , express and The distance between them; For similar matrices To find the square, that is... Until the first appearance , This is the transitive closure of the substitution, denoted as... ; Find the cut matrix of the transitive closure. , , Calculated by the following formula: ， In the formula: i, j = 1, 2, ..., 24; ,make Gradually decrease from 1, according to Dynamic clustering with a cluster size of 3 will yield cluster aggregations for peak, flat, and valley periods. ; In step three, the concept of set classification is applied, and the cluster sets of peak, flat, and trough periods are obtained based on the fuzzy clustering analysis method. Threshold index function It is calculated using the following method: ， , , and They are respectively The minimum load value corresponding to the collection time point. The maximum load value corresponding to the collection time point. The minimum load value in the load corresponding to the collection time point and The collection point corresponds to the maximum load value in the load. , for The set point corresponds to any two distinct load values ​​in the load. , for The set point corresponds to any two distinct load values ​​in the load. , for The set of time points corresponds to any two distinct load values ​​within the load; threshold index function. The numerator represents the minimum distance between samples in adjacent sets, and the denominator represents the maximum difference between samples within a set. Based on the concept of set classification, this makes the differences between samples in different sets more explicit, while blurring the differences between samples within the same set. Therefore... The larger the value, the better the division of peak, flat, and valley periods.

2. The improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing method according to claim 1, characterized in that, In step one, Peak and trough membership degree at any given time and It is calculated using the following method: ， for The load values ​​at each time point are a and b, which are the minimum and maximum load values ​​at each time point, respectively.

3. The improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing method according to claim 1, characterized in that, In step four, to address the issue that the membership function threshold is difficult to define the boundary time points of each time interval, the following correction scheme is proposed: The number of time points within the three time periods—peak, normal, and off-peak—should be controlled between 6 and 10; the division scheme should conform to the characteristics of a typical daily load curve; specifically, this can be achieved by adjusting the membership function threshold and then comparing the threshold index function. To reasonably regulate the size of the peak, flat, and valley time periods; The time periods should be feasible and easy to implement; therefore, each time period in the combination of peak, normal, and off-peak hours should not be less than 2 hours. If a point in time is isolated, adjustments should be made based on the basic scheme derived from the fuzzy clustering analysis method and the relative magnitudes of the load values ​​corresponding to the isolated point and its neighboring points.

4. The improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing method according to claim 1, characterized in that, In step five, based on the final peak-valley time period division scheme, the user elastic response matrix is ​​determined, and the user load demand response model is established as follows: User Elastic Response Matrix as follows: ， In the formula, the subscripts f, p, and g represent the three time periods of peak, flat, and trough, respectively. The elements on the diagonal represent the self-elasticity coefficient, and the elements off the diagonal represent the cross-elasticity coefficient. The electricity consumption after the user load demand response is the sum of the original electricity consumption and the change in electricity consumption in each time period, as shown in the following model: ， In the formula, This refers to the electricity consumption during each time period after the implementation of peak-valley time-of-use pricing; This represents the original electricity consumption for each time period; , , These are the electricity prices for each time period before the implementation of time-of-use pricing; , , These are the changes in electricity prices for each time period before and after the implementation of time-of-use pricing. Based on this, the total change in electricity consumption for each peak, flat, and valley period is allocated to each hour using the proportional coefficient corresponding to the original hourly electricity consumption in each time period. This yields the change in electricity consumption for each hour after the implementation of time-of-use pricing, and thus the load value at each time point after implementation.

5. The improved Tianying optimization algorithm for optimizing load peak-valley time period division and peak-valley electricity pricing method according to claim 1, characterized in that, In step six, the established models for user satisfaction with electricity usage and user satisfaction with electricity expenditure are as follows: Satisfaction with electricity usage methods Represented as: ， in, This represents the sum of changes in electricity consumption at various points in time after the implementation of peak-valley time-of-use pricing, where... To calculate the electricity load during time period t after the implementation of time-of-use pricing, These are the electricity prices for peak, off-peak, and valley periods, respectively. This represents the electricity load during a period when peak-valley time-of-use pricing is not implemented; it is the electricity price for period t. The function; This reflects the user's comfort level after adjusting their electricity usage time. This means that the user's satisfaction with their electricity usage is highest when their electricity consumption remains unchanged at all points in time. Satisfaction with electricity expenditure Represented as: ， in, To calculate the total electricity cost for users after implementing peak-valley time-of-use pricing, The total electricity cost for users before implementation; Overall user satisfaction is calculated as a weighted average of satisfaction with electricity usage methods and satisfaction with electricity costs. The specific model is as follows: ， in, , and The selection can be flexibly made based on the user's emphasis on electricity usage and electricity costs, and the assignment method can be selected by referring to the fuzzy description based on the user type. Based on the objective function of maximizing system valley load, minimizing peak-valley load difference, and maximizing overall user satisfaction in step six, the peak-valley time-of-use pricing and load optimization model is constructed as follows: ， in, ; and The weights representing user satisfaction with peak shaving and valley filling, and overall satisfaction. and These represent the minimum load and peak-valley difference before the implementation of time-of-use pricing, respectively. and These represent the minimum load and the peak-valley difference after the implementation of time-of-use pricing, respectively. The ratio between the two is calculated to set its value range to around 1, in order to correlate with overall user satisfaction. Compare at the same level; The improved Skyhawk Optimization Algorithm (IAO) includes the following steps: Step 1, Algorithm Initialization: Step 1.1: During population initialization, a chaotic mapping is introduced to embed positional information between particles, thus broadening the search scope. The population size is set to N, the solution space dimension to Dim, the maximum number of iterations to Miter, and two counters are set. , Initialize N sets of position vectors, the first set... Randomly generated, the remaining N-1 groups are derived from the following formula: Calculations show that As a change factor, it can be determined according to Changes in these states produce different chaotic states; initialization ; Step 1.2, during the initialization process using chaotic mapping, the following conditions need to be met. i, j = 1, 2, N, ;in, This represents the distance between position vectors; a smaller value indicates a greater distance between the two particles. The calculation method is as follows: ， For threshold; Step 1.3: Resolve the initialized N sets of position vectors in the solution space. Mapping is performed in the process; Step 2: Calculate the fitness value of the population and sort these position vectors to preliminarily determine the global optimal solution; Step 3, during each iteration, the position update of the Skyhawk is described as follows: Step 3.1, Expand the search ( At this point, the eagle identifies the prey area and selects the best hunting area by flying vertically with its back bent. To increase population diversity and solve the "precocious" problem, a cosine variation factor can be added to the position update. The mathematical model is as follows: ， in, The solution generated by the first search method for iteration t+1; represents the best solution obtained before the t-th iteration, which reflects the approximate location of the prey; rand is a random value between 0 and 1; This represents the average value of the current solution at the t-th iteration, calculated as follows: ， Step 3.2, narrow down the search ( In the second method, when the eagle spots the prey area from high altitude, it hovers above the target prey, preparing to land and then attack. This method is called short-gliding attack contour flight. Here, the AO narrowly explores a selected area of ​​the target prey in preparation for the attack. The mathematical model of this behavior is shown in the following formula: ， In the formula, It is the solution for the (t+1)th iteration generated by the second search method; It is the Levy flight distribution function. It is a random solution obtained in the range [1, N] during the t-th iteration; ， In the formula, s = 0.01, A random number between 0 and 1. , The calculation formula is as follows: ， Represents the spiral shape in the search, where, ; ; ; ; A value between 1 and 20 is used to fix the number of search cycles. , It is an integer ranging from 1 to the dimension Dim of the search space. ; Step 3.3, Extended Development ( In the third method, when the eagle has accurately designated the prey area and is ready to land and attack, it descends vertically and launches an initial attack to probe the prey's reaction; this method is called a low-altitude descent attack; here, the AO uses the selected area of ​​the target to approach the prey and launch an attack, and the mathematical model of this behavior is shown in the following formula: ， In the formula, It is the solution generated by the third search method in the (t+1)th iteration; and It is a development adjustment parameter that is fixed at a small value (0.1). These are the upper and lower bounds of the position vector; Step 3.4, narrow down the development ( In the fourth method, when the eagle approaches its prey, it attacks the prey on land based on its random movement; this method is called "walking and seizing the prey." Finally, the AO attacks the prey from the last position. The mathematical model of this behavior is shown in the following formula: ， In the formula, It is the solution generated by the fourth search method in the (t+1)th iteration; This represents the quality function used to balance the search strategy at the t-th iteration. This refers to the various movements used to track prey during a hunt. This indicates the flight speed of an eagle tracking its prey; It is the Lévy flight function. It is the position at the t-th iteration; The formula for calculating the mass function is: ; The flight speed was changed from linearly decreasing to: ; Step 4: Calculate the updated fitness value and update the population extreme value. If this iteration If no update is performed, then... ; Step 5: Evaluate whether the algorithm exhibits premature convergence and make corrections accordingly; Step 5.1, if ,but At the same time, ; Step 5.2, if , This will cause the group to reach an extreme value. The update is performed along its negative gradient direction, calculated as follows: ， In the formula, for The value before the most recent update; Step 6: Determine if the termination condition is met. If it is, output the optimal solution and end the program; otherwise, repeat the above Tianying optimization algorithm process to continue the optimization iteration.

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