Local power grid pumped storage capacity configuration method considering cost dredging

Abstract

The invention discloses a local power grid pumped storage capacity configuration method considering cost dredging, and the method comprises the steps: collecting wind power, photovoltaic and runoff type small hydropower station output and load power curves in a typical scene, and generating a typical electricity price scene; establishing a multi-objective optimization configuration model, and constructing an objective function 1 of the multi-objective optimization configuration model by taking maximum pumped storage investment benefit as an objective; constructing a target function 2 of the multi-target optimization configuration model by taking the minimum net load fluctuation variance as a target; setting constraint conditions of the multi-objective optimization configuration model; using an improved NSGA-II algorithm, and introducing an adaptive scale factor and a normal distribution crossover operator to obtain a Pareto frontier of the multi-target optimization configuration model; through a fuzzy membership function method, compromise solutions in various scenes are selected in combination with an entropy weight method, and then the optimal pumped storage capacity and installed capacity are obtained. According to the method, the economical efficiency of investment cost recovery and configuration can be ensured, the new energy network access fluctuation can be inhibited, and the system operation condition can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of pumped storage capacity planning, and in particular to a method for configuring the pumped storage capacity of a local power grid taking into account cost relief. Background Art

[0002] As the most mature and largest-scale green regulating power source for the power system, pumped storage has broad prospects for industry development. The current construction of pumped storage is mainly restricted by investment costs and operation methods. The investment and construction of pumped storage rarely consider the effective transmission of investor willingness and construction costs. In terms of cost guidance of pumped storage, considering the economic value of auxiliary services provided by pumped storage is the key to stimulating investor enthusiasm. The operation of traditional pumped storage power stations has the problem of difficulty in recovering construction costs due to its unclear market positioning.

[0003] For example, reference [1]: Liu Fei, Che Yanying, Tian Xu. Cost relief mechanism of pumped storage power stations under new power systems: review and prospect [J]. Journal of Shanghai Jiao Tong University, 2023, 57(7): 757-768. describes the diversification of pumped storage power station construction in my country, but the pumped storage regulation costs cannot be effectively relieved, which affects the enthusiasm of pumped storage investors.

[0004] Reference [2]: Duan Jingdong. Research on the profitability of investment and construction of pumped storage power stations under the new price formation mechanism [J]. Hydropower and Pumped Storage, 2021, 7(6): 69-73. It is mentioned that the operation mechanism of pumped storage power stations is not mature and is constrained by multiple factors such as local power grid demand, electricity price tolerance, and geographical resource conditions.

[0005] Reference [3]: Zhang Bailin, Cui Jian, Wu Guodong. Analysis of the profit model of the energy storage market based on the multiple values ​​of pumped storage [J]. China Hydropower and Electrification, 2022, 202(1): 49-54. The investment profit problem considering the multiple regulation values ​​of pumped storage was studied, and the cost recovery path of the electricity market and capacity market was explored.

[0006] Reference [4]: ​​Zhong Hao, Wu Fan, Zhang Lei, et al. Optimal capacity allocation of pumped storage power stations based on multi-time scale decision-making in the power market [J]. High Voltage Technology, 2023, 49(10): 4109-4119. In view of the current problem that the return on investment of pumped storage is difficult to guarantee, a method for optimal capacity allocation of pumped storage power stations based on multi-time scale decision-making in the power market is proposed, and development suggestions are put forward for the multi-market operation of pumped storage in my country.

[0007] Reference [5]: Wang Jin, Zhang Lizi, Zhao Zhifang, et al. Market-oriented operation mechanism of pumped storage power stations and day-ahead market clearing model [J]. Automation of Electric Power Systems, 2023, 47(12): 145-153. The operation mechanism of pumped storage participating in the spot market was studied to achieve the rational application of pumped storage resources, but the impact of different installed capacity of pumped storage on its participation in the spot market was not considered.

[0008] In summary, in the issue of pumped storage capacity allocation, some researchers have gradually focused on the market mechanism and electricity price formation of pumped storage. Combined with my country's special electricity market environment and diversified construction capital forms, it is necessary to further study the differences in the regulation benefits and service needs of pumped storage serving multiple users, and explore effective ways to achieve pumped storage investment cost recovery and profitability, so as to improve the investment and operation benefits of pumped storage power stations. Summary of the invention

[0009] In view of the problems of unclear market positioning of pumped storage power stations, limited profit margins, and weak willingness of social capital to invest, the present invention provides a method for configuring the pumped storage capacity of local power grids considering cost relief. With the goal of maximizing the profit of pumped storage investment and minimizing the net load fluctuation variance, the cost recovery mechanism of pumped storage capacity price, electricity price and its multiple auxiliary services is considered, and a multi-objective optimization configuration model of pumped storage capacity of local power grids containing renewable energy is established. The improved fast non-dominated sorting genetic algorithm (NSGA-Ⅱ) algorithm is used to solve the multi-objective optimization configuration model to improve the algorithm space search capability and the quality of Pareto solutions. This method can be used as an effective way to achieve pumped storage investment cost recovery and profitability, which is conducive to enhancing the enthusiasm for investment and construction of pumped storage power stations.

[0010] The technical solution adopted by the present invention is:

[0011] The method for configuring pumped storage capacity of local power grid considering cost diversion includes the following steps:

[0012] Step 1: Collect wind power, photovoltaic, run-of-river small hydropower output and load power curves under typical scenarios to generate typical electricity price scenarios;

[0013] Step 2: Establish a multi-objective optimization configuration model. Take the maximum investment benefit of pumped storage as the goal, and construct the objective function 1 of the multi-objective optimization configuration model; take the minimum net load fluctuation variance as the goal, and construct the objective function 2 of the multi-objective optimization configuration model;

[0014] Step 3: Set installed capacity constraints, operating power constraints, pumping / generation status and reservoir capacity regulation constraints as constraints for the multi-objective optimization configuration model;

[0015] Step 4: Using the improved NSGA-II algorithm, introducing the adaptive scaling factor and the normal distribution crossover operator, the Pareto frontier of the multi-objective optimization configuration model is obtained;

[0016] Step 5: Use the fuzzy membership function method combined with the entropy weight method to select compromise solutions under various scenarios, and then obtain the optimal storage capacity and installed capacity of pumped storage.

[0017] In step 1, in the local power grid containing pumped storage power stations and renewable energy, the power grid shall preferentially absorb clean energy such as wind power, photovoltaic power and run-of-river small hydropower, and the remaining load after supporting the load is the net load. The power variation characteristics of wind power, photovoltaic power, run-of-river small hydropower and regional power grid load in a typical week are collected, and the power curves of wind power, photovoltaic power, run-of-river small hydropower and load are constructed in the flood season scenario and the dry season scenario.

[0018] In step 1, since electricity prices fluctuate due to market adjustments, operators cannot accurately predict future electricity prices. The values ​​of electricity prices in each time period can be represented by a normal distribution probability density function, as shown in formula (1).

[0019]

[0020] In formula (1): and They are the predicted values ​​of electricity price for electric quantity and electricity price for frequency regulation mileage at time t respectively; and are the expected values ​​of electricity price for electricity quantity and frequency regulation mileage price at time t respectively; and are the variances of electricity price for electric quantity and electricity price for frequency regulation mileage respectively.

[0021] According to the electricity price prediction model of formula (1), the Monte Carlo algorithm is used to sample and generate scenarios, and then the k-means clustering algorithm is used to perform clustering reduction to generate a limited number of typical electricity price scenarios and the probability of each scenario.

[0022] Assuming that the number of typical scenes is M, the random sample feature value is the cluster center, and the process of scene reduction using the k-means clustering algorithm is as follows: Figure 1 As shown, the main steps are as follows:

[0023] 1) According to the normal distribution model of electricity price prediction, M samples are randomly generated using the Monte Carlo method, and the sample data are normalized.

[0024] 2) Randomly select N from the sample o The scene is used as the initial electricity price cluster center λ k ,k=1,2,…,N o ;

[0025] 3) Calculate the Euclidean distance between the electricity price data in each remaining scenario and each cluster center.

[0026] D ik =|λ i -λ k |(2)

[0027] Where: D ik represents the Euclidean distance; λ i represents the electricity price of scenario i, λ k Represents the electricity price of scene k in the initial cluster center.

[0028] 4) According to the Euclidean distance, each electricity price sample and its nearest cluster center are clustered together, and then the mean of all sample points in each cluster is used as the new cluster center.

[0029]

[0030] In formula (3), N k and Ik are the amount of electricity price data of the kth cluster center and the set of its clusters.

[0031] 5) Repeat steps 3) and 4) until the new cluster center is equal to the original cluster center or the Euclidean distance is less than the specified threshold (ε=0.01), and the algorithm ends.

[0032] 6) The obtained cluster center is the typical electricity price scenario obtained after reduction and denormalization, and the proportion of each type of scenario to the initial number of scenarios is the probability value of the typical scenario.

[0033] In step 2, the constructed electricity price scenario is introduced into the objective function of the multi-objective optimization model. The first optimization objective is to maximize the investment benefit of pumped storage, which is the economic benefit after the operation of pumped storage minus its investment and construction cost;

[0034] The objective function f is constructed by deducting the estimated investment income of the pumped storage power station from the construction cost. 1 , that is, the comprehensive cost is the lowest, and the objective function is shown in formula (4):

[0035]

[0036] In formula (4): C PS is the investment and construction cost of pumped storage, and the investment and construction cost of pumped storage is C PS Includes: Investment cost C inv , Operation and maintenance cost C om , turbine replacement cost C re etc. T pump is the whole life cycle of the unit; C cap C is the capacity-based electricity price leasing income; l is the income from the electricity market; Caux for ancillary services market revenue;

[0037]

[0038] In formula (5): C pc V is the unit price per cubic meter of upstream storage capacity; pcap is the upstream storage volume; C pp P is the unit price per kilowatt of turbine installed capacity; pcap is the installed capacity of the pumped storage unit; T a C is the project life; OM_pc is the unit maintenance cost of upstream storage capacity; C OM_pp is the unit operation and maintenance cost of installed capacity; r is the discount rate; C re_pp is the turbine replacement cost, including depreciation; T pump is the whole life cycle of the unit, N x is the number of replacements that occur within the life of the project; n is a natural year.

[0039] The regulating function of pumped storage is reflected in the consumption of clean energy (wind, solar, run-of-river hydropower), that is, smoothing the fluctuation of clean energy into the grid. The objective function f is constructed by minimizing the variance of pumped storage to smooth the fluctuation of residual load. 2 , its objective function f 2 As shown in formula (9):

[0040]

[0041] In formula (9): T is the length of a day; dP t L is the net load power after pumped storage regulation at time t;

[0042]

[0043] In formula (10): △P t L is the unbalanced net load power of the system at time t; P t L , P t WT , P t PV , P t HY are the output of load, wind power, photovoltaic power and non-adjustable small hydropower at time t respectively; P t T , P t P are the generating power and pumping power of the pumped storage at time t respectively.

[0044] In step 3, the constraints include: installed capacity constraints, upper and lower limits of operating power constraints, pumping / power generation state constraints, reservoir capacity regulation constraints, etc.;

[0045] 1) Installed capacity constraints:

[0046]

[0047] In formula (11): V p_pcapmax is the upper limit of upstream storage capacity; P p_capmax is the upper limit of the unit capacity; V pcap is the upstream storage volume.

[0048] 2) Operating power upper and lower limit constraints:

[0049]

[0050] In formula (12): P pcap P is the installed capacity of the pumped storage unit; t e ,P t re ,P t r They are respectively the power generation power of pumped storage in the electric energy market, the power generation power of frequency regulation market and the power generation power of standby market at time t; P t d ,P t rd They are respectively the pumped power of the electric energy market and the pumped power of the frequency regulation market at time t.

[0051] 3) Pumping / power generation state constraints:

[0052]

[0053] 4) Storage capacity adjustment constraints:

[0054]

[0055] In formula (14): V t is the storage capacity at time t; Q P (t) and Q T (t) represent the pumping flow and power generation flow at time t respectively; K t and K p are the flow rate power ratios under power generation and pumping conditions respectively; η wp is the pipeline efficiency; η P is the pump operating efficiency; η T is the operating efficiency of the generator set; ρ represents the water density; g is the standard acceleration of gravity; h is the design water head of the pumped storage unit. △t is the time interval; V(t+1) is the storage capacity at time (t+1).

[0056] The multi-objective optimization configuration model includes:

[0057] Objective function 1: formula (4);

[0058] Objective function 2: formula (9);

[0059] Constraints: Equation (11) to (14).

[0060] In step 4, the improvement strategy of the NSGA-II algorithm includes: improving the proportional factor in the selection mechanism strategy in view of the shortcomings of the traditional NSGA-II; introducing the normal distribution crossover operator (NDX) in the crossover process, which can effectively enhance the spatial search ability of the algorithm, further improve the convergence speed, and reduce the computational cost;

[0061] The adaptive scale factor improvement method is as follows:

[0062] The selection mechanism of the NSGA-II algorithm is the league selection method. In this rule, the indicators for judging the quality of individuals are the non-dominated level and the crowding distance. In the same non-dominated layer, the crowding degree of individual n (except the two endpoints) is only determined by the difference between the objective function values ​​of the two adjacent individuals, resulting in poor population diversity. In order to reduce the number of repeated individuals and increase the diversity of the population, the proportional factor in the selection strategy is improved. The rule is shown in formula (15):

[0063]

[0064] In formula (15): C m is the number of individuals obtained from the mth non-dominated layer of the selected population; N m is the number of individuals in the mth non-dominated layer. ξ m is the scale factor; D max is the number of non-dominated layers; z m 、x m is a variable parameter with a value range of [0.5,1], and z m <x m ; k is the number of iterations; k max is the maximum number of iterations;

[0065] It should be noted that z m 、x m Only related to m, its initial value is set to z m =0.5,x m =1, as m increases, z m and x m The proportional factor ξ is reduced by 0.01. mis a dynamic variable determined by m and k. From the perspective of the hierarchical sorting of the non-dominated layers, the later the non-dominated layers are, the fewer dominant individuals they contain. m It decreases as m increases, which can effectively reduce the number of disadvantaged individuals.

[0066] In step 4, the normal distribution crossover operator is as follows:

[0067] Traditional NSGA-II generally uses simulated binary crossover operator (SBX) to generate offspring. Due to its limited search range, it is easy to produce local optimality and cause instability in the evolution process. In view of the shortcomings of traditional NSGA-II, the introduction of normal distribution crossover operator (NDX) in the crossover process can effectively enhance the algorithm's spatial search ability, further improve the convergence speed, and reduce the computational cost. Assume that the parent population is P 1 , P 2 , the offspring population is Q 1 , Q 2 For individual i, the process of generating offspring using NDX crossover is as follows:

[0068] Generate a random number r∈(0,1], when r≤0.5:

[0069]

[0070] In formula (16): P 1,i and P 2,i Two parent populations randomly generated for individual i, Q 1,i and Q 2,i Respectively represent the parent population P of individual i 1,i and P 2,i The offspring population generated by crossover from a normal distribution.

[0071] When r>0.5:

[0072]

[0073] Where N(0,1) is a normally distributed random variable.

[0074] In step 4, the multi-objective optimization configuration model is solved as follows: Figure 2 As shown, the following steps are included:

[0075] Step 4.1: Input the improved NSGA-Ⅱ parameters and model data;

[0076] Step 4.2: Randomly generate the initial population P 0 ;

[0077] Step 4.3: According to the objective function formula (4) and formula (9), calculate the objective function fitness value and constraint violation value of each individual in the population;

[0078] Step 4.4: Fast non-dominated sort;

[0079] Step 4.5: Update the scale factor;

[0080] Step 4.6: Pick N P / 2 dominant individuals as the parent population P k ; N P is the population number;

[0081] Step 4.7: Improve the crossover operator, introduce adaptive scaling factor and normal distribution crossover operator;

[0082] Step 4.8: Crossover and mutation to generate offspring population Q k ;

[0083] Step 4.9: Implement the elite strategy to generate a new population P k ∪Q k ;

[0084] Step 4.10: Calculate the individual fitness value and constraint violation value of the new population;

[0085] Step 4.11: Determine the termination condition: If the number of iterations reaches the maximum evolutionary generation, proceed to step 4.12; otherwise, update the number of iterations k = k + 1 and return to step 4.4;

[0086] Step 4.12: Output the Pareto non-inferior solution set; and select the compromise solution.

[0087] In step 5, the entropy weight method is a typical objective weighting method that uses information entropy to measure the differences between evaluation indicators and assigns higher weights to indicators with larger differences. It is more objective and has a simpler calculation process. It has been applied to various comprehensive evaluation problems in power systems. The specific calculation process is as follows:

[0088] S5.1: Calculate the ratio of the kth data of the ith indicator to the sum of all ith indicators The formula is as follows:

[0089]

[0090] In formula (18): is the probability of the objective function value of a solution in the probability space.

[0091] S5.2: Calculate the entropy value e of the i-th indicator i :

[0092]

[0093] In formula (19), 1 / lnM is a constant related to the number of non-inferior solutions, so that e i ∈[0,1]; when the entropy value e i The larger it is, the less data information the corresponding ith indicator contains, and the smaller its contribution to the ranking of evaluation indicators. Conversely, the greater its contribution.

[0094] S5.3: Calculate the weight λ of each attribute i :

[0095]

[0096] In formula (20): 1-e i Represents the information deviation of the i-th indicator.

[0097] The step 5 also includes an expert weighting method, which depends on the decision maker's preference, including the weight λ of objective function 1 1 and the weight λ of objective function 2 2 If the system requires better economy, λ can be appropriately increased. 1 On the contrary, for systems with high stability and peak-to-valley difference performance, λ can be appropriately increased. 1 The weight of .

[0098] In step 5, the fuzzy membership function method is a method for selecting a compromise solution in the Pareto frontier, and the optimal storage capacity and installed capacity of the pumped storage are obtained through the compromise solution. The specific steps are as follows:

[0099] Step 1: Record the maximum value F of the i-th objective function in the Pareto front i max and the minimum value F i min , where the number of non-inferior solution sets is M and the number of objective functions is N.

[0100] Step 2: Use formula (21) to calculate the membership degree corresponding to the i-th objective function of the k-th solution in the set of M Pareto non-inferior solutions:

[0101]

[0102] In formula (21): F i k is the value of the objective function i corresponding to the kth solution.

[0103] Step 3: The optimal solution to the multi-objective problem is the non-dominated solution corresponding to the normalized value of the maximum membership.

[0104] The u obtained in the actual calculation is kThere may be more than one because the weight coefficients of each objective are the same, and the objective values ​​of some solutions fall exactly on the upper and lower limits, making it difficult to distinguish the quality of the solution. To solve this problem, weight each objective value as shown in the following formula:

[0105]

[0106] In formula (22): i is the weight coefficient of objective function i, satisfying Weight coefficient λ i Subjective weighting can be performed based on the decision maker's preference for each goal or expert advice, or objective weighting can be used. After correcting the weights, the maximum and only weighted normalization u is determined. k value, and then select the best decision solution.

[0107] The present invention provides a method for configuring the capacity of pumped storage energy in a local power grid taking into account cost dredging, and the technical effects are as follows

[0108] 1) The present invention considers the comprehensive investment benefits in the pumped storage capacity configuration model. The obtained pumped storage configuration scheme can ensure the recovery of investment costs and the economy of configuration. The auxiliary service regulation value of pumped storage is an important way to increase its investment benefits.

[0109] 2) The present invention establishes a multi-objective optimization configuration model to achieve optimal capacity configuration. In typical scenarios of flood season and dry season, pumped storage can balance the fluctuation of clean energy access to the local power grid, improve system operating conditions, and promote the coordinated development of pumped storage and clean energy. The proposed model can provide a reference for the investment benefit estimation in the initial stage of pumped storage power station construction.

[0110] 3) In the present invention, by adopting the adaptive scaling factor and the normal distribution crossover operator, the improved NSGA-II algorithm can achieve the optimal Pareto front, spatial metric index and solution speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 Generate a typical scenario flow for the k-means clustering algorithm.

[0112] Figure 2 Flowchart for solving this model using the improved NSGA-II algorithm.

[0113] Figure 3 Figure IEEE30 is the test case system diagram.

[0114] Figure 4(a) shows the power curves of wind power, photovoltaic power, run-of-river small hydropower and load in the flood season scenario.

[0115] Figure 4(b) shows the power curves of wind power, photovoltaic power, run-of-river small hydropower and load in the dry season scenario.

[0116] Figure 5 This is the expected value diagram of electricity price and frequency regulation mileage price.

[0117] Figure 6(a) shows 10 typical scenarios of electricity volume and electricity price.

[0118] Figure 6(b) shows 10 typical scenarios of frequency regulation mileage electricity prices.

[0119] Figure 7 Probabilities of various typical scenarios.

[0120] Figure 8(a) shows the Pareto frontier of pumped storage capacity configuration in the flood season scenario.

[0121] Figure 8(b) shows the Pareto frontier of pumped storage capacity configuration in the dry season scenario.

[0122] Figure 9(a) shows the results of the pumped storage power station smoothing the fluctuation of clean energy access to the grid during the flood season.

[0123] Figure 9(b) shows the results of the pumped storage power station smoothing the fluctuations of clean energy access to the grid during the dry season.

[0124] Fig.10 This is a comparison chart of the Pareto front under each algorithm. DETAILED DESCRIPTION

[0125] A method for configuring the pumped storage capacity of a local power grid considering cost relief. This method constructs a multi-objective optimization configuration model for the pumped storage capacity of a local power grid considering cost relief, and establishes an objective function with the maximum investment benefit of pumped storage and the minimum net load fluctuation variance as the optimization objectives. Consider installed capacity constraints, upper and lower limits of operating power constraints, pumping / power generation state constraints, reservoir capacity regulation constraints, etc. This optimization model uses the improved NSGA-Ⅱ algorithm to solve the model, optimizes the selection, crossover and diversity maintenance mechanisms of the population, and thus achieves better performance in multi-objective optimization problems. The specific implementation methods are as follows:

[0126] Step 1: Collect the power variation characteristics of wind power, photovoltaic power, run-of-river small hydropower and regional power grid load in a typical week, and construct the corresponding power curve.

[0127] A typical week represents the most representative dispatch period of clean energy output characteristics in a year. The power variation characteristics of photovoltaics and loads are displayed in days; the output characteristics of run-of-river small hydropower are particularly obvious in the flood season and the dry season, especially in the dry season, when it basically does not have the conditions for power generation, and in the flood season, it is affected by natural water and the downstream flow of hydropower in the basin, and its output volatility is quite obvious within a week; the intermittent and volatile nature of wind power is the most significant, manifested as a strong daily and weekly change rate. The present invention selects a week in the flood season as the dispatch period, which can effectively characterize the output characteristics of each clean energy source.

[0128] The Monte Carlo method and k-means clustering method are used to predict market prices and generate typical electricity price scenarios. Under the regulation of the market mechanism, the market price of electric energy and the price of frequency regulation mileage will fluctuate, and the market price in each period is assumed to obey the normal distribution. According to the historical data such as the transaction volume of each period, the deployment of pumped storage units, and the marginal clearing price, the values ​​of the electricity price and the frequency regulation mileage price in each period can be expressed by the probability density function under the normal distribution, as shown in formula (1).

[0129]

[0130] In formula (1): and They are the predicted values ​​of electricity price for electric quantity and electricity price for frequency regulation mileage at time t respectively; and are the expected values ​​of electricity price for electricity quantity and frequency regulation mileage price at time t respectively; and are the variances of electricity price for electric quantity and electricity price for frequency regulation mileage respectively.

[0131] According to the electricity price prediction model of formula (1), the Monte Carlo algorithm is used to sample and generate scenarios, and then the k-means clustering algorithm is used to perform cluster reduction to generate a finite number of typical scenarios of electricity prices and the probability of each scenario. Assuming that the number of typical scenarios is M, the random sample feature value is the center of each cluster, and the process of using the k-means clustering algorithm to achieve scenario reduction is as follows: Figure 1 As shown, the main steps are as follows:

[0132] 1) According to the normal distribution model of electricity price prediction, M samples are randomly generated using the Monte Carlo method, and the sample data are normalized.

[0133] 2) Randomly select N from the sample o The scene is used as the initial electricity price cluster center λ k (k=1,2,…,N o ).

[0134] 3) Calculate the Euclidean distance between the electricity price data in each remaining scenario and each cluster center.

[0135] Dik=|λi-λk|(2)

[0136] Where: D ik represents the Euclidean distance; λ i represents the electricity price of scenario i, λ k Represents the electricity price of scene k in the initial cluster center.

[0137] 4) According to the Euclidean distance, each electricity price sample and its nearest cluster center are clustered together, and then the mean of all sample points in each cluster is used as the new cluster center.

[0138]

[0139] In formula (3), N k and Ik are the amount of electricity price data of the kth cluster center and the set of its clusters.

[0140] 5) Repeat steps 3) and 4) until the new cluster center is equal to the original cluster center or the Euclidean distance is less than the specified threshold (ε=0.01), and the algorithm ends.

[0141] 6) The obtained cluster center is the typical electricity price scenario obtained after reduction and denormalization, and the proportion of each type of scenario to the initial number of scenarios is the probability value of the typical scenario.

[0142] Step 2: Establish a multi-objective optimization configuration model, with the goal of maximizing the investment benefit of pumped storage as the goal, construct objective function 1 of the multi-objective optimization configuration model; with the goal of minimizing the net load fluctuation variance, construct objective function 2 of the multi-objective optimization configuration model;

[0143] S2.1: Construct objective function 1 of multi-objective optimization configuration model:

[0144] The objective function f is constructed by deducting the estimated investment income of the pumped storage power station from the construction cost. 1 , the investment and construction cost of pumped storage is C PS , Capacity-based electricity price leasing income C cap = Electricity market revenue C l ; Ancillary service market revenue C aux Introduce f 1 In the middle, the comprehensive cost is the lowest, as shown in formula (4):

[0145]

[0146] 1): Investment and construction cost of pumped storage C PS :

[0147] Including investment cost C inv , Operation and maintenance cost C om, turbine replacement cost C re wait.

[0148]

[0149] In formula (5): C pc V is the unit price per cubic meter of upstream storage capacity; pcap is the upstream storage volume; C pp P is the unit price per kilowatt of turbine installed capacity; pcap is the installed capacity of the pumped storage unit; T a C is the project life; OM_pc is the unit maintenance cost of upstream storage capacity; C OM_pp is the unit operation and maintenance cost of installed capacity; r is the discount rate; C re_pp is the turbine replacement cost, including depreciation; T pump is the whole life cycle of the unit, N x is the number of replacements that occur within the life of the project; n is a natural year.

[0150] 2) Capacity-based electricity price rental income C cap :

[0151] C cap =λ cap P pcap (6);

[0152] In formula (6): Capacity electricity price λ cap Based on the comprehensive assessment of the internal rate of return on capital (6% to 8%) and the static investment per kilowatt, the variation range is generally 500 to 800 yuan / kW.

[0153] 3) Electricity market revenue C l :

[0154] In the early stage of the formation of the electricity market, the electricity price can be implemented according to the benchmark on-grid electricity price of coal-fired units. As the electricity market gradually matures, the two-part electricity price of pumped hydropower and electricity price is allowed to fluctuate to a certain extent under the influence of the market. The electricity revenue of pumped storage is shown in formula (7):

[0155]

[0156] In formula (7), n represents the number of scenarios of electricity quantity and electricity price; π i represents the probability of scenario i; They represent the predicted value of the pumped storage electricity price at time t in scenario i; T is the length of a day; P t e ,P t re ,P t rThey are respectively the power generation power of pumped storage in the electric energy market, the power generation power of frequency regulation market and the power generation power of standby market at time t; P t d ,P t rd They are respectively the pumped power of the electric energy market and the pumped power of the frequency regulation market at time t.

[0157] 4) Ancillary services market revenue C aux :

[0158]

[0159] In formula (8): m represents the number of scenarios of frequency regulation mileage electricity price; is the frequency regulation capacity compensation price; is the reserve capacity compensation price; is the predicted value of the frequency modulation mileage price at time t in scenario i; R is the ratio of frequency modulation mileage to frequency modulation capacity.

[0160] S2.2: Construct objective function 2 of the multi-objective optimization configuration model:

[0161] The regulating function of pumped storage is reflected in the consumption of clean energy (wind, solar, run-of-river hydropower), that is, smoothing the fluctuation of clean energy into the grid. The objective function f is constructed by minimizing the variance of pumped storage to smooth the fluctuation of residual load. 2 , as shown in formula (9):

[0162]

[0163] In formula (9): dP t L is the net load power after pumped storage regulation at time t.

[0164] Considering the priority consumption of renewable energy (wind, solar, run-of-river small hydropower), the base load is borne by the maximum output. The randomness and unadjustability of renewable energy will cause the output power to not match the load demand. The unbalanced power generated is adjusted by pumped storage, which can achieve the smoothing of net load fluctuations, as shown in formula (10):

[0165]

[0166] In formula (10): △P t L is the unbalanced net load power of the system at time t; P t L , P t WT , P t PV , P t HYare the output of load, wind power, photovoltaic power and non-adjustable small hydropower at time t respectively; P t T , P t P are the generating power and pumping power of the pumped storage at time t respectively.

[0167] Step 3: Construct the constraints of the multi-objective optimization configuration model, including installed capacity constraints, upper and lower limits of operating power constraints, pumping / power generation status constraints, reservoir capacity regulation constraints, etc.

[0168] 1) Installed capacity constraints:

[0169]

[0170] In formula (11): V p_pcapmax is the upper limit of upstream storage capacity; P p_capmax The upper limit of the unit capacity.

[0171] 2) Operating power upper and lower limit constraints:

[0172]

[0173] 3) Pumping / power generation state constraints:

[0174]

[0175] 4) Storage capacity adjustment constraints:

[0176]

[0177] In formula (14): V t is the storage capacity at time t; Q P (t) and Q T (t) represent the pumping flow and power generation flow at time t respectively; K t and K p are the flow rate power ratios under power generation and pumping conditions respectively; η wp is the pipeline efficiency; η P is the pump operating efficiency; η T is the operating efficiency of the generator set; ρ represents the water density; g is the standard acceleration of gravity; h is the design water head of the pumped storage unit; △t is the time interval; V(t+1) is the storage capacity at time (t+1).

[0178] Step 4: Use the improved NSGA-II algorithm to solve this multi-objective optimization configuration model:

[0179] Take objective function 1: formula (4);

[0180] Objective function 2: formula (9);

[0181] Constraints: Equation (11) to (14);

[0182] A multi-objective optimization model for pumped storage capacity configuration is constructed, and a Pareto non-inferior solution set that satisfies all constraints is obtained through a multi-objective optimization algorithm (NSGA-II). Although the NSGA-II algorithm has been widely used as a classic algorithm, there is still room for improvement: for example, the dominant individuals of the external elite population lose their eliteness in the early stage of evolution, and the spatial search ability is not strong. In view of the shortcomings of the traditional NSGA-II, the proportional factor in the selection mechanism strategy is improved: an adaptive proportional factor and a normal distribution crossover operator are introduced.

[0183] S4.1: Improvement strategy of scaling factor:

[0184] The selection mechanism of the NSGA-II algorithm is the league selection method. In this rule, the indicators for judging the quality of individuals are the non-dominated level and the crowding distance. In the same non-dominated layer, the crowding degree of individual n (except the two endpoints) is only determined by the difference between the objective function values ​​of the two adjacent individuals, resulting in the deterioration of population diversity. In order to reduce the number of repeated individuals and increase the diversity of the population, the proportional factor in the selection strategy is improved, and the rule is shown in formula (15).

[0185]

[0186] In formula (15): C m is the number of individuals obtained from the mth non-dominated layer of the selected population; N m is the number of individuals in the mth non-dominated layer; ξ m is the scale factor, z m 、x m is a variable parameter with a value range of [0.5,1], and z m <x m ; k is the number of iterations; k max is the maximum number of iterations; D max is the number of non-dominated layers.

[0187] It should be noted that z m 、x m Only related to m, its initial value is set to z m =0.5,x m =1, as m increases, z m and x m The proportional factor ξ is reduced by 0.01. m is a dynamic variable determined by m and k. From the perspective of the hierarchical sorting of the non-dominated layers, the later the non-dominated layers are, the fewer dominant individuals they contain. m It decreases as m increases, which can effectively reduce the number of disadvantaged individuals.

[0188] S4.2: Crossover operator improvement strategy:

[0189] Traditional NSGA-II generally uses simulated binary crossover operator (SBX) to generate offspring. Due to its limited search range, it is easy to produce local optimality and cause instability in the evolution process. In view of the shortcomings of traditional NSGA-II, the introduction of normal distribution crossover operator (NDX) in the crossover process can effectively enhance the algorithm's spatial search ability, further improve the convergence speed, and reduce the computational cost. Assume that the parent population is P 1 , P 2 , the offspring population is Q 1 , Q 2 , for individual i, the process of generating offspring using NDX crossover is as follows.

[0190] Generate a random number r∈(0,1], when r≤0.5:

[0191]

[0192] When r>0.5:

[0193]

[0194] Where N(0,1) is a normally distributed random variable; P 1,i and P 2,i Two parent populations randomly generated for individual i, Q 1,i and Q 2,i is the parent population of individual i (P 1,i and P 2,i ) is the offspring population generated by crossover from a normal distribution.

[0195] S4.3: The solution process of this multi-objective optimization model using the improved NSGA-Ⅱ is as follows: Figure 2 As shown, the steps are as follows:

[0196] Step 4.1: Input the improved NSGA-Ⅱ parameters and model data;

[0197] Step 4.2: Randomly generate the initial population P 0 ;

[0198] Step 4.3: According to the objective function formula (4) and formula (9), calculate the objective function fitness value and constraint violation value of each individual in the population;

[0199] Step 4.4: Fast non-dominated sort;

[0200] Step 4.5: Update the scale factor;

[0201] Step 4.6: Pick NP / 2 dominant individuals as the parent population P k , N P is the population number;

[0202] Step 4.7: Improve the crossover operator, introduce adaptive scaling factor and normal distribution crossover operator;

[0203] Step 4.8: Crossover and mutation to generate offspring population Q k ;

[0204] Step 4.9: Implement the elite strategy to generate a new population P k ∪Q k ;

[0205] Step 4.10: Calculate the individual fitness value and constraint violation value of the new population;

[0206] Step 4.11: Determine the termination condition: If the number of iterations reaches the maximum evolutionary generation, proceed to step 4.12; otherwise, update the number of iterations k = k + 1 and return to step 4.4;

[0207] Step 4.12: Output the Pareto non-inferior solution set.

[0208] Step 5: Through the fuzzy membership function method, combined with expert weighting and entropy weight method, the Pareto non-inferior solution set output in step 5 is selected to select a compromise solution, and then the optimal storage capacity and installed capacity of the pumped storage are obtained.

[0209] When choosing a compromise solution, it is necessary to determine the weight λ of objective function 1 1 and the weight λ of objective function 2 2 The weights of each objective function can be set subjectively based on expert advice. If the decision maker pursues higher profits, the weight λ can be increased. 1 If the decision maker pursues a lower net load fluctuation variance, the weight λ can be increased 2 , if the two objective functions are balanced, they can be given equal weights. Objective weighting can also be used. As a typical objective weighting method, the entropy weight method uses information entropy to measure the differences of various evaluation indicators, and gives higher weights to indicators with larger differences. It is more objective and has a simpler calculation process. It has been applied to various comprehensive evaluation problems in power systems.

[0210] S5.1: Use entropy weight method to complete objective weighting:

[0211] As a typical objective weighting method, the entropy weight method uses information entropy to measure the differences of various evaluation indicators, and assigns higher weights to indicators with larger differences. It is more objective and has a simpler calculation process. It has been applied to various comprehensive evaluation problems in power systems. The specific calculation process is as follows:

[0212] Step 1: Calculate the ratio of the kth data of the i-th indicator to the sum of all i-th indicators The formula is as follows:

[0213]

[0214] In formula (18): is the probability of the objective function value of a solution in the probability space.

[0215] Step 2: Calculate the entropy value e of the i-th indicator i :

[0216]

[0217] In formula (19), 1 / lnM is a constant related to the number of non-inferior solutions, so that e i ∈[0,1]; when the entropy value e i The larger it is, the less data information the corresponding ith indicator contains, and the smaller its contribution to the ranking of evaluation indicators. Conversely, the greater its contribution.

[0218] Step 3: Calculate the weight λ of each attribute i :

[0219]

[0220] In formula (20): 1-e i Represents the information deviation of the i-th indicator.

[0221] S5.2: Use the fuzzy membership function method to calculate the normalized value of the membership function of each non-dominated solution, and the decision maker selects the non-dominated solution with the largest normalized membership value as the compromise solution of this multi-objective optimization model. The steps are as follows:

[0222] Step 1: Record the maximum value F of the Pareto frontier objective function of each objective under the multi-objective problem i max and the minimum value F i min .

[0223] Step 2: Calculate the membership degree u corresponding to each objective function of each solution in each Pareto non-inferior solution set.

[0224]

[0225] In formula (21): F i k is the value of the objective function i corresponding to the kth solution.

[0226] Step 3: Calculate the normalized value u of the membership function corresponding to each non-dominated solution k in the Pareto frontk , as shown below:

[0227]

[0228] In formula (22): i is the weight coefficient of objective function i, satisfying Normalize the largest and only weight u k The non-dominated solution corresponding to the value is taken as the compromise solution of this multi-objective optimization model, and then the optimal storage capacity and installed capacity of the pumped storage power station are obtained.

[0229] The solution process of this multi-objective optimization configuration model can be divided into two parts:

[0230] In the first step, the output of the pumped storage power station, upstream storage capacity, installed capacity, interconnection line power, thermal power unit output, etc. are used as optimization variables, and a multi-objective optimization configuration model is established with objective function 1: formula (3) and objective function 2: formula (8) and constraints: formulas (11) to (14). The Pareto frontier of the multi-objective optimization problem is obtained through the improved NSGA-Ⅱ algorithm.

[0231] In the second step, the weights of each objective function are selected according to user preferences and the entropy weight method, and the compromise solution is selected from the Pareto solution set using the fuzzy membership function. The optimal storage capacity and installed capacity of the local power grid pumped storage corresponding to the compromise solution are obtained.

[0232] Verification example:

[0233] The simulation example is based on the IEEE30 node system. On this basis, a pumped storage power station, a photovoltaic cluster, a wind power cluster, etc. are introduced. Clean energy consists of photovoltaic, wind power, and run-of-river small hydropower, and the user load is connected to the local power grid. Among them, the total installed capacity of the two thermal power units is 200MW; the installed capacity of the wind power cluster is 180MW, the installed capacity of the photovoltaic power is 12.6MW, and the total load capacity is 120MW. The modified IEEE30 node network is as follows Figure 3 As shown: Among them, small hydropower, photovoltaic, pumped storage, and wind power are connected to nodes 11, 13, 18, and 24 respectively, and the remaining units are conventional thermal power units. The basic parameters of the pumped storage power station to be invested and constructed are as follows: the project life is 25 years, the full life cycle of the turbine is 15 years, the turbine equipment is replaced once within the project life, the discount rate is 0.05, the design head height is about 79 meters, the generator efficiency is 0.64, the pump efficiency is 0.65, the pipeline efficiency is 0.95, the maximum and minimum operating storage capacity of the reservoir are 100% and 20% of the maximum capacity respectively, and the configuration parameters and construction cost parameters of the pumped storage power station are shown in Tables 1 and 2.

[0234] Table 1 Configuration parameters of pumped storage power station

[0235]

[0236] Table 2 Investment and construction cost parameters of pumped storage power station

[0237]

[0238] The static investment per kilowatt of the pumped storage power station is about 3,500 yuan / kW. If the internal rate of return of capital is 8%, the capacity electricity price should reach 532.78 yuan / kW. The improved NSGA-II algorithm is used to program and solve the optimization model. The population size is set to 100, the maximum number of iterations is 100, the crossover rate is 0.9, and the mutation rate is 0.1. In the Windows 10 system, the simulation program is compiled using the Matlab 2016a platform. The simulation computer processor is Intel core i7-6500U and the memory is 8GB.

[0239] The electricity price scenario is generated according to the Monte Carlo method, and the electricity price and frequency regulation mileage price of the typical scenario are obtained by combining the k-means clustering method. The specific details are as follows: Since the seasonal characteristics of wind power and run-of-river hydropower are relatively obvious, the simulation calculation is carried out on a certain dispatching day in July of a certain year as the flood season scenario and a certain dispatching day in March of a certain year as the dry season scenario. Figure 4 contains the clean energy output and load power curves under the flood season and dry season scenarios. The variance of electricity price σ e =10 yuan / MWh, frequency regulation mileage price variance σ rd =2 yuan / MW, the expected value of electricity price for each period and frequency regulation mileage price is as follows Figure 5 According to the Monte Carlo method, 1000 electricity price scenarios are generated, and the electricity price and frequency regulation mileage price of 10 typical scenarios are obtained by combining the k-means clustering method, as shown in Figure 6. The corresponding probability of each scenario is as follows Figure 7 In addition, the frequency regulation capacity price in each scenario is dynamic. The reserve capacity electricity price is 80 yuan / MW. The ratio of frequency regulation mileage to frequency regulation capacity is R=6, and the reserve call coefficient is k r =0.2.

[0240] The improved NSGA-II algorithm is used to solve the multi-objective optimization model and select the optimal solution. The Pareto frontier of the pumped storage capacity configuration results in each scenario is shown in Figure 8. As can be seen from Figure 8, the Pareto non-inferior solution set obtained by the optimization model of the present invention is evenly distributed in space, and the improved NSGA-Ⅱ algorithm can obtain a good Pareto optimal solution. It should be noted that the run-of-river small hydropower output is relatively large during the flood season, which reduces the pressure on load power supply. Through the complementary effect of clean energy, the regulation pressure of pumped storage is reduced, and the load fluctuation variance is larger than that in the dry season, and its operating efficiency is relatively low.

[0241] According to the fuzzy set theory, the Pareto compromise solution for each scenario is obtained, and the corresponding pumped storage capacity configuration scheme is shown in Table 3. It can be seen from the table that the pumped storage power station can still obtain a certain profit after deducting its own investment and construction costs, indicating that this configuration result can ensure the recovery of investment costs. By comparing the configuration results under the two scenarios, it can be seen that in the dry season, due to the low output of run-of-river small hydropower, the configured pumped storage capacity is relatively large compared to the flood season, and the regulation demand for pumped storage in the dry season scenario is also greater. In the typical scenarios of flood season and dry season, the Pareto non-inferior solution set obtained by the improved NSGA-II algorithm can obtain the optimal storage capacity and installed capacity of the pumped storage power station.

[0242] Taking the 160MW configuration scheme as an example, in the dry season scenario, due to the low output of run-of-river small hydropower, the configured pumped storage capacity is relatively larger than that in the flood season, which indicates that the regulation demand for pumped storage is greater in the dry season.

[0243] Table 3 Optimal configuration of pumped storage power station capacity corresponding to the compromise solution

[0244]

[0245] Table 4 is a comparison of the cost recovery period of pumped storage under different configuration schemes. Under the four different capacity configuration schemes, the payback period of the pumped storage power station is less than 6 years. If the ancillary service income is not considered, its cost recovery period will increase significantly, which shows that the ancillary service income is an important way to increase the investment benefits of pumped storage. Comparing the results of the four capacity configurations, it can be seen that if the ancillary service costs are not considered, the cost recovery period of pumped storage under the 169MW configuration is relatively longer; and after considering the ancillary services, the cost recovery period under the 160MW configuration is shorter, which shows that the regulatory advantages of pumped storage in the ancillary service market are conducive to the rapid recovery of pumped storage costs. With the development of the ancillary service market mechanism, the mature market environment in the future will bring huge economic benefits to pumped storage. After comprehensive analysis, the economic benefits are best when the pumped storage capacity is configured to 160MW, which can be used as the optimal configuration scheme for pumped storage capacity in the current scenario.

[0246] Table 4 Cost recovery period of pumped storage under different configuration schemes

[0247]

[0248] The capacity configuration results and operating benefits of pumped storage power stations under different scenarios are as follows:

[0249] Figure 9 shows the residual load fluctuation suppression in each scenario under the 160MW capacity configuration scheme. As can be seen from Figure 9: the original load peak-to-valley difference during the flood season is 44.898MW, and the load fluctuation variance is 304.09MW. 2After wind, solar and run-of-river small hydropower were connected to the grid, the peak-to-valley difference of load increased to 82.39MW, and the net load fluctuation variance increased to 574.2MW. 2 Through the smoothing control of pumped storage, the net load fluctuation is greatly reduced, the peak-to-valley difference is reduced to 30.23MW, and the load fluctuation variance is reduced to 325MW 2 Compared with the regulation effect in the flood season, the pumped storage is frequently regulated in the dry season, and the effect of stabilizing the fluctuation of clean energy access to the grid is more obvious. In summary, through the regulation of pumped storage, the load fluctuation after the clean energy access to the grid can be significantly suppressed in all scenarios.

[0250] In order to demonstrate the superiority of the improved NSGA-II algorithm in solving this optimization problem, the calculation results in the dry season scenario are compared with the simulation results of NSGA and NSGA-II. The Pareto frontiers obtained by each algorithm are as follows: Fig.10 As shown in the figure, the Pareto solution set obtained by the improved NSGA-II algorithm is more evenly distributed and has higher quality. Under the same comprehensive cost or load fluctuation variance index, the quality of the Pareto solution set obtained by the improved NSGA-II algorithm is relatively better.

[0251] Table 5 shows the spatial metric values ​​of the non-inferior solution set under each algorithm. Compared with other algorithms, the introduction of the normal distribution crossover operator can effectively enhance the algorithm's spatial search capability, and the spatial distribution of the Pareto frontier is more uniform. In addition, from the perspective of algorithm execution time, due to the introduction of the normal distribution crossover operator in the improved NSGA-II algorithm, its convergence speed is relatively faster. In summary, the solution results of the improved NSGA-II algorithm are better than those of other algorithms. Therefore, the improved NSGA-II algorithm can obtain better performance indicators.

[0252] Table 5. Spatial metrics and running time of Pareto frontier under each algorithm

[0253]

Claims

1. A method for configuring pumped storage capacity in a local power grid considering cost easing, characterized in that The following steps are involved: Step 1: Collect wind power, photovoltaic, run-of-river small hydropower output and load power curves under typical scenarios to generate typical electricity price scenarios; Step 2: Establish a multi-objective optimization configuration model. Take the maximum investment benefit of pumped storage as the goal, and construct the objective function 1 of the multi-objective optimization configuration model; take the minimum net load fluctuation variance as the goal, and construct the objective function 2 of the multi-objective optimization configuration model; Step 3: Set installed capacity constraints, operating power constraints, pumping / generation status and reservoir capacity regulation constraints as constraints for the multi-objective optimization configuration model; Step 4: Using the improved NSGA-II algorithm, introducing the adaptive scaling factor and the normal distribution crossover operator, the Pareto frontier of the multi-objective optimization configuration model is obtained; Step 5: Use the fuzzy membership function method combined with the entropy weight method to select compromise solutions under various scenarios, and then obtain the optimal storage capacity and installed capacity of pumped storage.

2. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 1, characterized in that: In the step 1, in the local power grid containing pumped storage power stations and renewable energy, the power grid gives priority to absorbing wind power, photovoltaic and run-of-river small hydropower clean energy, and the remaining load after supporting the load is the net load; the power change characteristics of wind power, photovoltaic, run-of-river small hydropower and regional power grid load in a typical week are collected, and wind power, photovoltaic, run-of-river small hydropower and load power curves are constructed in the flood season scenario and the dry season scenario.

3. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 2, characterized in that: In step 1, the value of the electricity price in each time period is represented by a normal distribution probability density function, as shown in formula (1); In formula (1): and They are the predicted values ​​of electricity price for electric quantity and electricity price for frequency regulation mileage at time t respectively; and are the expected values ​​of electricity price for electricity quantity and frequency regulation mileage price at time t respectively; and are the variances of electricity price for electric quantity and electricity price for frequency regulation mileage respectively; According to the electricity price prediction model of formula (1), the Monte Carlo algorithm is used to sample and generate scenarios, and then the k-means clustering algorithm is used to perform cluster reduction to generate a limited number of typical electricity price scenarios and the probability of each scenario; Assuming the number of typical scenes is M, the random sample feature value is the cluster center, and the process of scene reduction using the k-means clustering algorithm includes the following steps: 1) Based on the normal distribution model of electricity price prediction, M samples are randomly generated using the Monte Carlo method, and the sample data are normalized; 2) Randomly select N from the sample o The scene is used as the initial electricity price cluster center λ k ,k=1,2,…,N o ; 3) Calculate the Euclidean distance between the electricity price data in each remaining scenario and each cluster center; D ik =|λ i -l k |(2) Where: D ik represents the Euclidean distance; λ i represents the electricity price of scenario i, λ k represents the electricity price of scene k in the initial cluster center; 4) According to the Euclidean distance, each electricity price sample is clustered with its nearest cluster center, and then the mean of all sample points in each cluster is used as the new cluster center; In formula (3), N k and Ik are the amount of electricity price data of the kth cluster center and the set of its clusters; 5) Repeat steps 3) and 4) until the new cluster center is equal to the original cluster center or the Euclidean distance is less than the specified threshold, and the algorithm ends; 6) The obtained cluster center is the typical electricity price scenario obtained after reduction and denormalization, and the proportion of each type of scenario to the initial number of scenarios is the probability value of the typical scenario.

4. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 3 is characterized by: In the step 2, the constructed electricity price scenario is introduced into the objective function of the multi-objective optimization model; The first optimization goal is to maximize the investment benefit of pumped storage, which is the economic benefit after pumped storage operation minus its investment and construction cost; The objective function f1 is constructed by deducting the estimated investment income of the pumped storage power station from the construction cost, that is, the comprehensive cost is the lowest. The objective function is shown in formula (4): In formula (4): C PS is the investment and construction cost of pumped storage, and the investment and construction cost of pumped storage is C PS Includes: Investment cost C inv , Operation and maintenance cost C om , turbine replacement cost C re ; T pump is the whole life cycle of the unit; C cap C is the capacity-based electricity price leasing income; l is the income from the electricity market; C aux for ancillary services market revenue; In formula (5): C pc V is the unit price per cubic meter of upstream storage capacity; pcap is the upstream storage volume; C pp P is the unit price per kilowatt of turbine installed capacity; pcap is the installed capacity of the pumped storage unit; T a C is the project life; OM_pc is the unit maintenance cost of upstream storage capacity; C OM_pp is the unit operation and maintenance cost of installed capacity; r is the discount rate; C re_pp is the turbine replacement cost, including depreciation; T pump is the whole life cycle of the unit, N x is the number of replacements that occur within the life of the project; n is a natural year; The objective function f2 is constructed by minimizing the variance of residual load fluctuation by pumped storage, and its objective function f2 is shown in formula (9): In formula (9): T is the length of a day; is the net load power after pumped storage regulation at time t; In formula (10): is the unbalanced net load power of the system at time t; They are the output of load, wind power, photovoltaic power, and non-adjustable small hydropower at time t respectively; are the generating power and pumping power of the pumped storage at time t respectively.

5. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 4 is characterized by: In step 3, the constraints include: installed capacity constraints, upper and lower limits of operating power constraints, pumping / power generation state constraints, and reservoir capacity regulation constraints; 1) Installed capacity constraints: In formula (11): V p_pcapmax is the upper limit of upstream storage capacity; P p_capmax is the upper limit of the unit capacity; V pcap is the upstream storage volume; 2) Operating power upper and lower limit constraints: In formula (12): P pcap Assemble the capacity of the pumped storage unit; They are respectively the power generation power of pumped storage in the electric energy market, the power generation power of frequency regulation market, and the power generation power of standby market at time t; They are respectively the pumping power of the electric energy market and the pumping power of the frequency regulation market at time t; 3) Pumping / power generation state constraints: 4) Storage capacity adjustment constraints: In formula (14): V t is the storage capacity at time t; Q P (t) and Q T (t) represent the pumping flow and power generation flow at time t respectively; K t and K p are the flow rate power ratios under power generation and pumping conditions respectively; η wp is the pipeline efficiency; η P is the pump operating efficiency; η T is the operating efficiency of the generator set; ρ represents the water density; g is the standard acceleration of gravity; h is the design water head of the pumped storage unit; △t is the time interval; V(t+1) is the storage capacity at time (t+1).

6. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 5, characterized in that: In step 4, the adaptive scaling factor improvement method is as follows: In order to reduce the number of repeated individuals and increase the diversity of the population, the proportional factor in the selection strategy is improved. The rule is shown in formula (15): In formula (15): C m is the number of individuals obtained from the mth non-dominated layer of the selected population; N m is the number of individuals in the mth non-dominated layer; ξ m is the scale factor; D max is the number of non-dominated layers; z m 、x m is a variable parameter, and z m <x m ; k is the number of iterations; k max is the maximum number of iterations; The normal distribution crossover operator is as follows: Introducing the normal distribution crossover operator (NDX) in the crossover process can effectively enhance the algorithm's spatial search capability, further improve the convergence speed, and reduce the computational cost. Assuming that the parent population is P1 and P2, and the offspring population is Q1 and Q2, for individual i, the process of using NDX crossover to generate offspring is as follows: Generate a random number r∈(0,1], when r≤0.5: In formula (16): P 1,i and P 2,i Two parent populations randomly generated for individual i, Q 1,i and Q 2,i Respectively represent the parent population P of individual i 1,i and P 2,i The offspring population is generated by crossover from a normal distribution; When r>0.5: Where N(0,1) is a normally distributed random variable.

7. The method for configuring pumped storage capacity of a local power grid considering cost easing according to claim 6, characterized in that: In step 4, solving the multi-objective optimization configuration model includes the following steps: Step 4.1: Input the improved NSGA-Ⅱ parameters and model data; Step 4.2: Randomly generate the initial population P0; Step 4.3: According to the objective function formula (4) and formula (9), calculate the objective function fitness value and constraint violation value of each individual in the population; Step 4.4: Fast non-dominated sort; Step 4.5: Update the scale factor; Step 4.6: Pick N P / 2 dominant individuals as the parent population P k ; N P is the population number; Step 4.7: Improve the crossover operator, introduce adaptive scaling factor and normal distribution crossover operator; Step 4.8: Crossover and mutation to generate offspring population Q k ; Step 4.9: Implement the elite strategy to generate a new population P k ∪Q k ; Step 4.10: Calculate the individual fitness value and constraint violation value of the new population; Step 4.11: Determine the termination condition: If the number of iterations reaches the maximum evolutionary generation, proceed to step 4.12; otherwise, update the number of iterations k = k + 1 and return to step 4.4; Step 4.12: Output the Pareto non-inferior solution set; and select the compromise solution.

8. The method for configuring the pumped storage capacity of a local power grid considering cost dredging according to claim 1, characterized in that: In step 5, the entropy weight method uses information entropy to measure the differences of various evaluation indicators, and assigns higher weights to indicators with larger differences. The specific calculation process is as follows: S5.1: Calculate the ratio of the kth data of the ith indicator to the sum of all ith indicators The formula is as follows: In formula (18): is the probability of the objective function value of a solution in the probability space; S5.2: Calculate the entropy value e of the i-th indicator i : In formula (19), 1 / lnM is a constant related to the number of non-inferior solutions, so that e i ∈[0,1]; when the entropy value e i The larger the value is, the less data information the corresponding i-th indicator contains, and the smaller its contribution to the ranking of evaluation indicators is; conversely, the greater its contribution is. S5.3: Calculate the weight λ of each attribute i : In formula (20): 1-e i Represents the information deviation of the i-th indicator.

9. The method for configuring pumped storage capacity of a local power grid considering cost easing according to claim 8, characterized in that: The step 5 also includes an expert weighting method, which depends on the decision maker's preference, including the weight λ1 of objective function 1 and the weight λ2 of objective function 2; if the system requires better economy, increase the λ1 value; conversely, for systems with higher stability and peak-to-valley difference performance, increase the weight of λ1.

10. The method for configuring pumped storage capacity of a local power grid considering cost management according to claim 9, characterized in that: In step 5, the fuzzy membership function method is a method for selecting a compromise solution in the Pareto frontier, and the optimal storage capacity and installed capacity of the pumped storage are obtained through the compromise solution. The specific steps are as follows: Step 1: Record the maximum value of the i-th objective function in the Pareto front and minimum value Among them, the number of non-inferior solution sets is M, and the number of objective functions is N; Step 2: Use formula (21) to calculate the membership degree corresponding to the i-th objective function of the k-th solution in the set of M Pareto non-inferior solutions: In formula (21): is the value of the objective function i corresponding to the kth solution; Step 3: The optimal solution of the multi-objective problem is the non-dominated solution corresponding to the normalized value of the maximum membership degree; The u obtained in the actual calculation is k There may be more than one because the weight coefficients of the objectives are the same, and the objective values ​​of some solutions fall exactly on the upper and lower limits, making it difficult to distinguish the pros and cons of the solutions. To solve this problem, weight each objective value as shown in the following formula: In formula (22): i is the weight coefficient of objective function i, satisfying Weight coefficient λ i Subjectively assign weights based on decision makers’ preferences for each goal or expert advice; after correcting the weights, determine the maximum and only weighted normalization u k value, and then select the best decision solution.

Images