A water, wind and light storage capacity planning method considering high-dimensional uncertainty

Abstract

The application belongs to the field of storage capacity planning, and provides a water, wind and light storage capacity planning method considering high-dimensional uncertainty, comprising: time correlation model construction, space correlation model construction, high-dimensional uncertainty scenario set generation, water, wind and light storage capacity planning model construction, benefit matrix construction, multi-objective optimization function construction and Pareto frontier solution. The application generates a scenario set covering high-dimensional uncertainty through a transfer probability matrix C-VineCopula method, can comprehensively capture the time and space correlation and multi-dimensional random characteristics of natural conditions such as light intensity and wind power, introduces a utopia line optimization strategy to realize an ideal trade-off between economy and safety, improves the efficiency and quality of multi-objective optimization solution, and provides diversified trade-off decision support for the system.

Description

Technical Field

[0001] This invention relates to the field of energy storage capacity planning, and in particular to a method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties. Background Technology

[0002] With the continuous growth of global energy demand and the increasing prominence of environmental issues, clean and renewable energy has gradually become the mainstream direction of energy development, among which hydropower, wind power, and photovoltaics have received widespread attention. However, the output characteristics of renewable energy exhibit strong uncertainties, which can lead to fluctuations in grid frequency and voltage instability, thereby affecting the security of the power system. Therefore, it is crucial to rationally plan systems with a high proportion of renewable energy integration to improve the system's economic efficiency and reliability. Currently, a large amount of research has been conducted on the planning of systems with a high proportion of renewable energy integration. Existing technologies have utilized clustering and voltage fluctuation indicators to formulate energy storage system installation schemes within photovoltaic-energy storage systems, and employed cooperative game theory to determine the optimal storage capacity. By establishing an energy storage optimization model, the impact of temporal variations in photovoltaic power and load on the power grid was analyzed, and a capacity configuration and optimization method for energy storage systems under high photovoltaic penetration was proposed. An integrated demand response program was designed to explore the potential interaction capabilities of electricity, gas, heat, cooling, and flexible electric vehicle loads, and an optimized scheduling method for a wind power-photovoltaic-gas-electric vehicle community integrated energy system was proposed. By constructing a digital twin model of the integrated energy system, the predictive capabilities of the digital twin were used to improve coordination among various energy converters, thereby improving energy efficiency, reducing costs, and decreasing carbon emissions. A game theory-based system planning method was established, enabling the system to not only meet the demands of cooling, heating, and electricity loads but also achieve optimal system economics. While the above research has made some progress in system planning for high-proportion renewable energy integration, it has failed to fully consider the uncertainties of renewable energy. Existing technologies describe the uncertainty of wind and solar power output through the maximum uncertainty set, and propose an optimization scheduling method that considers uncertainty and equipment coupling. Considering both wind and solar power output and uncertainty, an interval linear programming method is used to handle uncertainty problems, and a two-level optimization configuration method is proposed. Considering the uncertainty of wind and solar power output and electrical coupling equipment, and taking into account economic costs and environmental emission reduction, an economic scheduling model for a comprehensive energy system is established. Considering the impact of photovoltaic power output uncertainty on system economy, a vector machine method is used to predict photovoltaic power output, and an economic operation strategy is proposed.

[0003] However, the aforementioned studies have not fully considered the inherent temporal correlation of various meteorological conditions with seasonal variations in systems with a high proportion of renewable energy integration, as well as the high-dimensional uncertainty brought about by the spatial correlation of meteorological conditions within the same region. Traditional empirical planning methods estimate equipment capacity based on past experience, which are simple to operate and have low initial costs, but lack consideration for uncertainty, easily leading to unreasonable capacity allocation and high long-term operating costs. Deterministic optimization planning methods are based on deterministic data and do not consider uncertainty, making calculations relatively simple and feasible when data is limited, but their practical adaptability is poor, unable to cope with fluctuations in wind and solar resources, and unable to balance economy and security. Planning methods that consider partial uncertainty only consider some uncertainty factors, with computational complexity and data requirements falling between the two. Although they have some adaptability, because they do not fully consider high-dimensional uncertainty, the planning is not accurate enough and cannot fully leverage the synergistic effects of the system. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a hydro-wind-solar-storage capacity planning method that considers high-dimensional uncertainty, thereby solving the problems of traditional methods not deeply handling high-dimensional dependencies, insufficient depth in characterizing complex dependencies and dynamic characteristics, lack of systematic scheduling optimization strategies, and neglect of multi-objective balance in optimization scheduling.

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

[0006] A method for planning hydro-wind-solar-storage capacity considering high-dimensional uncertainties includes:

[0007] Based on the fluctuations in monthly data, the historical data of water, wind and light are divided into several state intervals. A transition probability matrix is ​​constructed based on the transition frequency of variables in different state intervals in each month. All the transition probability matrices are integrated to obtain the time correlation model.

[0008] The marginal distribution of each variable in the historical water, wind, and light data was fitted using a nonparametric kernel density estimation method to obtain the cumulative distribution function;

[0009] Calculate the Kendall correlation coefficient for each variable in the historical water and landscape data, and select the variable with the largest Kendall correlation coefficient as the root node of the vine structure. Use a binary Copula function to describe the correlation between the root node and the remaining variables in the historical water and landscape data to construct the first layer of the vine structure. Recursively describe the interdependencies between the remaining variables layer by layer to obtain the multidimensional joint probability density function.

[0010] By integrating the cumulative distribution function, the multidimensional joint probability density function, and the hybrid Copula function, a spatial correlation model is obtained.

[0011] An initial scene set considering time correlation is generated based on the time correlation model and the spatial correlation model. The initial scene corresponding to the variable with the largest sum of Kendall correlation coefficients in the initial scene set is used to generate a first random variable that satisfies a uniform distribution through cumulative probability. The first random variable is used as the first sample point.

[0012] A second random variable and a third random variable that satisfy a uniform distribution are generated by cumulative probability. The second sample point is calculated based on the first sample point and the second random variable. The third sample point is calculated based on the second sample point and the third random variable.

[0013] The inverse transformation sampling method is used to map the first sample point, the second sample point, and the third sample point to the actual distribution to obtain a high-dimensional uncertainty scenario set.

[0014] A capacity planning model for hydropower, wind power, solar power, energy storage, and storage is constructed. The capacity planning model includes an upper-level capacity configuration model and a lower-level capacity configuration model. The upper-level capacity configuration model includes an upper-level objective function, equipment sub-models, and capacity constraints. The lower-level capacity configuration model includes a lower-level objective function, constraint conditions, and power balance constraints.

[0015] The upper-level objective function and the lower-level objective function are transformed into standard forms. A profit matrix is ​​constructed based on the transformed upper-level objective function and the lower-level objective function, and the profit matrix is ​​normalized.

[0016] The utopian line is extracted from the normalized payoff matrix, and the distance between the target point in the standardized space and the utopian line is calculated to obtain the utopian line distance. A multi-objective optimization function is then constructed based on the utopian line distance.

[0017] The multidimensional joint probability density function is optimally solved based on the high-dimensional uncertainty scenario set and the hydro-wind-solar-storage capacity planning model to obtain the Pareto front, and the Pareto front is then updated in the target system control strategy.

[0018] Preferably, the transition probability matrix is:

[0019]

[0020] in, P w Let s be the transition probability matrix; t+1 and s t Let f(i,j) represent the illumination state in month t+1 and month t, respectively; f(i,j) represents the frequency of transition from state i to state j; and θ is the total number of the state intervals.

[0021] Preferably, the Kendall correlation coefficient is calculated using the following formula:

[0022]

[0023] in, τ l,m The Kendall correlation coefficient is given; P(·) represents the probability density function; L represents the total number of variables in the historical water, wind, and light data; X l and X m These represent the l-th and m-th variables in the historical data of water, wind, and light, respectively.

[0024] Preferably, the formula for calculating the second sample point is:

[0025]

[0026] Where Y2 is the second random variable; Z1 is the first sample point; and Z2 is the second sample point.

[0027] Preferably, the upper-level objective function includes:

[0028]

[0029] as well as

[0030]

[0031] Where F represents the minimum total annual cost; This refers to the initial investment cost of the equipment. For the later operation and maintenance costs of the equipment; Revenue generated from selling electricity to the upper-level power grid; k is the scenario index; w k E represents the probability of scenario k; wi E pv and E eh These are the annual value coefficients for wind power, photovoltaic, and energy storage equipment, respectively; R wi R pv and R eh These are the unit capacity investment costs for each piece of equipment; and C represents the total investment capacity of each device in scenario k; op,wa C op,pv and C op,eh These are the unit maintenance costs for each piece of equipment; and These represent the power generation capacity of each device; and These are the charging and discharging power of the energy storage system; The unit electricity price at time t; The system sells electricity to the upper-level power grid.

[0032] Preferably, the device sub-model includes:

[0033]

[0034] as well as

[0035]

[0036] in, The power generation capacity of photovoltaics; η represents the power generation capacity of hydropower. pv For the efficiency of the photovoltaic panel; k pv The conversion factor of the photovoltaic panel; Solar irradiance; k pv Photovoltaic panel temperature coefficient; T t Let T be the ambient temperature at time t; ref The reference temperature for the photovoltaic panel; k wa This refers to the power generation coefficient of the hydropower station. For power generation water flow; This refers to the head height for power generation. It is runoff; S i,t-1 For water discharge; SOC t+1 and SOC t These correspond to the energy states at time t+1 and time t, respectively. These are the charging power and discharging power, respectively; η charge η discharge These are the charging coefficient and the discharging coefficient, respectively. These are the charging indicator and the discharging indicator, respectively.

[0037] Preferably, the payoff matrix is:

[0038]

[0039] Wherein, φ is the profit matrix; f1(x) and f2(x) represent the transformed upper-level objective function and the lower-level objective function, respectively; Let f1(x) be the decision variable corresponding to the optimal solution when only f1(x) is optimized. Let f2(x) be the decision variable corresponding to the optimal solution when only f2(x) is optimized.

[0040] Preferably, the multi-objective optimization function is:

[0041]

[0042] Where β = [β1, β2] T;0≤β1,β2≤1;β1+β2=1; β represents the coordinates of the target point; The normal unit vector representing the utopian line; is the normalized objective function vector; g(x) and h(x) are both constraints of the optimization problem.

[0043] Preferably, the lower-level objective function includes:

[0044] and

[0045]

[0046] in, The expected value of selling electricity to the upper-level power grid.

[0047] Preferably, the power balance constraint is:

[0048]

[0049] The present invention discloses the following technical effects:

[0050] This invention provides a method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainty. By generating a scene set encompassing high-dimensional uncertainty through the C-VineCopula method of transition probability matrix, it solves the problems of traditional methods not deeply handling high-dimensional dependencies and insufficient depth in characterizing complex dependencies and dynamic characteristics. It achieves the capture of the spatiotemporal correlation and multi-dimensional random characteristics of natural conditions such as light intensity and wind power. By introducing the Utopian line optimization strategy, it solves the problems of traditional methods lacking a systematic scheduling optimization strategy and ignoring the multi-objective balance in optimization scheduling, achieving an ideal trade-off between economic and safety objectives and diversified trade-off decision support. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A schematic diagram of the water, wind, solar, and energy storage capacity planning process considering high-dimensional uncertainties is provided for an embodiment of the present invention. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] The purpose of this invention is to provide a capacity planning method for hydropower, wind power, solar power, and energy storage that considers high-dimensional uncertainty, and to solve the problems of traditional methods that do not deeply handle high-dimensional dependencies, lack depth in characterizing complex dependencies and dynamic characteristics, lack systematic scheduling optimization strategies, and ignore multi-objective balance in optimization scheduling.

[0055] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0056] Figure 1 A schematic diagram of the hydro-wind-solar-storage capacity planning process considering high-dimensional uncertainties is provided for an embodiment of the present invention, as follows: Figure 1 As shown, this invention provides a method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties, comprising:

[0057] Step 100: Based on the monthly data fluctuations, divide the historical data of water, wind and light into several state intervals. Construct a transition probability matrix based on the transition frequency of variables in different state intervals in each month. Integrate all transition probability matrices to obtain the time correlation model.

[0058] Step 200: Use the nonparametric kernel density estimation method to fit the marginal distribution of each variable in the historical water, wind and light data to obtain the cumulative distribution function;

[0059] Step 300: Calculate the Kendall correlation coefficient of each variable in the historical data of water, scenery and light, and select the variable with the largest Kendall correlation coefficient as the root node of the vine structure. Use a binary Copula function to describe the correlation between the root node and the remaining variables in the historical data of water, scenery and light to construct the first layer of the vine structure. Recursively describe the interdependence between the remaining variables layer by layer to obtain the multidimensional joint probability density function.

[0060] Step 400: Integrate the cumulative distribution function, the multidimensional joint probability density function, and the hybrid Copula function to obtain the spatial correlation model;

[0061] Step 500: Generate an initial scene set considering time correlation based on the time correlation model and the spatial correlation model. Generate a first random variable that satisfies uniform distribution by using the cumulative probability of the initial scene corresponding to the variable with the largest sum of Kendall correlation coefficients in the initial scene set. Use the first random variable as the first sample point.

[0062] Step 600: Generate a second random variable and a third random variable that satisfy a uniform distribution using the cumulative probability; calculate the second sample point based on the first sample point and the second random variable; calculate the third sample point based on the second sample point and the third random variable.

[0063] Step 700: Use the inverse transformation sampling method to map the first sample point, the second sample point, and the third sample point to the actual distribution to obtain a high-dimensional uncertainty scenario set;

[0064] Step 800: Construct a hydro-wind-solar-storage capacity planning model; the hydro-wind-solar-storage capacity planning model includes: an upper-level capacity configuration model and a lower-level capacity configuration model; the upper-level capacity configuration model includes: an upper-level objective function, equipment sub-models, and capacity constraints; the lower-level capacity configuration model includes: a lower-level objective function, constraints, and power balance constraints;

[0065] Step 900: Transform the upper-level objective function and the lower-level objective function into standard form, construct the profit matrix based on the transformed upper-level objective function and lower-level objective function, and normalize the profit matrix;

[0066] Step 1000: Extract the Utopia line from the normalized payoff matrix, calculate the distance between the target point and the Utopia line in the standardized space, obtain the Utopia line distance, and construct a multi-objective optimization function based on the Utopia line distance.

[0067] Step 1100: Based on the high-dimensional uncertainty scenario set and the hydro-wind-solar-storage capacity planning model, the multidimensional joint probability density function is optimally solved to obtain the Pareto front, and the Pareto front is updated into the target system control strategy.

[0068] Specifically, the transition probability matrix is:

[0069]

[0070] in, P w The transition probability matrix; s t+1 and s t Let f(i,j) represent the illumination state in month t+1 and month t, respectively; f(i,j) represents the frequency of transition from state i to state j; and θ is the total number of state intervals.

[0071] Furthermore, the formula for calculating the Kendall correlation coefficient is as follows:

[0072]

[0073] in, τ l,m Kendall correlation coefficient; P(·) represents the probability density function; L represents the total number of variables in the historical data of water, scenery, and light; X l and X m Let l and m represent the l-th and m-th variables in the historical data of water, scenery, and landscape, respectively.

[0074] Specifically, the formula for calculating the second sample point is:

[0075]

[0076] Where Y2 is the second random variable; Z1 is the first sample point; and Z2 is the second sample point.

[0077] Furthermore, the upper-level objective function includes:

[0078]

[0079] as well as

[0080]

[0081] Where F represents the minimum total annual cost; This refers to the initial investment cost of the equipment; For the later operation and maintenance costs of the equipment; Revenue generated from selling electricity to the upper-level power grid; k is the scenario index; w k E represents the probability of scenario k; wi E pv and E eh These are the annual value coefficients for wind power, photovoltaic, and energy storage equipment, respectively; R wi R pv and R eh These are the unit capacity investment costs for each piece of equipment; and C represents the total investment capacity of each device in scenario k; op,wa C op,pv and C op,eh These are the unit maintenance costs for each piece of equipment; and These represent the power generation capacity of each device; and These are the charging and discharging power of the energy storage system; The unit electricity price at time t; The system sells electricity to the upper-level power grid.

[0082] Specifically, the equipment sub-model includes:

[0083]

[0084] as well as

[0085]

[0086] in, The power generation capacity of photovoltaics; η represents the power generation capacity of hydropower. pv For the efficiency of the photovoltaic panel; k pv The conversion factor of the photovoltaic panel; Solar irradiance; k pv Photovoltaic panel temperature coefficient; T t Let T be the ambient temperature at time t; ref The reference temperature for the photovoltaic panel; k wa This refers to the power generation coefficient of the hydropower station. For power generation water flow; This refers to the head height for power generation. It is runoff; S i,t-1 For water discharge; SOC t+1 and SOC t These correspond to the energy states at time t+1 and time t, respectively. These are the charging power and discharging power, respectively; η charge η discharge These are the charging coefficient and the discharging coefficient, respectively. These are the charging indicator and the discharging indicator, respectively.

[0087] Furthermore, the payoff matrix is ​​as follows:

[0088]

[0089] Where φ is the payoff matrix; f1(x) and f2(x) represent the transformed upper-level objective function and lower-level objective function, respectively; Let f1(x) be the decision variable corresponding to the optimal solution when only f1(x) is optimized. Let f2(x) be the decision variable corresponding to the optimal solution when only f2(x) is optimized.

[0090] Specifically, the multi-objective optimization function is:

[0091]

[0092] Where β = [β1, β2] T ;0≤β1,β2≤1;β1+β2=1; β represents the coordinates of the target point; The normal unit vector representing the utopian line; is the normalized objective function vector; g(x) and h(x) are both constraints of the optimization problem.

[0093] Furthermore, the lower-level objective function includes:

[0094] and

[0095]

[0096] in, The expected value of selling electricity to the upper-level power grid.

[0097] Preferably, the power balance constraint is:

[0098]

[0099] Specifically, in terms of temporal correlation modeling, the computer equipment uses light intensity as an example (other natural conditions are similar). It divides state intervals based on data fluctuations in different months, statistically analyzes the transition frequency of variables between different states in each month to construct a transition probability matrix, and then calculates the transition frequency matrix. Next, in spatial correlation modeling, the computer uses a C-Vine Copula-based model. It first fits the marginal distributions of each variable to obtain a cumulative distribution function, calculates the Kendall correlation coefficient between variables, selects the variable with the highest correlation as the root node of the vine structure, constructs the first layer of the vine structure using a binary Copula function, and then recursively describes the dependencies of the remaining variables layer by layer, using a mixed Copula function to estimate its weights and dependency parameters. Then, in the scene generation stage, the computer first generates an initial scene set considering temporal correlation, determines the state and light intensity of each month using random numbers, iterates multiple times to obtain the initial scene set, then selects the variable with the largest absolute sum of correlation coefficients as the starting point, uses cumulative probability, random numbers, and related calculations to obtain uniformly distributed random variables, obtains sample points through specific calculations, and then uses an inverse transformation sampling method to generate the final scene set. In the hydropower, wind power, hydropower, and energy storage capacity planning model, the upper-level capacity configuration model's computer optimization objective is to minimize the total annual cost. This involves calculations of various equipment costs and revenues, and is constrained by equipment models (including rules related to the power generation and charging / discharging power of photovoltaic, wind power, hydropower, and energy storage systems) and capacity constraints (the capacity of each piece of equipment is limited by site factors). The lower-level collaborative optimization model takes a typical scenario as input. Based on the capacity determined in the upper level, the computer adjusts the reservoir water level to ensure optimal system economy and safety, constrained by equipment power generation power (each piece of equipment has an upper limit on power generation) and power balance constraints (total power generation meets power consumption). Finally, when solving the multi-objective optimization problem, the computer first transforms the bi-objective optimization problem into a standard form, constructs a revenue matrix to describe the optimal solution, normalizes the objective function and revenue matrix, connects anchor points to form a utopian line, introduces the distance between points and the utopian line to transform the multi-objective problem, and obtains non-dominated solutions through optimization to form the Pareto front to balance system economy and safety.

[0100] Furthermore, time-related modeling is employed. Since the modeling methods for solar irradiance, wind, temperature, and runoff are similar, solar irradiance is used as an example. Based on the data fluctuations across different months, the historical photovoltaic data is divided into several state intervals. Each month's variables can be divided into θ states, resulting in a total of θ×12 state intervals. The transition frequency of variables between different states for each month is statistically analyzed, and a transition probability matrix P is constructed. w :

[0101]

[0102] In this matrix, each row is summed to 1. The transition frequency matrix Q can be calculated from the transition probability matrix. w Qw Let be an s×s matrix, where the elements are...

[0103] Specifically, spatial correlation modeling is employed. To accurately capture the spatial correlation within the hydro-wind-solar-storage system, a C-Vine Copula-based modeling approach is used. The C-Vine Copula model effectively handles nonlinear dependencies between multidimensional variables. For each variable X... l First, a nonparametric kernel density estimation method needs to be used to fit the marginal distribution of each variable to obtain the cumulative distribution function F(X) of each variable. l ), where l∈{1,2,...,L}, can provide input for the subsequent Copula model. Secondly, to determine the correlation between different variables, the Kendall correlation coefficient between the variables needs to be calculated. For each pair of variables X... l and X m Its Kendall correlation coefficient τ l,m The calculation formula is:

[0104]

[0105] Based on the calculated Kendall correlation coefficient, the variable with the highest correlation to other variables is selected as the root node of the vine structure, denoted as X1. The first layer of the vine structure is then constructed by describing the correlation between the root node and other variables using a binary Copula function. After constructing the first layer, the dependencies between the remaining variables are recursively described layer by layer. This hierarchical approach allows for the recursive description of complex dependencies between multidimensional variables. The multidimensional joint probability density function of the vine structure is f(X1,X2,...,X...). L It can be decomposed using the following formula:

[0106]

[0107] Where cm, m+1|1,...,m-1 represent the variables X given the first m-1 variables. m and X m+1 Copula function between, F(X) m |X1,...,X m-1 Given X1,...,X m-1 Below, variable X m The distribution function is given by the following formula:

[0108]

[0109] Among them, Y m Let m be the m-th element of vector Y; Represents vector Y without Ym The resulting vector. Since a single Copula function is insufficient to accurately describe the dependencies between variables, a hybrid Copula function is used:

[0110]

[0111] in, It is the o-th Copula function, λ o These are the corresponding weights, and These are the dependent parameters of the Copula function. The expectation-maximization algorithm is used to adjust the weight parameters λ. o and dependent parameters Make an estimate.

[0112] Preferably, scene generation. To generate a high-dimensional uncertain scene that considers spatiotemporal correlation, an initial scene set considering temporal correlation must first be generated. Assume the current month's illumination state is... The intensity of light is P t v Generate a random number a that follows a uniform distribution. t ∈[0,1], determine the current month's cumulative frequency matrix. The data in the row and a t The size of the light source is used to determine the illumination status for the following month. t+1 After determining the state, generate a random number b. t ∈[0,1], and assume state a t+1 The corresponding light intensity range is [β] min ,β max ], then β t+1 =β min +b t (β max -β min Repeat the above steps until t = 12, thus completing the generation of one scene sequence. Loop B times to obtain an initial scene set S containing B scenes:

[0113]

[0114] Where N is the length of the light intensity sequence.

[0115] Furthermore, the process of generating high-dimensional uncertain scenarios considering spatiotemporal correlation is as follows: First, calculate the Kendall correlation coefficients of each variable with other variables, and select the variable with the largest absolute value of the sum of correlation coefficients as the starting point for scenario generation. Generate a uniformly distributed random variable Y1, Y1∈[0,1], corresponding to its initial scenario using cumulative probability. Let the three sets of variables to be determined be Z1, Z2, and Z3, and let Z1 = Y1. Generate two uniformly distributed random numbers Y2 and Y3:

[0116]

[0117] C2 and Z1 are known quantities, and the sample points for Z2 are obtained from them. Similarly, Z3 is obtained. After obtaining these three sets of sample points Z1, Z2 and Z3, the inverse transformation sampling method is used to map these uniformly distributed sample points to the actual distribution of each variable, generating the final scene set containing each natural condition.

[0118] Specifically, a capacity planning model for hydropower, wind power, solar power, and energy storage is proposed. Considering the uncertainties of renewable energy, the model plans to configure wind power, solar power, and energy storage systems for existing hydropower stations, and proposes a two-layer optimization model for capacity planning. The upper-layer model uses optimal economic efficiency as the objective function and determines the optimal capacity of wind power, solar power, and energy storage systems based on a set of typical scenarios. The lower-layer model, based on the optimal capacity determined by the upper layer, performs coordinated optimization scheduling with the objectives of optimal economic efficiency and safety.

[0119] Furthermore, in the upper-level capacity configuration model, the objective function is to minimize the total annual cost F, which includes the initial investment cost of the equipment. Post-operation and maintenance costs At the same time, the revenue generated from the system selling electricity to the upper-level power grid must also be deducted. The objective function is as follows:

[0120]

[0121] Constraints:

[0122] 1) Equipment Model:

[0123] Photovoltaic power generation It is mainly affected by solar radiation intensity and ambient temperature, and the specific formula is as follows:

[0124]

[0125] Wind power generation capacity P k,t wi It is mainly affected by wind speed, and the specific formula is as follows:

[0126]

[0127] Among them, v k,t V represents wind speed. c Cut-in wind speed; V f To cut off the wind speed; V r Rated wind speed; C wi ρ is the coefficient of performance of the fan; A is the air density; ρ is the air density. wi The area swept by the rotor;

[0128] The power generation capacity of hydropower depends primarily on the water flow and the water head, as shown in the following formula:

[0129]

[0130] The charging and discharging behavior of a storage system must follow the law of conservation of energy. The energy state of the stored energy is a dynamic evolution process, influenced by charging power and discharging power. The formula is as follows:

[0131]

[0132] When charging When discharging,

[0133] 2) Capacity constraints:

[0134] The decision variables for upper-level optimization are the capacities of each piece of equipment. Due to limitations such as site conditions, the following inequalities must be satisfied:

[0135]

[0136] in, and These are the upper limits for the configuration capacity of wind power, photovoltaic power, and energy storage, respectively.

[0137] Specifically, the objective function of the lower-level collaborative optimization model is:

[0138] The lower-level model takes typical water, wind, and light scenarios as input, and based on the optimal capacity of each device determined by the upper-level capacity configuration model, it ensures the optimal economy and safety of the system by adjusting the reservoir water level.

[0139]

[0140] Constraints: To ensure safe operation of the equipment, the power generation capacity of each device must meet the following constraints:

[0141]

[0142] in, and These are the upper limits for wind power, hydropower, photovoltaic power, and energy storage charging and discharging power, respectively.

[0143] Power balance constraint: The total power generation of the system at any given time must meet the power consumption at that time. The specific constraints are as follows:

[0144]

[0145] Furthermore, a multi-objective optimization problem-solving method is employed. A multi-objective optimization model is used to balance the economics and safety of the hydro-wind-solar-storage system. To achieve this, the bi-objective optimization problem is first transformed into a standard form:

[0146] min{f1(x),f2(x)},

[0147] st.g(x)≤0,h(x)=0,x∈R

[0148] Here, f1(x) and f2(x) represent the economic objective and the safety objective, respectively, which need to be optimized simultaneously. The constraints g(x)≤0 and h(x)=0 define the solution space R.

[0149] To analyze the trade-offs between objective functions, a payoff matrix needs to be constructed to describe the optimal solution under different optimization objectives. The payoff matrix φ is defined as follows:

[0150]

[0151] To eliminate scale differences between different objectives, the objective function and the payoff matrix need to be normalized. The normalization formula is as follows:

[0152]

[0153] The normalized payoff matrix can be represented as:

[0154]

[0155] in, and Let P be the anchor point obtained in the payoff matrix. Connecting these two anchor points forms the Utopian line. This line represents the ideal trade-off between the two objective functions. To measure the quality of the solution, we introduce the distance D between the point P(β1,β2) in the normalized space and the Utopian line, i.e., the normal vector perpendicular to the Utopian line drawn through point P. Therefore, the multi-objective problem can be transformed into the following form:

[0156] max D

[0157]

[0158] {x∈R|g(x)≤0,h(x=0}

[0159] Through different The optimization is performed under the combination to obtain multiple different non-dominated solutions, and these solutions are used to form the approximate Pareto front.

[0160] The beneficial effects of this invention are as follows:

[0161] This invention generates a scene set encompassing high-dimensional uncertainty through the C-VineCopula method of transition probability matrix, which can comprehensively capture the spatiotemporal correlation and multidimensional random characteristics of natural conditions such as light intensity and wind force. By introducing the Utopian line optimization strategy, an ideal trade-off is achieved between economic and safety objectives, improving the efficiency and quality of multi-objective optimization solutions and providing diversified trade-off decision support for the system.

[0162] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0163] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties, characterized in that, include: Based on the fluctuations in monthly data, the historical data of water, wind and light are divided into several state intervals. A transition probability matrix is ​​constructed based on the transition frequency of variables in different state intervals in each month. All the transition probability matrices are integrated to obtain the time correlation model. The marginal distribution of each variable in the historical water, wind, and light data was fitted using a nonparametric kernel density estimation method to obtain the cumulative distribution function; Calculate the Kendall correlation coefficient of each variable in the historical water and scenery data, and select the variable with the largest Kendall correlation coefficient as the root node of the vine structure. Use a binary Copula function to describe the correlation between the root node and the remaining variables in the historical water and scenery data to construct the first layer of the vine structure. Recursively describe the interdependencies between the remaining variables layer by layer to obtain the multidimensional joint probability density function. By integrating the cumulative distribution function, the multidimensional joint probability density function, and the hybrid Copula function, a spatial correlation model is obtained. An initial scene set considering time correlation is generated based on the time correlation model and the spatial correlation model. The initial scene corresponding to the variable with the largest sum of Kendall correlation coefficients in the initial scene set is used to generate a first random variable that satisfies a uniform distribution through cumulative probability. The first random variable is used as the first sample point. A second random variable and a third random variable that satisfy a uniform distribution are generated by cumulative probability. The second sample point is calculated based on the first sample point and the second random variable. The third sample point is calculated based on the second sample point and the third random variable. The inverse transformation sampling method is used to map the first sample point, the second sample point, and the third sample point to the actual distribution to obtain a high-dimensional uncertainty scenario set. Construct a planning model for water, wind, solar, and energy storage capacity; The hydro-wind-solar-storage capacity planning model includes: an upper-level capacity configuration model and a lower-level capacity configuration model; the upper-level capacity configuration model includes: an upper-level objective function, equipment sub-models, and capacity constraints; the lower-level capacity configuration model includes: a lower-level objective function, constraint conditions, and power balance constraints. The upper-level objective function and the lower-level objective function are transformed into standard forms. A profit matrix is ​​constructed based on the transformed upper-level objective function and the lower-level objective function, and the profit matrix is ​​normalized. The utopian line is extracted from the normalized payoff matrix, and the distance between the target point in the standardized space and the utopian line is calculated to obtain the utopian line distance. A multi-objective optimization function is then constructed based on the utopian line distance. The multidimensional joint probability density function is optimally solved based on the high-dimensional uncertainty scenario set and the water-wind-solar-storage capacity planning model to obtain the Pareto front, and the Pareto front is then updated in the target system control strategy. The transition probability matrix is: ； in, ; The transition probability matrix is... and They represent and The state of light on the moon; Representing state Transition to state The frequency of; The total number of the state intervals; The profit matrix is ​​as follows: ； in, The aforementioned profit matrix; and These represent the transformed upper-level objective function and the lower-level objective function, respectively. For optimization only The decision variables corresponding to the optimal solution at that time; For optimization only The decision variables corresponding to the optimal solution at that time; The multi-objective optimization function is: ； in, ; ; ; ; ; ; Represents the coordinates of the target point; The normal unit vector representing the utopian line; This is the normalized objective function vector; and All of these are constraints for optimization problems; The hybrid Copula function is formed by weighted superposition of multiple Copula functions according to weight parameters, and the weight parameters and dependency parameters are estimated using the expectation-maximization algorithm. When generating an initial scene set considering time correlation, a first random number following a uniform distribution between zero and one is generated for the current month's illumination state. The first random number is compared with the corresponding row data of the current month's cumulative frequency matrix to determine the illumination state of the next month. Then, a second random number following a uniform distribution between zero and one is generated. Within the illumination intensity range corresponding to the determined illumination state, the illumination intensity of the next month is determined by adding the lower limit of illumination intensity to the product of the second random number and the difference between the upper and lower limits of illumination intensity. This process is repeated until the sequence of illumination states and intensities for twelve months is completed, and the process is repeated a preset number of times to obtain the initial scene set. When solving the multi-objective optimization problem, optimization is performed under different combinations of unit vectors normal to the Utopian line to obtain multiple different non-dominated solutions, and the non-dominated solutions form an approximating Pareto front.

2. The method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties according to claim 1, characterized in that, The formula for calculating the Kendall correlation coefficient is as follows: ； in, ; The Kendall correlation coefficient is mentioned. Represents the probability density function; This represents the total number of variables in the historical data on water, scenery, and light. and These respectively represent the first in the historical data of water, wind, and light. and the One variable.

3. The method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties according to claim 1, characterized in that, The formula for calculating the second sample point is: ； in, Let it be the second random variable; This refers to the first sample point; This is the second sample point.

4. The method for planning hydro-wind-solar-storage capacity considering high-dimensional uncertainty according to claim 1, characterized in that, The upper-level objective function includes: 、 、 as well as ； in, To minimize the total annual cost; This refers to the initial investment cost of the equipment; For the later operation and maintenance costs of the equipment; Revenue generated from selling electricity to the upper-level power grid; For scene indexing; For the scene The probability of; , and These are the annual value coefficients for wind power, photovoltaic power, and energy storage equipment, respectively. , and These are the unit capacity investment costs for each piece of equipment; , and Scenes Total investment capacity of all equipment in the project; , and These are the unit maintenance costs for each piece of equipment; , , and These represent the power generation capacity of each device; and These are the charging and discharging power of the energy storage system; for Electricity price per unit time; The system sells electricity to the upper-level power grid.

5. The method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties according to claim 1, characterized in that, The device sub-model includes: 、 、 as well as ； in, The power generation capacity of photovoltaics; The generating capacity of hydropower; For the efficiency of photovoltaic panels; The conversion factor of the photovoltaic panel; Solar irradiance; Temperature coefficient of photovoltaic panels; for Ambient temperature at all times; This is the reference temperature for the photovoltaic panel. This refers to the power generation coefficient of the hydropower station. For power generation water flow; This refers to the head height for power generation. It is runoff; This refers to the amount of water discarded. and Corresponding to Time and Energy state at any given moment; , These are charging power and discharging power, respectively. , These are the charging coefficient and the discharging coefficient, respectively. , These are the charging indicator and the discharging indicator, respectively.

6. The method for planning hydropower, wind power, solar power, and energy storage capacity considering high-dimensional uncertainties according to claim 1, characterized in that, The lower-level objective function includes: and ； in, The expected value of selling electricity to the upper-level power grid.

7. A method for planning hydro-wind-solar-storage capacity considering high-dimensional uncertainty according to any one of claims 4 and 5, characterized in that, The power balance constraint is: 。

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