A Joint Scheduling Method for Water, Wind and Solar Power Based on Non-Stationary Uncertainty Modeling

Abstract

A joint scheduling method for hydro-wind-solar hybrid energy systems, based on non-stationary uncertainty modeling, is proposed, belonging to the field of long-term optimal scheduling of hydro-wind-solar hybrid energy systems. First, basic data required for long-term scheduling of hydro-wind-solar hybrid systems and uncertainty modeling of renewable energy are collected. Second, the climate factors with the most significant impact on wind and solar power output deviation sequences are screened, and a non-stationary marginal distribution probability model is constructed. Multiple distribution models are built based on time-varying Copula functions, and the optimal multivariate non-stationary joint probability model is evaluated. Third, scenarios of wind and solar power output deviation are generated and reduced to obtain typical wind and solar power output deviation scenarios. Finally, a joint long-term optimal scheduling model for hydro-wind-solar hybrid systems is constructed, and its solution yields joint scheduling strategies for hydro-wind-solar systems under different scenarios. This invention can characterize the non-stationary characteristics of wind and solar power output uncertainty under climate-driven conditions, improve the reliability and economy of long-term scheduling decisions for hydro-wind-solar systems, and has good engineering application value.

Description

Technical Field

[0001] This invention belongs to the field of long-term optimization scheduling of hydro-wind-solar hybrid energy systems, and relates to a joint scheduling method of hydro-wind-solar based on non-stationary uncertainty modeling. Background Technology

[0002] With the rapid growth of installed capacity for wind and solar power, the proportion of renewable energy in the power system is constantly increasing. In regions rich in hydropower resources, such as Southwest China, integrated hydro-wind-solar energy systems have gradually formed, with cascade hydropower as the core and wind and solar power developing in synergy. These systems utilize the regulation capabilities of hydropower units to mitigate the volatility of wind and solar power generation, achieving multi-energy complementary operation, which is of great significance for improving the absorption capacity of renewable energy and promoting the low-carbon transformation of the power system. However, the output of wind and solar power is significantly affected by meteorological conditions. Their randomness and volatility mean that hydro-wind-solar systems face complex uncertainties in long-term operation. Especially under the background of climate change, wind speed, solar radiation, and hydrological processes exhibit obvious time-varying and non-stationary characteristics, thus increasing the difficulty of long-term system scheduling decisions.

[0003] Currently, methods for quantifying the uncertainty of renewable energy mainly include parametric probability models, nonparametric probability density estimation methods, and multivariate joint probability modeling methods. Some studies describe the randomness by assuming that wind power or photovoltaic prediction deviations follow a specific probability distribution, while others use methods such as kernel density estimation to characterize uncertainty features, and utilize methods such as Copula functions to describe the correlation between wind power, photovoltaics, and other energy sources. Chinese invention patent CN120494448A further proposes an optimization method for long-term complementary scheduling rules of cascade hydro-wind-solar systems under multiple uncertainties. By constructing a multiple uncertainty quantification method based on Markov chains and ARMA models, and combining a long-term scheduling model with the SDDP algorithm, the optimization solution of long-term scheduling rules for cascade hydro-wind-solar systems is realized. The above methods have improved the level of uncertainty analysis and scheduling optimization of hydro-wind-solar systems to a certain extent, but their characterization of renewable energy uncertainty is still mainly based on traditional stationary stochastic processes, focusing more on the construction and solution of scheduling rules, and has not fully considered the non-stationarity of the probability distribution, fluctuation characteristics, and dynamic evolution of wind power and photovoltaic output over time under the background of climate change. In fact, during long-term planning and scheduling, there is a significant coupling relationship between wind power, photovoltaic power, and hydropower. Their uncertainty manifests not only as univariate fluctuations but also as dynamic changes in multivariate correlation structures. If stationary models based on historical statistical patterns are still used, it will be difficult to accurately reflect the uncertainties under future long-term operating conditions, thus affecting the rationality and reliability of reservoir regulation and joint scheduling of water, wind, and solar power.

[0004] Therefore, it is necessary to construct an uncertainty quantification method that can describe the non-stationary characteristics of multi-energy output and its related structural evolution, and integrate it into the long-term optimization scheduling framework of hydro-wind-solar systems to improve the reliability and adaptability of system operation decisions. Summary of the Invention

[0005] To address the problems of existing technologies, this invention provides a joint scheduling method for hydropower, wind power, and solar power based on non-stationary uncertainty modeling. This method considers climate-driven non-stationary uncertainties to characterize the time-varying uncertainty characteristics of wind and solar power output under climate change conditions, and achieves coordinated scheduling of hydropower, wind power, and solar power systems. This invention constructs an uncertainty quantification model that describes the multivariate non-stationary joint probability characteristics of wind and solar power output, and combines it with a joint scheduling model for hydropower, wind power, and solar power. This achieves a unified description of uncertainty propagation and coordinated regulation during the long-term operation of multi-energy systems, thereby improving the reliability and stability of long-term scheduling decisions for hydropower, wind power, and solar power systems. The invention provides a long-term optimized scheduling method for hydropower, wind power, and solar power considering climate-driven non-stationary uncertainties, constructs a multivariate non-stationary joint probability uncertainty modeling method, and establishes a long-term optimized scheduling model for hydropower, wind power, and solar power based on scenario sets. By jointly modeling the uncertainties of wind and solar power output and generating representative random scenarios, the optimal scheduling strategy for hydropower, wind power, and solar power systems under long-term operating conditions is obtained, achieving coordinated operation of multi-energy systems in complex and uncertain environments. This method can effectively reflect the time-varying patterns of the statistical characteristics of renewable energy output, enhance the adaptability of hydro-wind-solar systems to the impact of climate change, and improve the economic efficiency and reliability of system operation.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A joint scheduling method for hydropower, wind power, and solar power based on non-stationary uncertainty modeling is proposed. This method constructs a multivariate non-stationary joint probability model to quantitatively characterize the uncertainty of wind and solar power output, and combines this model with a scenario generation method and a joint optimization scheduling model for hydropower, wind power, and solar power to achieve long-term scheduling decisions under complex and uncertain environments. The method includes the following steps:

[0008] Step 1: Collect the basic data required for long-term scheduling of water, wind and solar power and uncertainty modeling of renewable energy.

[0009] The basic data mainly includes hydropower inflow observation data, spatial information of wind farms and photovoltaic power stations, wind power and photovoltaic power output forecast and measured data, local meteorological data, and large-scale climate indices.

[0010] The hydropower inflow observation data are used to characterize the inflow process of the cascade hydropower system and support the construction of a long-term joint scheduling model for hydropower, wind power, and solar power. The spatial information of wind farms and photovoltaic power stations is used for the spatial aggregation of regional wind and solar power stations. The predicted and measured output data of wind and solar power are used to construct a wind and solar output deviation sequence to express the uncertainty of wind and solar output. The local meteorological data and large-scale climate indices will be introduced as covariates into a multivariate non-stationary joint probability model to characterize the dynamic evolution of renewable energy uncertainty under the background of climate change.

[0011] Step 2: Construct a multivariate non-stationary joint probability model for the wind and solar power output deviation sequence. Details are as follows:

[0012] Step 2.1: Construction of wind and solar power output deviation sequence and correlation analysis with meteorological factors and atmospheric circulation index.

[0013] Based on spatial information of wind farms and photovoltaic power plants, representative wind and solar power plants were obtained through K-means clustering. The predicted deviation sequences of wind and solar power output at these representative plants were then extracted, referred to as the wind-solar power output deviation sequences, to characterize the uncertainty of renewable energy generation. After obtaining the wind-solar power output deviation sequences, Kendall correlation analysis was performed between these sequences and meteorological factors and atmospheric circulation indices to identify the climatic factors with the most significant impact on the wind-solar power output deviation sequences.

[0014] Furthermore, the statistical significance between variables was determined by calculating the p-value of the Kendall significance test. When the p-value was less than 0.05, the correlation was considered significant at the 95% confidence level, and the climate factors with the most significant impact on the wind and solar power output deviation sequence were selected accordingly.

[0015] Step 2.2: Constructing a non-stationary marginal distribution probability model. To describe the non-stationary characteristics of climate-driven renewable energy output uncertainty, this invention designs a Generalized Additive Models for Location, Scale and Shape (GAMLSS), or GAMLSS model for short. The GAMLSS model is used to model the wind and solar power output deviation sequences separately, obtaining the optimal non-stationary marginal distribution probability model. Specifically:

[0016] In the GAMLSS model, it is assumed that It follows a parameterized distribution with time-varying parameters. :

[0017] (1)

[0018] in, This indicates the monthly-scale prediction bias of wind and solar power output at time t; This represents the positional parameters that change over time. A scale parameter that represents how it changes over time; This represents the shape parameter as it changes over time; the superscript k indicates the sequence of wind and solar power output deviations. w represents the wind power output deviation, and p represents the photovoltaic power output deviation.

[0019] Furthermore, let the set of candidate covariates for the wind and solar power output deviation sequence at time t be . The candidate covariates mainly include local meteorological data and large-scale climate indices. The location parameters, scale parameters, and shape parameters are then linked to the candidate covariates through connection functions, the general expressions of which are:

[0020] (2)

[0021] (3)

[0022] (4)

[0023] in, , and These represent the connection functions for position parameters, scale parameters, and shape parameters, respectively. Let i represent the i-th candidate covariate, i = 1, 2, ..., M, where M represents the total number of candidate covariates; This is the intercept term for the position parameters; The intercept term is the scale parameter; The intercept term of the shape parameter; These are the regression coefficients of candidate covariates on the location parameters; The regression coefficients of candidate covariates on the scaling parameter; The regression coefficients of the candidate covariates on the shape parameters.

[0024] To further quantify the non-stationary characteristics of climate-driven renewable energy output uncertainty, this invention constructs multiple candidate marginal distribution models based on the GAMLSS model. By allowing different combinations of distribution parameters to vary with covariates (as shown in Equations 2, 3, and 4), fully stationary, partially non-stationary, or fully non-stationary models are formed. A fully stationary model refers to a model where the location, scale, and shape parameters do not change with the covariates; that is, its parameters are determined only by the intercept term and do not include covariate terms. , and All are 0. The partially non-stationary model refers to a model in which at least one of the position, scale, and shape parameters varies with the covariates, i.e. , and At least one of the parameters is not zero, while the remaining parameters are determined by the intercept term. The completely non-stationary model refers to a model where the position parameter, scale parameter, and shape parameter all change with the covariates, i.e. , and All values ​​are non-zero. The Schwarz Bayesian (SBC) criterion is used to evaluate various candidate marginal distribution models constructed based on the GAMLSS model, and the optimal non-stationary marginal distribution probability model is obtained.

[0025] Step 2.3: Construct a multivariate non-stationary joint probability model of the wind and solar power output deviation sequence.

[0026] After obtaining the optimal non-stationary marginal distribution probability model of the wind and solar power output deviation sequence through the GAMLSS model in step 2.2, the corresponding cumulative distribution functions are denoted as follows: and By calculating its cumulative probability value through probability integral transformation, we obtain:

[0027] (5)

[0028] in, The cumulative distribution function represents the optimal non-stationary marginal distribution model of the wind power output deviation sequence; The cumulative distribution function represents the optimal non-stationary marginal distribution model of the photovoltaic power output deviation sequence; , representing the cumulative distribution probability value of the optimal non-stationary marginal distribution model of the wind power output deviation sequence; , representing the cumulative distribution probability value of the optimal non-stationary marginal distribution model of the photovoltaic power output deviation sequence; This represents the wind power output deviation sequence; Represents the photovoltaic power output deviation sequence;

[0029] According to Sklar's theorem, the joint distribution of wind and solar power output deviation is expressed as:

[0030] (6)

[0031] in, This represents the wind power output deviation at time t. and photovoltaic output deviation The joint cumulative distribution function of , that is, the joint probability that both do not exceed a given value; This represents a time-varying Copula function used to describe the correlation structure between uncertainties in wind power and photovoltaics. The parameters of the Copula function vary with time; This represents the cumulative distribution probability value of the optimal non-stationary marginal distribution model for the wind power output deviation sequence; This represents the cumulative distribution probability value of the optimal non-stationary marginal distribution model for the photovoltaic power output deviation sequence.

[0032] To characterize the impact of climate change on the dynamic evolution of wind and solar power output-related structures, the same set of candidate covariates as in step 2.2 was used. Constructing candidate covariates and time-varying Copula function parameters The relationship between time-varying Copula function parameters. Represented as:

[0033] (7)

[0034] in, These represent the parameters of the time-varying Copula function. The join function; Let i represent the i-th candidate covariate, i = 1, 2, ..., M, where M represents the total number of candidate covariates; These are the intercept terms; These are candidate covariates paired with time-varying Copula function parameters. The regression coefficients.

[0035] To further quantify the joint non-stationary characteristics of climate-driven wind and solar power output deviation sequences, this invention constructs multiple candidate joint distribution models based on time-varying Copula functions. The Akaike Information Criterion (AIC) is used to evaluate these multiple candidate joint distribution models based on time-varying Copula functions, and the optimal multivariate non-stationary joint probability model is obtained.

[0036] The third step involves generating and reducing typical wind and solar power output deviation scenarios based on the multivariate non-stationary joint probability model of the wind and solar power output deviation sequence constructed in the second step. Specifically:

[0037] Step 3.1: Based on the optimal multivariate non-stationary joint probability model of the wind and solar power output deviation sequence obtained in the second step, a large number of stratified samples are generated in the Copula space using the Latin hypercube sampling method to achieve uniform and efficient sampling in the unit hypercube space, thereby obtaining random samples that can reflect the time-varying correlation structure of the wind and solar power output deviation sequences.

[0038] Step 3.2: Using the optimal non-stationary marginal distribution probability model of the wind and solar power output deviation sequence obtained in Step 2.2, construct its corresponding inverse cumulative distribution function, and perform inverse probability integral transformation on the hierarchical samples generated in the Copula space in Step 3.1 to map the samples in the uniform space to the actual wind and solar power output deviation space, generating paired samples of wind and solar power output deviation. The resulting samples simultaneously satisfy the non-stationary marginal distribution characteristics and its time-varying joint correlation structure, thereby forming a wind and solar power output deviation scenario set, which is used to characterize the dynamic evolution characteristics of the joint uncertainty of wind and solar power output in the long-term scheduling time domain.

[0039] Step 3.3: Considering that a large-scale original scene set would significantly increase the solution complexity of the long-term stochastic scheduling model, a neural gas clustering method is used to reduce the wind and solar power output deviation scene set. First, the large number of wind and solar power output deviation scenes generated in Step 3.2 are used as the original scene set. Then, the neural gas clustering algorithm is used to perform similarity clustering on the original scene set. While preserving as much of the main statistical features and probability distribution characteristics of the original scene set as possible, a small number of representative typical scenes are represented by each cluster center. The occurrence probability of each typical scene is obtained by summing the probabilities of the original scenes belonging to the corresponding cluster, thus forming a reduced scene set suitable for subsequent long-term optimization scheduling solutions. At this point, typical wind and solar power output deviation scenes are obtained for subsequent long-term joint optimization scheduling of water, wind, and solar power.

[0040] The fourth step involves constructing a long-term joint optimization scheduling model for water, wind, and solar power based on the typical wind and solar power output deviation scenarios generated and reduced in the third step. Solving this model yields joint scheduling strategies for water, wind, and solar systems under different scenarios. Specifically:

[0041] Step 4.1, the objective function of the long-term optimization scheduling model for the combined water, wind, and solar power is:

[0042] (8)

[0043] Where S represents the total number of scenes, and s represents the scene index; Let represent the probability of scenario s occurring; T represents the total number of scheduling periods within the planning period, and t represents the scheduling period within the planning period. This represents the hydropower output during time period t; This represents the wind power output during time period t in scenario s. This represents the photovoltaic output under scenario s during time period t.

[0044] Step 4.2, the constraints of the long-term optimization scheduling model for combined hydropower, wind power, and solar power include water balance constraints, upper and lower water level constraints, water level-reservoir capacity constraints, tailrace level-outflow constraints, hydropower output constraints, water curtailment constraints, power curtailment constraints, and wind and solar power output under different scenarios, specifically:

[0045] The water balance constraint:

[0046] (9)

[0047] in, This represents the capacity of the i-th reservoir during time period t; This represents the capacity of the i-th reservoir during time period t+1; This represents the inflow rate of the i-th reservoir during time period t; This represents the outflow from the i-th reservoir during time period t; t represents the time corresponding to the time period t; formula (9) represents the water balance equation.

[0048] The upper and lower limits of the water level are constrained as follows:

[0049] (10)

[0050] in, This represents the water level of the i-th reservoir during time period t; This represents the dead water level of the i-th reservoir; This represents the normal water level of the i-th reservoir.

[0051] The water level-reservoir capacity constraint:

[0052] (11)

[0053] in, This represents the capacity of the i-th reservoir during time period t; The function representing the relationship between the water level and storage capacity of the i-th reservoir; This represents the water level of the i-th reservoir during time period t.

[0054] The tailwater level-discharge flow constraint:

[0055] (12)

[0056] in, This represents the tailwater level of the i-th reservoir during time period t; The function representing the relationship between the tailwater level and discharge flow of the i-th reservoir is denoted by . This represents the outflow from the i-th reservoir during time period t.

[0057] The hydropower output constraint:

[0058] (13)

[0059] (14)

[0060] in, This represents the hydropower output of the i-th power station during time period t; This represents the maximum output of the i-th power station; This represents the power generation flow of the i-th power station during time period t; This represents the output coefficient of the i-th power station; Let be the head of the i-th hydropower station during time period t.

[0061] The wastewater disposal constraint:

[0062] (15)

[0063] in, The maximum water discharge limit of the i-th power station; Let be the discharge flow of the i-th power station during time period t.

[0064] The power curtailment constraint:

[0065] (16)

[0066] in, This represents the maximum power generation flow limit of the i-th power station; Let be the power generation flow of the i-th power station during time period t.

[0067] The power output of the landscape in different scenarios:

[0068] (17)

[0069] (18)

[0070] (19)

[0071] in, This represents the total wind power output during time period t in scenario s; This represents the predicted wind power output for time period t. This represents the wind power prediction deviation for time period t under scenario s; This represents the total photovoltaic output during time period t in scenario s; This indicates the predicted photovoltaic power output for time period t. This represents the photovoltaic prediction deviation in time period t under scenario s; This represents the total power output of wind and solar energy during time period t; t represents the time period.

[0072] Step 4.3 involves solving the long-term optimization scheduling model for combined hydropower, wind power, and solar power using a scenario-discretization-based mixed-integer linear programming method. This yields the optimal power output of hydropower, wind power, and solar power for each scheduling period, as well as the optimal operation process of the reservoir. Specifically:

[0073] Step 4.3.1: First, the typical wind and solar power output deviation scenarios and their corresponding probabilities are introduced into the long-term optimization scheduling model of water, wind and solar power to characterize the uncertainty of wind and solar power output. The original stochastic optimization problem is transformed into a deterministic equivalent model of long-term optimization scheduling of water, wind and solar power that comprehensively considers each typical scenario and its probability of occurrence through scenario discretization.

[0074] Step 4.3.2: Subsequently, for the nonlinear relationships in the deterministic equivalent model of long-term optimal scheduling of water, wind and solar power, a piecewise linearization method is used for approximation, and binary variables are introduced in the linearization process, thereby transforming the deterministic equivalent model of long-term optimal scheduling of water, wind and solar power into a computable mixed integer linear programming model of long-term optimal scheduling of water, wind and solar power.

[0075] Step 4.3.3 Finally, the mixed-integer linear programming model is solved using a commercial optimization solver to obtain the optimal power output process of hydropower, wind power and photovoltaic power during each scheduling period, as well as the optimal storage and release process, water level change process and water abandonment process of each reservoir during the scheduling cycle, thereby realizing the long-term optimized scheduling of the hydropower-wind-solar integrated system.

[0076] The beneficial effects of this invention are as follows:

[0077] This invention constructs a multivariate non-stationary joint probability model of wind and solar power output deviation sequences using local meteorological data, large-scale climate indices, and wind and solar power output deviation sequences. Combining scenario generation, scenario reduction, deterministic equivalent transformation, and optimization solution methods, it establishes a long-term optimal scheduling model for water-wind-solar joint operation, improving the scientific rigor of long-term scheduling analysis and optimization decisions. Furthermore, based on the joint operation process of water-wind-solar systems under typical wind and solar power output deviation scenarios, it can more accurately characterize the time-varying patterns of renewable energy output statistical characteristics and their impact on reservoir operation and system joint scheduling, improving the solution efficiency and reliability of scheduling results under complex and uncertain conditions, thereby achieving long-term coordinated and optimized operation of the water-wind-solar system. Attached Figure Description

[0078] Figure 1 This is a map showing the distribution of meteorological factors in Yunnan Province. Figure 1 (a) represents a wind speed of 10m. Figure 1 (b) in the text represents the air temperature at 2m. Figure 1 (c) in the figure represents the surface air pressure; Figure 1 (d) Solar radiation; Figure 1 (e) in the figure represents the total precipitation; Figure 1 (f) in the equation represents potential evapotranspiration.

[0079] Figure 2 A line graph of atmospheric circulation indicators; Figure 2 (a) in the figure represents the Atlantic Multidecadal Oscillation Index; Figure 2(b) in the figure represents the Arctic Oscillation Index; Figure 2 (c) in the figure represents the North Atlantic Oscillation Index; Figure 2 (d) in the figure represents the North Pacific Index; Figure 2 (e) in the figure represents the Pacific Decadal Oscillation Index; Figure 2 (f) in the figure represents the El Niño-Southern Oscillation Index.

[0080] Figure 3 This is the clustering result for wind power stations.

[0081] Figure 4 The results show the clustering of photovoltaic power plants.

[0082] Figure 5 The figure shows the optimal fitting result for the non-stationary edge distribution of the power output deviation of representative wind and solar power plants.

[0083] Figure 6 This is a contour plot of the cumulative probability of the joint distribution of the Gumbel Copula function for W1 and P1.

[0084] Figure 7 This is a contour plot of the cumulative probability of the joint distribution of the Clayton Copula function for W2 and P2.

[0085] Figure 8 A set of 81 landscape output deviation scenarios sampled by Latin hypercube sampling.

[0086] Figure 9 Four typical scenarios of wind and solar power output deviation after neural gas clustering.

[0087] Figure 10 The diagram shows the long-term scheduling results of the water-wind-solar system under four typical scenarios of wind and solar power output deviation. Detailed Implementation

[0088] The present invention will be further described below with reference to specific implementation examples.

[0089] A joint scheduling method for water, wind, and solar power based on non-stationary uncertainty modeling includes the following steps:

[0090] Step 1: Collect the basic data required for long-term scheduling of water, wind and solar power and uncertainty modeling of renewable energy.

[0091] The embodiments of this invention are described using the cascade hydropower stations and surrounding wind and solar power stations in Yunnan Province as background. The distribution of meteorological factors and atmospheric circulation indices in Yunnan Province from 2001 to 2020 are shown below. Figure 1 , Figure 2As shown. Meteorological factors include: 10m wind speed (Wind), 2m air temperature (TEM), surface air pressure (SP), solar radiation (SSR), total precipitation (TP), and potential evapotranspiration (PEV). Atmospheric circulation indices include: Atlantic Multidecadal Oscillation (AMO), Arctic Oscillation (AO), North Atlantic Oscillation (NAO), North Pacific Model (NP), Pacific Decadal Oscillation (PDO), and El Niño Southern Oscillation Index (SOI). Two cascade hydropower stations were included in the study: Xiaowan and Nuozhadu, with a total installed capacity of 10050MW. There were 69 wind power stations with a total installed capacity of 8697.35MW; and 134 photovoltaic power stations with a total installed capacity of 9655.69MW. The wind and photovoltaic power stations were clustered according to their coordinates and installed capacity, resulting in two virtual wind power stations (W1 and W2) and two virtual photovoltaic power stations (P1 and P2). The coordinates and results of the wind and photovoltaic clustering are shown below. Figure 3 , Figure 4 As shown.

[0092] Step 2: Construct a multivariate nonstationary joint probability model. Details are as follows:

[0093] Step 2.1: Construction of the wind and solar power output deviation sequence and correlation analysis with meteorological factors and atmospheric circulation indices. Based on the clustering results of Step 1, the power output prediction deviations at W1, W2, P1, and P2 are extracted. Then, Kendall correlation analysis is performed on the wind and solar power output deviations, meteorological factors, and atmospheric circulation indices. The statistical significance between variables is determined by calculating the p-value of the Kendall significance test. When the p-value is less than 0.05, the correlation is considered significant at the 95% confidence level. The most significant climatic factor is selected and used as a covariate in the next step. The climatic factors selected after Kendall correlation analysis and their p-values ​​are shown in Table 1.

[0094] Table 1: Kendall Correlation Analysis Results

[0095]

[0096] Step 2.2: Constructing a non-stationary marginal distribution probability model. After completing the covariate selection, this invention uses the most basic Gumbel (GU) distribution, normal (NO) distribution, gamma distribution (GA) distribution, Weibull distribution (WEI) distribution, and log-normal distribution (LOGNO) to perform non-stationary marginal distribution fitting optimization on the wind and solar power output deviation based on the GAMLSS model, obtaining the distribution function with the best fitting effect. Thus, the optimal non-stationary marginal distribution probability model for the wind and solar power output deviation sequences W1, W2, P1, and P2 is constructed. The SBC evaluation results are as follows... Figure 5As shown, the Weibull distribution provides the best fit for wind power plants W1 and W2. For photovoltaic power plants P1 and P2, the gamma distribution provides the best fit.

[0097] Step 2.3: Construct a multivariate non-stationary joint probability model. Based on the optimal non-stationary marginal distribution model of the wind and solar power output deviation sequence constructed in Step 2.2, this invention constructs a multivariate non-stationary joint probability model of the wind and solar power output deviation sequence using a time-varying Copula function. The optimal fitting results of the time-varying Copula function are shown in Table 2. For W1 and P1, the Gumbel Copula function provides the best fit. The best result for W1 and P1 is the Clayton Copula function. The cumulative probability values ​​of their joint function joint distribution are as follows: Figure 6 and Figure 7 As shown.

[0098] Table 2: Optimal Fitting of Time-Varying Copula Function

[0099]

[0100] The third step involves generating and reducing typical wind and solar power output deviation scenarios based on the multivariate non-stationary joint probability model constructed in the second step. Specifically, Latin hypercube sampling was used to sample 81 wind and solar power output deviation scenarios, which were then reduced to four typical scenarios using neural gas clustering. The results are shown below. Figure 8 and Figure 9 As shown.

[0101] The fourth step involves constructing a long-term optimization scheduling model for the joint water, wind, and solar power output deviation based on the four typical wind and solar power output deviation scenarios generated and reduced in the third step. Solving this model yields joint scheduling strategies for the water, wind, and solar power systems under different scenarios.

[0102] Power generation in different scenarios, such as Figure 10As shown in the figure, the overall system output exhibits stable periodic fluctuations, with consistent trends across different scenarios, indicating that the proposed method effectively maintains the temporal structure of the system operation. Furthermore, significant differences exist between peak and trough phases across different scenarios: during high-output phases, the total system output of scenarios 3 and 4 is significantly higher than that of scenarios 1 and 2, while the differences between scenarios decrease relatively during low-output phases. This suggests that the system's response is more sensitive during high-load periods as the wind and solar power output deviation levels change. By introducing climate-driven non-stationary uncertainties, this method not only characterizes the time-varying fluctuations of wind and solar power output but also effectively transmits these uncertainties to the hydropower dispatch decision-making level, thereby achieving dynamic adjustment and coordinated optimization of the system's total output. Therefore, this invention can effectively characterize the non-stationary fluctuations of wind and solar power output and achieve reasonable transmission of uncertainty to dispatch results, thus improving the reliability and adaptability of system operation.

[0103] The above embodiments are merely illustrative of the implementation methods of the present invention, but should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A joint scheduling method for water, wind, and solar power based on non-stationary uncertainty modeling, characterized in that, The method for joint scheduling of water, wind, and solar power includes the following steps: Step 1: Collect the basic data required for long-term scheduling of water, wind and solar power and uncertainty modeling of renewable energy; Step 2: Construct a multivariate non-stationary joint probability model of the wind and solar power output deviation sequence; Step 2.1: Construct the wind and solar power output deviation sequence and perform correlation analysis with meteorological factors and atmospheric circulation index to screen the climate factors that have the most significant impact on the wind and solar power output deviation sequence. Step 2.2: Construct a non-stationary marginal distribution probability model; A generalized additive location-scale-shape model, or GAMLSS model for short, is designed. The wind and solar power output deviation sequence is modeled using the GAMLSS model to obtain the optimal non-stationary marginal distribution probability model. Step 2.3: Construct a multivariate nonstationary joint probability model for the wind and solar power output deviation sequence; After obtaining the optimal non-stationary marginal distribution probability model of the wind and solar power output deviation sequence through the GAMLSS model in step 2.2, the corresponding cumulative distribution functions are denoted as follows: and By calculating its cumulative probability value through probability integral transformation, we obtain: （5） in, The cumulative distribution function represents the optimal non-stationary marginal distribution model of the wind power output deviation sequence; The cumulative distribution function represents the optimal non-stationary marginal distribution model of the photovoltaic power output deviation sequence; , representing the cumulative distribution probability value of the optimal non-stationary marginal distribution model of the wind power output deviation sequence; , representing the cumulative distribution probability value of the optimal non-stationary marginal distribution model of the photovoltaic power output deviation sequence; This represents the wind power output deviation sequence; Represents the photovoltaic power output deviation sequence; According to Sklar's theorem, the joint distribution of wind and solar power output deviation can be expressed as: （6） in, This represents the wind power output deviation at time t. and photovoltaic output deviation The joint cumulative distribution function; Represents a time-varying Copula function; The parameters of the Copula function vary with time; This represents the cumulative distribution probability value of the optimal non-stationary marginal distribution model for the wind power output deviation sequence; This represents the cumulative distribution probability value of the optimal non-stationary marginal distribution model for the photovoltaic power output deviation sequence; To characterize the impact of climate change on the dynamic evolution of wind and solar power output-related structures, the same set of candidate covariates as in step 2.2 was used. Constructing candidate covariates and time-varying Copula function parameters The relationship is used to obtain the parameters of the time-varying Copula function. , is represented as: （7） in, These represent the parameters of the time-varying Copula function. The join function; Let i represent the i-th candidate covariate, i = 1, 2, ..., M, where M represents the total number of candidate covariates; These are the intercept terms; These are candidate covariates paired with time-varying Copula function parameters. The regression coefficients; The Akaike information criterion was used to evaluate various candidate joint distribution models constructed based on time-varying Copula functions, and the optimal multivariate nonstationary joint probability model was obtained. The third step is to generate and reduce the scene of wind and light output deviation to obtain a typical scene of wind and light output deviation. Step 3.1: Based on the optimal multivariate nonstationary joint probability model, obtain random samples that can reflect the time-varying structure of the wind power and photovoltaic power output deviation sequence; Step 3.2: Based on the optimal non-stationary edge distribution probability model, a set of wind and solar power output deviation scenarios is formed; Step 3.3: Reduce the set of scenes with wind and solar power output deviation to obtain typical scenes with wind and solar power output deviation. The fourth step is to construct a long-term optimization scheduling model for water, wind and solar power systems based on typical wind and solar power output deviation scenarios, and solve the model to obtain joint scheduling strategies for water, wind and solar power systems under different scenarios. Step 4.1, the objective function of the long-term optimization scheduling model for the combined water, wind, and solar power is: （8） Where S represents the total number of scenes, and s represents the scene index; Let represent the probability of scenario s occurring; T represents the total number of scheduling periods within the planning period, and t represents the scheduling period within the planning period. This represents the hydropower output during time period t; This represents the wind power output during time period t in scenario s. This represents the photovoltaic output under scenario s in time period t; Step 4.2: Determine the constraints of the long-term optimization scheduling model for the combined water, wind, and solar power; Step 4.3: Solve the long-term optimization scheduling model for the combined hydropower, wind power and solar power to obtain the optimal output results of hydropower, wind power and solar power in each scheduling period and the optimal operation process of the reservoir.

2. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 1, characterized in that, In the first step: The basic data includes hydropower inflow observation data, spatial information of wind farms and photovoltaic power stations, wind power and photovoltaic power predicted and measured output data, local meteorological data, and large-scale climate indices; The hydropower inflow observation data are used to characterize the inflow process of the cascade hydropower system and support the construction of a long-term joint scheduling model for hydropower, wind power, and solar power. The spatial information of wind farms and photovoltaic power stations is used for the spatial aggregation of regional wind and solar power stations. The predicted and measured output data of wind and solar power are used to construct a wind and solar output deviation sequence to express the uncertainty of wind and solar output. The local meteorological data and large-scale climate index will be introduced as covariates into the multivariate non-stationary joint probability model to characterize the dynamic evolution of renewable energy uncertainty under the background of climate change.

3. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 2, characterized in that, Step 2.1 specifically involves: Based on the spatial information of wind farms and photovoltaic power plants, representative wind and solar power plants are obtained through K-means clustering, and the wind and solar power output prediction deviation sequence at the representative wind and solar power plants is extracted, referred to as the wind and solar power output deviation sequence, which is used to characterize the uncertainty of renewable energy power generation. After obtaining the wind and solar power output deviation sequence, Kendall correlation analysis is performed on the wind and solar power output deviation sequence with meteorological factors and atmospheric circulation index to screen the climate factors that have the most significant impact on the wind and solar power output deviation sequence.

4. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 3, characterized in that, In step 2.1, the screening method is as follows: the statistical significance between variables is determined by calculating the p-value of the Kendall significance test; when the p-value is less than 0.05, the correlation is considered significant at the 95% confidence level, and the climate factors that have the most significant impact on the wind and solar power output deviation sequence are screened accordingly.

5. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 4, characterized in that, Step 2.2 specifically involves: In the GAMLSS model, it is assumed that It follows a parameterized distribution with time-varying parameters. : （1） in, This indicates the monthly-scale prediction bias of wind and solar power output at time t; This represents the positional parameters that change over time. A scale parameter that represents how it changes over time; This represents the shape parameter as it changes over time; the superscript k indicates the sequence of wind and solar power output deviations. w represents wind power output deviation, and p represents photovoltaic power output deviation; Let the set of candidate covariates for the wind and solar power output deviation sequence at time t be . The candidate covariates mainly include local meteorological data and large-scale climate indices; the location parameters, scale parameters, and shape parameters are respectively linked to the candidate covariates through connection functions, the expressions of which are: （2） （3） （4） in, , and These represent the connection functions for position parameters, scale parameters, and shape parameters, respectively. Let i represent the i-th candidate covariate, i = 1, 2, ..., M, where M represents the total number of candidate covariates; This is the intercept term for the position parameters; The intercept term is the scale parameter; The intercept term of the shape parameter; These are the regression coefficients of candidate covariates on the location parameters; These are the regression coefficients of candidate covariates on the scaling parameter; These are the regression coefficients of candidate covariates on the shape parameter; To quantify the non-stationary characteristics of climate-driven renewable energy output uncertainty, multiple candidate marginal distribution models are constructed based on the GAMLSS model. By allowing different combinations of distribution parameters to vary with covariates, fully stationary, partially non-stationary, or fully non-stationary models are formed. The multiple candidate marginal distribution models constructed based on the GAMLSS model are evaluated to obtain the optimal non-stationary marginal distribution probability model.

6. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 5, characterized in that, In step 2.2, the fully stationary model refers to a model in which the position, scale, and shape parameters do not change with the covariates; that is, its parameters are determined only by the intercept term and do not include covariate terms. , and All are 0; the partially non-stationary model refers to a model in which at least one of the position parameter, scale parameter, and shape parameter varies with the covariate, i.e. , and At least one of the parameters is not zero, while the remaining parameters are determined by the intercept term; the completely non-stationary model refers to a model where the position parameter, scale parameter, and shape parameter all change with the covariates, i.e. , and None of them are 0.

7. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 6, characterized in that, Step 3 specifically involves: Specifically, step 3.1 involves: based on the optimal multivariate nonstationary joint probability model obtained in the second step, generating a large number of stratified samples in the Copula space using the Latin hypercube sampling method to obtain random samples that can reflect the time-varying structure of the wind power and photovoltaic power output deviation sequence. Step 3.2 specifically involves: using the optimal non-stationary marginal distribution probability model obtained in step 2.2, constructing its corresponding inverse cumulative distribution function, and performing an inverse probability integral transformation on the hierarchical samples generated in the Copula space in step 3.1 to map the samples in the uniform space to the actual wind and solar power output deviation space, generating paired wind and solar power output deviation samples, so that the obtained samples simultaneously satisfy the non-stationary marginal distribution characteristics and its time-varying joint correlation structure, forming a wind and solar power output deviation scenario set, which is used to characterize the dynamic evolution characteristics of the joint uncertainty of wind and solar power output in the long-term scheduling time domain; In step 3.3, the neural gas clustering method is used to reduce the set of wind and solar power output deviation scenarios. Specifically, the wind and solar power output deviation scenarios generated in step 3.2 are used as the original scenario set. Then, the original scenario set is clustered by similarity using the neural gas clustering algorithm, with each cluster center representing a representative typical scenario. The probability of occurrence of each typical scenario is obtained by summing the probabilities of the original scenarios belonging to the corresponding cluster, forming a reduced scenario set suitable for subsequent long-term optimization scheduling. Thus, typical wind and solar power output deviation scenarios are obtained for subsequent long-term optimization scheduling of water, wind and solar power.

8. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 7, characterized in that, The constraints in step 4.2 include water balance constraints, upper and lower water level constraints, water level-reservoir capacity constraints, tailrace level-discharge flow constraints, hydropower output constraints, water curtailment constraints, power curtailment constraints, and wind and solar power output under different scenarios, specifically: The water balance constraint: （9） in, This represents the capacity of the i-th reservoir during time period t; This represents the capacity of the i-th reservoir during time period t+1; This represents the inflow rate of the i-th reservoir during time period t; This represents the outflow from the i-th reservoir during time period t; This represents the time corresponding to time period t; The upper and lower limits of the water level are constrained as follows: （10） in, This represents the water level of the i-th reservoir during time period t; This represents the dead water level of the i-th reservoir; This represents the normal water level of the i-th reservoir; The water level-reservoir capacity constraint: （11） in, This represents the capacity of the i-th reservoir during time period t; The function representing the relationship between the water level and storage capacity of the i-th reservoir; This represents the water level of the i-th reservoir during time period t; The tailwater level-discharge flow constraint: （12） in, This represents the tailwater level of the i-th reservoir during time period t; The function representing the relationship between the tailwater level and discharge flow of the i-th reservoir is denoted by . This represents the outflow from the i-th reservoir during time period t; The hydropower output constraint: （13） （14） in, This represents the hydropower output of the i-th power station during time period t; This represents the maximum output of the i-th power station; This represents the power generation flow of the i-th power station during time period t; This represents the output coefficient of the i-th power station; Let the head of the i-th hydropower station be measured in time period t. The wastewater disposal constraint: （15） in, The maximum water discharge limit of the i-th power station; Let be the discharge flow rate of the i-th power station in time period t; The power curtailment constraint: （16） in, This represents the maximum power generation flow limit of the i-th power station; Let i be the power generation flow of the i-th power station in time period t; The power output of the landscape in different scenarios: （17） （18） （19） in, This represents the total wind power output during time period t in scenario s; This represents the predicted wind power output for time period t. This represents the wind power prediction deviation for time period t under scenario s; This represents the total photovoltaic output during time period t in scenario s; This indicates the predicted photovoltaic power output for time period t. This represents the photovoltaic prediction deviation in time period t under scenario s; This represents the total power output of wind and solar energy during time period t; t represents the time period.

9. The water-wind-solar joint scheduling method based on non-stationary uncertainty modeling according to claim 8, characterized in that, In step 4.3, a mixed-integer linear programming method based on scene discretization is used to solve the long-term optimization scheduling model for the joint water, wind, and solar power system. Specifically: Step 4.3.1 introduces typical wind and solar power output deviation scenarios and their corresponding probabilities into the long-term optimization scheduling model of water, wind and solar power joint operation to characterize the uncertainty of wind and solar power output. The original stochastic optimization problem is transformed into a deterministic equivalent model of long-term optimization scheduling of water, wind and solar power joint operation by discretizing the scenarios. Step 4.3.2: For the nonlinear relationship in the deterministic equivalent model of long-term optimization scheduling of water, wind and solar power, a piecewise linearization method is used for approximation. Binary variables are introduced in the linearization process to transform the deterministic equivalent model of long-term optimization scheduling of water, wind and solar power into a computable mixed integer linear programming model of long-term optimization scheduling of water, wind and solar power. Step 4.3.3: Solve the mixed integer linear programming model to obtain the optimal power output process of hydropower, wind power and photovoltaic power in each scheduling period, as well as the optimal storage and release process, water level change process and water abandonment process of each reservoir in the scheduling cycle, so as to realize the long-term optimized scheduling of the hydropower, wind power and photovoltaic system.

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