A Multi-Objective Scheduling Method for Water, Wind, Solar and Storage Based on an Improved Hybrid Particle Swarm Optimization (HSO) Algorithm (Grey Wolf)

Abstract

This invention belongs to the field of power system optimization and dispatching technology, specifically relating to a multi-objective day-ahead peak-shaving dispatching method for a cascade hydropower-wind-solar-storage complementary power generation system. The specific steps include: establishing a mathematical model of the hydropower-wind-solar-storage complementary system and constructing a multi-objective optimization framework considering power generation benefits and peak-shaving effects; using an adaptive multi-timescale improved LSTNet to construct a prediction network to perform day-ahead predictions of water inflow, photovoltaic power generation, and wind farm power generation in the cascade basin intervals as input data for the model; employing an improved multi-objective hybrid particle swarm optimization algorithm (IMOPSO-GWO) to solve the established model, coordinating global exploration and local development capabilities through an adaptive convergence factor adjustment mechanism, and introducing a dynamic mutation operator to enhance the Pareto front search efficiency, ultimately obtaining the day-ahead dispatching scheme for the complementary system. This invention significantly improves power generation revenue and reduces grid surplus load fluctuations by optimizing the output of cascade hydropower units and energy storage.

Description

Technical Field

[0001] This invention belongs to the field of power system optimization and dispatching technology, specifically relating to a multi-objective day-ahead peak-shaving dispatching method for a cascade hydro-wind-solar-storage complementary power generation system. Background Technology

[0002] Large-scale grid connection of renewable energy sources, with hydropower, wind power, and solar power as the core, has become a key path for energy structure transformation. Cascade hydropower-wind power-solar power-storage integrated complementary systems, through multi-energy synergistic optimization, can effectively mitigate fluctuations in renewable energy output, improve peak-shaving capacity and power supply reliability, and serve as an important carrier for achieving integrated operation of power generation, grid, load, and storage. As of 2022, Sichuan Province, as the largest clean energy base in China, had hydropower installed capacity accounting for over 75% and renewable energy installed capacity accounting for 6.1%. Conducting research on the optimized scheduling of cascade hydropower-wind power-solar power-storage systems can not only improve water resource utilization efficiency but also fully leverage the reservoir's regulation and storage function, maximizing economic benefits.

[0003] The short-term operation of cascade hydropower stations is a complex multi-stage optimization problem, characterized by multidimensionality, multiple constraints, nonlinearity, and dynamics. The main task is to comprehensively consider reservoir water levels, inflow rates, and the actual operation of the power grid under the electricity market environment to study the optimal operation and load allocation of the hydropower stations, ensuring their safe and economical operation. Under the premise of ensuring stable grid operation, the goal is to maximize the utilization benefits of hydropower resources through refined load allocation. CN118801486B proposes a short-term risk dispatching method for hydropower, wind power, and solar power that considers the utilization of water resources during the residual period, while CN116667393A proposes a collaborative optimization method for day-ahead power generation plans and flexibility response rules for cascade hydropower, wind power, and solar power, providing new technical pathways for short-term operation optimization.

[0004] With the advancement of power market reform, power plants and the power grid are being separated. Cascade hydropower, as the main generators, must be self-sufficient and pursue maximum power generation efficiency, while simultaneously undertaking peak shaving and frequency regulation tasks to ensure the security of the power grid. This trade-off between economics and security significantly increases the difficulty of multi-timescale operation planning. Overemphasizing power generation efficiency weakens the grid's peak shaving capacity, while prioritizing peak shaving tasks easily leads to the waste of hydropower resources. Therefore, there is an urgent need to construct an optimized decision-making mechanism that balances grid-source coordination. Against this backdrop, developing a collaborative scheduling technology for cascade hydropower, wind power, solar power, and energy storage systems that integrates multi-objective optimization and intelligent decision-making has become a core issue for overcoming the bottleneck of efficient water resource utilization and ensuring the safe and economical operation of new power systems, possessing both theoretical research value and engineering practical significance. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective day-ahead peak-shaving scheduling method for a cascade hydropower-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm. This method solves the multi-objective collaborative optimization problem in the scheduling of cascade hydropower stations and new energy sources, improves the system's peak-shaving capacity and economic benefits, and ensures the safe and stable operation of the power grid.

[0006] The technical solution adopted in this invention is: a multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm, which is implemented according to the following steps:

[0007] Step 1: Establish a mathematical model for an integrated hydropower-wind-solar-storage complementary system. Taking into account constraints such as UHVDC interconnection line, cascade hydropower, energy storage, and demand response, construct a multi-objective optimization framework for cascade hydropower-wind-solar-storage that considers power generation benefits and peak-shaving effects.

[0008] Step 2: Propose an adaptive multi-timescale improved LSTNet framework for predicting water, wind, and solar days. A multi-scale convolutional kernel design is used to extract features from different time series scales, enhancing the model's ability to capture multi-level temporal patterns with varying periodicity, trends, and randomness. Simultaneously, an adaptive convolutional mechanism is incorporated to dynamically adjust the model based on data features.

[0009] Step 3: An improved multi-objective hybrid particle swarm optimization algorithm (IMOPSO-GWO) is proposed to solve the established model. The gray wolf population is initialized using the Tent-Logistic-Bernoulli multi-chaotic mapping. The global exploration and local exploitation capabilities are coordinated through the convergence factor adaptive adjustment mechanism. A dynamic Gaussian mutation operator is introduced to enhance the Pareto front search efficiency. Finally, a multi-objective day-ahead scheduling scheme for complementary systems is obtained.

[0010] The invention is further characterized by:

[0011] Step 1 is implemented as follows:

[0012] In peak load regulation, the average absolute value of the surplus load anomaly is an important indicator for evaluating the effectiveness of peak load regulation. It represents the degree of fluctuation in the surplus load, that is, the degree of deviation of the surplus load from the ideal smooth state. The smaller the average absolute value of the surplus load anomaly, the smaller the fluctuation in the surplus load and the better the peak load regulation effect; conversely, it indicates a poor peak load regulation effect. Therefore, in the short-term scheduling optimization of cascade hydropower stations, this indicator is selected as the objective function for power grid peak load regulation.

[0013]

[0014] Where: F1 is the sum of the average absolute values ​​of the remaining load anomalies of all power grids; G is the number of power grids; T is the total number of dispatch periods; L is the number of UHVDC interconnection lines; Dg,t and D' g,t These represent the system load and residual load of power grid g in time period t; P l,g,t The power transmitted from the interconnection line l to the g grid during time period t for the integrated hydro-wind-solar-storage complementary system; Let g be the demand response power of the grid during time period t.

[0015] The optimization scheduling strategy with the objective function of maximizing the power generation of cascade hydropower stations aims to maximize the benefits of power production by rationally allocating the power generation tasks of each hydropower station and making full use of available water resources, so as to optimize the overall power generation capacity of the cascade reservoir system.

[0016]

[0017] In the formula: F2 is the total power generation of the cascade hydropower; I is the number of cascade hydropower stations; N represents the output of the nth generating unit of hydropower station i during time period t; i Let i be the number of generating units in hydropower station i.

[0018] Multi-objective optimization model of integrated hydro-wind-solar-storage complementary system with constraints on UHVDC interconnection lines:

[0019] (a) Upper and lower limits of tie line power constraints

[0020] P l,min ≤P l,t ≤P l,max (3)

[0021] In the formula: P l,t P represents the transmission power of tie line l during time period t. l,min and P l,max These are the minimum and maximum values ​​of the transmission power of tie line l, respectively.

[0022] (b) Tie line power variation constraint

[0023] |P l,t -P l,t-1 |≤ΔP l (4)

[0024] Where: ΔP l This represents the maximum fluctuation range of the transmission power of tie line l in adjacent time periods.

[0025] Multi-objective optimization model of integrated hydropower, wind power, solar power and energy storage system with constraints on cascade hydropower:

[0026] (a) Water balance constraints

[0027]

[0028] In the formula: Vi,t I represents the reservoir capacity of power station i at the end of time period t. i,t Let Q be the inflow rate of power station i in time period t; τ be the flow lag time between power station i and its upstream power station i-1; i,t Q represents the outflow from power plant i during time period t. i-1,t-τ To account for the flow delay of power station i-1 during the time interval t-τ; R i,t Let i be the flow rate between power station i-1 and power station i during time period t. and These represent the power generation flow and water discharge flow of power station i during time period t, respectively. U represents the power generation flow of unit n in power plant i during time period t; i,n,t The flag representing the start / stop status of the nth generating unit of hydropower station i during time period t is a 0-1 variable.

[0029] (b) Reservoir water level constraints

[0030]

[0031] In the formula: Let i be the water level of the reservoir at the end of time period t. and These represent the upper and lower limits of the water level in the i hydropower station reservoir, respectively.

[0032] (c) Outbound flow constraints

[0033] Q i,min ≤Q i,t ≤Q i,max (7)

[0034] In the formula: Q i,max With Q i,min These are the upper and lower limits of the outflow from the i hydropower station, respectively.

[0035] (d) Power plant output constraints

[0036]

[0037] In the formula: Let i be the power output of power station i during time period t; and These represent the upper and lower limits of the output of power station i, respectively.

[0038] (e) Water level-reservoir capacity relationship

[0039]

[0040] In the formula: Let be the nonlinear relationship curve function between water level and reservoir capacity of the reservoir where power station i is located.

[0041] (f) Tailwater level-discharge ratio

[0042]

[0043] In the formula: Let be the nonlinear curve function relating the tailwater level to the discharge flow of power station i. Let be the tailwater level of power station i during time period t.

[0044] (g) Generating head constraint of the unit

[0045]

[0046] Where: H i,n,t and Let be the generating head and head loss of the nth generating unit of power station i during time period t.

[0047] (h) Head loss function

[0048]

[0049] In the formula: α i With β i These are the head loss coefficient and loss constant of power station i, respectively, which can generally be obtained through hydraulic tests.

[0050] (i) Relationship between unit output characteristics

[0051]

[0052] In the formula: η i Let be the unit efficiency of power station i; ρ be the density of water; and g be the acceleration due to gravity.

[0053] (j) Unit output constraints

[0054]

[0055] In the formula: and These are the upper and lower limits of the output of the nth generating unit of hydropower station i, respectively.

[0056] (k) Unit output ramp-up constraints

[0057]

[0058] α i,n,t +β i,n,t ≤1(16)

[0059] In the formula: α represents the maximum fluctuation range of the nth generating unit of power station i in adjacent time periods. i,n,t ∈{0,1} and β i,n,t∈{0,1} represents the power regulation index variable of the nth generating unit of power station i during time period t, α i,n,t =1 indicates that the power is adjusted downwards during time period t+1, β i,n,t =1 indicates that the power is adjusted upwards during time period t+1. When the power does not change, α i,n,t =0 and β i,n,t =0.

[0060] Multi-objective optimization model for integrated hydro-wind-solar-storage complementary system with energy storage constraints:

[0061] (a) Energy storage power constraints

[0062]

[0063] In the formula: These represent the charging and discharging power of the battery during time period t. These represent the maximum and minimum charging and discharging power of the battery, respectively. These are the charging and discharging status flags for the battery; a value of 1 indicates operation, and a value of 0 indicates stop.

[0064] (b) Energy storage capacity constraints

[0065]

[0066] In the formula: η represents the remaining capacity of the battery at the end of time period t. ES,cha η ES,dis These are the charging and discharging efficiencies of the battery, respectively. These represent the maximum and minimum remaining battery capacity, respectively.

[0067] (c) Constraints on energy storage charging and discharging frequency

[0068]

[0069] In the formula: N is the maximum number of charge and discharge cycles of the battery within one scheduling cycle.

[0070] Demand response constraints of the multi-objective optimization model for integrated hydro-wind-solar-storage complementary systems:

[0071]

[0072] Where: γ is the maximum adjustable power coefficient of demand response in a single time period; This represents the total adjustable power of the demand response within the scheduling cycle.

[0073] Step 2 is implemented as follows:

[0074] Historical and meteorological data related to cascade hydropower and wind farm forecasting are collected, including historical hydrological data for the watershed area, power generation of photovoltaic power plants and wind farms, rainfall, solar irradiance, wind speed, and temperature. This data is then compiled into a single time window. Subsequently, outlier removal and missing value imputation are performed. This invention uses the Z-score method to process outliers in the collected data, and sets a rule that if the relative difference is greater than 3, the data is considered an outlier and removed.

[0075]

[0076] In the formula: X is the sample data, μ is the sample mean, and σ is the standard deviation.

[0077] For blank values, inverse distance weighted interpolation was used, combined with reasonable guidance from meteorological data and expert experience for filling. Because the aforementioned time series data exhibits significant seasonal fluctuations, masking underlying trends or periodic changes, Seasonal-Trend Decomposition using LOESS (STL) was employed to separate seasonal fluctuations from the original data. This allows the model to focus more on data trends and residuals, thereby improving prediction accuracy.

[0078] The core of the STL method is to process the time series Y. t It is decomposed into three parts. The trend component is estimated by smoothing the original data using Loess regression; the seasonal component is obtained by smoothing the data using Loess after removing the trend component; and the residual component is the result of subtracting the trend and seasonal components from the original data.

[0079] Y t =T t +S t +R t (twenty two)

[0080] T t =Loess(Y t ) (twenty three)

[0081] S t =Loess(Y t -T t ) (twenty four)

[0082] R t =Y t -T t -S t (25)

[0083] In the formula: Y t This is the original time series data; T t For trend components; S tIt is a seasonal component; R t This represents the residual components.

[0084] To make the training of the Improved LSTNet model more stable, the Min-Max normalization method is applied to normalize the input data.

[0085] By employing a multi-scale convolutional kernel design, features at different scales of the time series are extracted, enhancing the model's ability to capture multi-level time series patterns, including periodicity, trend, and randomness. The time series data is defined as X = {x1, x2, ... x...}. T},in Let d be the input vector at time t, d be the feature dimension of the input, and T be the data length. The LSTNet model simultaneously applies convolutional kernels of different sizes K1, K2, ..., K. m Convolution operations are performed in parallel.

[0086]

[0087] In the formula: It is the convolution output at the i-th scale, representing the output at scale k. i The temporal characteristic response.

[0088] The outputs of convolutional kernels at different scales are combined by weighted averaging:

[0089]

[0090] In the formula: where ω i These are the weights of each convolution kernel. Different weights are assigned to the convolution results at each scale to enhance features at specific scales.

[0091] By incorporating an adaptive convolution mechanism, the model dynamically adjusts based on data features. To address the issue of potentially losing important information in long sequences with highly nonlinear and complex patterns, a bidirectional LSTM is applied, enabling the model to learn from both past and future information of the sequence simultaneously, thereby capturing more nuanced temporal dependencies.

[0092] By introducing residual connections and adding skip connections, information can be passed directly without bypassing certain layers, thus alleviating the gradient vanishing problem.

[0093] Finally, an L2 regularization method based on weight decay is adopted to limit the complexity of the model by penalizing the magnitude of the weights, thus preventing overfitting when the amount of training data is small or the data noise is large.

[0094] Step 3 is implemented as follows:

[0095] This invention proposes a method for initializing a gray wolf population based on the Tent-Logistic-Bernoulli multiple chaotic mapping. By leveraging the unpredictability and non-traversability of multiple chaotic sequences, a diverse and comprehensive population is generated, making the gray wolf population's exploration in the solution space more balanced, avoiding premature convergence of the algorithm, and enhancing global search capabilities.

[0096]

[0097] In the formula: These are the initial populations generated by the Tent chaotic map, the Logistic chaotic map, and the Bernoulli chaotic map, respectively. The initial gray wolf population is generated, and r and u are the chaos control parameters.

[0098] In the original algorithm, the convergence factor 'a' decreases linearly from 2 to 0 with each iteration. However, the convergence process is not linear; that is, the linearly decreasing convergence factor 'a' cannot fully reflect the actual optimization search process. Therefore, this invention proposes an adaptive adjustment mechanism for the convergence factor based on a sinusoidal change to coordinate global exploration and local development capabilities.

[0099]

[0100] In the formula: a initial and a final Let be the initial and final values ​​of the convergence factor 'a', and k be the current iteration number. max The maximum number of iterations is n, where n is the decreasing exponent, and 0 is the maximum number of iterations. <n≤1。

[0101] The improved convergence factor 'a' is represented by a curve that varies sinusoidally. It decreases more slowly in the early stages of iteration, allowing 'a' to remain at a relatively large value for a longer period, thus improving search efficiency. Conversely, it decreases more rapidly in the later stages of iteration, allowing 'a' to remain at a relatively small value for a longer period, thus improving search accuracy. Therefore, this approach balances the algorithm's global and local search capabilities.

[0102] To address the issues of premature convergence due to local optima attraction in multi-peak or complex multi-objective optimization problems, and insufficient solution diversity caused by the concentration of wolf pack positions during iteration, an improved method based on dynamic Gaussian mutation operator is proposed to enhance the efficiency of Pareto front search. By adaptively adjusting the mutation intensity at different search stages, the method effectively balances global exploration and local exploitation capabilities.

[0103] Dynamic control formula for mutation probability based on iteration count decay:

[0104]

[0105] In the formula: Pmutation (k) represents the mutation probability in the k-th iteration; P start α represents the initial mutation probability; α is a parameter controlling the descent rate.

[0106] Dynamic mutation operator based on Gaussian mutation:

[0107] X mutation =X current +σN(0,1) (34)

[0108] In the formula: X mutation This indicates the location of the mutated gray wolf; X current σ represents the position of the gray wolf before mutation; σ is the standard deviation that changes dynamically with iteration.

[0109] The beneficial effects of this invention are as follows: First, a mathematical model of an integrated hydro-wind-solar-storage complementary system is established, and a multi-objective optimization framework considering both power generation benefits and peak-shaving effects is constructed. Then, an adaptive multi-timescale improved LSTNet framework for day-ahead prediction of hydro-wind-solar power is proposed. Multi-scale convolutional kernels are used to extract features at different time series scales, enhancing the model's ability to capture multi-level time series patterns with different periodicity, trends, and randomness. Simultaneously, an adaptive convolution mechanism is combined to dynamically adjust the model based on data features. The predicted values ​​of hydro-wind-solar power are then input into the multi-objective optimization framework. Finally, an improved multi-objective hybrid particle swarm optimization algorithm (Grey Wolf Optimization Algorithm) is proposed to solve the established model. The Grey Wolf population is initialized using a Tent-Logistic-Bernoulli multi-chaotic mapping, and a convergence factor adaptive adjustment mechanism coordinates global exploration and local development capabilities. A dynamic Gaussian mutation operator is introduced to enhance the Pareto front search efficiency, ultimately yielding a multi-objective day-ahead scheduling scheme for the complementary system. The proposed method achieves a good balance between peak-shaving effects and power generation benefits, effectively reducing the peak-valley difference in the power grid and improving the stability of the power system. Attached Figure Description

[0110] Figure 1 A schematic diagram of a cascade hydropower-wind-solar-storage complementary system;

[0111] Figure 2 Load diagram of the power grid connected to the cascade hydro-wind-solar-storage system;

[0112] Figure 3 This is a chart showing the forecast data for the day before the solar term.

[0113] Figure 4 Flowchart for solving IMOPSO-GWO;

[0114] Figure 5 Diagrams showing the power output process of different cascade hydropower stations;

[0115] Figure 6A diagram showing the power receiving process of the power grid connected to the cascade hydro-wind-solar-storage system.

[0116] Figure 7 This is a diagram showing the scheduling results of energy storage devices;

[0117] Figure 8 The result of the IMOPSO-GWO multi-objective optimization is shown in the figure. Detailed Implementation

[0118] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0119] This invention discloses a multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm, which is implemented according to the following steps:

[0120] Step 1 is implemented as follows:

[0121] The objective function for peak shaving is established with the goal of minimizing the average absolute value of the residual load anomaly.

[0122]

[0123] Where: F1 is the sum of the average absolute values ​​of the remaining load anomalies of all power grids; G is the number of power grids; T is the total number of dispatch periods; L is the number of UHVDC interconnection lines; D g,t and D' g,t These represent the system load and residual load of power grid g in time period t; P l,g,t The power transmitted from the interconnection line l to the g grid during time period t for the integrated hydro-wind-solar-storage complementary system; Let g be the demand response power of the grid during time period t.

[0124] Establish an objective function for power generation with the goal of maximizing the power generation of cascade hydropower stations:

[0125]

[0126] In the formula: F2 is the total power generation of the cascade hydropower; I is the number of cascade hydropower stations; N represents the output of the nth generating unit of hydropower station i during time period t; i Let i be the number of generating units in hydropower station i.

[0127] Mathematical models were established for the constraints of UHVDC interconnection lines, cascade hydropower, energy storage, and demand response in the multi-objective optimization model of the integrated hydro-wind-solar-storage complementary system.

[0128] UHVDC interconnection line constraints include upper and lower power limits and amplitude constraints. Cascade hydropower constraints include water balance constraints, reservoir level limits, outflow constraints, power station output limits, water level-reservoir capacity relationships, tailrace level-discharge relationships, generator head constraints, head loss function, generator output characteristics, generator output constraints, and generator output ramp-up constraints. Energy storage constraints include energy storage power constraints, capacity constraints, and charge / discharge frequency constraints.

[0129] Step 2 is implemented as follows:

[0130] Historical and meteorological data related to cascade hydropower and wind farm forecasting are collected, including historical hydrological data for the watershed area, power generation of photovoltaic power plants and wind farms, rainfall, solar irradiance, wind speed, and temperature. This data is then compiled into a single time window. Subsequently, outlier removal and missing value imputation are performed. This invention uses the Z-score method to process outliers in the collected data, and sets a rule that if the relative difference is greater than 3, the data is considered an outlier and removed.

[0131]

[0132] In the formula: X is the sample data, μ is the sample mean, and σ is the standard deviation.

[0133] For blank values, inverse distance weighted interpolation was used, combined with reasonable guidance from meteorological data and expert experience for filling. Because the aforementioned time series data exhibits significant seasonal fluctuations, masking underlying trends or periodic changes, STL seasonal decomposition was employed to separate seasonal fluctuations from the original data. This allows the model to focus more on data trends and residuals, thereby improving prediction accuracy.

[0134] The core of the STL method is to process the time series Y. t It is decomposed into three parts. The trend component is estimated by smoothing the original data using Loess regression; the seasonal component is obtained by smoothing the data using Loess after removing the trend component; and the residual component is the result of subtracting the trend and seasonal components from the original data.

[0135] Y t =T t +S t +R t (38)

[0136] T t =Loess(Y t (39)

[0137] S t =Loess(Y t -T t (40)

[0138] R t =Y t -T t -S t (41)

[0139] In the formula: Y t This is the original time series data; T t For trend components; S t It is a seasonal component; R t This represents the residual components.

[0140] To make the training of the Improved LSTNet model more stable, the Min-Max normalization method is applied to normalize the input data.

[0141] By using multi-scale convolutional kernel design, features at different scales of time series are extracted, enhancing the model's ability to capture multi-level time series patterns such as periodicity, trend, and randomness.

[0142] By incorporating an adaptive convolution mechanism, the kernel is dynamically adjusted based on data features. Unlike traditional fixed convolution kernels, adaptive convolution operations can automatically adjust the kernel size, weights, or stride according to different data characteristics, improving model performance in various data environments. Adaptive convolution kernel sizes k are generated through reinforcement learning. adaptive Adaptive convolution weights K adaptive Adaptive step size s adaptive .

[0143] k adaptive =f size (X) (42)

[0144] K adaptive =f weight (X) (43)

[0145] s adaptive =f stride (X) (44)

[0146] In the formula: X = {x1, x2, ... x} T Let} be the input sequence, where each f is the input vector at time t, d is the feature dimension of the input, and T is the sequence length; size (X), f weight (X), f stride (X) represent reinforcement learning modules.

[0147] Combining the three adaptive mechanisms mentioned above, the convolution operation is as follows:

[0148]

[0149] In the formula: y t This indicates the output of the convolution.

[0150] To address the issue of lost important information in long sequences with highly nonlinear and complex patterns, a bidirectional LSTM is applied, enabling the model to learn from both past and future information of the sequence simultaneously, thereby capturing more nuanced temporal dependencies. Residual connections (ResNet) are introduced, adding skip connections to allow information to bypass certain layers and directly propagate, mitigating the vanishing gradient problem. An L2 regularization method based on weight decay is employed, penalizing the magnitude of the weights to limit model complexity and prevent overfitting when training data is limited or noisy.

[0151] An adaptive multi-timescale improved LSTNet neural network is used to perform day-ahead predictions of water, wind, and solar energy. The predicted data is then input into a multi-objective optimization framework for cascade water, wind, solar, and storage.

[0152] Step 3 is implemented as follows:

[0153] This invention proposes a method for initializing a gray wolf population based on the Tent-Logistic-Bernoulli multiple chaotic mapping. By leveraging the unpredictability and non-traversability of multiple chaotic sequences, a diverse and comprehensive population is generated, making the gray wolf population's exploration in the solution space more balanced, avoiding premature convergence of the algorithm, and enhancing global search capabilities.

[0154]

[0155] In the formula: These are the initial populations generated by the Tent chaotic map, the Logistic chaotic map, and the Bernoulli chaotic map, respectively. The initial gray wolf population is generated, and r and u are the chaos control parameters.

[0156] In the original algorithm, the convergence factor 'a' decreases linearly from 2 to 0 with each iteration. However, the convergence process is not linear; that is, the linearly decreasing convergence factor 'a' cannot fully reflect the actual optimization search process. Therefore, this invention proposes an adaptive adjustment mechanism for the convergence factor based on a sinusoidal change to coordinate global exploration and local development capabilities.

[0157] A = 2ar1 - a (50)

[0158] C = 2r² (51)

[0159]

[0160] In the formula: A and C are coefficient vectors; r1 and r2 are random numbers between [0,1]; a initial and a final Here, represents the initial and final values ​​of the convergence factor 'a'; k is the current iteration number; k max n is the maximum number of iterations; n is the decreasing exponent, 0 <n≤1。

[0161] The improved convergence factor 'a' is represented by a curve that varies sinusoidally. It decreases more slowly in the early stages of iteration, allowing 'a' to remain at a relatively large value for a longer period, thus improving search efficiency. Conversely, it decreases more rapidly in the later stages of iteration, allowing 'a' to remain at a relatively small value for a longer period, thus improving search accuracy. Therefore, this approach balances the algorithm's global and local search capabilities.

[0162] Led by alpha, beta, and delta wolves, the wolf pack relentlessly approaches its prey. Throughout this process, their positions are constantly shifting until the hunt is successful. This process can be represented by the following formula:

[0163]

[0164] ω (t) =(ω ini -ω end (k) max -k) / k max +ω end (56)

[0165] In the formula: D α D β D δ X represents the distances between other individuals in the wolf pack and α, β, and δ, respectively; α X β X δ X1, X2, and X3 represent the current positions of α, β, and δ wolves, respectively; X1, X2, and X3 represent the positions that other individuals in the population need to adjust due to the influence of α, β, and δ wolves, respectively; c1 and c2 represent the individual learning factor and the global learning factor, respectively; ω represents the inertia weight, which adopts a linear decreasing weight strategy, starting from the initial value ω. ini linearly decreasing to ω en d.

[0166] After each hunt, the wolf pack updates its non-dominated optimal solution set. An external population Archive mechanism is introduced to store these solutions. A leader selection strategy is employed, choosing leaders from the external population Archive during the predation process. A grid mechanism is used to measure the crowding of the non-dominated solution set.

[0167] To address the issues of premature convergence due to local optima attraction in multi-peak or complex multi-objective optimization problems, and insufficient solution diversity caused by the concentration of wolf pack positions during iteration, an improved method based on dynamic Gaussian mutation operator is proposed to enhance the efficiency of Pareto front search. By adaptively adjusting the mutation intensity at different search stages, the method effectively balances global exploration and local exploitation capabilities.

[0168] Dynamic control formula for mutation probability based on iteration count decay:

[0169]

[0170] In the formula: P mutation (k) represents the mutation probability in the k-th iteration; P start α represents the initial mutation probability; α is a parameter controlling the descent rate.

[0171] Dynamic mutation operator based on Gaussian mutation:

[0172] X mutation =X current +σN(0,1) (58)

[0173] In the formula: X mutation This indicates the location of the mutated gray wolf; X current σ represents the position of the gray wolf before mutation; σ is the standard deviation that changes dynamically with iteration.

[0174] Example

[0175] This study focuses on a complementary system constructed using four hydropower stations (15 generating units), one wind farm, and one photovoltaic power station in a river basin in southwestern China as references. The simplified cascade hydraulic relationships and network topology are described below. Figure 1 As shown in the diagram, four hydroelectric power stations are each connected to a cross-section of a power grid in a given region, transmitting electricity. The loads of the four power grids are as follows: Figure 2 As shown.

[0176] First, a mathematical model of an integrated hydro-wind-solar-storage complementary system is established, and a multi-objective optimization framework considering power generation efficiency and peak-shaving effect is constructed. Then, the adaptive multi-timescale Improved LSTNet day-ahead prediction framework is used to predict hydro-wind-solar power output. The wind and solar power output is as follows: Figure 3 As shown.

[0177] The predicted values ​​of water, wind, and solar energy are input into a multi-objective optimization model. An improved multi-objective hybrid particle swarm optimization algorithm (Grey Wolf) is used to solve the model. The solution process is as follows: Figure 4 As shown.

[0178] The power output process of a cascade hydropower station is as follows: Figure 5As shown in the figure, from the perspective of power output, after considering the constraints of unit start-up and shutdown and the duration of fluctuations, the power output of each power station is relatively stable, without frequent fluctuations, which meets the actual operating requirements of the power stations. In addition, the cascade hydropower stations have a high degree of adaptability to the grid load demand, and can effectively meet the requirements of stable and controllable operation scheduling.

[0179] Table 1 and Figure 6 It provides a detailed overview of the output distribution, hydropower consumption, and peak-shaving response of the cascade hydropower stations in the basin during the power grid peak-shaving process.

[0180] Table 1 shows the power consumption and peak-shaving effect of each power grid. Grid IV received the largest power consumption at 19077 MW·h, while Grid III received the smallest at only 8199 MW·h. After receiving power from hydropower stations, the surplus load of each power grid tended to stabilize, and the peak-valley difference was effectively regulated. Analysis results show that Grid I had the best peak-shaving effect, reducing the peak-valley difference by 77.15% and the average absolute value of the anomaly by 90.31%. Grid IV had the second best peak-shaving effect, reducing the average absolute value of the anomaly by 90.05%. Comprehensive analysis of the power grid load characteristics shows that Grid I has a relatively small peak-valley difference, and Hydropower Station I can effectively smooth load fluctuations. Although Grid IV has the largest peak-valley difference, it also effectively smooths surplus load due to its five generating units and large installed capacity. In contrast, Grids II and III have larger peak-valley differences, and the corresponding cascade hydropower stations have smaller installed capacities, resulting in their power transmission being unable to accurately track load changes, thus facing greater peak-shaving pressure.

[0181] Table 1 Peak Shaving Effect Indicators

[0182]

[0183] The scheduling results of photovoltaic power plants and wind farm energy storage devices are as follows: Figure 7 As shown, IMOPSO-GWO can obtain a given number of solution sets, yielding representative scheduling schemes. Given 30 solutions, it is expected to obtain 30 scheduling schemes. Figure 8 The results of the multi-objective optimization obtained by solving the IMOPSO-GWO algorithm are presented. The grid peak-shaving objective and the total power generation objective of the cascade hydropower stations are mutually constrained and contradictory. At the Pareto front, as the grid peak-shaving effect improves, the total power generation of the cascade hydropower stations decreases. Furthermore, after applying the grid mechanism and leader selection mechanism, the Pareto solution set is more evenly distributed, and each solution is highly representative, providing a reliable decision-making basis for practical engineering applications.

[0184] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm, characterized in that, The specific steps are as follows: Step 1: Establish the peak-shaving objective function 1 with the minimum average absolute value of the surplus load anomaly; establish the power generation objective function 2 with the maximum power generation of cascade hydropower; comprehensively consider the constraints of UHVDC interconnection line, cascade hydropower, energy storage, and demand response, and construct a multi-objective optimization model of the cascade hydropower-wind-solar-storage complementary system that considers power generation benefits and peak-shaving effects. Step 2: Construct an adaptive multi-timescale improved LSTNet neural network. After predicting the hydro-wind-solar hybrid system day-ahead, the predicted data is input into the multi-objective optimization model of the cascade hydro-wind-solar-storage complementary system. A multi-scale convolutional kernel design is used to extract features at different time-series scales, enhancing the model's ability to capture multi-level time-series patterns with different periodicity, trends, and randomness. An adaptive convolution mechanism is combined to dynamically adjust the model based on data features. Residual connections are introduced, allowing information to bypass certain layers and be directly transmitted, alleviating the gradient vanishing problem. An L2 regularization method based on weight decay is adopted to penalize the weights, limiting the model's complexity and preventing overfitting when the training data volume is small or the data noise is high. Step 3: Construct an improved multi-objective hybrid particle swarm optimization algorithm (IMOPSO-GWO) to solve the multi-objective optimization model of the constructed cascade hydro-wind-solar-storage complementary system. The gray wolf population is initialized using the Tent-Logistic-Bernoulli multivariate chaotic mapping. The global exploration and local exploitation capabilities are coordinated through the convergence factor adaptive adjustment mechanism. A dynamic Gaussian mutation operator is introduced to enhance the Pareto front search efficiency. Finally, the multi-objective day-ahead scheduling scheme of the complementary system is obtained.

2. The multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm according to claim 1, characterized in that, The peak-shaving objective function established with the goal of minimizing the average absolute value of the residual load anomaly is as follows: Where: F1 is the sum of the average absolute values ​​of the remaining load anomalies of all power grids; G is the number of power grids; T is the total number of dispatch periods; L is the number of UHVDC interconnection lines; D g,t and D' g,t These represent the system load and residual load of power grid g in time period t; P l,g,t The power transmitted from the interconnection line l to the g grid during time period t for the integrated hydro-wind-solar-storage complementary system; This represents the demand response power of grid G ​​during time period t. The objective function for power generation, established with the goal of maximizing the power generation of cascade hydropower, is as follows: In the formula: F2 is the total power generation of the cascade hydropower; I is the number of cascade hydropower stations; N represents the output of the nth generating unit of hydropower station i during time period t; i Let i be the number of generating units in hydropower station i. The multi-objective optimization model of the integrated hydropower, wind power, solar power and energy storage system includes the following constraint types: UHVDC interconnection line constraints, cascade hydropower constraints, energy storage constraints and demand response constraints. UHVDC interconnection line constraints include upper and lower power limits and amplitude constraints; cascade hydropower constraints include water balance constraints, reservoir water level limits, outflow constraints, power station output limits, water level-reservoir capacity relationship, tailrace water level-discharge relationship, generator head constraints, head loss function, generator output characteristic relationship, generator output constraints, and generator output ramp-up constraints; energy storage constraints include energy storage power constraints, capacity constraints, and charging / discharging frequency constraints.

3. The multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm according to claim 1, characterized in that, Step 2 is implemented as follows: (1) Data preprocessing Historical and meteorological data related to cascade hydropower, wind power, and solar power prediction were collected, including historical hydrological data of the watershed area, power generation of photovoltaic power stations and wind farms, rainfall, solar irradiance, wind speed, and temperature. This data was then organized into the same time window. Outlier removal and missing value imputation were then performed. The Z-score method was used to remove outliers, with a setting that data with a relative difference greater than 3 was considered an outlier. For missing values, inverse distance weighted interpolation was used, combined with reasonable guidance from meteorological data and expert experience for imputation. Because the time series data exhibits significant seasonal fluctuations, masking potential trends or periodic changes, Seasonal-Trend Decomposition using LOESS (STL) was employed to separate seasonal fluctuations from the original data, allowing the model to focus more on data trends and residuals, thereby improving prediction accuracy. Furthermore, to make the ImprovedLSTNet model training more stable, Min-Max normalization was applied to normalize the input data. (2) Construct and train the adaptive multi-timescale improved LSTNet prediction network A multi-scale convolutional kernel design is used to extract features from time series at different scales, enhancing the model's ability to capture multi-level time series patterns with varying periodicity, trends, and randomness. Simultaneously, an adaptive convolution mechanism is incorporated to dynamically adjust the model based on data features. To address the potential loss of important information in highly nonlinear and complex long sequences, a bidirectional LSTM is applied, enabling the model to learn from both past and future information of the sequence, thus capturing more nuanced temporal dependencies. Residual connections are introduced, allowing information to bypass certain layers and be directly transmitted, mitigating the gradient vanishing problem. Finally, an L2 regularization method based on weight decay is employed to penalize the magnitude of weights, limiting model complexity and preventing overfitting when training data is limited or noisy.

4. A multi-objective day-ahead peak-shaving scheduling method for a cascade hydro-wind-solar-storage complementary system based on an improved hybrid particle swarm optimization algorithm, as described in claim 1, is characterized in that... Step 3 is implemented as follows: (1) The method for initializing the gray wolf population using multiple chaotic mappings in the improved multi-objective hybrid particle swarm optimization algorithm is as follows: In the formula: These are the initial populations generated by the Tent chaotic map, the Logistic chaotic map, and the Bernoulli chaotic map, respectively. The initial gray wolf population is generated, where r and u are the chaos control parameters. (2) The improved multi-objective hybrid particle swarm optimization algorithm for gray wolf optimization coordinates the global exploration and local exploitation capabilities through an adaptive adjustment mechanism of the convergence factor as follows: In the formula: a initial and a final Let be the initial and final values ​​of the convergence factor 'a', and k be the current iteration number. max The maximum number of iterations is n, where n is the decreasing exponent, and 0 is the maximum number of iterations. <n≤1; The improved convergence factor 'a' is a curve based on a sinusoidal change. It decreases more slowly in the early stages of iteration, allowing 'a' to remain at a larger value for a longer period, thus improving search efficiency. In the later stages of iteration, it decreases more rapidly, allowing 'a' to remain at a smaller value for a longer period, thus improving search accuracy. Therefore, it balances the algorithm's global search and local search capabilities. (3) The introduction of a dynamic Gaussian mutation operator to enhance the Pareto front search efficiency in the improved multi-objective hybrid particle swarm optimization algorithm is as follows: Dynamic control formula for mutation probability based on iteration count decay: In the formula: P mutation (k) represents the mutation probability in the k-th iteration; P start α represents the initial mutation probability; α is a parameter controlling the descent rate. Dynamic mutation operator based on Gaussian mutation: X mutation =X current +σN(0,1) (9) In the formula: X mutation This indicates the location of the mutated gray wolf; X current σ represents the position of the gray wolf before mutation; σ is the standard deviation that changes dynamically with iteration.

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