Water-wind-light optimal scheduling method and system based on two-stage dual-population evolutionary algorithm

Abstract

The invention belongs to the field of water-wind-light multi-energy complementary optimal scheduling, and particularly discloses a water-wind-light optimal scheduling method and system based on a two-stage dual-population evolutionary algorithm, and the method comprises the steps: taking the water level of a reservoir as a decision variable, taking the maximum power generation amount and the minimum residual load mean square deviation as objective functions, and constructing a multi-objective scheduling model; the two populations are initialized, and the water-wind-light multi-target scheduling model is solved; the two populations are initially in a fixed division stage, and operators A and B are respectively adopted for iterative updating; when a switching condition is met, switching to a self-adaptive cooperation stage for iterative updating, determining the selection probability of the operators A and B according to population performance at the moment, and selecting the operators based on the selection probability for iterative updating; the switching condition is that after the population is iteratively updated each time, if the population diversity is smaller than a threshold value or the evaluation frequency reaches the threshold value, stage switching is carried out. According to the method, the contradiction between convergence and diversity in water-wind-light multi-objective optimization can be solved, and accurate optimization is realized.

Description

Technical Field

[0001] This invention belongs to the field of multi-energy complementary optimization scheduling of water, wind and solar power, and more specifically, relates to a water, wind and solar power optimization scheduling method and system based on a two-stage dual-population evolution algorithm. Background Technology

[0002] The core of multi-objective optimal scheduling of hydropower, wind power, and solar power systems lies in resolving the competitive trade-off between power generation efficiency and grid peak-shaving demand. It aims to increase the total power generation of hydropower, wind power, and solar power plants to ensure economic viability, while simultaneously reducing grid load fluctuations to improve power supply stability. However, increased power generation is often accompanied by increased load fluctuations, creating a coupling conflict between these objectives. This problem is a typical dynamic nonlinear multi-objective optimization problem, and traditional methods have significant limitations in solving the optimal scheduling problem of hydropower, wind power, and solar power systems. (1) Existing water, wind and solar energy optimization scheduling technology mainly uses a single population evolution algorithm (such as NSGA-II, MOPSO, SPEA2). All individuals follow the same evolutionary rules, which makes it difficult to take into account the needs of global exploration and local exploitation. This can easily lead to premature loss of population diversity or slow convergence, and cannot adapt to the dynamic needs of water, wind and solar energy scheduling in the early stage of wide-area exploration of high-quality solution space and in the later stage of precise optimization of local areas. Different operator update mechanisms often have different focuses. If the focus is on global exploration, it is easy to lead to slow convergence in the later stage, making it difficult to obtain a high-precision scheduling scheme. If the focus is on local exploitation, it is easy to lose population diversity prematurely and fall into local optima.

[0003] (2) Although some technologies have adopted dual-population strategies or multi-operator methods (such as multi-objective trading strategies and systems for hydropower, wind power and solar power based on improved hybrid algorithms), dual-population only uses different algorithms (such as MOPSO and NSGAII) to independently optimize and update the population. Only some populations are archived and migrated in the later stage. There is no exponential decay scoring and dynamic selection probability allocation logic for the real-time success rate of operators, which is difficult to adapt to the characteristics of multi-objective scheduling engineering and multi-objective collaborative optimization requirements of hydropower, wind power and solar power. Traditional multi-operator algorithms use fixed probability or random methods to select operators (such as GA and DE), which cannot be adjusted according to the optimization process and the real-time performance of operators, resulting in mismatch of search resources and low efficiency. When global exploration is required, local search operators are still used extensively, or when local optimization is required, global operators are still relied upon.

[0004] (3) Most co-evolutionary algorithms only focus on horizontal information exchange between populations and ignore the vertical guiding role of historical elite solutions in external archives. Historical elite solutions carry key high-quality genes, resulting in insufficient information utilization, easy loss of high-quality genes, and reduced convergence stability.

[0005] (4) Existing technologies all adopt a single strategy. If the NSGA-II selection strategy is used throughout the process, insufficient selection pressure is likely to occur under the high-dimensional target space or complex constraints of water, wind and solar scheduling, resulting in a lack of solution set diversity and difficulty in providing rich power generation and peak shaving trade-off schemes. If the SPEA2 selection strategy is used throughout the process, it is necessary to calculate the dominance strength between individuals and the target space distance, which significantly increases the computational cost and cannot meet the real-time requirements of engineering scheduling. It is difficult to balance the two, which has become a key bottleneck restricting the algorithm's adaptation to water, wind and solar multi-target scheduling scenarios.

[0006] In summary, there is an urgent need for an optimization method that can dynamically balance exploration and mining, adaptively match operator resources, efficiently utilize elite information, and balance efficiency and quality. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a water, wind and solar energy optimization scheduling method and system based on a two-stage dual-population evolutionary algorithm. Its purpose is to resolve the contradiction between convergence and diversity in multi-objective optimization of water, wind and solar energy, and achieve accurate optimization.

[0008] To achieve the above objectives, according to one aspect of the present invention, a water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm is proposed, comprising the following steps: Using reservoir water level as the decision variable and the objective functions of maximizing power generation and minimizing the mean square error of surplus load in the hydro-wind-solar multi-energy complementary system, a multi-objective scheduling model for hydro-wind-solar is constructed. Two populations are initialized, and the multi-objective scheduling model for water, wind, and solar power is solved. Initially, both populations are in a fixed division of labor phase. When the phase switching condition is met, they switch to an adaptive cooperative phase for iterative updates, ultimately obtaining the solution set and achieving optimized scheduling of water, wind, and solar power. Wherein: Fixed division of labor phase: The two populations are iteratively updated using operators A and B respectively; Adaptive and cooperative phase: The selection probabilities of operators A and B are determined based on the real-time performance of the population, and the two populations iteratively update by selecting operator A or B based on the selection probabilities. The phase switching condition is as follows: In the fixed division of labor phase, the population diversity is evaluated after each iteration update. When the population diversity is less than the diversity threshold or the number of iterations reaches the evaluation number threshold, the phase switching is performed.

[0009] As a further optimization, the selection probabilities of operators A and B are determined based on the real-time performance of the population, including: For operators A and B, the success rate of an operator is the proportion of offspring produced by the operator that are retained by the next generation population. Based on the operator success rate, an attenuation mechanism is used to update the operator score:

[0010] in, t This represents the current iteration number. , The first t Alternative operators The rating and success rate For operator type, The attenuation coefficient; The probability of selecting an operator is determined by the proportion of its score to the sum of the scores of the two operators.

[0011] As a further preferred method, the population diversity is determined by calculating the diversity of the two populations separately using the following formula, and then taking the mean of the diversity of the two populations as the final population diversity.

[0012] in, For the diversity of a single population, N is the population size. , Let be the objective function values ​​of the i-th and j-th individuals in the population, respectively. This is the Euclidean distance operator.

[0013] As a further optimization, in the adaptive cooperation phase, after each population is updated, the top 10% of elite solutions are selected from another population and the top 10% of elite solutions are selected from the external archive. Then, the union of the two types of elite solutions is migrated to the current population and participates in the next environment selection.

[0014] As a further preferred method, the elite solution selection method is as follows: first, the individuals in the migration source are sorted in ascending order according to the non-dominance level; then, the individuals in the migration source are sorted in descending order according to the crowding distance; and finally, the top 10% of the individuals in the sorted migration source are selected as the elite solution; the migration source is another group or an external archive.

[0015] As a further preferred embodiment, the external archive is updated as follows: every K generations, individuals are selected from the population to update the external archive based on Pareto strength and Euclidean distance truncation; in the remaining generations, individuals are selected from the population to update the external archive based on non-dominance level and crowding distance.

[0016] As a further selection criterion, individuals are selected from the population based on non-dominance level and crowding distance, specifically as follows: The population is sorted by non-dominated hierarchy to obtain several non-dominated layers sorted from high to low. Individuals in the non-dominated layers are placed into the external archive in order of sorting, and the process stops when the external archive reaches the archive size. For non-dominated layers that have just reached the archive size, the crowding distance of all individuals in the dominant layer is calculated, and some individuals are selected based on the crowding distance to be placed into the external archive, so that the individuals in the external archive reach the archive size.

[0017] As a further selection criterion, individuals are selected from the population based on Pareto strength and Euclidean distance truncation, specifically as follows: Individuals in the population with a Pareto strength value less than 1 were selected; If the number of individuals selected does not exceed the archive size, all selected individuals will be directly stored in the external archive. If the number of selected individuals exceeds the archive size, first calculate the Euclidean distance between the selected individuals and construct a distance matrix. Based on this distance matrix, calculate the crowding degree of each individual and delete the most crowded individual. Then repeat the above process until the number of remaining individuals exactly matches the archive size, and store the remaining individuals in an external archive.

[0018] As a further preferred embodiment, operators A and B are a genetic operator and a difference operator, respectively.

[0019] According to another aspect of the present invention, a water, wind and solar energy optimization scheduling system based on a two-stage dual-population evolutionary algorithm is provided, including a processor, the processor being used to execute the above-described water, wind and solar energy optimization scheduling method based on the two-stage dual-population evolutionary algorithm.

[0020] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages: 1. Unlike traditional multi-objective algorithms that use a single population, this invention breaks through the traditional single-population evolution mode and designs an evolutionary system composed of two parallel populations. By dynamically switching from a fixed division of labor exploration stage to an adaptive collaborative development stage, it balances global exploration and local mining capabilities, and solves the contradiction between convergence and diversity in multi-objective optimization.

[0021] 2. Traditional multi-operator algorithms often use fixed probabilities or random methods to select operators, which cannot be dynamically adjusted according to the optimization process and the real-time performance of operators, resulting in low search efficiency. This invention proposes a dynamic operator selection strategy based on the success rate under different historical environments. It dynamically adjusts the selection probabilities of the two operators. The higher the proportion of high-quality offspring produced by an operator and that are retained, the higher its score, and the greater the probability of it being selected later. This allows the algorithm to autonomously learn the optimal operator in the current optimization stage, improving evolutionary efficiency.

[0022] 3. Most co-evolutionary algorithms have limitations, focusing only on information exchange between populations while neglecting the guiding role of historical elite solutions, leading to insufficient information utilization. To overcome this limitation, this invention designs a bidirectional, multi-source, multi-level elite migration mechanism, organically combining horizontal migration between populations and vertical migration from external archives. This mechanism not only promotes horizontal communication between populations, accelerating the spread of superior patterns and genes, but also realizes the vertical inheritance of historical elites, effectively avoiding the problem of populations becoming trapped in local optima and losing superior genes. Ultimately, this not only significantly improves the algorithm's convergence speed but also enriches population diversity, enhancing the algorithm's robustness and global search capability.

[0023] 4. To address the challenge of a single environment selection strategy failing to comprehensively consider both computational efficiency and solution quality, this invention designs a scenario-specific, differentiated hybrid selection system. The core advantages of two strategies are adapted to different scenarios. For each generation of external archive updates, a computationally efficient fast non-dominated sorting and crowding distance strategy is employed to prioritize algorithm iteration speed and meet the timeliness requirements of water, wind, and solar power scheduling. For external archive maintenance, Pareto intensity calculation and minimum distance truncation strategies are periodically triggered. Leveraging their dual advantages in diversity and convergence, these strategies accurately maintain the uniformity and coverage of historical elite solutions, ensuring that the archive retains high-quality solutions with broad coverage and reasonable distribution. This hybrid strategy cleverly balances efficiency during the algorithm process with the quality of the final solution set, avoiding a significant increase in overall computational cost. The diversity advantage compensates for the convergence of solution sets under a single strategy, ultimately outputting a solution set that meets Pareto optimality and possesses sufficient diversity. This perfectly adapts to the practical needs of multi-scheme decision-making in scenarios such as water, wind, and solar power multi-objective scheduling, where a rich selection of options is required. Attached Figure Description

[0024] Figure 1 This is a flowchart of the water, wind and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm according to an embodiment of the present invention.

[0025] Figure 2 This is a comparison chart of the Pareto frontiers of various algorithms in embodiments of the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0027] This invention addresses the multi-objective scheduling problem of water, wind, and solar power, proposing a two-stage dual-population evolutionary algorithm (TS-DPEA). Based on a two-stage dual-population architecture, with an adaptive operator selection strategy at its core, multi-source elite migration as support, and hybrid environment selection as a guarantee, this systematic design enables optimized scheduling of water, wind, and solar power across multiple objectives. Details are as follows: (1) Two-population-two-stage-adaptive collaborative framework Unlike traditional multi-objective algorithms that use a single population, this algorithm breaks through the traditional single-population evolutionary model by designing an evolutionary system composed of two parallel populations (Pop1 and Pop2). Through dynamic switching between a fixed-division exploration phase and an adaptive collaborative development phase, it balances global exploration and local resource extraction capabilities, resolving the contradiction between convergence and diversity in multi-objective optimization. Specifically: 1) Population diversity Population diversity quantifies the dispersion of individuals in the target space and is one of the core indicators for stage switching, reflecting the algorithm's exploration capability in the early stages. For two populations (denoted as Population 1 and Population 2), where each individual contains two targets, the diversity of each population must be calculated separately, and then the average of the two values ​​is taken as the overall diversity index, as follows: Diversity of population 1:

[0028] Diversity of population 2:

[0029] The overall diversity index is the average of the diversity of the two populations:

[0030] In the formula: These represent the sizes of population 1 and population 2, respectively. , These are the diversity values ​​for population 1 and population 2, respectively. The average diversity of the two populations reflects the overall degree of dispersion. The larger the value, the higher the degree of dispersion of the population and the stronger its exploration ability. Describe the objective function for the i-th individual; This is the Euclidean distance operator, used to calculate the spatial distance between two target vectors, for example... , , These are the first and second objective function values ​​of individual i in population 1, respectively.

[0031] 2) Phase switching conditions The algorithm automatically triggers stage switching based on a diversity threshold or the percentage of function evaluations. The switching logic formula is as follows:

[0032] In the formula: The numbers represent stages, with 0 indicating a fixed division of labor and 1 indicating an adaptive collaboration stage. FE is the diversity threshold; FE is the number of algorithm evaluations; maxFE is the maximum number of evaluations. This is the threshold for the percentage of evaluations.

[0033] 3) Two-population evolutionary model The two populations use different operator rules at different stages to achieve a combination of division of labor and cooperation. The GA operator and DE operator are preferred as examples for further explanation, and the formula is described as follows: (5) In the formula: For the k-th population ( GA stands for Genetic Algorithm operator, and DE stands for Differential Evolution Algorithm operator. Both can maintain population diversity and prevent the population from getting trapped in local optima. , Let represent the selection probabilities of GA and DE during the adaptive cooperative phase.

[0034] Phase 1 (Fixed Division of Labor Phase): The two populations initially adopt a fixed division of labor to conduct extensive exploration. The two populations use the GA and DE operators respectively, making full use of the characteristics of different operators to conduct global exploration, aiming to quickly locate promising areas and maintain a high level of diversity.

[0035] The second stage (adaptive collaborative stage): When the population diversity is below the threshold or the number of evaluations reaches a certain proportion, the algorithm automatically switches to this stage. It dynamically switches to the adaptive collaborative mode based on the population diversity. Both populations dynamically mix and use GA and DE operators based on real-time performance, combining the global exploration advantage of GA with the local fine-grained search advantage of DE for continuous variables (such as water level). The operator is selected dynamically and adaptively based on the success rate of the operator under different environmental selection strategies.

[0036] The dual-population, two-stage, adaptive collaborative framework avoids the shortcomings of a single algorithm, ensuring the sufficiency of global exploration in the early stage, while possessing the adaptability and efficiency of local mining in the later stage. This mechanism ensures the dual enhancement and effective connection of the algorithm's global exploration capability and local development capability from the system architecture level, providing a structural foundation for resolving the contradiction between convergence and diversity.

[0037] (2) Dynamic adaptive mechanism oriented towards operator performance Traditional multi-operator algorithms often use fixed probabilities or random methods to select operators, which cannot be dynamically adjusted according to the optimization process and the real-time performance of operators, resulting in low search efficiency. This invention proposes a dynamic operator selection strategy based on success rates under different historical environments. This strategy dynamically adjusts the selection probability of operators; the higher the proportion of high-quality offspring produced and retained by an operator, the higher its score, and the greater its probability of being selected subsequently. This allows the algorithm to autonomously learn the optimal operator for the current optimization stage, improving evolutionary efficiency. The proportion of offspring produced by an operator and retained by the next generation is considered its current success rate. This score is smoothly updated through a decay mechanism, as detailed below: 1) Calculation of operator success rate The success rate of an operator is defined as the proportion of its offspring that are retained by the next generation of the population, and is calculated as follows:

[0038] In the formula: Let be the success rate of the t-th generation operator; The operator type is t; the current iteration number is t. Let be the total number of offspring generated by the operator in generation t; The number of offspring generated by the operator in generation t that are retained by the environment selection strategy in generation t.

[0039] 2) Operator score update To avoid the impact of single success rate fluctuations on selection, while retaining the overall historical operator performance, a decay mechanism is used to update the operator score, with the following formula: (7) In the formula: The t-th generation operator The initial value of the score ; This is the decay coefficient, used to balance the weights of historical scores and current success rates.

[0040] 3) Calculation of operator selection probability Selection probabilities are dynamically allocated based on operator scores, with higher-performing operators receiving a greater chance of selection. This ensures resources are allocated to efficient operators, addressing the inefficiency and resource waste inherent in traditional fixed-probability selection. The calculation formula is as follows:

[0041] In the formula: For the t-th generation operator The probability of choosing, and .

[0042] (3) Multi-level and multi-source elite migration strategy Most co-evolutionary algorithms have limitations, focusing only on information exchange between populations while neglecting the guiding role of historical elite solutions, leading to insufficient information utilization. To overcome this limitation, this invention designs a bidirectional, multi-source, multi-level elite migration mechanism, organically combining horizontal migration between populations and vertical migration from the external archive. In the cooperative adaptation phase, after each population update, it selects the top 10% of elite solutions from another population and the top 10% of historical elite solutions from the external archive, achieving multi-source elite fusion. Then, both types of elite solutions are migrated to the current population and participate in the next environmental selection. This mechanism promotes horizontal communication between populations, accelerating the spread of superior patterns and genes; it also realizes the vertical inheritance of historical elites, effectively avoiding the problem of populations becoming trapped in local optima and extinct superior genes. Ultimately, it not only significantly improves the convergence speed of the algorithm but also enriches population diversity and enhances the algorithm's robustness and global search capability. The specific steps are as follows: 1) Number of elite migrants The calculation of the number of elites migrating needs to take into account both the effectiveness of information transmission and the stability of the population. The number of elites selected from each migration source is 10% of the current total number of effective individuals in that migration source. This proportion is determined based on the solution space characteristics of the water, wind and solar scheduling problem. The 10% proportion can ensure that the migrating elites carry enough high-quality information (such as high-power scheduling schemes explored by different populations and low-overload fluctuation schemes preserved in the archives), and will not interfere with the evolutionary direction of the current population due to the large number of migrants. The result of the 10% proportion calculation may be a decimal, which needs to be rounded up.

[0043] 2) Ranking rules for elite selection The elite selection for both types of migration sources follows a dual standard of non-dominance priority and dispersion priority, prioritizing elite convergence:

[0044] In the formula: The non-dominated ranking rank of individuals in migration source X; The crowding distance of individuals in migration source X; First press Ascending order, then by Descending order.

[0045] 3) Construction and merging of migration elite sets Merge the heterogeneous elites with the archived elites to form the final migration set, using the following formula:

[0046] In the formula: Elite subsets extracted from heterogeneous populations are used for lateral migration to transmit real-time optimization information; A subset of elite data extracted from external archives is used to achieve vertical migration and transmit high-quality historical information. As the final elite group to be migrated into the current population, it will be merged with the offspring of the current population after environmental selection, and participate in the next round of evolutionary iteration.

[0047] (4) Mixed Environment Selection Strategy To address the challenge of single-environment selection strategies failing to comprehensively consider computational efficiency and solution quality, this invention designs a scenario-specific, differentiated hybrid selection system. The core advantages of two strategies are adapted to different scenarios. For each generation of external archive updates, a computationally efficient fast non-dominated sorting and congestion distance strategy is employed to prioritize algorithm iteration speed and meet the timeliness requirements of water, wind, and solar power scheduling. For external archive maintenance, Pareto intensity calculation and minimum distance truncation strategies are periodically triggered. Leveraging their dual advantages in diversity and convergence, these strategies precisely maintain the uniformity and coverage of historical elite solutions, ensuring that the archive retains high-quality solutions with broad coverage and reasonable distribution. This hybrid strategy cleverly balances efficiency during the algorithm process with the quality of the final solution set, avoiding a significant increase in overall computational cost. The diversity advantage compensates for the convergence of solution sets under a single strategy, ultimately outputting a solution set that meets Pareto optimality and possesses sufficient diversity. This perfectly adapts to the practical needs of multi-scheme decision-making in scenarios such as water, wind, and solar power multi-objective scheduling, where a rich selection of options is required. Specific steps are as follows: The external archive is updated every K generations using Pareto strength and Euclidean distance truncation selection for environment selection, and at other times it is filtered using fast non-dominated sort and crowding distance.

[0048] 1) Environment selection using non-dominated sorting stratification and crowding distance filtering can achieve efficient population selection, ensuring that the computational cost of each generation iteration is controllable. Individuals in the population are divided into different Front No values ​​according to the objective function. The smaller the Front No value, the higher the non-dominated level of the individual. First, filtering is performed based on the non-dominated level, and then filtering is performed using crowding distance. Crowding distance calculates the sparsity of an individual within its respective Front No., avoiding convergence of solution sets. The formula is:

[0049] In the formula: m is the number of objective functions; The maximum and minimum values ​​of the m-th target in the current frontier; Let be the target value of the adjacent individuals of the i-th individual after sorting the m-th target.

[0050] Specifically, the current population is first sorted using non-dominated methods to obtain several non-dominated layers. The first non-dominated layer has the highest non-dominated level, and the dominance level of subsequent layers decreases sequentially. Individuals from each layer are added to the external archive in descending order of non-dominated layer priority: if the cumulative number of individuals in the archive does not reach the archive size after being added to the current layer, the next layer is added, and so on. If the cumulative number of individuals in the archive exceeds the archive size after being added to a certain layer, addition to subsequent layers is stopped, and only the crowding distance is calculated for all individuals in that layer. Individuals in that layer are sorted in descending order of crowding distance, and the top k individuals (k is the archive size minus the total number of individuals already added to all previous layers) are added to the external archive, ensuring that the number of individuals in the archive is exactly equal to the archive size. If the cumulative number still does not reach the archive size after all non-dominated layer individuals have been added, all added individuals are directly stored in the external archive (generally, the population size before selection is definitely greater than the archive size).

[0051] 2) By calculating Pareto intensity and optimizing the distribution of Archive solution sets using minimum distance truncation, Pareto intensity reflects the overall dominance relationship and nearest neighbor distance, quantifying the quality of individual solutions. The calculation formula is as follows:

[0052] In the formula: This indicates the degree to which the archive is dominated by high-quality individuals. The smaller the value, the lower the degree of dominance the individual experiences; This indicates the degree of isolation of an individual within the target space. The Euclidean distance between nearest neighbors is given. The smaller the value, the more isolated the individual, thus avoiding the concentration of unsets.

[0053] Specifically, the process begins with a preliminary screening based on Pareto strength values, identifying all individuals in the population with Pareto strength values ​​less than 1. If the number of selected individuals does not exceed the archive size, all qualified individuals are directly stored in the external archive. If the number exceeds the archive size, the pairwise Euclidean distances between these individuals are calculated, and a distance matrix Dist is constructed. Then, the minimum nearest neighbor distance is used as the crowding index, and the crowding degree of each individual is calculated based on this matrix. The most crowded individual is then identified and deleted. Subsequently, the pairwise Euclidean distances are recalculated for the remaining individuals, the distance matrix is ​​updated, and the process of calculating crowding degree and identifying and deleting the most crowded individual is repeated to maintain the uniformity of the solution set. This truncation selection is performed until the number of remaining individuals exactly matches the archive size, and finally, these individuals are stored in the external archive.

[0054] Based on the aforementioned TS-DPEA algorithm, this invention provides a water-wind-solar multi-energy complementary system optimization scheduling method based on a two-stage dual-population evolutionary algorithm. The method uses reservoir water level as the decision variable and the objective functions are maximizing power generation and minimizing the mean square error of surplus load. Various constraints are also set to construct a multi-objective scheduling model for water-wind-solar systems. The multi-objective scheduling model is then optimized and solved, as follows: Figure 1 As shown, it includes the following steps: S1: Parameters and Population Initialization Set the core parameters of the algorithm: population size N=100, maximum number of evaluations maxFE, external archive size=1000, population diversity threshold=1e-4, evaluation frequency percentage threshold=0.2, operator score decay coefficient=0.9, initialize the archive to store elite solutions during the iteration process, initially empty; generate two parallel initial populations (Pop1, Pop2).

[0055] S2: Phase One – Fixed Division of Labor and Global Exploration According to the population evolution rules, in the first stage, Pop1 uses the Genetic Algorithm (GA) operator to leverage its global search characteristics, while Pop2 uses the Differential Evolutionary Algorithm (DE) operator to leverage its local search advantages based on the continuous water level variable. Wide-area exploration is achieved through the differences in the characteristics of the two types of operators. Offspring generation and selection are performed by generating offspring individuals based on the GA / DE operators, and eliminating infeasible solutions by combining water, wind, and solar scheduling constraints (such as water balance and upper and lower limits of hydropower station output). Population and archive updates are then performed: the population is updated using a fast non-dominated sorting and crowding distance environment selection strategy, retaining high-quality solutions. Simultaneously, the non-dominated solutions generated during iteration are stored in an external archive, completing one iteration and proceeding to S3.

[0056] S3: Phase Switching Condition Judgment Calculate the current population diversity and quantify the degree of individual dispersion in the target space; if any of the following conditions are met, trigger a phase switch and enter the second phase: ① Population diversity is less than the set threshold; ② The percentage of algorithm evaluations (FE / maxFE) is greater than the evaluation percentage threshold; if not met, return to S2 to continue fixed division of labor exploration.

[0057] S4: Phase Two – Adaptive Cooperative Local Mining The success rate of the GA / DE operator is calculated based on the proportion of offspring generated by the GA / DE operator in generation t that are retained, i.e., the proportion of retained offspring to the total number of offspring. A decay mechanism is used to smoothly update the GA / DE operator score, retaining the overall historical score and avoiding the impact of single fluctuations. The selection probability is calculated based on the operator score, and the probability sum is 1. Pop1 and Pop2 both dynamically select the GA / DE operator to generate offspring, combining the advantages of the two types of operators.

[0058] Determine the number of individuals to migrate: Calculate the number of individuals to migrate based on 10% of the population size and the size of the external archive, and carry out multi-level elite migration; Select elite solutions: Select the top 10% of elite solutions from the heterogeneous population for horizontal migration to pass on real-time optimization information, and select the top 10% of historical elite solutions from the external archive for vertical migration to pass on historical high-quality information, and merge them into a set of elite migration solutions; Merge the set of elite migration solutions with the offspring of the current population to participate in the subsequent environmental selection of the population.

[0059] Archive maintenance: K=5 generations can ensure the uniformity of the archive solution distribution while avoiding efficiency loss caused by frequent calculations. Therefore, the external archive is updated every 5 generations using Pareto intensity calculation and Euclidean distance truncation environment selection strategy. In other iterations, the fast non-dominated sorting and crowding distance environment selection strategy are still used to ensure the algorithm iteration efficiency, improve the convergence and distribution of elite solutions, complete 1 iteration, return to S3, until the termination condition is met.

[0060] S5: Iteration Termination and Optimization Result Output If the number of algorithm evaluations reaches maxFE, the iteration terminates; non-dominated solutions are extracted from the external archive to form the Pareto front, and a set of multi-objective scheduling optimization schemes for hydropower, wind power and solar power is output, covering multiple scheduling schemes with maximum power generation, minimum surplus load variance and compromise, for decision-making selection.

[0061] The following are specific examples: Taking the Baihetan Hydropower Station in 2022 as the research object, a multi-objective scheduling model was constructed for optimization. The optimization objectives were to maximize power generation on the power source side and minimize the standard deviation of surplus load on the grid side. The dry season of the Baihetan Hydropower Station (strong winds and strong sunlight in March 2022) was selected as the research scenario to conduct multi-objective optimization scheduling research on the hydro-wind-solar hybrid system. The water level of the power station at the beginning of March 2022 was 788.91m, and the final water level was 795.75m, with an average inflow of 1790.32 m³ / s. In this example, 50% of the power output of the Baihetan Hydropower Station was sent to Zhejiang Province, and the average monthly load in Zhejiang Province in March 2022 was approximately 60081MW.

[0062] (1) Model building Using water level as the decision variable, a multi-objective function model is established with the objectives of maximizing the power generation of the hydro-wind-solar multi-energy complementary system and minimizing the mean square error of the surplus load. Constraints such as water level, flow rate, and output are set to jointly constitute a multi-objective scheduling model. The power output of the hydropower station in each time period is calculated based on the net head and water consumption rate curve of the hydropower station in each time period. At the same time, the wind and solar power output in the corresponding time period is added. The first objective function is established with the combined power output of hydropower, wind and solar power in each time period, with the goal of maximizing the power generation of the hydropower-wind-solar multi-energy complementary system:

[0063] In the formula: The total power generation of the complementary system is represented by T, the total number of time periods within the scheduling period is represented by T, and t is the time period sequence number. , It is the scheduling period. It is the total output during time period t. This represents the power output of the hydropower station during time period t. and These represent the power output of wind power stations and photovoltaic power stations during the same time period, respectively.

[0064] Meanwhile, in addition to considering the power generation benefits on the power supply side, the power station should also consider the peak-shaving effect on the grid side. Therefore, a second objective function was established based on the load demand of the power station's transmission area and the total output process of the hydro-wind-solar system:

[0065] In the formula: This represents the mean square error of the residual load of the power grid after being supplied by a multi-energy complementary system of water, wind, and solar power. Indicates the power grid load demand. This indicates the surplus load of the power grid after being supplied by the hydro-wind-solar multi-energy complementary system. This represents the average surplus load of the power grid.

[0066] Set model constraints for the multi-objective scheduling model. These constraints include: reservoir water level constraints, water balance constraints, reservoir characteristic constraints, power output characteristic constraints, flow rate constraints, water level / flow rate variation constraints, hydropower station power output constraints, wind farm wind speed constraints, and photovoltaic power generation capacity constraints. Specific constraint settings are as follows: 1) Reservoir water level constraints.

[0067] In the formula: Indicates that the reservoir is Water level in front of the dam during the specified time period and Reservoirs at The upper and lower limits of the water level in front of the dam during a certain period.

[0068] 2) Water balance constraints

[0069] In the formula: and These represent the reservoir capacity at time t and time t-1, respectively. Reservoir Inbound flow during a specific time period; Reservoir Outbound flow during a specific time period.

[0070] 3) Reservoir characteristic constraints

[0071] In the formula: For reservoir Average upstream water level over a given period; For reservoir Average tailwater level downstream during the period; , These represent the reservoir's water level-capacity curve and tailwater level-discharge curve, respectively.

[0072] 4) Output characteristic constraints

[0073] In the formula: This represents the function for calculating reservoir output. For the reservoir in t The amount of clean water generated during a given time period; For the reservoir in t The power generation flow rate during a given time period.

[0074] 5) Flow constraints

[0075] In the formula: and These respectively represent the reservoir at t Upper and lower limits of discharge flow during different time periods.

[0076] 6) Water level / flow rate variation constraints

[0077] In the formula: This indicates the allowable range of water level changes within the reservoir's operational time interval.

[0078] 7) Power output constraints of hydropower stations

[0079] In the formula: and These respectively represent the reservoir at t The upper and lower limits of output during different time periods.

[0080] 8) Wind speed constraints at wind farms

[0081] In the formula: and These respectively represent wind farms in t Upper and lower limits of wind speed for entry and exit points during specific time periods.

[0082] 9) Capacity constraints of photovoltaic panels

[0083] In the formula: and They represent the photoelectric field at... t Upper and lower limits of the capacity of the power generation panels during different time periods.

[0084] This invention employs the TS-DPEA algorithm for solving the problem and selects classic multi-objective optimization algorithms NSGAⅡ, MOBCA, SPEA2, and MOEA / D as comparative algorithms. The parameters of the TS-DPEA algorithm are set as follows: population size N=100, maximum number of iterations MaxIter=1000, external archive Archive=100; all other algorithm parameters are set to default.

[0085] After algorithm optimization, each algorithm retains 100 solutions to form the Pareto front solution. Table 1 shows the multi-objective scheduling schemes obtained by TS-DPEA optimization: Table 1 Optimization Results of TS-DPEA Algorithm

[0086] As shown in Table 1, when the system's power generation increases, the mean square error of the remaining load also increases, and the peak-shaving efficiency decreases, indicating a significant competitive relationship between power generation and the mean square error of the remaining load. Therefore, the non-dominated solution set obtained from the example can effectively reflect the game between the economic benefits on the source side and the peak-shaving demand on the grid side, which is consistent with engineering practice.

[0087] Pareto fronts of various algorithms, for example Figure 2 As shown, both have reached convergence. The Pareto front of the TS-DPEA algorithm lies in the dual objective space of power generation and residual load mean square error. When the residual load mean square error is at a low level, TS-DPEA can achieve significantly higher power generation. Moreover, as power generation increases, the growth of residual load mean square error is more gradual, resulting in better efficiency in the trade-off between the two objectives. At the same time, TS-DPEA has a wider range of values ​​for the two objective functions of power generation and residual load mean square error, providing richer scheduling schemes for subsequent decisions.

[0088] In comparison, the Pareto front distribution of SPEA2, MOBCA, and NSGAII is further back, resulting in lower power generation under the same surplus load, or a higher surplus load variance under the same power generation. Although MOEA / D pursues high power generation, the surplus load variance increases more significantly, and its dual-objective balancing ability is weaker than TS-DPEA. Its scheduling schemes are limited and cannot meet the needs of actual scheduling schemes.

[0089] It is evident that the TS-DPEA proposed in this invention demonstrates a more prominent performance balance in the dual-objective optimization of power generation enhancement and surplus load fluctuation control, and can provide more diverse scheduling schemes.

[0090] To evaluate the characteristics of data from different perspectives, the hypervolume index (HV) reflects the size of the volume covered by the non-dominated solution set in the target space; a larger value usually indicates better performance of the solution set. The distribution uniformity index (ΔP) measures the degree of uniformity of the solution set distribution in the target space; a smaller value indicates a more uniform distribution. The diversity index (DM) reflects the diversity of the solution set in various target dimensions; a larger value indicates higher diversity.

[0091] As shown in Table 2, the TS-DPEA algorithm proposed in this invention achieves a hypervolume index of 149830, which is more than 2.3 times the best value among the compared algorithms. This directly proves that the present invention, through systematic improvement, has achieved a synergistic improvement in the convergence and diversity of the solution set, demonstrating significant technical effectiveness. The diversity index of TS-DPEA far exceeds that of all compared algorithms, indicating that its technical solution effectively avoids premature convergence, explores a broader target space, and generates more diverse scheduling schemes, perfectly meeting the urgent need for multi-scheme decision-making in engineering practice. This leap in performance is precisely the unexpected technical effect produced by the synergistic effect of the various technical features of this invention. Although the distribution uniformity is not optimal, overall, it provides more diverse and high-quality solutions for decision-making scenarios such as multi-objective optimization scheduling of water, wind, and solar power, making it more competitive in multi-objective optimization problems of water, wind, and solar power.

[0092] Table 2 Comparison of Evaluation Metrics for Various Algorithms

[0093] In summary, this invention provides a foundation through a dual-population architecture, achieves intelligent search through adaptive operator selection, promotes historical information collaboration and real-time information updates through elite migration, and balances efficiency and quality through hybrid environment selection. Ultimately, it has been successfully applied to the complex hydro-wind-solar multi-energy complementary optimization scheduling problem, providing a Pareto front scheduling scheme for hydro-wind-solar multi-energy complementary systems that can efficiently and with high quality generate Pareto front scheduling schemes with high convergence and high diversity.

[0094] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm, characterized in that, Includes the following steps: Using reservoir water level as the decision variable and the objective functions of maximizing power generation and minimizing the mean square error of surplus load in the hydro-wind-solar multi-energy complementary system, a multi-objective scheduling model for hydro-wind-solar is constructed. Two populations are initialized, and the multi-objective scheduling model for water, wind, and solar power is solved. Initially, both populations are in a fixed division of labor phase. When the phase switching condition is met, they switch to an adaptive cooperative phase for iterative updates, ultimately obtaining the solution set and achieving optimized scheduling of water, wind, and solar power. Wherein: Fixed division of labor phase: The two populations are iteratively updated using operators A and B respectively; Adaptive and cooperative phase: The selection probabilities of operators A and B are determined based on the real-time performance of the population, and the two populations iteratively update by selecting operator A or B based on the selection probabilities. The phase switching condition is as follows: In the fixed division of labor phase, the population diversity is evaluated after each iteration update. When the population diversity is less than the diversity threshold or the number of iterations reaches the evaluation number threshold, the phase switching is performed.

2. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 1, characterized in that, The selection probabilities of operators A and B are determined based on the real-time performance of the population, including: For operators A and B, the success rate of an operator is the proportion of offspring produced by the operator that are retained by the next generation population. Based on the operator success rate, an attenuation mechanism is used to update the operator score: in, t This represents the current iteration number. , The first t Alternative operators The rating and success rate For operator type, The attenuation coefficient; The probability of selecting an operator is determined by the proportion of its score to the sum of the scores of the two operators.

3. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 1, characterized in that, The method for determining population diversity is as follows: calculate the diversity of the two populations separately using the following formula, and then take the mean of the diversity of the two populations as the final population diversity. in, For the diversity of a single population, N is the population size. , Let be the objective function values ​​of the i-th and j-th individuals in the population, respectively. This is the Euclidean distance operator.

4. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 1, characterized in that, In the adaptive cooperation phase, after each population is updated, the top 10% of elite solutions are selected from another population and the top 10% of elite solutions are selected from the external archive. Then, the union of the two types of elite solutions is migrated to the current population and participates in the next environment selection.

5. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 4, characterized in that, The method for selecting elite solutions is as follows: first, individuals in the migration source are sorted in ascending order according to their non-dominance level; then, individuals in the migration source are sorted in descending order according to their crowding distance; and finally, the top 10% of individuals in the migration source after sorting are selected as elite solutions; the migration source is another group or an external archive.

6. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 4, characterized in that, The method for updating the external archive is as follows: every K generations, individuals are selected from the population to update the external archive based on Pareto strength and Euclidean distance truncation; in the remaining generations, individuals are selected from the population to update the external archive based on non-dominance level and crowding distance.

7. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 6, characterized in that, Individuals are selected from the population based on non-dominance level and crowding distance, specifically as follows: The population is sorted by non-dominated hierarchy to obtain several non-dominated layers sorted from high to low. Individuals in the non-dominated layers are placed into the external archive in order of sorting, and the process stops when the external archive reaches the archive size. For non-dominated layers that have just reached the archive size, the crowding distance of all individuals in the dominant layer is calculated, and some individuals are selected based on the crowding distance to be placed into the external archive, so that the individuals in the external archive reach the archive size.

8. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in claim 6, characterized in that, Individuals were selected from the population based on Pareto strength and Euclidean distance truncation, specifically as follows: Individuals in the population with a Pareto strength value less than 1 were selected; If the number of individuals selected does not exceed the archive size, all selected individuals will be directly stored in the external archive. If the number of selected individuals exceeds the archive size, first calculate the Euclidean distance between the selected individuals and construct a distance matrix. Based on this distance matrix, calculate the crowding degree of each individual and delete the most crowded individual. Then repeat the above process until the number of remaining individuals exactly matches the archive size, and store the remaining individuals in an external archive.

9. The water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in any one of claims 1-8, characterized in that, Operators A and B are the genetic operator and the difference operator, respectively.

10. A water, wind, and solar energy optimization scheduling system based on a two-stage dual-population evolutionary algorithm, characterized in that, Includes a processor, the processor being configured to execute the water, wind, and solar energy optimization scheduling method based on a two-stage dual-population evolutionary algorithm as described in any one of claims 1-9.

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