Improved NSGA-II algorithm-based locomotive depot micro-grid multi-objective optimization scheduling method under source-load interaction

Abstract

The invention provides a locomotive depot micro-grid multi-target optimization scheduling method based on an improved NSGA-II algorithm under source-load interaction, and the method comprises the steps: obtaining power utilization data according to the daily operation condition of a micro-grid, and building a constraint condition of the intra-day optimization scheduling of the locomotive depot micro-grid; establishing an intra-day optimal dispatching model of the locomotive depot micro-grid by taking minimization of the operation and maintenance cost of the micro-grid and maximization of the photovoltaic consumption rate of the micro-grid as objective functions; the new energy locomotive is regarded as a flexible load to participate in the intra-day scheduling of the locomotive depot micro-grid, and four operation strategies of the new energy locomotive are designed according to the degree of source-load interaction; and a WOA algorithm is introduced in the individual evolution process of the main cycle of the NSGA-II algorithm, and a Levy flight mechanism is embedded to obtain an improved fusion multi-objective optimization algorithm to solve the locomotive depot micro-grid intra-day optimization scheduling model, and a scheduling result is obtained. Through deep source-load interaction and an improved solution algorithm, the operation and maintenance cost of the micro-grid is effectively reduced, and the photovoltaic power generation consumption rate of the micro-grid is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-objective optimization scheduling of a locomotive depot microgrid, and in particular to a multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction. Background Art

[0002] As an important component of the new power system, microgrids often have multi-objective scheduling objectives (such as minimizing operating costs and maximizing renewable energy consumption) and complex constraints (such as energy balance and energy storage state restrictions). Therefore, the solution process places higher demands on the algorithm's convergence speed, solution diversity, and feasibility. In the field of multi-objective optimization, the non-dominated sorting genetic algorithm (NSGA-II) has been widely used in multi-objective scheduling and optimization problems due to its excellent solution set distribution characteristics, strong global search capabilities, and Pareto frontier maintenance capabilities. However, NSGA-II still has the following shortcomings in practical applications:

[0003] 1. Insufficient local development capabilities: Due to the randomness of crossover and mutation operations, it is impossible to take into account the stable development of each individual, resulting in weak individual fine search capabilities in the neighborhood;

[0004] 2. Limited convergence speed: In the late stages of population evolution, the population may stagnate or converge prematurely due to converging to a local optimal solution and lacking a way to escape the cycle.

[0005] 3. Unstable population distribution control: Individuals in the population are independent of each other and lack an active collaboration mechanism, which may lead to sparse solution distribution in some areas.

[0006] To address these shortcomings, researchers have recently begun experimenting with combining heuristic algorithms with NSGA-II. The Whale Optimization Algorithm (WOA) is an emerging swarm intelligence algorithm that optimizes targets by simulating the encirclement, spiral, and search strategies of humpback whales. It exhibits strong global search and local exploitation capabilities. The Whale Optimization Algorithm (WOA) possesses adaptive search capabilities, dynamically adjusting the balance between exploration and exploitation based on the iterative process. In the initial stages of the algorithm, a larger search radius is used to achieve global exploration, improving solution space coverage. In the later stages, the search radius is gradually narrowed to strengthen local exploration, thereby improving convergence accuracy and effectively avoiding the risk of being trapped in a local optimum. Levy flight, a random walk strategy with a long tail, introduces non-Gaussian perturbations during the local search process, enabling large-step jumps and increasing the uncertainty and diversity of the search path. This helps the algorithm escape local minima and enhances global optimization capabilities.

[0007] The invention patent with application number 202010131935.9 discloses a multi-objective optimization scheduling method for microgrids, including determining the microgrid structure and uncertainty modeling; establishing a load model and a default model according to different load characteristics; considering the optimal cost of the microgrid and the maximization of user satisfaction and performing multi-objective modeling; and using an improved NSGA-II algorithm for solving. The beneficial effects of the above invention are: first, by improving the generation of the cross operator coefficients of the NSGA-II algorithm, the complexity of the algorithm is effectively reduced, and the convergence speed and accuracy are further improved; second, the scheduling method that comprehensively considers the comprehensive operating cost of the microgrid and user satisfaction is compared. When the economic efficiency of the microgrid is considered alone, user satisfaction is greatly improved, and the actual electricity demand is met. However, the above method is prone to falling into local extreme values, and the convergence accuracy of the scheduling results is limited. Summary of the Invention

[0008] In response to the technical problems of low efficiency and accuracy of the multi-objective optimization scheduling method of the locomotive depot microgrid, the present invention proposes a multi-objective optimization scheduling method for the locomotive depot microgrid based on the improved NSGA-II algorithm under source-load interaction, establishes a microgrid scheduling model under four operation strategies of new energy locomotives, and proposes an improved non-dominated sorting genetic algorithm (FWOA-NSGA-II) that integrates the whale optimization algorithm (WOA) and the Levy flight mechanism to solve the multi-objective optimization scheduling problem of the locomotive depot microgrid. The proposed solution method can take into account the operating economy of the system and the utilization efficiency of renewable energy, and improve the diversity and convergence accuracy of the scheduling results. The established multi-objective scheduling model under source-load interaction can be effectively applied to the optimization scheduling scenario of the locomotive depot microgrid under the access of new energy.

[0009] In order to achieve the above object, the technical solution of the present invention is implemented as follows: a multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction, the steps of which are as follows:

[0010] Step 1: Obtain power consumption data based on the daily operation of the microgrid and establish constraints for the daily optimal scheduling of the locomotive depot microgrid;

[0011] Step 2: Taking minimizing the microgrid operation and maintenance costs and maximizing the microgrid photovoltaic absorption rate as the objective function, establish the intraday optimization scheduling model of the locomotive depot microgrid;

[0012] Step 3: Establish a source-load interaction mechanism: Consider new energy locomotives as flexible loads and participate in the daily scheduling of the locomotive depot microgrid. Based on the level of source-load interaction, design four operation strategies for new energy locomotives;

[0013] Step 4: The WOA algorithm is introduced into the individual evolution process of the main loop of the NSGA-II algorithm and the Levy flight mechanism is embedded to obtain an improved fusion multi-objective optimization algorithm. The improved fusion multi-objective optimization algorithm is used to solve the intraday optimization scheduling model of the locomotive depot microgrid and obtain the scheduling results.

[0014] Preferably, the photovoltaic power generation data for the day is predicted based on the original 24-hour power generation data of the microgrid on the day before, and a 5% disturbance range is added; the photovoltaic power generation prediction data is obtained using the Beta distribution;

[0015] The electricity consumption data includes daily electricity load data of the microgrid, charging and discharging range of the energy storage system, charging and discharging range of the locomotive, capacity of the energy storage system, capacity of the locomotive, state of charge of the energy storage, state of charge of the locomotive, and power purchase range of the microgrid;

[0016] The constraints include: power balance constraints, simultaneous charging and discharging of locomotives and energy storage, state of charge (SOC) range constraints, photovoltaic output uncertainty, and energy storage system state constraints;

[0017] The modeling object of the established locomotive depot microgrid intraday optimization scheduling model is the locomotive depot microgrid system, considering the energy supply of photovoltaic output, energy storage system, and power purchase from the power grid, and incorporating the charging and discharging of new energy locomotives as controllable loads into the optimization scheduling; the decision variables are the charging and discharging timing and scale of the new energy locomotives at each moment, and the charging and discharging timing and scale of the energy storage system; the intraday scheduling model has a 24-hour cycle, and makes decisions and scheduling every 1 hour.

[0018] Preferably, the state constraints of the energy storage system are:

[0019]

[0020] in, is the charge capacity of the energy storage system at time t, is the discharge amount of the energy storage system at time t, is the maximum charge capacity of the energy storage system, is the maximum discharge capacity of the energy storage system, the coefficient and is a 0-1 variable;

[0021] The state of charge (SOC) range constraint is:

[0022]

[0023] Where, is the current state of charge of the battery of the energy storage system at time t, is the battery charge state of the energy storage system at time t-1, and are the minimum and maximum battery state of charge, P t is the power of the energy storage system at time t, P rate is the rated power of the energy storage system, is the remaining capacity of the energy storage system at time t, is the remaining capacity of the energy storage system at time t-1, η ch and η dis are the charging efficiency and discharging efficiency of the energy storage system, respectively, and Δt is the time interval;

[0024] The state constraints of the locomotive are:

[0025]

[0026] Where, The charging capacity of new energy locomotives, The maximum charging capacity of new energy locomotives, is the discharge capacity of new energy locomotives, is the maximum discharge capacity of new energy locomotives, and are the charge coefficient and the discharge coefficient respectively;

[0027]

[0028] Where, is the remaining power of the new energy locomotive at time t, is the remaining power of the new energy locomotive at time t+1, and are the minimum and maximum remaining power of new energy locomotives, η el,ch and η el,dis is the charging efficiency and discharging efficiency of new energy locomotives, E el,p The power consumption of a new energy locomotive for one day;

[0029] The state of charge of new energy locomotives is expressed as

[0030]

[0031] Where, is the state of charge of the new energy locomotive at time t, is the state of charge of the new energy locomotive at time t-1, is the rated power of the new energy locomotive, and They are the minimum and maximum states of charge of new energy locomotives respectively;

[0032] At the initial time 0, both the new energy locomotive and the microgrid have a normal initial charge state to ensure normal dispatching:

[0033]

[0034] In the formula, SOC(0) represents the state of charge of the microgrid at the initial time 0, SOC min and SOC max They are the minimum and maximum values ​​of the microgrid state of charge, SOC el (0) is the charge state of the new energy locomotive at the initial time 0;

[0035] The timing and scale of charging and discharging of new energy locomotives must be able to complete the operating tasks assigned by managers:

[0036]

[0037] Where, is the charging capacity of the new energy locomotive at time t;

[0038] The energy storage system and new energy locomotive both follow the "one-way operation" principle and can only perform one operation between charging and discharging at any time:

[0039]

[0040] Where, and is a binary variable, and is a binary variable;

[0041] The total active power balance constraint of the locomotive depot microgrid is:

[0042]

[0043] Where, is the photovoltaic power generation of the microgrid at time t, is the amount of electricity purchased from the upper power grid at time t, is the charge of the energy storage system at time t, is the power consumption of other non-locomotive fixed loads at time t, is the charge or discharge amount of the new energy locomotive at time t, is the discharge amount of the energy storage system at time t; is the charge and discharge power of the new energy locomotive at time t, is the locomotive charging power at time t, is the locomotive discharge power at time t.

[0044] Preferably, the expression for minimizing the microgrid operation and maintenance cost TC is:

[0045] Min TC=C grid +C pv +C storage (twenty one)

[0046] Among them, C grid is the cost of interaction between the microgrid and the grid, C pv is the operation and maintenance cost of the photovoltaic power generation system, C storage It is the charging and discharging loss and maintenance cost of the energy storage system;

[0047] The maximum microgrid photovoltaic absorption rate R is expressed as:

[0048]

[0049] Among them, P pv,used Indicates the photovoltaic power generation used by the microgrid, P pv It represents the total photovoltaic power generation of the microgrid, which is obtained by Beta distribution prediction. Beta distribution conforms to the probability distribution characteristics of photovoltaic power generation and is very suitable for fitting the uncertainty of photovoltaic power generation.

[0050] Preferably, the four operating strategies of the new energy locomotive include:

[0051] Strategy 1: New energy locomotives are considered fixed loads and do not participate in source-load interaction:

[0052]

[0053] Strategy 2: The charge and discharge capacity of new energy locomotives has a time-shifting characteristic, which can be regarded as a shiftable load. That is, a new scheduling plan is formed by shifting part of the charge and discharge power of the locomotive at a certain time to other times:

[0054]

[0055] Strategy 3: The charging and discharging power of new energy locomotives can be reduced. Based on the completion of the target tasks assigned by the superior user, the system can autonomously control whether the reduction operation can be performed at the time point:

[0056]

[0057] Strategy 4: The charging and discharging power of new energy locomotives is both reducible and transferable:

[0058]

[0059] Where, is the power change of the mining new energy locomotive at time t, is the basic power requirement of the new energy locomotive at time t; is the movable load of the new energy locomotive at time t, and are the maximum and minimum values ​​of the translational load of the new energy locomotive, is a binary variable, is the load that can be reduced by the new energy locomotive at time t, P el,p To meet the total power requirements of new energy locomotives to complete the tasks assigned by superior users.

[0060] Preferably, the method for solving the intraday optimal dispatch model of the locomotive depot microgrid using the improved fusion multi-objective optimization algorithm is:

[0061] S1. Set algorithm parameters: including the maximum number of iterations Ite max , population size Npop, initial crossover rate Final crossover rate f crossover , adaptive mutation rate, adaptive crossover rate, variable asynchronous length, define two objective functions of minimizing microgrid operation and maintenance costs and maximizing photovoltaic absorption rate;

[0062] S2. Initialize the population individual information: including individual position, individual fitness value, individual level, individual domination number, and individual crowding degree;

[0063] S3. Perform an initial evaluation on the initialized population, use individual positions to screen individuals in the population that meet the constraints, and use a penalty function to reset the individual fitness values ​​of individuals that do not meet the constraints to inf;

[0064] S4. Perform non-dominated sorting on the population;

[0065] S5. Enter the main iteration loop, obtain the number of iterations, and update the number of crossover and mutation individuals;

[0066] S6. Using an adaptive crossover rate to reduce the crossover rate generation by generation, performing a crossover operation, generating two individuals each crossover operation;

[0067] S7. Calculate the mutation rate using the adaptive mutation rate and perform the mutation operation;

[0068] S8. Merge the two offspring populations obtained by the crossover and mutation operations with the initial population to generate a new population;

[0069] S9. Perform non-dominated sorting on the newly generated population again;

[0070] S10. Calculate the crowding distance of the population;

[0071] S11. Update the individuals in the population based on non-dominated sorting and crowding distance sorting;

[0072] S12. Truncate the population and keep only the top Npop individuals;

[0073] S13. Traverse all individuals in the population and apply optimization operations that combine the WOA algorithm and the Levy flight mechanism to each individual;

[0074] S14. Perform non-dominated sorting, crowding degree calculation, and crowding distance sorting on the new population obtained after optimization, and retain Npop top individuals;

[0075] S15. Perform the next iteration until the convergence condition is reached or the loop reaches the number of iterations;

[0076] S16. Obtaining the optimal target value is the optimal scheduling solution for all.

[0077] Preferably, the method for updating the number of crossover and mutation individuals in step S5 is: the number of mutation individuals and the number of crossover individuals are based on the adaptive crossover rate in the current number of iterations. and adaptive mutation rate μ Ite The number of mutation individuals is nCrossover=2*round(μ Ite *Npop / 2); the number of crossover individuals is round is the rounding down function;

[0078] The adaptive crossover rate for:

[0079]

[0080] Where, is the initial crossover rate, f Crossover is the final crossover rate, Ite is the number of iterations of the main loop of the current algorithm, Ite max is the maximum number of iterations;

[0081] The adaptive mutation rate decreases from generation to generation in the form of exponential decay, and

[0082] μ Ite =max(0.1,u Ite-1 ·γ)γ<1 (30)

[0083] Where μ Ite is the adaptive mutation rate of the Ite-th iteration, γ is the attenuation coefficient, μ Ite-1 is the adaptive mutation rate of the Ite-1th iteration.

[0084] Preferably, the method for optimizing the operation of integrating the WOA algorithm and the Levy flight mechanism in step S13 is:

[0085] S131 obtains the current individual position and individual fitness value, records the individual position as the optimal position, and records the individual fitness value as the optimal fitness value;

[0086] S132 performs WOA algorithm and Levy flight optimization cycle on individuals;

[0087] S133 selects the target prey location and sets the dynamic attenuation parameters of the WOA algorithm;

[0088] S134 gradually narrows the search range: sets the control search direction and control movement amplitude of the WOA algorithm, sets the probability parameter P to determine whether the whale performs spiral movement and surrounds the prey, and sets the execution probability of controlling Levy flight;

[0089] S135 sets the parameters for controlling the flight jump intensity in the Levy flight mechanism and calculates the individual Levy flight step length;

[0090] S136 determines an updated position based on the individual's movement behavior, determines whether the updated position performs a Levy flight mechanism operation, and records the updated position as a new individual position;

[0091] S137 imposes upper and lower bounds on the updated position: directly comparing the decision vector of the updated position to see if it is still within the variable constraints, ensuring that the new position is within the search space;

[0092] S138 calculates the objective function value of the new individual as the fitness value through the updated position. If the fitness value of the new individual is better than the fitness value of the best individual, the position of the new individual is used as the best position and the fitness value of the new individual is used as the best fitness value. At the same time, the new individuals obtained after traversing the population and performing the WOA algorithm and Levy flight mechanism optimization are merged into a new population.

[0093] Preferably, the WOA algorithm performs fine search optimization as follows:

[0094] Exploration phase:

[0095]

[0096] Shrinking and surrounding mechanism:

[0097]

[0098] Spiral update mechanism:

[0099]

[0100] The Levy flight mechanism is:

[0101]

[0102] Where, is the currently selected population individual, is the current optimal individual, is the individual obtained by the exploration operation at the ite+1th iteration of the FWOA sub-cycle, is the randomly selected prey position, β is the parameter controlling the intensity of flight jump; and are the parameters for controlling the search direction and the motion amplitude, respectively, and

[0103]

[0104] Among them, w is the parameter that controls dynamic attenuation, r and q are random numbers in the range of 0-1, is the distance between the current individual and the best individual after adding the disturbance; bl is a random number, ite is the number of iterations of the FWOA sub-cycle; L is the flight step length of the population individual, u and v are random variables sampled from the normal distribution, ε is a small disturbance factor, R is a random disturbance of the standard normal distribution, X (ite) and X (ite+1) They represent the individuals obtained after performing Levy flight operations after ite and ite+1 iterations, respectively. The parameters controlling dynamic attenuation are

[0105]

[0106] Preferably, the operation steps of performing non-dominated sorting on the population in step S4 are:

[0107] (1) Get the current population size, initialize the dominance index set of each individual to an empty set, and the number of dominated individuals to 0;

[0108] (2) Select two individuals in the population and compare them pairwise. If individual a dominates individual b, add the index of individual b to the dominance index set of individual a, add 1 to the number of dominated individuals of individual b, and return the updated information to the original individual.

[0109] (3) If the number of individuals dominated is always 0, it means that they are not dominated by any individual. The individual is added to the frontier solution set F1 and the individual level is set to 1;

[0110] (4) Construct each non-dominated frontier layer by layer according to the dominant individual index in the dominant index set of the individual: First, select an individual from the frontier with level 1, find the position of the dominated individual through the dominant individual index of the individual, and subtract 1 from the number of dominated individuals of the dominated individual. If the number of dominated individuals becomes 0 after subtracting 1, set the level of the current dominated individual to 2, and then select an individual from the frontier with level 2, add the dominance level to the dominated individual, and so on, traverse the population and add the dominance level to all individuals;

[0111] The implementation method of step S6 is:

[0112] 1) Traverse all crossover individuals, randomly select two individuals from the population as parents, and perform a crossover operation on the positions of the two parents;

[0113] 2) The crossover operation generates two new positions, i.e., the positions of the offspring, by performing a weighted combination of the random position vectors;

[0114] 3) Calculate the objective function through the offspring position and obtain the offspring fitness value;

[0115] 4) Screen the offspring population according to the constraints and retain the offspring population that meets the constraints;

[0116] The implementation method of step S7 is:

[0117] S71 traverses all mutation individuals and randomly selects an individual from the population as the parent to perform the mutation operation;

[0118] S72 obtains the number of mutations and uses an adaptive Gaussian mutation operation to adjust the range boundary. When the individual position approaches the center, the step size approaches the initial step size. When the position approaches the boundary, the step size approaches 0. Adaptive perturbation is performed to obtain the position of the offspring individual after the mutation.

[0119] S73 calculates the objective function value according to the individual position of the offspring to obtain the fitness value;

[0120] S74 performs constraint screening on the offspring population and retains the offspring population that meets the constraint conditions;

[0121] The method for calculating the crowding distance of the population in S10 is as follows: obtaining the hierarchical level of the non-dominated frontier solution set, traversing the frontier solution sets of all levels and performing the following operations: extracting the objective function value of the individual in the current frontier solution set, obtaining the number of objective functions of the current frontier solution set, and obtaining the number of individuals in the current frontier solution set; sorting the individuals in the solution set according to the value of the objective function, wherein the crowding degree of the boundary individuals is set to infinity, and the intermediate values ​​are calculated according to the normalization of adjacent differences to obtain the crowding distance between each individual; summing the crowding distances of each individual to other individuals to obtain the crowding degree value of the current individual;

[0122] The implementation method of S11 is as follows: sorting all individuals in the population according to the crowding distance, where individuals with larger crowding distances are ranked higher; sorting individuals in the population according to their levels from small to large; obtaining the frontier levels of all individuals and the maximum frontier level of all individuals, initializing an index for each frontier solution set, and obtaining the number of indexes according to the number of frontier levels;

[0123] Extract all individuals with a frontier level of 1 in the population, and the decision vectors of individual positions are all optimal scheduling solutions;

[0124] The crossover operation is implemented by performing a "gene-by-gene crossover" on the position information x1 and x2 of the two parents to obtain two offspring:

[0125] y1=m·x1+(1-m)·x2 (39)

[0126] y2=m·x2+(1-m)·x1

[0127] Where y1 and y2 are the offspring position information, and m represents a random vector of the same size as x1 with a value of [0,1].

[0128] In step S71, the corresponding variable step length is set for each decision vector of each hour in 24 hours as follows:

[0129]

[0130] Where, is the adjusted variable step length corresponding to the j-th decision vector, σ j is the initial variable asynchronous length, and is the maximum and minimum value of the j-th decision variable.

[0131] Compared with the existing technology, the beneficial effects of the present invention are as follows: in order to further improve the local search efficiency and the ability to jump out of local extreme values, the present invention introduces the Levy Flight Mechanism into the WOA framework, and introduces a fine-tuning strategy that combines the WOA algorithm and the Levy Flight Mechanism into the traditional NSGA-II framework, and locally strengthens the search of individual positions in each generation of population, constructing a fusion multi-objective optimization algorithm (FWOA-NSGA-II). While inheriting the advantages of NSGA-II's fast non-dominated sorting and elite retention strategy, it fully utilizes the WOA algorithm's capabilities in adaptive search direction adjustment and local surround search, and uses Levy flight to introduce jump disturbances to improve population diversity and the ability to jump out of local optimal values, greatly enhancing the individual's local development intensity and global search balance, improving the solution's convergence speed and solution space coverage capability, and is more suitable for microgrid optimization scheduling problems in photovoltaic-energy storage-load coupling scenarios.

[0132] The present invention introduces an optimization mechanism that integrates the WOA algorithm and Levy flight into the traditional evolutionary optimization framework, and proposes a multi-objective optimization method that takes into account both search depth and solution set diversity. It prevents the algorithm from falling into local optimality while improving the diversity of the population. Under the scheduling effect of the optimization method, the controllable load model with translatable and reducible characteristics actively adjusts the power consumption sequence and scale to achieve efficient coordination with photovoltaic power generation. It not only significantly improves the photovoltaic power generation absorption rate and reduces the microgrid operation and maintenance costs, but also gives full play to the advantages of the source-load interaction mechanism in optimizing resource allocation and improving system flexibility, showing an operating performance far superior to that of the uncontrollable load mode. The present invention takes into account the impact of the dynamic changes in the locomotive charging and discharging sequence and scale on the optimization scheduling decision. Through deep source-load interaction and an improved solution algorithm, it effectively reduces the operation and maintenance costs of the microgrid and improves the photovoltaic power generation absorption rate of the microgrid. BRIEF DESCRIPTION OF THE DRAWINGS

[0133] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0134] Figure 1 Flowchart of the present invention.

[0135] Figure 2 Flowchart of the multi-objective optimization algorithm of the present invention.

[0136] Figure 3A comparison chart of the Parato frontiers of the present invention and the original NSGA-II algorithm.

[0137] Figure 4 This is a graph showing the average minimum operation and maintenance of the present invention and the NSGA-II algorithm changing with the number of iterations.

[0138] Figure 5 This is a graph showing the minimum operation and maintenance of the present invention, NSGA-II algorithm, and WOA algorithm as the number of iterations changes.

[0139] Figure 6 This is a graph showing how the maximum photovoltaic absorption rate of the present invention, NSGA-II algorithm, and WOA algorithm changes with the number of iterations.

[0140] Figure 7 A comparison diagram of the Parato frontiers of different controllable load models of the present invention.

[0141] Figure 8 This is a comparison chart of the average minimum operation and maintenance changing with the number of iterations under different controllable load models of the present invention.

[0142] Figure 9 This is a 24-hour total load change curve diagram under different controllable load models of the present invention. DETAILED DESCRIPTION

[0143] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0144] like Figure 1 As shown, the present invention proposes a multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction. The steps are: obtaining relevant data information based on the daily operation of the microgrid in the area, establishing constraint conditions for the intraday optimization scheduling of the locomotive depot microgrid, minimizing the microgrid operation and maintenance costs and maximizing the microgrid photovoltaic absorption rate as the objective function, establishing a locomotive depot microgrid intraday optimization scheduling model, and using the obtained data information as the input parameter of the locomotive depot microgrid intraday optimization scheduling model to solve and obtain an optimized scheduling solution. The specific implementation method of the present invention is:

[0145] Step 1: Obtain relevant data information based on the daily operation of the microgrid and establish the constraints for the daily optimal scheduling of the locomotive depot microgrid.

[0146] Using the microgrid's 24-hour daily raw power generation data from the previous day and adding a 5% disturbance range, we can simulate a more realistic typical photovoltaic power generation scenario. We also collected data on the microgrid's daily power load, energy storage system charge and discharge range, locomotive charge and discharge range, energy storage system capacity, locomotive capacity, energy storage state of charge, locomotive state of charge, and microgrid power purchase range. This data was taken from a typical microgrid scenario in Henan Province.

[0147] The constraints of the present invention include:

[0148] Energy storage system-related constraints

[0149]

[0150] Energy storage system charge at any time Do not exceed the maximum charging amount Discharge Do not exceed the maximum discharge amount in, For maximum charge capacity, is the maximum discharge capacity. and is a 0-1 variable.

[0151]

[0152] Where, is the current remaining capacity of the battery in the energy storage system at time t, is the battery charge state of the energy storage system at time t-1, and are the minimum and maximum battery state of charge, P t Expressed as the power of the energy storage system at time t, P rate is the rated power of the energy storage system, is the remaining capacity of the energy storage system at time t, is the remaining capacity of the energy storage system at time t-1, η ch and η dis are the charging and discharging efficiencies of the energy storage system, respectively, and Δt is the time interval.

[0153] Restrictions on new energy locomotives

[0154]

[0155] Charging capacity of new energy locomotives Do not exceed the maximum charging amount Discharge capacity of new energy locomotives Do not exceed the maximum discharge amount and are the charge and discharge coefficients respectively.

[0156]

[0157]

[0158] Where, is the remaining power of the new energy locomotive at time t, is the remaining power of the new energy locomotive at time t+1, and are the minimum and maximum remaining power of new energy locomotives respectively. el,ch and η el,dis is the charging and discharging efficiency of new energy locomotives. E el,p The power consumption of a new energy locomotive in one day.

[0159] Similarly, the state of charge of a new energy locomotive can be expressed as

[0160]

[0161] Where, is the state of charge of the new energy locomotive at time t, is the state of charge of the new energy locomotive at time t-1, is the charge and discharge amount of the new energy locomotive at time t-1, It is the rated power of new energy locomotive. and They are the minimum and maximum charge states of new energy locomotives respectively.

[0162] At the initial time 0, both the new energy locomotive and the microgrid have a normal initial charge state to ensure normal operation of the dispatching

[0163]

[0164] In the formula, SOC(0) represents the state of charge of the microgrid at the initial time 0, SOC min and SOC max are the minimum and maximum values ​​of the microgrid state of charge. el (0) is the charge state of the mining new energy locomotive at the initial time 0, and It is the minimum and maximum value of the state of charge of the new energy locomotive.

[0165] The timing and scale of charging and discharging of new energy locomotives must ensure that they can complete the operating tasks assigned by managers.

[0166]

[0167] Where, is the charging capacity of the new energy locomotive at time t, Eel,p The power consumption of a new energy locomotive in one day.

[0168] Taking practical factors into consideration, both energy storage systems and new energy locomotives follow the "one-way operation" principle, that is, only one operation between charging and discharging can be performed at any time.

[0169]

[0170] Where, and It is a binary variable that indicates whether the energy storage system performs a charging operation or a discharging operation at any time t (1 for performing the operation, 0 for not performing the operation). and It is also a binary variable, indicating whether the new energy locomotive performs charging or discharging operation at any time t.

[0171] Step 2: Taking minimizing the microgrid operation and maintenance costs and maximizing the microgrid photovoltaic absorption rate as the objective functions, an intraday optimization scheduling model for the locomotive depot microgrid is established.

[0172] This paper performs multi-objective optimization scheduling on a locomotive depot microgrid, which includes photovoltaic power generation, energy storage power stations, mining locomotives, and conventional production loads. The optimization objectives of microgrid scheduling are to minimize the microgrid's operation and maintenance costs and maximize the microgrid's photovoltaic power generation absorption rate. The minimization of the operation and maintenance cost (TC) in the objective function is expressed as follows:

[0173] Min TC=C grid +C pv +C storage (59)

[0174] Among them, C grid is the cost of interaction between the microgrid and the grid, C pv is the operation and maintenance cost of the photovoltaic power generation system, C storage It is the charging and discharging loss and maintenance cost of the energy storage system.

[0175] The part of the objective function that maximizes the photovoltaic power generation consumption rate of the microgrid is expressed as follows:

[0176]

[0177] Among them, R represents the photovoltaic absorption rate of the microgrid, P pv,used Indicates the photovoltaic power generation used by the microgrid, P pv Represents the total photovoltaic power generation of the microgrid. Specifically, Beta distribution is used to obtain the photovoltaic power generation prediction data P pv , Beta distribution is consistent with the probability distribution characteristics of photovoltaic power generation and is very suitable for fitting the uncertainty of photovoltaic power generation.

[0178] The total active power balance constraint of the locomotive depot microgrid is:

[0179]

[0180] Where, is the photovoltaic power generation of the microgrid at time t, is the amount of electricity purchased from the upper power grid at time t, is the charge of the energy storage system at time t, is the power consumption of the normal production load at time t, is the charge amount (positive value) or discharge amount (negative value) of the new energy locomotive at time t, is the discharge capacity of the energy storage system at time t. The new energy locomotive is regarded as a flexible load, which is essentially the charging and discharging power of the new energy locomotive at time t. is the locomotive charging power at time t, is the locomotive discharge power at time t.

[0181] The established intraday optimization dispatch model of the locomotive depot microgrid includes:

[0182] (1) Modeling object: It is oriented towards the microgrid system of the locomotive depot, taking into account the energy supply such as photovoltaic output, energy storage system, and power purchase from the grid, and incorporating the charging and discharging of new energy locomotives as controllable loads into the optimized scheduling.

[0183] (2) Optimization objectives: minimizing microgrid operation and maintenance costs and maximizing photovoltaic power generation absorption rate;

[0184] (3) Decision variables: the charging and discharging sequence and scale of the locomotive at each moment, and the charging and discharging sequence and scale of the energy storage.

[0185] (4) Constraints: power balance constraints, simultaneous charging and discharging of locomotives and energy storage, state of charge (SOC) range constraints, photovoltaic output uncertainty, and upper-level task requirements.

[0186] (5) Intraday scheduling model: with a 24-hour cycle, decision scheduling is performed every hour.

[0187] (6) Algorithm: FOWA-NSGA-II algorithm is used to solve this model.

[0188] Step 3: Establish a source-load interaction mechanism: Consider new energy locomotives as flexible loads to participate in the daily scheduling of the locomotive depot microgrid. Based on the degree of source-load interaction, design four operation strategies for mining new energy locomotives.

[0189] Unlike the reality of household electric vehicles, which are owned by individuals, mining new energy locomotives are managed by the locomotive depot microgrid, thus offering greater scheduling flexibility and controllability. This paper considers new energy locomotives as flexible loads and participates in the daily scheduling of the locomotive depot microgrid, achieving a high degree of source-load interaction in the microgrid. Based on the level of source-load interaction, four operating strategies for mining new energy locomotives are designed, as follows:

[0190] Strategy 1: Mining new energy locomotives are regarded as fixed loads and do not participate in source-load interaction. That is, the charging and discharging strategy of new energy locomotives in daily optimized scheduling adopts the direct plan issued by the railway locomotive depot to complete daily work. The charging and discharging plan of the locomotive will not be changed according to the scheduling results. The optimized scheduling is completed only by controlling the charging and discharging timing and scale of the energy storage system.

[0191]

[0192] Strategy 2: The charge and discharge capacity of mining new energy locomotives has a time-shifting characteristic, which can be regarded as a shiftable load. That is, by shifting part of the locomotive's charge and discharge power at a certain time to other times to form a new scheduling plan to achieve optimization results:

[0193]

[0194] Strategy 3: The charging and discharging power of new energy mining locomotives is curtailable. This is important to note, as this differs from traditional curtailable load operations. Because this invention targets new energy locomotives, their charging behavior is centrally managed by the railway locomotive depot, making them more controllable and predictable, compared to the uncertainty inherent in electric vehicle user behavior. Therefore, when utilizing curtailable load, the system does not set curtailable ranges at curtailable time points. Instead, it autonomously controls whether curtailment can be executed at a given time point, predicated on achieving the target task assigned by the superior user.

[0195]

[0196] Strategy 4: The charging and discharging power of mining new energy locomotives has the characteristics of being both reducible and transferable. At this time, the source-load interaction of the microgrid is the strongest.

[0197]

[0198] Where, is the power change of the mining new energy locomotive at time t, is the basic power requirement of the new energy locomotive at time t. is the movable load of the new energy locomotive at time t, and are the maximum and minimum values ​​of the translational load of the new energy locomotive, is a 0-1 variable (0 means no translation operation is performed, 1 means translation operation is performed), is the load that can be reduced by the new energy locomotive at time t, P el,p To meet the total power requirements of new energy locomotives to complete the tasks assigned by superior users.

[0199] Step 4: In the individual evolution process of the main loop of the NSGA-II algorithm, the WOA algorithm is introduced and the Levy flight mechanism is embedded to obtain an improved fusion multi-objective optimization algorithm (FWOA-NSGAII). The improved fusion multi-objective optimization algorithm is used to solve the intraday optimization scheduling model of the locomotive depot microgrid and obtain the scheduling results.

[0200] The traditional NSGA-II algorithm is a fast non-dominated sorting genetic algorithm with an elite strategy. It is a multi-objective optimization algorithm based on a genetic algorithm. Because of its good global convergence and high versatility, it is often used in multi-objective optimization. However, as the number of iterations increases, the disadvantage of insufficient population diversity will become apparent and it is easy to fall into local optimality. In response to the above problems, the present invention introduces the whale optimization algorithm (WOA) embedded in the Levy flight fusion improvement mechanism FWOA in the individual evolution process of the main loop of the NSGA-II algorithm. Through the shrinkage and encirclement mechanism and spiral search strategy in the WOA algorithm, a fine search of individuals in the local neighborhood is achieved, thereby improving the development ability of the population. The solution space jumping ability is enhanced through the Levy flight mechanism, effectively avoiding the NSGA-II algorithm from converging to a suboptimal solution in the early stage, and improving the population convergence speed and diversity. The specific implementation steps of the FWOA-NSGAII algorithm of the present invention are:

[0201] S1. Set algorithm parameters: including maximum number of iterations, population size, initial crossover rate Adaptive mutation rate, variable asynchronous length, and define objective function. Two objective functions are set: the first is to minimize the operation and maintenance costs of the microgrid, and the second is to maximize the photovoltaic power generation absorption rate. The maximum number of iterations MaxIt is 100, the population size Npop is 100, the initial crossover rate Pcrossover is 0.8, and the final crossover rate f is 0. crossover =0.1, the mutation rate mu is reduced generation by generation through mu=max(0.1,mu*0.99), and the crossover rate is reduced generation by generation through pCrossover=pCrossover-(pCrossover-fCrossover)*(it / MaxIt).

[0202] S2. Initialize individual population information: including individual position, individual fitness value, individual rank, individual domination count, and individual crowding. For a population of 100, initialize 100 individuals. Each individual's information consists of its position (Position), fitness value (cost), domination level (Rank), domination index (Dominationset), domination count (DominationCount), and crowding distance (CrowdingDistance).

[0203] S3. Perform an initial evaluation of the initialized population, screen the individuals that meet the constraints, use the penalty function to impose penalties on the individuals that do not meet the constraints, and reset the objective function value of the individuals that do not meet the constraints to inf. This can quickly exclude infeasible solutions from the feasible solution range and accelerate the convergence of the algorithm. The specific operation is to build the function ConstraintsHanding.m based on the constraints in the previously mentioned locomotive depot microgrid optimization scheduling model, substitute the position Position of each individual into the function for constraint. The function ConstraintsHanding.m will return 1 if the position meets the constraint requirements and return 0 if it does not meet the requirements. When it returns 0, it indicates that this individual is an infeasible solution. The individual's fitness value Cost is set to inf to quickly exclude the feasible solution range.

[0204] S4. Perform non-dominated sorting on the population. The specific operations are:

[0205] (1) Get the current population size, initialize the dominating index set of each individual to an empty set, and the number of dominated individuals to 0.

[0206] (2) Select two individuals in the population and compare them pairwise. If individual a dominates individual b (dominance means that the operation and maintenance costs of individual a are less than those of individual b, and the photovoltaic absorption rate of individual a is higher than that of individual b), add the index of individual b to the dominance index set of individual a, add 1 to the number of dominated individuals of individual b, and return the updated information to the original individual.

[0207] (3) If the number of individuals dominated is always 0, indicating that they are not dominated by any individual, the individual is added to the frontier solution set F1 and the individual level is set to 1. This ensures that the optimal solution Parato can be quickly and correctly identified.

[0208] (4) Construct each non-dominated frontier layer by layer based on the dominant individual index in the dominant index set of the individual. First, select an individual from the frontier with level 1, find the position of the dominated individual through the dominant individual index of the individual, and subtract 1 from the number of dominated individuals of the dominated individual. If the number of dominated individuals becomes 0 after subtracting 1, set the level of the current dominated individual to 2. Then select an individual from the frontier with level 2, add the dominance level to the dominated individual, and so on. Traverse the population and add the dominance level to all individuals. This can provide accurate hierarchical information when performing selection operations in the population, which helps maintain population diversity.

[0209] S5. Enter the main iteration loop, get the number of iterations, and update the number of crossover and mutation individuals. The number of mutation and crossover individuals will change accordingly according to the changes in the crossover rate and mutation rate in the current number of iterations. Specifically, nCrossover = 2*

[0210] round(pCrossover * nPop / 2); nMutation = round(pMutation * nPop), where nPop represents the population size and pMutation is the mutation rate mu. This is an effective adaptive control strategy that avoids the problem of fixed parameters being insufficiently adaptable across different evolutionary stages, achieving a better balance between the exploration and exploitation phases.

[0211] S6. Perform a crossover operation. Each crossover operation generates two individuals. The operation is as follows:

[0212] (1) Traverse all crossover individuals, use adaptive crossover rate calculation to reduce the crossover rate from generation to generation, randomly select two individuals from the population as parents, and perform a crossover operation on the positions of the two parents. The crossover operation is to perform a "gene position crossover" on the position information x1 and x2 of the two parents to obtain two offspring. Among them, y1 and y2 are the offspring position information, and m represents a random vector of the same size as x1 and with a value of [0,1]; so that the position information after crossover still conforms to the constraints of the model, ensuring the diversity and distribution of the generated offspring.

[0213] The adaptive crossover rate is:

[0214]

[0215] Where, is the initial crossover rate, f Crossover is the final crossover rate, Ite is the number of iterations of the main loop of the current algorithm, Ite max is the maximum number of iterations of the main loop of the algorithm. Represents the calculated adaptive crossover rate.

[0216] (2) The crossover operation generates two new positions, namely the positions of the offspring, by performing a weighted combination of random position vectors.

[0217] (3) Calculate the objective function through the offspring position and obtain the offspring fitness value.

[0218] (4) Screen the offspring population according to the constraints and retain the offspring population that meets the constraints.

[0219] S7. Perform mutation operation

[0220] (1) Traverse all mutant individuals and use the adaptive mutation rate to calculate the mutation rate. As the number of iterations increases, the mutation rate gradually decreases. Randomly select an individual from the population as the parent to perform the mutation operation.

[0221] First, obtain the step length of the position of the individual that needs to be mutated, that is, the scheduling time length of 24 hours. In particular, set the corresponding step length for each decision vector of each hour in 24 hours. Specifically,

[0222]

[0223] Where, is the adjusted variable step length corresponding to the j-th decision vector, σ j is the initial variable step length, obtained by the constraint range of each decision variable * 0.1, and is the maximum and minimum value of the j-th decision variable.

[0224] In this way, the closer the individual is to the boundary, the smaller the variation, and the closer it is to the middle area, the larger the variation. This effectively avoids individuals crossing the boundary after mutation and improves the stability of the algorithm.

[0225] The adaptive mutation rate decreases from generation to generation in the form of exponential decay, and

[0226] μ Ite =max(0.1,u Ite-1 ·γ)γ<1 (73)

[0227] Where μ Ite is the mutation rate of the algorithm's main loop iteration, γ is the attenuation coefficient, μ Ite-1 is the mutation rate of the Ite-1th iteration.

[0228] (2) Obtain the number of mutations and use an adaptive Gaussian mutation operation to adjust the range boundary. When the individual position approaches the center, the step size approaches the initial step size sigma. When the position approaches the boundary, the step size approaches 0. Adaptive perturbation is performed to obtain the position of the mutated offspring individual.

[0229] (3) Calculate the objective function value based on the individual position of the offspring to obtain the fitness value.

[0230] (4) Screen the offspring population according to the constraints and retain the offspring population that meets the constraints.

[0231] S8. Merge the two offspring populations obtained by the crossover and mutation operations with the initial population to generate a new population.

[0232] S9. Perform non-dominated sorting on the newly generated population again

[0233] S10. Calculate the crowding distance of the population. The specific operations are as follows:

[0234] (1) Obtain the level number of the non-dominated frontier solution set, traverse all levels of the frontier solution sets and perform the following operations;

[0235] (2) Extract the objective function value of the individual in the current frontier solution set, obtain the number of objective functions in the current frontier solution set, and obtain the number of individuals in the current frontier solution set.

[0236] (3) Sort the individuals in the solution set according to the objective function value, where the crowding degree of the boundary individuals is set to infinity, and the intermediate values ​​are calculated by normalizing the adjacent differences to obtain the “crowding distance” between each individual.

[0237] (4) Sum the “crowding distance” of each individual to other individuals to obtain the crowding degree value of the current individual. The crowding degree of each individual is used to re-rank the population in the frontier level where the individual is located.

[0238] S11. Update the individuals in the population based on the non-dominated sorting and crowding distance sorting. The specific operations are as follows;

[0239] (1) Sort all individuals in the population according to the crowding distance. Individuals with larger crowding distances are ranked higher.

[0240] (2) Then sort the individuals in the population from small to large according to their levels.

[0241] (3) Obtain the frontier ranks of all individuals and the maximum frontier rank of all individuals. Initialize the index F(i) for each frontier solution set and obtain the number of indexes F from the number of frontier ranks. In this way, the updated population will sort individuals from low to high frontier ranks and from high to low crowding degrees, implementing an elite retention strategy and ensuring convergence.

[0242] S12. Truncate the population and only retain the top Npop individuals in the original population.

[0243] S13. Traverse all individuals in the population and apply optimization operations that combine WOA and Levy flight mechanisms to each individual. The specific operations are as follows:

[0244] (1) Obtain the current individual position and fitness information. The individual position is recorded as the best position, and the individual fitness value is recorded as the best fitness value.

[0245] (2) Perform WOA and Levy flight optimization cycles on the individual and set the number of iterations.

[0246] In each iteration, the WOA algorithm is introduced to each individual in the population for fine search optimization:

[0247] Exploration phase;

[0248]

[0249] Shrinking and surrounding mechanism;

[0250]

[0251] Spiral renewal mechanism;

[0252]

[0253] Levy flight mechanism:

[0254]

[0255] Where, is the currently selected population individual, is the current optimal individual, is the individual obtained by the exploration operation at the ite-th FWOA iteration, is the randomly selected prey location.

[0256] are the parameters for controlling the search direction and the motion amplitude, respectively, and

[0257]

[0258] Wherein, w is a parameter for controlling exploration and development, and the value of the present invention is 2, r and q are random numbers ranging from 0 to 1, is the distance between the current individual and the best individual after adding the perturbation. bl is a random number, ite is the number of FWOA sub-cycle iterations. L is the flight step length of the population individual, u and v are random variables sampled from the normal distribution, ε is a small perturbation factor, R is a random perturbation of the standard normal distribution, X (ite) and X (ite+1)The WOA algorithm uses a Levy flight mechanism to expand the solution space by alternating between encircling and spiraling behaviors, guiding individuals to converge toward the optimal Pareto front, improving search accuracy and solution diversity. This improvement balances global search capabilities with local development capabilities, significantly enhancing optimization efficiency and solution quality.

[0259] (3) Select the target prey location and set the dynamic attenuation parameter w. This parameter is the parameter that controls exploration and development.

[0260]

[0261] The purpose of doing this is to gradually transition the exploration method from global search to local fine search.

[0262] (4) Gradually narrow the search range. Set the control search direction, i.e., the parameter Setting parameters Control the amplitude of movement. Set the probability parameter P to determine whether the whale performs spiral motion and surrounds its prey. The probability parameter P is more inclined to surround its prey in the later stages of the iteration. The initial probability parameter P is set to 0.5. Set the parameter Pflight to control the probability of executing Levy flight. Pflight is a fixed parameter that expresses the probability of executing Levy flight operations. It can be changed according to the convergence of the algorithm. In this invention, Pflight is set to 0.3.

[0263] (5) Set the parameter β to control the flight jump intensity, and

[0264] u~N(0,σ 2 )

[0265] v~N(0,1)

[0266] (6) The individual's Levy flight step length is then calculated using the current individual position and parameter beta.

[0267] (7) Determine the updated position based on the individual's movement behavior, and determine whether the updated position performs the Levy flight mechanism operation, and record the updated position as the new individual position.

[0268] (8) Apply upper and lower bound constraints to the updated position, and directly compare whether the decision vector of the updated position is still within the variable constraint range.

[0269] (9) Ensure that the new position is within the search space.

[0270] (10) The objective function value of the new individual is calculated as the fitness value based on the updated position. If the fitness value of the new individual is better than the fitness value of the best individual, the position of the new individual is taken as the best position, and the fitness value of the new individual is taken as the best fitness value. The new individuals obtained after traversing the population and performing WOA and Levy flight optimization are merged into a new population.

[0271] S14. Perform non-dominated sorting, congestion calculation and sorting on the new population obtained after optimization again, and finally perform interception to retain the initial population size.

[0272] S15. Perform the next iteration until the convergence condition is reached or the loop reaches the number of iterations.

[0273] S16. The algorithm ends and the optimal target value is obtained.

[0274] The updated population is sorted by the results of minimizing the microgrid operation and maintenance costs and the photovoltaic power generation absorption rate, and all individuals with a frontier level of 1 in the population are extracted. The decision vectors of these individual positions are all the optimal scheduling solutions obtained by the algorithm.

[0275] The key steps in the present invention are:

[0276] 1. Multi-objective modeling: Construct an optimization scheduling model that includes the dual objectives of minimizing operating costs and maximizing photovoltaic absorption. This model takes into account the charging and discharging regulation of locomotive batteries, the uncertainty of photovoltaic power, and the state constraints of the energy storage system. Furthermore, the modeling considers the locomotive as a controllable load under four different operating modes with different combinations of curtailment and shifting.

[0277] 2. NSGA-II main structure design:

[0278] Initialize the population individuals, each individual represents a feasible intraday scheduling plan;

[0279] Perform adaptive crossover and adaptive mutation operations, with the crossover rate and mutation amplitude dynamically adjusted with the number of iterations to enhance the feasibility and search capability of the algorithm;

[0280] Apply feasibility constraint handling mechanisms to ensure that the generated solutions meet physical constraints such as battery SOC, power balance, and locomotive load limits;

[0281] Perform non-dominated sorting and crowding distance calculations, retaining the Pareto front solution set.

[0282] 3. WOA algorithm and Levy flight optimization embedded mechanism (FWOA):

[0283] In each main loop iteration, the current population individuals are extracted and their positions are searched using the WOA algorithm and Levy flight mechanism optimization.

[0284] According to the distance between the individual and the current global optimal solution and search probability, perform spiral encirclement or convergence search to the prey; through the iterative formula of the WOA algorithm

[0285]

[0286] Achieve perturbation optimization of the solution in the search space;

[0287] The Levy flight mechanism is used to realize the flying jump search of the solution in the search space;

[0288] If the optimized solution dominates the original solution, the individual position is updated.

[0289] 4. Fusion Strategy and Termination Criteria

[0290] The individuals optimized by FWOA are reintegrated into the NSGA-II population to continue the non-dominated sorting and selection process. The iterations are repeated until the maximum number of iterations is reached or the convergence criterion is met, and the final Pareto optimal solution set is output.

[0291] The advantages of this invention over the traditional NSGA-II algorithm are:

[0292] The local development capability of the WOA algorithm is utilized to significantly improve the sophistication of the solution and the search efficiency; the Levy flight mechanism greatly enhances the algorithm's ability to escape the local optimum and the convergence speed; the introduction of the adaptive cross-mutation mechanism enhances the dynamic adjustment capability of the algorithm; through the embedded fusion strategy, the heuristic optimization and swarm intelligence algorithm are effectively coupled, which improves the global convergence speed of the algorithm and the uniformity of the solution set distribution; it is applied to the optimization and scheduling problems of the power system, and is particularly suitable for the microgrid operating environment with photovoltaic access, battery participation, and adjustable load.

[0293] Example

[0294] 1. Algorithm optimization performance test

[0295] To validate the multi-objective optimization performance of the proposed improved non-dominated genetic algorithm (FWOA-NSGA-II) that integrates the whale optimization algorithm and the Levy flight mechanism, we selected five ZDT functions to evaluate the algorithm's performance, including convex (ZDT1), concave (ZDT2), discontinuous (ZDT3), multimodal (ZDT4), and non-uniform distribution (ZDT5). The algorithm's overall solution quality, stability, solution set distribution, and exploration capability were tested. The algorithm's decision variables were uniformly set to 30, with a variable range of [0, 1], 100 iterations, and 100 populations.

[0296] Table 1 Algorithm optimization performance comparison

[0297]

[0298] Experimental results show that the improved algorithm achieves smaller mean and median values ​​for the test function, significantly improving the overall solution quality. Reduced standard deviations and interquartile ranges indicate a more concentrated solution set and enhanced algorithm stability. The optimization effect on the multimodal function ZDT4 is superior to that of other functions, indicating that the improved algorithm's ability to escape local optima is significantly improved compared to the original algorithm.

[0299] 2. Algorithm Example Optimization Test

[0300] To verify the effectiveness of the proposed multi-objective optimization method for power system scheduling based on the fusion of the whale optimization algorithm, the Levy flight mechanism and the NSGA-II algorithm, a typical intraday scheduling scenario of a power microgrid system was designed. The optimization performance of the FWOA-NSGA-II algorithm of the present invention was compared with that of the original NSGA-II algorithm. The impact of the constructed controllable load model (including shiftable loads, curtailable loads and their combination) on the operating effect was further analyzed.

[0301] First, add the scheduling scenario parameters, as shown in Table 2 and Table 3.

[0302] Table 2 Equipment operating parameters

[0303]

[0304] Table 3 Equipment charging requirements

[0305]

[0306] Table 4 Parato frontier data comparison

[0307]

[0308] Depend on Figure 3 Comparison of the Parato frontier distribution plots for the FWOA-NSGA-II algorithm and the NSGA-II algorithm, as well as the Parato frontier data in Table 4, demonstrate that the algorithm improvements significantly expand the distribution range of the frontier solution set, resulting in lower operation and maintenance costs and higher PV power generation absorption rates, effectively improving population diversity. The improved frontier solution set becomes more evenly distributed and "surrounds" the pre-improvement solution set, significantly improving overall solution quality and convergence accuracy. This demonstrates that the FWOA-NSGA-II algorithm possesses stronger global search capabilities and local fine-tuning capabilities than the NSGA-II algorithm.

[0309] The average minimum operation and maintenance of the present invention, the minimum operation and maintenance of the NSGA-II algorithm, and the WOA algorithm vary with the number of iterations, and the maximum photovoltaic absorption rate varies with the number of iterations, such as Figure 4-Figure 6 The data are shown in Table 5.

[0310] Table 5 Comparison of algorithms with different focuses

[0311]

[0312] Figure 4 The average minimum operation and maintenance cost of FWOA-NSGA-II in our invention is reduced from 4154 yuan to 3598 yuan with the number of iterations, which is 27% lower than that of NSGA-II, which is reduced from 4148 yuan to 3710 yuan. Figure 5 and Figure 6 The optimal values ​​of the three algorithms vary with the number of iterations when the objective functions focus on minimizing operating costs and maximizing photovoltaic power consumption efficiency, respectively. Test results show that the FWOA-NAGA-II algorithm of our invention has significantly more iterations than the NGGA-II and WOA algorithms, possessing a stronger solution set exploration capability. Operating and maintenance costs are 1.3% lower than the 3498.24 yuan of the NSGA-II algorithm and 4.7% lower than the 3623.58 yuan of the WOA algorithm. The photovoltaic power consumption efficiency is increased by two percentage points compared to the NSGA-II algorithm and four percentage points compared to the WOA algorithm.

[0313] Figure 7 and Figure 8 This paper compares the optimization effects of different operating strategies for new energy mining locomotives. Specifically, Strategy 1: ignoring source-load interaction and treating the new energy locomotive as an uncontrollable load; Strategy 2: considering source-load interaction and treating the new energy locomotive as a shiftable load; Strategy 3: considering source-load interaction and treating the new energy locomotive as a reducible load; and Strategy 4: maximizing source-load interaction and enabling the new energy locomotive to be both shiftable and reducible.

[0314] Depend on Figure 7 It can be seen that after the introduction of source-load interaction, the Pareto frontiers of various strategies have shown an overall trend of shifting to the left and upward, indicating that under the conditions of the same or lower operating costs, the system photovoltaic power generation absorption rate has been significantly improved. Compared with the case without the introduction of controllable loads, the optimized scheduling strategy not only improves the efficiency of photovoltaic energy utilization, but also effectively reduces the comprehensive operating costs of the microgrid, reflecting the advantages of controllable loads in promoting the friendly access of new energy and improving the economic efficiency of the system. Figure 8As can be seen, as the number of algorithm iterations increases, Strategy 1 converges the slowest and lacks flexible adjustment capabilities, demonstrating the importance of source-load interaction for cost reduction. Strategies 2 and 3 converge at moderate speeds, indicating that a single, scalable and adaptable control approach can improve system optimization to a certain extent. Strategy 4 quickly reduces O&M costs in the initial stages and exhibits the fastest convergence speed. Strategy 4 ultimately achieves the lowest average O&M costs, demonstrating that the combination of two controllable load mechanisms provides the system with greater adaptability and optimization capabilities.

[0315] Figure 9 The comparison results of the 24-hour total load curves under four load models are shown. It can be clearly seen that the uncontrollable load mode (strategy 1) has a significant peak-to-valley difference and the load regulation space is limited. The introduction of source-load interaction makes the overall load curve tend to be stable, especially in the load peak periods of 08:00-10:00 and 11:00-15:00, which is effectively reduced, reducing the pressure of photovoltaic power abandonment and energy storage charging and discharging. Among them, the load curve is the smoothest under the mode with both shiftable and curtailable characteristics (strategy 4), which plays an obvious role in peak shaving and valley filling, further verifying its advantages in load flexible regulation. This shows that the FWOA-NSGA-II algorithm proposed in the present invention is not only superior to traditional methods in solution set distribution and performance optimization, but also significantly enhances the flexibility and regulation ability of system operation by introducing the source-load interaction mechanism, reflecting the optimization benefit of the source-load interaction mechanism for system load management.

[0316] Experimental results show that Strategy 4 exhibits the best scheduling performance under the optimization algorithm of the present invention, significantly outperforming other comparison strategies. Under the premise of ensuring stable system operation, it can effectively improve the photovoltaic resource absorption rate and significantly reduce the operating costs of the microgrid. By introducing flexible load control methods, efficient source-load coordinated scheduling is achieved. Therefore, in scenarios with flexible load resources, the "flexible load modeling method based on joint control of translation and reduction" proposed in the present invention can achieve higher economic efficiency and scheduling optimization effects, provide strong support for achieving low-carbon and efficient system operation, and have broad application prospects and important engineering significance.

[0317] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction, characterized by: The steps are as follows: Step 1: Obtain power consumption data based on the daily operation of the microgrid and establish constraints for the daily optimal scheduling of the locomotive depot microgrid; Step 2: Taking minimizing the microgrid operation and maintenance costs and maximizing the microgrid photovoltaic absorption rate as the objective function, establish the intraday optimization scheduling model of the locomotive depot microgrid; Step 3: Establish a source-load interaction mechanism: Consider new energy locomotives as flexible loads and participate in the daily scheduling of the locomotive depot microgrid. Based on the level of source-load interaction, design four operation strategies for new energy locomotives; Step 4: The WOA algorithm is introduced into the individual evolution process of the main loop of the NSGA-II algorithm and the Levy flight mechanism is embedded to obtain an improved fusion multi-objective optimization algorithm. The improved fusion multi-objective optimization algorithm is used to solve the intraday optimization scheduling model of the locomotive depot microgrid and obtain the scheduling results.

2. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 1 is characterized in that: The photovoltaic power generation data for the day is predicted based on the original 24-hour power generation data of the microgrid on the previous day, and a 5% disturbance range is added. The Beta distribution is used to obtain the photovoltaic power generation forecast data. The electricity consumption data includes daily electricity load data of the microgrid, charging and discharging range of the energy storage system, charging and discharging range of the locomotive, capacity of the energy storage system, capacity of the locomotive, state of charge of the energy storage, state of charge of the locomotive, and power purchase range of the microgrid; The constraints include: power balance constraints, simultaneous charging and discharging of locomotives and energy storage, state of charge (SOC) range constraints, photovoltaic output uncertainty, and energy storage system state constraints; The modeling object of the established locomotive depot microgrid intraday optimization scheduling model is the locomotive depot microgrid system, considering the energy supply of photovoltaic output, energy storage system, and power purchase from the power grid, and incorporating the charging and discharging of new energy locomotives as controllable loads into the optimization scheduling; the decision variables are the charging and discharging timing and scale of the new energy locomotives at each moment, and the charging and discharging timing and scale of the energy storage system; the intraday scheduling model has a 24-hour cycle, and makes decisions and scheduling every 1 hour.

3. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 2 is characterized in that: The state constraints of the energy storage system are: in, is the charge capacity of the energy storage system at time t, is the discharge amount of the energy storage system at time t, is the maximum charge capacity of the energy storage system, is the maximum discharge capacity of the energy storage system, the coefficient and is a 0-1 variable; The state of charge (SOC) range constraint is: Where, is the current state of charge of the battery of the energy storage system at time t, is the battery charge state of the energy storage system at time t-1, and are the minimum and maximum battery state of charge, P t is the power of the energy storage system at time t, P rate is the rated power of the energy storage system, is the remaining capacity of the energy storage system at time t, is the remaining capacity of the energy storage system at time t-1, η ch and η dis are the charging efficiency and discharging efficiency of the energy storage system, respectively, and Δt is the time interval; The state constraints of the locomotive are: Where, The charging capacity of new energy locomotives, The maximum charging capacity of new energy locomotives, is the discharge capacity of new energy locomotives, is the maximum discharge capacity of new energy locomotives, and are the charge coefficient and the discharge coefficient respectively; Where, is the remaining power of the new energy locomotive at time t, is the remaining power of the new energy locomotive at time t+1, and are the minimum and maximum remaining power of new energy locomotives, η el,ch and η el,dis is the charging efficiency and discharging efficiency of new energy locomotives, E el,p The power consumption of a new energy locomotive for one day; The state of charge of new energy locomotives is expressed as Where, is the state of charge of the new energy locomotive at time t, is the state of charge of the new energy locomotive at time t-1, is the rated power of the new energy locomotive, and They are the minimum and maximum states of charge of new energy locomotives respectively; At the initial time 0, both the new energy locomotive and the microgrid have a normal initial charge state to ensure normal dispatching: In the formula, SOC(0) represents the state of charge of the microgrid at the initial time 0, SOC min and SOC max They are the minimum and maximum values ​​of the microgrid state of charge, SOC el (0) is the charge state of the new energy locomotive at the initial time 0; The timing and scale of charging and discharging of new energy locomotives must be able to complete the operating tasks assigned by managers: Where, is the charging capacity of the new energy locomotive at time t; The energy storage system and new energy locomotive both follow the "one-way operation" principle and can only perform one operation at any time: charging or discharging: Where, and is a binary variable, and is a binary variable; The total active power balance constraint of the locomotive depot microgrid is: Where, is the photovoltaic power generation of the microgrid at time t, is the amount of electricity purchased from the upper power grid at time t, is the charge of the energy storage system at time t, is the power consumption of other non-locomotive fixed loads at time t, is the charge or discharge amount of the new energy locomotive at time t, is the discharge amount of the energy storage system at time t; is the charge and discharge power of the new energy locomotive at time t, is the locomotive charging power at time t, is the locomotive discharge power at time t.

4. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 3 is characterized in that: The expression for minimizing the microgrid operation and maintenance cost TC is: Min TC=C grid +C pv +C storage (21) Among them, C grid is the cost of interaction between the microgrid and the grid, C pv is the operation and maintenance cost of the photovoltaic power generation system, C storage It is the charging and discharging loss and maintenance cost of the energy storage system; The maximum microgrid photovoltaic absorption rate R is expressed as: Among them, P pv,used Indicates the photovoltaic power generation used by the microgrid, P pv It represents the total photovoltaic power generation of the microgrid, which is obtained by Beta distribution prediction. Beta distribution conforms to the probability distribution characteristics of photovoltaic power generation and is very suitable for fitting the uncertainty of photovoltaic power generation.

5. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 3 or 4, characterized in that: The four operating strategies of new energy locomotives include: Strategy 1: New energy locomotives are considered fixed loads and do not participate in source-load interaction: Strategy 2: The charge and discharge capacity of new energy locomotives has a time-shifting characteristic, which can be regarded as a shiftable load. That is, a new scheduling plan is formed by shifting part of the charge and discharge power of the locomotive at a certain time to other times: Strategy 3: The charging and discharging power of new energy locomotives can be reduced. Based on the completion of the target tasks assigned by the superior user, the system can autonomously control whether the reduction operation can be performed at the time point: Strategy 4: The charging and discharging power of new energy locomotives is both reducible and transferable: Where, is the power change of the mining new energy locomotive at time t, is the basic power requirement of the new energy locomotive at time t; is the movable load of the new energy locomotive at time t, and are the maximum and minimum values ​​of the translational load of the new energy locomotive, is a binary variable, is the load that can be reduced by the new energy locomotive at time t, P el,p To meet the total power requirements of new energy locomotives to complete the tasks assigned by superior users.

6. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 5 is characterized in that: The method for solving the intraday optimal dispatch model of the locomotive depot microgrid using the improved fusion multi-objective optimization algorithm is as follows: S1. Set algorithm parameters: including the maximum number of iterations Ite max , population size Npop, initial crossover rate Final crossover rate f crossover , adaptive mutation rate, adaptive crossover rate, variable asynchronous length, define two objective functions of minimizing microgrid operation and maintenance costs and maximizing photovoltaic absorption rate; S2. Initialize the population individual information: including individual position, individual fitness value, individual level, individual domination number, and individual crowding degree; S3. Perform an initial evaluation on the initialized population, use individual positions to screen individuals in the population that meet the constraints, and use a penalty function to reset the individual fitness values ​​of individuals that do not meet the constraints to inf; S4. Perform non-dominated sorting on the population; S5. Enter the main iteration loop, obtain the number of iterations, and update the number of crossover and mutation individuals; S6. Using an adaptive crossover rate to reduce the crossover rate generation by generation, performing a crossover operation, generating two individuals each crossover operation; S7. Calculate the mutation rate using the adaptive mutation rate and perform the mutation operation; S8. Merge the two offspring populations obtained by the crossover and mutation operations with the initial population to generate a new population; S9. Perform non-dominated sorting on the newly generated population again; S10. Calculate the crowding distance of the population; S11. Update the individuals in the population based on non-dominated sorting and crowding distance sorting; S12. Truncate the population and keep only the top Npop individuals; S13. Traverse all individuals in the population and apply optimization operations that combine the WOA algorithm and the Levy flight mechanism to each individual; S14. Perform non-dominated sorting, crowding degree calculation, and crowding distance sorting on the new population obtained after optimization, and retain Npop top individuals; S15. Perform the next iteration until the convergence condition is reached or the loop reaches the number of iterations; S16. Obtaining the optimal target value is the optimal scheduling solution for all.

7. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 6 is characterized in that: The method for updating the number of crossover and mutation individuals in step S5 is: the number of mutation individuals and the number of crossover individuals are based on the adaptive crossover rate in the current number of iterations. and adaptive mutation rate μ Ite The number of mutation individuals is nCrossover=2*round(μ Ite *Npop / 2); the number of crossover individuals is round is the rounding down function; The adaptive crossover rate for: Where, is the initial crossover rate, f Crossover is the final crossover rate, Ite is the number of iterations of the main loop of the current algorithm, Ite max is the maximum number of iterations; The adaptive mutation rate decreases from generation to generation in the form of exponential decay, and m Ite =max(0.1,u Ite-1 ·c)c<1 (30) Where μ Ite is the adaptive mutation rate of the Ite-th iteration, γ is the attenuation coefficient, μ Ite-1 is the adaptive mutation rate of the Ite-1th iteration.

8. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 6 or 7, characterized in that: The method for optimizing the operation of integrating the WOA algorithm and the Levy flight mechanism in step S13 is: S131 obtains the current individual position and individual fitness value, records the individual position as the optimal position, and records the individual fitness value as the optimal fitness value; S132 performs WOA algorithm and Levy flight optimization cycle on individuals; S133 selects the target prey location and sets the dynamic attenuation parameters of the WOA algorithm; S134 gradually narrows the search range: sets the WOA algorithm's control search direction and control movement amplitude, sets the probability parameter P to determine whether the whale performs spiral movement and surrounds the prey, and sets the execution probability of the Levy flight control; S135 sets the parameters for controlling the flight jump intensity in the Levy flight mechanism and calculates the individual Levy flight step length; S136 determines an updated position based on the individual's movement behavior, determines whether the updated position performs a Levy flight mechanism operation, and records the updated position as a new individual position; S137 imposes upper and lower bounds on the updated position: directly comparing the decision vector of the updated position to see if it is still within the variable constraints, ensuring that the new position is within the search space; S138 calculates the objective function value of the new individual as the fitness value through the updated position. If the fitness value of the new individual is better than the fitness value of the best individual, the position of the new individual is used as the best position and the fitness value of the new individual is used as the best fitness value. At the same time, the new individuals obtained after traversing the population and performing the WOA algorithm and Levy flight mechanism optimization are merged into a new population.

9. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 8, characterized in that: The WOA algorithm performs fine search optimization as follows: Exploration phase: Shrinking and surrounding mechanism: Spiral update mechanism: The Levy flight mechanism is: X (ite+1) =X (ite) +ε·L·R (36) Where, is the currently selected population individual, is the current optimal individual, is the individual obtained by the exploration operation at the ite+1th iteration of the FWOA sub-cycle, is the randomly selected prey position, β is the parameter controlling the intensity of flight jump; and are the parameters for controlling the search direction and the motion amplitude, respectively, and Among them, w is the parameter that controls dynamic attenuation, r and q are random numbers in the range of 0-1, is the distance between the current individual and the best individual after adding the disturbance; bl is a random number, ite is the number of iterations of the FWOA sub-cycle; L is the flight step length of the population individual, u and v are random variables sampled from the normal distribution, ε is a small disturbance factor, R is a random disturbance of the standard normal distribution, X (ite) and X (ite+1) They represent the individuals obtained after performing Levy flight operations after ite and ite+1 iterations, respectively. The parameters controlling dynamic attenuation are 10. The multi-objective optimization scheduling method for a locomotive depot microgrid based on an improved NSGA-II algorithm under source-load interaction according to claim 8, characterized in that: The operation steps of performing non-dominated sorting on the population in step S4 are: (1) Get the current population size, initialize the dominance index set of each individual to an empty set, and the number of dominated individuals to 0; (2) Select two individuals in the population and compare them pairwise. If individual a dominates individual b, add the index of individual b to the dominance index set of individual a, add 1 to the number of dominated individuals of individual b, and return the updated information to the original individual. (3) If the number of individuals dominated is always 0, it means that they are not dominated by any individual. The individual is added to the frontier solution set F1 and the individual level is set to 1; (4) Construct each non-dominated frontier layer by layer according to the dominant individual index in the dominant index set of the individual: First, select an individual from the frontier with level 1, find the position of the dominated individual through the dominant individual index of the individual, and subtract 1 from the number of dominated individuals of the dominated individual. If the number of dominated individuals becomes 0 after subtracting 1, set the level of the current dominated individual to 2, and then select an individual from the frontier with level 2, add the dominance level to the dominated individual, and so on, traverse the population and add the dominance level to all individuals; The implementation method of step S6 is: 1) Traverse all crossover individuals, randomly select two individuals from the population as parents, and perform a crossover operation on the positions of the two parents; 2) The crossover operation generates two new positions, i.e., the positions of the offspring, by performing a weighted combination of the random position vectors; 3) Calculate the objective function through the offspring position and obtain the offspring fitness value; 4) Screen the offspring population according to the constraints and retain the offspring population that meets the constraints; The implementation method of step S7 is: S71 traverses all mutation individuals and randomly selects an individual from the population as the parent to perform the mutation operation; S72 obtains the number of mutations and uses an adaptive Gaussian mutation operation to adjust the range boundary. When the individual position approaches the center, the step size approaches the initial step size. When the position approaches the boundary, the step size approaches 0. Adaptive perturbation is performed to obtain the position of the offspring individual after the mutation. S73 calculates the objective function value according to the individual position of the offspring to obtain the fitness value; S74 performs constraint screening on the offspring population and retains the offspring population that meets the constraint conditions; The method for calculating the crowding distance of the population in S10 is as follows: obtaining the hierarchical level of the non-dominated frontier solution set, traversing all levels of the frontier solution sets and performing the following operations: extracting the objective function value of the individual in the current frontier solution set, obtaining the number of objective functions of the current frontier solution set, and obtaining the number of individuals in the current frontier solution set; sorting the individuals in the solution set according to the value of the objective function, wherein the crowding degree of the boundary individuals is set to infinity, and the intermediate values ​​are calculated according to the normalization of adjacent differences to obtain the crowding distance between each individual; summing the crowding distances of each individual to other individuals to obtain the crowding degree value of the current individual; The implementation method of S11 is as follows: sorting all individuals in the population according to the crowding distance, where individuals with larger crowding distances are ranked higher; sorting individuals in the population according to their levels from small to large; obtaining the frontier levels of all individuals and the maximum frontier level of all individuals, initializing an index for each frontier solution set, and obtaining the number of indexes according to the number of frontier levels; Extract all individuals with a frontier level of 1 in the population, and the decision vector of the individual position is all the optimal scheduling solutions; The crossover operation is implemented by performing a "gene-by-gene crossover" on the position information x1 and x2 of the two parents to obtain two offspring: y1=m·x1+(1-m)·x2 y2=m·x2+(1-m)·x1 (39) Where y1 and y2 are the offspring position information, and m represents a random vector of the same size as x1 with a value of [0,1]. In step S71, the corresponding variable step length is set for each decision vector of each hour in 24 hours as follows: Where, is the adjusted variable step length corresponding to the j-th decision vector, σ j is the initial variable asynchronous length, and is the maximum and minimum value of the j-th decision variable.

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