Improved strength pareto algorithm and multi-objective scheduling method based on the algorithm

Abstract

The application belongs to the field of water and electricity energy optimization, and discloses an improved strength pareto algorithm and a multi-objective scheduling method based on the algorithm. The algorithm comprises an initialization stage: a Latin hypercube method is used for sampling, and a maximum minimum criterion is introduced to adjust the position of sample points; an adaptability assignment stage: a weighted Euclidean distance calculation formula is used to weight the difference of each target; an environment selection and truncation operation stage: all individuals with an adaptability less than 1 are selected from a merged set to be reserved, and individuals exceeding an archive threshold are truncated according to a mixed distance; a genetic operation: individuals are selected as parents through a tournament to perform adaptive crossover, and adaptive mutation operation is performed on the offspring individuals obtained through the crossover; a boundary correction and iteration termination step; higher efficiency information is improved through one-time global calculation; and the multi-objective scheduling method based on the algorithm has more excellent effects in reservoir optimization scheduling.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of water and electricity energy optimization, in particular to an improved strength pareto algorithm and a multi-objective scheduling method based on the algorithm. BACKGROUND

[0002] Traditional reservoir scheduling is limited to single targets such as power generation, peak regulation, ecology, navigation, etc., and other related targets are ignored, which often leads to the sacrifice of the benefits of other targets while meeting a certain target, and cannot truly meet the design requirements of the power station. Therefore, it is of great significance to build a multi-objective scheduling model suitable for the design requirements of the power station to balance the demands of multiple parties and play the expected role of the power station construction.

[0003] Pareto evolutionary algorithm (SPEA) is a multi-objective optimization algorithm based on genetic algorithm, the core idea of which is to assign fitness values to individuals using pareto dominance relationship, and to evolve the population through genetic operations to approach the pareto optimal set. Due to the shortcomings of the algorithm in fitness assignment and archive maintenance, Zitzler et al. proposed an improved version of SPEA-SPEA2, which solved some defects of the original algorithm. Although SPEA2 performs well in multi-objective optimization, it still has defects such as high computational complexity, premature convergence, and insufficient local search capability, and its application in the multi-objective scheduling model of the power station lacks the ability of global exploration. In view of these defects, the present inventors propose an improved strength pareto algorithm-LMSPEA2, and a multi-objective scheduling method based on the improved strength pareto algorithm. SUMMARY

[0004] In view of the above defects or improvement needs of the prior art, the present application provides an improved strength pareto algorithm and a multi-objective scheduling method based on the algorithm.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, an improved strength pareto algorithm is provided, comprising the following steps:

[0006] a. Initialization stage: Latin hypercube method is used for sampling, and maximum minimum criterion is introduced to adjust the position of sample points, so that individuals can be uniformly distributed in space;

[0007] b. Fitness assignment: based on step a, the weighted Euclidean distance calculation formula is used to weight the difference of each target, which more accurately reflects the influence of different targets on the distribution of solution set;

[0008] c. Environmental selection and truncation operation: on the basis of step b, the current population and the archive are combined, all individuals with fitness value less than 1 are selected from the combined set for reservation, and the hybrid distance of individuals exceeding the archive threshold is calculated for truncation;

[0009] d. Genetic operation: after the selection and truncation operation in step c, individuals are selected as parents from the current population and the external archive through tournament selection, and adaptive crossover is performed on the parent individuals to obtain offspring individuals, and adaptive mutation operation is performed on the offspring individuals;

[0010] e. Boundary correction: after the crossover operation in step d, boundary correction is performed on the offspring individuals, and after the mutation operation, boundary correction is performed on the parent individuals;

[0011] f. Iteration termination: steps b-e are repeated until the maximum number of iterations is reached, and the current objective function value and the decision variable change process are obtained.

[0012] As preferred, the specific steps of step a are: Latin hypercube method is used to divide the space of each dimension into N small intervals, then a position is randomly selected in each sub-interval to form a preliminary sample set, and once all sample points are generated, the positions of the sample points are further optimized by the maximum minimum criterion to avoid the sample points being too close to each other. The maximum minimum criterion selects the minimum distance between two points to ensure that the minimum distance is maximized during sample adjustment.

[0013] As preferred, the specific steps of step b are: the strength value of each individual i is calculated , the strength value is equal to the number of individuals in the population dominated by it, and the original fitness value is equal to the sum of the strengths of all individuals dominated by i.

[0014] The Euclidean distance between each pair of individuals is calculated , and the calculation formula is:

[0015]

[0016] In the formula, is the dimension of the objective space, represents the value of individual i on the kth objective;

[0017] The density estimation value is calculated, and the calculation formula is:

[0018]

[0019] Finally, the fitness value of each individual i is calculated , and the calculation formula is:

[0020]

[0021] wherein, is the original fitness value of each individual i.

[0022] As a preference, the screening principle in step c is that the global relative position between each individual i and other individual j is obtained by the following formula, the hybrid distance in the target space is obtained, the calculated hybrid distance of each individual is sorted from large to small, and finally the first N individuals equal to the population number are reserved, and the calculation formula is

[0023]

[0024]

[0025]

[0026]

[0027] wherein, is the value of the normalized individual i on the kth target, is the value of the normalized individual i on the kth target, is the value of the normalized individual i on the kth target, and are the maximum value and the minimum value of the individual on the target k, and are the Euclidean distance and the cosine distance of the two individuals on the kth target after normalization, is the new individual-to-individual calculation formula, is a weight parameter.

[0028] As a preference, step d includes the following steps:

[0029] d1 tournament selection: randomly sampling k individuals from the current population and the external archive with replacement, and retaining the individual with the minimum fitness each time, and performing multiple tournaments until the same number of individuals as the parent population is generated;

[0030] d2 crossover stage: dividing the individuals generated in step d1 into two parts Parent1 and Parent2, calculating judging the probability of the parent body to perform the crossover operation, and calculating the crossover factor for the parent body that needs to perform the crossover operation , and the calculation formula is:

[0031]

[0032] wherein, disC is the crossover distribution index, is a random number between 0 and 1;

[0033] the calculated is subjected to a random operation to obtain , and the calculation formula is:

[0034]

[0035] in the formula, is a random integer of 0 or 1;

[0036] a random number between 0 and 1 is randomly generated, if the generated random number is greater than 0.5, then , otherwise ;

[0037] the crossover factor is combined to obtain two offspring after the crossover, and the calculation formula is:

[0038]

[0039]

[0040] in the formula, and are the genes of the parent individual, and are the offspring generated by the crossover operation;

[0041] d3 mutation stage: the offspring and generated in step d2 are combined into a matrix , and determine the probability of the offspring that will be subjected to the mutation operation, and the mutation step of the offspring that needs to be subjected to the mutation operation is calculated , and the calculation formula is:

[0042]

[0043] in the formula, is a random number between 0 and 1, is a mutation distribution index;

[0044] the offspring is subjected to the mutation operation, and the calculation formula is:

[0045]

[0046] in the formula, is the offspring generated by the mutation operation, is the upper limit of the decision variable, is the lower limit of the decision variable.

[0047] As a preferred, the crossover probability and mutation probability The improved formula is:

[0048]

[0049]

[0050]

[0051] In the formula, Indicates the first The first individual One decision variable, Indicates the first The mean of each decision variable, The number of individuals in the population. For the number of decision variables, It represents population diversity.

[0052] Preferably, step e includes the following steps:

[0053] e1: If the gene value is less than the lower bound, the gene value is set as the lower bound; if the gene value is greater than the upper bound, the gene value is set as the upper bound. The correction formula is as follows:

[0054]

[0055] In the formula, This indicates the corrected offspring genes;

[0056] e2: An additional boundary correction is added to prevent the generation of particles exceeding the constraints after the crossover operation, thus preventing invalid mutations. The correction formula is as follows:

[0057]

[0058] In the formula, This represents the modified parental genes.

[0059] To achieve the above objectives, according to another aspect of the present invention, a multi-objective scheduling method based on an improved strength Pareto algorithm is provided, comprising the following steps:

[0060] S1 Model Construction: Determining decision variables and setting constraints together constitute a multi-objective scheduling model, and constructing multiple objective functions;

[0061] S2: Apply model constraints to the multi-objective scheduling model established in step S1;

[0062] S3: Solve the objective function using the improved strength Pareto algorithm described above.

[0063] As a preferred option, the specific method for step S1 is as follows:

[0064] S11: taking water level as a decision variable, taking maximum power generation of the power station and minimum residual load variance as targets, and setting constraint conditions to jointly constitute a multi-target scheduling model;

[0065] S12: calculating the output of the hydropower station in each time period according to the net water head of the hydropower station in each time period and the water consumption rate curve of the hydropower station, adding the wind and light output in the corresponding time period, and establishing a first target function with the common output of water, wind and light in each time period as the target of maximum power generation of the hydropower station, and the formula is:

[0066]

[0067]

[0068] In the formula, represents the total power generation of the complementary system, T represents the total number of time periods in the scheduling period, t is the time period sequence number, , is the scheduling time period, is the total output of the t time period, represents the output of the hydropower station in the t time period, and respectively represent the output of the wind power station and the photovoltaic power station in the same time period;

[0069] S13: establishing a second target function by combining the load demand of the power station power transmission area with the total output process of the water, wind and light system, and the formula is:

[0070]

[0071]

[0072] In the formula, represents the residual load variance of the power grid after being powered by the water, wind and light multi-energy complementary system, represents the load demand of the power grid, represents the residual load of the power grid after being powered by the water, wind and light multi-energy complementary system, represents the residual load variance of the power grid.

[0073] As preferred, the constraint conditions include water level, flow and output.

[0074] As preferred, the model constraints of step S2 include: reservoir water level constraint, water balance constraint, reservoir characteristic constraint, output characteristic constraint, flow constraint, water level / flow amplitude constraint, hydropower station output constraint, wind farm wind speed constraint, and photovoltaic farm power generation capacity constraint.

[0075] Overall, compared with the prior art, the above technical solutions conceived by the present application have the following beneficial effects:

[0076] 1、The improved intensity pareto algorithm of the application improves more efficient information through one-time global calculation, can better capture the structure of target space, reduces redundant calculation amount, and avoids repeated calculation especially when facing large-scale population calculation;

[0077] 2、The multi-objective scheduling method of the application can play a more outstanding effect in reservoir optimization scheduling by using the improved intensity pareto algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 is a flowchart of the improved intensity pareto algorithm of the application;

[0079] Figure 2 is a pareto front comparison chart of multiple algorithms. DETAILED DESCRIPTION

[0080] In order to make the purpose, technical scheme and advantages of the application more clear, the application is further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application, and are not used to limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0081] Please refer to Figure 1 , based on the existing defects of the SPEA2 algorithm, the improved intensity pareto algorithm provided by the application includes the following steps:

[0082] a initialization stage: the Latin hypercube method is used for sampling, and the maximum minimum criterion is introduced to adjust the position of the sample points, so that the individuals can be uniformly distributed in space;

[0083] The original SPEA2 algorithm uses random sampling to initialize the generation of population , the size is , and an empty archive set is created For storing non-dominated solutions. Random sampling is easy to cause some sample points to gather in some areas, thus lacking the ability of global exploration. The improved strength pareto algorithm uses the Latin hypercube method for sampling and introduces the maximum minimum criterion to adjust the position of sample points, that is, the Latin hypercube method is used to divide the space of each dimension into N small intervals, and then a position is randomly selected in each sub-interval to form a preliminary sample set. Once all sample points are generated, the position of the sample points is further optimized by the maximum minimum criterion to avoid the sample points being too close to each other. The maximum minimum criterion selects the minimum distance between two points by calculating the distance between all sample points to ensure that the minimum distance is maximized during sample adjustment.

[0084] b Fitness assignment: On the basis of step a, the weighted Euclidean distance calculation formula is used to weight the difference of each target, and the influence of different targets on the distribution of solution set is more accurately reflected;

[0085] In the original SPEA2 algorithm, the fitness value of each individual is equal to the original fitness value of the individual plus the density estimation value of the individual The calculation of the density estimation value is as follows:

[0086]

[0087] The Euclidean distance between each pair of individuals in the calculated population is as follows:

[0088]

[0089] In the formula, is the dimension of the target space, indicates the value of individual i on the kth target, indicates the value of individual j on the kth target.

[0090] The Euclidean distance between individuals calculated by the formula does not take into account the differences between targets and the scale of target values, that is, the numerical range of different targets may differ greatly. Therefore, the weighted Euclidean distance calculation formula is used, which can more accurately reflect the influence of different targets on the distribution of solution set by weighting the difference of each target.

[0091] The weighted Euclidean distance formula obtained by the improved strength pareto algorithm is as follows:

[0092]

[0093] In the formula, is the weighted Euclidean distance of the kth target, and max and min represent the maximum and minimum value of the kth objective respectively.

[0094] By introducing the weighted Euclidean distance, the value range of each objective is considered, making the distance calculation more accurate, avoiding the influence of different scale objectives on distance calculation, and the improved distance calculation method also more accurately reflects the similarity between individuals, which helps to maintain the diversity of the population more effectively in the environment selection stage and avoid premature convergence to local optimal solution.

[0095] c. Environment selection and truncation operation: on the basis of step b, the current population and the archive set are merged into ∪ , all individuals with fitness less than 1 are selected from the merged set for preservation, and the individuals exceeding the archive threshold are calculated for hybrid distance for truncation;

[0096] This kind of individual means that it is not dominated by any other individual on all objectives, in other words, these individuals are potential pareto optimal solution, representing better solution in the optimization process. If the number of individuals with fitness less than 1 is more than the number of objective population, these individuals will be screened and deleted, and finally the number of individuals equal to the number of objective population is reserved.

[0097] In the original SPEA2 algorithm, the distance between adjacent solutions of an individual is calculated to reflect the crowding distance, and the average distance between each individual and all other individuals is calculated to reflect the relative distance, and then the calculated crowding degree and relative distance are added to obtain a new comprehensive evaluation index CM, the CM value of each individual is arranged from large to small, and the first N individuals equal to the population number are reserved, and the calculation formula is as follows:

[0098]

[0099] In the formula, CD is the crowding distance, RD is the relative distance, is the value of individual i on the kth objective, is the value of individual j on the kth objective, and max and min represent the maximum and minimum value of the kth objective respectively.

[0100] The distance calculation method combining crowding distance and relative distance can intuitively reflect the geometric distribution characteristics of the solution in low-dimensional space through Euclidean distance, and can efficiently solve multi-objective problems in low-dimensional space. However, it still has certain limitations when facing high-dimensional problems. First, the multi-objective space is not normalized, leading to spatial distribution deviation caused by dimensional differences. That is, the target dimension with a larger numerical range dominates in Euclidean distance calculation, weakening the algorithm's ability to uniformly explore the Pareto front. Second, the traditional Euclidean distance is easily affected by the curse of dimensionality in high-dimensional target space. As the number of targets increases, the distance between individuals decreases significantly, making it difficult to effectively maintain the diversity of the solution set.

[0101] To solve the above problems, the improved distance calculation model realizes multi-dimensional optimization through systematic reconstruction. First, the independent normalization mapping of target dimension is introduced, and a linear transformation with minimal constant protection is used to constrain each target value to the (0, 1) interval, eliminating the interference of different dimensions. Second, a hybrid distance measurement function is designed to combine Euclidean distance, which represents absolute position difference, and cosine distance, which describes direction similarity, through a weight parameter The target dimension is adaptively adjusted (Euclidean distance is emphasized in low-dimensional space, and cosine contribution is strengthened in high-dimensional space), thereby preserving the uniformity of low-dimensional space while enhancing the directional diversity of high-dimensional solutions. The new distance calculation formula combines distance architecture and normalized target space, and the calculation process is as follows:

[0102] That is, the selection principle is to obtain the global relative position between each individual i and other individual j through the following formula, obtain the hybrid distance in the target space, sort the calculated hybrid distance of each individual from large to small, and finally retain the top N individuals equal to the population size. The calculation formula of the pair distance is:

[0103]

[0104] where, is the value of the normalized individual i in the kth target, and are the Euclidean distance and cosine distance of the two individuals in the kth target after normalization, is the new individual calculation formula, is the weight parameter, which is set to 0.7 in this study.

[0105] d Genetic operation: After the selection and truncation operation in step c, the individuals are selected as parents through tournament selection from the current population and the external archive to perform adaptive crossover, and the offspring individuals obtained by crossover are subjected to adaptive mutation operation;

[0106] The specific steps are as follows:

[0107] d1 tournament selection: randomly select k individuals from the current population and the external archive with replacement, keep the individual with the minimum fitness each time, and perform multiple tournaments until the same number of individuals as the parent population is generated;

[0108] d2 crossover stage: split the individuals generated in step d1 into two parts, Parent1 and Parent2, and determine whether to perform simulated binary crossover (SBX) on the parents by the crossover probability proC. Calculate the crossover factor , the calculation formula is:

[0109] Determine whether to perform simulated binary crossover (SBX) on the parents by generating a random number between 0 and 1 and comparing it with the crossover probability proC. If crossover occurs, calculate the crossover factor , the calculation formula is:

[0110]

[0111] where disC is the crossover distribution index, which is a set value, is a random number between 0 and 1, used to determine which calculation to perform.

[0112] Further, the calculated is subjected to the following operations:

[0113]

[0114] where is a random integer of 0 or 1, the positive and negative of means that the direction of crossover is random, so that the offspring can be generated on both sides of the parents, increasing diversity.

[0115] Further, the is subjected to the following operations: a random number between 0 and 1 is generated, if the generated random number is greater than 0.5, then , otherwise . That is, the calculated crossover factor will have a 50% probability of being set to 1.

[0116] The two offspring after crossover are generated by linear combination of the parent genes, where the crossover factor determines the proportion of parent gene combination, the calculation formula of the two offspring is as follows:

[0117]

[0118] where and is the gene of the parent individual, and is the offspring generated by the crossover operation;

[0119] d3 mutation stage: the offspring generated in step d2 and are merged into a matrix , calculate to determine how much probability the offspring will be subjected to mutation operation.

[0120] Whether the offspring will be subjected to mutation is determined by generating a random number between 0 and 1 and comparing it with the mutation probability proM / D, where D is the number of decision variables. The mutation degree of each individual is related to the mutation step, which is calculated by the polynomial mutation formula as follows:

[0121]

[0122] In the formula, is a random number between 0 and 1, is the mutation distribution index, which controls the size of the mutation step and is a set value.

[0123] After calculating the mutation step, the offspring and are subjected to mutation according to the following formula:

[0124]

[0125] In the formula, is the offspring generated by the mutation operation, is the upper bound of the decision variable, is the lower bound of the decision variable.

[0126] In the original SPEA2 algorithm, the crossover probability and the mutation probability are both set to a fixed value of 1, resulting in all parents being subjected to crossover and all offspring being subjected to mutation. In the early stages of the algorithm, the population diversity is high, and a large crossover probability and genetic probability help to quickly explore the solution space and promote the combination of excellent genes. However, as the evolution progresses, the population tends to converge, and a too high crossover probability and genetic probability may lead to the destruction of excellent genes, reducing the convergence speed of the algorithm. Therefore, timely reducing the crossover probability and genetic probability helps to maintain the diversity of the population and avoid falling into local optimal solutions. Therefore, dynamically adjusting the crossover probability and genetic probability can make them play their specific roles at different stages and improve the performance of the algorithm. The following is the improvement of the improved algorithm to the crossover probability and the mutation probability :

[0127]

[0128] In the formula, Indicates the first The first individual One decision variable, Indicates the first The mean of each decision variable, The number of individuals in the population. For the number of decision variables, It represents population diversity.

[0129] When the population has high diversity, crossover operations should be relied upon more heavily to enhance information exchange between individuals and help the algorithm escape local optima. In this case, a higher crossover probability can accelerate the search process. However, when the population has converged, excessive crossover may not bring much benefit and may even introduce more noise. Therefore, dynamically reducing the crossover probability and increasing the mutation probability can guide the algorithm to escape the current local optima and continue exploring the solution space.

[0130] e. Boundary correction: After completing the crossover operation in step d, the boundary of the offspring is corrected; after completing the mutation operation, the boundary of the parent is corrected.

[0131] e1: During the mutation phase, the offspring's gene value will increase according to the mutation time. Random perturbation may cause some gene values ​​to exceed the constraints of the problem. Therefore, boundary correction after mutation is a crucial step to ensure that the mutated individuals still satisfy the problem's constraints. The correction principle is as follows: if the offspring's gene value is less than the lower bound, then the offspring's gene value is set as the lower bound; if the offspring's gene value is greater than the upper bound, then the offspring's gene value is set as the upper bound. The correction formula is shown below:

[0132]

[0133] In the formula, This indicates the modified offspring genes.

[0134] If out-of-bounds solutions are allowed, the algorithm may waste a lot of time exploring the invalid search space. By correcting out-of-bounds solutions, the algorithm can focus its efforts on optimizing in the valid search space.

[0135] e2: The improved strength Pareto algorithm adds a boundary correction to the parent body after the crossover operation to prevent the generation of particles that exceed the constraints and undergo invalid mutations. Adding the boundary correction operation can effectively reduce unnecessary computation. The boundary correction formula is as follows:

[0136]

[0137] In the formula, This represents the modified parental genes.

[0138] f. Iteration Termination: Repeat step be until the maximum number of iterations is reached, then terminate the iteration and obtain the current objective function value and the change process of the decision variables.

[0139] This invention provides a multi-objective scheduling method based on an improved strength Pareto algorithm, comprising the following steps:

[0140] S1 Model Construction: Determining decision variables and setting constraints together constitute a multi-objective scheduling model, and constructing multiple objective functions;

[0141] S11: Using water level as the decision variable, a multi-objective function model is established with the objectives of maximizing power generation and minimizing the mean square error of surplus load. Constraints such as water level, flow rate, and output are set to form a multi-objective scheduling model.

[0142] S12: The power output of the hydropower station in each time period is calculated based on the net head and water consumption rate curve of the hydropower station in each time period. This is combined with the wind and solar power output in the corresponding time periods. The first objective function, with the goal of maximizing the power generation of the hydropower station, is then established using the combined output of water, wind, and solar power in each time period. The formula is as follows:

[0143]

[0144] In the formula, The total power generation of the complementary system is represented by T, the total number of time periods within the scheduling period is represented by T, and t is the time period sequence number. , It is the scheduling period. It is the total output during time period t. This represents the power output of the hydropower station during time period t. and These represent the power output of wind power stations and photovoltaic power stations during the same time period, respectively.

[0145] S13: In addition to considering the power generation benefits on the power source side, the peak-shaving effect on the grid side should also be considered. Therefore, a second objective function was established based on the load demand in the power plant's transmission area and the total output of the hydro-wind-solar system:

[0146]

[0147] In the formula, This represents the mean square error of the residual load of the power grid after being supplied by a multi-energy complementary system of water, wind, and solar power. Indicates the power grid load demand. This indicates the surplus load of the power grid after being supplied by the hydro-wind-solar multi-energy complementary system. This represents the average surplus load of the power grid.

[0148] S2: model constraint is performed on the multi-objective scheduling model established in step S1;

[0149] The model constraint includes: reservoir water level constraint, water balance constraint, reservoir characteristic constraint, output characteristic constraint, flow constraint, water level / flow amplitude constraint, hydropower station output constraint, wind farm wind speed constraint, and photovoltaic field power generation capacity constraint. The specific constraint settings are as follows: 1) reservoir water level constraint

[0150]

[0151] In the formula: represents the dam front water level of the reservoir at time period, and are respectively the upper and lower limits of the dam front water level of the reservoir at time period.

[0152] 2) water balance constraint

[0153]

[0154] In the formula: and respectively represent the reservoir storage capacity at t time period and t-1 time period; represents the inflow of the reservoir at time period; represents the outflow of the reservoir at time period.

[0155] 3) reservoir characteristic constraint

[0156]

[0157] In the formula: is the average upstream water level of the reservoir at time period; is the average downstream tail water level of the reservoir at time period; , respectively represent the water level-storage capacity curve and the tail water level-discharge flow curve of the reservoir.

[0158] 4) output characteristic constraint

[0159]

[0160] In the formula: represents the reservoir output calculation function, is the net water head of the reservoir at t time period; is the power generation reference flow of the reservoir at t time period.

[0161] 5) flow constraint

[0162]

[0163] In the formula: and respectively represent the upper and lower limits of the reservoir discharge at time t.

[0164] 6) Water level / flow amplitude constraint

[0165]

[0166] In the formula: represents the allowable change interval of the water level within the reservoir scheduling time interval.

[0167] 7) Hydropower station output constraint

[0168]

[0169] In the formula: and respectively represent the upper and lower limits of the output of the reservoir at time t.

[0170] 8) Wind farm wind speed constraint

[0171]

[0172] In the formula: and respectively represent the upper and lower limits of the cut-in and cut-out wind speed of the wind farm at time t.

[0173] 9) Photovoltaic field generating panel capacity constraint

[0174]

[0175] In the formula: and respectively represent the upper and lower limits of the generating panel capacity of the photovoltaic field at time t.

[0176] S3: Solve the objective function by the improved strength Pareto algorithm, which specifically includes the following steps:

[0177] S31: Initialize the population

[0178] Generate N individuals by the Latin hypercube initialization method, representing the decision variable water level process Z, and the water level of each time interval satisfies the water level constraint, then optimize the distribution of the initial individuals by the maximum and minimum criterion to make the individuals uniformly distributed in space, increase the initial population exploration performance. At the same time, create an empty archive set for storing non-dominated solutions.

[0179] S32: Fitness assignment

[0180] At this stage, the water head of each individual generated after initialization is calculated according to Z , the power generation flow , the power station output , and the objective function is further calculated . The intensity value of each individual i is calculated according to the obtained objective function value , which is equal to the number of individuals in the population dominated by it, and then the original fitness value is equal to the sum of the intensities of all individuals dominated by i. Then the Euclidean distance between each pair of individuals is calculated according to formula (3b) , the density estimation value is calculated through formula (2) , and finally the fitness value of each individual i is calculated through formula (1) .

[0181] S33: Environment selection and truncation operation

[0182] The current population and the archive set are merged into ∪ , and all individuals with fitness less than 1 are selected from the merged set for preservation, which means that it is not dominated by any other individual on all objectives, in other words, these individuals are potential pareto optimal solutions, representing better solutions in the optimization process. If the number of individuals with fitness less than 1 is more than the target population size, these individuals will be screened and deleted, and finally the number of individuals equal to the target population size is retained. The principle of screening is to calculate the hybrid distance of each individual in the objective space according to formula (12), and the calculated hybrid distance of each individual is sorted from large to small, and finally the first N individuals equal to the population size are retained.

[0183] S34: Genetic operation

[0184] Individuals are selected as parents from the current population and the external archive through tournament selection for simulated binary crossover (SBX), and the tournament principle is similar to the "elimination round" in sports competitions, which selects better individuals from the population through small-scale competition. First, determine the number of participants k in each tournament, randomly select k individuals from the current population and the external archive with replacement, and retain the individual with the smallest fitness each time, and perform multiple tournaments until the same number of individuals as the parent population is generated. The generated individuals are divided into two parts Parent1 and Parent2 by random uniform division. According to formula (20) , determine the probability of the parent body performing crossover operation, and for the parent body that needs to perform crossover operation, first calculate the crossover factor according to formula (13) and formula (14) , the gene value of the offspring individual is calculated according to formula (15) and formula (16). The generated offspring and are merged into a matrix , and the offspring is calculated by formula (21) to determine the probability of the offspring to be mutated, and the mutation step of the offspring to be mutated is calculated according to formula (17) , and then the offspring is mutated according to formula (19).

[0185] S35: boundary correction

[0186] In the crossing process of the parent and the mutation process of the offspring, part of the individuals may exceed the set boundary due to random disturbance, so boundary correction is needed after the crossing and mutation operations are completed according to formula (23) and formula (24).

[0187] S36: iteration termination

[0188] Repeat steps S32-S35 until the maximum number of iterations is reached, then terminate the iteration, and obtain the current objective function value and decision variable change process.

[0189] The following is described by specific embodiments:

[0190] In 2022, Baihetan Power Station was constructed as a research target to build a multi-objective scheduling model for optimization, with the goal of maximizing power generation on the power supply side and minimizing the residual load variance on the grid side. Selecting the Baihetan hydropower station flood season (weak light and weak wind in September 2022) as an example, a multi-objective optimization scheduling of the water-wind-solar complementary system was carried out. The water level of Baihetan Power Station in early September 2022 was 777.69m, and the end water level was 801.03m. The average inflow was 5328.36 , in this embodiment, the output of Baihetan Power Station is sent to Zhejiang Province according to a 50% power transmission ratio, and the average monthly load of Zhejiang Province in September 2022 is about 66940MW. The improved multi-objective algorithm LMSPEA2 is used for solving in the embodiment, and the parameters are set as , , for comparison algorithm. The parameter settings in the improved algorithm are as follows: population size =50, maximum iteration number =3000. The remaining algorithm parameters are set according to the default parameters.

[0191] The final 50 groups of solutions of each algorithm are reserved to form the pareto front solution according to the congestion calculation, Table 1 is the multi-objective scheduling scheme obtained after optimization of the improved strength pareto algorithm, and Table 2 is the result comparison chart of scheme 1 (maximum power generation scheme), scheme 2 (compromise scheme) and scheme 3 (minimum residual load mean square error scheme) obtained by optimization of each algorithm.

[0192]

[0193]

[0194] During the flood season, the power station often cannot fully utilize the incoming water for power generation, resulting in waste of water resources. Therefore, selecting the flood season (weak light and weak wind in September 2022) of Baihetan Hydropower Station as the research object can more obviously reflect the optimization performance of each optimization algorithm, give more play space, and show the difference in algorithm performance.

[0195] As can be seen from Table 1, with the increase of system power generation, the residual load mean square error also increases, that is, the system peak shaving benefit decreases, indicating that there is a significant competitive relationship between the two objectives. Therefore, the non-inferior solution set obtained in the embodiment can effectively reflect the game relationship between the source side economic benefit and the network side peak shaving demand, and conforms to the actual engineering situation.

[0196] Further, according to Table 2, the optimization results of each algorithm are analyzed. In order to more effectively compare, three typical schemes are selected in the embodiment, that is, the maximum power generation scheme, the compromise scheme and the minimum residual load mean square error scheme. The three selected schemes typically show the difference in different target preferences. Through comparison, it is found that under the three schemes, the optimization results of the improved LMSPEA2 algorithm are better than those of the other three algorithms, that is, under the three schemes, the LMSPEA2 algorithm has achieved the maximum power generation and the minimum residual load mean square error.

[0197] In combination with Figure 2The pareto front curve obtained by the LMSPEA2 algorithm is compared with the pareto front curves obtained by other algorithms. Any straight line parallel to the x axis and intersecting the four curves is drawn on the graph, and the intersection of the pareto obtained by the LMSPEA2 algorithm and the straight line is on the right side, that is, when the optimization results of the four algorithms for the residual load mean square error are the same value, the improved LMSPEA2 algorithm can obtain the maximum power generation, that is, the maximum peak shaving benefit; similarly, any straight line parallel to the y axis and intersecting the four curves is drawn on the graph, and the intersection of the pareto obtained by the LMSPEA2 algorithm and the straight line is on the lower side, that is, when the optimization results of the four optimization algorithms for the power generation are the same value, the improved LMSPEA2 algorithm can obtain the minimum residual load mean square error, that is, the best peak shaving effect. Therefore, it is not difficult to see that the improved algorithm can play a more outstanding effect in the reservoir optimal scheduling.

[0198] Those skilled in the art will easily understand that the above description is only the preferred embodiment of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A multi-objective scheduling method based on an improved strength Pareto algorithm, characterized in that, Includes the following steps: S1 Model Construction: Determining decision variables and setting constraints together constitute a multi-objective scheduling model, and constructing multiple objective functions; It includes step S11: using water level as a decision variable, taking the maximum power generation of the power station and the minimum mean square error of the surplus load as objectives, and setting constraints to jointly form a multi-objective scheduling model; S2: Apply model constraints to the multi-objective scheduling model established in step S1; S3: Solve the objective function using an improved intensity Pareto algorithm; the improved intensity Pareto algorithm includes the following steps: a. Initialization phase: The Latin hypercube method was used for sampling, and the maximum-minimum criterion was introduced to adjust the position of the sample points; b. Fitness assignment: Based on step a, the weighted Euclidean distance calculation formula is used to weight the differences of each target; c. Environment selection and truncation operation: Based on step b, merge the current population and the archive set, select all individuals with fitness less than 1 from the merge set for retention, and calculate the truncation distance for individuals exceeding the archive threshold; the truncation distance is the normalized Euclidean distance and cosine distance. d. Genetic operations: After the selection and truncation operations in step c, individuals are selected from the current population and external archives through a tournament to serve as parents for adaptive crossover, and adaptive mutation operations are performed on the offspring individuals obtained from the crossover. e. Boundary correction: After completing the crossover operation in step d, the boundary of the offspring is corrected; after completing the mutation operation, the boundary of the parent is corrected. f. Iteration Termination: Repeat step be until the maximum number of iterations is reached, then terminate the iteration and obtain the current objective function value and the change process of the decision variables. The specific steps of step b are as follows: calculate the strength value of each individual, the strength value is equal to the number of individuals in the population it dominates, and the original fitness value is equal to the sum of the strengths of all dominant individuals. Calculate the Euclidean distance between each pair of individuals. The calculation formula is: In the formula, It is the dimension of the target space. This represents the value of individual i for the k-th objective. This represents the value of individual j for the k-th objective. The weighted Euclidean distance to the k-th target and These represent the maximum and minimum values ​​of the k-th target, respectively. Calculate density estimate The calculation formula is: Finally, the fitness value of each individual i is calculated. The calculation formula is: In the formula, The original fitness value for each individual i; 2. The multi-objective scheduling method based on the improved strength Pareto algorithm as described in claim 1, characterized in that, Step S1 also includes: S12: The power output of the hydropower station in each time period is calculated based on the net head and water consumption rate curve of the hydropower station in each time period. This is combined with the wind and solar power output in the corresponding time periods. The first objective function, with the goal of maximizing the power generation of the hydropower station, is then established using the combined output of water, wind, and solar power in each time period. The formula is as follows: In the formula, The total power generation of the complementary system is represented by T, the total number of time periods within the scheduling period is represented by T, and t is the time period sequence number. , It is the scheduling period. It is the total output during time period t. This represents the power output of the hydropower station during time period t. and These represent the power output of the wind power station and the photovoltaic power station respectively during the same period; S13: A second objective function is established by combining the load demand of the power station's transmission area with the total output of the hydro-wind-solar system. Its formula is as follows: In the formula, This represents the mean square error of the residual load of the power grid after being supplied by a multi-energy complementary system of water, wind, and solar power. Indicates the power grid load demand. This indicates the surplus load of the power grid after being supplied by the hydro-wind-solar multi-energy complementary system. This represents the average surplus load of the power grid.

3. The multi-objective scheduling method based on the improved strength Pareto algorithm as described in claim 1, characterized in that, The model constraints in step S2 include: reservoir water level constraints, water balance constraints, reservoir characteristic constraints, power output characteristic constraints, flow constraints, water level / flow variation constraints, hydropower station power output constraints, wind farm wind speed constraints, and photovoltaic power generation capacity plate constraints.

4. A multi-objective scheduling method based on an improved strength Pareto algorithm as described in claim 1, characterized in that, The specific steps of step a are as follows: The Latin hypercube method is used to divide the space of each dimension into N small intervals, and then a position is randomly selected in each sub-interval to form a preliminary sample set. Once all sample points are generated, the minimum-maximum criterion is further used to select the minimum distance between two points by calculating the distance between all current sample points to ensure that the minimum distance is maximized during the sample adjustment process.

5. A multi-objective scheduling method based on an improved strength Pareto algorithm as described in claim 1, characterized in that, The selection principle in step c is as follows: The global relative position of each individual i to other individuals j is obtained using the following formula, resulting in the mixing distance in the target space. The calculated mixing distances of each individual are then sorted from largest to smallest, and finally, the top N individuals, equal to the population size, are retained. The calculation formula is as follows: In the formula, Let i be the normalized value of individual i at the k-th objective. For normalized individuals The value at the k-th target, and These are the maximum and minimum values ​​of the individual on target k, respectively. and Let Euclidean distance and cosine distance be the normalized Euclidean distance and cosine distance between two individuals on the k-th target. For the new inter-individual calculation formula. These are the weight parameters.

6. A multi-objective scheduling method based on an improved strength Pareto algorithm as described in claim 1, characterized in that, Step d includes the following steps: d1 tournament selection: The number of participants k in each tournament is randomly selected from the current population and external archives with replacement. The individual with the lowest fitness is retained each time. The tournament is conducted multiple times until the number of individuals is the same as the number of the parent population. d2 Crossover Phase: The individuals generated in step d1 are split into two parts, Parent1 and Parent2, randomly and uniformly divided. The crossover probability proC determines whether the parent generation should undergo simulated binary crossover. The crossover factor is calculated for the parent generation that needs to undergo crossover. The calculation formula is: In the formula, disC is the cross-distribution index. It is a random number between 0 and 1; right Obtain by performing random operations The calculation formula is: In the formula, It is a random integer of 0 or 1; randomly generate a random number between 0 and 1. If the generated random number is greater than 0.5, then let... Otherwise ; Combining cross factors The formula for calculating the two offspring obtained after crossover is: In the formula, and It is the genes of the parent individual. and It is a offspring generated through a crossover operation; d3 mutation stage: The offspring generated in step d2 and Merge into a single matrix Through mutation probability To determine whether a mutation operation should be performed on offspring, the variable time length is calculated for offspring that require mutation. The calculation formula is: In the formula, A random number between 0 and 1. It is the variation distribution index; The mutation operation is performed on the offspring, and the calculation formula is as follows: In the formula, It is a offspring generated through mutation operations. The upper bound of the decision variable, This represents the lower bound of the decision variable.

7. A multi-objective scheduling method based on an improved strength Pareto algorithm as described in claim 6, characterized in that, The crossover probability and mutation probability The improved formula is: In the formula, Indicates the first The first individual One decision variable, Indicates the first The mean of each decision variable, The number of individuals in the population. For the number of decision variables, It represents population diversity.

8. A multi-objective scheduling method based on an improved strength Pareto algorithm as described in claim 1, characterized in that, Step e includes the following steps: e1: If the offspring's gene value is less than the lower bound, then the offspring's gene value is set to the lower bound; if the offspring's gene value is greater than the upper bound, then the offspring's gene value is set to the upper bound. The correction formula is as follows: In the formula, This indicates the corrected offspring genes; The upper bound of the decision variable, This serves as the lower bound for the decision variable. e2: The parent body after the crossover operation has an additional boundary correction, the correction formula of which is: In the formula, This represents the modified parental genes.

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