Power grid power-cut plan scheduling method based on backtracking search optimization algorithm of wide learning strategy

Abstract

The invention discloses a power grid power-cut plan scheduling method based on a backtracking search optimization algorithm of a wide learning strategy. A power-cut plan scheduling multi-objective optimization model considering preference is established. A traditional backtracking search algorithm is improved, and the solving efficiency and the global search capability are improved. Aiming at the problem of low convergence speed caused by lack of optimal solution guidance in a backtracking search algorithm, a mutation operation and a crossover mechanism are optimized, and the global exploration capability of understanding the space is enhanced; aiming at the defect that a backtracking search algorithm is easy to fall into local optimum, a guiding mechanism based on a wide learning strategy is provided, a candidate solution set is constructed by learning optimal solution information currently searched in a population and combining global exploration, and the search direction of the algorithm is effectively controlled, so that the convergence capability of the population to a global optimal solution is improved. And finally, through the optimized power outage scheduling scheme generated through multiple iterations, global optimization and balance of the power outage plan scheduling of the power grid can be realized, and the safety and economical efficiency of power grid operation are remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of power grid outage plan scheduling, and particularly relates to a power grid outage plan scheduling method based on a backtracking search optimization algorithm with an extensive learning strategy. Background Art

[0002] The outage plan scheduling service of the power grid is directly related to factors such as the power supply reliability, operation economy of the power grid, and the smooth progress of outage work. It is a frequent and key task in power grid operation. Reasonably and scientifically arranging the outage plan to reduce the number of outages of equipment, and thus reducing the impact of equipment outages on power grid operation, is the core goal of the outage plan scheduling service. Therefore, an intelligent and reasonable outage plan is of crucial importance.

[0003] In existing technical literature: The literature "Power Grid Outage Plan Scheduling Method Based on Elastic Network Algorithm" (Leqin Luo. Power Grid Outage Plan Scheduling Method Based on Elastic Network Algorithm [J]. Electrical Technology and Economy, 2023, (04): 238-239+242.) starts from the actual business needs of the power grid and establishes a scheduling model based on the elastic network algorithm. However, it is only an optimization of a single objective affecting scheduling and does not analyze the cost issues brought by outages. The literature "Research on Key Technologies and Preliminary Empirical Evidence of the Intelligent Scheduling System for Monthly Power Grid Outage Plans" (Weining Tang. Research on Key Technologies and Preliminary Empirical Evidence of the Intelligent Scheduling System for Monthly Power Grid Outage Plans [D]. South China University of Technology, 2022. DOI: 10.27151 / d.cnki.ghnlu.2022.004176.) constructs a power grid outage scheduling model considering multiple factors and gives a multi-objective optimization model. However, it does not design and improve the solution algorithm to achieve the balance of fast convergence and global optimality, which may limit the efficiency and effect of the model in practical applications. The backtracking search optimization algorithm is easier to improve and has a wider applicability. The literature "Research on the Optimization Configuration Method of Massive Resources in Multi-Photovoltaic-Storage Microgrid Systems" (Kun Chen, Hangtong Zhang, Zhengsheng Liu, etc. Research on the Optimization Configuration Method of Massive Resources in Multi-Photovoltaic-Storage Microgrid Systems [J]. Electronic Design Engineering, 2024, 32(17): 146-149+154. DOI: 10.14022 / j.issn1674-6236.2024.17.030.) applies the backtracking search algorithm to solve specific problems, but does not optimize the algorithm, and the algorithm still has the defect of being easily trapped in local optimal solutions. Summary of the Invention

[0004] To solve the above technical problems, the present invention discloses a power grid outage plan scheduling method based on a backtracking search optimization algorithm with an extensive learning strategy, which can achieve global optimization and balance of power grid outage plan scheduling, and significantly improve the safety and economy of power grid operation.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A power grid outage plan scheduling method based on a backtracking search optimization algorithm with an extensive learning strategy, comprising the following steps:

[0007] Step 1: Establish a multi-objective optimization model for outage plan scheduling considering preferences;

[0008] Step 2: Improve the mutation and crossover equations; integrate the extensive learning strategy to control the search direction by learning the optimal information currently searched by the population;

[0009] Step 3: Improve the backtracking search algorithm by integrating the improved mutation and crossover equations and the extensive learning strategy;

[0010] Step 4: Use the improved backtracking search algorithm to solve the multi-objective optimization model for outage plan scheduling considering preferences to obtain a better strategy.

[0011] In the said Step 1, the multi-objective optimization model for outage plan scheduling considering preferences specifically includes:

[0012] (1) Scheduled outage set:

[0013] Let the power grid topology of the outage plan scheduling object be G, where all devices are the execution objects of the outage plan, denoted by Z, and the length of the entire outage plan scheduling cycle is T. If the outage object z i ∈Z is in the outage state on the t-th day, then z i (t) = 1, otherwise z i (t) = 0, z i (t) represents the state of the i-th device on the t-th day;

[0014] Define a plan p i ={z i (t s ),...,z i (t e )}, z i (t s ) represents the state of the i-th device at the start date of the plan, z i (t e ) represents the state of the i-th device at the end date of the plan, p i is a plan for performing an outage on the outage object zi for several days, where: t s represents the start date of the plan, t e represents the end date of the plan, z i satisfies:

[0015] z i (t) = 1 t ∈ [t s ,te (1);

[0016] All plans p form a feasible plan scheme P = {p 1 , …, p n}, P = {p 1 , …, p n} is the set of feasible plans. Define Ω = {P 0 , P 1 , P 2 , … P i} as the possible solution domain, where P 0 represents the initial power outage demand set, P 1 represents the feasible power outage plan for the first device, and P 2 represents the feasible power outage plan for the second device.

[0017] (2) Definition of the objective function:

[0018] The objective function in the power grid outage plan scheduling problem is planned from three aspects: economic benefits, network risks, and practicality in actual implementation, corresponding to three objective functions: the time adjustment amount of the outage plan, the outage economic cost, and the outage quantity balance degree;

[0019] a. Time adjustment amount:

[0020] Adjusting the outage plan time often affects the implementation of other work in the power grid and brings trouble to the execution of the outage plan. Therefore, the time adjustment amount during the scheduling process should be minimized as much as possible. Let the outage plan reporting unit be a certain plan P i specified with a scheduled execution time of [t s , t e , and the execution time given by the plan scheme P is [t' s , t' e , and it satisfies:

[0021] t’ e - t’ s = t e - t s (2);

[0022] In the above formula, t’ e represents the end date of the plan execution time, and t’ s represents the start date of the plan execution time.

[0023] Then the time adjustment amount of this plan is:

[0024] Δt i = |t' e - t e | = |t’ s - ts | (3);

[0025] In the above formula, Δt i represents the planned time adjustment amount of the i-th device.

[0026] b. Economic cost of power outage:

[0027] The power grid outage will cause the withdrawal of the corresponding maintenance objects, resulting in corresponding economic losses. Minimizing this loss is also one of the important optimization indicators in the scheduling process. Let a certain plan P i The daily economic loss within the scheduling period T is {s 1 , s 2 ,... st}, where s 1 represents the economic loss on the first day of the plan, and s 2 represents the economic loss on the second day of the plan. Then the total economic cost within the execution time [t s , t e is expressed as:

[0028] S i = ∑s t t∈[t s , t e (4);

[0029] In the above formula, S i represents the total economic loss of device i, and s t represents the economic loss of each day.

[0030] c. Degree of balance of power outage amount:

[0031] The large-scale withdrawal of a large number of devices caused by the power outage plan will weaken the stability of the grid framework during grid operation. To avoid the risks to the grid topology caused by the withdrawal of maintenance objects, it is necessary to avoid a large number of concentrated power outage plans being executed suddenly within a certain period of the month, that is, the number of maintenance objects in each period within the same time period should be kept as balanced as possible. Let there be a total of n pending plans {p 1 , …, p n} in the network G within the period T. The variance of the daily power outage plan number is used to represent the degree of balance of the power outage amount within this time period, that is:

[0032]

[0033] In the above formula, represents the degree of balance of the power outage amount of the plan, represents the end date of plan i, represents the start date of plan i, and z i (t) represents the state of the i-th device on the t-th day, and n represents a total of n pending plans.

[0034] (3) Constraint conditions:

[0035] The constraints for the power outage plan scheduling in this invention are divided into four types: non-changeable plan constraint, mutual exclusion relationship constraint, combined execution constraint, and maximum daily workload constraint.

[0036] ①. Non-changeable plan constraint:

[0037] For the situations that need to ensure power supply for major activities, etc., according to the subjective will of the scheduling specialist, the time of this kind of power outage plan is directly determined. Suppose there is a non-changeable plan z 0 whose initial power outage time is Then this constraint condition can be expressed as:

[0038]

[0039] In the above formula, z 0 (t) represents the non-changeable plan, represents the start time of the non-changeable plan, represents the end time of the non-changeable plan.

[0040] ②. Mutual exclusion relationship constraint:

[0041] To avoid the formation of network system islands, specific plan combinations cannot be executed on the same day. pi represents the i-th plan, p j respectively represents the j-th plan. If p i , p j both belong to the plan set P, and the corresponding power outage objects are z i , z j , where z i is the state of the equipment corresponding to the i-th plan, and z j is the state of the equipment corresponding to the j-th plan. Then the constraint condition can be expressed as:

[0042] z i (t)·z j (t)=0, t∈T (7);

[0043] In the above formula, z i (t) represents the state of the i-th equipment on the t-th day, and z j (t) represents the state of the j-th equipment on the t-th day, and T represents a power outage cycle.

[0044] ③. Maximum daily workload constraint:

[0045] Suppose the daily manual workload required for a certain power outage object z∈G in the network G is w z , then the total daily workload in the network G is:

[0046] W=∑w z, z ∈ G (8);

[0047] In the above formula, W represents the total daily workload within the network G.

[0048] Given that the maximum daily workload of the network G is W max , then the maximum daily workload constraint can be expressed as:

[0049] W ≤ W max (9).

[0050] (4) Selection of the optimization solution considering subjective preferences:

[0051] Based on the above analysis of the power grid outage schedule problem, from the three aspects of economic benefits, network risks, and practical operability of implementation, the present invention combines three objective functions of outage time adjustment amount, outage economic cost, and outage quantity balance degree, comprehensively weighs the impact of the outage plan on the power grid operation and users, and finally establishes an optimization model that meets the actual needs and has the ability to balance multiple objectives, as follows:

[0052]

[0053] In the above formula, F(P) represents the overall objective function, which includes three objective functions of outage time adjustment amount, outage economic cost, and outage quantity balance degree, Δt i represents the outage time length, z k (t)·z l (t) = 1 means that equipment k and l must be out of service simultaneously; P 0 represents the initial outage demand set, P 1 represents the feasible outage plan for the first device, P 2 represents the feasible outage plan for the second device.

[0054] The result of solving the above multi-objective optimization model is a solution set Ω = {P 0 , P 1 , P 2 , … P i};

[0055] Among them: P 0 represents the initial outage demand set, P 1 represents the feasible outage plan for the first device, P 2 represents the feasible outage plan for the second device; under the condition of considering subjective preferences, the scheduling specialist needs to, according to the different values of various objective functions (f 1 (P), f 2 (P), f 3 (P)) of the scheduling result, where f 1(P) represents the objective function corresponding to the power outage time adjustment amount, f 2 (P) represents the economic cost of power outage, f 3 (P) represents the balance degree of the power outage amount. Considering the schedules of multiple parties such as the dispatching center, the operation and maintenance department, the construction party, and the design institute, the preference solution that best meets the needs in the current scenario is selected.

[0056] Therefore, a weight vector form such as (ω 1 , ω 2 , ω 3 ) can be adopted. ω 1 represents the weight of the power outage time adjustment amount, ω 2 represents the weight of the economic cost of power outage, ω 3 represents the weight of the balance degree of the power outage amount. Quantify the degree of importance inclination between different objective functions (f 1 (P), f 2 (P), f 3 (P)) for the scheduling specialist in different scenarios. Specifically:

[0057] For the optimization problem of the plan scheduling of the three objectives, assume that the importance degrees corresponding to the respective objective functions assumed by the specialist in the scheduling process are (ω 1 , ω 2 , ω 3 ). Then the vector formed by the origin (0, 0, 0) and the point (ω 1 , ω 2 , ω 3 ) is the preference reference direction. The objective function value corresponding to a certain plan set P is calculated as the point Then the preference evaluation value of the plan set P is:

[0058]

[0059] In the above formula, τ(P) represents the preference evaluation of the plan set P, and the smaller its value, the better the preference evaluation.

[0060] According to the above formula, the most suitable preference solution is selected for subsequent method adjustment, and the top several preference solutions are selected from the solution set as alternative solutions for the scheduling specialist to compare and select.

[0061] This method can replace the process of manual comparison and selection from a large number of optimal solution sets, and at the same time leave a certain space for the scheduling specialist to select other alternative plan sets.

[0062] In step 2, it specifically includes:

[0063] (1) Extensive learning strategy:

[0064] The present invention proposes a new mutation strategy. By selecting superior individuals from p% of the population individuals selected from the current population as the control vector for controlling the search direction of the algorithm, the convergence speed of the algorithm is effectively improved.

[0065] M i = Pop i + F × (P gr-best - Pop i + Pop r - Pop g )(11);

[0066] In the formula, M i represents the mutation equation of the i-th population, determining the priority of the next exploration. Pop i represents population i, F represents the mutation scale coefficient, Pop r represents population r, Pop g represents population g, P gr-best is the selected superior individual. i, r, g ∈ [1, 2, 3,..., N] and they are not equal to each other. N represents the total scale of the population.

[0067] The present invention improves the above mutation strategy by fully learning the optimal information currently searched by the population individuals, and proposes an optimal learning mutation equation. At the same time, in order to prevent the algorithm from falling into local optimum, the present invention introduces an evolutionary strategy based on DE:

[0068] M i = P best + F × (P gr-best - Pop i + OPop r - Pop g )(12);

[0069] M i = Pop i + F × (Pop m - Pop n + Pop r - Pop g )(13);

[0070] In the formula, P best is the optimal position searched by the current population; OPop r represents the historical population of population r, Pop m represents population m, Pop n represents population n, where i, m, n, r, g ∈ [1, 2, 3,..., N] and they are not equal to each other.

[0071] By randomly selecting the above two formulas, the exploration and exploitation capabilities of the algorithm are balanced.

[0072] Considering that after the population completes the optimal learning and evolution operation, the population needs to further search the search space in order to quickly search for the global optimal solution, the present invention proposes an optimal learning search equation:

[0073]

[0074] In the formula, V i,j Optimal learning search equation, and μ i,j are random numbers in [-1, 1] and [0, 1.5] respectively; Pop best,j is the j-th dimension of the current optimal solution vector; Pop gr-best is the better population individual selected as the direction guiding vector for further search after randomly selecting p% from the updated Pop population; OPop i,j represents the j-th dimension of the historical record population i; Pop k,j represents the j-th dimension of the individual randomly selected from the updated new population k; Pop i,j represents the j-th dimension of population i.

[0075] (2) Mutation:

[0076] The mutation equation of the backtracking search algorithm (BSA) is as follows:

[0077] M = pop + F × (oldpop - pop)(15);

[0078] Where: M is the mutation equation, which determines the priority of the next exploration; pop represents the current population; oldpop - pop represents the difference from the current solution to the historical solution.

[0079] F is the mutation scale coefficient, which is used to control the amplitude of the search direction matrix (oldpop - pop); F = 3 × randn, randn ~ N(0, 1), so randn is a random number obeying the standard normal distribution. And because the distribution range of this mutation scale coefficient is too wide, it is easy to generate larger or smaller extreme values, which is not conducive to the rapid convergence of the population. For this reason, the present invention proposes a mutation scale coefficient based on the t-distribution. Its expression is:

[0080]

[0081] where: trnd(df) is a random number following a t-distribution. The t-distribution has only one parameter, namely the degrees of freedom df. Its density function has a thicker tail compared to the density function of the standard normal distribution, and its shape approaches the normal distribution infinitely as df increases. Therefore, compared to the normal distribution, the shape of the t-distribution can be conveniently controlled through the degrees of freedom df. And due to its thick-tail characteristic, on the basis that the overall distribution trend is relatively concentrated, extreme values at the boundary can also be obtained with a certain probability, thus preventing the algorithm from converging too much and falling into a local optimum.

[0082] (3) Crossover:

[0083] The backtracking search algorithm (BSA) has stronger global search ability due to its unique crossover equation. However, since it only controls the search direction under the guidance of the historical population, the convergence speed of this algorithm is slow and its local development ability is not strong enough. The present invention introduces the guidance of the optimal individual and proposes a new crossover equation as follows:

[0084]

[0085] Gpop = rempat((normrnd(1,1).×Gminimizer),N)(18);

[0086] where: T i,j is the crossover equation; M i,j represents the historical optimal solution in the mutation step; pop i,j represents the j-th dimension of the current population i; map i,j is the mixing ratio parameter, which is an N×D binary integer matrix; the initial value is 1, normrnd(1,1) normalizes the data into a normal distribution variable with a mean of 1 and a standard deviation of 1, Gminimizer represents the minimized objective function value in the population, N represents the population size, C is a random number following a standard normal distribution; Gpop is an N×D matrix, and the matrix elements are composed of the normal distribution of the optimal individual in the current population. In this way, the crossover and mutation equations of the backtracking search algorithm (BSA) tend to be complete, and not only is there the guidance of the historical population, but also the current optimal individual controls the search direction.

[0087] In step 3, the backtracking search algorithm (BSA) is an evolutionary algorithm based on swarm intelligence. Its algorithm structure is similar to that of other evolutionary algorithms, mainly including five steps, namely population initialization, selection I, population mutation, population crossover, and selection II;

[0088] 1) Population initialization:

[0089] Since the performance of BSA is little affected by the initial population value, a method of randomly generating the population is adopted for initialization in the BSA algorithm. Its search direction is affected by the historical population, and the historical population is set to implement the memory function of the algorithm for the population position:

[0090] pop i,j ~U(low j , up j ) (19);

[0091] oldpop i,j ~U(low j , up j ) (20);

[0092] where: i ∈ {1, 2, …, N}; j ∈ {1, 2, …, D}; N is the number of populations; D is the dimension of the population; low and up are respectively the lower and upper bounds of the search space; U is the random uniform distribution function. pop i,j represents the j-th dimension of population i; oldpop i,j represents the j-th dimension of the individual in the historical record population; low j represents the lower bound of population i in the search space; up j represents the upper bound of population i in the search space; Equation (19) means that the j-th individual of population i follows the uniform distribution in the interval (low j , up j ).

[0093] 2) Selection I:

[0094] BSA controls the search direction through the historical population. The purpose of Selection I is to select a new historical population at the beginning of each iteration. The selection strategy is as follows:

[0095] oldpop = pop, a < b (21);

[0096] where: pop is the initial population; oldpop is the historical population; a, b are random numbers uniformly distributed on (0, 1); after determining oldpop, rearrange the positions of the populations in oldpop, and the formula is as follows:

[0097] oldpop = randperm(oldpop) (21);

[0098] where: randperm is the rearrangement function.

[0099] 3) Mutation:

[0100] The mutation equations of the improved BSA are shown in Equations (12) and (13):

[0101] The optimal learning search equation proposed by the present invention improves the global search ability during mutation, as shown in Equation (14):

[0102] Improve the mutation scale coefficient. Its expression is as shown in Equation (16);

[0103] 4) Crossover:

[0104] A new crossover strategy proposed by BSA controls the number of population particle crossovers by setting a mixing ratio parameter.

[0105] The specific formula is as shown in Equation (22) below.

[0106]

[0107] Among them: map i,j is an N×D binary integer matrix; the initial assignment is 1. The specific formula is as shown in Equation (23) below.

[0108]

[0109] Among them: randi(D) is an integer randomly taken from [0, D]; rand, a, and b are random numbers in [0, 1]; mixrate is the crossover probability; mixrate·rand·D is the crossover length; u = randperm(D) is an integer vector after reordering [1, 2,..., D]. BSA effectively controls the number of mutated elements in the new population T by calling these two equally probable map generation methods.

[0110] Introduce the improved mutation equations in Step 2, as shown in Equations (17) and (18);

[0111] After the new population T is determined, perform boundary detection on the elements in the population. If it exceeds the search range, generate a new individual again.

[0112] 5) Selection II:

[0113] Select individuals with better fitness values in the new population and the initial population through the greedy rule. Select and generate a new population T during crossover i , compare the fitness of the new population with the initial population pop i , record the current global optimal solution and the corresponding solution vector, and update the initial population at the same time. The update equation is as follows:[[]]

[0114]

[0115] Among them: T i represents the crossover equation i, and fitness(T i ) represents the new solution T iThe fitness, fitness(pop i ) represents pop i 's fitness.

[0116] Repeat the above process until the termination condition is met, and finally output the optimal solution. The optimal solution is in the population with higher fitness. As shown in Equation (24), after the crossover and mutation operation steps, compare the fitness and output the population with the highest fitness. Step 4 includes the following steps:

[0117] S4.1: Population initialization: Determine the population size N and dimension D, including the number of variables for the power outage schedule, including power outage areas, power outage time periods, etc.;

[0118] S4.2: Randomly generate the initial population, and each variable is randomly generated, where each individual represents a power outage plan schedule;

[0119] S4.3: Record the historical population:

[0120] S4.4: Selection I: Use the historical population to control the search direction and improve the global exploration ability;

[0121] S4.5: Mutation: Randomly select the improved mutation equations (17) and (18), and during the mutation evolution process, ensure the adjusted solution constraint conditions;

[0122] S4.6: Crossover: Guide the population towards high-quality solutions through crossover. In the power outage plan schedule, the crossover operation will mix the information of different plan schemes to generate new feasible schemes;

[0123] S4.7: Selection II: Evaluate the current population, compare the fitness values in Equation (24), and select the better one to enter the next generation;

[0124] S4.8: Repeat the steps of selection in S4.4, mutation in S4.5, crossover in S4.6, and selection II in S4.7, and gradually iterate the population solution set until the optimal solution, that is, the power outage schedule, is output.

[0125] A power grid outage plan scheduling method based on a broad learning strategy backtracking search optimization algorithm of the present invention has the following technical effects:

[0126] 1) Step 1 of the present invention establishes a multi-objective optimization model for power outage plan scheduling considering preferences. The multi-objective collaborative optimization avoids the sub-optimal solutions caused by single-objective optimization; and through weight allocation, facing different preferences, comprehensively consider the scheduling of multiple aspects such as the dispatching center, operation and maintenance department, construction party, and design institute, and select the preference solution that best meets the needs in the current scenario.

[0127] 2) Step 2 of the present invention improves the traditional crossover and mutation equation and integrates the wide learning strategy. By improving the traditional crossover and mutation equation, the convergence speed of the algorithm is accelerated, and the global search ability of the algorithm is improved; while the integration of the wide learning strategy realizes the reduction of randomness dependence by controlling the search direction of the population.

[0128] 3) Step 3 of the present invention integrates the improvement strategy into the backtracking search algorithm, improving the adaptability of the algorithm and optimizing the iteration direction and solution space of the backtracking search algorithm.

[0129] 4) Step 4 of the present invention uses the improved algorithm to solve the model. Compared with the steps before the optimization algorithm, it can quickly screen high-quality solutions, with a faster convergence speed and fewer steps, enabling the power outage plan to have higher adaptability and select a more efficient and stable solution according to different preferences. BRIEF DESCRIPTION OF THE DRAWINGS

[0130] The present invention will be further described below in conjunction with the drawings and examples;

[0131] Figure 1 It is the flowchart of the method of the present invention.

[0132] Figure 2 It is the comparison chart of the calculation efficiency of the improved backtracking search optimization algorithm, backtracking search algorithm and genetic algorithm of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0133] The present invention will be further described in detail below in conjunction with the embodiments and the drawings, but the embodiments of the present invention are not limited thereto.

[0134] Figure 1 It is the flowchart of the power grid outage plan scheduling method of a backtracking search optimization algorithm based on the wide learning strategy proposed by the present invention. First, a multi-objective optimization model for power grid outage plan scheduling considering preferences is established, including three objective functions: the time adjustment amount of the power outage plan, the outage economic cost, and the workload balance degree. Secondly, to efficiently solve the above optimization model, the present invention improves the traditional backtracking search algorithm and enhances its solution efficiency and global search ability. Aiming at the problem of slow convergence speed of the backtracking search algorithm due to the lack of optimal solution guidance, the present invention optimizes the mutation operation and crossover mechanism, enhancing the global exploration ability of the solution space; aiming at the disadvantage that the backtracking search algorithm is prone to falling into local optimum, the present invention proposes a guidance mechanism based on the wide learning strategy, which effectively controls the search direction of the algorithm by learning the optimal solution information currently searched in the population and constructing a candidate solution set in combination with global exploration, thereby enhancing the convergence ability of the population to the global optimum. Finally, the optimized power outage scheduling plan generated through multiple iterations can achieve the global optimization and balance of the power grid outage plan scheduling, significantly improving the safety and economy of the power grid operation.

[0135] Figure 2 Comparison of the computational efficiency of the improved backtracking search optimization algorithm, backtracking search algorithm, and genetic algorithm of the present invention. The horizontal axis represents the number of algorithm iterations, and the vertical axis represents the outage economic cost (unit: 10,000 yuan). From Figure 2 it can be seen that the improved BSA algorithm is superior to the traditional BSA and genetic algorithms in terms of optimization speed and final result:

[0136] (1) Optimization speed:

[0137] The improved BSA rapidly reduced the outage cost in the first 50 iterations, showing strong early convergence ability. Compared with the BSA and genetic algorithms, it significantly accelerated the convergence speed.

[0138] (2) Final result: The improved BSA finally optimized the outage cost to approximately 1.3 million yuan, which has a better optimization effect than the traditional BSA (about 1.33 million yuan) and genetic algorithm (about 1.35 million yuan).

[0139] (3) Convergence: After 200 iterations, the improved BSA has basically converged and remained stable, indicating its good global convergence ability and stability. This shows that the improved BSA significantly improves the performance of the algorithm in the power grid outage plan scheduling problem by introducing more efficient mutation and crossover strategies and a mechanism for optimizing the search direction. It can not only quickly find better solutions but also further reduce the outage cost, thus better meeting the actual needs of power grid operation.

[0140] Table 1 Comparison of the indexes of the optimization solution results of each algorithm

[0141]

[0142] Table 1 is a comparison table of the indicators of the optimized solution results of each algorithm, including the results analysis of the initial plan, improved BSA, traditional BSA, and genetic algorithm. The initial plan, as an unoptimized benchmark scheme, has problems such as a high daily plan variance (1.352) and a high power outage cost (1.485 million yuan), indicating great potential for optimization. In contrast, the improved BSA performs best in all indicators. Its daily plan variance is reduced to 0.823, the power outage cost is reduced to 1.304 million yuan, and the number of days of plan disturbance is only 15 days, with fewer optimization adjustments and greater feasibility for actual implementation. At the same time, the improved BSA shows a faster optimization speed and higher efficiency with an average iteration number of 52.3 times and a total time of 5.18 seconds. The performance of the traditional BSA is inferior to that of the improved BSA. Its daily plan variance is 0.841, the power outage cost is 1.309 million yuan, and the number of days of plan disturbance is 18 days. The optimization result is close to that of the improved BSA, but the efficiency is low, with an average iteration number of 81.9 times and a total time of 8.01 seconds. The optimization ability of the genetic algorithm is the weakest. Although the daily plan variance and power outage cost have improved, they are 0.834 and 1.318 million yuan respectively, and the optimization efficiency is low, with an average iteration number as high as 102.7 times and a total time of 99.89 seconds.

[0143] Generally speaking, through efficient optimization strategies and fast convergence ability, the improved BSA significantly reduces the power outage cost, improves the plan balance, and has fewer days of plan disturbance, showing excellent comprehensive performance and being an ideal choice for the optimization of the power grid outage plan schedule.

Claims

1. A power grid outage scheduling method based on a backtracking search optimization algorithm with extensive learning strategy, characterized by The following steps are involved: Step 1: Establish a multi-objective optimization model for outage scheduling considering preferences; Step 2: Improve the mutation and crossover equations; integrate the extensive learning strategy to control the search direction by learning the optimal information currently searched by the population; Step 3: Improve the backtracking search algorithm by integrating the improved mutation and crossover equations and the extensive learning strategy; Step 4: Use the improved backtracking search algorithm to solve the multi-objective optimization model of power outage scheduling considering preferences to obtain a better strategy.

2. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 1 is characterized in that: In step 1, the multi-objective optimization model for scheduling power outage plans considering preferences includes: a planned power outage set, specifically as follows: Assume that the grid topology of the outage scheduling object is G, where all devices are the execution objects of the outage plan, represented by Z, and the length of the entire outage scheduling cycle is T; if the outage object z i ∈Z is in a power outage state on day t, then z i (t)=1, otherwise z i (t) = 0, z i (t) represents the status of the i-th device on day t; Define a plan p i ={z i (t s ),...,z i (t e )},z i (t s ) represents the status of the i-th equipment on the planned start date, z i (t e ) represents the status of the i-th device on the planned termination date, p i For the power outage object z i Implement a power outage plan for several days, where: s represents the planned start date, t e Indicates the planned termination date, z i satisfy: z i (t)=1 t∈[t s ,t e ] (1); All plans p form a feasible plan P = {p1,…,p n }, P={p1,…,p n } is a set of feasible plans, and Ω={P0,P1,P2,…P i } is the possible solution domain, where P0 represents the initial power outage demand set, P1 represents the feasible power outage plan for the first device, and P2 represents the feasible power outage plan for the second device.

3. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 2 is characterized by: The objective function of the power outage scheduling problem is planned from the three aspects of economic benefits, network risks and practicality in actual implementation, corresponding to the three types of objective functions: time adjustment of power outage plan, economic cost of power outage and balance of power outage. a. Time adjustment: Assume that the unit reporting the power outage plan is a certain plan P i The specified scheduled execution time is [t s ,t e ], the execution time given by plan P is [t' s ,t' e ], and satisfy: t' e -t' s =t e -t s (2); In the above formula, t' e Indicates the end date of the planned execution time, t' s Indicates the start date of the planned execution time; The time adjustment of the plan is: Δt i =|t' e -t e |=|t' s -t s | (3); In the above formula, Δt i represents the time adjustment amount of the i-th equipment plan; b. Economic cost of power outage: Suppose a plan P i The daily economic loss in the scheduling period T is {s1, s2, ...st}, s1 represents the economic loss on the first day of the plan, and s2 represents the economic loss on the second day of the plan. s ,t e The total economic cost within ] is expressed as: S i =∑s t t∈[t s ,t e ] (4); In the above formula, S i represents the total economic loss of equipment i, s t Indicates the economic loss per day; c. Power outage balance: Suppose that all pending plans {p1,…,p n There are n items in total, and the variance of the daily power outage plan number is used to represent the balance of power outages in this time period, that is: In the above formula, Indicates the balance of planned outages, represents the end date of plan i, represents the start date of plan i, z i (t) represents the status of the i-th device on the t-th day, and n represents the n pending plans.

4. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 2 is characterized in that: The constraints of power outage scheduling are divided into four types: unchangeable plan constraints, mutually exclusive relationship constraints, combined execution constraints, and single-day maximum workload constraints; ①. Unchangeable plan constraints: Suppose the initial power outage time of a certain unchangeable plan z0 is Then the constraint can be expressed as: In the above formula, z0(t) represents the irreversible plan. Indicates the start time of the plan that cannot be changed. Indicates the end time of the irreversible plan; ②. Mutually exclusive constraints: To avoid the formation of isolated network systems, specific plan combinations cannot be executed on the same day; i represents the i-th plan, p j Represents the jth plan respectively. If p i 、p j Belong to the same plan set P, where the corresponding power outage object is z i 、z j , where z i is the state of the equipment corresponding to the i-th plan, z j is the state of the equipment corresponding to the jth plan, then the constraint can be expressed as: z i (t)·z j (t)=0,t∈T (7); In the above formula, z i (t) represents the status of the i-th device on the t-th day, z j (t) represents the status of the jth device on the tth day, and T represents a power outage cycle; ③. Maximum daily workload constraints: Suppose the daily manual workload required by a planned power outage object z∈G in network G is w z , then the total workload per day in network G is: W=∑w z ,z∈G (8); In the above formula, W represents the total workload in a single day in the network G; Given that the maximum daily workload of network G is W max , then the maximum workload constraint for a single day can be expressed as: W≤W max (9)。 5. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 4 is characterized in that: Combining the three objective functions of outage time adjustment, outage economic cost, and outage quantity balance, the impact of the outage plan on power grid operation and users is comprehensively weighed, and finally an optimization model with multi-objective trade-off capability is established, as follows: In the above formula, F(P) represents the overall objective function, which includes three types of objective functions: power outage time adjustment, power outage economic cost, and power outage balance. i Indicates the length of power outage, z k (t)·z l (t)=1 indicates that devices k and l must be powered off at the same time; P0 indicates the initial power outage requirement set, P1 indicates the feasible power outage plan for the first device, and P2 indicates the feasible power outage plan for the second device.

6. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 5 is characterized by: The result of solving the multi-objective optimization model is a set of solutions containing many power outage plan sets P. Ω={P0,P1,P2,…P i }; Where: P0 represents the initial power outage demand set, P1 represents the feasible power outage plan for the first device, and P2 represents the feasible power outage plan for the second device; Under the condition of considering subjective preferences, according to the different values ​​of various objective functions (f1(P), f2(P), f3(P)) of the scheduling results, where f1(P) represents the objective function corresponding to the power outage time adjustment, f2(P) represents the economic cost of power outage, and f3(P) represents the balance of power outage, comprehensively consider multiple aspects of scheduling and select the preference solution that best meets the needs in the current scenario; The weight vector form of (ω1,ω2,ω3) is adopted, where ω1 represents the weight of the power outage time adjustment, ω2 represents the weight of the power outage economic cost, and ω3 represents the weight of the power outage balance; the degree of inclination of the importance of different objective functions (f1(P), f2(P), f3(P)) in different scenarios is quantified.

7. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 6 is characterized by: In the three-objective scheduling optimization problem, let the importance of each objective function assumed in the scheduling process be (ω1, ω2, ω3), then the vector formed by the origin (0, 0, 0) and the point (ω1, ω2, ω3) is the preferred reference direction, and the objective function value corresponding to a certain plan set P is calculated as point Then the preference evaluation value of plan set P is: In the above formula, τ(P) represents the preference evaluation of the plan set P. The smaller its value, the better the preference evaluation; According to the above calculation, the most suitable preference solution is selected for subsequent method adjustment, and the first several preference solutions are selected from the solution set as alternative solutions for comparison and selection by the arrangement specialist.

8. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 1 is characterized by: The step 2 specifically includes: (1) Extensive learning strategies: By selecting the better individuals from the p% individuals in the current population as the control vector of the search direction of the control algorithm; M i =Pop i +F×(P gr-best -Pop i +Pop r -Pop g ) (11); Where M i Represents the mutation equation of the i-th population, which determines the priority of the next exploration. Pop i represents population i, F represents the coefficient of variation, Pop r represents the population r, Pop g represents the population g, P gr-best are the selected better individuals, i, r, g∈[1,2,3,…,N] and they are not equal to each other, N represents the total size of the population; By fully learning the optimal information currently searched by individuals in the population, the above mutation strategy is improved, and the optimal learning mutation equation is proposed. At the same time, in order to avoid the algorithm falling into the local optimum, the evolutionary strategy based on DE is introduced: M i =P best +F×(P gr-best -Pop i +OPop r -Pop g ) (12); M i =Pop i +F×(Pop m -Pop n +Pop r -Pop g ) (13); Where P best The optimal position searched for the current population; OPop r represents the historical population of population r, Pop m The population m, Pop n represents a population n, where i, m, n, r, g∈[1,2,3,…,N] and they are not equal to each other; By randomly selecting the above two formulas, the exploration and exploitation capabilities of the algorithm are balanced; Considering that after the population completes the optimal learning evolution operation, it needs to further search the search space in order to quickly search for the global optimal solution, the optimal learning search equation is proposed: Where V i,j The optimal learning search equation, and μ i,j Random numbers in [-1,1] and [0,1.5] respectively; Pop best,j is the jth dimension of the current optimal solution vector; Pop gr-best After randomly selecting p% from the updated Pop population, the better population individuals are selected as the direction guide vector for further search; OPop i,j represents the jth dimension of historical record population i; Pop k,j Pop represents the jth dimension of an individual randomly selected from the updated new population k; i,j represents the jth dimension of population i; (2) Variation: The mutation equation of the backtracking search algorithm is as follows: M=pop+F×(oldpop-pop)(15); Where: M is the variation equation, which determines the priority of the next exploration; pop represents the current population; oldpop-pop represents the difference from the current solution to the historical solution; F is the variation scale coefficient, which is used to control the amplitude of the search direction matrix (oldpop-pop); F = 3 × randn, randn ~ N (0, 1), so randn is a random number that obeys the standard normal distribution; The expression of the coefficient of variation scale based on t distribution is: Where: trnd(df) is a random number that follows a t-distribution, which has only one parameter, the degree of freedom df; (3) Crossover: By introducing the optimal individual bootstrapping, a new crossover equation is proposed as follows: Gpop=rempat((normrnd(1,1).×Gminimizer),N)(18); Where: T i,j is the crossover equation; M i,j Indicates the historical optimal solution in the mutation step; pop i,j Represents the jth dimension of the current population i; map i,j is the mixing ratio parameter, which is an N×D binary integer matrix; the initial value is 1, normrnd(1,1) standardizes the data into a normally distributed variable with a mean of 1 and a standard deviation of 1, Gminimizer represents the minimized objective function value in the population, and N represents the population size; Gpop is an N×D matrix, and the matrix elements are composed of the normal distribution of the optimal individuals in the current population.

9. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 8 is characterized by: In step 3, the backtracking search algorithm includes five steps, namely population initialization, selection I, population mutation, population crossover, and selection II; 1) Population initialization: In the BSA algorithm, the method of randomly generating a population is used for initialization; and its search direction is affected by the historical population. The historical population is set to realize the algorithm's memory function of the population position: pop i,j ~U(low j ,up j )(19); oldpop i,j ~U(low j ,up j )(20); Where: i∈{1,2,…,N}; j∈{1,2,…,D}; N is the number of populations; D is the population dimension; pop i,j represents the jth dimension of population i; oldpop i,j represents the jth dimension of individuals in the historical record population; low j represents the lower bound of the search space population i; up j represents the upper bound of the search space population i; Formula (19) represents the j-th individual of population i obeys the interval (low j ,up j ) is uniformly distributed; 2) Option I: BSA controls the search direction through the historical population. The purpose of selection I is to select a new historical population at the beginning of each iteration. The selection strategy is as follows: oldpop=pop,a, where: pop is the initial population; oldpop is the historical population; a and b are random numbers that obey uniform distribution on (0, 1); after determining oldpop, the positions of the population in oldpop are rearranged, and the formula is as follows: oldpop=randperm(oldpop) (21); Among them: randperm is the reordering function; 3) Mutation: The variation equations of the improved BSA are shown in equations (12) and (13): The optimal learning search equation improves the global search capability during mutation, as shown in formula (14): Improved coefficient of variation scale; its expression is shown in formula (16); 4) Crossover: The number of crossovers of population particles is controlled by setting the mixing ratio parameter. The specific formula is shown in formula (22); ​ Where: map i,j is an N×D binary integer matrix; the initial value is 1; the specific formula is shown in formula (23); Where: randi(D) is an integer randomly selected from [0,D]; rand, a, b are random numbers in [0,1]; mixrate is the crossover probability; mixrate·rand·D is the crossover length; u=randperm(D) is the integer vector after [1, 2, ..., D] is reordered; Introduce the improved variation equation in step 2, as shown in equations (17) and (18); After the new population T is determined, the elements in the population are checked for boundaries. If they are beyond the search range, new individuals are generated. 5) Select II: The greedy rule is used to select individuals with better fitness values ​​from the new population and the initial population, and a new population, T, is generated in the crossover. i , the new population is combined with the initial population pop i Compare the fitness, record the current global optimal solution and the corresponding solution vector, and update the initial population; the update equation is as follows: Where: T i represents the crossover equation i, fitness(T i ) represents the new solution T i Fitness(pop i ) means pop i Adaptability; Repeat the above process until the termination condition is met, and finally output the optimal solution.

10. The method for scheduling power outages based on the backtracking search optimization algorithm of the extensive learning strategy according to claim 8 is characterized in that: The step 4 includes the following steps: S4.1: Population initialization: Determine the population size N and dimension D, including the number of outage scheduling variables, including outage areas and outage periods; S4.2: Randomly generate the initial population, each variable is randomly generated, and each individual represents a power outage scheduling plan; S4.3: Record historical populations: S4.4: Option I: Use historical populations to control search direction and improve global exploration capabilities; S4.5: Mutation: Randomly select the improved mutation equations (17) and (18), and ensure the adjusted solution constraints during the mutation evolution process; S4.6: Crossover: Crossover is used to guide the population towards a high-quality solution. In the power outage scheduling, the crossover operation mixes the information of different plans to generate a new feasible plan. S4.7: Selection II: Evaluate the current population, compare fitness values, and select the better ones to enter the next generation; S4.8: Repeat the steps of selection in S4.4, mutation in S4.5, crossover in S4.6, and selection II in S4.7, and gradually iterate the population solution set until the optimal solution, that is, the power outage scheduling plan, is output.

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