A method for site selection of mobile transformers based on NSGA-2 algorithm

Abstract

The present invention discloses a method for site selection of mobile transformers based on NSGA-2 algorithm, and relates to the technical field of transformers in agricultural irrigation areas. The method comprises the following steps: constructing a site selection model of mobile transformers with the goal of minimizing comprehensive operation costs; establishing multi-constraint rules based on the site selection model of mobile transformers, wherein the multi-constraint rules include node voltage constraints, branch current constraints, network structure topology constraints, and flow constraints; linearizing the flow constraints, and optimizing the site selection model of mobile transformers using NSGA-2 algorithm and tournament selection method, solving the optimized model, and outputting a site selection path strategy for mobile transformers. The present invention comprehensively considers social benefit costs, network loss costs, mobile transformer production costs, and travel costs, and constructs a site selection model of mobile transformers with the goal of minimizing comprehensive operation costs, which can optimize the economic benefits of distribution network operation.

Description

Technical Field

[0001] The present invention relates to the technical field of transformers in agricultural irrigation areas, and in particular to a method for selecting a mobile transformer site based on an NSGA-2 algorithm. Background Art

[0002] With the vigorous development of the agricultural economy and the strong support of a series of positive measures, the cultivated area is constantly expanding. In order to meet the growing demand for agricultural production, agricultural irrigation plays a vital role. Taking a certain northeast region as an example, in the near future, it is expected that the area of ​​spring irrigation in the region will reach nearly four million mu. The geographical distribution of irrigation is diversified, and some key areas have attracted much attention because they are located in important irrigation areas; the climate characteristics of these areas are dry in spring and autumn, with relatively less precipitation, while summer is the period with the most concentrated precipitation. Therefore, the irrigation load is divided into three main stages in a year: spring, summer and autumn. Spring irrigation is generally arranged from late spring to early summer, and summer and autumn irrigation runs throughout the summer to autumn. In addition, the size of the irrigation load fluctuates greatly due to the weather.

[0003] However, the long irrigation activities throughout the year have brought certain challenges to the relevant power equipment in the distribution network. In particular, in the process of agricultural irrigation, transformers often bear the task of transmitting electrical energy to water pumps and play a vital role. Especially during the summer irrigation period, due to the large agricultural irrigation load, the centralized power supply of water pumps will cause agricultural irrigation transformers to be overloaded, resulting in transformer overheating, thereby shortening its service life; at the same time, considering that the irrigation cycle of important irrigation areas is long, long-term heavy overload requires frequent inspection and maintenance of transformers to ensure their normal operation and long-term stability, which greatly increases the maintenance cost. In order to effectively meet this challenge, it is particularly urgent to introduce modular and movable transformer equipment. These mobile transformers usually have a wheeled base or a draggable structure, which is not only easy to move and deploy between different places, but also easy to transport and assemble due to its modular design. It can well cope with the complex terrain of rural areas and plays a vital role in ensuring normal and orderly agricultural production.

[0004] Faced with various emergency situations such as agricultural irrigation, emergency power supply, temporary power supply and disaster recovery, traditional distribution networks are unable to meet the diverse power needs. Upgrading and transformation is not only costly but also inefficient. Mobile transformers, with their flexibility and rapid deployment capabilities, can significantly improve the efficiency of power restoration when responding to major destructive events such as natural disasters, and are gradually becoming a focus of attention at home and abroad.

[0005] Currently, no effective solution has been proposed for the problems in the related technologies. Summary of the invention

[0006] In view of the problems in the related technology, the present invention proposes a mobile transformer site selection method based on the NSGA-2 algorithm, which has the characteristics of effective utilization of the rapid deployment and flexibility of mobile transformers, provides a mobile transformer site selection-path strategy, and optimizes the economic benefits of distribution network operation, thereby solving the problem in the prior art that the traditional distribution network is unable to meet the diversified power demands in various emergency situations such as agricultural irrigation, emergency power supply, temporary power supply and disaster recovery, and the upgrading and transformation is not only costly but also inefficient.

[0007] To this end, the specific technical solution adopted by the present invention is as follows:

[0008] A mobile transformer site selection method based on NSGA-2 algorithm, the mobile transformer site selection method based on NSGA-2 algorithm comprises the following steps:

[0009] S1. Construct a mobile transformer site selection model with the goal of minimizing the comprehensive operating cost;

[0010] S2. Based on the mobile transformer site selection model, a multi-constraint rule is established, wherein the multi-constraint rule includes node voltage constraint, branch current constraint, network structure topology constraint and power flow constraint;

[0011] S3. Linearize the power flow constraints, and use the NSGA-2 algorithm and the tournament selection method to optimize the mobile transformer site selection model, solve the optimized model, and output the mobile transformer site selection-path strategy. The mobile transformer site selection-path strategy includes the location and moving path of the mobile transformer in different time periods.

[0012] Furthermore, with the goal of minimizing the comprehensive operating cost, the construction of the mobile transformer site selection model includes the following steps:

[0013] S11, constructing a transformer loss model, solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and calculating the network loss cost based on the difference loss;

[0014] S12, constructing a distance cost model, solving the distance cost model to obtain the distance cost of the mobile transformer, and combining the network loss cost with the production cost of the mobile transformer to calculate the economic benefit cost;

[0015] S13. Calculate the comprehensive operating cost according to the social benefit cost and the economic benefit cost, construct the objective function based on the comprehensive operating cost, and establish the mobile transformer site selection model.

[0016] Furthermore, a transformer loss model is constructed, and solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and the network loss cost is calculated based on the difference loss, including the following steps:

[0017] S111. Calculating the load factor of the mobile transformer based on the load borne by the mobile transformer and the rated capacity;

[0018] S112, calculating the load factor of the rear area transformer after the mobile transformer changes position, and analyzing the loss difference before and after the mobile transformer changes position in combination with the load factor of the mobile transformer;

[0019] S113. Calculate the network loss cost based on the analysis result of the loss difference and in combination with the distance loss.

[0020] Furthermore, the expression for calculating the load factor of the mobile transformer is:

[0021] ;

[0022] The expression for calculating the load factor of the rear area transformer after the mobile transformer changes position is:

[0023] ;

[0024] The expression for analyzing the loss difference before and after the mobile transformer changes position is:

[0025] ;

[0026] ;

[0027] In the formula, x represents the number of mobile transformers connected to the Y station area, β x represents the load factor of the mobile transformer, Indicates the load borne by the mobile transformer, Indicates the rated capacity of the mobile transformer. It indicates the load factor after adding x mobile transformers to the Y station area. Indicates the load borne by the transformer in the substation area. Indicates the rated capacity of the transformer in the Y station area, p 0,Y represents the no-load active power loss of the transformer in the Y station area, p k It represents the rated load loss of the rear transformer after adding x mobile transformers. Indicates the no-load loss of the mobile transformer, Indicates the rated load loss of the mobile transformer, and They represent the transformer losses at time t and time t+1 respectively, and f Y,y,x Indicates the loss difference before and after the mobile transformer changes position.

[0028] Furthermore, based on the analysis results of the loss difference and combined with the path loss, the network loss cost is calculated, including the following steps:

[0029] S1131, analyzing the total transformer loss based on the loss difference before and after the mobile transformer changes position;

[0030] S1132. Analyze the distance loss according to the operation duration of the mobile transformer;

[0031] S1133. Calculate the network loss cost based on the distance loss and the total transformer loss.

[0032] Furthermore, based on the mobile transformer site selection model, establishing multi-constraint rules includes the following steps:

[0033] S21, establishing node voltage constraints based on the node voltage at time t;

[0034] S22. Establish branch current constraints based on line current safety transmission restrictions;

[0035] S23, with the goal of maintaining the network in a radial shape, establish network structure topology constraints;

[0036] S24. Establish power flow constraints based on active power and reactive power.

[0037] Furthermore, the power flow constraints are linearized, and the mobile transformer site selection model is optimized using the NSGA-2 algorithm and the tournament selection method. Solving the optimized model and outputting the mobile transformer site selection-path strategy include the following steps:

[0038] S31, linearize the power flow constraints using second-order cone convex optimization and large M method;

[0039] S32. Use the NSGA-2 algorithm to optimize the global search capability of the mobile transformer site selection model;

[0040] S33. Solve the optimized mobile transformer site selection model and output the mobile transformer site selection-path strategy.

[0041] Furthermore, using the second-order cone convex optimization and the large-M method, the linearized power flow constraint includes the following steps:

[0042] S311. Based on linear transformation and duality theory, select nonlinear constraints in power flow constraints;

[0043] S312. Based on the nonlinear constraint conditions, the corresponding square terms are eliminated to transform the non-convex power flow constraint into a convex second-order cone constraint;

[0044] S313. Use the Big M method to relax the transformed constraints.

[0045] Furthermore, using the NSGA-2 algorithm, the global search capability of optimizing the mobile transformer site selection model includes the following steps:

[0046] S321, traverse and search all transformers in the substation area, and number them in sequence;

[0047] S322, performing fast non-dominated sorting based on the numbering result;

[0048] S323, based on the sorting results, using the tournament selection method to conduct individual competition to obtain offspring, and sorting by congestion to select several individuals to participate in the next iteration;

[0049] S324. Combine the parent population with the generated offspring population to compete together to produce the next generation of individuals.

[0050] Further, based on the numbering results, performing fast non-dominated sorting includes the following steps:

[0051] S3221. Stratify the individuals in the numbering results according to the relationship between dominance and non-dominance;

[0052] S3222. Based on the stratification result, assigning the optimal stratum number to the non-dominated individuals;

[0053] S3223. After each non-dominated sorting, the individual with the smallest total cost is placed at the front, and the ranking of the corresponding individuals is listed.

[0054] The beneficial effects of the present invention are:

[0055] The present invention comprehensively considers social benefit cost, network loss cost, mobile transformer production cost and distance cost, and establishes an objective function with the goal of minimizing the comprehensive operating cost. A mobile transformer site selection model for agricultural irrigation areas is constructed based on the transformer loss model and the distance cost model. At the same time, in view of the nonlinearity and multi-constraints of the mobile transformer site selection model for agricultural irrigation areas, second-order cone convex optimization and large M method are used for linearization, and NSGA-2 algorithm and tournament selection method are introduced to improve the global search capability. In addition, by performing simulation examples on the distribution network in the agricultural irrigation area, a mobile transformer site selection-path strategy is obtained, which optimizes the economic benefits of the distribution network operation and improves the heavy overload problem in the agricultural irrigation area. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0057] Figure 1 is a flow chart of a method for selecting a mobile transformer site based on the NSGA-2 algorithm according to an embodiment of the present invention;

[0058] Figure 2 is a specific implementation diagram of a mobile transformer site selection method based on the NSGA-2 algorithm according to an embodiment of the present invention;

[0059] Figure 3 is a flow chart of mobile transformer site selection of a mobile transformer site selection method based on NSGA-2 algorithm according to an embodiment of the present invention;

[0060] Figure 4 is a 24-hour comprehensive cost radar chart of a mobile transformer site selection method based on the NSGA-2 algorithm according to an embodiment of the present invention;

[0061] Figure 5 This is a mobile transformer location distribution diagram of a mobile transformer site selection method based on the NSGA-2 algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0062] To further illustrate each embodiment, the present invention provides drawings, which are part of the disclosure of the present invention and are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, ordinary technicians in the field should be able to understand other possible implementations and advantages of the present invention. The components in the figures are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0063] According to an embodiment of the present invention, a method for selecting a mobile transformer site based on the NSGA-2 algorithm is provided.

[0064] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1-Figure 2 As shown, according to one embodiment of the present invention, a mobile transformer site selection method based on the NSGA-2 algorithm is provided, and the mobile transformer site selection method based on the NSGA-2 algorithm includes the following steps:

[0065] S1. Construct a mobile transformer site selection model with the goal of minimizing the comprehensive operating cost;

[0066] S2. Based on the mobile transformer site selection model, a multi-constraint rule is established, wherein the multi-constraint rule includes node voltage constraint, branch current constraint, network structure topology constraint and power flow constraint;

[0067] S3. Linearize the power flow constraints, and use the NSGA-2 algorithm and the tournament selection method to optimize the mobile transformer site selection model, solve the optimized model, and output the mobile transformer site selection-path strategy. The mobile transformer site selection-path strategy includes the location and moving path of the mobile transformer in different time periods.

[0068] In one embodiment, with the goal of minimizing the comprehensive operating cost, constructing a mobile transformer site selection model includes the following steps:

[0069] S11, constructing a transformer loss model, solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and calculating the network loss cost based on the difference loss;

[0070] S12, constructing a distance cost model, solving the distance cost model to obtain the distance cost of the mobile transformer, and combining the network loss cost with the production cost of the mobile transformer to calculate the economic benefit cost;

[0071] Specifically, assuming that the mobile transformer moves from the current substation Y to the next target substation y at time t, the total distance cost within time T is expressed as:

[0072] ;

[0073] In the formula, f path represents the distance cost of the mobile transformer, f Y,y represents the fuel cost required for the trailer carrying the mobile transformer to move from area Y to area y, Δt represents the length of each time period, and T represents the duration of the mobile transformer operation.

[0074] Specifically, the expression of the production cost of the mobile transformer is:

[0075] ;

[0076] In the formula, f cost represents the production cost of mobile transformer, n0 represents the number of mobile transformers, and C represents the cost of producing one mobile transformer.

[0077] S13. Calculate the comprehensive operating cost according to the social benefit cost and the economic benefit cost, construct the objective function based on the comprehensive operating cost, and establish the mobile transformer site selection model.

[0078] Specifically, with the goal of minimizing the comprehensive operating cost and taking into account the impact of social benefits, the present invention proposes a site selection model considering x modular mobile transformers. The objective function of the mobile transformer site selection model is the comprehensive operating cost constructed based on the social benefit cost and the economic benefit cost. The expression of the comprehensive operating cost is:

[0079] ;

[0080] Where: minf represents the minimum value of the comprehensive operating cost, k1 and k2 represent the social benefit weight coefficient and economic benefit weight coefficient respectively, f soc With f eco They represent social benefit cost and economic benefit cost respectively.

[0081] Specifically, the calculation expression of social benefit cost is:

[0082] ;

[0083] The calculation expression of economic benefit cost is:

[0084] ;

[0085] Where x represents the number of mobile transformers, c1, c2 and c3 represent the network loss cost coefficient, mobile transformer production cost coefficient and mobile transformer travel cost coefficient respectively, and f loss 、f cost and f path They represent network loss cost, mobile transformer production cost and mobile transformer travel cost respectively.

[0086] In one embodiment, constructing a transformer loss model, solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and calculating the network loss cost based on the difference loss includes the following steps:

[0087] S111. Calculating the load factor of the mobile transformer based on the load borne by the mobile transformer and the rated capacity;

[0088] S112, calculating the load factor of the rear area transformer after the mobile transformer changes position, and analyzing the loss difference before and after the mobile transformer changes position in combination with the load factor of the mobile transformer;

[0089] S113. Calculate the network loss cost based on the analysis result of the loss difference and in combination with the distance loss.

[0090] Specifically, in this embodiment, it is assumed that there are x mobile transformers, N agricultural irrigation transformers, the starting position is transformer area Y, the target position at the next moment is transformer area y, and at time t, x mobile transformers move from area Y to area y, and the expression of the corresponding transformer loss is obtained as follows:

[0091] ;

[0092] ;

[0093] In the formula, p 0,Y represents the no-load active power loss of the transformer in the Y station area, p k,Y Indicates the rated loss of load in the Y area, S represents the load of the transformer in the Y area at time t; Y,N Indicates the rated capacity of the transformer in the Y station area, β Y Indicates the load factor of the Y stage area.

[0094] Specifically, when x mobile transformers are connected to Y stations, the transformer loss formula is:

[0095] ;

[0096] ;

[0097] ;

[0098] In the formula, β x represents the load factor of the mobile transformer, Indicates the load borne by the mobile transformer, Indicates the rated capacity of the mobile transformer. It indicates the load factor after adding x mobile transformers to the Y station area. Indicates the load borne by the transformer in the substation area. Indicates the rated capacity of the transformer in the Y station area, p 0,Y represents the no-load active power loss of the transformer in the Y station area, p k It represents the rated load loss of the rear transformer after adding x mobile transformers. Indicates the no-load loss of the mobile transformer, Indicates the rated load loss of the mobile transformer, and They represent the transformer losses at time t and time t+1 respectively, and f Y,y,x Indicates the loss difference before and after the mobile transformer changes position.

[0099] Specifically, the expression of the loss difference before and after the mobile transformer changes position is:

[0100] ;

[0101] In the formula, and They represent the transformer losses at time t and time t+1 respectively, and f Y,y,x Indicates the loss difference before and after the mobile transformer changes position.

[0102] In one embodiment, the expression for calculating the load factor of the mobile transformer is:

[0103] ;

[0104] The expression for calculating the load factor of the rear area transformer after the mobile transformer changes position is:

[0105] ;

[0106] The expression for analyzing the loss difference before and after the mobile transformer changes position is:

[0107] ;

[0108] ;

[0109] In the formula, x represents the number of mobile transformers connected to the Y station area, β x represents the load factor of the mobile transformer, Indicates the load borne by the mobile transformer, Indicates the rated capacity of the mobile transformer. It indicates the load factor after adding x mobile transformers to the Y station area. Indicates the load borne by the transformer in the substation area. Indicates the rated capacity of the transformer in the Y station area, p 0,Y represents the no-load active power loss of the transformer in the Y station area, p k Indicates the rated load loss of the transformer in the substation area. Indicates the no-load loss of the mobile transformer, Indicates the rated load loss of the mobile transformer, and They represent the transformer losses at time t and time t+1 respectively, and f Y,y,x Indicates the loss difference before and after the mobile transformer changes position.

[0110] In one embodiment, based on the analysis result of the loss difference and in combination with the path loss, calculating the network loss cost includes the following steps:

[0111] S1131, analyzing the total transformer loss based on the loss difference before and after the mobile transformer changes position;

[0112] S1132. Analyze the distance loss according to the operation duration of the mobile transformer;

[0113] S1133. Calculate the network loss cost based on the distance loss and the total transformer loss.

[0114] Specifically, the expression of network loss cost is:

[0115] ;

[0116] ;

[0117] ;

[0118] In the formula, f loss represents the network loss cost, f Lloss represents the distance loss, f trlossrepresents the total transformer loss, I ij,t represents the effective value of the current flowing through the branch ij at time t, T represents the working time of the mobile transformer, R ij represents the resistance of branch ij, and Ω represents the branch set.

[0119] In one embodiment, based on the mobile transformer site selection model, establishing multiple constraint rules includes the following steps:

[0120] S21, establishing node voltage constraints based on the node voltage at time t;

[0121] Specifically, the expression of the node voltage constraint is:

[0122] ;

[0123] Where U i min with U i max They represent the upper and lower limits of the voltage amplitude at node i, respectively. i,t Represents the voltage amplitude of node i at time t.

[0124] S22. Establish branch current constraints based on line current safety transmission restrictions;

[0125] Specifically, considering the safety transmission limit of line current, the expression of branch current constraint is:

[0126] ;

[0127] In the formula, I ij,t represents the current flowing through branch ij at time t, It indicates the maximum value of the current allowed to flow through branch ij.

[0128] S23, with the goal of maintaining the network in a radial shape, establish network structure topology constraints;

[0129] Specifically, to ensure that the network is radial, the expression of the topology constraint is:

[0130] ;

[0131] In the formula, α ij It represents the switch state of branch ij, and z represents the number of network nodes.

[0132] S24. Establish power flow constraints based on active power and reactive power.

[0133] Specifically, considering the nonlinearity of the power flow constraint, it is difficult to solve. In the present invention, the second-order cone convex optimization and the big M method are used to transform the constraint. The second-order cone optimization method is based on linear transformation and duality theory, and can achieve rapid convergence to obtain the optimal solution. The expression of the power flow constraint is:

[0134] ;

[0135] ;

[0136] ;

[0137] ;

[0138] Where P ij,t With Q ij,t They represent the active power and reactive power flowing through branch ij at time t, respectively. j,t With Q j,t They represent the active power and reactive power injected into node j at time t, respectively, ik,t With Q ik,t They represent the active power and reactive power of branch jk at time t, U j,t represents the voltage of node j at time t; r ij With x ij Respectively represent the resistance and conductance of branch ij, α jk represents the switch state of branch jk, γ(j) and φ(j) represent the parent node set and child node set of node j respectively.

[0139] In one embodiment, linearizing the power flow constraints, optimizing the mobile transformer site selection model using the NSGA-2 algorithm and the tournament selection method, solving the optimized model, and outputting the mobile transformer site selection-path strategy include the following steps:

[0140] S31, linearize the power flow constraints using second-order cone convex optimization and large M method;

[0141] S32. Use the NSGA-2 algorithm to optimize the global search capability of the mobile transformer site selection model;

[0142] S33. Solve the optimized mobile transformer site selection model and output the mobile transformer site selection-path strategy.

[0143] In one embodiment, using second-order cone convex optimization and large-M method, linearizing power flow constraints includes the following steps:

[0144] S311. Based on linear transformation and duality theory, select nonlinear constraints in power flow constraints;

[0145] S312. Based on the nonlinear constraint conditions, the corresponding square terms are eliminated to transform the non-convex power flow constraint into a convex second-order cone constraint;

[0146] S313. Use the Big M method to relax the transformed constraints.

[0147] Specifically, in the above embodiment, the power flow constraint is based on the improved Disflow power flow model, which is still non-convex, so it is converted into a convex second-order cone constraint here. Let I sqr ij,t =I 2 ij,t , U sqr ij,t =U 2 ij,t , eliminating the square term, we get the expression:

[0148] ;

[0149] ;

[0150] ;

[0151] Specifically, when branch ij is in the disconnected state, the large M method is used to relax it so that the constraint is applicable to all distribution network branches, and the expression is obtained:

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] In the formula, m ij represents the number of switch states considered, and M represents an arbitrarily large (not infinite) positive number.

[0157] In one embodiment, using the NSGA-2 algorithm, optimizing the global search capability of the mobile transformer site selection model includes the following steps:

[0158] S321, traverse and search all transformers in the substation area, and number them in sequence;

[0159] S322, performing fast non-dominated sorting based on the numbering result;

[0160] S323, based on the sorting results, using the tournament selection method to conduct individual competition to obtain offspring, and sorting by congestion to select several individuals to participate in the next iteration;

[0161] S324. Combine the parent population with the generated offspring population to compete together to produce the next generation of individuals.

[0162] Specifically, the non-dominated sorting genetic algorithm with elite strategy (NSGA-2) is an evolutionary algorithm for multi-objective optimization problems. It is an improvement on the non-dominated sorting genetic algorithm NSGA. NSGA-2 divides the individuals in the population into different levels by non-dominated sorting, thereby retaining the non-dominated solutions. At the same time, the concept of crowding is introduced to ensure the diversity of the population during the selection operation.

[0163] Specifically, after the population is initialized, the parent generation is selected. In this embodiment, the tournament selection method is selected to randomly select a part of individuals in the parent generation population to compete to obtain offspring. The advantage of this method is that a large number of samples are traversed and each individual has the opportunity to participate in the competition, which improves the global search capability and avoids falling into the local optimal solution. At the same time, in order to improve the convergence speed, the offspring fitness values ​​generated by each iteration are arranged from small to large, and the ranks are arranged in descending order, and then in ascending order according to the congestion degree, and then the selection probability of each individual is allocated. In the above embodiment, the process of mobile transformer site selection based on NSGA-2 is as follows:

[0164] (1) Real numbers are used to represent the transformers corresponding to the agricultural irrigation areas in a certain area of ​​Jilin.

[0165] (2) Fast non-dominated sorting. There are currently h mobile transformer loss-position samples, i.e., h individuals. First, the individuals in the population are stratified according to the relationship between dominance and non-domination, and the non-dominated optimal layer number is assigned. Each time the non-dominated sorting is used, the one with the smallest total cost is placed at the front, and the ranking of the corresponding individuals is listed.

[0166] (3) Selection operation: use the linear tournament selection method to obtain offspring through individual competition. Sorting by crowding degree, take the first 40 columns and the individuals in the initial population to participate in the next iteration.

[0167] (4) Elite retention strategy: combining the parent population and the offspring population it produces to compete together to produce the next generation, which is conducive to retaining the excellent individuals in the parent generation into the next generation.

[0168] Specifically, through the mobile transformer site selection model and NSGA-2 key theoretical analysis and the application of the tournament selection method, the site selection process of mobile transformers in agricultural irrigation areas based on NSGA-2 can be obtained, such as Figure 3 shown.

[0169] In one embodiment, performing a fast non-dominated sort based on the numbering result includes the following steps:

[0170] S3221. Stratify the individuals in the numbering results according to the relationship between dominance and non-dominance;

[0171] S3222. Based on the stratification result, assigning the optimal stratum number to the non-dominated individuals;

[0172] S3223. After each non-dominated sorting, the individual with the smallest total cost is placed at the front, and the ranking of the corresponding individuals is listed.

[0173] In order to facilitate understanding of the above technical solution of the present invention, the actual situation of a rural distribution network in Northeast China is taken as an example for specific description as follows:

[0174] According to the actual situation of rural distribution network in Northeast China, a distribution network with 3 mobile transformers and 120 heavily overloaded transformers is taken as an example. Considering the predicted load data of agricultural irrigation in a certain year, the location-path strategy of mobile transformers is analyzed. Figure 4 , Table 1 is the 24-hour comprehensive cost table.

[0175] From the expression of comprehensive cost, we can know that the smaller the value, the better the actual economic benefit. Figure 4 It can be seen that the dashed line represents the mean of the 24-hour comprehensive cost, and the envelope is the 24-hour real-time comprehensive cost. The comprehensive cost during the 5-9 period is not only less than the mean cost, but also less than 0. This shows that the total cost after adding three mobile transformers is less than the total cost when no mobile transformers are added, thereby improving the economic benefits of the rural distribution network; although at other times, the addition of mobile transformers did not improve the total cost in the short-term economic benefits, but effectively improved the heavy overload situation of the transformer.

[0176] Table 1 24-hour comprehensive cost table

[0177] Time / Hour Comprehensive cost / yuan Time / Hour Comprehensive cost / yuan 1 14.33 13 20.26 2 4.89 14 9.533 3 9.98 15 4.04 4 8.77 16 1.29 5 -10.45 17 4.36 6 -41.18 18 4.20 7 -37.68 19 11.16 8 -5.73 20 19.15 9 -0.12 21 15.55 10 9.52 22 11.57 11 11.06 23 9.08 12 20.26 24 6.05

[0178] From the values ​​of the 24-hour comprehensive cost in Table 1, it can be seen that the comprehensive costs at moments 5-9 are -10.45, -41.18, -37.68, -5.73 and -0.12 yuan respectively, all of which are less than 0, and the comprehensive cost at moment 6 is -41.18 yuan, at which time the economic benefits brought by the addition of the mobile transformer are the best.

[0179] Table 2 Mobile transformer site selection-path strategy table

[0180] Mobile transformer number Site selection-path strategy 1 Keep it unchanged at 1 node 2 1-1-1-59-58-69-69-71-69-4-18-65-65-9-15-15-66-18-15-15-13-9-11-11 3 113-106-75-77-39-31-78-30-33-48-47-37-60-28-44-47-34-77-41-31-29-29-31-78

[0181] from Figure 5It can be seen from Table 2 that when three mobile transformers are added to the transformers in the agricultural irrigation area, considering that the comprehensive cost includes the impact of the mobile transformer manufacturing cost and its own loss cost, transformer No. 1 will remain unchanged at position 1; because position 1 is a substation, when considering adding three mobile transformers to the agricultural irrigation area, it can be assumed that two mobile transformers work, and the site selection path strategies for mobile transformers No. 2 and No. 3 are shown in Table 2.

[0182] The above results show that in the context of heavy overload in agricultural irrigation areas, measures such as adding mobile transformers and adopting appropriate site selection-path strategies can effectively reduce the operating costs of the distribution network, improve the problem of heavy overload in agricultural irrigation areas, and improve the economy of system operation by reducing network losses and transformer losses.

[0183] In summary, with the help of the above-mentioned technical scheme of the present invention, the social benefit cost, network loss cost, mobile transformer production cost and travel cost are comprehensively considered, and the objective function is established with the goal of minimizing the comprehensive operating cost. The mobile transformer site selection model in the agricultural irrigation area is constructed on the basis of the transformer loss model and the travel cost model; at the same time, in view of the nonlinearity and multi-constraints of the mobile transformer site selection model in the agricultural irrigation area, the second-order cone convex optimization and large M method are used for linearization, and the NSGA-2 algorithm and the tournament selection method are introduced to improve the global search capability; in addition, through the simulation example of the distribution network in the agricultural irrigation area, the mobile transformer site selection-path strategy is obtained, the economic benefits of the distribution network operation are optimized, and the heavy overload problem in the agricultural irrigation area is improved.

[0184] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A mobile transformer site selection method based on NSGA-2 algorithm, characterized in that: The mobile transformer site selection method based on the NSGA-2 algorithm includes the following steps: S1. Construct a mobile transformer site selection model with the goal of minimizing the comprehensive operating cost; S2. Based on the mobile transformer site selection model, a multi-constraint rule is established, wherein the multi-constraint rule includes node voltage constraint, branch current constraint, network structure topology constraint and power flow constraint; S3, linearizing the power flow constraints, and optimizing the mobile transformer site selection model by using the NSGA-2 algorithm and the tournament selection method, solving the optimized model, and outputting the mobile transformer site selection-path strategy, wherein the mobile transformer site selection-path strategy includes the location and moving path of the mobile transformer in different time periods; The construction of the mobile transformer site selection model with the goal of minimizing the comprehensive operating cost includes the following steps: S11, constructing a transformer loss model, solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and calculating the network loss cost based on the difference loss; S12, constructing a distance cost model, solving the distance cost model to obtain the distance cost of the mobile transformer, and combining the network loss cost with the production cost of the mobile transformer to calculate the economic benefit cost; S13. Calculate the comprehensive operation cost according to the social benefit cost and the economic benefit cost, and construct the objective function based on the comprehensive operation cost to establish the mobile transformer site selection model; The calculation expression of the social benefit cost is: f SOC =1.21*x 2 -96.5*x+55; In the formula, f SOC represents the social benefit cost, x represents the number of mobile transformers; The step of constructing a transformer loss model, solving the transformer loss model to obtain the difference loss before and after the mobile transformer changes position, and calculating the network loss cost based on the difference loss includes the following steps: S111. Calculating the load factor of the mobile transformer based on the load borne by the mobile transformer and the rated capacity; S112, calculating the load factor of the rear area transformer after the mobile transformer changes position, and analyzing the loss difference before and after the mobile transformer changes position in combination with the load factor of the mobile transformer; S113, calculating the network loss cost based on the analysis result of the loss difference and in combination with the path loss; The expression for calculating the load factor of the mobile transformer is: The expression for calculating the load factor of the rear area transformer after the mobile transformer changes position is: The expression for analyzing the loss difference before and after the mobile transformer changes position is: In the formula, x represents the number of mobile transformers connected to the Y station area, β x represents the load factor of the mobile transformer, Indicates the load borne by the mobile transformer, Indicates the rated capacity of the mobile transformer. It indicates the load factor after adding x mobile transformers to the Y station area. Indicates the load borne by the transformer in the substation area. Indicates the rated capacity of the transformer in the Y station area, p 0，Y represents the no-load active power loss of the transformer in the Y station area, p k It represents the rated load loss of the rear transformer after adding x mobile transformers. Indicates the no-load loss of the mobile transformer, Indicates the rated load loss of the mobile transformer, and They represent the transformer losses at time t and time t+1 respectively, and f Y，y，x Indicates the loss difference before and after the mobile transformer changes position; The calculation of the network loss cost based on the analysis result of the loss difference and combined with the path loss includes the following steps: S1131, analyzing the total transformer loss based on the loss difference before and after the mobile transformer changes position; S1132. Analyze the distance loss according to the operation duration of the mobile transformer; S1133. Calculate network loss cost based on the distance loss and the total transformer loss; The expression of the network loss cost is: f loss =f Lloss +f trloss ; In the formula, f loss represents the network loss cost, f Lloss represents the distance loss, f trloss represents the total transformer loss, I ij，t represents the effective value of the current flowing through the branch ij at time t, T represents the working time of the mobile transformer, R ij represents the resistance of branch ij, Ω represents the branch set; The linearized power flow constraint, optimizing the mobile transformer site selection model using the NSGA-2 algorithm and the tournament selection method, solving the optimized model, and outputting the mobile transformer site selection-path strategy include the following steps: S31, linearize the power flow constraints using second-order cone convex optimization and large M method; S32. Use the NSGA-2 algorithm to optimize the global search capability of the mobile transformer site selection model; S33. Solve the optimized mobile transformer site selection model and output the mobile transformer site selection-path strategy.

2. The method for selecting a mobile transformer site based on the NSGA-2 algorithm according to claim 1 is characterized in that: The establishment of multi-constraint rules based on the mobile transformer site selection model includes the following steps: S21, establishing node voltage constraints based on the node voltage at time t; S22. Establish branch current constraints based on line current safety transmission restrictions; S23, with the goal of maintaining the network in a radial shape, establish network structure topology constraints; S24. Establish power flow constraints based on active power and reactive power.

3. The method for selecting a mobile transformer site based on the NSGA-2 algorithm according to claim 1 is characterized in that: The linearization of power flow constraints using the second-order cone convex optimization and the large M method includes the following steps: S311. Based on linear transformation and duality theory, select nonlinear constraints in power flow constraints; S312. Based on the nonlinear constraint conditions, the corresponding square terms are eliminated to transform the non-convex power flow constraint into a convex second-order cone constraint; S313. Use the Big M method to relax the transformed constraints.

4. The method for selecting a mobile transformer site based on the NSGA-2 algorithm according to claim 1 is characterized in that: The method of optimizing the global search capability of the mobile transformer site selection model by using the NSGA-2 algorithm includes the following steps: S321, traverse and search all transformers in the substation area, and number them in sequence; S322, performing fast non-dominated sorting based on the numbering result; S323, based on the sorting results, using the tournament selection method to conduct individual competition to obtain offspring, and sorting by congestion to select several individuals to participate in the next iteration; S324. Combine the parent population with the generated offspring population to compete together to produce the next generation of individuals.

5. The method for selecting a mobile transformer site based on the NSGA-2 algorithm according to claim 4 is characterized in that: The method of performing fast non-dominated sorting based on the numbering result comprises the following steps: S3221. Stratify the individuals in the numbering results according to the relationship between dominance and non-dominance; S3222. Based on the stratification result, assigning the optimal stratum number to the non-dominated individuals; S3223. After each non-dominated sorting, the individual with the smallest total cost is placed at the front, and the ranking of the corresponding individuals is listed.

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