CN106941256B - Optimal planning method for distribution network main transformer connection structure considering MPSC and MCCC - Google Patents

Abstract

The present invention is a distribution network main transformer connection structure optimization planning method considering MPSC and MCCC. The present invention starts with the comprehensive consideration of the maximum power supply capacity and investment cost, uses the feeder interconnection matrix as the decision variable to construct the optimization model of the main transformer connection structure, and proposes a method for optimizing the connection structure of the medium-voltage distribution network considering geographical factors, revealing the geographical environment It has the influence on the connection structure and shows the connection relationship between each feeder, which has the advantages of scientific and reasonable method, strong applicability and good effect.

Description

Optimal planning method for distribution network main transformer connection structure considering MPSC and MCCC

technical field

The invention relates to the field of distribution network planning in an electric power system, and relates to an optimization planning method for the main transformer connection structure of a distribution network considering MPSC and MCCC.

Background technique

With the rapid development of urban economy, the increasing shortage of urban land makes the selection of substation site and power channel corridor very difficult. Since the tie line is used as a channel for power supply restoration and load transfer, less resources can be used to enlarge the substation station. Inter-load transfer capacity, improve equipment utilization, and realize the reduction of construction scale and land resource consumption while meeting the power supply demand of various user loads at all levels. Therefore, the optimization of the main transformer connection structure has become the choice of distribution network operation mode and grid structure. Important elements of structural planning. As the concept of maximum power supply capacity of distribution network is more and more used in guiding distribution network planning, at present, the weighted Voronoi diagram and the analysis method of maximum power supply capacity of distribution network based on main transformer interconnection and N-1 criterion have been proposed. Based on the optimization method of the connection structure between main transformer stations, the multi-objective optimization model of the connection structure between main transformer stations based on improving the regional power supply capacity and simplifying the connection channel, the planning method of the connection channel considering the cost of unit power supply capacity and based on Bottleneck analysis and transformation methods of distribution network tie-lines with maximum power supply capacity, etc. However, the above-mentioned methods only use the main transformer interconnection matrix as a decision variable to study the optimization of the communication channel and the communication scale between the main transformers. As a physical concept, the communication channel is a collection of contact branches between the main transformers. It does not include the specific number of outgoing lines, and the obtained planning results cannot indicate the number and location of the contact branches in the channel, and cannot guide the contact relationship between specific feeders. factors.

In this regard, the present invention starts from comprehensively considering the maximum power supply capacity and investment cost, and uses the feeder interconnection matrix as the decision variable to construct the optimization model of the main transformer connection structure, and proposes a method for optimizing the connection structure of the medium-voltage distribution network considering geographical factors, showing that The connection relationship between feeders is revealed and the influence of geographical environment on the connection structure is revealed.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies in the prior art, to provide a scientific and reasonable, strong applicability, good effect considering maximum power supply capability (Maximum Power Supply Capability, MPSC) and minimum contact construction cost (Minimum Contact Construction Cost, MCCC) distribution network main transformer connection structure optimization planning method.

The technical scheme that realizes the object of the present invention adopts is, a kind of distribution network main transformation connection structure optimization planning method that considers MPSC and MCCC, it is characterized in that, it comprises the following content:

1) Establishment of contact structure optimization model

①Maximum power supply capacity model of distribution network based on feeder interconnection

The maximum power supply capacity model based on feeder interconnection is:

Among them, A _TSC is the calculated maximum power supply capacity of the distribution network; F _m is the feeder m, is the load on feeder m, m=1,2,...,M; P _{trf mn} is the load transferred to feeder n when N-1 fault occurs on feeder m, n=1,2,...,M; T _i Main transformer i, P _i is the load carried by main transformer i, i=1,2,...,N; P _{trt ij} is the load transferred to main transformer j when N-1 fault occurs in main transformer i, j =1,2,...,N; N is the number of main variables; M is the number of feeders; R _Fn is the capacity of feeder n; F _m ∈ T _i means that feeder m comes from the corresponding bus of main variable i; L ^f is the feeder interconnection matrix , its matrix expression is formula (2), l ^f _m,n represents the contact relationship between feeder m and feeder n, when there is a contact relationship between them, l ^f _m,n = 1, otherwise l ^f _{m, n} = 0; L ^t is the main transformer interconnection matrix, and its matrix expression is formula (3), which represents the connection relationship between main transformer i and main transformer j. When there is a connection relationship between them, l ^t _{i, j} =1, otherwise l ^t _i,j =0; R' _j is the capacity of main transformer j after correction, R' _j =R _j -P _F·fsi , R _j is the capacity of main transformer j, P _F·fsi is Single radial line load on main transformer j; P _D is the lower limit of load in a certain heavy-duty area; Z is the set of all main transformers in the heavy-duty area;

②Construction cost model considering geographical factors

Establish a main transformer connection construction cost model considering geographical factors, see formula (4),

Among them, C _Link is the cost of connection construction taking into account geographical factors, is the new connection line capacity between feeder m and feeder n, α is the tortuosity coefficient; for Tie line unit length cost under capacity; D _mn is the distance between feeder m and feeder n, according to the direction of the power flow, define the start and end points of the main feeder, and take the distance between the end nodes of the main feeder as the distance between the two feeders; W _mn is the feeder m and When the geographical factors are not considered between feeder lines n, the cost of new tie lines; Z _mn is the additional construction cost required to cross unfavorable terrain when laying lines between feeder m and feeder n. The more obstacles, the greater Z _mn , when feeder m and feeder n When there is no unfavorable terrain between n, Z _mn = 0; r ₀ is the discount rate, and p is the depreciation period of the line;

③Optimization model of connection structure based on Pareto optimality

The connection between main transformers is realized by the connection between feeders. After the feeder interconnection is clarified, the main transformer interconnection is also determined, that is, the main transformer interconnection matrix L ^t is obtained according to the feeder interconnection matrix L ^f . The solution process is shown in formula (8 ) to formula (13), with L ^f as the decision variable, an optimization model of the main transformer connection structure that simultaneously optimizes multiple objectives is established, see formula (6),

Among them, L ^f is the solution of the multi-objective optimization model; Ω is the feasible solution set, F(L ^f ) is the objective vector with n components, f _k (L ^f ) is the optimization sub-objective, k=1,2, …,n; n is the number of components of F(L ^f ), for the minimization multi-objective optimization problem, if both L ^f _l and L ^f _k are feasible solutions, and

It is said that L ^f _l dominates L ^f _k , recorded as L ^f _l <L ^f _k , < indicates the dominance relationship, L ^f _l indicates the l-th feasible solution, L ^f _k indicates the k-th feasible solution, if in the set of feasible solutions There is no solution dominating L ^f _l in , then L ^f _l is called a non-dominated solution of the multi-objective optimization problem, that is, a non-inferior solution, and the area formed by all non-dominated solutions becomes the Pareto front;

In order to obtain L ^t through L ^f , the following numbering rules are adopted: if there are N main transformers in the planning area, the corresponding numbers are 1, 2, ..., N, and the number of feeders corresponding to each main transformer is M ₁ , M ₂ ,...,M _N , record the feeder m as F _m , if it is the dth feeder of the i-th main transformer, i=1,2,...,N, d=1,2,...,M _i , then the number m is obtained according to formula (8), so that M represents the total number of feeders in the planning area;

Among them, M _k is the number of feeders from the main transformer k, M _k ∈ {M ₀ ,M ₁ ,M ₂ ,…,M _i-1 }, M ₀ =0; k=1,2,…,i-1 ; i=1,2,...,N; d=1,2,...,M _i ,

L ^f is divided into blocks according to the main transformer to which the feeder belongs, see formula (9):

Among them, M is the total number of feeders in the planning area, N is the total number of main transformers in the planning area, m=1,2,...,M, n=1,2,...,M, S _i,j is the i-th main transformer after the block is completed The feeder contact relationship matrix between the transformer and the jth main transformer, for the convenience of writing in the matrix, the denoted as M _(i-1)∑ , Recorded as M _(j-1)∑ , i=1,2,...,N, j=1,2,...,N, d=1,2,...,M _i , b=1,2,...,M _j , the matrix expression of S _{i, j} is shown in formula (10),

Define a piecewise function h(X), as shown in formula (11),

Among them, X represents any matrix, h(X) is the mapping from variable X to piecewise function,

Bringing X=S _i,j into formula (11), l ^t _i,j can be obtained, see formula (12),

L ^t =[h(S _i,j )] _N×N (13)

If only the two sub-optimization objectives of "maximum power supply capacity" and "connection construction cost considering geographical factors" are considered comprehensively, formula (6) can be simplified and written as formula (14),

minF(L ^f )=[f ₁ (L ^f ),f ₂ (L ^f )] (14)

Among them, f ₁ (L ^f ) is the mapping function from the decision variable L ^f to the reciprocal of the sub-optimization goal "maximum power supply capacity", obtained by f ₁ (L ^f )=1/A _TSC , and f ₂ (L ^f ) is the decision The mapping function of the variable L ^f to the sub-optimization goal "the cost of link construction considering geographical factors" is obtained by f ₂ (L ^f )=C _Link ,

2) Solving the optimization model of the connection structure

①Solution of contact structure optimization model based on non-dominated sorting genetic algorithm with elitist strategy

The non-dominated sorting genetic algorithm (Non-dominated Sorting Genetic Algorithm-Ⅱ, NSGA-Ⅱ) with elite strategy is used to solve the model. The specific steps of the single-connection model are:

a) Encoding: Encode the feeder contact matrix. According to the characteristics that the feeder contact matrix is symmetrical and each row and column has and only one element is 1, real number encoding is used. The number of genes on a chromosome is equal to the total number of feeder lines, and one chromosome represents a plan Scheme, each gene represents the serial number of the feeder interconnected with the feeder and is different from each other. For example, if the feeder m is connected to the feeder n, the mth gene on the chromosome is coded as n;

b) Population initialization: The initial population is randomly generated according to the designed genetic coding method, each individual represents a connection structure optimization scheme, and the A _TSC calculation program is called to calculate the values of each objective function according to formula (1) and formula (4). fitness value;

c) Genetic operation: Each population uses the NSGA-II algorithm for genetic operations. After non-dominated sorting, the selection operator is selected according to the non-dominated order and crowding degree of the individual according to the round-robin system, and the selected individuals are cross-recombined. and mutation operations to form a new offspring population, that is, a new planning scheme;

d) Verification and elite strategy: verify the decoding of the new offspring population generated by genetic operations, judge whether its contact structure meets the constraint conditions, eliminate the schemes that have not passed the verification, and use the elite strategy to select the parent population and the verified Individuals in the collection of offspring populations form a new parent population;

Add 1 to the number of iterations, return to substep c) of substep ① in step 2), until the maximum number of iterations is reached, all non-dominated solutions in the population constitute the Pareto optimal solution set;

3) Selection of the best solution

①The coefficient of variation method to determine the index weight

There are m objects, each object has n indicators, and the evaluation index value of each object is represented by a vector, recorded as Xi = ( _{xi ,1} , _xi,2 ,..., _xi,n ) ^T , so as to obtain the original evaluation matrix X _i =( _xi,j ) _m×n , normalize the original evaluation matrix, eliminate the influence of dimensions, choose the mean value processing method, and use formula (15) to calculate:

Among them, i=1,2,...,m; j=1,2,...,n;

The coefficient of variation of the jth evaluation index is calculated by formula (16);

Among them, δ _j is the coefficient of variation of the jth evaluation index; d _j is the mean square error of the jth evaluation index, which is calculated by formula (17); is the mean value of the jth evaluation index, calculated by formula (18);

The weight of the jth evaluation index is calculated by formula (19):

Among them, w _j is the weight of the jth evaluation index;

② Weighted TOPSIS method to select the optimal solution

After determining the index weight according to the coefficient of variation method, use the weighted approximation to the ideal point sorting method (Technique fororder by similarity to an idea solution, TOPSIS) to sort the alternatives, and get the optimal contact structure planning scheme;

In the process of sorting the alternatives by the weighted TOPSIS method, firstly, the original data needs to be established as an initial matrix, and the indicators should be processed in the same trend. In view of the characteristics that A _TSC is a high-quality indicator and the contact construction cost is a low-quality indicator , in order to make the direction of the two indicators consistent, so the A _TSC indicator is processed by the reciprocal method, and the index matrix X after the same trend is obtained, and its expression is shown in formula (20). Secondly, X is normalized, Establish a normalized matrix Z, whose expression is shown in formula (21), and determine Z ⁺ corresponding to the optimal solution and Z ^- corresponding to the worst solution in the finite solution, and finally, calculate the relationship between each evaluation object and the optimal solution and the weighted Euclidean distance D _i ⁺ and D _i ^- between the worst solution and the closeness C _i of each evaluation object to the optimal solution, sort the non-inferior solution set according to the size of C _i , and obtain the optimal solution. The above calculation In , the specific solution method of each variable is shown in formula (22) to formula (27),

In the formula, Z ⁺ is the index vector corresponding to the optimal scheme in the finite scheme, Z ^- is the index vector corresponding to the worst scheme in the finite scheme, x _i,j is the jth index value of the i-th scheme, z _i,j is the j-th index value of the i-th scheme after normalization, D _i ⁺ is the weighted Euclidean formula between each evaluation object and the optimal scheme Distance, D _i ^- is the weighted Euclidean distance between each evaluation object and the worst solution, i=1,2,...,m, m is the number of evaluation objects; j=1,2,...,n, n is the number of evaluation indicators w _j is the weight of the jth index, C _i is the closeness of each evaluation object to the optimal solution, C _i ∈ [0,1], the larger the value of C _i is, the closer the evaluation object is to the optimal solution The higher the value, the better the corresponding planning scheme.

The present invention considers the MPSC and MCCC main transformer contact structure optimization planning method, comprehensively considers the maximum power supply capacity and investment cost, uses the feeder interconnection matrix as the decision variable to construct the main transformer contact structure optimization model, and proposes a geographically The optimization method of the connection structure of the medium-voltage distribution network based on factors reveals the influence of the geographical environment on the connection structure and shows the connection relationship between each feeder. It has the advantages of scientific and reasonable method, strong applicability and good effect.

Description of drawings

Figure 1 is a schematic diagram of the existing radiation network structure in an economic and technological development zone of a certain city in Northeast China;

Figure 2 is a schematic diagram of the Pareto front of A _TSC - contact construction cost;

Figure 3 is a schematic diagram of the theoretical planning of the main transformer connection structure without considering geographical factors;

Figure 4 is a schematic diagram of the post-event optimal scheme of the main transformer connection structure without considering geographical factors;

Figure 5 is a schematic diagram of the geographical connection structure of the planning results of the main transformer connection structure considering geographical factors;

Figure 6 is a schematic diagram of the main transformer connection structure planning results considering geographical factors.

Detailed ways

The present invention will be further described below using the accompanying drawings and examples.

A method for optimizing the planning of the distribution network main transformer connection structure considering MPSC and MCCC of the present invention includes the following content:

1) Establishment of contact structure optimization model

①Maximum power supply capacity model of distribution network based on feeder interconnection

The maximum power supply capacity model based on feeder interconnection is:

Among them, A _TSC is the calculated maximum power supply capacity of the distribution network; F _m is the feeder m, is the load on feeder m, m=1,2,...,M; P _{trf mn} is the load transferred to feeder n when N-1 fault occurs on feeder m, n=1,2,...,M; T _i Main transformer i, P _i is the load carried by main transformer i, i=1,2,...,N; P _{trt ij} is the load transferred to main transformer j when N-1 fault occurs in main transformer i, j ＝1,2,...,N; N is the number of main variables; M is the number of feeders; is the capacity of feeder _n ; ^F _m ∈ T _i means that feeder m comes from the corresponding busbar of main variable i; L ^f is feeder interconnection matrix, and its matrix expression is formula (2), The relationship between them, when there is a relationship between them, l ^f _{m, n} = 1, otherwise l ^f _{m, n} = 0; L ^t is the interconnection matrix of the main transformer, and its matrix expression is formula (3), Indicates the contact relationship between the main transformer i and the main transformer j. When there is a contact relationship between them, l ^t _i,j = 1, otherwise l ^t _i,j = 0; R' _j is the main variable j after correction Capacity, R' _j ＝R _j －P _F·fsi , R _j is the capacity of the main transformer j, P _F·fsi is the load of the single radial line on the main transformer j; P _D is the lower limit of the load in a certain heavy-duty area; Z It is the collection of all main variables in the overload area;

②Construction cost model considering geographical factors

Establish a main transformer connection construction cost model considering geographical factors, see formula (4),

Among them, C _Link is the cost of connection construction taking into account geographical factors, is the new connection line capacity between feeder m and feeder n, α is the tortuosity coefficient; for Tie line unit length cost under capacity; D _mn is the distance between feeder m and feeder n, according to the direction of the power flow, define the start and end points of the main feeder, and take the distance between the end nodes of the main feeder as the distance between the two feeders; W _mn is the feeder m and When the geographical factors are not considered between feeder lines n, the cost of new tie lines; Z _mn is the additional construction cost required to cross unfavorable terrain when laying lines between feeder m and feeder n. The more obstacles, the greater Z _mn , when feeder m and feeder n When there is no unfavorable terrain between n, Z _mn = 0; r ₀ is the discount rate, and p is the depreciation period of the line. Since the tie line is only put into use when there is a fault, its annual operating cost is very small, so only the construction cost of the tie line is considered ;

③Optimization model of connection structure based on Pareto optimality

In general, multiple objective functions in multi-objective optimization problems cannot be compared and often conflict with each other. The improvement of one objective function is often at the expense of the value of another objective function. Therefore, it can be seen that multi-objective optimization Problems often contain multiple solutions, and the advantages and disadvantages of each solution cannot be compared. These solutions are collectively called the Pareto solution set. Pareto optimality represents the state in which each sub-goal of the problem solution can no longer continue to optimize at the same time , since the connection between the main transformers is realized by the connection between the feeders, after the feeder interconnection is clarified, the main transformer interconnection is also determined, that is, the main transformer interconnection matrix L ^t is obtained according to the feeder interconnection matrix L ^f , and the solution process is shown in Formulas (8) to (13), with L ^f as the decision variable, establish a main transformer connection structure optimization model that optimizes multiple objectives at the same time, see formula (6),

Among them, L ^f is the solution of the multi-objective optimization model; Ω is the feasible solution set, F(L ^f ) is the objective vector with n components, f _k (L ^f ) is the optimization sub-objective, k=1,2, …,n; n is the number of components of F(L ^f ), for the minimization multi-objective optimization problem, if both L ^f _l and L ^f _k are feasible solutions, and

It is said that L ^f _l dominates L ^f _k , recorded as L ^f _l <L ^f _k , < indicates the dominance relationship, L ^f _l indicates the l-th feasible solution, L ^f _k indicates the k-th feasible solution, if in the set of feasible solutions There is no solution dominating L ^f _l in , then L ^f _l is called a non-dominated solution of the multi-objective optimization problem, that is, a non-inferior solution, and the area formed by all non-dominated solutions becomes the Pareto front;

In order to obtain L ^t through L ^f , the following numbering rules are adopted: if there are N main transformers in the planning area, the corresponding numbers are 1, 2, ..., N, and the number of feeders corresponding to each main transformer is M ₁ , M ₂ ,...,M _N , record the feeder m as F _m , if it is the dth feeder of the i-th main transformer, i=1,2,...,N, d=1,2,...,M _i , then the number m is obtained according to formula (8), so that M represents the total number of feeders in the planning area;

Among them, M _k is the number of feeders from the main transformer k, M _k ∈ {M ₀ ,M ₁ ,M ₂ ,…,M _i-1 }, M ₀ =0; k=1,2,…,i-1 ; i=1,2,...,N; d=1,2,...,M _i ,

L ^f is divided into blocks according to the main transformer to which the feeder belongs, see formula (9):

Among them, M is the total number of feeders in the planning area, N is the total number of main transformers in the planning area, m=1,2,...,M, n=1,2,...,M, S _i,j is the i-th main transformer after the block is completed The feeder contact relationship matrix between the transformer and the jth main transformer, for the convenience of writing in the matrix, the denoted as M _(i-1)∑ , Recorded as M _(j-1)∑ , i=1,2,...,N, j=1,2,...,N, d=1,2,...,M _i , b=1,2,...,M _j , the matrix expression of S _{i, j} is shown in formula (10),

Define a piecewise function h(X), as shown in formula (11),

Among them, X represents any matrix, h(X) is the mapping from variable X to piecewise function,

Bringing X=S _i,j into formula (11), l ^t _i,j can be obtained, see formula (12),

L ^t =[h(S _i,j )] _N×N (13)

If only the two sub-optimization objectives of "maximum power supply capacity" and "connection construction cost considering geographical factors" are considered comprehensively, formula (6) can be simplified and written as formula (14),

minF(L ^f )=[f ₁ (L ^f ),f ₂ (L ^f )] (14)

Among them, f ₁ (L ^f ) is the mapping function from the decision variable L ^f to the reciprocal of the sub-optimization goal "maximum power supply capacity", obtained by f ₁ (L ^f )=1/A _TSC , and f ₂ (L ^f ) is the decision The mapping function of the variable L ^f to the sub-optimization goal "the cost of link construction considering geographical factors" is obtained by f ₂ (L ^f )=C _Link ,

2) Solving the optimization model of the connection structure

①Solution of contact structure optimization model based on non-dominated sorting genetic algorithm with elitist strategy

Since the connection structure optimization is a large-scale combinatorial optimization problem, the model is solved by using the non-dominated sorting genetic algorithm (Non-dominated Sorting Genetic Algorithm-Ⅱ, NSGA-Ⅱ) with elitist strategy. The specific steps of the single connection connection model are as follows: :

e) Coding: Coding the feeder contact matrix. Since the feeder lines in the single-connection wiring mode correspond to each other in pairs, the feeder contact matrix is symmetrical and each row and column has only one element that is 1. Accordingly, the real number code is adopted, and the chromosome The number of genes is equal to the total number of feeders. A chromosome represents a planning scheme, and each gene represents the serial number of the interconnected feeder with this feeder and is different from each other. For example, if feeder m is connected to feeder n, the code of the mth gene on the chromosome is n ;

f) Population initialization: The initial population is randomly generated according to the designed genetic coding method, each individual represents a connection structure optimization scheme, and the A _TSC calculation program is called to calculate the values of each objective function according to formula (1) and formula (4). fitness value;

g) Genetic operation: NSGA-II algorithm is used for each population to carry out genetic operation. After non-dominated sorting, the selection operator is selected according to the non-dominated order and crowding degree of the individual according to the round-robin system, and the selected individuals are cross-recombined and mutation operations to form a new offspring population, that is, a new planning scheme;

h) Verification and elite strategy: verify the decoding of the new offspring population generated by genetic operations, judge whether its contact structure meets the constraint conditions, eliminate the schemes that have not passed the verification, and use the elite strategy to select the parent population and the verified Individuals in the collection of offspring populations form a new parent population;

Add 1 to the number of iterations, return to substep c) of substep ① in step 2), until the maximum number of iterations is reached, all non-dominated solutions in the population constitute the Pareto optimal solution set;

3) Selection of the best solution

③Variation coefficient method to determine index weight

There are m objects, each object has n indicators, and the evaluation index value of each object is represented by a vector, recorded as Xi = ( _{xi ,1} , _xi,2 ,..., _xi,n ) ^T , so as to obtain the original evaluation matrix X _i =( _xi,j ) _m×n , normalize the original evaluation matrix, eliminate the influence of dimensions, choose the mean value processing method, and use formula (15) to calculate:

Among them, i=1,2,...,m; j=1,2,...,n;

The coefficient of variation of the jth evaluation index is calculated by formula (16);

Among them, δ _j is the coefficient of variation of the jth evaluation index; d _j is the mean square error of the jth evaluation index, which is calculated by formula (17); is the mean value of the jth evaluation index, calculated by formula (18);

The weight of the jth evaluation index is calculated by formula (19):

Among them, w _j is the weight of the jth evaluation index;

④ Weighted TOPSIS method to select the optimal solution

After determining the index weight according to the coefficient of variation method, use the weighted approximation to the ideal point sorting method (Technique fororder by similarity to an idea solution, TOPSIS) to sort the alternatives, and get the optimal contact structure planning scheme;

In the process of sorting the alternatives by the weighted TOPSIS method, firstly, the original data needs to be established as an initial matrix, and the indicators are processed in the same trend. Since A _TSC is a high-quality index, and the contact construction cost is a low-quality index, as Make the direction of the two indicators consistent, so use the reciprocal method to process the A _TSC index, and get the index matrix X after the same trend, and its expression is shown in formula (20). Normalized matrix Z, whose expression is shown in formula (21), and determine Z ⁺ corresponding to the optimal solution and Z ^- corresponding to the worst solution in the finite solution, and finally, calculate the relationship between each evaluation object and the optimal solution and the most The weighted Euclidean distance D _i ⁺ and D _i ^- between the inferior solutions and the degree of proximity C _i between each evaluation object and the optimal solution, sort the non-inferior solution set according to the size of C _i , and obtain the optimal solution. In the above calculation, See formula (22) to formula (27) for the specific solution method of each variable.

In the formula, Z ⁺ is the index vector corresponding to the optimal scheme in the finite scheme, Z ^- is the index vector corresponding to the worst scheme in the finite scheme, x _i,j is the jth index value of the i-th scheme, z _i,j is the j-th index value of the i-th scheme after normalization, D _i ⁺ is the weighted Euclidean formula between each evaluation object and the optimal scheme Distance, D _i ^- is the weighted Euclidean distance between each evaluation object and the worst solution, i=1,2,...,m, m is the number of evaluation objects; j=1,2,...,n, n is the number of evaluation indicators w _j is the weight of the jth index, C _i is the closeness of each evaluation object to the optimal solution, C _i ∈ [0,1], the larger the value of C _i is, the closer the evaluation object is to the optimal solution The higher the value, the better the corresponding planning scheme. Concrete example: A method for optimizing the planning of the distribution network main transformer connection structure considering the maximum power supply capacity and the minimum connection construction cost of the present invention includes the following content:

1) Data processing

The main transformer connection optimization method based on Pareto optimality is used to plan the connection structure of some main transformers in an economic and technological development zone of a city in Northeast China. There are three 66/10kV substations and six main transformers in the planning area, each with a capacity of 40MVA. The main line of the medium-voltage distribution network is selected from three-phase turnkey aluminum core cross-linked polyethylene 300mm ² (YJLV-300) double In operation, the construction cost per unit length is 110,000 yuan/km, the ultimate transmission capacity is 10.65MVA, the depreciation period is 20 years, and the discount rate is 0.08. The additional wiring fee for crossing unfavorable terrain is 50,000 yuan. When there is no inter-station contact, the A _TSC of this part of the distribution network is 120MVA, and the existing radial network structure is shown in Figure 1.

_Taking A _TSC and C _Link as indexes for evaluating each alternative planning scheme, the index vector becomes Xi = (x _i1 , x _i2 ) ^T = (A _TSC , C _Link ) ^T .

2) Solve the Pareto frontier

A single ring network is used, that is, hand in hand and single connection. Since the connection structure is simple and is the most commonly used connection structure in 10kV cable network, the single connection is taken as an example for calculation, and the NSGA-II algorithm is used to solve equation (14).

minF(L ^f )=[f ₁ (L ^f ),f ₂ (L ^f )] (14)

Among them, f ₁ (L ^f ) is the mapping from the decision variable L ^f to the reciprocal of the maximum power supply capacity of the sub-objective function, which can be obtained by f ₁ (L ^f )=1/A _TSC , and f ₂ (L ^f ) is the decision variable L The mapping from ^f to the sub-objective function considering the connection construction cost of geographic information can be obtained by f ₂ (L ^f )=C _Link ;

Figure 2 shows the Pareto frontier between the maximum power supply capacity of the distribution network in the region and the cost of connection construction obtained from the solution.

3) Choose the best solution

See Table 1 for A _TSC , C _Link and C corresponding to the four planning schemes that do not take into account the influence of geographical factors.

Table 1 Planning scheme of liaison structure without considering geographical factors

plan 1 Scenario 2 Option 3 Option 4 A_TSC(MVA) 141.300 146.625 157.275 159.75 C_Link (10,000 yuan) 47.368 52.227 56.174 60.006 C 0.507 0.542 0.512 0.361 C'_Link (10,000 yuan) 52.368 67.227 71.174 85.006 C' 0.503 0.518 0.548 0.315

In Table 1, A _TSC is the maximum power supply capacity calculated by the distribution network, C _Link is the connection construction cost, and C is the closeness of each scheme to the ideal scheme. According to the coefficient of variation method, combined with the values of A _TSC and C _Link , the weights of A _TSC and C _Link are determined to be 0.517 and 0.483, respectively, and then the weighted TOPSIS method is used to obtain C. Because C is a high-quality index, the scheme 3 is the best Excellent, in which the connection structure of feeders between main transformers is shown in Figure 3.

However, plan 2 shown in Figure 3 faces the problem of increased construction costs due to the crossing of the river by the three connecting lines in practical application, and plans 1, 3, and 4 may also have similar situations. The actual connection construction costs of the four schemes are shown in C' _Link in Table 1. At this time, the weights of A _TSC and C' _Link are 0.521 and 0.479 respectively, and the corresponding degree of closeness to the optimal scheme in practical application is C'. It can be seen that Scheme 2 is no longer the optimal scheme, and scheme 3 becomes the ex post optimal scheme of the main transformer connection structure, and its geographical connection structure diagram is shown in Figure 4.

Further analysis of planning schemes that consider geographical factors before practical application. See Table 2 for A _TSC , C _Link and C corresponding to the four schemes in Figure 3 that take into account the influence of geographical factors. The weights of A _TSC and C _Link are 0.524 and 0.476, respectively. It can be seen that scheme 6 is the ex post optimal scheme of the main transformer connection structure, in which the connection structure of the feeders between the main transformers is shown in Figure 5 and Figure 6.

Table 2 Planning scheme of liaison structure considering geographical factors

Option 5 Option 6 Option 7 Option 8 A_TSC(MVA) 141.300 151.950 157.275 159.75 C_Link (10,000 yuan) 52.368 62.036 65.238 75.897 C 0.504 0.681 0.542 0.328

Comparing Figure 4 and Figure 5 and combining Table 1 and Table 2, it can be seen that the C of the optimal planning scheme (pre-existing optimal scheme) that considers the influence of geographical factors before practical application is 0.681, and the actual application does not consider the influence of geographical factors. The C' of the optimal planning scheme (ex post optimal scheme) that is forced to be considered in application is 0.548, that is, scheme 6 is better than scheme 3.

The specific embodiment used in the present invention has made detailed description to the content of the present invention, but is not limited to this embodiment, and any obvious changes that those skilled in the art do according to the enlightenment of the present invention all belong to the right of the present invention scope of protection.

Claims (1)

1. an MPSC and MCCC considered power distribution network main transformer contact structure optimization planning method is characterized by comprising the following steps:

1) Establishment of connection structure optimization model

Feeder interconnection relation-based power distribution network maximum power supply capacity model

The maximum power supply capacity model based on the feeder interconnection relationship is as follows:

Wherein A is_TSCCalculating the maximum power supply capacity of the obtained power distribution network; f_mIs a feeder line m, and is a feed line,The load of feeder M, M is 1,2, …, M; p_trf·mnTransferring the load quantity to the feeder line N when the feeder line M has an N-1 fault, wherein N is 1,2, …, M; t is_iIs mainly changed into i, P_iThe load of a main transformer i is 1,2, …, N; p_trt·ijThe load quantity transferred to a main transformer j when the main transformer i has an N-1 fault is 1,2, …, N; n is the number of main transformers; m is the number of feeder lines;Is the capacity of the feeder n; f_m∈T_iRepresenting a corresponding bus of a feeder line m from a main transformer i; l is^fis a feeder interconnection matrix, and the expression of the matrix is formula (2), l^f _m,nrepresenting the connection between feeder m and feeder n, when there is a connection between them, l^f _m,n1, otherwise^f _m,n＝0；L^tThe method is a main transformer interconnection matrix, the matrix expression is formula (3), the interconnection relationship between a main transformer i and a main transformer j is represented, and when the interconnection relationship exists between the main transformer i and the main transformer j, l^t _i,j1, otherwise^t _i,j＝0；R'_jis the capacity, R 'of the corrected main transformer j'_j＝R_j－P_F·fsi，R_jIs the capacity of the main transformer j, P_F·fsiThe load of the main transformer j is a single radial line; p_DThe lower limit of the load of a certain heavy-load area; z is a set of all main transformers in the heavy-load area;

Second, contact construction cost model considering geographical factors

Establishing a main transformer contact construction cost model considering geographic factors, see formula (4),

Wherein, C_LinkTo account for the contact construction costs of the geographic factors,The capacity of a connecting line is newly built between the feeder m and the feeder n,Alpha is a tortuosity coefficient;Is composed ofThe unit length of the connecting line under the capacity is the cost; d_mnDefining a head end point of a main feeder line for the distance between the feeder line m and the feeder line n according to the tidal current direction, and taking the distance between end nodes of the main feeder line as the distance between the two feeder lines; w_mnestablishing a tie line cost for the feeder line m and the feeder line n when geographical factors are not considered; z_mnThe more obstacles, Z, the additional construction cost required for traversing unfavorable terrain when laying lines between feeder m and feeder n_mnThe larger, when there is no adverse terrain between the feed m and the feed n,Z_mn＝0；r₀For the discount rate, p is the depreciation age of the line;

Third, contact structure optimization model based on pareto optimization

The interconnection between the main transformers is realized by the interconnection between the feeders, and after the interconnection relationship of the feeders is determined, the interconnection relationship of the main transformers is determined, namely a main transformer interconnection matrix L^tInterconnection matrix L according to feeder^fthe solution process is shown in formula (8) to formula (13) and is expressed as L^fas decision variables, a main transformer contact structure optimization model for simultaneously optimizing a plurality of targets is established, see formula (6),

Wherein L is^fa solution to the multi-objective optimization model; Ω is a set of feasible solutions, F (L)^f) For a target vector having n components, f_k(L^f) To optimize the sub-goals, k is 1,2, …, n; n is F (L)^f) For minimized multi-objective optimization problems, if L^f _lAnd L^f _kare all feasible solutions, and

Then call L^f _ldominating L^f _kIs marked as denotes a dominating relationship, L^f _lDenotes the L feasible solution, L^f _kRepresenting the kth feasible solution if there is no dominance L in the feasible solution set^f _lThe solution of (1) is called L^f _lFor a non-dominant solution, namely a non-inferior solution, of the multi-objective optimization problem, all regions formed by the non-dominant solution become pareto frontiers;

To pass through L^fFind L^tThe following numbering rules are adopted: if N main transformers are arranged in the planning area, the numbers of the N main transformers are 1,2, … and N, and the number of the feeder lines corresponding to each main transformer is M₁，M₂，…，M_Nlet the feeder m be F_mif the feeder is the d feeder of the ith main transformer, i is 1,2, …, N, d is 1,2, …, M_iIf m is obtained according to formula (8), letM represents the total number of feeder lines of the planning area;

Wherein M is_kNumber of feeder lines, M, from main transformer k_k∈{M₀,M₁,M₂，…，M_i-1}，M₀＝0；k＝1,2,…,i-1；i＝1,2,…,N；d＝1,2,…,M_i，

mixing L with^fAnd (3) carrying out block processing according to the main transformer to which the feeder belongs, and obtaining a formula (9):

wherein, M is the total number of feeder lines in the planning area, N is the total number of main transformers in the planning area, M is 1,2, …, M, N is 1,2, …, M, S_i,jFor the feeder line contact relation matrix between the ith main transformer and the jth main transformer after the blocking is finished, for the convenience of writing in the matrix, the method will useis marked as M_(i-1)∑，Is marked as M_(j-1)∑，i＝1,2,…,N，j＝1,2,…,N，d＝1,2,…,M_i，b＝1,2,…,M_jObtaining S_i,jis expressed byas shown in the formula (10),

defining a piecewise function h (X), as shown in formula (11),

Where X represents any matrix, h (X) is the mapping of variable X to the piecewise function,

Changing X to S_i,jin the formula (11), l is obtained^t _i,jAs shown in the formula (12),

L^t＝[h(S_i,j)]_N×N (13)

If only the two sub-optimization goals of "maximum power supply capacity" and "contact construction cost taking geographical factors into account" are considered together, equation (6) is simplified and written as equation (14),

min F(L^f)＝[f₁(L^f),f₂(L^f)] (14)

Wherein f is₁(L^f) As a decision variable L^fMapping function to inverse of sub-optimization objective "maximum power supply capability", by f₁(L^f)＝1/A_TSCObtaining f₂(L^f) As a decision variable L^fMapping function to sub-optimization objective "contact construction cost taking geographical factors into account", by f₂(L^f)＝C_Linkto obtain the result of the above-mentioned method,

2) Solution of contact structure optimization model

solving of contact structure optimization model based on non-dominated sorting genetic algorithm with elite strategy

solving the model by adopting a Non-dominant sequencing Genetic Algorithm (NSGA-II) with an elite strategy, wherein the specific steps of the single-connection wiring model are as follows:

a) and (3) encoding: coding a feeder line contact matrix, adopting real number coding according to the characteristics that the feeder line contact matrix is symmetrical, each row and each column of the feeder line contact matrix are provided with only one element of 1, wherein the number of genes on a chromosome is equal to the total number of the feeder lines, one chromosome represents a planning scheme, each gene represents the number of the feeder lines which are interconnected with the feeder line and is different from each other, and if a feeder line m is connected with a feeder line n, the mth gene on the chromosome is coded into n;

b) Population initialization: randomly generating an initial population according to a designed genetic coding mode, wherein each individual represents a contact structure optimization scheme, and calling A_TSCa calculation program for calculating an adaptive value of each objective function according to the expressions (1) and (4);

c) Genetic manipulation: each population is subjected to genetic operation by adopting an NSGA-II algorithm, after non-dominant sorting is carried out, selection operation is carried out according to the non-dominant sorting and crowding degree of individuals and a race system selection operator, and cross recombination and mutation operation are carried out on the selected individuals to form a new filial generation population, namely a new planning scheme;

d) Checksum elitism strategy: the new offspring population generated by genetic operation is decoded and checked, whether the connection structure of the new offspring population meets the constraint condition is judged, the scheme which is not checked is eliminated, and the elite strategy is utilized to select the parent population and the individuals in the offspring population set after checking to form a new parent population;

adding 1 to the iteration times, and returning to the substep c) of the first substep in the step 2) until the maximum iteration times are reached, wherein all non-dominated solutions in the population form a pareto optimal solution set;

3) Selection of optimal solution

Determining index weight by variation coefficient method

M objects are arranged, each object has n indexes, the evaluation index value of each object is represented by a vector and is marked as X_i＝(x_i,1,x_i,2,...,x_i,n)^TTo obtain the original evaluation matrix X_i＝(x_i,j)_m×nnormalizing the original evaluation matrix to eliminate dimension shadowAnd (3) selecting an averaging processing method, and calculating by using an equation (15):

Wherein i is 1,2, …, m; j is 1,2, …, n;

The coefficient of variation of the jth evaluation index is calculated by equation (16);

wherein, delta_jThe coefficient of variation is the jth evaluation index; d_jthe mean square error of the jth evaluation index is calculated by the formula (17);The mean value of the jth evaluation index is calculated by the formula (18);

The weight of the jth evaluation index is calculated by equation (19):

wherein, w_jThe weight of the jth evaluation index;

② selecting optimal scheme by weighted TOPSIS method

after determining the index weight according to the coefficient of variation method, sorting the alternative schemes by using a weighted approximation ideal point sorting method (TOPSIS) to obtain an optimal contact structure planning scheme;

in implementing weighted TOPSIS method pair alternativeIn the process of sequencing, firstly, an initial matrix needs to be established for the original data, and the indexes are subjected to homotrending treatment aiming at A_TSCThe method is characterized by high-quality index and low-quality index of contact construction cost, and uses reciprocal method to measure A_TSCProcessing the indexes to obtain an index matrix X with the same trend, wherein the expression is shown as a formula (20), normalizing the X to establish a normalization matrix Z, the expression is shown as a formula (21), and determining the Z corresponding to the optimal scheme in the limited schemes⁺Z corresponding to the worst case^-Finally, calculating the weighted Euclidean distance D between each evaluation object and the optimal scheme and the worst scheme_i ⁺And D_i ^-And the degree of closeness C of each evaluation object to the optimal scheme_iaccording to C_iThe non-inferior solution set is sequenced according to the size of the variable to obtain an optimal scheme, in the calculation, the concrete solving method of each variable is shown in the formula (22) to the formula (27),

In the formula, Z⁺for the index vector corresponding to the optimal solution in the finite solution,Z^-for the indicator vector corresponding to the worst case among the finite cases,x_i,jIs the jth index value, z, of the ith scheme_i,jis the j index value of the ith scheme after normalization, D_i ⁺Weighted Euclidean distances, D, of the respective evaluation objects from the optimal solution_i ^-The weighted Euclidean distance between each evaluation object and the worst scheme is represented by i being 1,2, …, m and m being the number of the evaluation objects; j is 1,2, …, n, n is the number of evaluation indexes; w is a_jIs the jth index weight, C_ifor the closeness of each evaluation object to the optimal solution, C_i∈[0,1]，C_iThe larger the value, the higher the proximity of the evaluation object to the optimal plan, i.e. the better the corresponding planning plan.