CN106941256A - The power distribution network main transformer contact structure optimization planing method of meter and net capability and minimum contact construction cost - Google Patents

Abstract

The present invention is the power distribution network main transformer contact structure optimization planing method of a kind of meter and net capability and minimum contact construction cost, is characterized in, including：Get in touch with the foundation of model of structural optimization, get in touch with the content such as the solution of model of structural optimization and the selection of optimal case.The present invention is from considering net capability and investment cost is started with, the structure that main transformer gets in touch with model of structural optimization is carried out using feeder line interconnection matrix as decision variable, propose the medium voltage distribution network contact structural optimization method for considering geographic factor, disclose communication relationship of the geographical environment getting in touch with the influence of structure and indicating each feeder line, it is reasonable with methodological science, strong applicability, the advantages of effect is good.

Description

Power distribution network main transformer contact structure optimization planning method considering maximum power supply capacity and minimum contact construction cost

Technical Field

The invention relates to the field of power distribution network planning in a power system, in particular to a power distribution network main transformer contact structure optimization planning method considering maximum power supply capacity and minimum contact construction cost.

Background

With the high-speed development of urban economy, the increasingly tense urban land utilization leads the selection of substation sites and power channel corridors to be very difficult, and because a connecting line is used as a channel for power supply recovery and load transfer, less resources can be utilized, the load transfer capacity between the substation sites is increased, the utilization rate of equipment is improved, the power supply requirements of various user loads of various levels are met while the construction scale is reduced and the land resource consumption is reduced, so that the optimization of a main transformer contact structure becomes an important content for the selection of a power distribution network operation mode and the planning of a grid structure. With the increasing application of the concept of the maximum power supply capacity of the power distribution network to the guidance of the power distribution network planning, at present, a main transformer inter-station contact structure optimization method based on a weighted Voronoi diagram and a main transformer interconnection and N-1 criterion-based power distribution network maximum power supply capacity analysis method, a multi-objective optimization model of a main transformer inter-station contact structure with the purposes of improving regional power supply capacity and simplifying contact channels as basic footholds, a contact channel planning method considering unit power supply capacity cost, a power distribution network connection line bottleneck analysis and transformation method based on the maximum power supply capacity and the like have been proposed. However, in the methods, only the main transformer interconnection matrix is used as a decision variable to carry out optimization research on the communication channels and the communication scale between the main transformers, the communication channels are used as a physical concept, the communication channels are a set formed by the communication branches between the main transformers and do not comprise specific outgoing line numbers, the obtained planning result cannot indicate the number and the position of the communication branches in the channels, the communication relation between specific feeder lines cannot be guided, and meanwhile, the influence of geographic factors is not considered when the communication structure optimization modeling is carried out.

In view of the above, the invention starts from comprehensive consideration of the maximum power supply capacity and the investment cost, constructs the optimization model of the main transformer contact structure by taking the feeder interconnection matrix as a decision variable, provides a medium-voltage distribution network contact structure optimization method considering geographic factors, shows the contact relationship among the feeders and reveals the influence of the geographic environment on the contact structure.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide the optimization planning method for the main transformer contact structure of the power distribution network, which is scientific, reasonable, high in applicability and good in effect, and takes the maximum power supply capacity and the minimum contact construction cost into consideration.

The technical scheme adopted for realizing the purpose of the invention is that the method for optimally planning the contact structure of the main transformer of the power distribution network, which takes the maximum power supply capacity and the minimum contact construction cost into consideration, is characterized by comprising the following steps of:

1) establishment of connection structure optimization model

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

The maximum power supply energy 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, the matrix expression is formula (2),representing the relationship between feeder m and feeder n, and when there is a relationship between them,otherwiseL^tThe method is a main transformer interconnection matrix, the matrix expression is formula (3), which represents the communication relationship between a main transformer i and a main transformer j, when the communication relationship exists between the main transformer i and the main transformer j,otherwiseR'_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

Considering that in the actual engineering, the lines need to pass through the underground tunnel calandria when crossing the highway and need to be comprehensively constructed with the bridge when crossing the river, and the geographic factors which are not favorable for crossing the wiring will additionally increase the line laying cost, a main transformer contact construction cost model considering the geographic factors is established, 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,α is the tortuosity factor;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, Z, when there is no adverse terrain between feeder m and feeder n_mn＝0；r₀In order to achieve the current rate, p is the depreciation age limit of the line, and because the connecting line is only put into use when in fault, the annual operation cost is very low, the construction cost of the connecting line is only considered;

third, contact structure optimization model based on pareto optimization

Generally, a plurality of objective functions in the multi-objective optimization problem cannot be compared and often conflict with each other, the improvement of one objective function is usually at the expense of the value of another objective function, so that the multi-objective optimization problem often comprises a plurality of solutions, the advantages and the disadvantages of the solutions cannot be compared, the solutions are collectively called a pareto solution set, the pareto optimal represents the state that each sub-objective of the problem solution cannot be continuously optimized at the same time, and the main transformer is in communication with each otherThe interconnection is realized by the interconnection among the feeders, so that the interconnection of the main transformer is determined after the interconnection of the feeders 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, ifAndare all feasible solutions, and

then callDominatingIs marked asThe relationship of dominance is represented by,the first possible solution is shown as,representing the k-th feasible solution if no dominance exists in the feasible solution setThe solution of (1) is calledFor 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 a planning area feederN 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 by 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)＝1A_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

Because the connection structure optimization is a large-scale combination optimization problem, the model is solved by adopting a Non-dominant sequencing Genetic Algorithm (NSGA-II) with an elite strategy, and the specific steps of the single-connection wiring model are as follows:

a) and (3) encoding: the feeder line connection matrix is coded, and the feeder line connection matrix is symmetrical due to the fact that the feeder lines in the single-connection mode correspond to each other in pairs, only one element in each row is 1, accordingly, real number coding is adopted, 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 the feeder line m is connected with the feeder line n, the mth gene on the chromosome is coded to be 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, eliminating dimensional influence, selecting a mean processing method, and calculating by using a formula (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,_jthe coefficient of variation is the jth evaluation index; d_jIs the mean square error of the jth evaluation index,calculated by equation (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 the process of realizing the sequencing of the alternative schemes by the weighted TOPSIS method, firstly, an initial matrix needs to be established for the original data, and the homotrending processing is carried out on the indexes, because A_TSCThe method uses reciprocal method for A to obtain the high-quality index and the low-quality index_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, the evaluation objects and the maximum are calculatedWeighted Euclidean distance D between superior and inferior schemes_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.

The planning method for the main transformer contact structure of the power distribution network, which takes the maximum power supply capacity and the minimum contact construction cost into consideration, comprehensively considers the maximum power supply capacity and the investment cost, constructs the optimization model of the main transformer contact structure by taking the feeder interconnection matrix as a decision variable, provides the optimization method for the contact structure of the medium-voltage power distribution network by taking the geographic factors into consideration, reveals the influence of the geographic environment on the contact structure, and shows the contact relationship among all feeders, and has the advantages of scientific and reasonable method, strong applicability, good effect and the like.

Drawings

Fig. 1 is a schematic view of an existing radiation network structure in an economic technology development area of a certain city in northeast;

FIG. 2 is A_TSC-a graphical representation of the pareto frontier condition of the contact construction costs;

FIG. 3 is a schematic diagram of theoretical planning of a main transformer communication structure without consideration of geographic factors;

FIG. 4 is a schematic diagram of a post-event optimal scheme of a main transformer contact structure without considering geographic factors;

FIG. 5 is a schematic diagram of a geographical contact structure of a planning result of a main transformer contact structure taking geographic factors into account;

fig. 6 is a schematic diagram of a main transformer communication structure planning result considering geographic factors.

Detailed Description

The invention is further illustrated below with reference to the figures and examples.

The invention relates to a power distribution network main transformer contact structure planning method considering maximum power supply capacity and minimum contact construction cost, which comprises the following contents:

1) establishment of connection structure optimization model

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

The maximum power supply energy 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·ijIs a main transformerWhen an N-1 fault occurs in i, the load quantity transferred to a main transformer j 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, the matrix expression is formula (2),representing the relationship between feeder m and feeder n, and when there is a relationship between them,otherwiseL^tThe method is a main transformer interconnection matrix, the matrix expression is formula (3), which represents the communication relationship between a main transformer i and a main transformer j, when the communication relationship exists between the main transformer i and the main transformer j,otherwiseR'_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

Considering that in the actual engineering, the lines need to pass through the underground tunnel calandria when crossing the highway and need to be comprehensively constructed with the bridge when crossing the river, and the geographic factors which are not favorable for crossing the wiring will additionally increase the line laying cost, a main transformer contact construction cost model considering the geographic factors is established, 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,α is the tortuosity factor;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, Z, when there is no adverse terrain between feeder m and feeder n_mn＝0；r₀For discount rate, p is the depreciation age of the line, due to the junctorThe system is only put into use when in fault, and the annual operation cost is very low, so that only the construction cost of the connecting line is considered;

third, contact structure optimization model based on pareto optimization

Generally, a plurality of objective functions in a multi-objective optimization problem cannot be compared and often conflict with each other, the improvement of one objective function is usually at the cost of sacrificing the value of another objective function, so that the multi-objective optimization problem often comprises a plurality of solutions, the advantages and the disadvantages of the solutions cannot be compared, the solutions are collectively called a pareto solution set, the pareto optimal represents the state that each sub-target of the problem solution cannot be continuously optimized at the same time, and the main transformer interconnection is realized by the interconnection among feeders, so that the main transformer interconnection relationship is determined after the main transformer interconnection relationship 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, ifAndare all feasible solutions, and

then callDominatingIs marked as< indicates a dominant relationship,the first possible solution is shown as,representing the k-th feasible solution if no dominance exists in the feasible solution setThe solution of (1) is calledFor 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 by 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), can obtainAs 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)＝1A_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

Because the connection structure optimization is a large-scale combination optimization problem, the model is solved by adopting a Non-dominant sequencing Genetic Algorithm (NSGA-II) with an elite strategy, and the specific steps of the single-connection wiring model are as follows:

e) and (3) encoding: the feeder line connection matrix is coded, and the feeder line connection matrix is symmetrical due to the fact that the feeder lines in the single-connection mode correspond to each other in pairs, only one element in each row is 1, accordingly, real number coding is adopted, 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 the feeder line m is connected with the feeder line n, the mth gene on the chromosome is coded to be n;

f) 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);

g) 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;

h) 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, eliminating dimension influence, and selectingUsing an averaging method, the calculation is performed by 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,_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;

weighted TOPSIS method for selecting optimal scheme

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 the process of realizing the sequencing of the alternative schemes by the weighted TOPSIS method, firstly, an initial matrix needs to be established for the original data, and the homotrending processing is carried out on the indexes, because A_TSCThe method uses reciprocal method for A to obtain the high-quality index and the low-quality index_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. Specific examples are as follows: the invention relates to a power distribution network main transformer contact structure optimization planning method considering maximum power supply capacity and minimum contact construction cost, which comprises the following contents:

1) data processing

Main transformer communication optimization method based on pareto optimizationAnd planning the contact structure of part of main transformers in an economic technology development area of a certain city in the northeast. The planning area has 3 66/10kV transformer stations and 6 main transformers, the capacity of each main transformer is 40MVA, and the trunk line of the medium-voltage distribution network selects 300mm of aluminum core crosslinked polyethylene of three-phase system²(YJLV-300) is operated in two groups, the construction cost per unit length is 11 ten thousand yuan/km, the limit transmission capacity is 10.65MVA, the depreciation life is 20 years, and the discount rate is 0.08. The extra wiring across an unfavorable terrain costs 5 ten thousand dollars. When no inter-station contact is carried out, the part of the distribution network A_TSCThe conventional radiation net structure is shown in fig. 1, which is 120 MVA.

A is to be_TSCAnd C_LinkAs an index to evaluate each alternative planning solution, the index vector becomes X_i＝(x_i1,x_i2)^T＝(A_TSC, C_Link)^T。

2) Solving pareto frontier

And a single looped network, namely hand-in-hand single connection, is adopted, and the connection structure is simple and is the most common connection structure in a 10kV cable network, so that the single connection is taken as an example for calculation, and the formula (14) is solved by using an NSGA-II algorithm.

min F(L^f)＝[f₁(L^f),f₂(L^f)](14)

Wherein f is₁(L^f) As a decision variable L^fMapping to the reciprocal of the maximum power supply capacity of the sub-objective function by f₁(L^f)＝1A_TSCObtaining f₂(L^f) As a decision variable L^fMapping of contact construction costs to sub-targeting functions taking into account geographic information may be by f₂(L^f)＝C_LinkObtaining;

fig. 2 is a pareto frontier between the maximum power supply capacity of the distribution network in the area and the contact construction cost obtained through solving.

3) Selecting the optimal scheme

In no account ofA corresponding to four planning schemes influenced by geographic factors_TSC、C_LinkAnd C are shown in Table 1.

TABLE 1 contact Structure planning scheme without consideration of geographic factors

	Scheme 1	Scheme 2	Scheme 3	Scheme 4
					ATSC(MVA)	141.300	146.625	157.275	159.75
CLink(Wanyuan)	47.368	52.227	56.174	60.006
					C	0.507	0.542	0.512	0.361
C'Link(Wanyuan)	52.368	67.227	71.174	85.006
					C'	0.503	0.518	0.548	0.315

A in Table 1_TSCMaximum power capacity, C, calculated for the distribution network_LinkFor the contact construction cost, C is the approach degree of each scheme and the ideal scheme. According to the coefficient of variation method, combining A_TSCAnd C_LinkDetermining A from the numerical value of (A)_TSCAnd C_LinkThe weights of the main transformers are 0.517 and 0.483 respectively, and a weighted TOPSIS method is used for obtaining C, the scheme 3 is optimal because C is a high-quality index, wherein the feeder line communication structure among the main transformers is shown in figure 3.

However, the solution 2 shown in fig. 3 is actually applied to a problem that the construction cost is increased due to the fact that the three links cross the river, and similar situations may exist in the solutions 1, 3 and 4. The actual contact construction cost of the four schemes is shown as C 'in Table 1'_LinkAt this time A_TSCAnd C'_LinkThe weights of (2) and (3) are respectively 0.521 and 0.479, and the corresponding proximity degree to the optimal scheme in practical application is C', it can be seen that the scheme 2 is no longer optimal, and the scheme 3 becomes the post optimal scheme of the main transformer connection structure, and the geographical connection structure diagram is shown in fig. 4.

And further analyzing the planning scheme considering geographic factors before practical application. A corresponding to the four schemes in FIG. 3 for accounting for geographic factor effects_TSC、C_LinkAnd C are shown in Table 2. A. the_TSCAnd C_LinkAre weighted at 0.524 and 0.476, respectively. Scheme 6 is shown as the main transformerThe post optimization scheme of the interconnection structure is shown in fig. 5 and fig. 6.

TABLE 2 contact Structure planning scheme taking into account geographic factors

	Scheme 5	Scheme 6	Scheme 7	Scheme 8
					ATSC(MVA)	141.300	151.950	157.275	159.75
CLink(Wanyuan)	52.368	62.036	65.238	75.897
					C	0.504	0.681	0.542	0.328

As can be seen from comparing fig. 4 and fig. 5 with table 1 and table 2, C of the optimal planning plan (pre-optimal plan) in which the influence of the geographic factors is considered before the actual application is 0.681, and C' of the optimal planning plan (post-optimal plan) in which the influence of the geographic factors is not considered before the actual application but is forced to be considered when the actual application is performed is 0.548, i.e., plan 6 is better than plan 3.

While the present invention has been described in detail and with reference to specific embodiments thereof, it will be apparent to one skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope thereof as defined in the appended claims.

Claims (1)

1. A distribution network main transformer contact structure optimization planning method considering maximum power supply capacity and minimum contact construction cost 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 energy model based on the feeder interconnection relationship is as follows:

$\begin{array}{c}\max A_{TSC}=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{P}_i\\ s.t.\left\{\begin{array}{cc}{P}_{F_m}=\underset{n}{\mathrm{\&Sigma;}}{P}_{trf\&CenterDot;mn}& \\ P_i=\underset{F_m\&Element;T_i}{\mathrm{\&Sigma;}}{P}_{F_m}& \&ForAll;i=1,2,\mathrm{...},N\\ P_{trt\&CenterDot;ij}=\underset{F_m\&Element;T_i,F_n\&Element;T_j}{\mathrm{\&Sigma;}}{l}_{m,n}^f{P}_{trf\&CenterDot;mn}& \\ l_{m,n}^f{P}_{trf\&CenterDot;mn}+P_{F_n}\&le;R_{F_n}& \&ForAll;m,n=1,2,\mathrm{...},M\\ l_{i,j}^t{P}_{trt\&CenterDot;ij}+P_j\&le;R_j^{\&prime;}& \&ForAll;i,j=1,2,\mathrm{...},N\\ P_D\&le;\underset{i\&Element;Z}{\mathrm{\&Sigma;}}{P}_i& \\ P_{F_m}\&le;\underset{Hv\&Element;F_m}{\mathrm{\&Sigma;}}{R}_{Hv}& \end{array}\right.\end{array}---\left(1\right)$

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, the matrix expression is formula (2),representing the relationship between feeder m and feeder n, and when there is a relationship between them,otherwiseL^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

Considering that in the actual engineering, the lines need to pass through the underground tunnel calandria when crossing the highway and need to be comprehensively constructed with the bridge when crossing the river, and the geographic factors which are not favorable for crossing the wiring will additionally increase the line laying cost, a main transformer contact construction cost model considering the geographic factors is established, see formula (4),

$C_{Link}=\underset{i,j=1}{\overset{N}{\&Sigma;}}\underset{F_n\&Element;T_j}{\underset{F_m\&Element;T_i}{\mathrm{\&Sigma;}}}(W_{mn}+Z_{mn})\&times;l_{m,n}^f\&times;\frac{r_0{(r_0+1)}^p}{{(1+r_0)}^p-1}---\left(4\right)$

$W_{mn}=\mathrm{\&alpha;}\&times;c_{mn}\left(R_{F_{mn}}\right)\&times;D_{mn}---\left(5\right)$

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,α is the tortuosity factor;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_mnFor no geographical reasons between feeder m and feeder nThe cost of establishing new connecting lines in prime hours; 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, Z, when there is no adverse terrain between feeder m and feeder n_mn＝0；r₀In order to achieve the current rate, p is the depreciation age limit of the line, and because the connecting line is only put into use when in fault, the annual operation cost is very low, the construction cost of the connecting line is only considered;

third, contact structure optimization model based on pareto optimization

Generally, a plurality of objective functions in a multi-objective optimization problem cannot be compared and often conflict with each other, the improvement of one objective function is usually at the cost of sacrificing the value of another objective function, so that the multi-objective optimization problem often comprises a plurality of solutions, the advantages and the disadvantages of the solutions cannot be compared, the solutions are collectively called a pareto solution set, the pareto optimal represents the state that each sub-target of the problem solution cannot be continuously optimized at the same time, and the main transformer interconnection is realized by the interconnection among feeders, so that the main transformer interconnection relationship is determined after the main transformer interconnection relationship 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),

$\begin{array}{c}\min F\left(L^f\right)=\&lsqb;f_1\left(L^f\right),f_2\left(L^f\right),...,f_n\left(L^f\right)\&rsqb;\\ \begin{array}{cc}s.t.& L^f\&Element;\mathrm{\&Omega;}\end{array}\end{array}---\left(6\right)$

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, ifAndare all feasible solutions, and

$\left\{\begin{array}{cc}{f}_i\left(L_l^f\right)\&le;f_i\left(L_k^f\right),& \&ForAll;i\&Element;\{1,2,...,n\}\\ f_i\left(L_l^f\right)<f_i\left(L_k^f\right),& \&Exists;i\&Element;\{1,2,...,n\}\end{array}\right.---\left(7\right)$

then callDominatingIs marked as< indicates a dominant relationship,the first possible solution is shown as,representing the k-th feasible solution if no dominance exists in the feasible solution setThe solution of (1) is calledFor one non-dominant solution, i.e. non-inferior solution, of the multi-objective optimization problem, all non-dominant solution formsThe resulting region becomes the pareto front;

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;

$m=\left\{\begin{array}{cc}d& i=1\\ \underset{k=1}{\overset{i-1}{\mathrm{\&Sigma;}}}{M}_k+d& i=2,3,...N\end{array}\right.---\left(8\right)$

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 by the formula (10),

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

$h\left(X\right)=\left\{\begin{array}{cc}0& X=0\\ 1& X\&NotEqual;0\end{array}\right.---\left(11\right)$

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),

$l_{i,j}^t=h\left(S_{i,j}\right)=\left\{\begin{array}{cc}0& S_{i,j}=0\\ 1& S_{i,j}\&NotEqual;0\end{array}\right.---\left(12\right)$

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),

minF(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

Because the connection structure optimization is a large-scale combination optimization problem, the model is solved by adopting a Non-dominant sequencing Genetic Algorithm (NSGA-II) with an elite strategy, and the specific steps of the single-connection wiring model are as follows:

a) and (3) encoding: the feeder line connection matrix is coded, and the feeder line connection matrix is symmetrical due to the fact that the feeder lines in the single-connection mode correspond to each other in pairs, only one element in each row is 1, accordingly, real number coding is adopted, 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 the feeder line m is connected with the feeder line n, the mth gene on the chromosome is coded to be n;

b) population initialization: randomly generating an initial population according to a designed genetic coding mode, wherein each individual generationA plan for optimizing the connection structure is called 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, eliminating dimensional influence, selecting a mean processing method, and calculating by using a formula (15):

$x_{i,j}^{\&prime;}=\frac{x_{i,j}-\underset{i}{min}\left\{x_{i,j}\right\}}{\underset{i}{max}\left\{x_{i,j}\right\}-\underset{i}{\min }\left\{x_{i,j}\right\}}---\left(15\right)$

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);

${\mathrm{\&delta;}}_j=d_j/\stackrel{\&OverBar;}{u_j}---\left(16\right)$

wherein,_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);

$d_j=\sqrt{\frac{1}{m-1}\underset{i=1}{\overset{m}{\&Sigma;}}{(x_{i,j}^{\&prime;}-\stackrel{\&OverBar;}{u_j})}^2}---\left(17\right)$

$\stackrel{\&OverBar;}{u_j}=\frac{1}{m}\underset{i=1}{\overset{m}{\&Sigma;}}{x}_{i,j}^{\&prime;}---\left(18\right)$

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

$w_j={\mathrm{\&delta;}}_j/\underset{j=1}{\overset{n}{\&Sigma;}}{\mathrm{\&delta;}}_j---\left(19\right)$

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 the process of realizing the sequencing of the alternative schemes by the weighted TOPSIS method, firstly, an initial matrix needs to be established for the original data, and the homotrending processing is carried out on the indexes, because A_TSCThe method uses reciprocal method for A to obtain the high-quality index and the low-quality index_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 size of the solution is used for sequencing the non-inferior solution sets to obtain the optimal partyIn the above calculation, the specific solving method of each variable is shown in the formula (22) to the formula (27),

$z_{i,j}=x_{i,j}/\sqrt{\underset{i=1}{\overset{m}{\&Sigma;}}{x}_{i,j}^2}---\left(22\right)$

$Z^{+}=\left(z_1^{+},z_2^{+},...,z_n^{+}\right)---\left(23\right)$

$Z^{-}=(z_1^{-},z_2^{-},...,z_n^{-})---\left(24\right)$

$D_i^{+}=\sqrt{\underset{j=1}{\overset{n}{\&Sigma;}}{\&lsqb;w_j(z_{i,j}-z_j^{+})\&rsqb;}^2}---\left(25\right)$

$D_i^{-}=\sqrt{\underset{j=1}{\overset{n}{\&Sigma;}}{\&lsqb;w_j(z_{i,j}-z_j^{-})\&rsqb;}^2}---\left(26\right)$

$C_i=D_i^{-}/(D_i^{+}+D_i^{-})---\left(27\right)$

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.