CN112186738B - Power distribution network rapid reconstruction method based on particle swarm and branch exchange method - Google Patents
Power distribution network rapid reconstruction method based on particle swarm and branch exchange method Download PDFInfo
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- CN112186738B CN112186738B CN202010921956.0A CN202010921956A CN112186738B CN 112186738 B CN112186738 B CN 112186738B CN 202010921956 A CN202010921956 A CN 202010921956A CN 112186738 B CN112186738 B CN 112186738B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/008—Circuit arrangements for ac mains or ac distribution networks involving trading of energy or energy transmission rights
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
- H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
- Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
- Y04S10/00—Systems supporting electrical power generation, transmission or distribution
- Y04S10/50—Systems or methods supporting the power network operation or management, involving a certain degree of interaction with the load-side end user applications
Abstract
The invention relates to a power distribution network rapid reconstruction method based on a particle swarm and a branch exchange method, wherein a power distribution network is a radial topological structure and is regarded as a radial tree, namely a communicated network structure which contains all nodes in the network but does not contain any loop, the particle swarm method and the branch exchange method are combined, each dimension of particles represents one branch exchange operation of the topological structure, and a new radial topological structure is generated by performing D times of branch exchange operations on the topological structure, wherein D is the number of tree branches of the topological structure; therefore, the power distribution network is rapidly reconstructed.
Description
Technical Field
The invention belongs to the field of distribution network automation, and particularly relates to a new distribution network reconfiguration method.
Background
With the rapid development of economy in China, power load is increased year by year, the construction of urban power distribution networks is also rapidly developed, the power distribution networks are usually operated in a closed-loop design and an open loop mode, and power distribution network reconfiguration namely the recombination of power distribution network switches is an effective means for reducing power distribution network loss and improving power quality, so that the power distribution networks are valued by researchers.
In general, algorithms for power distribution network reconstruction can be classified into three categories: a heuristic method represented by a branch exchange method and an optimal flow method, an evolutionary algorithm represented by a particle swarm optimization and a genetic algorithm, and an analysis method represented by branch and bound. The heuristic method has high calculation speed, but the solving result is poor; the analysis method needs to carry out branch-and-bound solution on the large-scale mixed integer problem, so that the solution efficiency is low; compared with the heuristic method, the evolutionary method has a good solving effect and short solving time compared with the analytic method, so that the evolutionary method is concerned.
The distribution network reconstruction is one of important functions of realizing optimal scheduling and operation of distribution automation, and the research on rapid and effective network reconstruction modeling and a calculation method thereof has important practical significance for promoting the intelligent construction of a distribution network. The convergence is poor, and the local optimization is an important difficult problem to be solved urgently by the evolutionary algorithm. When the universal evolutionary algorithm is used for solving the network reconstruction, topological radioactivity judgment needs to be carried out on the random solution, so that the solving efficiency is greatly slowed down. The invention provides a power distribution network rapid reconstruction strategy based on the combination of a particle swarm optimization method and a heuristic method, so that radioactivity judgment on a random solution is not needed, and the solving efficiency is greatly improved.
Disclosure of Invention
In order to solve the problems, the invention provides a power distribution network rapid reconstruction method based on the combination of a particle swarm optimization method and a heuristic method. The technical scheme is as follows:
a power distribution network rapid reconstruction method based on a particle swarm and branch exchange method is characterized in that a power distribution network is a radial topological structure and is regarded as a radial tree, namely a communicated network structure which contains all nodes in the network but does not contain any loop, the particle swarm method and the branch exchange method are combined, each dimension of particles represents one branch exchange operation of the topological structure, a new radial topological structure is generated by performing D times of branch exchange operations on the topological structure, and D is the number of tree branches of the topological structure, and the power distribution network rapid reconstruction method comprises the following steps:
1) initialising a population of particles, initialising the velocity v of the particles i,j Position x i,j I is more than or equal to 1 and less than or equal to N, j is more than or equal to 1 and less than or equal to D, and N is the number of particle populations; d is the particle dimension, the value is equal to the number of the tree branches of the power distribution network, and v is satisfied min ≤v i,j ≤v max ，x min ≤x i,j ≤x max ，v max v min Upper and lower limits of particle velocity, respectively; x is the number of max x min And respectively representing the upper limit and the lower limit of the particle position, generating a particle for D times of branch exchange operation of the topological structure, and generating a radial topological structure through the D times of branch exchange.
2) Calculating the value of the objective function f i,t And t represents the number of iterations of the particle, and the calculation steps are as follows:
a. randomly initializing a radial tree;
b. calculating a commutative branch matrix M according to the current tree;
c. traversing the k-th row element of M to obtain the sum of all elements which are not 0 and marking as q k ；
d. Select the first
The branch represented by a nonzero element is subjected to state exchange with the kth tree branch, wherein ceil () represents an upward rounding function when p k When 1, this operation is not exchanged.
e. B, obtaining the new tree after exchanging, and turning to the step b until D times of exchanging;
f. calculating the network loss of the obtained topology with a value f i,t
g. Updating the velocity and position of particles
h. Calculating the objective function of all the particles in the current generation and updating the optimal position of the history
i. Calculating the next generation of particles until T is T, wherein T is the maximum iteration coefficient of the particles
j. And outputting the result, namely the topological structure corresponding to the optimal particle and the grid loss value.
The steps for determining the exchangeable branch matrix M are as follows:
1) for a connectivity graph G, the number of its tree branches n t Number of connected branches n l One tree is denoted as T, the incidence matrix is denoted as A, and A is expressed as A' according to the following sequence:
2) the loop matrix B' is found according to the following formula:
in the formula: e l Represents n l An order unit matrix.
3) Obtaining the exchangeable branch matrix M according to the following formula:
the branch represented by each element in the matrix M with a row different from 0 is a branch that can be swapped with the row tree branch.
The rapid power distribution network reconstruction strategy based on the combination of the particle swarm optimization method and the heuristic method provided by the invention realizes the advantage complementation of the particle swarm optimization method and the heuristic method, obviously improves the calculation efficiency and the solving quality of the power distribution network, improves the economical efficiency of the power distribution network, reduces the network loss of a system, and effectively saves the labor cost, the time cost and the economic cost.
Detailed description of the invention
Usually, the distribution network operates in a radial topology, i.e. the radial topology can be regarded as a tree, i.e. a connected network structure comprising all nodes in the network but not comprising any loops. The particle swarm method and the branch exchange method are combined, each dimension of particles represents one branch exchange operation of a topological structure, D times of branch exchange operations of the topological structure are carried out, and D is the tree branch number of the topological structure, so that a new radial topological structure is generated. Comprises the following steps:
3) initialising a population of particles, initialising the velocity v of the particles i,j Position x i,j I is more than or equal to 1 and less than or equal to N, j is more than or equal to 1 and less than or equal to D, and N is the number of particle populations; d is the particle dimension, the value is equal to the number of the tree branches of the power distribution network, and v is satisfied min ≤v i,j ≤v max ，x min ≤x i,j ≤x max ，v max v min Upper and lower limits of particle velocity, respectively; x is the number of max x min The upper limit and the lower limit of the particle position are respectively, each particle represents D times of branch exchange operation of the topological structure, and a radial topological structure is generated through the D times of branch exchange.
4) Calculating the value of the objective function f i,t And t represents the number of iterations of the particle, and the calculation steps are as follows:
a. randomly initializing a radial tree
b. Calculating exchangeable branch matrix M from current tree
c. Traversing the k-th row element of M to obtain the sum of all elements which are not 0 and marking as q k
d. Select the first
The branch represented by a nonzero element is subjected to state exchange with the kth tree branch, wherein ceil () represents an upward rounding function when p k When 1, this operation is not performedAnd (4) exchanging.
e. Obtaining new tree after exchange, turning to step b until D times of exchange
f. Calculating the network loss of the obtained topology with a value f i,t
g. Updating the velocity and position of particles
h. Calculating the objective function of all the particles in the current generation and updating the optimal position of the history
i. Calculating the next generation of particles until T is T, wherein T is the maximum iteration coefficient of the particles
j. Output results, i.e. topology and net loss values corresponding to optimal particles
Wherein: the steps for determining the exchangeable branch matrix M are as follows:
4) for a connectivity graph G, the number of its tree branches n t Number of connected branches n l One tree is denoted as T, the incidence matrix is denoted as A, and A is expressed as A' according to the following sequence:
5) the loop matrix B' is found according to the following formula:
in the formula: e l Represents n l An order unit matrix.
6) The matrix M is found according to the following formula:
the branch represented by each element in the matrix M with a row different from 0 is a branch that can be swapped with the row tree branch.
The present invention is further described below.
One, objective function and related constraint
1. Objective function
The specific expression of the objective function is:
in the formula: f is the network active loss, R i Is the resistance of the ith branch, I i For the current flowing in the i-th branch, N b Is the sum of the number of all branches.
2. Constraint conditions
(1) Topological radiation constraint:
λ∈Ψ T (2)
in the formula: λ is the topology of the network, Ψ T Is me, the set of all network structures that satisfy the topological radioactivity constraint.
(2) And (3) line capacity constraint:
S j ≤S j,max ,j＝1,…,N b (3)
in the formula: s j For complex power flowing through branch j, its value is less than maximum limit S j,max 。
(3) Node voltage constraint
V i,min ≤V i ≤V i,max ,i＝1,…,N (4)
In the formula: v i Representing the voltage at node i, at an upper node voltage limit V i,max And a lower limit V i,min In the meantime.
(4) Flow restraint
In the formula: p g,i ，Q g,i Respectively representing active power and reactive power injected by node i, P l,i ，Q l,i Representing active and reactive loads, G, respectively, of node i ij ，B ij Respectively representing the conductance and susceptance, delta, of branch ij ij Representing the phase angle difference of branch ij.
Second, the implementation process
1. Determination of exchangeable leg pairs
For a connectivity graph G, a tree T with a number of tree branches n can be initialized randomly t Number of connected branches n l Its incidence matrix is denoted as a, and a is expressed as a' according to the formula (6):
the loop matrix B' is obtained according to equation (7):
in the formula: e l Represents n l An order unit matrix.
Obtaining a matrix M according to equation (8)
The branch represented by each element in the matrix M with a row different from 0 is a branch that can be swapped with the row tree branch.
2. Particle encoding and decoding
The particles have n in common t Individual dimensions, noted as:
respectively represent n t Secondary tree branch transformation, upper limit of particle position is marked as x max Lower limit is denoted as x min And satisfying the constraint:
x min ≤x i ＜x max ,1≤i≤n t (9)
the description will be given by taking the ith tree branch transformation as an example:
step 1: the matrix M after the previous switching is obtained according to the formula (6) to the formula (8)
Step 2: traversing the ith row element of M to obtain the sum of all elements which are not 0 and marking as q i
And step 3: select the first
The branch represented by a non-zero element is exchanged with the ith branch, wherein ceil () represents an upward rounding function when k i When 1, this operation is not exchanged.
3. Solving process
Step 1: a particle group (a particle group having n particles) is initialized, and a random initial position and velocity are given to each particle.
Step 2: decoding each particle, performing load flow calculation on the decoded network structure, and calculating a particle adaptive value p according to an equation (10):
and step 3: and for each particle, comparing the adaptive value of the current position of the particle with the adaptive value corresponding to the historical optimal position of the particle, and if the adaptive value of the current position is higher, updating the historical optimal position by using the current position.
And 4, step 4: and for each particle, comparing the adaptive value of the current position of the particle with the adaptive value corresponding to the global optimal position of the particle, and updating the global optimal position by using the current position if the adaptive value of the current position is higher.
And 5: the velocity and position of each particle is updated.
Step 6: and returning to the step 2 until the cycle is ended.
And 7: an optimal reconstruction scheme is obtained.
Claims (2)
1. A power distribution network rapid reconstruction method based on a particle swarm and branch exchange method is characterized in that a power distribution network is a radial topological structure and is regarded as a radial tree, namely a communicated network structure which contains all nodes in the network but does not contain any loop, the particle swarm method and the branch exchange method are combined, each dimension of particles represents one branch exchange operation of the topological structure, a new radial topological structure is generated by performing D times of branch exchange operations on the topological structure, and D is the number of tree branches of the topological structure, and the power distribution network rapid reconstruction method comprises the following steps:
1) initialising a population of particles, initialising the velocity v of the particles i,j Position x i,j I is more than or equal to 1 and less than or equal to N, j is more than or equal to 1 and less than or equal to D, and N is the number of particle populations; d is the particle dimension, the value is equal to the number of the tree branches of the power distribution network, and v is satisfied min ≤v i,j ≤v max ，x min ≤x i,j ≤x max ，v max v min Upper and lower limits of particle velocity, respectively; x is the number of max x min Respectively representing the upper limit and the lower limit of the particle position, generating a particle for D times of branch exchange operation of the topological structure, and generating a radial topological structure through the D times of branch exchange;
2) calculating the value of the objective function f i,t And t represents the number of iterations of the particle, and the calculation steps are as follows:
a. randomly initializing a radial tree;
b. calculating a commutative branch matrix M according to the current tree;
c. traversing the k-th row element of M to obtain the sum of all elements which are not 0 and marking as q k ；
d. Select the first
The branch represented by a nonzero element is subjected to state exchange with the kth tree branch, wherein ceil () represents an upward rounding function when p k When 1, this operation is not exchanged;
e. b, obtaining the new tree after exchanging, and turning to the step b until D times of exchanging;
f. calculating the network loss of the obtained topology with a value f i,t ；
g. Updating the speed and position of the particles;
h. calculating all particle target functions of the current generation, and updating the historical optimal position;
i. calculating the next generation of particles until T is T, wherein T is the maximum iteration coefficient of the particles;
j. and outputting the result, namely the topological structure corresponding to the optimal particle and the grid loss value.
2. Method according to claim 1, characterized in that the step of determining the exchangeable branch matrix M is as follows:
1) for a connectivity graph G, the number of its tree branches n t Number of connected branches n l One tree is denoted as T, the incidence matrix thereof is denoted as a, and a is expressed as a' according to the order of formula (1):
2) the loop matrix B' is obtained according to equation (2):
in the formula: e l Represents n l An order identity matrix;
3) obtaining an exchangeable branch matrix M according to the formula (3):
the branch represented by each element in the matrix M whose row is not 0 is a branch that can be exchanged with the row.
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