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CN114865617A - Distributed power flow optimization method based on large-network and small-network splitting - Google Patents

Distributed power flow optimization method based on large-network and small-network splitting Download PDF

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CN114865617A
CN114865617A CN202210379240.1A CN202210379240A CN114865617A CN 114865617 A CN114865617 A CN 114865617A CN 202210379240 A CN202210379240 A CN 202210379240A CN 114865617 A CN114865617 A CN 114865617A
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陈雨薇
夏冰清
徐志辉
王霄鹤
郦洪柯
王克
徐晗
黄松阁
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PowerChina Huadong Engineering Corp Ltd
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    • H—ELECTRICITY
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Abstract

The invention relates to a distributed power flow optimization method based on large network and small network splitting, which comprises the following steps: selecting any line from a ring topology structure in an electric power system as a broken line, splitting a network topology structure of the electric power system into a plurality of radiation type networks, and generating a breakpoint at the broken line; carrying out convex relaxation on a mathematical optimization model of a radiation type network power system, and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network; and solving the distributed optimization model, and when the convergence condition is met, terminating the algorithm, ending the iteration process, and obtaining the variable value which is the optimization solution. The invention enables the relaxation domain to be gradually reduced through a distributed optimization model for splitting a large network into a small network and a solving method. The invention has simpler iteration, can quickly realize the optimization solution, has good convergence performance and ensures the feasibility of understanding; meanwhile, the distributed architecture ensures the privacy of the inside of the system, and the splitting of the large network and the small network ensures the accuracy and the solving efficiency of the convex relaxation.

Description

Distributed power flow optimization method based on large-network and small-network splitting
Technical Field
The invention relates to a distributed power flow optimization method based on large-network and small-network splitting. The method is suitable for the field of power systems.
Background
At present, with the continuous development of social economy and technology, the power load in the global range is increased year by year, and the power grid is increasingly huge. In order to ensure the reliability of power transmission, a partial ring topology is often presented in a large-scale power grid. Meanwhile, with the access of new energy power generation systems such as solar energy, wind power and the like, the traditional power grid presents a distributed topology according to the characteristics of regions, loads and the like.
In order to improve the energy utilization rate and better schedule the power distribution so as to realize the economic stable operation of the system, a series of optimization means are applied to the power system. The optimization of the power system essentially finds node, branch energy, voltage and current distribution in a system with an optimal target, and the problem has certain difficulty in optimization and solution: on one hand, because the power flow equation of the power system in the optimization is a nonlinear constraint, the optimization problem is a nonlinear programming problem, so that a global optimal solution is difficult to efficiently seek in a short time; on the other hand, the existing system mostly adopts a centralized scheduling control scheme, and is difficult to meet the requirements of actual scenes in power system optimization.
In the traditional power system optimization, a common algorithm has an approximate solution, namely, an approximate optimal solution is obtained by linear approximate fitting of a nonlinear power flow equation, but the solution method cannot ensure the feasibility of the solution; in addition, some analytic solutions such as newton method and PQ decomposition method, and heuristic algorithms developed with artificial intelligence are also gradually applied to power system optimization, and these methods can solve the optimization problem, but it is difficult to ensure the global optimality, convergence and computational efficiency of the solution. Meanwhile, the traditional power system optimization mainly adopts a centralized optimization algorithm, and the system global information is often required to be acquired, so that the privacy of the system is difficult to ensure.
To obtain a globally optimal solution, convex relaxation techniques gradually walk into the human horizon. This is because when an optimization problem is convex, the found local optimal solution is globally optimal. Therefore, a certain relaxation method is adopted to relax the non-convex non-linear constraint, and the relaxation accuracy is proved to be a common method in the field of non-linear programming at present.
In power system optimization, second-order cone relaxation is widely applied due to fast calculation, but node phase angle information is lost due to the existence of relaxation variables; semi-positive definite relaxation is also often used because it contains the variable intact, but it is computationally inefficient.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the existing problems, a distributed power flow optimization method based on large-network and small-network splitting is provided.
The technical scheme adopted by the invention is as follows: a distributed power flow optimization method based on large network and small network splitting is characterized in that:
selecting any line from a ring topology structure in an electric power system as a broken line, splitting a network topology structure of the electric power system into a plurality of radiation type networks, and generating a breakpoint at the broken line;
carrying out convex relaxation on a mathematical optimization model of a radiation type network power system, and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network;
and solving the distributed optimization model, and when the convergence condition is met, terminating the algorithm, ending the iteration process, and obtaining the variable value which is the optimization solution.
Convex relaxation is carried out on the mathematical optimization model of the radiation type network power system by adopting a semi-positive relaxation method.
Coupling constraints between breakpoints on the various radiation-type networks include:
Figure BDA0003591988510000021
Figure BDA0003591988510000022
wherein,
Figure BDA0003591988510000031
and
Figure BDA0003591988510000032
generating variables of break points in each radiation type network for broken lines; x is a vector where a decision variable in the large power system is located; a. b is the mark of the node at the two ends of the broken line; m and n are labels of corresponding radiation type networks; z is a global variable representing the information variable exchanged in the distributed optimization.
The solution distributed optimization model adopts an improved alternating direction multiplier distributed algorithm.
The improved alternating direction multiplier distributed algorithm comprises the following steps:
solution process requiring only iteration of variable x for each radial network
Figure BDA0003591988510000033
The variable z is solved by
Figure BDA0003591988510000034
The original residual error is expressed as
r k ＝x k a，m -z k
Dual residual is
s k ＝-ρ(z k -z k-1 )
The algorithm is terminated by
Figure BDA0003591988510000035
Figure BDA0003591988510000036
Wherein n is the dimension of the original variable, epsilon abs 、ε rel Get 10 -5 Is a constant; and when the convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is the optimized solution.
The utility model provides a distributed trend optimizing apparatus based on big net is torn little net open which characterized in that:
the network splitting module is used for selecting any line on a ring topology structure in the power system as a broken line, splitting the network topology structure of the power system into a plurality of radiation type networks and generating a breakpoint at the broken line;
the convex relaxation module is used for performing convex relaxation on a mathematical optimization model of the radiation type network power system and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network;
and the distributed optimization module is used for solving the distributed optimization model, and when a convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is an optimized solution.
A storage medium having stored thereon a computer program executable by a processor, the computer program comprising: the computer program, when executed, implements the steps of the distributed power flow optimization method based on big and small net splitting.
A computer device having a memory and a processor, the memory having stored thereon a computer program executable by the processor, the computer program comprising: the computer program, when executed, implements the steps of the distributed power flow optimization method based on big and small net splitting.
The invention has the beneficial effects that: the invention enables the relaxation domain to be gradually reduced through a distributed optimization model for splitting a large network into a small network and a solving method. The invention has simpler iteration, can quickly realize the optimization solution, has good convergence performance and ensures the feasibility of understanding; meanwhile, the distributed architecture ensures the privacy of the inside of the system, and the splitting of the large network and the small network ensures the accuracy and the solving efficiency of the convex relaxation.
Drawings
Fig. 1 is a schematic diagram of a five-node ring network topology according to an embodiment, where the topology has 5 nodes and 5 edges.
Fig. 2 is a schematic diagram of a broken line of the five-node ring network system shown in fig. 1, wherein a dotted line part is represented as a broken edge, and an implementation part is an original edge of the system.
Fig. 3 is a schematic diagram of two areas after the five-node ring network system is disconnected, where the left area is area 1 and the right area is area 2. The solid line represents the original line in the system, the solid circle is the original node in the system, the dotted line is the line after the system is broken, and the hollow circle represents the node generated by the broken line.
Fig. 4 is a variation curve of dual residuals in the iteration process, wherein the abscissa represents the number of iterations and the ordinate represents the dual residual value.
Fig. 5 is a variation curve of the original residual error in the iterative process, wherein the abscissa is the iteration number and the ordinate is the original residual error value.
Detailed Description
The embodiment is a distributed power flow optimization method based on large-network and small-network splitting, and specifically includes:
and S1, establishing a mathematical optimization model of the power system.
S1-1, establishing an optimization objective function f (x);
in the power system, the active power variable P generated by the node i i g (ii) a Recording the power generation cost quadratic coefficient of a power generation node i as c i 2 A first order coefficient of c i 1 Constant coefficient of c i 0 (ii) a Recording the set of the power generation nodes as P; the optimal setting of the power generation cost of the whole system as an objective function comprises
Figure BDA0003591988510000051
S1-2, establishing power system constraint based on the power system operation condition;
in modeling a model of an electric power system, a voltage variable V is to be varied according to each node i in an electric network i ＝U i ∠θ i Complex power variable for node i power generation
Figure BDA0003591988510000052
Establishing an equality and an inequality relation equation for the complex power variable of the node i load; while for lines i-j, the line admittance constant Y ij Complex power variable S through which lines i-j flow ij And establishing an equation of the variable between the node and the node. Is a conjugate operation. The optimization model of the power system mainly relates to power flow constraint, energy constraint, voltage constraint and output constraint of each load and power generation; in addition, the network topology, the wiring method, and the like of the power system need to be considered.
Its equation constrains equation g (x) to be:
Figure BDA0003591988510000053
Figure BDA0003591988510000054
the inequality constraint equation h (x) is:
Figure BDA0003591988510000061
Figure BDA0003591988510000062
Figure BDA0003591988510000063
Figure BDA0003591988510000064
s1-3, establishing an optimization model of the power system through modeling, wherein the mathematical expression of the optimization problem is as follows:
min(1)
s.t.(2),(3) (4)
s2, selecting any line on the ring topology structure in the power system as a broken line, splitting the network topology structure of the power system into a plurality of radiation type networks, and generating a break point at the broken line.
S2-1, network decomposition. The network decomposition mainly comprises the step of carrying out network splitting, so that a large-scale ring topology power system is converted into a plurality of radiation type networks.
Through research, effective convex relaxation means can ensure the efficient optimization of the power system of the radiation type network topology, and meanwhile, the method can ensure the relaxation accuracy so as to ensure the solving accuracy and the most solution uniqueness. Based on this, the present embodiment performs network decomposition of the power system based on a wire breaking method, which is to break one line, thereby causing a ring in a ring network structure to be broken into a radiation type.
The break line principle in this embodiment can be broken down into: 1) observing the network topology, and identifying the number of nodes, branches and rings in the graph; 2) extracting nodes and corresponding branches forming a ring in the graph; 3) selecting any one line in each ring as a broken line; 4) splitting the broken line midpoint and corresponding branches connected with the broken line midpoint, and unfolding the original topology in multiple regions to ensure that each region topology is radial; (5)defining the node number connected with the broken line: if the line between the node label a and the node label b is disconnected and the two parts of the network are respectively split into m and n, the breakpoint numbers of the two areas are defined as
Figure BDA0003591988510000065
And
Figure BDA0003591988510000066
after the network decomposition is completed, the original power system is split into a plurality of power systems of radiation type networks, so that distributed operation can be performed on the topology.
To explain the principle of splitting in more detail, reference is made to the accompanying figure 1 as an example. In the ring topology network of fig. 1, there are five nodes, five branches in the figure. It can be seen that nodes 1-2-3 form a ring topology. According to the principle of disconnection, any line in each ring can be disconnected, as shown in fig. 2, and the dotted line between nodes 2-3 represents the line that is selected to be disconnected. The system can be split into two regions as shown in fig. 3 according to the broken line, wherein the region 1 is four nodes, the nodes 1, 2 and 3 are nodes before splitting, the hollow nodes in the figure are marked as (2.5 and 1) according to the numbering principle, and the broken line is a broken line part; among the four nodes in the area 2, the nodes 3, 4 and 5 are nodes of the system before splitting, and the hollow nodes are nodes generated after the network is split due to disconnection. According to the numbering principle, the hollow node in the area 2 is numbered as (2.5, 2). Similarly, the broken line in region 2 is the portion of the broken line in region 2.
S3, performing convex relaxation on the mathematical optimization model of the radiation type network power system, and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network.
S3-1, performing convex relaxation on the optimization problem of the power system: in an electric power system, for each node, node active power, reactive power, node voltage phase angle and node voltage amplitude need to be determined. The present embodiment selects a semi-positive definite relaxation so that the complete phase angle information can be preserved. The semi-definite programming can ensure the solving speed in a small-scale system, so the method is more suitable for carrying out optimal solving on each part of small networks after the large network is split.
This embodiment defines the node i relaxation variable W i And the voltage product variable W between lines i-j ij I.e. by
W i ＝V i V i *
W ij ＝V i V j *
The power flow constraint is thus converted into a linear constraint
Figure BDA0003591988510000071
Figure BDA0003591988510000072
For the relaxation variable W, a semi-positive definite relaxation is adopted
W≥0
While the relaxation variables have corresponding variable ranges according to their definitions
(V min ) 2 ≤W≤(V max ) 2
Thus, the standard optimization form of the optimization problem after convex relaxation is:
Figure BDA0003591988510000081
s3-2, adopting the wire break method to disassemble the network, so as to generate a new node variable which can be marked as x according to the marking principle of wire break (2.5，1) And x (2.5，2) Where the vector x contains the complex power, complex voltage variables of the defined disconnection point. In region 1, x (2.5，1) The node is the midpoint between lines 2-3, so the node voltage is node 2 minus the voltage drop accounting for half the line 2-3 impedance. Similarly, in region 2, x (2.5，2) The node is the midpoint between lines 2-3, and thus the node voltage isNode 3 subtracts the value after taking into account the voltage drop of half the line 2-3 impedance. Meanwhile, the complex power of the node needs to meet the power flow constraint, so that the node has the constraints in the formulas (2) and (3).
A relaxation variable W is defined for the midpoint of the broken line, and the power flow constraint is subjected to semi-positive relaxation as shown in formula (5). Compared with the problem before disconnection, the node is added with a new node generated after disconnection.
And defining a global vector z containing information variables which need to be exchanged in the distributed optimization of the whole system. Since the nature of a broken line is to split a point in the middle of the line into two points, the two points have the same properties. It can be seen that the optimization problem is
Figure BDA0003591988510000091
s.t.S i ＝∑S ij ＝∑S i g -S i c ,
Figure BDA0003591988510000092
Figure BDA0003591988510000093
Figure BDA0003591988510000094
Figure BDA0003591988510000095
W≥0,
(V min ) 2 ≤W≤(V max ) 2 ，
x (2.5，1) {S,W}＝z
x (2.5，2) {S,W}＝z (6)
And S4, solving the distributed optimization model by adopting an improved alternative direction multiplier method-based distributed algorithm, and terminating the algorithm when a convergence condition is met, ending the iteration process, and obtaining a variable value which is an optimized solution.
Firstly, based on the simple writing method of the alternative multiplier method, the unconstrained Lagrangian function is constructed into
Figure BDA0003591988510000096
Wherein u and u' are dual variables, and both u and p are lagrange multipliers. Since the global augmented Lagrangian function has resolvability, it can be written in the following mathematical form
Figure BDA0003591988510000097
Wherein z is a global variable, x a 、u a Is a regional local variable. Known from the iterative process of the standard alternative multiplier method
Figure BDA0003591988510000098
Figure BDA0003591988510000099
u a，m k+1 ＝u a，m k +x a，m k+1 -z a k+1
u a，n k+1 ＝u a，n k +x a，n k+1 -z n k+1
According to u a,m k+1 And u a,n k+1 Respectively solve for z a k+1 Expressions for variables u and x. Z is expressed by means of an arithmetic mean a k+1 Is composed of
Figure BDA0003591988510000101
On the other hand, according to z a k+1 By solving an iterative equation of
Figure BDA0003591988510000102
Can obtain z a k+1 Is expressed as
Figure BDA0003591988510000103
Comparison z a k+1 Two expressions can be found
u k+1 a，m ＝0
u k+1 a，n ＝0
Thus z a k+1 Can be directly expressed by an analytic formula as
Figure BDA0003591988510000104
The constructed augmented Lagrangian function can be written as
Figure BDA0003591988510000105
Solving process in which only the iteration variable x is needed for each solving area
Figure BDA0003591988510000106
And variable z a k+1 The value of (c) can then be directly found by analyzing the expression.
Accordingly, the original residual is expressed as
r k ＝x k a，m -z k
Dual residual is
s k ＝-ρ(z k -z k-1 )
The algorithm is terminated by
Figure BDA0003591988510000107
Figure BDA0003591988510000108
Wherein n is the dimension of the original variable, epsilon abs 、ε rel Get 10 -5 Is a constant. And when the convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is the optimized solution.
Taking the system in fig. 1 as an example, as a simulation test system, the distributed optimization method in the embodiment is adopted in the surfaces in fig. 4 and 5, so that an optimized solution can be solved in an iteration manner, and meanwhile, both the dual residual error and the original residual error can be converged.
This embodiment still provides a distributed trend optimization device based on big net is torn down little net, includes: the device comprises a network splitting module, a convex relaxation module and a distributed optimization module.
In this example, the network splitting module is configured to select any one line as a broken line on a ring topology structure in the power system, split the network topology structure of the power system into a plurality of radiation-type networks, and generate a break point at the broken line; the convex relaxation module is used for performing convex relaxation on a mathematical optimization model of the radiation type network power system, and combining coupling constraints among breakpoints on each radiation type network to form a convex optimization problem; and the distributed optimization module is used for solving the formed convex optimization problem by adopting a distributed algorithm, when a convergence condition is met, the algorithm is terminated, and the obtained variable value is an optimized solution.
The present embodiment also provides a storage medium, on which a computer program executable by a processor is stored, where the computer program when executed implements the steps of the distributed power flow optimization method based on big-net and small-net splitting in this example.
The present embodiment also provides a computer device having a memory and a processor, where the memory stores a computer program executable by the processor, and the computer program when executed implements the steps of the distributed power flow optimization method based on big-net and small-net splitting in this example.

Claims (8)

1. A distributed power flow optimization method based on large network and small network splitting is characterized in that:
selecting any line from a ring topology structure in an electric power system as a broken line, splitting a network topology structure of the electric power system into a plurality of radiation type networks, and generating a breakpoint at the broken line;
carrying out convex relaxation on a mathematical optimization model of a radiation type network power system, and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network;
and solving the distributed optimization model, and when the convergence condition is met, terminating the algorithm, ending the iteration process, and obtaining the variable value which is the optimization solution.
2. The distributed power flow optimization method based on the large-network and small-network splitting as claimed in claim 1, wherein: convex relaxation is carried out on the mathematical optimization model of the radiation type network power system by adopting a semi-positive relaxation method.
3. The distributed power flow optimization method based on large-network and small-network splitting as claimed in claim 1, wherein the coupling constraints between the break points on each radiation-type network comprise:
Figure FDA0003591988500000011
Figure FDA0003591988500000012
wherein,
Figure FDA0003591988500000013
and
Figure FDA0003591988500000014
generating variables of break points in each radiation type network for broken lines; x is a vector where a decision variable in the large power system is located; a. b is the mark of the node at the two ends of the broken line; m and n are labels of corresponding radiation type networks; z is a global variable representing the information variable exchanged in the distributed optimization.
4. The distributed power flow optimization method based on the large-network and small-network splitting as claimed in claim 3, wherein: the solution distributed optimization model adopts an improved alternating direction multiplier distributed algorithm.
5. The distributed power flow optimization method based on large network and small network splitting according to claim 4, wherein the improved alternative direction multiplier distributed algorithm comprises:
solution process requiring only iteration of variable x for each radial network
Figure FDA0003591988500000015
The variable z is solved by
Figure FDA0003591988500000021
The original residual error is expressed as
r k ＝x k a，m -z k
Dual residual is
s k ＝-ρ(z k -z k-1 )
The algorithm is terminated by
Figure FDA0003591988500000022
Figure FDA0003591988500000023
Wherein n is the dimension of the original variable, epsilon abs 、ε rel Get 10 -5 Is a constant; when the convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is the optimized solution.
6. The utility model provides a distributed trend optimizing apparatus based on little net is torn open to big net which characterized in that:
the network splitting module is used for selecting any line on a ring topology structure in the power system as a broken line, splitting the network topology structure of the power system into a plurality of radiation type networks and generating a breakpoint at the broken line;
the convex relaxation module is used for performing convex relaxation on a mathematical optimization model of the radiation type network power system and constructing a distributed optimization model by combining coupling constraints among breakpoints on each radiation type network;
and the distributed optimization module is used for solving the distributed optimization model, and when a convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is an optimized solution.
7. A storage medium having stored thereon a computer program executable by a processor, the computer program comprising: the computer program is executed to realize the steps of the distributed power flow optimization method based on the large-network and small-network splitting of any one of claims 1-5.
8. A computer device having a memory and a processor, the memory having stored thereon a computer program executable by the processor, the computer program comprising: the computer program is executed to realize the steps of the distributed power flow optimization method based on the large-network and small-network splitting of any one of claims 1-5.
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