Distributed power flow optimization method based on quadratic voltage relaxation

Abstract

This invention relates to a distributed power flow optimization method based on secondary voltage relaxation. This invention is applicable to the power system field. The technical solution adopted by this invention is: a distributed power flow optimization method based on secondary voltage relaxation, characterized by: S1, establishing a power system power flow calculation model, including an optimization objective function and power system constraints; S2, applying secondary voltage convex relaxation to the power flow calculation model, where the secondary voltage variables include node variables 'a'. i and b i and line variable a ij b ij s ij and s ji S3. The network structure of the power system is disassembled using the breakpoint method. Coupling constraints are established based on the relationship between the same nodes in the network structure generated by each disassembly. A distributed optimization model is established by combining the power flow calculation model with convex relaxation. S4. The distributed optimization model is solved. When the convergence condition is met, the algorithm terminates, the iteration process ends, and the obtained variable values ​​are the optimization solutions.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of distributed power flow optimization method based on quadratic voltage relaxation.It is suitable for power system field. BACKGROUND

[0002] In recent years, the implementation of the national new energy strategy layout and the formulation and release of related policies have promoted the rapid development of distributed power based on new energy, showing a "point multiple, local high-density grid-connected" situation. As an important part of modern energy system, distributed power has the advantages of low investment, small occupation and high power supply flexibility. Vigorously promoting the development of distributed power is conducive to optimizing energy structure, reducing the consumption of fossil resources such as coal, and realizing low-carbon energy supply, which has positive practical significance for achieving the "double carbon" goal.

[0003] Therefore, in order to reduce the energy loss of the system, under the premise that the power system meets the qualified parameters such as voltage and frequency, the power generation power and other adjustable factors are adjusted to safely, stably and economically distribute electric energy to each power load. Optimizing power energy transmission based on the power grid to achieve overall economy is the research content of the optimal power flow problem. For actual power systems, especially ring-shaped network topology systems, the optimal power flow problem is difficult to accurately solve in polynomial time. Therefore, how to efficiently obtain the global optimal solution is the key and difficulty of the optimal power flow problem of the network power system with distributed power.

[0004] In the solution algorithm of optimal power flow, common methods include linear approximation method, analytical method and heuristic algorithm for local optimal solution or approximate global optimal solution, and convex relaxation algorithm for global optimal solution. In the linear approximation method, since the sine function is approximated as the angle, the accuracy of the optimization solution obtained will be poor when the phase angle difference is large. In the analytical method and heuristic algorithm, due to the non-convexity of the optimal power flow problem, the algorithm cannot simultaneously consider the solving efficiency and solving accuracy.

[0005] In the optimization of network power systems, the sum of the voltage phase angle difference in each ring should be 0°. The existence of this condition makes many common relaxation and approximation algorithms unsuitable for ring topology. For example, in the typical second-order cone relaxation-based power flow optimization algorithm, the angle information is relaxed and can only be restored under specified conditions; and the semi-definite relaxation has a very large system matrix when the system is too large, resulting in reduced calculation efficiency. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a distributed power flow optimization method based on quadratic voltage relaxation in view of the above problems.

[0007] The technical scheme adopted by the application is: A distributed power flow optimization method based on quadratic voltage relaxation, characterized in that:

[0008] S1, a power system power flow calculation model is established, including an optimization objective function and power system constraints;

[0009] S2, quadratic voltage convex relaxation is used for the power flow calculation model, and the quadratic voltage variables include node variables a i and b i , and line variables a ij , b ij , s ij and s ji ;

[0010]

[0011]

[0012] a ij = U i cosθ i U j cosθ j

[0013] b ij = U i sinθ i U j sinθ j

[0014] s ij = U i cosθ i U j sinθ j

[0015] s ji = U j cosθ j U i sinθ i

[0016] wherein each node i voltage variable V i = U i ∠θ i ; each node j voltage variable V j = U j ∠θ j ;

[0017] S3, the network structure of the power system is disassembled by using the breakpoint method, the coupling constraints are established according to the relationship between the same nodes in the network structure generated by disassembling, and the distributed optimization model is established in combination with the power flow calculation model subjected to convex relaxation;

[0018] S4, solving the distributed optimization model, when the convergence condition is met, the algorithm terminates, the iteration process ends, and the obtained variable value is the optimization solution.

[0019] Step S2 includes modifying the optimization objective function in step S1 using a penalty function:

[0020]

[0021] Where f(x) is the optimization objective function in step S1; β ij and β ji are penalty factors, and are fixed constants; is the set of all lines.

[0022] Step S2 includes:

[0023]

[0024] The coupling constraint is established according to the relationship between the same nodes in the network structure generated by each disassembly, including:

[0025] Ax m,a +Bz m =C m

[0026] x m′,a =z m

[0027] Where z m is a vector composed of global variables; x m,a and x m′,a are the corresponding nodes of node m in the network structure generated by each disassembly.

[0028] The improved alternating direction multiplier method is used to solve the distributed optimization model, including:

[0029] In the disassembly generated network structure region a, the iteration process is

[0030]

[0031]

[0032]

[0033] For the selection of variable initial value, the original variable x a initial value can be given arbitrarily, and the initial value of the auxiliary variable ω a is selected as and

[0034] In the process of iterative calculation, the original residual and its convergence criterion are derived, and the expression is

[0035]

[0036]

[0037] The dual residual and its convergence criterion are

[0038]

[0039]

[0040] Where n is the dimension size of the original variable, ∫ ab , ∫ re Take 10 -5 As a constant;

[0041] When the above convergence conditions are met, the algorithm terminates, the iteration process ends, and the obtained variable value is the optimization solution.

[0042] A distributed power flow optimization device based on quadratic voltage relaxation, characterized in that:

[0043] A model establishing module is configured to establish a power system power flow calculation model, including an optimization objective function and power system constraints;

[0044] A quadratic voltage relaxation module is configured to perform quadratic voltage convex relaxation on the power flow calculation model, and the quadratic voltage variables include node variables a i And b i , and line variables a ij , b ij , s ij And s ji ;

[0045]

[0046]

[0047] a ij = U i cosθ i U j cosθ j

[0048] b ij = U i sinθ i U j sinθ j

[0049] s ij = Ui cosθ i U j sinθ j

[0050] s ji =U j cosθ j U i sinθ i

[0051] Wherein, the voltage variable V at each node i i =U i ∠θ i Voltage variable V at each node j j =U j ∠θ j ;

[0052] The network disassembly module is used to disassemble the network structure of the power system using the breakpoint method. It establishes coupling constraints based on the relationship between the same nodes in the network structure generated by each disassembly, and establishes a distributed optimization model by combining the power flow calculation model with convex relaxation.

[0053] The distributed solution module is used to solve distributed optimization models. When the convergence condition is met, the algorithm terminates, the iterative process ends, and the obtained variable values ​​are the optimal solutions.

[0054] A storage medium storing a computer program executable by a processor, characterized in that: when the computer program is executed, it implements the steps of the distributed power flow optimization method based on secondary voltage relaxation.

[0055] A computer device having a memory and a processor, wherein the memory stores a computer program that can be executed by the processor, characterized in that: when the computer program is executed, it implements the steps of the distributed power flow optimization method based on secondary voltage relaxation.

[0056] The beneficial effects of this invention are as follows: Through a series of derivations, this invention creates a distributed optimization model and solution method based on secondary voltage relaxation. Compared with existing methods, this invention has simpler iterations, can quickly achieve optimization solutions, and has good convergence performance, ensuring the feasibility of the solution. At the same time, the distributed architecture ensures the privacy of the system, and the splitting of the large network into smaller networks ensures the accuracy of convex relaxation and the efficiency of the solution. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of a 13-node ring network topology in an embodiment. The topology has 13 nodes and 16 edges.

[0058] Figure 2 for Figure 1The figure shows the schematic diagram of the 13-node ring network system breakpoint. The solid circle in the figure represents the breakpoint, and the hollow circle represents the original node. The left area is area 1, and the right area is area 2.

[0059] Figure 3 The figure shows the change curve of the dual residual in the iteration process in the embodiment, in which the abscissa represents the iteration number, and the ordinate represents the dual residual value.

[0060] Figure 4 The figure shows the change curve of the original residual in the iteration process in the embodiment, in which the abscissa represents the iteration number, and the ordinate represents the original residual value. DETAILED DESCRIPTION

[0061] The embodiment is a distributed power flow optimization method based on quadratic voltage relaxation, which specifically comprises the following steps:

[0062] S1, a power system power flow calculation model is established, including an optimization objective function and power system constraints;

[0063] S1.1, an optimization objective function is established;

[0064] In the power system, the active power variable P i g of the power generation node i is i 2 the quadratic coefficient of the power generation cost of the power generation node i is c i 1 the linear coefficient is c i 0 the constant coefficient is c

[0065]

[0066] S1.2, based on the power system operation condition, the power system constraints are established;

[0067] In the modeling of the power system model, according to the voltage variable V i =U i ∠θ i of each node i in the power grid, the complex power variable of the power generation node i, and the complex power variable of the load node i, the equation and inequality relationship equation is established; at the same time, for the line i~j, the line admittance constant Y ij =G ij -iB ij , the complex power variable S ij flowing through the line i~j, and the equation with the node variable is established.

[0068] The optimization model of the power system mainly involves flow constraints, energy constraints, voltage constraints, and output constraints of each load and power generation; in addition, network topology and wiring mode of the power system need to be considered.

[0069] The equality constraint equation thereof is:

[0070]

[0071] Wherein, * is a conjugate operation.

[0072] The inequality constraint equation thereof is:

[0073]

[0074] S1.3, establishing an optimization model of the power system;

[0075] Through modeling, the mathematical expression of the optimization problem is:

[0076]

[0077] S2, using quadratic voltage convex relaxation for the flow calculation model, and the quadratic voltage variables include node variables a i and b i , and line variables a ij , b ij , s ij and s ji .

[0078] For a node i in the system, define the node variables a i and b i

[0079]

[0080]

[0081] Wherein, each node i voltage variable V i = U i ∠θ i , and cos and sin are cosine function and sine function respectively. For a transmission line i~j, define the line variables

[0082] a ij = U i cosθ i U j cosθ j

[0083] b ij = U i sinθ i U j sinθj

[0084] s ij = U i cos θ i U j sin θ j

[0085] s ji = U j cos θ j U i sin θ i

[0086] where each node i voltage variable V i = U i ∠ θ i , each node j voltage variable V j = U j ∠ θ j .

[0087] According to the new defined variables, the above power flow equation constraint (2) becomes

[0088]

[0089] where P ij , Q ij are the active power and reactive power transmitted on line i ~ j, G ij and B ij are constants.

[0090] The constraint (3) becomes

[0091]

[0092] where According to the range of θ i and the trigonometric function relationship, the values of and can be obtained.

[0093] The six new defined variables can be divided into three groups, but this causes some variables to be repeated. According to the variable definition, there is an internal relationship between the six groups of variables, and the mathematical expression is

[0094]

[0095]

[0096]

[0097]

[0098] By introducing four sets of second-order cones, the above equality constraints can be converted into inequality constraints

[0099]

[0100] In order to ensure the accuracy of the quadratic voltage relaxation, the objective function needs to be modified. In the second-order cone relaxation, it is hoped that the value on the left side of the inequality is as large as possible, so as to ensure the accuracy of the cone relaxation. Therefore, the objective function is modified by using a penalty function:

[0101]

[0102] Where f(x) is the optimization objective function in step S1; β ij And β ji is a penalty factor, and is a fixed constant; is the set of all lines.

[0103] In this objective function, s ij And s ji will continuously take its upper bound, thereby realizing accurate relaxation. For variables a ij And b ij , since they tend to take their upper bounds in the objective function f(x), they are not penalized here.

[0104] Therefore, the expression of the power flow calculation model after the quadratic voltage relaxation is

[0105]

[0106] In the power system, for each node, the node active power, reactive power, node voltage phase angle, and node voltage amplitude need to be determined. In the above quadratic voltage relaxation, the node phase angle information is retained.

[0107] S3, the network structure of the power system is decomposed by using the breakpoint method, and the coupling constraints are established according to the relationship between the same nodes in the network structure generated by each decomposition, and a distributed optimization model is established in combination with the power flow calculation model after convex relaxation.

[0108] According to the location of the distributed power supply, the network is decomposed, so that the distributed power supply is in different distributed networks. Take any node on the ring topology structure in the power system as the breakpoint of the split, and the breakpoint number is m. The split node m and its shadow node m' are defined as x m,a And x m′,a , where x m,a represents the node m in the a region, and x m′,a represents the shadow node m' of the node m in the a region.

[0109] Since a breakpoint splits a node into two points, these two points have the same voltage properties, and the sum of the active and reactive power injected into the two nodes should be equal to that before the node was split. That is:

[0110]

[0111] Where, p m With q m Let Ax be the injected active and reactive power at node m. Rearranging the above equation into Ax m,a +Bx m′,a =C m A, B, and C are all constants.

[0112] Define z as a vector of global variables, which can be used to...

[0113] Ax m,a +Bx m′,a =C m

[0114] Ax m,a +Bx m′,a =C m

[0115] Replace with constraints

[0116] Ax m,a +Bz m =C m

[0117] x m′,a =z m

[0118] Meanwhile, after the line is split, the node variables and the original system variables satisfy the power flow constraints and operation constraints of the power system. Therefore, there are power flow equality constraints and node inequality constraints. The constraints here are all power flow constraints after secondary voltage relaxation. Therefore, the equality constraints are linear and the inequality constraints are convex.

[0119] like Figure 1 , 2 As shown, due to the use of the breakpoint method to decompose the network, new shadow node variables are generated. According to the numbering principle mentioned above, these can be denoted as x. (1,2) x (2,2’) ;x (1,5) x (2,5') ;x (1,6) x (2,6') ;x (1,10) x (2,10')where x contains the complex power and complex voltage variables of the defined break point. Meanwhile, the complex power of the break point needs to satisfy the power flow constraints, thus constraints in (5)-(7) are needed. A global vector z is defined, which contains the information variables needed to be exchanged in the distributed optimization. Since the essence of the break point method is to split a node into two points, the two points have the same voltage attributes and the sum of the injected power is equal to the original node. Therefore, the optimization problem can be written as

[0120]

[0121] s.t.P ij =-(a ij +b ij )G ij +B ij (s ji -s ij )+G ij (a i +b i )

[0122] P ji =-(a ij +b ij )G ij -B ij (s ji -s ij )+G ij (a j +b j )

[0123] Q ij =-(a ij +b ij )B ij -G ij (s ji -s ij )+B ij (a i +b i )

[0124] Q ji =-(a ij +b ij )B ij +G ij (s ji -s ij )+B ij (a j +b j )

[0125] P i =∑P ij =∑P i g-P i c

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132] S4, solve the distributed optimization model by using the improved alternating direction multiplier method based on the above distributed algorithm, when the convergence condition is met, the algorithm is terminated, the iteration process is ended, and the obtained variable value is the optimization solution.

[0133] The simple writing method based on the alternating multiplier method is used to construct the unconstrained Lagrange function as

[0134]

[0135] Wherein, u and u' are dual variables, and u and p are both Lagrange multipliers. Because the global augmented Lagrange function has decomposability, in the specified decomposition network structure region a, it can be written in the following mathematical form

[0136]

[0137] Wherein z is a global variable, x a , u a are regional local variables. From the iteration process of the standard alternating multiplier method

[0138]

[0139]

[0140] u a,m k+1 =u a,m k +x a,m k+1 -z m k+1

[0141] u a,m' k+1 =u a,m' k +Ax a,m' k+1 +Bzm k+1 -C m

[0142] According to u a,m k+1 with u a,m' k+1 The iterative process allows us to solve for z separately. a k+1 An expression relating variables u and x.

[0143] z is expressed using the arithmetic mean method k+1 for

[0144]

[0145] Where a and b represent regions a and b respectively, and the two are adjacent.

[0146] On the other hand, according to z m k+1 The iterative equation is solved by... z can be obtained m k+1 The parsing expression is

[0147]

[0148] Compare z m k+1 From the two expressions, we can see

[0149] -u b,m' k+1 +B -1 u a,m k+1 =0

[0150] Therefore z m k+1 z m k+1 It can be directly expressed using analytical expressions as follows:

[0151]

[0152] Therefore, the dual variable u a,m The iterative steps are as follows

[0153]

[0154] Dual variable u a,m’ The iterative steps are as follows

[0155]

[0156] To simplify the mathematical model of distributed power flow optimization, an auxiliary variable ω is introduced.a , for replacing the dual variable U in each region a in the original ADMM iteration process a , the auxiliary variable ω a is defined as follows:

[0157]

[0158]

[0159] Substituting the above formula, we can get

[0160]

[0161]

[0162] After the above processing, in each region a, the following distributed power flow optimization mathematical model is obtained

[0163]

[0164]

[0165]

[0166] For the selection of variable initial value, the original variable x a initial value can be given arbitrarily, and the initial value of the auxiliary variable ω a is selected as and In the process of iterative calculation, the original residual and its convergence criterion are derived, and the expression is

[0167]

[0168]

[0169] The dual residual and its convergence criterion are

[0170]

[0171]

[0172] Where n is the dimension size of the original variable, and ∫ ab , ∫ re take 10 -5 as a constant. When the above convergence condition is met, the algorithm terminates, the iteration process ends, and the obtained variable value is the optimization solution.

[0173] As Figure 3 , Figure 4 ​As shown, by using the distributed optimization method in the embodiment, the optimization solution can be solved in iteration, and both the dual residual and the original residual can be converged.

[0174] The embodiment also provides a distributed power flow optimization device based on quadratic voltage relaxation, which comprises a model establishing module, a quadratic voltage relaxation module, a network disassembling module and a distributed solving module.

[0175] The model establishing module is used to establish a power system power flow calculation model, including an optimization objective function and power system constraints; the quadratic voltage relaxation module is used to perform quadratic voltage convex relaxation on the power flow calculation model, quadratic voltage variables including node variables a i and b i , and line variables a ij , b ij , s ij and s ji ; the network disassembling module is used to disassemble the network structure of the power system by using a breakpoint method, to establish coupling constraints according to the relationship between the same nodes in the network structure generated by disassembling, and to establish a distributed optimization model in combination with the power flow calculation model subjected to convex relaxation; and the distributed solving module is used to solve 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 the optimization solution.

[0176] The embodiment also provides a storage medium, which stores a computer program capable of being executed by a processor, and the computer program, when executed, implements the steps of the distributed power flow optimization method based on quadratic voltage relaxation in the embodiment.

[0177] The embodiment also provides a computer device, which has a memory and a processor, and the memory stores a computer program capable of being executed by the processor, and the computer program, when executed, implements the steps of the distributed power flow optimization method based on quadratic voltage relaxation in the embodiment.

[0178] The above description of the embodiments is for facilitating those of ordinary skill in the art to understand and apply the present application. Those skilled in the art can easily make various modifications to the above embodiments, and apply the general principles described herein to other embodiments without creative labor. Therefore, the present application is not limited to the above embodiments, and the improvements and modifications of the present application made by those skilled in the art according to the disclosure of the present application should be within the protection scope of the present application.

Claims

1. A distributed power flow optimization method based on secondary voltage relaxation, characterized in that: S1. Establish a power flow calculation model for the power system, including the optimization objective function and power system constraints; S2. The power flow calculation model adopts a second-order voltage convex relaxation, and the second-order voltage variables include node variables and variable a. i and b i and line variable a ij b ij s ij and s ji ; ； ； Each node Voltage Variable Each node Voltage Variable ; S3. The network structure of the power system is decomposed using the breakpoint method. Coupling constraints are established based on the relationship between the same nodes in the network structure generated by each decomposition. A distributed optimization model is established by combining the power flow calculation model with convex relaxation. S4. Solve the distributed optimization model. When the convergence condition is met, the algorithm terminates, the iterative process ends, and the obtained variable values ​​are the optimization solutions. The establishment of coupling constraints based on the relationships between identical nodes in the network structures generated by each decomposition includes: ； ； Among them, z m A vector consisting of global variables; and These are the nodes corresponding to node m in the network structures generated by each decomposition; The distributed optimization model is solved using a distributed algorithm based on an improved alternating direction multiplier method, including: Within region 'a' of the decomposed network structure, the iterative process is as follows: ； Regarding the selection of initial values ​​for variables, the original variable x a initial value Auxiliary variables can be given arbitrarily. The initial value is chosen as and ; During the iterative calculation, the original residuals and their convergence criteria are derived, and their expressions are as follows: ； Dual residuals and their convergence criteria are ； Where n is the size of the original variable dimension, , Take 10 -5 It is a constant; When the above convergence conditions are met, the algorithm terminates, the iterative process ends, and the obtained variable values ​​are the optimal solution. Step S2 involves modifying the optimization objective function in step S1 using a penalty function: ； Where f(x) is the optimization objective function in step S1; and It is a penalty factor and is a fixed constant; This is the set containing all routes; Step S2 includes: 。 2. A distributed power flow optimization device based on secondary voltage relaxation, characterized in that: The model building module is used to build a power flow calculation model for the power system, including the optimization objective function and power system constraints; The secondary voltage relaxation module is used to apply secondary voltage convex relaxation to the power flow calculation model. The secondary voltage variables include node variables and variable a. i and b i and line variable a ij b ij s ij and s ji ; ； ； Each node Voltage Variable Each node Voltage Variable ; The network disassembly module is used to disassemble the network structure of the power system using the breakpoint method. It establishes coupling constraints based on the relationship between the same nodes in the network structure generated by each disassembly, and establishes a distributed optimization model by combining the power flow calculation model with convex relaxation. The distributed solution module is used to solve the distributed optimization model. When the convergence condition is met, the algorithm terminates, the iterative process ends, and the obtained variable values ​​are the optimal solution. The establishment of coupling constraints based on the relationships between identical nodes in the network structures generated by each decomposition includes: ； ； Among them, z m A vector consisting of global variables; and These are the nodes corresponding to node m in the network structures generated by each decomposition; The distributed optimization model is solved using a distributed algorithm based on an improved alternating direction multiplier method, including: Within region 'a' of the decomposed network structure, the iterative process is as follows: ； Regarding the selection of initial values ​​for variables, the original variable x a initial value Auxiliary variables can be given arbitrarily. The initial value is chosen as and ; During the iterative calculation, the original residuals and their convergence criteria are derived, and their expressions are as follows: ； Dual residuals and their convergence criteria are ； Where n is the size of the original variable dimension, , Take 10 -5 It is a constant; When the above convergence conditions are met, the algorithm terminates, the iterative process ends, and the obtained variable values ​​are the optimal solution. The secondary voltage relaxation module includes modifying the optimization objective function in step S1 using a penalty function: ； Where f(x) is the optimization objective function in step S1; and It is a penalty factor and is a fixed constant; This is the set containing all routes; The secondary voltage relaxation module includes: 。 3. A storage medium storing a computer program executable by a processor, characterized in that: When the computer program is executed, it implements the steps of the distributed power flow optimization method based on secondary voltage relaxation as described in claim 1.

4. A computer device comprising a memory and a processor, wherein the memory stores a computer program executable by the processor, characterized in that: When the computer program is executed, it implements the steps of the distributed power flow optimization method based on secondary voltage relaxation as described in claim 1.

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