CN-119623688-B - Sequence correction second order cone global optimization method suitable for radial power distribution network

CN119623688BCN 119623688 BCN119623688 BCN 119623688BCN-119623688-B

Abstract

The invention provides a sequence correction second order cone global optimization method suitable for a radial power distribution network, which comprises the steps of decoupling an original non-convex optimization problem in a power system by introducing auxiliary variables, converting the original non-convex optimization problem into a double-layer planning problem, carrying out convex correction on an upper layer planning problem by adopting a second order cone relaxation technology, carrying out centralized solution, decomposing a lower layer planning problem into a plurality of quadratic programming sub-problems containing single non-convex quadratic constraint, converting the quadratic programming sub-problems into semi-definite programming sub-problems by using a Shull compensation method, establishing a strong dual gap by using a standard S-procedure, and carrying out iterative calculation and sequence correction on an optimization result of the decoupled upper layer planning problem and the decoupled lower layer planning problem according to an alternate direction multiplier method so as to ensure that the non-convex constraint is strictly established. The invention avoids errors caused by convex relaxation, can effectively ensure the reliability and global optimality of the result, and provides an accurate and reliable mathematical model for the power distribution network with high proportion of renewable energy source duty ratio.

Inventors

DING TAO
BAI XINGZHONG
MA ZHIJIE
HE YUANKANG
YUAN YI
JIA WENHAO
Mu Chenggang
HUANG YUHAN
YANG YUEYANG
ZHANG HONGJI
WANG SHUNQI
ZHANG YUHAN

Assignees

西安交通大学
陕西电力交易中心有限公司
陕西数智能科电力科技有限公司
国家电网有限公司西北分部

Dates

Publication Date: 20260505
Application Date: 20241025

Claims (7)

1. The sequence correction second order cone global optimization method suitable for the radial power distribution network is applied to a photovoltaic bearing capacity evaluation scene with inaccurate convex relaxation in the power distribution network, and is characterized by comprising the following steps: Decoupling an original non-convex optimization problem in a power system according to an auxiliary variable introduced by a sequence correction second order cone algorithm, so as to equivalently convert the original non-convex optimization problem into a double-layer planning problem to cope with non-convexity in a photovoltaic bearing capacity assessment model, wherein the double-layer planning problem comprises an upper-layer planning problem and a lower-layer planning problem, and the photovoltaic bearing capacity assessment model aims at maximizing a distributed photovoltaic grid-connected capacity and minimizing network loss as objective functions: (1) Wherein N PV is a node set configured with a distributed photovoltaic unit, and p t,PV represents the actual active output of the photovoltaic unit of a node t; The equation constraint conditions satisfied by the photovoltaic bearing capacity evaluation model are as follows: (2) (3) (4) (5) (6) Wherein, C i represents a node set taking i as a father node, v i is the square of complex voltage of the node i, l (t,i) is the square of complex current of a branch (t, i), and N θ respectively represent a set containing feeder nodes and a set not containing feeder nodes; 、 representing the active power and the reactive power of the branch (i, F i ), respectively; 、 P i and q i respectively represent the injected active power and the injected reactive power of the node i, s i,PV and s i,L respectively represent the actual output force and the electrical load of the photovoltaic unit of the node i, and j represents the imaginary unit; the inequality constraint conditions satisfied by the photovoltaic bearing capacity evaluation model are as follows: (7) (8) (9) (10) In the formula, , Respectively representing the upper limit and the lower limit of the voltage of the node i; And (3) with Respectively representing the upper and lower limits of the output force of the distributed photovoltaic unit; 、 The upper limit of the current and the upper limit of the active power which are allowed to pass through by the branch circuits (i, F i ) respectively, wherein the lower limit of the left end of the formula (10) is negative, which means that after a distributed power supply is added to part of nodes of the radial power distribution network, local reverse power flow is generated; Adopting a second order cone relaxation technology to carry out convexity on the upper layer planning problem and then carrying out centralized solution; decomposing the lower-layer planning problem into a plurality of quadratic programming sub-problems containing single non-convex quadratic constraint through strategy decomposition; converting the quadratic programming sub-problem into a semi-programming sub-problem through ShuerBu, and establishing a strong dual gap through a standard S-procedure to ensure that the optimal solution of the semi-programming sub-problem is converged to the KKT point of the original non-convex optimization problem; And carrying out iterative calculation and sequence correction on the optimization result of the decoupled upper layer planning problem and the decoupled lower layer planning problem according to an alternate direction multiplier method so as to ensure that the non-convex constraint is strictly established.
2. The method of claim 1, wherein the model for decoupling the original non-convex optimization problem in the power system from the introduced auxiliary variables is: Wherein y is a vector formed by decision variables of the upper layer model, x is a vector formed by decision variables of the lower layer model, g i and h j are equations and inequality constraint conditions of safe operation of the upper layer model, the formed feasible domains are convex sets, M k is a unique non-convex secondary constraint condition of the lower layer model, and N and M are coefficient matrixes of consensus constraint conditions of the upper layer model and the lower layer model respectively.
3. The method according to claim 2, wherein the model for performing centralized solution after the upper layer planning problem is raised by using a second order cone relaxation technique is: Where g i and h j are the equality and inequality constraints for the safe operation of the upper layer model.
4. A method according to claim 3, wherein the model for decomposing the underlying planning problem into a plurality of quadratic programming sub-problems with single non-convex quadratic constraints by policy decomposition is: wherein x i is a lower layer decision variable of the node i, A i 、B i is a quadratic term coefficient in an original objective function of the node i sub-problem and an augmented Lagrangian term of the original objective function, C i is a linear term coefficient in an augmented Lagrangian form, and M i is a unique non-convex quadratic constraint of the node i.
5. The method of claim 4, wherein the model for converting the quadratic programming sub-problem to a semi-programming sub-problem by sulzer is: Wherein v i is the dual variable of the non-convex quadratic constraint of the node i, and gamma i is the maximum feasible upper bound of the optimal solution of the node i dual problem.
6. The method of claim 5, wherein the standard S-procedure is: X 2 if present satisfies: Then x is present to satisfy: The filling condition is that no lambda satisfies: Wherein a 1 、A 2 is an n×n real matrix, b 1 、b 2 is an n×1 real vector, c 1 、c 2 is a real scalar, and x is an n×1 vector.
7. The method according to claim 1, wherein the process of performing iterative computation and sequence correction on the optimization result of the decoupled upper layer planning problem and the decoupled lower layer planning problem according to the alternate direction multiplier method comprises: Initializing the maximum iteration times, and optimally solving an upper model of the decoupled upper planning problem to obtain an upper variable; Solving a lower model of the decoupled lower planning problem according to the upper variable to obtain a lower variable; Judging whether the residual error of the upper layer variable and the lower layer variable is smaller than a preset threshold value or not according to the upper layer variable and the lower layer variable; if the upper and lower layer variable residual errors are smaller than the preset threshold value, ending calculation; If the upper and lower layer variable residuals are not smaller than the preset threshold, updating the Lagrange multiplier, adding one to the iteration times, and optimizing and solving the upper layer variable and the lower layer variable in sequence again until the upper and lower layer variable residuals are smaller than the preset threshold or the iteration times reach the maximum iteration times, and ending calculation.

Description

Sequence correction second order cone global optimization method suitable for radial power distribution network Technical Field The embodiment of the invention relates to the technical field of power distribution network optimization operation, in particular to a sequence correction second order cone global optimization method suitable for a radial power distribution network. Background At present, under the background of a 'double-carbon' target and a novel power system, a large number of distributed power sources represented by wind power photovoltaics are connected into a power distribution network, and the novel power system in China gradually presents the characteristic of high new energy duty ratio. The problems of power distribution network voltage fluctuation, voltage out-of-limit, transformer capacity overload, local reverse and even regional reverse power flow and the like brought by the method are serious, and the traditional power distribution network model is insufficient for supporting accurate calculation and engineering application in certain scenes of a novel power system. The simplified branch tidal current model is widely used in the industry at present, the model reduces the variable relation of the original complex domain into the variable relation of the real domain by applying the simplified condition, and uses different relaxation technologies to relax the original non-convex constraint, thereby reducing the solving difficulty. According to the optimization theory, the accuracy of convex relaxation is closely related to the objective function and boundary conditions of the original problem. However, in an actual power system application scenario, since objective functions are different and boundary conditions to be set in a model are various for application, it is expected that it is extremely difficult to secure the accuracy of convex relaxation by a generalized method. Therefore, a novel power distribution network model with low form complexity, small relaxation error and wide application scene is needed to be provided. Disclosure of Invention In view of the above, the embodiment of the invention provides a sequence correction second order cone global optimization method suitable for a radial distribution network, which is characterized in that auxiliary variables are introduced, the original non-convex optimization problem is decomposed and convex according to the Shuerbu and the S-procedure, the condition that the original non-convex optimization problem is converged to the KKT point is deduced, the problem that the existing radial distribution network model has errors in convex relaxation is solved, and a new solution is provided for the non-convex optimization problem of the radial distribution network. According to a first aspect of the embodiment of the invention, a sequence correction second order cone global optimization method suitable for a radial distribution network is provided, and the sequence correction second order cone global optimization method comprises the steps of decoupling an original non-convex optimization problem in a power system according to an introduced auxiliary variable to equivalently convert the original non-convex optimization problem into a double-layer planning problem, wherein the double-layer planning problem comprises an upper-layer planning problem and a lower-layer planning problem, performing centralized solution after the upper-layer planning problem is subjected to convexity by adopting a second order cone relaxation technology, decomposing the lower-layer planning problem into a plurality of secondary planning sub-problems containing single non-convex secondary constraints through strategy decomposition, converting the secondary planning sub-problems into a semi-planning sub-problem through Shull compensation, establishing a strong dual gap through a standard S-procedure to ensure that the optimal solution of the semi-planning sub-problem is converged to a KKT point of the original non-convex optimization problem, and performing calculation and sequence correction on the optimal result of the decoupled upper-layer planning problem and the decoupled lower-layer problem according to an alternate direction multiplier method to ensure that the non-convex constraints are strictly established. In one implementation, the model for decoupling the original non-convex optimization problem in the power system according to the introduced auxiliary variables is: Wherein y is a vector formed by decision variables of the upper layer model, x is a vector formed by decision variables of the lower layer model, g i and h j are equations and inequality constraint conditions of safe operation of the upper layer model, the formed feasible domains are convex sets, M k is a unique non-convex secondary constraint condition of the lower layer model, and N and M are coefficient matrixes of consensus constraint conditions of the upper layer model and the lower lay