Application method of second-order cone relaxation modeling in power flow analysis of power system

Abstract

The invention belongs to the technical field of electric power, and relates to an application method of second-order cone relaxation modeling in power flow analysis of an electric power system. The method comprises the following steps: reading network topology, load, power generation data and initial conditions, calculating and standardizing an admittance matrix, converting the data into a second-order cone programming model, defining an objective function and constraint conditions, and converting complex nonlinear constraints into a convex optimization problem, so that the nonlinear constraints which are difficult to process originally become solvable; the constructed model is input into a convex optimization solver, calculation is carried out through the solver, and the optimal value of each variable is obtained; the voltage amplitude and the phase angle are extracted from the solving result, the branch power flow is calculated, and the reasonability and the practical applicability of the solution are ensured by verifying the constraint and the physical range, so that the power flow analysis of the power system is more efficient and reliable; second-order cone relaxation and convex optimization technologies are effectively utilized, and the problems of calculation complexity and nonlinear constraint processing in power flow analysis of the power system are solved.

Description

Technical Field

[0001] The present application belongs to the field of electric power technology, and more specifically, to an application method of second-order cone relaxation modeling in power system flow analysis. Background Art

[0002] Power system flow analysis is a key link in power system engineering, which is mainly used to determine the voltage amplitude, voltage phase angle and power flow of each branch at each node in the system. The purpose of flow analysis is to ensure that the system is stable and reliable in operation and that the load of each component is within a safe range.

[0003] Traditional power flow analysis methods usually use numerical solutions such as the Newton-Raphson method or the Gauss-Seidel method. Although these methods are effective, they have high computational complexity and difficulty in handling nonlinear constraints for large-scale systems; and as the scale of power systems continues to expand, the computational complexity also increases. Traditional computational methods may be inefficient when dealing with large-scale systems. Summary of the invention

[0004] The present invention provides an application method of second-order cone relaxation modeling in power system power flow analysis, which is intended to solve the current technical problems of high complexity and difficulty in handling nonlinear constraints.

[0005] The application method of second-order cone relaxation modeling in power system power flow analysis includes the following steps:

[0006] Step 1: Read network topology data, power generation data and initial conditions; wherein the initial conditions are initial guesses of node voltage load and phase angle; extract the conductance and susceptance of each branch from the network topology data, calculate the admittance matrix based on the extracted conductance and susceptance, and standardize the admittance matrix;

[0007] Step 2: Based on the data read in step 1 and the admittance matrix, a second-order cone programming model is constructed, and the objective function and constraint conditions are defined to obtain the constructed second-order cone programming model;

[0008] Step 3: Input the constructed second-order cone programming model into the convex optimization solver. The solver calculates based on the objective function and constraints provided to obtain the optimal value of each variable.

[0009] Step 4: Extract the voltage amplitude and phase angle of each node from the results obtained by the solver, and use the solved voltage amplitude and phase angle to calculate the power flow of each branch; verify whether all constraints are satisfied and check whether the results are within the actual physical range. If so, execute step 5; if not, execute step 2;

[0010] Step 5: Output analysis report, including node voltage, phase angle and power flow of each branch.

[0011] The second-order cone relaxation modeling method provided by the present invention effectively solves the problems of high complexity and difficulty in handling nonlinear constraints in power system flow analysis. By reading network topology, load, power generation data and initial conditions, and calculating and standardizing the admittance matrix, an accurate basis is provided for subsequent modeling; these data are converted into a second-order cone programming model, the objective function and constraints are defined, and the complex nonlinear constraints are converted into convex optimization problems, so that the nonlinear constraints that were originally difficult to handle become solvable; the constructed model is input into a convex optimization solver, and the solver is used to calculate to obtain the optimal value of each variable; the voltage amplitude and phase angle are extracted from the solution results, and the branch power flow is calculated, and the rationality and practical applicability of the solution are ensured by verifying the constraints and physical range; finally, an analysis report is output, which summarizes the node voltage, phase angle and branch power flow, making the power system flow analysis more efficient and reliable; the second-order cone relaxation and convex optimization technology are effectively used to solve the computational complexity and nonlinear constraint processing problems in power system flow analysis.

[0012] Preferably, the steps of constructing the admittance matrix are as follows:

[0013] Extract conductance and susceptance: Extract the conductance G of each branch based on the network topology data ij and electrosusceptor B ij ;

[0014] Compute the admittance matrix:

[0015] Diagonal elements: diagonal elements Y of each node i ii is the sum of the admittance and susceptance of all branches connected to the node:

[0016] Y ii =∑ j≠i (G ij +jB ij );

[0017] Where: Y ii represents the diagonal element of node i, which represents the total admittance of the node; G ij represents the conductance of the branch between node i and node j; B ij represents the susceptance of the branch between node i and node j; j represents the imaginary unit, which is the complex part;

[0018] Non-diagonal elements: The admittance between node i and node j is the conductance of branch (i, j) plus the imaginary part of the admittance:

[0019] Y ij =-(G ij +jB ij );

[0020] Where: Yij represents the off-diagonal elements between nodes i and j, representing the negative admittance of the branch;

[0021] All diagonal and off-diagonal elements are combined into a negative matrix Y to form a complete admittance matrix.

[0022] Preferably, the constructed second-order cone programming model is as follows:

[0023] minimize f=∑ i ∑ j≠i |S ij | 2 ;

[0024]

[0025] Where: |S ij | represents the power flow of branch (i, j); P i and Q i represents the active power and reactive power of node i; P i gen and Indicates the active and reactive power provided by the generator; G ij and B ij represents the conductance and susceptance of branch (i, j); V i and V j represents the voltage amplitude of node i and node j; θ i and θ j represents the phase angle between node i and node j; ||·||2 represents the second norm, which is used to calculate the length of a two-dimensional vector. Here, it represents the size of the power flow vector from node i to node j; P ij represents the active power from node i to node j; Q ij represents the reactive power from node i to node j; V min and V max Indicates the maximum and minimum limits of the voltage amplitude.

[0026] The beneficial effects of the present invention include:

[0027] The second-order cone relaxation modeling method provided by the present invention effectively solves the problems of high complexity and difficulty in handling nonlinear constraints in power system flow analysis. By reading network topology, load, power generation data and initial conditions, and calculating and standardizing the admittance matrix, an accurate basis is provided for subsequent modeling; these data are converted into a second-order cone programming model, the objective function and constraints are defined, and the complex nonlinear constraints are converted into convex optimization problems, so that the nonlinear constraints that were originally difficult to handle become solvable; the constructed model is input into a convex optimization solver, and the solver is used to calculate to obtain the optimal value of each variable; the voltage amplitude and phase angle are extracted from the solution results, and the branch power flow is calculated, and the rationality and practical applicability of the solution are ensured by verifying the constraints and physical range; finally, an analysis report is output, which summarizes the node voltage, phase angle and branch power flow, making the power system flow analysis more efficient and reliable; the second-order cone relaxation and convex optimization technology are effectively used to solve the computational complexity and nonlinear constraint processing problems in power system flow analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0029] Figure 1 An overall step block diagram provided for an embodiment of the present invention. DETAILED DESCRIPTION

[0030] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0031] See also Figure 1 As shown, the best embodiment of the present invention is further described;

[0032] The application method of second-order cone relaxation modeling in power system power flow analysis includes the following steps:

[0033] Step 1: Read network topology data, power generation data and initial conditions; wherein the initial conditions are initial guesses of node voltage load and phase angle; extract the conductance and susceptance of each branch from the network topology data, calculate the admittance matrix based on the extracted conductance and susceptance, and standardize the admittance matrix;

[0034] Step 2: Based on the data read in step 1 and the admittance matrix, a second-order cone programming model is constructed, and the objective function and constraint conditions are defined to obtain the constructed second-order cone programming model;

[0035] Step 3: Input the constructed second-order cone programming model into the convex optimization solver. The solver calculates based on the objective function and constraints provided to obtain the optimal value of each variable.

[0036] Step 4: Extract the voltage amplitude and phase angle of each node from the results obtained by the solver, and use the solved voltage amplitude and phase angle to calculate the power flow of each branch; verify whether all constraints are satisfied and check whether the results are within the actual physical range. If so, execute step 5; if not, execute step 2;

[0037] Step 5: Output analysis report, including node voltage, phase angle and power flow of each branch.

[0038] The second-order cone relaxation modeling method provided by the present invention effectively solves the problems of high complexity and difficulty in handling nonlinear constraints in power system flow analysis. By reading network topology, load, power generation data and initial conditions, and calculating and standardizing the admittance matrix, an accurate basis is provided for subsequent modeling; these data are converted into a second-order cone programming model, the objective function and constraints are defined, and the complex nonlinear constraints are converted into convex optimization problems, so that the nonlinear constraints that were originally difficult to handle become solvable; the constructed model is input into a convex optimization solver, and the solver is used to calculate to obtain the optimal value of each variable; the voltage amplitude and phase angle are extracted from the solution results, and the branch power flow is calculated, and the rationality and practical applicability of the solution are ensured by verifying the constraints and physical range; finally, an analysis report is output, which summarizes the node voltage, phase angle and branch power flow, making the power system flow analysis more efficient and reliable; the second-order cone relaxation and convex optimization technology are effectively used to solve the computational complexity and nonlinear constraint processing problems in power system flow analysis.

[0039] As a possible implementation of this embodiment, the steps of constructing the admittance matrix are as follows:

[0040] Extract conductance and susceptance: Extract the conductance G of each branch based on the network topology data ij and electrosusceptor B ij ;

[0041] Compute the admittance matrix:

[0042] Diagonal elements: diagonal elements Y of each node i ii is the sum of the admittance and susceptance of all branches connected to the node:

[0043] Y ii =∑ j≠i (Gij +jB ij );

[0044] Where: Y ii represents the diagonal element of node i, which represents the total admittance of the node; G ij represents the conductance of the branch between node i and node j; B ij represents the susceptance of the branch between node i and node j; j represents the imaginary unit, which is the complex part;

[0045] Non-diagonal elements: The admittance between node i and node j is the conductance of branch (i, j) plus the imaginary part of the admittance:

[0046] Y ij =-(G ij +jB ij );

[0047] Where: Y ij represents the off-diagonal elements between nodes i and j, representing the negative admittance of the branch;

[0048] All diagonal and off-diagonal elements are combined into a negative matrix Y to form a complete admittance matrix.

[0049] As a possible implementation of this embodiment, the steps of constructing the second-order cone programming model are as follows:

[0050] Define variables:

[0051] Node voltage amplitude V i : represents the voltage amplitude of each node;

[0052] Node phase angle θ i : represents the voltage phase angle of each node;

[0053] Branch power flow S ij : represents the power flow from node i to node j.

[0054] Objective function: The optimization goal is to minimize power loss:

[0055] minimize f=∑ i ∑ j≠i |S ij | 2 ;

[0056] Build constraints:

[0057] Power balance constraint: For each node i, the power balance constraint is expressed as:

[0058]

[0059] Second-order cone constraint: For each branch (i, j), a second-order cone relaxation is used to express the power flow restriction:

[0060]

[0061] Voltage amplitude limitation: For each node i, the voltage amplitude limitation is expressed as:

[0062] V min ≤V i ≤V max ;

[0063] Phase angle difference limit: Since the difference in phase angle affects the power flow, the limits on the phase angle difference are as follows:

[0064] -π≤θ i -θ j ≤π;

[0065] Integrating the above objective function and constraints into a second-order cone programming model is expressed as follows:

[0066] minimize f=∑ i ∑ j≠i |S ij | 2 ;

[0067]

[0068] Where: S ij represents the power flow of branch (i, j); P i and Q i represents the active power and reactive power of node i; P i gen and Indicates the active and reactive power provided by the generator; G ij and B ij represents the conductance and susceptance of branch (i, j); V i and V j represents the voltage amplitude of node i and node j; θ i and θ j represents the phase angle between node i and node j; ||·||2 represents the second norm, which is used to calculate the length of a two-dimensional vector. Here, it represents the size of the power flow vector from node i to node j; P ij represents the active power from node i to node j; Q ij represents the reactive power from node i to node j; V min and V max Indicates the maximum and minimum limits of the voltage amplitude.

[0069] Using the MOSEK solver, the constructed second-order cone programming model (including the objective function and constraints) is formatted into an input format recognizable by the solver, that is, the objective function and constraints are converted into a standard second-order cone programming form;

[0070] Start the MOSEK solver to solve the problem. The MOSEK solver uses a numerical optimization algorithm to find the variable value that minimizes the objective function to ensure that all constraints are satisfied. The numerical optimization algorithm uses an interior point method.

[0071] The MOSEK solver outputs the optimal value of each variable, including the voltage amplitude and voltage phase angle at each node and the power flow of the branch;

[0072] Verify whether the MOSEK solver results meet all second-order cone constraints and the physical limitations of the power system, and check whether there are calculation errors or unstable solutions:

[0073] The voltage amplitude and voltage phase angle of each node are extracted from the solver results. These data are the basis for further calculation of power flow.

[0074] Calculate the power flow of each branch: Use the extracted voltage magnitude and phase angle to calculate the power flow of each branch:

[0075] P ij =V i ·Y j ·(G ij cos(θ i -θ j )+B ij sin(θ i -θ j ));

[0076] Q ij =V i ·V j ·(-G ij sin(θ i -θ j )+B ij cos(θ i -θ j ));

[0077] Where: P ij and Q ij are the active power and reactive power from node i to node j respectively;

[0078] Verify the constraints:

[0079] Check whether the calculated power flow meets all constraints in the second-order cone programming model. Confirm that the power flow is within the specified physical range.

[0080] Check physical plausibility:

[0081] Verify that the calculation results are consistent with the physical limitations of the actual power system, such as whether the voltage amplitude is within the acceptable range and whether the power flow is within the rated capacity of the branch.

[0082] If the result does not meet the constraints or is not within the physical range, you need to readjust the model or go back to step 2 to rebuild the second-order cone programming model.

[0083] If all constraints and physical limitations are met, proceed to step 5 to generate the final analysis report.

[0084] In this embodiment, by constructing a second-order cone programming model based on the admittance matrix, and defining the objective function and constraints, the originally difficult nonlinear constraint problem is successfully converted into a convex optimization problem. Convex optimization problems have better solvability and stability, so existing efficient optimization algorithms such as the interior point method can be used to solve them. Compared with traditional power flow analysis methods, this method greatly reduces the complexity of calculations and improves the calculation speed. The constructed second-order cone programming model is solved using a convex optimization solver, and the optimal value of each variable can be effectively obtained. Through this efficient optimization solution, the voltage amplitude and phase angle of each node can be accurately obtained, and the method ensures the physical rationality of the solution by verifying the constraints, reducing the calculation error problem that may occur in the traditional method. And in step 4, if the result does not meet the physical constraints, the system will automatically return to step 2 to solve again. This iterative solution process ensures the accuracy of the final result and the stability of the system, and effectively avoids the non-convergence problem. At the same time, based on the optimal value of the solver, the power flow of each branch is further calculated to accurately analyze the power flow distribution of the power system.

[0085] The above are only preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. The application method of second-order cone relaxation modeling in power system power flow analysis is characterized by: The following steps are involved: Step 1: Read network topology data, power generation data and initial conditions; The initial conditions are initial guesses of node voltage loads and phase angles; The conductance and susceptance of each branch are extracted from the network topology data, the admittance matrix is ​​calculated based on the extracted conductance and susceptance, and the admittance matrix is ​​standardized; Step 2: Based on the data read in step 1 and the admittance matrix, a second-order cone programming model is constructed, and the objective function and constraint conditions are defined to obtain the constructed second-order cone programming model; Step 3: Input the constructed second-order cone programming model into the convex optimization solver. The solver calculates based on the objective function and constraints provided to obtain the optimal value of each variable. Step 4: Extract the voltage amplitude and phase angle of each node from the results obtained by the solver, and use the solved voltage amplitude and phase angle to calculate the power flow of each branch; verify whether all constraints are satisfied and check whether the results are within the actual physical range. If so, execute step 5; if not, execute step 2; Step 5: Output analysis report, including node voltage, phase angle and power flow of each branch.

2. The method for applying the second-order cone relaxation modeling in power system power flow analysis according to claim 1 is characterized in that: The steps of constructing the admittance matrix are as follows: Extract conductance and susceptance: Extract the conductance G of each branch based on the network topology data ij and electrosusceptor B ij ; Compute the admittance matrix: Diagonal elements: diagonal elements Y of each node i ii is the sum of the admittance and susceptance of all branches connected to the node: Y ii =∑ j≠i (G ij +jB ij ); Where: Y ii represents the diagonal element of node i, which represents the total admittance of the node; G ij represents the conductance of the branch between node i and node j; B ij represents the susceptance of the branch between node i and node j; j represents the imaginary unit, which is the complex part; Non-diagonal elements: The admittance between node i and node j is the conductance of branch (i, j) plus the imaginary part of the admittance: Y ij =-(G ij +jB ij ); Where: Y ij represents the off-diagonal elements between nodes i and j, representing the negative admittance of the branch; All diagonal and off-diagonal elements are combined into a negative matrix Y to form a complete admittance matrix.

3. The method for applying the second-order cone relaxation modeling in power system power flow analysis according to claim 1 is characterized in that: The constructed second-order cone programming model is as follows: minimize f=∑ i ∑ j≠i |s ij | 2 ; Where: |S ij | represents the power flow of branch (i, j); P i and Q i represents the active power and reactive power of node i; and Indicates the active and reactive power provided by the generator; G ij and B ij represents the conductance and susceptance of branch (i, j); V i and V j represents the voltage amplitude of node i and node j; θ i and θ j represents the phase angle between node i and node j; ||·||2 represents the second norm, which is used to calculate the length of a two-dimensional vector. Here, it represents the size of the power flow vector from node i to node j; P ij represents the active power from node i to node j; Q ij represents the reactive power from node i to node j; V min and V max Indicates the maximum and minimum limits of the voltage amplitude.

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