A three-phase power distribution network topology identification method

Abstract

This invention discloses a method for identifying the topology of a three-phase distribution network, belonging to the field of power grid topology identification technology. The method includes: establishing a nonlinear constraint equation with branch switch states, node voltages, and branch currents as decision variables based on the relationship between voltage, current, and power; establishing an objective function by minimizing the residual between measured and estimated values; establishing a nonlinear topology identification model of the three-phase distribution network based on the nonlinear constraint equation and the objective function; linearizing the nonlinear topology identification model; and solving the linearized topology identification model to obtain the three-phase distribution network topology identification result. Using the three-phase distribution network topology identification method described in this invention, topology identification of three-phase distribution networks under normal operation and network reconfiguration is achieved, and it is applicable to unbalanced distribution networks; it also solves the problem of low accuracy in three-phase distribution network topology identification.

Description

Technical Field

[0001] This invention relates to the field of power grid topology identification technology, and in particular to a method for identifying the topology of a three-phase distribution network. Background Technology

[0002] With the large-scale grid connection of distributed renewable energy sources, the operation and control of distribution networks face new technical challenges. Distribution network analysis (including state estimation, renewable energy integration and optimization, and economic operation) all rely on accurate network topology. Accurate topology acquisition is a crucial foundation for optimized scheduling and intelligent control of distribution networks. However, the limited availability of distribution automation switching equipment in rural distribution networks and the presence of numerous outdated switches lacking communication capabilities make topology identification difficult. Furthermore, frequent reconfiguration operations (such as load balancing and fault recovery) and intermittent switching of distributed power sources cause frequent topology changes, further increasing the complexity of real-time topology identification.

[0003] Common topology identification methods involve manual line inspection, which is time-consuming and labor-intensive. Another approach uses measurement data for distribution network topology identification, addressing the high cost of manual inspection. Currently, measurement-based topology identification methods are mainly divided into model-driven and data-driven methods. Model-driven methods treat line states as binary variables and utilize measured power information to establish a hybrid non-integer linear programming model, solving the topology identification problem. Data-driven methods primarily identify topology by calculating the Pearson correlation coefficient between transformer voltage data and measured voltage data. Some research has also employed deep learning to identify topology structures, but this requires acquiring large amounts of historical operational data.

[0004] The fundamental difference between a three-phase distribution network and a single-phase distribution network lies in the significant interphase admittance among the A, B, and C phases. Branch currents are affected not only by their own phase but also by the coupling effects of other phases. Furthermore, three-phase distribution networks exhibit three-phase imbalance characteristics. Existing model-driven methods are based solely on the linear relationships of single-phase topologies, resulting in models that cannot accurately describe the current and voltage transmission patterns of three-phase distribution networks and hindering precise identification of their topologies. Summary of the Invention

[0005] The purpose of this invention is to provide a method for identifying the topology of a three-phase distribution network, thereby solving the problem of low accuracy in identifying the topology of a three-phase distribution network.

[0006] To achieve the above objectives, the present invention provides a method for identifying the topology of a three-phase distribution network, comprising the following steps: S1. Establish nonlinear constraint equations with branch switch states, node voltages, and branch currents as decision variables by using the relationship between voltage, current, and power. S2. Establish the objective function by minimizing the residual between the measured value and the estimated value; S3. Based on the nonlinear constraint equations and objective function, establish a nonlinear topology identification model for a three-phase distribution network, and linearize the nonlinear topology identification model. S4. The linearized topology identification model is solved using the mixed-integer linear programming method to obtain the topology identification results of the three-phase distribution network.

[0007] Preferably, in step S1, the specific process of establishing the nonlinear constraint equations is as follows: S11. Establish current balance constraints according to Kirchhoff's current law; S12. Considering the influence of branch switch status, voltage difference and branch admittance on the inter-node current, establish branch current constraints. S13. Establish three-phase injection current constraints based on the relationship between three-phase injection current, three-phase power, and voltage.

[0008] Preferably, in step S11, when all switches in the three-phase distribution network are closed, the current balance constraint is: ; In the formula, For nodes i of ph Phase injection current variable, For the line ij Between ph Phase branch current variation, N i For nodes i A set of connected nodes. ph ∈{ A , B , C}, A , B , C It refers to the three phases in a three-phase distribution network.

[0009] Preferably, in S12, the branch current constraint is: ; In the formula, for A The binary variable representing the state of the phase branch switch. for B The binary variable representing the connection state of the phase branch. for C The binary variable representing the connection state of the phase branch. forA Phase self-guided absorber, for B Phase self-guided absorber, for C Phase self-guided absorber, for A, B Alternating admittance, for A, C Alternating admittance, for B, C Alternating admittance, for B, A Alternating admittance, for C, A Alternating admittance, for C, B Alternating admittance, For nodes i of A Phase voltage variable, For nodes i of B Phase voltage variable, For nodes i of C Phase voltage variable, For nodes j of A Phase voltage variable, For nodes j of B Phase voltage variable, For nodes j of C Phase voltage variable, For the line ij Between A Phase branch current variation, For the line ij Between B Phase branch current variation, For the line ij Between C Phase branch current variables.

[0010] Preferably, in step S13, the specific process for establishing the three-phase injection current constraint is as follows: S131. According to the power flow calculation equations, the node injected current and the node injected power satisfy the following formula: ; In the formula, For installation on the node i The total load power per phase measured by the SM on the distribution transformer at the location. For nodes i The voltage variation per phase, Indicates conjugate; S132. Using Taylor expansion, the above formulas for nodal injection current and nodal injection power are linearized to obtain a linear relationship between injection power and injection current in a single phase: ; The three-phase injection current constraint is: ; In the formula, for ph The reference voltage of the phase.

[0011] Preferably, in step S2, the specific process of establishing the objective function includes: S21. Establish an objective function by minimizing the residual between the measured value and the estimated value. The objective function is: ; In the formula, Nodes measured for PMU i of ph Phase voltage, Branches measured for PMU ij of ph Phase current, K1 is the set of distribution network nodes, K2 is the set of branches; S22. Introduce relaxation error into the current balance constraint. e， The relaxed current balance constraint is: ; In the formula, node i of ph Phase relaxation error variable; S23. Minimize the relaxation error in the objective function. The final objective function is: .

[0012] Preferably, in step S3, the linearization process includes the following steps: S31. Linearize the final objective function; Introducing auxiliary variables E , F , G After separately processing the voltage error, current error, and relaxation error in the final objective function, the linearized final objective function is as follows: ; In the formula, For nodes i The absolute value of the real part of the voltage residual. For nodes i The absolute value of the imaginary part of the voltage residual. branch road ij The absolute value of the real part of the current residual. branch road ij The absolute value of the imaginary part of the current residual. For nodes i The absolute value of the real part of the relaxation error. For nodes i The absolute value of the imaginary part of the relaxation error; Introducing objective function linearization to handle inequality constraints: ; In the formula, Re is the real part and Im is the imaginary part; S32. Linearize the branch current constraint; S33. Obtain the final three-phase distribution network topology identification model.

[0013] Preferably, in step S32, the branch current constraint linearization process specifically includes the following steps: S321. Introducing binary auxiliary variables z And inequality constraints handle the product of branch switch state variables ,make The branch current constraint is modified as follows: ; The equivalent constraint is established as follows: ; In the formula, , All A , B , C One of the ones I've chosen; S322, Introducing auxiliary variables The branch current constraint is linearized. The expression is: ; S323, The final branch current constraint after linearization is: ; The linearization of branch current constraints involves the following inequality constraints: ; In the formula, M This is the boundary parameter for the maximum amplitude.

[0014] Preferably, in step S33, the final three-phase distribution network topology identification model is: .

[0015] Preferably, the commercial solvers Cplex and Lingo are used to solve the linearized topology identification model.

[0016] The advantages and positive effects of the three-phase distribution network topology identification method described in this invention are: this invention realizes the topology identification of three-phase distribution networks under normal operation and network reconfiguration, and is applicable to unbalanced distribution networks; it solves the problem of low accuracy in three-phase distribution network topology identification.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a flowchart of the three-phase power distribution network topology identification method of the present invention; Figure 2 This invention provides a three-phase distribution network topology identification method and a three-phase distribution network system coupling relationship diagram. Figure 3 This is an actual wiring diagram of a three-phase distribution network system according to an embodiment of the three-phase distribution network topology identification method of the present invention; Figure 4 This is a three-phase distribution network topology estimation result from an embodiment of the three-phase distribution network topology identification method of the present invention; Figure 5 This refers to the voltage estimation error in an embodiment of the three-phase distribution network topology identification method of the present invention. Figure 6 This refers to the current estimation error in an embodiment of the three-phase distribution network topology identification method of the present invention. Detailed Implementation

[0019] In this application, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. In case of any inconsistency, the meaning set forth in this specification or derived from the content described herein shall prevail. Furthermore, the terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit the scope of this application.

[0020] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0021] like Figure 1 As shown, a method for identifying the topology of a three-phase distribution network includes the following steps: S1. Establish nonlinear constraint equations with branch switch states, node voltages, and branch currents as decision variables by utilizing the relationships between voltage, current, and power. The nonlinear constraint equations consider the coupling relationships of the three-phase distribution network.

[0022] The specific process of establishing the nonlinear constraint equations is as follows: S11. Establish current balance constraints according to Kirchhoff's current law.

[0023] S12. Considering the influence of branch switch status, voltage difference and branch admittance on the inter-node current, establish branch current constraints.

[0024] S13. Establish three-phase injection current constraints based on the relationship between three-phase injection current, three-phase power, and voltage.

[0025] In S11, for a given... N Each node and N L In a three-phase distribution network with multiple branches, assuming all switches are closed, according to Kirchhoff's current law, the node injection current of each phase is equal to the sum of the currents of all branches connected to that phase. The current balance constraint is: ; In the formula, For nodes i of ph Phase injection current variable, For the line ij Between ph Phase branch current variation, N i For nodes i A set of connected nodes. ph ∈{ A , B , C}, A , B , C It refers to the three phases in a three-phase distribution network.

[0026] In S12, the current between two nodes depends on the state of the branch switch, the voltage difference, and the branch admittance. The coupling relationships in a three-phase distribution network are as follows: Figure 2 As shown, in a three-phase distribution network, the branch current constraint is: .

[0027] When considering the state variables of branch switches, the three-phase branch current constraints are as follows: ; In the formula, for A The binary variable representing the state of the phase branch switch. for B The binary variable representing the connection state of the phase branch. for C The binary variable representing the connection state of the phase branch. for A Phase self-guided absorber, for B Phase self-guided absorber, forC Phase self-guided absorber, for A, B Alternating admittance, for A, C Alternating admittance, for B, C Alternating admittance, for B, A Alternating admittance, for C, A Alternating admittance, for C, B Alternating admittance, For nodes i of A Phase voltage variable, For nodes i of B Phase voltage variable, For nodes i of C Phase voltage variable, For nodes j of A Phase voltage variable, For nodes j of B Phase voltage variable, For nodes j of C Phase voltage variable, For the line ij Between A Phase branch current variation, For the line ij Between B Phase branch current variation, For the line ij Between C Phase branch current variables.

[0028] The above formula reflects the relationship between branch current and switch state. Taking phase A as an example, When it is 0, the corresponding branch current The value is 0; for phase B, the mutual admittance between phases A and B is not considered; for phase C, the mutual admittance between phases C and C is not considered.

[0029] In S13, the specific process for establishing three-phase injection current constraints is as follows: S131. According to the power flow calculation equations, the node injected current and the node injected power satisfy the following formula: ; In the formula, For installation on the node iThe total load power per phase measured by the SM on the distribution transformer at the location. For nodes i The voltage variation per phase, Indicates conjugate.

[0030] S132. To address the nonlinear relationship between voltage and current variables in the above equation, a Taylor expansion is used to linearize the formulas for nodal injection current and nodal injection power, resulting in a linear relationship between injection power and injection current in a single phase: .

[0031] The above formula is the calculation expression for single-phase. When considering a three-phase distribution network, the three-phase injection current constraint is: ; In the formula, for ph The reference voltage of the phase.

[0032] Assumption A The phase reference voltage amplitude is 1, and the phase is 0. According to the phase relationship, B , C The reference voltage value for the phase is: In the formula, For phase rotation operator, the value is... .

[0033] Finally, the relationship between the three-phase injection current, three-phase power, and voltage is obtained as follows: .

[0034] S2. Establish the objective function by minimizing the residual between the measured value and the estimated value.

[0035] The specific process of establishing the objective function includes: S21. Establish an objective function by minimizing the residual between the measured value and the estimated value. The objective function is: ; In the formula, Nodes measured for PMU i of ph Phase voltage, Branches measured for PMU ij of ph Phase current, K1 is the set of distribution network nodes, K2 is the set of branches.

[0036] In steps S22 and S13, an approximation was made to the relationship between the injected current and power. This results in the sum of the branch currents not necessarily being exactly equal to the injected current. To ensure the solvability of the optimization problem, a relaxation error is introduced into the current balance constraint. e， After relaxing the KCL equations, the relaxed current balance constraint is: ; In the formula, node i of ph Phase relaxation error variable.

[0037] S23. To prevent excessive relaxation from causing the calculated value to differ too much from the actual value, the relaxation error is minimized in the objective function. The final objective function is: .

[0038] S3. Establish a nonlinear topology identification model for a three-phase distribution network based on nonlinear constraint equations and objective functions, and then linearize the nonlinear topology identification model.

[0039] The linearization process includes the following steps: S31. Linearize the final objective function.

[0040] For the absolute value terms existing in the objective function The absolute value term is linearized by introducing an auxiliary variable E and inequality constraints. The equivalent constraints are: .

[0041] Therefore, auxiliary variables are introduced. E , F , G After separately processing the voltage error, current error, and relaxation error in the final objective function, the linearized final objective function is as follows: ; In the formula, For nodes i The absolute value of the real part of the voltage residual. For nodes i The absolute value of the imaginary part of the voltage residual. branch road ij The absolute value of the real part of the current residual. branch road ij The absolute value of the imaginary part of the current residual. For nodes i The absolute value of the real part of the relaxation error. For nodes i The absolute value of the imaginary part of the relaxation error.

[0042] Introduce objective function linearization to handle inequality constraints and make them equivalent to the original constraints: .

[0043] S32. Linearize the branch current constraint.

[0044] The branch current constraint linearization process specifically includes the following steps: S321, Branch current constraints exist Multiplying three variables together can lead to nonlinearity in the model. First, consider the product of the two switching variables. s 1× s 2. Introduce binary auxiliary variables z Inequality constraints are used to handle nonlinear constraints. The equivalent constraint is: .

[0045] Therefore, binary auxiliary variables are introduced. z And inequality constraints handle the product of branch switch state variables ,make The branch current constraint is modified as follows: .

[0046] The equivalent constraint is established as follows: ; In the formula, , All A , B , C One of the ones I've chosen.

[0047] S322. After linearizing the branch current constraints, binary auxiliary variables still exist in the branch current constraints. With voltage variables Non-linear form of multiplication. This applies to multiplication of binary variables with continuous variables. Form, by introducing auxiliary variables And the handling of inequality constraints. The equivalent constraint is: .

[0048] Therefore, auxiliary variables are introduced. The branch current constraint is linearized. The expression is: .

[0049] S323, The final branch current constraint after linearization is: .

[0050] Due to variables Since it's a complex number, consider separating the real and imaginary parts, and then introduce linear constraints that are equivalent to the original problem. The linearization inequality constraint for the branch current constraint is as follows: ; In the formula, M This is the boundary parameter for the maximum amplitude.

[0051] S33. Obtain the final three-phase distribution network topology identification model.

[0052] The final three-phase distribution network topology identification model is as follows: .

[0053] S4. The linearized topology identification model is solved using a mixed-integer linear programming method to obtain the topology identification results of the three-phase distribution network. The commercial solvers Cplex and Lingo are used to solve the linearized topology identification model.

[0054] To facilitate understanding, a simulation test of the method described in this invention is performed in conjunction with a specific embodiment.

[0055] The IEEE 13 distribution system is a three-phase unbalanced distribution system. The system has a base voltage of 4.16 kV, 13 nodes, and 12 lines. Its topology is as follows: Figure 3 As shown. To obtain measurement sets under different operating topologies, a radial topology is first randomly generated for a given distribution system. Then, for a given topology, the Newton-Laurel method is used to calculate the unbalanced power flow to obtain the measurement set. The established model is solved using the Cplex commercial solver, ensuring a globally optimal solution.

[0056] The accuracy of the proposed method is verified by defining the topology estimation accuracy and the estimation errors of voltage and current.

[0057] The accuracy of topology estimation is defined as follows: In the formula, S cor,t For topology t Set the correct number of switches. S tol This represents the total number of switches. T This represents the total number of topologies.

[0058] A total of 22 topologies were verified on the IEEE 13 power distribution system. All 22 topologies could be accurately identified. The topology identification results under normal conditions are as follows: Figure 4 As shown. The estimation errors of node voltages and branch currents are as follows. Figure 5 and Figure 6 As shown, the largest voltage estimation error occurs in phase B of node 5, at 1.2%; the largest current error occurs in phase A of branch 8, at 6.8%.

[0059] To evaluate the performance of the method described in this invention in practical applications, considering the impact of different error levels on the SM measurement data, the errors of the SM measurement data were set to 1%, 5%, 10%, and 20%. The recognition accuracy under different measurement errors was calculated, as shown in Table 1. Table 1 shows that the method described in this invention exhibits good robustness under different measurement error conditions. For the IEEE 13-node system, it can achieve a topology recognition accuracy of over 99% at error levels of 1%, 5%, 10%, and 20%.

[0060] Table 1. Recognition accuracy of this embodiment under different measurement errors

[0061] Therefore, the three-phase distribution network topology identification method described in this invention realizes the topology identification of three-phase distribution networks under normal operation and network reconfiguration, and is applicable to unbalanced distribution networks; it solves the problem of low accuracy in three-phase distribution network topology identification.

[0062] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for topology identification of a three-phase power distribution network, characterized in that, Includes the following steps: S1. Establish nonlinear constraint equations with branch switch states, node voltages, and branch currents as decision variables by using the relationship between voltage, current, and power. S2. Establish the objective function by minimizing the residual between the measured value and the estimated value; In S2, the specific process of establishing the objective function includes: S21. Establish an objective function by minimizing the residual between the measured value and the estimated value. The objective function is: ； In the formula, For the line ij Between ph Phase branch current variation, For nodes i The voltage variation per phase, Nodes measured for PMU i of ph Phase voltage, Branches measured for PMU ij of ph Phase current, K1 is the set of distribution network nodes, K2 is the set of branches, ph ∈{ A , B , C }, A , B , C For three phases in a three-phase distribution network; S22. Introduce relaxation error into the current balance constraint. e， The relaxed current balance constraint is: ； In the formula, For nodes i of ph Phase relaxation error variable, For nodes i of ph Phase injection current variable, N i For nodes i A set of connected nodes; S23. Minimize the relaxation error in the objective function. The final objective function is: ； S3. Based on the nonlinear constraint equations and objective function, establish a nonlinear topology identification model for a three-phase distribution network, and linearize the nonlinear topology identification model. In step S3, the linearization process includes the following steps: S31. Linearize the final objective function; Introducing auxiliary variables E , F , G After separately processing the voltage error, current error, and relaxation error in the final objective function, the linearized final objective function is as follows: ； In the formula, For nodes i The absolute value of the real part of the voltage residual. For nodes i The absolute value of the imaginary part of the voltage residual. branch road ij The absolute value of the real part of the current residual. branch road ij The absolute value of the imaginary part of the current residual. For nodes i The absolute value of the real part of the relaxation error. For nodes i The absolute value of the imaginary part of the relaxation error; Introducing objective function linearization to handle inequality constraints: ； In the formula, Re is the real part and Im is the imaginary part; S32. Linearize the branch current constraint; S33. Obtain the final three-phase distribution network topology identification model; S4. The linearized topology identification model is solved using the mixed-integer linear programming method to obtain the topology identification results of the three-phase distribution network.

2. The method for identifying the topology of a three-phase distribution network according to claim 1, characterized in that, In S1, the specific process of establishing the nonlinear constraint equations is as follows: S11. Establish current balance constraints according to Kirchhoff's current law; S12. Considering the influence of branch switch status, voltage difference and branch admittance on the inter-node current, establish branch current constraints. S13. Establish three-phase injection current constraints based on the relationship between three-phase injection current, three-phase power, and voltage.

3. The method for identifying the topology of a three-phase distribution network according to claim 2, characterized in that: In S11, when all switches in the three-phase distribution network are closed, the current balance constraint is: 。 4. The method for identifying the topology of a three-phase distribution network according to claim 3, characterized in that, In S12, the branch current constraint is: ； In the formula, for A The binary variable representing the state of the phase branch switch. for B The binary variable representing the connection state of the phase branch. for C The binary variable representing the connection state of the phase branch. for A Phase self-guided absorber, for B Phase self-guided absorber, for C Phase self-guided absorber, for A, B Alternating admittance, for A, C Alternating admittance, for B, C Alternating admittance, for B, A Alternating admittance, for C, A Alternating admittance, for C, B Alternating admittance, For nodes i of A Phase voltage variable, For nodes i of B Phase voltage variable, For nodes i of C Phase voltage variable, For nodes j of A Phase voltage variable, For nodes j of B Phase voltage variable, For nodes j of C Phase voltage variable, For the line ij Between A Phase branch current variation, For the line ij Between B Phase branch current variation, For the line ij Between C Phase branch current variables.

5. The method for identifying the topology of a three-phase distribution network according to claim 4, characterized in that, In S13, the specific process of establishing the three-phase injection current constraint is as follows: S131. According to the power flow calculation equations, the node injected current and the node injected power satisfy the following formula: ； In the formula, For installation on the node i The total load power per phase measured by the SM on the distribution transformer at the location. Indicates conjugate; S132. Using Taylor expansion, the above formulas for nodal injection current and nodal injection power are linearized to obtain a linear relationship between injection power and injection current in a single phase: ； The three-phase injection current constraint is: ； In the formula, for ph The reference voltage of the phase.

6. The method for identifying the topology of a three-phase distribution network according to claim 1, characterized in that, In step S32, the branch current constraint linearization process specifically includes the following steps: S321. Introducing binary auxiliary variables z And inequality constraints handle the product of branch switch state variables ,make The branch current constraint is modified as follows: ； The equivalent constraint is established as follows: ； In the formula, , All A , B , C One of the ones I've chosen; S322, Introducing auxiliary variables The branch current constraint is linearized. The expression is: ； S323, The final branch current constraint after linearization is: ； The linearization of branch current constraints involves the following inequality constraints: ； In the formula, M This is the boundary parameter for the maximum amplitude.

7. The method for identifying the topology of a three-phase distribution network according to claim 6, characterized in that, In S33, the final three-phase distribution network topology identification model is as follows: 。 8. The method for identifying the topology of a three-phase distribution network according to claim 7, characterized in that: The commercial solvers Cplex and Lingo were used to solve the linearized topology identification model.

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