A distribution network topology identification and line loss calculation method based on basis pursuit algorithm

Abstract

The present invention provides a distribution network topology identification and line loss calculation method based on the basis pursuit algorithm. First, the distribution network system is analyzed and modeled. Through theoretical derivation, a vector containing network topology information is extracted from the model, thereby converting the distribution network topology identification problem into a sparse vector signal solution problem; then the basis pursuit method is used to solve this problem to obtain an estimated value of the distribution network system topology; then, the estimated topology structure is used to calculate the power flow of the distribution network using the Newton-Raphson method to obtain the power distribution and line loss of the distribution network. These data can be used for advanced services such as distribution network line loss analysis and loss reduction measures. Finally, simulation tests were carried out on IEEE standard 9-node and 30-node distribution network systems, demonstrating the feasibility of the above method.

Description

Technical Field

[0001] The present invention relates to the field of distribution network topology identification and line loss calculation in an electric power system. Background Art

[0002] The power system is an integral whole consisting of power plants, transmission networks, distribution networks and power users. The function of the distribution network is to distribute electric energy directly from hub substations to users, or to distribute it to users via distribution substations. Therefore, in the power system, as an important infrastructure to ensure people's livelihood, the distribution network is the final link directly facing the end power users. Its safe and stable operation is directly related to the electricity benefits, quality and reliability of each user.

[0003] Compared with the transmission network, the topology of the distribution network will face more frequent changes. The main reasons include the following three aspects: First, the distribution network is being transformed, expanded and upgraded every day; new substations, new lines, and new user loads often occur in the distribution system. Second, the distribution network is equipped with a large number of switches or knife switches. In order to ensure the flexibility of operation and the reliability of power supply, their opening and closing states will change continuously, thereby changing the connection relationship of the power devices accordingly. Third, the large number of electric vehicle charging piles, high penetration rate, and large-scale access to distributed power sources make the topology of the distribution network more and more complex. In addition, the topology identification of the distribution network system is of great significance to its fault line identification, power flow calculation and distribution, and stable control. Therefore, it is particularly important to perform real-time and accurate topology identification of the distribution network system.

[0004] Line loss is the abbreviation of active energy loss generated during network transmission. Line loss calculation and analysis is an important part of the power industry. Through line loss analysis, managers can formulate more targeted loss reduction measures, save electricity, and increase economic benefits. The premise of line loss calculation is to know the topology of the distribution network, and the accuracy of line loss calculation can only be basically guaranteed when the topology is accurate.

[0005] Theoretically, the calculation of distribution network line loss is not a problem, but due to the time-varying nature of the load at each node in the actual system, the network flow distribution and network loss power have the characteristics of time-varying. Compared with the high-voltage distribution network with a voltage level of 35kV and above, the low-voltage distribution network system is more complex and faces more difficulties in the process of calculating line loss. Summary of the invention

[0006] The embodiment of the present application provides a distribution network topology identification and line loss calculation method based on a basis pursuit algorithm to solve the problem in the prior art that it takes a long time to obtain valid data for topology identification and the line loss calculation is not real-time.

[0007] In order to solve the above technical problems, the present invention provides

[0008] A method for distribution network topology identification and line loss calculation based on basis pursuit algorithm, characterized by comprising:

[0009] Given corresponding parameters, including the reference angular frequency of each system, the inertia coefficient of the generator node, the generator electromotive force and transient reactance, the damping coefficient of the node, the node phase angle, the node injection power, and the node voltage amplitude, the system model equation is constructed;

[0010] A vector containing network topology information is extracted from the model, and a sparse vector signal is solved. The sparse vector signal is solved based on an equivalent minimization solution. A basis pursuit algorithm in a convex optimization algorithm is used to solve the equivalent minimization problem to obtain an estimated value of the distribution network system topology.

[0011] Based on the estimated value of the distribution network system topology, the Newton-Raphson method is used to calculate the power flow and obtain the power distribution and line loss of the distribution network.

[0012] In the above-mentioned distribution network topology identification and line loss calculation method based on the basis pursuit algorithm, some parameters are collected by the phase angle measurement unit PMU (Phasor Measurement Units), including the node phase angle size δ i , node injection power Node voltage amplitude V i * , generator output power Grid operation data, known parameters include system reference frequency ω R , generator inertia coefficient H i , Generator transient reactance x d ,i , Node damping coefficient D i .

[0013] In the above distribution network topology identification and line loss calculation method based on basis pursuit algorithm,

[0014] The distribution network model is defined as n generators or loads and l transmission lines, with a connected graph set G = (S n , S l ) is used to represent the n represents all nodes in the network, S l Represents all the edges in the network. n =S ng ∪S nl , S ng represents the set of internal nodes of the generator, S nlrepresents the set of generator terminal nodes and all load nodes, then in the distribution network model, a total of ng+n=N nodes are considered; S l = {l i，j , j∈S n} represents a set of l edges, corresponding to l transmission lines of the distribution network. The dynamic equation corresponding to the entire system is corresponding to the internal nodes of the generator:

[0015]

[0016] Y i，i+ng =-(jx d，i ) -1

[0017] And corresponding to the generator terminal nodes and load nodes:

[0018]

[0019]

[0020] Y ij =|Y ij |exp(jα ij )

[0021] Where ω R is the reference angular frequency of the system, H i is the inertia coefficient of the ith generator node, D i represents the damping coefficient of the ith node, δ i is the phase angle of the ith node relative to the reference node, A i is the injected power of the ith node, represents the electromotive force of the ith generator, V i * represents the voltage amplitude of the ith node, x d，i represents the transient reactance of the ith generator node, Y ij is the (i, j)th element of matrix Y, which is defined as follows:

[0022]

[0023] where y i，j is the imaginary part of the admittance between node i and node j in the distribution network system.

[0024] In the above-mentioned distribution network topology identification and line loss calculation method based on basis pursuit algorithm, the distribution network topology identification problem is equivalent to solving:

[0025] sty i=A i x i

[0026] where x i is the vector containing the network topology information to be estimated, Since the l1 norm minimization problem is a convex optimization problem, the basis pursuit algorithm is used to solve it.

[0027] In the above-mentioned distribution network topology identification and line loss calculation method based on the basis pursuit algorithm, the basis pursuit algorithm includes

[0028] Step 6.1: For variables x without non-negative constraints i Decompose into two non-negative variables u i and v i The difference is x i =u i -v i ;

[0029] Step 6.2, the original formula becomes [A i , -A i ][u i ;v i ]=y i ;

[0030] Step 6.3: Under the definition of norm, rewrite the objective function as

[0031] Step 6.4: Switch to solving the linear programming problem minc T z i stA′ i zi=b i , z i ≥0, where c T =[1, 1, ..., 1] 1×2(n-1) , p = n-1, x i ∈R2 (n-1) , A′ i =[A i , -A i ], b = y;

[0032] Step 6.5: Solve the above linear programming problem to obtain the optimal solution

[0033] Step 6.6: Get the optimal solution to the original problem

[0034] According to the n-1 solutions obtained Construct the matrix Y.

[0035] In the above-mentioned distribution network topology identification and line loss calculation method based on basis pursuit algorithm, the specific execution process of Newton-Raphson power flow calculation is as follows.

[0036] Step 7.1, generate the node admittance matrix;

[0037] Step 7.2, set the initial voltage value for each node;

[0038] Step 7.3, Substitute the initial value into the power equation and find the unbalanced value in the correction equation;

[0039] Step 7.4, use the initial value of the node voltage to find each element in the Jacobian matrix;

[0040] Step 7.5, solve the correction equation to obtain the correction value of each node voltage;

[0041] Step 7.6, calculate the new initial voltage value of each node;

[0042] Step 7.7, check whether it has converged, and judge whether it has converged according to the given convergence standard;

[0043] Step 7.8: If it does not converge, the iterative value of each node voltage is used as the new initial value and the next iteration begins from the third step until it converges or reaches the maximum number of iterations S;

[0044] Step 7.9: Calculate the power distribution of each line, calculate the line loss, and output the results.

[0045] In the above-mentioned distribution network topology identification and line loss calculation method based on basis pursuit algorithm, the input data used in the line loss calculation comes from the solved topology structure vector data.

[0046] Compared with the prior art, the method for topology identification and line loss calculation of a distribution network based on a basis pursuit algorithm proposed in the present invention considers constructing a corresponding dynamic equation for each node in the distribution network based on the structure and dynamic behavior of the distribution network, and based on this model, converts the topology identification problem of the distribution network system into a sparse vector signal solution problem, and then uses the solution result to calculate the line loss of the distribution network. In the process, the comprehensive use of the steady-state and transient operation data of the distribution network system is considered to obtain more valid data and improve the identification efficiency. In addition, the real-time data of the distribution network is used to identify its real-time topological structure, and then the real-time line loss is calculated, so that the calculated data has higher accuracy and credibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of a distribution network topology identification and line loss calculation method based on a basis pursuit algorithm provided in an embodiment of the present invention.

[0048] Figure 2This is a transient operation diagram of the distribution network system provided by an embodiment of the present invention.

[0049] Figure 3 This is a diagram of the simulation results of the IEEE standard 9-node distribution network topology identification provided in an embodiment of the present invention.

[0050] Figure 4 This is a diagram of the simulation results of the IEEE standard 30-node distribution network topology identification provided in an embodiment of the present invention.

[0051] Figure 5 This is a diagram of the line loss calculation results of the IEEE standard 9-node distribution network provided in an embodiment of the present invention.

[0052] Figure 6 This is a diagram of the line loss calculation results of the IEEE standard 30-node distribution network provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0054] The core of the present invention is to provide a distribution network topology identification and line loss calculation method based on basis pursuit algorithm.

[0055] In order to enable those skilled in the art to better understand the solutions of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0056] Figure 1 The present invention provides a method for topology identification and line loss calculation of a distribution network based on a basis pursuit algorithm, such as Figure 1 As shown, the method includes:

[0057] S101: First, a system dynamics model is performed for a distribution network having n generators or loads and l transmission lines.

[0058] For a distribution network with n generators or loads and l transmission lines, a connected graph set G = (S n , S l ) is used to represent the n represents all nodes in the network, S l Represents all the edges in the network. n =S ng ∪S nl , Sng represents the set of internal nodes of the generator, S nl represents the set of generator terminal nodes and all load nodes. In this model, a total of ng+n=N nodes are considered; S l = {l i，j , i, j∈S n} represents a set of l edges, corresponding to l transmission lines of the distribution network. Considering that when the entire system is operating normally, the phase angle difference of all nodes in the distribution network is very small, the DC model is used to describe the dynamics of the entire distribution network system. The dynamic equation corresponding to the entire system is as follows:

[0059] Corresponding to the internal nodes of the generator:

[0060]

[0061] Y i,i+ng =-(jx d,i ) -1

[0062] And corresponding to the generator terminal nodes and load nodes:

[0063]

[0064]

[0065] Y ij =|Y ij |exp(jα ij )

[0066] Where ω R is the reference angular frequency of the system, H i is the inertia coefficient of the ith generator node, D i represents the damping coefficient of the ith node, δ i is the phase angle of the ith node relative to the reference node, A i is the injected power of the ith node, represents the electromotive force of the ith generator, V i * represents the voltage amplitude of the ith node, x d，i represents the transient reactance of the ith generator node, Y ij is the (i, j)th element of matrix Y, which is defined as follows:

[0067]

[0068] where y i，jis the imaginary part of the admittance between node i and node j in the distribution network system. The above is the dynamic equation of the entire distribution network system. The following is a theoretical derivation of the model.

[0069] S102: Perform theoretical derivation on the above model, extract data reflecting topological information from the model, and transform the topological identification problem into a sparse signal recovery problem.

[0070] To transform the above model of the generator terminal node and the load node, first replace A on the right side of the equation i Move to the left side of the equation, multiply both sides by -1, and expand the summation on the right side of the equation into a matrix calculation form to obtain the following equation:

[0071] y i =A i x i

[0072] where y i =[y i (t1), y i (t2), ..., y i (t s )] T ∈R s×1 , t s represents the sampling time point, S represents the maximum number of sampling times, A i =[φ i (t1),φ i (t2), ..., φ i (t s )] is the perception matrix,

[0073]

[0074] is a sparse vector containing network topology information to be calculated. One thing to note is that in the element x i There is no K in ii This term is not important because it has no value for the topology of the grid. i (t s ), φ i (t s ) is defined as follows:

[0075]

[0076] in Derivative of the node phase angle The first-order forward difference is used for approximate calculation, that is, Where Δt is the time interval of the difference. This transforms the above distribution network topology identification problem into a sparse vector recovery problem, which is equivalent to solving the following problem:

[0077] sty i =A i x i

[0078] where x i is the vector containing the network topology information to be estimated, Since the l1 norm minimization problem is a convex optimization problem, it can be solved using the basis pursuit algorithm.

[0079] The distribution network system generally has two operating states, one is the steady state during normal and stable operation, and the other is the transient state when disturbed, such as Figure 2 As shown in the figure. During steady-state operation, all node parameters remain basically stable with only small fluctuations. In this case, there is almost no difference between the data, resulting in very little valid data. During transient operation, the parameters of each node vary greatly, so more valid data can be collected for topology identification. During the operation of the distribution network system, the data of steady-state and transient operation can be used comprehensively to improve the efficiency of topology identification.

[0080] S103: According to the established model, a basis pursuit algorithm is used to solve the equivalent sparse signal recovery problem, thereby obtaining an estimated value of the distribution network system topology.

[0081] After modeling the system and obtaining an equivalent solution through theoretical derivation, the present invention uses the basis pursuit algorithm to solve the above optimization problem because the basis pursuit algorithm has a fast execution speed and high accuracy. After obtaining sufficient data and establishing the corresponding matrix A i and i After that, we can i The specific execution process of the basis pursuit algorithm is as follows.

[0082] Algorithm 1: Basis Pursuit Algorithm (BP)

[0083] Input: Matrix A i , vector y i , i=1,2,...,n

[0084] Output: Distribution network topology estimate Y.

[0085] Step 1: For variables x without non-negativity constraints i Decompose into two non-negative variables u i and v i The difference is x i =u i -v i ;

[0086] Step 2: The original formula becomes [A i , -A i ][u i ;v i ]=y i ;

[0087] Step 3: Under the definition of norm, rewrite the objective function as

[0088] Step 4: Switch to solving the linear programming problem min c T z i stA′ i z i =b i , z i ≥0, where c T =[1, 1, ..., 1] 1×2(n-1) , p = n-1, x i ∈R 2(n-1) , A′ i =[A i , -A i ], b = y;

[0089] Step 5: Solve the above linear programming problem to get the optimal solution

[0090] Step 6: Get the optimal solution to the original problem

[0091] End: According to the n-1 solutions obtained Construct the matrix Y.

[0092] The estimated value of the distribution network system topology can be solved through the above basis pursuit algorithm.

[0093] S104: After obtaining an estimated value of the distribution network system topology, a Newton-Raphson power flow algorithm is used to calculate the distribution network line loss.

[0094] After obtaining the estimated value of the distribution network system topology through the above analysis and calculation, the power flow calculation can be performed based on this value. Power flow calculation is the most widely used, basic and important calculation in the design and operation of power networks. By performing power flow calculation on various design schemes and various operation modes of power networks, the voltage of various nodes of the power grid can be obtained, and the power flow of the network and the power loss of each component in the network can be obtained, and then the power loss can be obtained.

[0095] The calculation of power flow is a mathematical problem of solving a system of multivariate nonlinear equations, and there are many ways to solve it. The Newton-Raphson method is an effective method for solving nonlinear equations mathematically, and has good convergence. The application of Newton's method to power flow calculation is based on the admittance matrix. Due to the use of the symmetry, sparsity and node numbering order optimization of the admittance matrix, the Newton method has relatively excellent performance in terms of convergence, memory usage, and calculation speed.

[0096] The specific execution process of Newton-Raphson power flow calculation is as follows.

[0097] (1) Generate node admittance matrix;

[0098] (2) Set the initial voltage value for each node;

[0099] (3) Substitute the initial value into the power equation to find the unbalanced value in the correction equation;

[0100] (4) Use the initial values ​​of node voltages to find the elements in the Jacobian matrix;

[0101] (5) Solve the correction equation to obtain the correction value of each node voltage;

[0102] (6) Calculate the new initial voltage value of each node;

[0103] (7) Check whether convergence has occurred and determine whether convergence has occurred based on a given convergence standard;

[0104] (8) If it does not converge, the iterative value of each node voltage is used as the new initial value and the next iteration begins from the third step until it converges or reaches the maximum number of iterations S;

[0105] (9) Calculate the power distribution of each line, calculate the line loss, output the results, and end.

[0106] The basic principles of power flow calculation and the detailed introduction of Newton-Raphson method can be found in reference [1].

[0107] S105: Simulate and test the above algorithm on IEEE standard 9-node and 30-node power distribution systems.

[0108] We conduct simulation tests on IEEE standard 9-bus and 22-bus distribution systems according to the above steps. The transient reactance of the three generators in the IEEE 9-bus distribution network system is x d，i [0.2, 0.4, 0.5], the transient reactance of the 6 generators in the 30-node distribution network system is x d，i =[0.2, 0.4, 0.5, 0.65, 0.82, 0.92]. Use MATLAB's ode45 algorithm to solve the differential equation to obtain δ iOther data such as and The node voltage can be obtained through MATPOWER simulation. In this model, considering that the node voltage fluctuation is very small, the node voltage is regarded as an unchanging constant.

[0109] The topology identification simulation results of IEEE standard 9-bus and 30-bus distribution network systems are shown in Figure 2. Figure 3 and Figure 4 As shown, the black grid in the figure represents that there is no connection relationship between the corresponding two nodes; the light black grid represents that there is a connection relationship between the corresponding two nodes; the gray grid represents that there is a connection relationship between the corresponding two nodes but the algorithm recognizes that there is no connection relationship, that is, the algorithm recognizes that there is an omission (there is no recognition omission in the figure); the light gray grid represents that there is no connection relationship between the corresponding two nodes but the algorithm recognizes that there is a connection relationship, that is, the algorithm recognizes that there is an error (there is no recognition error in the figure). It can be seen that the distribution network topology identification method based on the above-established model and the basis pursuit algorithm can completely restore the topological structure of the two distribution network systems, which also proves the feasibility of the method proposed in the present invention.

[0110] For the IEEE standard 9-node and 30-node distribution network systems, after identifying their topological structures, further line loss calculations can be performed. The calculation results are as follows: Figure 5 and Figure 6 shown.

[0111] The present invention provides a distribution network topology identification and line loss calculation method based on the basis pursuit algorithm. First, the distribution network system is analyzed and modeled. Through theoretical derivation, a vector containing network topology information is extracted from the model, thereby converting the distribution network topology identification problem into a sparse vector signal solution problem; then the basis pursuit method is used to solve this problem to obtain an estimated value of the distribution network system topology; then, the estimated topology structure is used to calculate the power flow of the distribution network using the Newton-Raphson method to obtain the power distribution and line loss of the distribution network. These data can be used for advanced services such as distribution network line loss analysis and loss reduction measures. Finally, simulation tests were carried out on IEEE standard 9-node and 30-node distribution network systems, demonstrating the feasibility of the above method.

[0112] The above is a detailed introduction to a distribution network topology identification and line loss calculation method based on a basis pursuit algorithm provided by the present invention. The principle and implementation process of the present invention are explained. The description of the above embodiments is only used to help understand the method and its core idea of ​​the present invention; at the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention. Those skilled in the art, without creative labor, should include in this application any modifications, equivalent substitutions, improvements, etc. made to the present invention.

[0113] It should also be noted that, in this specification, relational terms such as first and second, etc. are used only to distinguish one operation from another operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising" and similar words make a unit, device or system including a series of elements include not only those elements, but also other elements not explicitly listed, or also include elements inherent to such unit, device or system.

Claims

1. A distribution network topology identification and line loss calculation method based on basis pursuit algorithm, characterized in that: include: Given the corresponding parameters, including the reference angular frequency of each system, the inertia coefficient of the generator node, the generator electromotive force and transient reactance, the node damping coefficient, the node phase angle, the node injection power, and the node voltage amplitude, the system model equation is constructed; the distribution network model is defined as having n generators or loads and l transmission lines, using a connected graph set G=(S n , S l ) is used to represent the n represents all nodes in the network, S l represents all the edges in the network, S n =S ng ∪S nl , S ng represents the set of internal nodes of the generator, S nl represents the set of generator terminal nodes and all load nodes, then in the distribution network model, a total of ng+n=N nodes are considered; S l = {l i ,j,i,j∈S n } represents a set of l edges, corresponding to l transmission lines of the distribution network. The dynamic equation corresponding to the entire system is corresponding to the internal nodes of the generator: Y i，i+ng =-(jx d,i ) -1 And corresponding to the generator terminal nodes and load nodes: AND ij =|And ij |exp(jα ij ) Where ω R is the reference angular frequency of the system, H i is the inertia coefficient of the ith generator node, D i represents the damping coefficient of the ith node, δ i is the phase angle of the ith node relative to the reference node, A i is the injected power of the ith node, represents the generated electromotive force of the i-th generator, represents the voltage amplitude of the ith node, x d，i represents the transient reactance of the ith generator node, Inject power into the i-th node, is the output power of the ith generator, Y ij is the (i, j)th element of matrix Y, which is defined as follows: where y i，j is the imaginary part of the admittance between node i and node j in the distribution network system; A vector containing network topology information is extracted from the model to solve the sparse vector signal. The sparse vector signal solution is based on an equivalent minimization solution. The basis pursuit algorithm in the convex optimization algorithm is used to solve the equivalent minimization problem to obtain the distribution network system topology estimation value. The distribution network topology identification problem is equivalent to solving: where x i is the vector containing the network topology information to be estimated, Since the l1 norm minimization problem is a convex optimization problem, the basis pursuit algorithm is used to solve it; The basis pursuit algorithm includes Step 6.1: For variables x without non-negative constraints i Decompose into two non-negative variables u i and v i The difference is x i =u i -v i ; Step 6.2, the original formula becomes [A i , -A i ][u i ;v i ]=y i ; Step 6.3: Under the definition of norm, rewrite the objective function as Step 6.4: Solve the linear programming problem min c T z i stA′ i z i =b i , z i ≥0, where c T =[1, 1, ..., 1] 1×2(n-1) , p = n-1, x i ∈R 2(n-1) , A′ i =[A i , -A i ], b = y; Step 6.5: Solve the above linear programming problem to obtain the optimal solution Step 6.6: Get the optimal solution to the original problem According to the n-1 solutions obtained Construct matrix Y; Based on the estimated value of the distribution network system topology, the Newton-Raphson method is used to calculate the power flow and obtain the power distribution and line loss of the distribution network.

2. The method for distribution network topology identification and line loss calculation based on basis pursuit algorithm according to claim 1 is characterized in that: Some parameters are collected by the phase measurement unit PMU (Phasor Measurement Units), including the node phase angle δ i , node injection power Node voltage amplitude V i * , Generator output power Grid operation data, known parameters include system reference frequency ω R , generator inertia coefficient H i , Generator transient reactance x d,i , node damping coefficient D i .

3. The method for distribution network topology identification and line loss calculation based on basis pursuit algorithm according to claim 1, characterized in that: The specific execution process of Newton-Raphson power flow calculation is as follows Step 7.1, generate the node admittance matrix; Step 7.2, set the initial voltage value for each node; Step 7.3, Substitute the initial value into the power equation and find the unbalanced value in the correction equation; Step 7.4, use the initial value of the node voltage to find each element in the Jacobian matrix; Step 7.5, solve the correction equation to obtain the correction value of each node voltage; Step 7.6, calculate the new initial voltage value of each node; Step 7.7, check whether it has converged, and judge whether it has converged according to the given convergence standard; Step 7.8: If it does not converge, the iterative value of each node voltage is used as the new initial value and the next iteration begins from the third step until it converges or reaches the maximum number of iterations S; Step 7.9: Calculate the power distribution of each line, calculate the line loss, and output the results.

4. The method for distribution network topology identification and line loss calculation based on basis pursuit algorithm according to claim 3 is characterized in that: The input data used in the line loss calculation comes from the solved topology structure vector data.

Images