A method and system for calculating equivalent line loss of distribution network taking into account distributed power sources

Abstract

A method for calculating equivalent line losses in a distribution network that takes distributed power sources into account comprises: obtaining source data; data processing, wherein the processing of static data includes: topology analysis; conversion of main components to establish a conversion relationship between the main components of the distribution network and the transmission network, including head-end outgoing line conversion, loss-free distribution transformer conversion, loss-based distribution transformer conversion, and distributed power source conversion; reconstruction of the distribution network model; performing power flow calculations based on the reconstructed distribution network model using the Newton-Raphson algorithm; and outputting the line loss calculation results of the target distribution network. The present invention also provides a distribution network equivalent line loss calculation system that takes distributed power sources into account. The present invention establishes a new equivalent model of the main components of the distribution network and the transmission network by deeply analyzing the operating status and topological structure of the distribution network and comprehensively considering it with the operating characteristics of the transmission network. The Newton-Raphson method is then used for calculation based on the equivalent model. Compared with the traditional equivalent resistance method and average current method, the method proposed in the present invention has higher calculation accuracy and can more accurately reflect the line loss level of the distribution network.

Description

Technical Field

[0001] The present invention relates to the technical field of electric power grids, in particular to a method for calculating losses of grid lines. Background Art

[0002] Currently, the Newton-Raphson method is the most commonly used power flow algorithm for calculating line losses in transmission networks. This method uses an iterative approach to solve the voltage amplitudes and phase angles at all nodes in the grid by establishing a nonlinear system of equations relating power system node voltages and injected power. Once the node voltage solutions are obtained, the line currents are calculated based on the line impedance parameters and node voltages, and the active and reactive losses are then calculated.

[0003] Currently, the Newton-Raphson method performs well in calculating transmission line losses. However, it has obvious shortcomings when applied to distribution networks, as follows:

[0004] First, the main components and topological relationships of the distribution network and the transmission network are quite different, and the Newton-Raphson method cannot be directly used to calculate the distribution network line loss.

[0005] Second, with the development of new energy technologies, there are a large number of distributed power sources in the distribution network. The access of these power sources has changed the operating status of the distribution network. Directly using the Newton-Raphson method to calculate line losses is likely to cause difficulties in convergence. Summary of the Invention

[0006] The technical problem to be solved by the present invention is how to accurately calculate the line loss of the distribution network when a distributed power source is connected.

[0007] The present invention solves the above technical problems by the following technical means: a method for calculating equivalent line loss of a distribution network taking into account distributed power sources, comprising the following steps:

[0008] S1. Obtain source data: obtain distribution network source data based on the source system;

[0009] S2. Data processing, including:

[0010] S21. Processing of dynamic data, including determining whether the area containing distributed generation will affect the line loss of the distribution network, and reducing the impact of its volatility on the line loss calculation through data processing;

[0011] S22. Processing of static data, specifically including:

[0012] S221, performing topological analysis on static data;

[0013] S222. Conversion of main components to establish the conversion relationship between the main components of the distribution network and the transmission network, as follows:

[0014] (1) Head-end outgoing line conversion: The head-end outgoing line of the distribution network is equivalent to a combination structure consisting of a virtual busbar and a balancing node. Impedance equivalence, current injection, and power injection are performed simultaneously. The parameters of the components after conversion should be consistent with those before conversion.

[0015] (2) Conversion of distribution transformer without loss: refers to the conversion of distribution transformer without loss calculation, which is equivalent to a combination structure consisting of virtual bus and load. The component parameters before and after the conversion should remain consistent;

[0016] (3) Loss calculation of distribution transformer conversion: refers to the public transformer, which is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and loads. The loss of each distribution transformer is calculated through this structure. The component parameters before and after the conversion should remain consistent;

[0017] (4) Distributed power conversion, which is equivalent to a combination structure consisting of a virtual bus and a generator. Before the conversion, this step needs to determine the monthly average photovoltaic return power PPGFS of the distribution transformer i corresponding to the substation at time j. ij Is the value greater than 0? Conversion is required only when it is greater than 0. The component parameters before and after conversion should remain consistent.

[0018] S223, model reconstruction, reconstructing the distribution network model according to the distribution network topology analysis result in step S221 and the main component conversion result in step S222;

[0019] Step S3: flow calculation: performing flow calculation using the Newton-Raphson algorithm based on the reconstructed distribution network model;

[0020] Step S4: Output the result, and output the line loss calculation result of the target distribution network.

[0021] As a further specific technical solution, in step S21, determining whether the substation with distributed power supply access will affect the line loss of the distribution network includes: monthly statistics on the amount of power returned by the distributed power supply by substation, and the specific calculation is as follows:

[0022]

[0023] i∈{1,2,...,N} (2)

[0024] {t∈N|1≤t≤31} (3)

[0025] {j∈N|1≤j≤24} (4)

[0026] In the above formula (1), PGFS itjPGFD represents the value of photovoltaic power generation in the distribution area corresponding to distribution transformer i at time j on day t of the month that cannot be consumed locally and is returned to the distribution network; itj It represents the total photovoltaic power generation of the distribution transformer i corresponding to the area at time j on the tth day of the month; PFH itj It represents the load demand of the distribution area corresponding to distribution transformer i at time j on day t of the month. Equations (2)-(4) represent the value ranges of subscripts i, t, and j respectively.

[0027] As a further specific technical solution, in step S21, reducing the impact of the volatility of the distributed power supply on the line loss calculation by data processing includes:

[0028] (1) Calculate the average value of the amount of electricity returned by the distributed generation at the same time every day of the month, as follows:

[0029]

[0030] In the above formula (5), PPGFS ij It represents the monthly average photovoltaic return power of the distribution area corresponding to distribution transformer i at time j;

[0031] (2) Using PPGFS ij The value of represents the return power value of all distribution transformers corresponding to the substation at time j in the daily line loss calculation.

[0032] As a further specific technical solution, step S222, the conversion of main components also includes the conversion of operating data:

[0033] (1) After the outgoing line at the head end is equivalent to a balancing node, the voltage operating data of the outgoing line at the head end needs to be added to the balancing node;

[0034] (2) After the distribution transformer is equivalent to the combination structure of virtual bus and load, the load needs to add the power factor data of the distribution transformer, using PF bj It is expressed as follows:

[0035]

[0036] Among them, P is , Q is They represent the active power and reactive power of the i-th distribution transformer without loss;

[0037] (3) After the loss distribution transformer is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and load, the load needs to add the power factor data of the distribution transformer, using PF j It is expressed as follows:

[0038]

[0039] Among them, P is ', Q is 'represent the active power and reactive power of the i-th loss distribution transformer respectively;

[0040] (4) After the distributed power source is equivalent to a combination structure consisting of a virtual bus and a generator, the generator needs to add the power factor data of the distributed power source, using PF fj It is expressed as follows:

[0041]

[0042] Among them, P is ”、Q is ” represent the active power and reactive power of the i-th distributed generation respectively.

[0043] As a further specific technical solution, step S3, power flow calculation, specifically includes:

[0044] The basic equation for the power flow calculation problem is established as

[0045]

[0046] Among them, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, Y ij is the node admittance matrix element, is the node voltage column vector element;

[0047] For a PQ node, the node power P is known. is , Q is , then the corresponding equation is

[0048]

[0049] For a PV node, the node power P is known. is 、V is , then the corresponding equation is

[0050]

[0051] The general form of the tidal current equation is constructed by combining equations (19) to (20).

[0052]

[0053] If there is X * , so that Y(X * )=0, then X * is the solution of formula (21);

[0054] Introducing the parameter t in equation (21), we construct a family of images: Z(X,t) such that when t=1, Z is Y, and when t=0, the solution of the equation Y0(X)=0 is X 0 ; That is, the solution X defined as Z(X,0)=Y0(X), where Y0(X)=0 0 Since the initial value is known, the equation Z(X,1)=0 is equivalent to the original nonlinear equation (21), so we only need to calculate the following equivalent equation:

[0055] Z(X,t)=0,t∈[0,1] (22)

[0056] The equivalent equation is not unique, so it is assumed to be:

[0057] Z(X,t)=Y(X)-(1-t)Y(X 0 ) (twenty three)

[0058] If Y'(X) is continuous and non-singular, and there is a unique solution x = x(t) in equation (23), satisfying X(0) = X 0 , and X * =X(1) is the solution of Equation (21). Therefore, finding the solution of Equation (23) is equivalent to finding the initial value problem of the following Davidenko differential equation:

[0059]

[0060] Where M(X)=Y'(X) is M(θ,V) in equation (21), and the curve formed by the solution X=X(t) in equation (24) is called a homotopy curve. The homotopy curve in equation (21) is calculated using the midpoint integral formula, and its calculation formula is:

[0061]

[0062] Where N represents the number of segments of t, which leads to the step size h = 1 / N. Since the homotopy curve X = X(t) is close to a straight line, any numerical integration method of order 2 is used to solve it;

[0063] If the initial value calculated by formula (25) cannot meet the convergence requirements of Newton-Raphson, the number of segments N is increased until the convergence requirements of Newton-Raphson are met. A variable step size is used to shorten the calculation time. The variable step size means that the system will adjust the size of the time step according to the needs, and at the same time improve the accuracy of the homotopy curve as a whole. If a certain segment value is taken, it is calculated using formula (25) and then expanded using Newton-Raphson calculation formula (26). If the obtained ||x N+1 -x N || is small enough, or satisfies ||x k+1 -x k||<|x k -x k-1 I think X N is a good enough initial value for the Newton-Raphson iteration, otherwise X N Assuming it as the initial value, repeat the calculation of formula (25) to calculate the new X N ,

[0064] X k+1 =x k -[M(x k )] -1 Y(X) k ,K=N,N+1,... (26)

[0065] When performing equation (24) to find the homotopy curve, the initial value is given, and x 0 =[0,1] T , in some cases it appears as M(X 0 ) Strange and M(X * ) is non-singular, which makes the calculation process impossible, or M(X k ) Strange, in fact, when X 0 With X * On the surface det(Z X )=0, if we connect X 0 With X * The homotopy curve C exists, Z X There must be singular points on C, especially when a line in the power system is overloaded or near the stability boundary, the homotopy curve has singular points. To prevent this, the homotopy equation with parameters is used:

[0066] Z[x,t,α,x 0 ]=Y(x)-(1-t 3 )α(xx 0 ) (27)

[0067] Where α is a parameter matrix, and its value automatically changes according to whether M(X) is singular or not. For any x 0 ∈R, let α be determined, and the constructed homotopy equation (27) satisfies the condition Z(x 0 ,0)=0, Z(x,1)=Y(X), so the solution when Z(x,1)=0 is the solution of the original equation (21);

[0068] The method of solving Equation (27) is unified to solve the following Davidenko differential equation initial value problem, which can be written as:

[0069]

[0070] The calculation method is the same as formula (25).

[0071] The present invention also provides a distribution network equivalent line loss calculation system taking into account distributed power sources, comprising the following modules:

[0072] The source data acquisition module is used to obtain the source data of the distribution network based on the source system;

[0073] Data processing module, including:

[0074] The dynamic data processing unit performs the following steps: determining whether the substation containing distributed power generation will affect the line loss of the distribution network, and reducing the impact of its volatility on the line loss calculation through data processing;

[0075] The static data processing unit specifically includes:

[0076] A static data topology analysis subunit, used for performing topology analysis on static data;

[0077] The main component conversion subunit is used to establish the conversion relationship between the main components of the distribution network and the transmission network. The specific steps are as follows:

[0078] (1) Head-end outgoing line conversion: The head-end outgoing line of the distribution network is equivalent to a combination structure consisting of a virtual busbar and a balancing node. Impedance equivalence, current injection, and power injection are performed simultaneously. The parameters of the components after conversion should be consistent with those before conversion.

[0079] (2) Conversion of distribution transformer without loss: refers to the conversion of distribution transformer without loss calculation, which is equivalent to a combination structure consisting of virtual bus and load. The component parameters before and after the conversion should remain consistent;

[0080] (3) Loss calculation of distribution transformer conversion: refers to the public transformer, which is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and loads. The loss of each distribution transformer is calculated through this structure. The component parameters before and after the conversion should remain consistent;

[0081] (4) Distributed power conversion, which is equivalent to a combination structure consisting of a virtual bus and a generator. Before the conversion, this step needs to determine the monthly average photovoltaic return power PPGFS of the distribution transformer i corresponding to the substation at time j. ij Is the value greater than 0? Conversion is required only when it is greater than 0. The component parameters before and after conversion should remain consistent.

[0082] The model reconstruction module reconstructs the distribution network model based on the distribution network topology analysis results in the static data topology analysis subunit and the main component conversion results in the main component conversion subunit;

[0083] The power flow calculation module is used to perform power flow calculations using the Newton-Raphson algorithm based on the reconstructed distribution network model;

[0084] The result output module is used to output the line loss calculation results of the target distribution network.

[0085] As a further specific technical solution, in the dynamic data processing unit, determining whether the area with distributed power supply access will affect the line loss of the distribution network includes: monthly statistics on the amount of power returned by the distributed power supply area, specifically calculated as follows:

[0086]

[0087] i∈{1,2,...,N} (2)

[0088] {t∈N|1≤t≤31} (3)

[0089] {j∈N|1≤j≤24} (4)

[0090] In the above formula (1), PGFS itj PGFD represents the value of photovoltaic power generation in the distribution area corresponding to distribution transformer i at time j on day t of the month that cannot be consumed locally and is returned to the distribution network; itj It represents the total photovoltaic power generation of the distribution transformer i corresponding to the area at time j on the tth day of the month; PFH itj It represents the load demand of the distribution area corresponding to distribution transformer i at time j on day t of the month. Equations (2)-(4) represent the value ranges of subscripts i, t, and j respectively.

[0091] As a further specific technical solution, in the dynamic data processing unit, the influence of the volatility of the distributed power supply on the line loss calculation is reduced by data processing, including:

[0092] (1) Calculate the average value of the amount of electricity returned by the distributed generation at the same time every day of the month, as follows:

[0093]

[0094] In the above formula (5), PPGFS ij It represents the monthly average photovoltaic return power of the distribution area corresponding to distribution transformer i at time j;

[0095] (3) Using PPGFS ij The value of represents the return power value of all distribution transformers corresponding to the substation at time j in the daily line loss calculation.

[0096] As a further specific technical solution, the main component conversion subunit also includes the conversion of operating data:

[0097] (1) After the outgoing line at the head end is equivalent to a balancing node, the voltage operating data of the outgoing line at the head end needs to be added to the balancing node;

[0098] (2) After the distribution transformer is equivalent to the combination structure of virtual bus and load, the load needs to add the power factor data of the distribution transformer, using PF bj It is expressed as follows:

[0099]

[0100] Among them, P is , Q is They represent the active power and reactive power of the i-th distribution transformer without loss;

[0101] (3) After the loss distribution transformer is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and load, the load needs to add the power factor data of the distribution transformer, using PF j It is expressed as follows:

[0102]

[0103] Among them, P is ', Q is 'represent the active power and reactive power of the i-th loss distribution transformer respectively;

[0104] (4) After the distributed power source is equivalent to a combination structure consisting of a virtual bus and a generator, the generator needs to add the power factor data of the distributed power source, using PF fj It is expressed as follows:

[0105]

[0106] Among them, P is ”、Q is ” represent the active power and reactive power of the i-th distributed generation respectively.

[0107] As a further specific technical solution, the steps performed by the power flow calculation module specifically include:

[0108] The basic equation for the power flow calculation problem is established as

[0109]

[0110] Among them, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, Y ij is the node admittance matrix element, is the node voltage column vector element;

[0111] For a PQ node, the node power P is known. is , Q is , then the corresponding equation is

[0112]

[0113] For a PV node, the node power P is known. is 、V is , then the corresponding equation is

[0114]

[0115] The general form of the tidal current equation is constructed by combining equations (19) to (20).

[0116]

[0117] If there is X * , so that Y(X * )=0, then X * is the solution of formula (21);

[0118] Introducing the parameter t in equation (21), we construct a family of images: Z(X,t) such that when t=1, Z is Y, and when t=0, the solution of the equation Y0(X)=0 is X 0 ; That is, the solution X defined as Z(X,0)=Y0(X), where Y0(X)=0 0 Since the initial value is known, the equation Z(X,1)=0 is equivalent to the original nonlinear equation (21), so we only need to calculate the following equivalent equation:

[0119] Z(X,t)=0,t∈[0,1] (22)

[0120] The equivalent equation is not unique, so it is assumed to be:

[0121] Z(X,t)=Y(X)-(1-t)Y(X 0 ) (twenty three)

[0122] If Y'(X) is continuous and non-singular, and there is a unique solution x = x(t) in equation (23), satisfying X(0) = X 0 , and X * =X(1) is the solution of Equation (21). Therefore, finding the solution of Equation (23) is equivalent to finding the initial value problem of the following Davidenko differential equation:

[0123]

[0124] Where M(X)=Y'(X) is M(θ,V) in equation (21), and the curve formed by the solution X=X(t) in equation (24) is called a homotopy curve. The homotopy curve in equation (21) is calculated using the midpoint integral formula, and its calculation formula is:

[0125]

[0126] Where N represents the number of segments of t, which leads to the step size h = 1 / N. Since the homotopy curve X = X(t) is close to a straight line, any numerical integration method of order 2 is used to solve it;

[0127] If the initial value calculated by formula (25) cannot meet the convergence requirements of Newton-Raphson, the number of segments N is increased until the convergence requirements of Newton-Raphson are met. A variable step size is used to shorten the calculation time. The variable step size means that the system will adjust the size of the time step according to the needs, and at the same time improve the accuracy of the homotopy curve as a whole. If a certain segment value is taken, it is calculated using formula (25) and then expanded using Newton-Raphson calculation formula (26). If the obtained ||x N+1 -x N || is small enough, or satisfies ||x k+1 -x k ||<|x k -x k-1 I think X N is a good enough initial value for the Newton-Raphson iteration, otherwise X N Assuming it as the initial value, repeat the calculation of formula (25) to calculate the new X N ,

[0128] X k+1 =x k -[M(x k )] -1 Y(X) k ,K=N,N+1,... (26)

[0129] When performing equation (24) to find the homotopy curve, the initial value is given, and x 0 =[0,1] T , in some cases it appears as M(X 0 ) Strange and M(X * ) is non-singular, which makes the calculation process impossible, or M(X k ) Strange, in fact, when X 0 With X * On the surface det(Z X )=0, if we connect X 0 With X * The homotopy curve C exists, Z XThere must be singular points on C, especially when a line in the power system is overloaded or near the stability boundary, the homotopy curve has singular points. To prevent this, the homotopy equation with parameters is used:

[0130] Z[x,t,α,x 0 ]=Y(x)-(1-t 3 )α(xx 0 ) (27)

[0131] Where α is a parameter matrix, and its value automatically changes according to whether M(X) is singular or not. For any x 0 ∈R, let α be determined, and the constructed homotopy equation (27) satisfies the condition Z(x 0 ,0)=0, Z(x,1)=Y(X), so the solution when Z(x,1)=0 is the solution of the original equation (21);

[0132] The method of solving Equation (27) is unified to solve the following Davidenko differential equation initial value problem, which can be written as:

[0133]

[0134] The calculation method is the same as formula (25).

[0135] The advantages of the present invention are:

[0136] 1. This invention establishes a new equivalent model of the main components of the distribution network and the transmission network by deeply analyzing the operating status and topological structure of the distribution network and comprehensively considering it with the operating characteristics of the transmission network. Based on this equivalent model, the Newton-Raphson method is used for calculation. Compared with the traditional equivalent resistance method and average current method, the method proposed in this invention has higher calculation accuracy and can more accurately reflect the line loss level of the distribution network.

[0137] 2. In view of the problem that when distributed power sources are connected, the power generation of distributed power sources is greatly affected by the environment, resulting in large fluctuations and difficult to accurately calculate the distribution network line losses, the present invention adopts data averaging technology to effectively smooth the fluctuations in the output of distributed power sources and more accurately calculate the distribution network line losses when distributed power sources are connected.

[0138] 3. Due to the large R / X ratios of distribution network components, directly using the Newton-Raphson method for power flow calculations may result in non-convergence issues. Furthermore, the integration of distributed power grids changes the voltage profile of the distribution network, further weakening the convergence of the power flow calculations. Therefore, this paper proposes an improved power flow algorithm to solve the nonlinear system of equations, which effectively addresses the convergence issues of power flow calculations for distributed generation connected to the distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0139] Figure 1 This is an overall flow chart of a method for calculating equivalent line losses in a distribution network taking into account distributed power sources according to the present invention;

[0140] Figure 2 is the model diagram reconstructed in the model reconstruction step of the present invention; DETAILED DESCRIPTION

[0141] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0142] See also Figure 1 The present invention provides a method for calculating line loss based on the equivalent distribution network, comprising the following steps:

[0143] S1. Obtain source data

[0144] Based on the source-side system, the source-side data of the distribution network is obtained, including static data such as device information, device parameter information, and topology wiring information, as well as dynamic data such as voltage, active power, and reactive power of each load node of the distributed power source;

[0145] S2. Data processing, including:

[0146] S21. Processing of dynamic data

[0147] For distributed power sources, when the electricity they generate can be consumed locally, it will not affect the line losses of the distribution network; conversely, when the electricity they generate cannot be consumed locally, it will be returned to the distribution network, thereby increasing the line losses of the distribution network. In addition, the main component of distributed power sources in the distribution network is photovoltaic power generation, which is highly volatile due to environmental influences. Therefore, in order to more accurately calculate the line losses of the distribution network, the processing of distributed power generation operation data is divided into two aspects: one is to accurately determine whether it will affect the line losses of the distribution network, and the other is to reduce the impact of its volatility on the line loss calculation through data processing. The details are as follows:

[0148] S211. Accurately determine whether the area with distributed power generation will affect the line loss of the distribution network. Statistics on the amount of electricity returned by distributed power generation are calculated by area on a monthly basis. The specific calculation is as follows:

[0149]

[0150] i∈{1,2,...,N} (2)

[0151] {t∈N|1≤t≤31} (3)

[0152] {j∈N|1≤j≤24} (4)

[0153] In the above formula (1), PGFS itj PGFD represents the value of photovoltaic power generation in the distribution area corresponding to distribution transformer i at time j on day t of the month that cannot be consumed locally and is returned to the distribution network; itj It represents the total photovoltaic power generation of the distribution transformer i corresponding to the area at time j on the tth day of the month; PFH itj It represents the load demand of the distribution transformer i at the time j on the tth day of the month. Formulas (2)-(4) respectively represent the value ranges of the subscripts i, t, and j. From the above formula (1), it is possible to accurately determine whether the distribution area with distributed power generation access will affect the distribution network line loss, and to calculate the specific data of the impact PGFS itj ;

[0154] S212. Reduce the impact of the volatility of distributed power sources on line loss calculations through data processing. This includes:

[0155] (1) Calculate the average value of the amount of electricity returned by the distributed generation at the same time every day of the month, as follows:

[0156]

[0157] In the above formula (5), PPGFS ij It represents the monthly average photovoltaic return power of the distribution area corresponding to distribution transformer i at time j;

[0158] (2) Using PPGFS ij The value of represents the return power value of all distribution transformers in the corresponding substation at time j in the daily line loss calculation. The data averaging technology is used to effectively smooth the fluctuation of distributed power output, thereby laying the foundation for a more accurate calculation of the distribution network line loss when distributed power is connected.

[0159] S22. Processing of static data, specifically including:

[0160] S221. Topological analysis of static data

[0161] Analyze the topological wiring diagram of the distribution network, including the connection methods of all nodes and lines, as well as possible loops and network branches, to provide business logic support for subsequent model reconstruction;

[0162] S222, main component conversion

[0163] In order to calculate the line loss of the target distribution network using the Newton-Raphson power flow algorithm, it is necessary to establish the conversion relationship between the main components of the distribution network and the transmission network, as follows:

[0164] (1) Conversion of outgoing lines at the head end: The power flow algorithm requires that the grid structure must include a balancing node. Therefore, the outgoing lines at the head end of the distribution network are equivalent to a combination of a virtual busbar and a balancing node. At the same time, impedance equivalence, current injection, and power injection should be performed. The parameters of the components after conversion should be consistent with those before conversion.

[0165] (2) Conversion of distribution transformer without loss: This usually refers to the distribution transformer without loss calculation. The loss of this type of equipment is not considered in the distribution network, so it is equivalent to a combination structure consisting of a virtual bus and a load. Similar to the above step (1), the component parameters before and after the conversion should be consistent;

[0166] (3) Loss-calculating distribution transformer conversion: This usually refers to public transformers. In contrast to step (2), this type of equipment considers the calculated losses of distribution transformers in the distribution network, so it is equivalent to a combination structure consisting of two transformers, virtual jumpers on both sides, and loads. Through this structure, the loss of each distribution transformer can be calculated. Similarly, the component parameters before and after the conversion should remain consistent.

[0167] (4) Distributed power conversion, which is equivalent to a combination of virtual bus and generator. It should be noted that this step requires judging the PPGFS before the conversion. ij The value of is greater than 0. Conversion is required only when it is greater than 0. In addition, the component parameters before and after the conversion should also be consistent.

[0168] Run the data transformation:

[0169] (1) After the outgoing line at the head end is equivalent to a balancing node, the voltage operating data of the outgoing line at the head end needs to be added to the balancing node.

[0170] (2) After the distribution transformer is equivalent to the combination structure of virtual bus and load, the load needs to add the power factor data of the distribution transformer, using PF bj It is expressed as follows:

[0171]

[0172] Among them, P is , Q is They represent the active power and reactive power of the i-th distribution transformer without loss.

[0173] (3) After the loss distribution transformer is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and load, the load needs to add the power factor data of the distribution transformer, using PF j It is expressed as follows:

[0174]

[0175] Among them, P is ', Q is 'represent the active power and reactive power of the i-th loss distribution transformer respectively.

[0176] (4) After the distributed power source is equivalent to a combination structure consisting of a virtual bus and a generator, the generator needs to add the power factor data of the distributed power source, using PF fj It is expressed as follows:

[0177]

[0178] Among them, P is ”、Q is ” represent the active power and reactive power of the i-th distributed generation respectively.

[0179] S223, Model Reconstruction

[0180] According to the results of the distribution network topology analysis in step S221 and the component conversion results in step S222, the distribution network model is reconstructed. The reconstructed model is as follows: Figure 2 As shown;

[0181] Step S3: Power flow calculation

[0182] Power system flow calculation is a calculation that studies the steady-state operation of the power system. It determines the operating status of each part of the entire power system based on given operating conditions, system topology, and component parameters: the voltage of each bus, the power flowing through each component, the power loss of the system, etc. In the planning and design of power systems and the study of existing power system operation modes, flow calculations are needed to quantitatively analyze and compare the rationality, reliability, and economy of power supply plans or operation modes. It should be noted that there are no nodes in the distribution network that can be used for flow calculations. The balancing nodes here are equivalent to the head-end outgoing line nodes, and the other nodes are equivalent to the distributed power generation nodes. The conversion of other major components refers to step S222.

[0183] First, assume that the number of equivalent nodes in the distribution network is n, where the number of PV nodes is n1 and the number of PQ nodes is n2. Define the following node set:

[0184]

[0185] The mathematical model of the power network uses the following node voltage equation

[0186] I=YV (9)

[0187] Its expansion formula is

[0188]

[0189] In the formula, Y, Y ij are the node admittance matrix and its corresponding elements, Y ij =G ij +jB ij ;;I, are the node net injection current column vector and its corresponding elements respectively; V, are the node voltage column vectors and their corresponding elements respectively; n is the number of nodes in the power system.

[0190] In actual power systems, the known node injection quantity is often not the node current but the node power. The node current can be expressed as

[0191]

[0192] Among them, P i is the active power injected into the i-th node, Q i is the reactive power injected into the ith node, and substituting the above formula into formula (10) yields

[0193]

[0194] This is the most basic equation for power flow calculations, a system of nonlinear algebraic equations with node voltages V as variables. Separating the real and imaginary parts of this complex equation yields two real equations. Depending on the coordinate format used for the node voltages, the resulting power flow equation can be expressed in two forms: rectangular and polar.

[0195] (1) Tidal flow equation in rectangular coordinate form

[0196] If the voltage phasor of each node is expressed in the form of rectangular coordinates

[0197]

[0198] Then the equation (10) can be obtained by separating the real and imaginary parts:

[0199]

[0200] In formula (14), “jεi” represents the node j associated with node i.

[0201] For the PQ node, it is known that the active and reactive powers of the distribution transformer node, ignoring the loss, are P is , Q is , the active and reactive power of the distribution transformer node are P is ', Q is ', the active and reactive power of distributed generation are P is ”、Q is ", then the corresponding equation is

[0202]

[0203] Formula (15) represents the PQ node equation of the distribution transformer without considering the loss; when P is , Q is Replace with P respectively is ', Q is ', which can be expressed as the PQ node equation of the loss distribution transformer; when P in the formula is , Q is Replace with P respectively is ”、Q is ”, which can represent the distributed photovoltaic PQ node equation.

[0204] It should be noted that not all distributed power sources can provide reactive power. For distributed power sources that can provide reactive power, the size of reactive power and active power can be obtained by adjusting the power factor. For distributed power sources that cannot provide reactive power, the size of reactive power is zero.

[0205] For the PV node, it is known that the active power and voltage of the distribution transformer node are P respectively, ignoring the loss. is 、V is , the active power and voltage of the distribution transformer node are P is '、V is ',, then the corresponding equation is

[0206]

[0207] Equation (16) represents the PV node equation of the distribution transformer without considering the loss. is 、V is Replace with P respectively is '、V is ', which can be expressed as the PV node equation of the loss distribution transformer; when P in the formula is 、V is Replace with P respectively is ”、V is ”, which can represent the distributed power PV node equation.

[0208] For a system with n nodes, there are 2(n-1) equations in total.

[0209] (2) Tidal current equation in polar coordinate form

[0210] If the voltage phasor of each node is expressed in the form of polar coordinates

[0211]

[0212] Then (10) is separated by the real and imaginary parts to obtain

[0213]

[0214] For a PQ node, the node power P is known. is , Q is , then the corresponding equation is

[0215]

[0216] For a PV node, the node power P is known. is 、V is , then the corresponding equation is

[0217]

[0218] The problem of tidal flow calculation is to solve the nonlinear equations of equations (13) to (14) (in rectangular coordinate form) or equations (19) to (20) (in polar coordinate form).

[0219] Considering the large R / X ratio of distribution network components, directly using the Newton-Raphson method for power flow calculations may result in non-convergence problems. Furthermore, the connection of distributed power grids to the grid will change the voltage distribution of the distribution network, further weakening the convergence of the power flow calculation. Therefore, this proposal proposes an improved power flow algorithm to solve the nonlinear equations. The following is the detailed process of solving Equations (19) to (20):

[0220] The general form of the tidal current equation is constructed by combining equations (19) to (20).

[0221]

[0222] If there is X * , so that Y(X * )=0, then X * is the solution of formula (21).

[0223] Introducing the parameter t in equation (21), we construct a family of images: Z(X,t) such that when t=1, Z is Y, and when t=0, the solution of the equation Y0(X)=0 is X 0; That is, the solution X defined as Z(X,0)=Y0(X), where Y0(X)=0 0 Since the initial value is known, the equation Z(X,1)=0 is equivalent to the original nonlinear equation (21), so we only need to calculate the following equivalent equation:

[0224] Z(X,t)=0,t∈[0,1] (22)

[0225] The equivalent equation is not unique and can be assumed to be:

[0226] Z(X,t)=Y(X)-(1-t)Y(X 0 ) (twenty three)

[0227] If Y'(X) is continuous and non-singular, and there is a unique solution x = x(t) in equation (23), satisfying X(0) = X 0 , and X * =X(1) is the solution of Equation (21). Therefore, finding the solution of Equation (23) is equivalent to finding the initial value problem of the following Davidenko differential equation.

[0228]

[0229] Where M(X)=Y'(X) is M(θ,V) in formula (21), and the curve formed by the solution X=X(t) in formula (24) is called a homotopy curve. The homotopy curve in formula (21) can be calculated using the midpoint integral formula, which can ensure the calculation accuracy and reduce the calculation amount. The calculation formula is:

[0230]

[0231] Where N represents the number of segments of t, from which we can derive the step length h = 1 / N.

[0232] Since the homotopy curve X=X(t) is close to a straight line, any numerical integration method of order 2, such as the Runge-Kutta method, can be used to solve it.

[0233] After solving X(1), it is generally impossible to obtain the exact X *, but if it enters the convergence domain of Newton-Raphson, it can be accurately obtained using Newton-Raphson. If the initial value calculated by formula (25) cannot meet the convergence requirements of Newton-Raphson, the number of segments N can be increased until the convergence requirements of Newton-Raphson are met, so the selection of the number of segments in the calculation is particularly important. Theoretically, it can be proved that the value of N that meets the convergence requirements can be obtained, but the calculation process is time-consuming. In order to solve this problem, a variable step size is needed to shorten the calculation time. The variable step size means that the system will adjust the size of the time step according to the needs, and at the same time improve the accuracy of the homology curve as a whole. If a certain segment value is taken, it can be calculated using formula (25), and then the Newton-Raphson calculation formula (26) is used to expand the calculation. If the obtained ||x N+1 -x N || is small enough, or satisfies ||x k+1 -x k ||<|x k -x k-1 || then we can assume that X N is a good enough initial value for the Newton-Raphson iteration, otherwise X N Assuming it as the initial value, repeat the calculation of formula (25) to calculate the new X N .

[0234] X k+1 =x k -[M(x k )] -1 Y(X) k ,K=N,N+1,... (26)

[0235] When performing equation (24) to find the homotopy curve, the initial value is given and is usually x 0 =[0,1] T , in some cases it may appear as M(X 0 ) Strange and M(X * ) is non-singular, which makes the calculation process impossible. Or M(X k ) Strange, in fact, when X 0 With X * On the surface det(Z X )=0, if you connect X 0 With X * The homotopy curve C exists, Z X There must be singular points on C, especially when a line in the power system is running under heavy load or is near the stability boundary. The homotopy curve may have singular points. To prevent this situation, the homotopy equation with parameters is used.

[0236] Z[x,t,α,x 0 ]=Y(x)-(1-t 3)α(xx 0 ) (27)

[0237] Where α is a parameter matrix, and its value can be automatically changed according to whether M(X) is singular or not. 0 ∈R, let α be determined, and the constructed homotopy equation (27) satisfies the condition Z(x 0 ,0)=0,Z(x,1)=Y(X). Therefore, the solution when Z(x,1)=0 is the solution of the original equation (21).

[0238] The method of solving Equation (27) is unified to solve the following Davidenko differential equation initial value problem, which can be written as:

[0239]

[0240] The calculation method is the same as formula (25).

[0241] Step S4: Result output

[0242] Output the line loss calculation results of the target distribution network.

[0243] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for calculating equivalent line loss in a distribution network taking into account distributed power sources, characterized by: The steps include: S1. Obtain source data: obtain distribution network source data based on the source system; S2. Data processing, including: S21. Processing of dynamic data, including determining whether the area containing distributed generation will affect the line loss of the distribution network, and reducing the impact of its volatility on the line loss calculation through data processing; S22. Processing of static data, specifically including: S221, performing topological analysis on static data; S222. Conversion of main components to establish the conversion relationship between the main components of the distribution network and the transmission network, as follows: (1) Head-end outgoing line conversion: The head-end outgoing line of the distribution network is equivalent to a combination structure consisting of a virtual busbar and a balancing node. Impedance equivalence, current injection, and power injection are performed simultaneously. The parameters of the components after conversion should be consistent with those before conversion. (2) Conversion of distribution transformer without loss: refers to the conversion of distribution transformer without loss calculation, which is equivalent to a combination structure consisting of virtual bus and load. The component parameters before and after the conversion should remain consistent; (3) Loss calculation of distribution transformer conversion: refers to the public transformer, which is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and loads. The loss of each distribution transformer is calculated through this structure. The component parameters before and after the conversion should remain consistent; (4) Distributed power conversion, which is equivalent to a combination structure consisting of a virtual bus and a generator. Before the conversion, this step needs to determine the monthly average photovoltaic return power PPGFS of the distribution transformer i corresponding to the substation at time j. ij Is the value greater than 0? Conversion is required only when it is greater than 0. The component parameters before and after conversion should remain consistent. S223, model reconstruction, reconstructing the distribution network model according to the distribution network topology analysis result in step S221 and the main component conversion result in step S222; Step S3: flow calculation: performing flow calculation using the Newton-Raphson algorithm based on the reconstructed distribution network model; Step S4: Output the result, and output the line loss calculation result of the target distribution network.

2. The method for calculating equivalent line loss of a distribution network taking into account distributed power sources according to claim 1, wherein: In step S21, determining whether the area with distributed power supply will affect the line loss of the distribution network includes: monthly statistics of the amount of power returned by the distributed power supply area, specifically calculated as follows: i∈{1,2,...,N} (2) {t∈N|1≤t≤31} (3) {j∈N|1≤j≤24} (4) In the above formula (1), PGFS itj PGFD represents the value of photovoltaic power generation in the distribution area corresponding to distribution transformer i at time j on day t of the month that cannot be consumed locally and is returned to the distribution network; itj It represents the total photovoltaic power generation of the distribution transformer i corresponding to the area at time j on the tth day of the month; PFH itj It represents the load demand of the distribution area corresponding to distribution transformer i at time j on day t of the month. Equations (2)-(4) represent the value ranges of subscripts i, t, and j respectively.

3. The method for calculating equivalent line loss of a distribution network taking into account distributed power sources according to claim 2, wherein: In step S21, reducing the impact of the volatility of the distributed power supply on the line loss calculation by data processing includes: (1) Calculate the average value of the amount of electricity returned by the distributed generation at the same time every day of the month, as follows: In the above formula (5), PPGFS ij It represents the monthly average photovoltaic return power of the distribution area corresponding to distribution transformer i at time j; (4) Using PPGFS ij The value of represents the return power value of all distribution transformers corresponding to the substation at time j in the daily line loss calculation.

4. The method for calculating equivalent line loss of a distribution network taking into account distributed power sources according to claim 1, wherein: Step S222: The conversion of main components also includes the conversion of operating data: (1) After the outgoing line at the head end is equivalent to a balancing node, the voltage operating data of the outgoing line at the head end needs to be added to the balancing node; (2) After the distribution transformer is equivalent to the combination structure of virtual bus and load, the load needs to add the power factor data of the distribution transformer, using PF bj It is expressed as follows: Among them, P is , Q is They represent the active power and reactive power of the i-th distribution transformer without loss; (3) After the loss distribution transformer is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and load, the load needs to add the power factor data of the distribution transformer, using PF j It is expressed as follows: Among them, P is ', Q is 'represent the active power and reactive power of the i-th loss distribution transformer respectively; (4) After the distributed power source is equivalent to a combination structure consisting of a virtual bus and a generator, the generator needs to add the power factor data of the distributed power source, using PF fj It is expressed as follows: Among them, P is ”、Q is ” represent the active power and reactive power of the i-th distributed generation respectively.

5. The method for calculating equivalent line loss of a distribution network taking into account distributed power sources according to claim 4, characterized in that: Step S3, power flow calculation specifically includes: The basic equation for the power flow calculation problem is established as Among them, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, Y ij is the node admittance matrix element, is the node voltage column vector element; For a PQ node, the node power P is known. is , Q is , then the corresponding equation is For a PV node, the node power P is known. is 、V is , then the corresponding equation is The general form of the tidal current equation is constructed by combining equations (19) to (20). If there is X * , so that Y(X * )=0, then X * is the solution of formula (21); Introducing the parameter t in equation (21), we construct a family of images: Z(X,t) such that when t=1, Z is Y, and when t=0, the solution of the equation Y0(X)=0 is X 0 ; That is, the solution X defined as Z(X,0)=Y0(X), where Y0(X)=0 0 Since the initial value is known, the equation Z(X,1)=0 is equivalent to the original nonlinear equation (21), so we only need to calculate the following equivalent equation: Z(X,t)=0,t∈[0,1] (22) The equivalent equation is not unique, so it is assumed to be: Z(X,t)=Y(X)-(1-t)Y(X 0 ) (23) If Y'(X) is continuous and non-singular, and there is a unique solution x = x(t) in equation (23), satisfying X(0) = X 0 , and X * =X(1) is the solution of Equation (21). Therefore, finding the solution of Equation (23) is equivalent to finding the initial value problem of the following Davidenko differential equation: Where M(X)=Y'(X) is M(θ,V) in equation (21), and the curve formed by the solution X=X(t) in equation (24) is called a homotopy curve. The homotopy curve in equation (21) is calculated using the midpoint integral formula, and its calculation formula is: Where N represents the number of segments of t, which leads to the step size h = 1 / N. Since the homotopy curve X = X(t) is close to a straight line, any numerical integration method of order 2 is used to solve it; If the initial value calculated by formula (25) cannot meet the convergence requirements of Newton-Raphson, the number of segments N is increased until the convergence requirements of Newton-Raphson are met. A variable step size is used to shorten the calculation time. The variable step size means that the system will adjust the size of the time step according to the needs, and at the same time improve the accuracy of the homotopy curve as a whole. If a certain segment value is taken, it is calculated using formula (25) and then expanded using Newton-Raphson calculation formula (26). If the obtained ||x N+1 -x N || is small enough, or satisfies ||x k+1 -x k ||<|x k -x k-1 I think X N is a good enough initial value for the Newton-Raphson iteration, otherwise X N Assuming it as the initial value, repeat the calculation of formula (25) to calculate the new X N , X k+1 =x k -[M(x k )] -1 Y(X) k ,K=N,N+1,... (26) When performing equation (24) to find the homotopy curve, the initial value is given, and x 0 =[0,1] T , in some cases it appears as M(X 0 ) Strange and M(X * ) is non-singular, which makes the calculation process impossible, or M(X k ) Strange, in fact, when X 0 With X * On the surface det(Z X )=0, if we connect X 0 With X * The homotopy curve C exists, Z X There must be singular points on C, especially when a line in the power system is overloaded or near the stability boundary, the homotopy curve has singular points. To prevent this, the homotopy equation with parameters is used: Z[x,t,α,x 0 ]=Y(x)-(1-t 3 )α(x-x 0 ) (27) Where α is a parameter matrix, and its value automatically changes according to whether M(X) is singular or not. For any x 0 ∈R, let α be determined, and the constructed homotopy equation (27) satisfies the condition Z(x 0 ,0)=0, Z(x,1)=Y(X), so the solution when Z(x,1)=0 is the solution of the original equation (21); The method of solving Equation (27) is unified to solve the following Davidenko differential equation initial value problem, which can be written as: The calculation method is the same as formula (25).

6. A distribution network equivalent line loss calculation system taking into account distributed power sources, characterized by: Includes the following modules: The source data acquisition module is used to obtain the source data of the distribution network based on the source system; Data processing module, including: The dynamic data processing unit performs the following steps: determining whether the substation containing distributed power generation will affect the line loss of the distribution network, and reducing the impact of its volatility on the line loss calculation through data processing; The static data processing unit specifically includes: A static data topology analysis subunit, used for performing topology analysis on static data; The main component conversion subunit is used to establish the conversion relationship between the main components of the distribution network and the transmission network. The specific steps are as follows: (1) Head-end outgoing line conversion: The head-end outgoing line of the distribution network is equivalent to a combination structure consisting of a virtual busbar and a balancing node. Impedance equivalence, current injection, and power injection are performed simultaneously. The parameters of the components after conversion should be consistent with those before conversion. (2) Conversion of distribution transformer without loss: refers to the conversion of distribution transformer without loss calculation, which is equivalent to a combination structure consisting of virtual bus and load. The component parameters before and after the conversion should remain consistent; (3) Loss calculation of distribution transformer conversion: refers to the public transformer, which is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and loads. The loss of each distribution transformer is calculated through this structure. The component parameters before and after the conversion should remain consistent; (4) Distributed power conversion, which is equivalent to a combination structure consisting of a virtual bus and a generator. Before the conversion, this step needs to determine the monthly average photovoltaic return power PPGFS of the distribution transformer i corresponding to the substation at time j. ij Is the value greater than 0? Conversion is required only when it is greater than 0. The component parameters before and after conversion should remain consistent. The model reconstruction module reconstructs the distribution network model based on the distribution network topology analysis results in the static data topology analysis subunit and the main component conversion results in the main component conversion subunit; The power flow calculation module is used to perform power flow calculations using the Newton-Raphson algorithm based on the reconstructed distribution network model; The result output module is used to output the line loss calculation results of the target distribution network.

7. A distribution network equivalent line loss calculation system taking into account distributed power sources according to claim 6, characterized in that: In the dynamic data processing unit, determining whether the area with distributed power supply will affect the line loss of the distribution network includes: monthly statistics of the amount of power returned by the distributed power supply area, specifically calculated as follows: i∈{1,2,...,N}(2) {t∈N|1≤t≤31}(3) {j∈N|1≤j≤24}(4) In the above formula (1), PGFS itj PGFD represents the value of photovoltaic power generation in the distribution area corresponding to distribution transformer i at time j on day t of the month that cannot be consumed locally and is returned to the distribution network; itj It represents the total photovoltaic power generation of the distribution transformer i corresponding to the area at time j on the tth day of the month; PFH itj It represents the load demand of the distribution area corresponding to distribution transformer i at time j on day t of the month. Equations (2)-(4) represent the value ranges of subscripts i, t, and j respectively.

8. The distribution network equivalent line loss calculation system taking into account distributed power sources according to claim 6, characterized in that: In the dynamic data processing unit, reducing the impact of the volatility of distributed power sources on line loss calculation by data processing includes: (1) Calculate the average value of the amount of electricity returned by the distributed generation at the same time every day of the month, as follows: In the above formula (5), PPGFS ij It represents the monthly average photovoltaic return power of the distribution area corresponding to distribution transformer i at time j; (5) Using PPGFS ij The value of represents the return power value of all distribution transformers corresponding to the substation at time j in the daily line loss calculation.

9. The distribution network equivalent line loss calculation system taking into account distributed power sources according to claim 6, characterized in that: The main component conversion subunit also includes the conversion of operation data: (1) After the outgoing line at the head end is equivalent to a balancing node, the voltage operating data of the outgoing line at the head end needs to be added to the balancing node; (2) After the distribution transformer is equivalent to the combination structure of virtual bus and load, the load needs to add the power factor data of the distribution transformer, using PF bj It is expressed as follows: Among them, P is , Q is They represent the active power and reactive power of the i-th distribution transformer without loss; (3) After the loss distribution transformer is equivalent to a combination structure consisting of two coils, virtual jumpers on both sides and load, the load needs to add the power factor data of the distribution transformer, using PF j It is expressed as follows: Among them, P is ', Q is 'represent the active power and reactive power of the i-th loss distribution transformer respectively; (4) After the distributed power source is equivalent to a combination structure consisting of a virtual bus and a generator, the generator needs to add the power factor data of the distributed power source, using PF fj It is expressed as follows: Among them, P is ”、Q is ” represent the active power and reactive power of the i-th distributed generation respectively.

10. The distribution network equivalent line loss calculation system taking into account distributed power sources according to claim 9, characterized in that: The steps performed by the power flow calculation module include: The basic equation for the power flow calculation problem is established as Among them, P i is the active power injected into the i-th node, Q i is the reactive power injected into the i-th node, Y ij is the node admittance matrix element, is the node voltage column vector element; For a PQ node, the node power P is known. is , Q is , then the corresponding equation is For a PV node, the node power P is known. is 、V is , then the corresponding equation is The general form of the tidal current equation is constructed by combining equations (19) to (20). If there is X * , so that Y(X * )=0, then X * is the solution of formula (21); Introducing the parameter t in equation (21), we construct a family of images: Z(X,t) such that when t=1, Z is Y, and when t=0, the solution of the equation Y0(X)=0 is X 0 ; That is, the solution X defined as Z(X,0)=Y0(X), where Y0(X)=0 0 Since the initial value is known, the equation Z(X,1)=0 is equivalent to the original nonlinear equation (21), so we only need to calculate the following equivalent equation: Z(X,t)=0,t∈[0,1] (22) The equivalent equation is not unique, so it is assumed to be: Z(X,t)=Y(X)-(1-t)Y(X 0 ) (23) If Y'(X) is continuous and non-singular, and there is a unique solution x = x(t) in equation (23), satisfying X(0) = X 0 , and X * =X(1) is the solution of Equation (21). Therefore, finding the solution of Equation (23) is equivalent to finding the initial value problem of the following Davidenko differential equation: Where M(X)=Y'(X) is M(θ,V) in equation (21), and the curve formed by the solution X=X(t) in equation (24) is called a homotopy curve. The homotopy curve in equation (21) is calculated using the midpoint integral formula, and its calculation formula is: Where N represents the number of segments of t, which leads to the step size h = 1 / N. Since the homotopy curve X = X(t) is close to a straight line, any numerical integration method of order 2 is used to solve it; If the initial value calculated by formula (25) cannot meet the convergence requirements of Newton-Raphson, the number of segments N is increased until the convergence requirements of Newton-Raphson are met. A variable step size is used to shorten the calculation time. The variable step size means that the system will adjust the size of the time step according to the needs, and at the same time improve the accuracy of the homotopy curve as a whole. If a certain segment value is taken, it is calculated using formula (25) and then expanded using Newton-Raphson calculation formula (26). If the obtained ||x N+1 -x N || is small enough, or satisfies ||x k+1 -x k ||<|x k -x k-1 I think X N is a good enough initial value for the Newton-Raphson iteration, otherwise X N Assuming it as the initial value, repeat the calculation of formula (25) to calculate the new X N , X k+1 =x k -[M(x k )] -1 Y(X) k ,K=N,N+1,... (26) When performing equation (24) to find the homotopy curve, the initial value is given, and x 0 =[0,1] T , in some cases it appears as M(X 0 ) Strange and M(X * ) is non-singular, which makes the calculation process impossible, or M(X k ) Strange, in fact, when X 0 With X * On the surface det(Z X )=0, if we connect X 0 With X * The homotopy curve C exists, Z X There must be singular points on C, especially when a line in the power system is overloaded or near the stability boundary, the homotopy curve has singular points. To prevent this, the homotopy equation with parameters is used: Z[x,t,α,x 0 ]=Y(x)-(1-t 3 )α(x-x 0 ) (27) Where α is a parameter matrix, and its value automatically changes according to whether M(X) is singular or not. For any x 0 ∈R, let α be determined, and the constructed homotopy equation (27) satisfies the condition Z(x 0 ,0)=0, Z(x,1)=Y(X), so the solution when Z(x,1)=0 is the solution of the original equation (21); The method of solving Equation (27) is unified to solve the following Davidenko differential equation initial value problem, which can be written as: The calculation method is the same as formula (25).

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