A Transient Model of Transformer Winding

Abstract

The present invention provides a transformer winding transient model. The model treats the winding as equivalent to a multi-conductor transmission line, and based on the finite difference time domain method of a conventional multi-conductor transmission line, innovatively processes the discrete difference operation at the transmission line port, so that the model is freed from the terminal characteristics of the external network, and can be independently packaged and modularized to achieve the integration of the transformer winding transient model with the external complex substation network. Compared with the original finite difference time domain method, the algorithm of the transient model can reduce the error to 0.025%. The present invention lays a foundation for analyzing the propagation characteristics of high-frequency signals in the substation network and the influence of the topological structure on the online diagnosis of winding deformation.

Description

Technical Field

[0001] The present invention belongs to the field of online monitoring of electrical equipment, and specifically refers to innovatively processing a time-domain finite difference method for multi-conductor transmission lines to construct a transformer winding transient model that can be decoupled from an external network. Background Art

[0002] (1) Conventional multi-conductor transmission line finite-difference time-domain method

[0003] According to the existing transformer winding modeling method mentioned in "Modeling and Calculation of VFTO Wave Process in Transformer Winding" published by Yang Aimin et al. in Volume 33, Issue 5 of "High Voltage Technology" in May 2007, the transformer winding with a radius of r and N turns of winding to be studied is equivalent to a multi-conductor transmission line with a length of 2πr and N conductors, where the conductors are numbered 1, 2, 3, ..., N, and the head end of the multi-conductor transmission line is on the left and the end end is on the right, and the end of the i-th conductor is connected to the head end of the i+1-th conductor (i=1, 2, 3, ..., N-1).

[0004] Regarding transient analysis of multi-conductor transmission lines, the finite-difference time-domain (FDTD) method is often used to achieve approximate solutions to the time-domain numerical methods of transmission line equations. At present, most of the research results in this direction are limited to the fine mathematical modeling of single windings of offline transformers. According to the finite-difference time-domain theory of multi-conductor transmission lines as shown in Sections 8.1.8, 8.2.3.1, and 9.2.3 of "Analysis of Multiconductor Transmission Lines" written by Clayton R. Paul et al., published by Wiley-IEEE Press in 2008, each conductor of the multi-conductor transmission line equivalent to the winding is divided into P equal-length space segments (P is an integer greater than 0) in the length direction, and each space segment is numbered from 1 in order from left to right, and the solution time T is divided into Q equal-length time segments (Q is an integer greater than 0), and in order to ensure the stability of discretization and the accuracy of second-order calculations, each space segment and time segment is further divided into two halves, and the space and time of voltage and current are interleaved. Under the terminal condition that the external network can give the relationship between voltage and current at the same position and time, the recursive relationship between the voltage and current of the first and Pth space segments of the multi-conductor transmission line is:

[0005]

[0006]

[0007] Where C and G are the unit length capacitance matrix and conductance matrix between the conductors of the transformer winding, Δz is the length of each space segment, Δt is the length of each time period, is the voltage column vector at the left end of the first spatial segment in the mth time period, is the voltage column vector at the left end of the first spatial segment in the m+1th time period, is the voltage column vector at the right end of the Pth spatial segment in the mth time period, is the voltage column vector at the right end of the Pth spatial segment in the m+1th time period, is the current column vector at the left end of the first spatial segment in the mth time period, is the current column vector at the left end of the first spatial segment in the m+1th time period, is the current column vector at the right end of the Pth spatial segment in the mth time period, is the current column vector at the right end of the Pth spatial segment in the m+1th time period, is the current column vector in the middle of the first space segment in the m+1 / 2th time period, It is the current column vector in the middle of the Pth spatial segment in the m+1 / 2th time period.

[0008] The multi-conductor transmission line model is regarded as a multi-port network, and the boundary conditions of each conductor connected end to end are shown in equations (1-1) and (1-2) combined with equation (1-3).

[0009]

[0010] Where: n = 2, 3, ..., N, the admittance matrix equation is derived

[0011]

[0012] The derivation process and results are consistent with the article "Modeling and Calculation of VFTO Wave Process in Transformer Windings" published by Yang Aimin et al. in Volume 33, Issue 5 of High Voltage Technology in May 2007. C , column vector B, and When all are known, when solving the voltage of each wire end in the N+1th m+1th time period on the right side of the equation, it is found that the left side of the equation Unknown, N+1 equations contain N+3 unknowns in total. If you want to solve them, you need to combine the terminal characteristics of the external network. For example, the external internal resistance at the beginning of a multi-conductor transmission line is R S The voltage source U S , the end is connected through the resistor R L Grounding, its terminal characteristics are expressed as

[0013]

[0014] At this time, equations (1-4) and (1-5) form a set of N+3 equations, which can solve N+3 unknowns.

[0015] Calculated by formula (1-6)

[0016]

[0017] In the formula is the voltage column vector on the left side of the end of the kth space segment in the m+1th time period, is the voltage column vector at the left end of the kth spatial segment in the mth time period, is the current column vector in the middle of the kth space segment in the m+1 / 2th time period, is the current column vector in the middle of the k-1th spatial segment of the m+1 / 2th time period, k=2, 3, …, P.

[0018] Calculated by formula (1-7)

[0019]

[0020] In the formula is the voltage column vector on the left side of the end of the kth space segment in the m+1th time period, is the voltage column vector at the left end of the k+1th spatial segment in the m+1th time period, is the current column vector in the middle of the kth space segment in the m+1 / 2th time period, is the current column vector in the middle of the kth spatial segment in the m+3 / 2th time period, k=1, 2, …, P.

[0021] (2) Existing issues

[0022] This method has theoretical limitations. The discrete differential operation at the port requires that the terminal characteristics of the connected external network are known, that is, the functional relationship between the voltage and current of the external network port is known. However, the electrical network of the substation connected to the online transformer is complex and needs to be built using the power system electromagnetic transient simulation module of software such as EMTP or Simulink. The terminal characteristics of the built complex substation network are unknown, and the port electrical signal needs to be measured and obtained. It is impossible to directly obtain the functional relationship between the terminal voltage and current shown in formula (1-5), and it is impossible to solve the terminal voltage at the next moment on the right side of the equal sign in formula (1-4). Therefore, the conventional multi-conductor transmission line time-domain finite difference method cannot be directly packaged and embedded in the simulation software to complete the overall construction of the substation network.

[0023] The Distributed Parameters Line module in the Simulink simulation software was originally used to simulate three-phase circuits. When using it to build a transformer winding model composed of multiple turns of wire, there are the following problems: 1) The order of the input parameters is at most 30, that is, only 30 turns can be constructed at most, and the transformer winding model of 35kV and above cannot be constructed in units of turns (the model needs to contain hundreds or thousands of turns of wire); 2) When the winding is constructed by many turns, it is necessary to manually connect the ends of each turn. For windings that contain hundreds or thousands of turns, it is basically difficult to achieve modeling; 3) When the order increases, the requirements for computer performance increase sharply, and the ease of use becomes worse. Therefore, it cannot be used to build a fine multi-conductor transmission line model of transformer windings.

[0024] (3) Invention process

[0025] The root cause of the above problems is that the conventional finite-difference time-domain method uses the current I at the beginning and end of the multi-conductor transmission line in equations (1-1) and (1-2) as S and I L The average value is discretized, which results in two more unknowns in the admittance matrix equation (1-4) derived after discretization: It is known that the external complex circuit can be regarded as a multi-port network. After the voltage is injected into its port, the response current value will be measured at the same time. Therefore, it is still necessary to ensure that the terminal voltage and terminal current of the multi-conductor transmission line are at the same position and the same time during the recursive operation of the electrical quantity. It is still necessary to calculate the multi-conductor transmission line head and end current I in equations (1-1) and (1-2). S and I L To avoid the increase of unknown quantity, the present invention attempts to use and Directly replace I in formula (1-1) and (1-2) S and I L The average value of is discretized, so that the recursive relationship between the voltage and current of the first space segment and the Pth space segment of the multi-conductor transmission line is changed to:

[0026]

[0027]

[0028] So the derived admittance matrix equation becomes

[0029]

[0030] The difference from equation (1-4) is that equation (1-10) replaces the left side of the equation with Replace with Thus, N+1 equations contain N+1 unknowns, and equation (1-10) can be solved independently without knowing the terminal characteristics of the external network. The transformer winding transient model constructed by the time-domain finite difference method after substitution can be decoupled from the external network and solved in the time domain separately. However, this processing method will inevitably bring errors, so we analyze whether the model is feasible, whether the solution calculation converges, and whether the error is within an acceptable range.

[0031] Firstly, the error caused by the transformer winding transient model constructed by the finite difference time domain method after substitution processing compared with the conventional finite difference time domain method is analyzed. The transformer winding transient model is constructed by using the MATLAB Function programming module in the Simulink simulation software and the detection circuit is built (refer to the offline FRA wiring). The winding response voltage waveform and waveform deviation ratio before and after the measurement algorithm processing are Figure 2 As shown, the deviation between the two waveforms can be reduced to 0.025%, which shows that the error caused by the algorithm after substitution is very small and can be ignored.

[0032] The transformer winding transient model of the present invention is compared with the same simple multi-conductor transmission line model built using the DistributedParameters Line module in the Simulink simulation software, and the following parameters are injected: Figure 3 Different types of excitation signals, measured response signals and waveform deviation ratios are shown in Figure 2. Figure 3 As shown in the figure, it is found that the waveform deviation ratio measured by the two models can be reduced to 0.5%. And the study found that the closer Δt is set to the propagation time of a unit space segment, that is, Δt / v (v is the propagation speed of the wave), the smaller the error caused by this processing method.

[0033] The winding transient models of complex transformer winding connection forms such as high-low voltage double windings and three-phase six windings were also studied, and it was found that the errors of the transformer winding transient model of the present invention are very small. It can be considered that the transformer winding transient model of the present invention is feasible. Summary of the invention

[0034] The object of the present invention is to provide a transformer winding transient model, which, based on the conventional multi-conductor transmission line finite difference time domain method, innovatively processes the discrete difference operation at the transmission line port, so that the terminal characteristics of the external network can be eliminated when performing the model operation, thereby realizing independent time domain solution of the transformer winding transient model.

[0035] The model equates a transformer winding with a radius of r and N turns of wire to a multi-conductor transmission line with a length of 2πr and N wires, where the conductors are numbered 1, 2, 3, ..., N, and the head end of the multi-conductor transmission line is on the left and the tail end is on the right, and the tail end of the i-th wire is connected to the head end of the i+1-th wire (i = 1, 2, 3, ..., N-1); and the multi-conductor transmission line is spatially discretized and temporally discretized according to the existing multi-conductor transmission line finite difference time domain method, and the multi-conductor transmission line is divided into P equal-length space segments (P is an integer greater than 0) in the length direction, and each space segment is numbered from 1 in order from left to right, and the total solution time domain is divided into Q equal-length time segments (Q is an integer greater than 0); the recursive relationship between the voltage and current of the first space segment and the P-th space segment of the multi-conductor transmission line is:

[0036]

[0037]

[0038] Where C and G are the unit length capacitance matrix and conductance matrix between the conductors of the transformer winding, Δz is the length of each space segment, Δt is the length of each time period, is the voltage column vector at the left end of the first spatial segment in the mth time period, is the voltage column vector at the left end of the first spatial segment in the m+1th time period, is the voltage column vector at the right end of the Pth spatial segment in the mth time period, is the voltage column vector at the right end of the Pth spatial segment in the m+1th time period, is the current column vector at the left end of the first spatial segment in the mth time period, is the current column vector at the right end of the Pth spatial segment in the mth time period, is the current column vector in the middle of the first space segment in the m+1 / 2th time period, is the current column vector of the middle part of the Pth space segment in the m+1 / 2th time period; the recursive relationship between the voltage and current of other space segments of the multi-conductor transmission line conforms to the relationship given in the existing multi-conductor transmission line finite-difference time-domain method.

[0039] The beneficial effect of the present invention is that after processing the multi-conductor transmission line end equation of the time-domain finite difference method, the electrical quantity solution of the winding equivalent multi-conductor transmission line transient model port and the decoupling function of the external substation network terminal characteristics are realized, so that the model port can be directly connected to a complex substation network. The advantage of building the transformer winding model and the substation model separately is that the transformer winding transient model is built by autonomous programming of the time-domain finite difference algorithm, thereby ensuring the accuracy of the model; the substation network is directly built using various power system electromagnetic transient modules of the simulation software, which greatly reduces the difficulty of the work. The present invention can be used to simulate the transient process of the entire substation, laying a foundation for the subsequent analysis of the propagation characteristics of the signal and the influence of the topological structure on the online diagnosis of winding deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0041] Figure 1 It is a multi-conductor transmission line equivalent to the transformer winding.

[0042] Figure 2 The response voltage waveform (top) and waveform deviation ratio (bottom) obtained by simulating the transformer winding transient model constructed using the conventional time-domain finite-difference method and the transformer winding transient model invented in this paper.

[0043] Figure 3 Response waveforms and waveform deviation ratios of the transformer winding transient model and the multi-conductor transmission line model constructed by the Distributed Parameters Line module of the present invention when a sinusoidal signal (top), a step signal (middle), and a pulse signal (bottom) are injected.

[0044] Figure 4 These are the steps for solving the transient model of the transformer winding of this invention.

[0045] Figure 5 The voltage waveform at the head end of the transient model of the transformer winding connected to the electrical network containing overhead lines. Specific embodiments

[0046] A transformer winding model with 300 turns of winding was built in the MAXWELL electromagnetic field simulation software. Each turn of the winding was 3.85 m long, and a 300×300-order resistance, conductance, inductance and capacitance matrix was obtained by simulation. The transformer winding transient model of this invention was built using MATLAB simulation software.

[0047] First, use the MATLAB workspace to import the electrical parameter matrix into the transformer winding transient model. Divide each turn of the winding into 10 equal-length space segments, then Δz is 0.385m, thus forming a 300×11-order voltage lattice and a 300×10-order current lattice. The sampling time step Δt is set to 1ns, and the total simulation time is 30μs. The transformer winding transient model is connected to the electrical network containing overhead lines at the head end, and the end is connected to a 1MHz sinusoidal voltage source with an internal resistance of 50Ω. The initial voltage of each node of the winding is Initial current All are 0.

[0048] Measure the current of the external network port connected to the first and last ends of the winding transient model Substitute it into equation (1-10) to solve the voltage at the end of the multi-conductor transmission line at the first Δt simulation time: Then use formula (1-6) to calculate the internal voltage of the multi-conductor transmission line Then use formula (1-7) to calculate the internal current of multi-conductor transmission line The terminal voltage The digital signal is converted into an electrical signal and applied to the external network port connected to the first and last ends of the winding transient model after a delay of 1 Δt. The time is increased by one Δt, and then the current of the external network port connected to the first and last ends of the winding transient model is measured. Substitute it into equation (1-10) to solve the voltage at the end of the multi-conductor transmission line at the second Δt simulation time: ...and repeat this process until the total simulation time is reached. The solution steps for the transformer winding transient model are as follows: Figure 4 The voltage waveform measured at the beginning of the transformer winding is as follows: Figure 5 shown.

[0049] The present invention is described above by specific embodiments, but those skilled in the art may also recognize the various possibilities of variations and alternative embodiments, for example, by combining and / or changing the features of a single embodiment. Therefore, it is understood that these variations and alternative embodiments will be considered to be included in the present invention, and the scope of the present invention is limited only by the attached patent claims and their equivalents.

Claims

1. A transformer winding transient model, characterized in that: The model equates a transformer winding with a radius of r and N turns of wire to a multi-conductor transmission line with a length of 2πr and N wires, where the conductors are numbered 1, 2, 3, ..., N, and the head end of the multi-conductor transmission line is on the left and the end end is on the right, and the end of the i-th wire is connected to the head end of the i+1-th wire, where i = 1, 2, 3, ..., N-1; According to the existing finite difference time domain method for multi-conductor transmission lines, the multi-conductor transmission line is spatially discretized and temporally discretized, and the multi-conductor transmission line is divided into P equal-length space segments in the length direction, where P is an integer greater than 0, and each space segment is numbered from 1 in order from left to right, and the total solution time domain is divided into Q equal-length time segments, where Q is an integer greater than 0; the recursive relationship between the voltage and current of the first space segment and the Pth space segment of the multi-conductor transmission line is: Where C and G are the unit length capacitance matrix and conductance matrix between the conductors of the transformer winding, Δz is the length of each space segment, Δt is the length of each time period, is the voltage column vector at the left end of the first spatial segment in the mth time period, is the voltage column vector at the left end of the first spatial segment in the m+1th time period, is the voltage column vector at the right end of the Pth spatial segment in the mth time period, is the voltage column vector at the right end of the Pth spatial segment in the m+1th time period, is the current column vector at the left end of the first spatial segment in the mth time period, is the current column vector at the right end of the Pth spatial segment in the mth time period, is the current column vector in the middle of the first space segment in the m+1 / 2th time period, is the current column vector of the middle part of the Pth space segment in the m+1 / 2th time period; the recursive relationship between the voltage and current of other space segments of the multi-conductor transmission line conforms to the relationship given in the existing multi-conductor transmission line finite-difference time-domain method.

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