A method for calculating transformer winding overvoltage distribution based on ultra-wide frequency domain model

Abstract

The invention discloses a transformer winding overvoltage distribution calculation method based on an ultra-wide frequency domain model, comprising: 1) obtaining characteristic parameters of a HEMP E1 component; 2) fitting a conductor skin depth and an oil-paper dielectric response model to establish an ultra-wide frequency domain mathematical model of a transformer winding based on frequency-dependent distributed parameters; 3) establishing an ultra-wide frequency transmission line model based on frequency-dependent distributed parameters according to the ultra-wide frequency domain mathematical model of a transformer winding based on frequency-dependent distributed parameters and a multi-conductor transmission line model; 4) performing central difference processing on a transmission line equation according to the ultra-wide frequency transmission line model based on frequency-dependent distributed parameters to obtain iterative equations of voltage, current and boundary conditions, and then establishing a transmission line solution model based on the equations; 5) inputting the HEMP E1 component as a pulse source into the transmission line solution model to obtain transformer winding overvoltage distribution. The method can quickly and accurately obtain the voltage distribution of a power transformer winding under the action of HEMP E1.

Description

Technical Field

[0001] The invention belongs to the technical field of transformer insulation state analysis, and relates to a transformer winding overvoltage distribution calculation method based on an ultra-wide frequency domain model. Background Art

[0002] High-altitude nuclear electromagnetic pulse (HEMP) is a strong electromagnetic pulse generated by a nuclear bomb that explodes at high altitude. It can be divided into three stages according to the chronological order of occurrence. Among them, E1 is considered the most serious threat. Its maximum magnetic field is as high as 50kV / m, and the spectrum range is 0-100MHz, including almost all long and short waves. It has a wide range of hazards and a coverage radius of hundreds to thousands of kilometers. It will cause irreparable damage to almost all electrical equipment within the coverage area, and the degree of damage is much higher than that of common electromagnetic pulses, such as lightning and VFTO. Power transformers are important equipment in the operation of power systems. When strong electromagnetic pulses act on transformers, they will cause complex transient processes and threaten the insulation part. Therefore, studying the action mechanism of power transformers under HEMPE1 is of great significance to the safe and stable operation of power systems.

[0003] At present, when analyzing and solving the distribution problem of strong electromagnetic pulses acting on winding equipment, the numerical analysis models used are all based on the multi-conductor transmission line theory. The frequency range of the established broadband model is only 10MHz. The model considers the distribution parameters of frequency-dependent resistance, frequency-dependent inductance and frequency-dependent capacitance. Among them, the research on skin depth uses empirical coefficients or fitting within a narrow frequency band, which cannot well simulate the actual situation of the conductor under the action of HEMP E1; the research on capacitance considers that the dielectric constant is a constant or fits within a narrow frequency band, which ultimately leads to the establishment of a multi-conductor transmission line model that only studies the broadband model based on single relaxation Coil-Coil. The frequency range covered by HEMP E1 is 100MHz, and the single relaxation Coil-Coil model cannot fully describe this ultra-wide frequency band characteristic. Obviously, the existing broadband model has poor applicability in the ultra-high frequency area due to the narrow frequency band studied. It is necessary to construct a new ultra-wideband model to meet the needs of the study of winding voltage distribution of large power transformers in underground nuclear power plants under HEMP E1 impact. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method for calculating transformer winding overvoltage distribution based on an ultra-wide frequency domain model, which can quickly and accurately obtain the voltage distribution of the power transformer winding under the action of HEMP E1.

[0005] To achieve the above object, the transformer winding overvoltage distribution calculation method based on the ultra-wide frequency domain model described in the present invention includes:

[0006] 1) Obtaining characteristic parameters of HEMP E1 component;

[0007] 2) Fit the conductor skin depth and oil-paper dielectric response model, and establish an ultra-wide frequency domain mathematical model of transformer windings based on frequency-dependent distributed parameters;

[0008] 3) According to the ultra-wideband frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters and the multi-conductor transmission line model, an ultra-wideband transmission line model based on frequency-dependent distributed parameters is established;

[0009] 4) Perform central difference processing on the transmission line equation according to the ultra-wideband transmission line model based on frequency-dependent distributed parameters to obtain the iterative equations of voltage, current and boundary conditions, and then establish the transmission line solution model based on this;

[0010] 5) The HEMP E1 component characteristic parameters are input into the transmission line solution model as a pulse source to obtain the transformer winding overvoltage distribution.

[0011] The characteristic parameters of the HEMP E1 component in step 1) include pulse peak value, pulse leading edge parameter, pulse trailing edge parameter and correction coefficient.

[0012] The specific process of establishing the ultra-wide frequency domain mathematical model of the transformer winding based on frequency-dependent distributed parameters in step 2) is as follows:

[0013] According to the conductor skin effect, the ultra-wideband resistance model is:

[0014]

[0015] Where k is the empirical coefficient of skin depth;

[0016] The ultra-wideband inductor model is:

[0017]

[0018] The dielectric response model in the ultra-wideband capacitor model is:

[0019]

[0020] Combined with the capacitance analytical formula, the ultra-wideband capacitance model is obtained as follows:

[0021]

[0022] The characteristic parameters of the dielectric response model are obtained by dielectric impedance spectrometer, and the ultra-wide frequency domain mathematical model of the transformer winding based on frequency-dependent distributed parameters is established as follows:

[0023]

[0024] Among them, ε ∞is the high frequency dielectric constant, Δε α is the change of dielectric constant during α relaxation, τ α is the α relaxation time, Δε β is the change of dielectric constant during β relaxation, τ β is the β relaxation time, the two relaxation components α and β respectively describe the relaxation process of the dielectric in different frequency ranges, C1 is the non-frequency-variable capacitance matrix, and C2 and C3 represent the frequency-variable capacitance coefficient matrix.

[0025] The ultra-wideband transmission line model based on frequency-dependent distributed parameters established in step 3) is:

[0026]

[0027] The voltage, current and boundary iteration equations established in step 4) after central difference processing are:

[0028]

[0029] Where s is the spatial position, q is the temporal position, q=0 is the initial voltage position, q=1 / 2 is the initial current position, i S is the current at the beginning of the transmission line, i R is the terminal current.

[0030] The present invention has the following beneficial effects:

[0031] The transformer winding overvoltage distribution calculation method based on the ultra-wide frequency domain model described in the present invention is specifically operated by constructing an ultra-wide frequency domain frequency-variable distribution parameter model of the power transformer winding, obtaining key frequency-variable characteristic parameters through simulation and simulation, and combining the traditional multi-conductor transmission line theory to widen the applicable range of the transmission line to 100MHz. The established ultra-wide frequency transmission line model based on the frequency-variable distribution parameters is subjected to central differential processing, and programming analysis is performed to provide comprehensive and accurate data for the voltage distribution characteristics of the nuclear power plant power transformer winding to the ground, between turns, and between disks, which is helpful for the subsequent optimization and design of the insulation of sensitive parts of transformer windings with different capacities and voltage levels, improves the safety, stability and sustainability of transformer operation, and quickly and accurately obtains the voltage distribution of the power transformer winding under the action of HEMP E1. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of the present invention;

[0033] Figure 2 It is the fitting effect diagram of skin depth k;

[0034] Figure 3a This is the Coil-Coil fitting effect diagram of the real part of the complex dielectric constant of oil-paper;

[0035] Figure 3b This is the Coil-Coil fitting effect diagram of the imaginary part of the complex dielectric constant of oil-paper;

[0036] Figure 4a This is the Coil-Coil fitting effect diagram of the real part of the complex dielectric constant of oil-paper by double relaxation;

[0037] Figure 4b This is the Coil-Coil fitting effect diagram of the imaginary part of the complex dielectric constant of oil-paper by double relaxation;

[0038] Figure 5 Schematic diagram of transformer winding structure;

[0039] Figure 6 It is the time domain diagram of the voltage at the beginning of each turn of the first ten turns of the winding;

[0040] Figure 7 This is the distribution diagram of the maximum value of the voltage of each turn of the winding to ground. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only an embodiment of a part of the present invention, not all embodiments, and is not intended to limit the scope of the present invention. In addition, in the following description, the description of well-known structures and technologies is omitted to avoid unnecessary confusion of the concepts disclosed in the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work should fall within the scope of protection of the present invention.

[0042] The accompanying drawings show schematic diagrams of structures according to embodiments disclosed in the present invention. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0043] refer to Figure 1 The transformer winding overvoltage distribution calculation method based on the ultra-wide frequency domain model of the present invention comprises the following steps:

[0044] 1) Obtaining characteristic parameters of HEMP E1 component;

[0045] The characteristic parameters of the HEMP E1 component include pulse peak value, pulse leading edge parameter, pulse trailing edge parameter and correction coefficient, and adopt the IEC standard of the International Electrotechnical Commission.

[0046] 2) By studying the winding skin effect and oil-paper dielectric properties within 50Hz~100MHz, the conductor skin depth and oil-paper dielectric response model are fitted, and an ultra-wide frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters is established.

[0047] The process of establishing the ultra-wideband frequency domain mathematical model is as follows:

[0048] According to the conductor skin effect, the ultra-wideband resistance model is:

[0049]

[0050] Among them, k is the empirical coefficient of skin depth. The AC resistance is calculated in electromagnetic simulation software with a frequency of 50Hz to 100MHz. The software calculated value is compared with the model analytical value, k is fitted, and compared with the commonly used empirical coefficient 2 of the conductor. The fitting results are shown in Figure 2 .

[0051] The dielectric response model in the ultra-wideband capacitor model is:

[0052]

[0053] Combined with the capacitance analytical formula, the unified model of ultra-wideband capacitance is obtained as follows:

[0054]

[0055] A broadband dielectric impedance spectrometer is used to measure the complex dielectric constant of the pre-processed oil-paper. The characteristic parameters of the double relaxation Coil-Coil model are obtained by fitting the real and imaginary parts respectively. The fitting effects of single relaxation and double relaxation are shown in Figures 3 and 4 respectively. It can be found that the fitting effect of single relaxation Coil-Coil in the high frequency band is poor. For ultra-wideband excitations such as HEMP with a spectrum range of up to 100MHz, the single relaxation model Coil-Coil will bring large errors. Therefore, the transmission line modeling is performed based on the established dielectric model.

[0056] The ultra-wide frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters is finally established as follows:

[0057]

[0058] Among them, ε ∞ is the high frequency dielectric constant, Δε α represents the change of dielectric constant during α relaxation, τ α is the α relaxation time, Δε βrepresents the change of dielectric constant during β relaxation, τ β is the β relaxation time, the two relaxation components α and β respectively describe the relaxation process of the dielectric in different frequency ranges, C1 represents the non-frequency-variable capacitance matrix; C2 and C3 represent the frequency-variable capacitance coefficient matrix.

[0059] 3) Traditional multi-conductor transmission line models are mostly integer-order, and their complex frequency domain equations are:

[0060]

[0061] The ultra-wideband model established in step 2) is transformed into the complex frequency domain, that is:

[0062]

[0063] Y(s)=sC1+s 1-α C2+s 1-β C3

[0064] Ignoring the influence of conductivity, the ultra-wideband model in the complex frequency domain is substituted into the transmission line equation in the complex frequency domain, and the ultra-wideband transmission line model is obtained as follows:

[0065]

[0066] in, and They are all fractional differential terms of unit resistance and unit capacitance.

[0067] 4) Perform central difference processing on the ultra-wideband equation of multi-conductor transmission lines and discretize them in space and time respectively. The fractional order terms are discretized as follows:

[0068]

[0069] After discretization, we get the following formula:

[0070]

[0071]

[0072]

[0073]

[0074] Wherein, in the first formula, s represents the position in space, and in the first formula, s=1,2,...,N, and in the second formula, q represents the position in time, q=0 represents the initial position of the voltage, and q=1 / 2 represents the initial position of the current;

[0075] The voltage and current iteration formula can be derived as:

[0076]

[0077] Then consider the boundary condition equation of the transmission line, assuming that the current at the beginning of the transmission line is i S , the terminal current is i R , the beginning and end of the transmission line are discretized and described in matrix form:

[0078]

[0079] in:

[0080]

[0081] in, is the voltage value at the kth transmission line sΔx at position qΔt, S is the starting end, R represents the end end, and the same is true for the current.

[0082] By combining the voltage, current and boundary condition iterations, the ultra-wideband transmission line model can be solved.

[0083] Taking an actual oil-immersed transformer winding as an example, a model is established in MATLAB, and winding parameters are input for simulation analysis. Figure 5 As shown; the time domain diagram of the voltage at the head end of each turn for the first ten turns is as follows Figure 6 As shown, it can be seen that the peak value of each turn voltage decays in turn, which conforms to the overvoltage decay law. The voltage amplitudes at the ends of the first five turns account for 84%, 76.6%, 66.2%, 56.6%, and 48% of the voltage source respectively. Considering that the HEMP E1 pulse amplitude is very high, when the transformer works in this condition for a long time, it is very easy to cause the breakdown of the coil insulation, causing serious power accidents; the maximum value distribution diagram of the voltage of each turn of the winding to the ground is shown in Figure 7 As shown, further analysis can obtain the distribution diagram of the maximum voltage of the insulation part between turns and between disks. According to the above distribution diagram, combined with the insulation protection level of the transformer, the insulation weak points can be determined, providing data reference for the subsequent insulation protection design.

Claims

1. A method for calculating transformer winding overvoltage distribution based on an ultra-wide frequency domain model, characterized in that: include: 1) Obtaining characteristic parameters of HEMP E1 component; 2) Fit the conductor skin depth and oil-paper dielectric response model within 0-100MHz, and establish an ultra-wide frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters; 3) According to the ultra-wideband frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters and the multi-conductor transmission line model, an ultra-wideband transmission line model based on frequency-dependent distributed parameters is established; 4) Perform central difference processing on the transmission line equation according to the ultra-wideband transmission line model based on frequency-dependent distributed parameters to obtain the iterative equations of voltage, current and boundary conditions, and then establish the transmission line solution model based on this; 5) Inputting the HEMP E1 component as a pulse source into the transmission line solution model to obtain the transformer winding overvoltage distribution; The specific process of establishing the ultra-wide frequency domain mathematical model of the transformer winding based on frequency-dependent distributed parameters in step 2) is as follows: According to the conductor skin effect, the ultra-wideband resistance model is: The ultra-wideband inductor model is: The dielectric response model in the ultra-wideband capacitor model is: Combined with the capacitance analytical formula, the ultra-wideband capacitance model is obtained as follows: The characteristic parameters of the dielectric response model are obtained through dielectric impedance spectrometer, and an ultra-wide frequency domain mathematical model of the transformer winding based on frequency-dependent distributed parameters is established; The established ultra-wide frequency domain mathematical model of transformer winding based on frequency-dependent distributed parameters: Among them, ε ∞ is the high frequency dielectric constant, Δε α is the change of dielectric constant during α relaxation, τ α is the α relaxation time, Δε β is the change of dielectric constant during β relaxation, τ β is the β relaxation time, the two relaxation components α and β respectively describe the relaxation process of the dielectric in different frequency ranges, C1 is the non-frequency-variable capacitance matrix, C2 and C3 represent the frequency-variable capacitance coefficient matrix; The ultra-wideband transmission line model based on frequency-dependent distributed parameters established in step 3) is: The voltage, current and boundary iteration equations established in step 4) after central difference processing are: Current iteration: Voltage iteration: Where s is the spatial position, q is the temporal position, q=0 is the initial voltage position, q=1 / 2 is the initial current position, i S is the current at the beginning of the transmission line, i R is the terminal current, and the same is true for voltage; Boundary Iteration: in, is the voltage value at the kth transmission line sΔx at position qΔt, S is the starting end, R represents the end, and the current is the same. The specific expansion is as follows:

2. The transformer winding overvoltage distribution calculation method based on the ultra-wide frequency domain model according to claim 1 is characterized in that: The characteristic parameters of the HEMP E1 component in step 1) include pulse peak value, pulse leading edge parameter, pulse trailing edge parameter and correction coefficient.

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