Ferroresonance detection and prevention method for voltage transformer
By performing Fourier transform and window processing on the bus zero-sequence voltage signal of the voltage transformer, the ferromagnetic resonance category is detected, and corresponding prevention and control measures are taken, the threat of ferromagnetic resonance to the power system is solved and the system's safety is improved and stability.
Patent Information
- Application Number
- CN202411607590.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-12
- Publication Date
- 2025-02-18
AI Technical Summary
The ferromagnetic resonance phenomenon causes equipment insulation damage in the power system, threatening the safe and stable operation of the power system.
By collecting the zero-sequence voltage signal of the voltage transformer bus, performing Hanning window-adding processing and fast Fourier transformation, judging the ferromagnetic resonance category, and taking corresponding prevention and control measures based on the detection results.
Real-time detection and prevention of ferromagnetic resonance is realized, equipment damage and system shutdown caused by resonance are avoided, and the safety and stability of the power system are improved.
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Figure CN119471540A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of voltage transformer fault monitoring, and more particularly to a voltage transformer ferromagnetic resonance detection and prevention method. Background Art
[0002] With the rapid development of my country's power industry, 35kV power grid plays an increasingly important role in the power system. However, due to the frequent changes in the parameters, capacity, and operation mode of the power grid, the grounded electromagnetic voltage transformer (PT) in the system has saturation characteristics. When electromagnetic disturbance occurs in the system, the capacitor and inductor are prone to parameter matching to form a complex oscillation circuit, and in some cases, ferromagnetic resonance will occur;
[0003] Ferromagnetic resonance is mainly due to the saturation characteristics of the iron core of the electromagnetic PT, which leads to nonlinear changes in the inductance of the iron core. When electromagnetic disturbance occurs and the inductance and capacitance values in the resonant circuit reach a certain parameter matching condition, different types of resonance will be excited.
[0004] Ferromagnetic resonance overvoltage can cause insulation damage to equipment, posing a serious threat to the safe and stable operation of the power system.
[0005] Therefore, real-time detection and research of harmonics is of great significance. Summary of the invention
[0006] In view of this, in order to at least partially solve the above technical problems, the present invention provides a method for detecting and preventing ferromagnetic resonance of a voltage transformer; in order to achieve the above purpose, the present invention adopts the following technical solutions:
[0007] First, the present application discloses a voltage transformer ferromagnetic resonance detection method, by judging whether there is ferromagnetic resonance according to the capacitive reactance to ground of the voltage transformer and the excitation inductive reactance under the rated line voltage, if the following steps are performed:
[0008] Collect the zero-sequence voltage signal of the voltage transformer busbar for discretization;
[0009] The Hanning window is used to perform windowing on discrete signals;
[0010] Perform fast Fourier transform on the windowed signal to obtain the amplitude distribution of the spectrum signal;
[0011] The ferromagnetic resonance category is determined based on the frequency spectrum signal amplitude distribution.
[0012] According to an embodiment of the present invention, the capacitive reactance to ground of the voltage transformer is obtained by the following formula:
[0013]
[0014] In the formula, C represents the capacitance value of the voltage transformer, f represents the frequency of the voltage transformer, and ω represents the angular frequency of the voltage transformer;
[0015] The excitation inductive reactance at rated line voltage is obtained by the following formula:
[0016]
[0017] Where U m Indicates the line voltage of PT operation, I m Indicates the excitation current.
[0018] According to an embodiment of the present invention, determining whether ferromagnetic resonance exists includes:
[0019] Determine the ferromagnetic resonance threshold range, if X C / X m In the threshold range, it is determined that ferromagnetic resonance phenomenon exists; the ferromagnetic resonance threshold range is:
[0020] 0.01 <X C / X m <2.8
[0021] In the formula, X C Indicates the capacitive reactance of the voltage transformer to ground, X m It indicates the excitation inductive reactance of the voltage transformer at rated line voltage.
[0022] According to an embodiment of the present invention, the sampling frequency of the zero-sequence voltage signal of the voltage transformer bus is at least 10 times the fundamental frequency of the voltage transformer.
[0023] According to an embodiment of the present invention, the signal expression after the discrete signal is windowed using the Hanning window is:
[0024] x w [n] = x[n]·w(n)
[0025]
[0026] In the formula, x[n] represents the discrete signal in the time domain, w(n) represents the window function, M is the total harmonic number contained in the signal, and A is m represents the amplitude of the mth harmonic, f m represents the frequency of the mth harmonic, θ m represents the phase of the mth harmonic; f s is the sampling frequency, and N is the number of sampling points.
[0027] According to an embodiment of the present invention, performing a fast Fourier transform on the windowed signal includes:
[0028]
[0029] Where x[k] is the kth frequency component of the frequency domain signal, x w [n] is the windowed signal, and N is the number of sampling points.
[0030] According to an embodiment of the present invention, after obtaining the amplitude distribution of the spectrum signal, the amplitude and frequency are corrected respectively; wherein,
[0031] The amplitude is corrected using the following formula:
[0032]
[0033] Where |x[k0]| is the amplitude to be corrected, k1 and k2 are the discrete spectral lines located on the left and right sides of point k0, and x[k1]| and |x[k2]| are the amplitudes of the adjacent points on the left and right, respectively.
[0034] And use the following formula to correct the frequency:
[0035]
[0036] In the formula, f k0 is the frequency with correction, is the frequency resolution.
[0037] According to an embodiment of the present invention, determining the ferromagnetic resonance category according to the frequency spectrum signal amplitude distribution includes:
[0038] When the spectrum signal amplitude distribution is greater than 50Hz, the ferromagnetic resonance is a high-frequency resonance;
[0039] When the spectrum signal amplitude distribution is equal to 50Hz, the ferromagnetic resonance is the fundamental frequency resonance;
[0040] When the spectrum signal amplitude distribution is less than 50Hz,
[0041] If the peak value of the main peak is much lower than the fundamental frequency, the ferromagnetic resonance is a low-frequency resonance;
[0042] If the peak value of the main peak is an integer fraction of the fundamental frequency, the ferromagnetic resonance is a fractional frequency resonance.
[0043] Second, the present application also discloses a method for preventing and controlling ferromagnetic resonance of a voltage transformer, comprising detecting ferromagnetic resonance using any of the above-mentioned methods for detecting ferromagnetic resonance of a voltage transformer, and preventing and controlling ferromagnetic resonance according to the detection results, the prevention and control method comprising:
[0044] To address the frequency division resonance, the neutral point of the primary side of the voltage transformer is grounded via a nonlinear resistor detuning device;
[0045] To address low-frequency resonance, a damping resistor is added to the open delta winding of the voltage transformer;
[0046] For fundamental frequency resonance, change the voltage transformer parameters, or connect a damping resistor to the neutral point of the voltage transformer's high voltage measurement;
[0047] To address high-frequency resonance, add a filter or isolation device to the voltage transformer, or use a large damping resistor.
[0048] It can be seen from the above technical solutions that the present invention discloses a method for detecting and preventing ferromagnetic resonance of a voltage transformer, which can detect ferromagnetic resonance in real time by means of the capacitive reactance to ground and the excitation inductive reactance of the voltage transformer, thereby timely discovering potential problems and avoiding equipment damage and system shutdown caused by resonance.
[0049] Further real-time acquisition of the zero-sequence voltage signal of the voltage transformer busbar and spectrum analysis of the signal using Fast Fourier Transform (FFT) can accurately detect and identify the type of ferromagnetic resonance, thereby helping to deal with the resonance problem in a targeted manner and avoid the damage caused by the resonance to the power system;
[0050] In addition, according to the detected resonance type, the present application provides a corresponding prevention and control method to provide a basis for dealing with the resonance problem and effectively suppress the resonance phenomenon.
[0051] Compared with the prior art, the present application can accurately identify and classify ferromagnetic resonance by timely detecting and preventing ferromagnetic resonance, thereby improving detection efficiency, reducing the risk of system failure, and reducing the impact of resonance on power equipment, thereby effectively improving the safety of the power system and ensuring the stable and safe operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS
[0052] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.
[0053] Figure 1 This is a flow chart of ferromagnetic resonance category detection provided by the present invention.
[0054] Figure 2 A flow chart for identifying resonance categories based on spectrum signals;
[0055] Figure 3 A schematic diagram of PT ferromagnetic resonance in a 10-35KV neutral point ungrounded system in one embodiment;
[0056] Figure 4 It is a flowchart of a method for detecting and preventing ferromagnetic resonance based on FFT;
[0057] Figure 5 Schematic diagram of detuning measures. DETAILED DESCRIPTION
[0058] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in 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. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0059] The embodiment of the present invention discloses a method for detecting and preventing ferromagnetic resonance of a voltage transformer based on FFT, which is used to improve the accuracy of harmonic detection and analysis, and to accurately distinguish the types of ferromagnetic resonance so as to take corresponding suppression measures. The present invention can reduce system failures and is of great significance for ensuring the safe and stable operation of the power system.
[0060] In one embodiment, a method for detecting ferromagnetic resonance of a voltage transformer is disclosed. First, it is determined whether ferromagnetic resonance exists based on the capacitive reactance to ground of the voltage transformer and the excitation inductive reactance under the rated line voltage. If so, the following steps are performed:
[0061] Collect the zero-sequence voltage signal of the voltage transformer busbar for discretization;
[0062] The Hanning window is used to perform windowing on discrete signals;
[0063] Perform fast Fourier transform on the windowed signal to obtain the amplitude distribution of the spectrum signal;
[0064] The ferromagnetic resonance category is determined based on the frequency spectrum signal amplitude distribution.
[0065] In an exemplary embodiment, referring to Figure 1 ,include:
[0066] 1) Obtain the target system bus zero-sequence voltage signal and perform discrete sampling to obtain the sampling signal x(n);
[0067] In this embodiment, the system bus zero-sequence voltage signal is continuously sampled and discretized. The sampling frequency f s It is set to at least 10 times the fundamental frequency of the power system (such as 50 Hz) to ensure the capture of high-frequency harmonics. The number of sampling points N is selected according to the target frequency range of the detection to ensure that the frequency resolution after FFT processing is sufficient.
[0068] The sampled discrete time domain signal is:
[0069]
[0070] In the formula, x(n) represents the discrete signal in the time domain, M is the total harmonic number contained in the signal, and A is m represents the amplitude of the mth harmonic, f m represents the frequency of the mth harmonic, θ m represents the phase of the mth harmonic; f s is the sampling frequency, and N is the number of sampling points.
[0071] 2) Apply Hanning window to perform windowing processing on discrete signals to reduce spectrum leakage and improve frequency resolution;
[0072] In the present invention, before performing FFT processing, the Hanning window function w is applied to the sampled signal. (n) , it can effectively smooth the signal and reduce the sidelobe effect.
[0073] The window function expression is:
[0074]
[0075] The signal after the window function is:
[0076] x w [n] = x[n]·w(n)
[0077] The purpose of this step is to reduce the frequency leakage effect introduced by truncating the sampling points, so as to obtain more accurate spectrum analysis results.
[0078] 3) For the windowed signal x w [n] Perform fast Fourier transform (FFT); convert the time domain signal into a frequency domain signal, that is, decompose the time domain signal into harmonic components of different frequencies through FFT to form a spectrum diagram for subsequent analysis; the conversion process is:
[0079]
[0080] Where x[k] is the kth frequency component of the frequency domain signal, including the real part and the imaginary part, and x w [n] is the windowed signal, and N is the number of sampling points.
[0081] In a preferred embodiment, it also includes:
[0082] 4) Correct the amplitude and phase;
[0083] In the present invention, since the frequency resolution of the FFT result is limited, the frequency peak value usually does not fall precisely on the discrete spectrum point. Therefore, the FFT result needs to be corrected.
[0084] First, the amplitude calculation formula corresponding to the frequency component is:
[0085]
[0086] The corresponding frequency f k for:
[0087]
[0088] Assume that the peak of the spectrum is located between the spectrum lines k1 and k2 around point k0,
[0089] The amplitude is corrected using the following formula:
[0090]
[0091] Where |x[k0]| is the amplitude to be corrected, k1 and k2 are the discrete spectral lines located on the left and right sides of point k0, and x[k1]| and |x[k2]| are the amplitudes of the adjacent points on the left and right, respectively.
[0092] And use the following formula to correct the frequency:
[0093]
[0094] In the formula, f k0 is the frequency with correction, is the frequency resolution.
[0095] 5) Further, spectrum analysis and resonance identification are performed, and then the results are output.
[0096] The present invention obtains the judgment result corresponding to the ferromagnetic resonance by analyzing the FFT spectrum signal, and the judgment method is as follows: when the FFT spectrum signal amplitude of the bus zero-sequence voltage is mainly distributed less than 50, and its main peak is located at a frequency far lower than the fundamental wave, it is determined that the ferromagnetic component has a low-frequency resonance; when the spectrum signal amplitude is mainly distributed at less than 50Hz, and is an integer multiple of the fundamental wave frequency (such as 1 / 2, 1 / 3, etc.), it is determined that the ferromagnetic component has a frequency division resonance; when the spectrum signal amplitude is mainly distributed at 50, the ferromagnetic component has a fundamental frequency resonance; when the spectrum signal amplitude is mainly distributed greater than 50, it is determined that the ferromagnetic component has a double frequency resonance.
[0097] In one embodiment, referring to Figure 2 ,
[0098] First, determine whether the main distribution of amplitude is less than 50.
[0099] If yes, first determine whether the main peak is smaller than the fundamental wave, if yes, it is low-frequency resonance; if not, continue to determine whether it is an integer fraction of the fundamental wave frequency, if yes, it is frequency division resonance;
[0100] If not, determine whether the amplitude distribution is equal to 50. If so, it is fundamental frequency resonance; otherwise, it is high frequency resonance.
[0101] In another exemplary embodiment, whether ferromagnetic resonance exists is determined based on the capacitive reactance to ground of the voltage transformer and the excitation inductive reactance at the rated line voltage;
[0102] In this embodiment, the primary side voltage and excitation current corresponding to the voltage transformer in the power system are first obtained, wherein the primary side voltage may be the input voltage corresponding to the input end of the voltage transformer, and the excitation current may be the current corresponding to the working magnetic field generated by the voltage transformer.
[0103] Then, the ratio of the capacitive reactance of each phase of the system to the exciting inductive reactance of the winding of the electromagnetic PT under the rated line voltage is calculated, and the judgment result of whether the ferromagnetic resonance occurs in the ferromagnetic element is obtained according to the calculation result.
[0104] Specifically, the capacitive reactance of the voltage transformer to ground is obtained by the following formula:
[0105]
[0106] In the formula, C represents the capacitance value of the voltage transformer, f represents the frequency of the voltage transformer, and ω represents the angular frequency of the voltage transformer;
[0107] The excitation inductive reactance at rated line voltage is obtained by the following formula:
[0108]
[0109] Where U m Indicates the line voltage of PT operation, I m Indicates the excitation current.
[0110] The intersection of the two characteristic curves of inductance and capacitance is a necessary condition for the generation of ferromagnetic resonance, which is equivalent to requiring that the initial slope of the capacitor's volt-ampere characteristic be smaller than the initial slope L of the inductor's volt-ampere characteristic, that is: ωC is the capacitive reactance of each phase of the system to ground, and ωL is the excitation inductive reactance of the winding of the electromagnetic PT under the action of the rated line voltage. Meeting this condition is a necessary condition for the generation of ferromagnetic resonance.
[0111] Furthermore, the capacitive reactance X of the target system bus to ground is calculated. C The excitation inductance X of the winding of the electromagnetic PT under the rated line voltage m The ratio of X C =1 / ωC,X m =ωL, and determine X C / X m Is it within the threshold range? If X C / X m ≤0.01 or X C / X m≥2.8, the system will not have ferromagnetic resonance, otherwise, the system will have ferromagnetic resonance.
[0112] From this we can know that X C / X m When the ratio is too large or too small, ferromagnetic resonance is unlikely to occur.
[0113] This embodiment simulates and analyzes the ferromagnetic resonance of PT ferromagnetic components in a 10-35KV neutral point ungrounded system. Figure 3 As shown, where E a and I a is the three-phase voltage and current on the high-voltage side of the PT, E a1 and I b The three-phase voltage and current when ferromagnetic resonance occurs in a system with an ungrounded neutral point. Figure 3 The system is set to simulate the line maintenance disconnection at 0.3s. The change of the system-to-ground capacitance affects the system charge. When the line-to-ground equivalent capacitance and the PT equivalent inductance form a circuit, according to the zero-sequence equivalent loop, E a and I a The PT core is severely saturated, which reduces the equivalent impedance of the PT high-voltage side, causing the capacitance and inductance parameters in the system to reach the resonant matching condition. A large harmonic current will flow through the PT high-voltage side, triggering ferromagnetic resonance in the neutral point ungrounded system, causing a displacement overvoltage at the neutral point of the power grid, E a1 and I b This is because the different saturation levels of the three PT windings cause the two-phase or three-phase voltages to increase simultaneously, which is manifested as a shift in the neutral point potential of the system.
[0114] When ferromagnetic resonance occurs in the system, a fast Fourier transform is performed on the zero-sequence voltage of the system bus to obtain a corresponding ferromagnetic resonance type judgment result. The ferromagnetic resonance type judgment result can be a ferromagnetic resonance mode for characterizing the PT ferromagnetic element, and the ferromagnetic resonance mode includes one of low-frequency resonance, frequency division resonance, fundamental frequency resonance or high-frequency resonance.
[0115] Specific process reference Figure 4 , by analyzing the amplitude of the spectrum signal, the resonance category is obtained;
[0116] Preferably, corresponding measures are taken for resonances of different frequencies.
[0117] In one embodiment, the present application further discloses a method for preventing and controlling ferromagnetic resonance of a voltage transformer, comprising detecting ferromagnetic resonance using any of the above-described methods for detecting ferromagnetic resonance of a voltage transformer, and preventing and controlling the ferromagnetic resonance based on the detection result.
[0118] like Figure 5As shown in the figure, there are two main ideas for detuning measures: changing the system parameters by changing the system operation mode or adding or reducing system equipment so that it does not meet the resonance conditions, including adopting the 4PT wiring method, selecting PTs with good excitation characteristics, increasing the grid-to-ground capacitance, grounding the neutral point through an arc suppression coil, and changing parallel-operated PTs to separate-operated ones; increasing the system damping to consume the resonance energy and suppress the resonance, including connecting a microcomputer detuning device to the PT open triangle, connecting a linear resistor or a nonlinear resistor to the neutral point of the PT primary side, etc.
[0119] The present invention adopts corresponding specific detuning measures for different types of ferromagnetic resonance prevention and control functions as follows:
[0120] (1) For frequency division resonance, the neutral point on the primary side of the PT is grounded through a nonlinear resistor detuning device, which can effectively suppress the frequency division ferromagnetic resonance caused by the disappearance of the single-phase grounding fault. This method is characterized by consuming resonance energy and increasing resonance damping. Compared with the traditional linear resistor grounding method, the nonlinear resistor grounding has a more significant effect on limiting overvoltage, and will not affect the normal operation of the protection device. In addition, when the number of PTs in the system is small, the neutral point automatic arc suppression coil can be combined to compensate for the grounding capacitance current to further enhance the resonance suppression effect. This combination provides more reliable overvoltage control and system stability.
[0121] (2) For low-frequency resonance, a damping resistor is added to the open delta winding of the voltage transformer (PT) to suppress it, which is equivalent to connecting a resistor to the neutral point of the power transformer. During normal operation, the resistor connected to the open delta winding will not consume energy. When a single-phase grounding fault occurs in the system and the resonance is eliminated, the detuning device starts and a small resistor is connected to the circuit. This damping resistor can provide additional loss when resonance occurs. As long as a damping resistor with a suitable resistance value is selected, it can avoid large circulating currents causing PT to burn out, thereby better suppressing resonance.
[0122] (3) For fundamental frequency resonance, it can be avoided by changing system parameters, such as adjusting the setting of shunt reactor, or connecting damping resistor to the neutral point of primary side of PT. In addition, using voltage transformer with better excitation characteristics can also reduce the occurrence of fundamental frequency resonance. In practice, capacitor voltage transformer is selected, and semi-insulated PT is replaced with fully insulated PT. Combining the above detuning methods can fundamentally eliminate saturation, suppress resonant overvoltage, and thus eliminate resonance.
[0123] (4) For high-frequency resonance, it is usually necessary to add appropriate filters or isolation devices to the system to reduce the impact of high-frequency harmonics. Two damping resistors can also be connected in parallel on the open triangle side of the PT. The large damping resistor is put into use for a long time to actively suppress high-frequency resonance. The large damping resistor can effectively suppress high-frequency resonance in advance. In combination with the small damping resistor, the high-frequency resonance can be effectively eliminated in a short time, reducing the harm of high-frequency resonance to the PT body and the system. Compared with the traditional detuning method, this method can eliminate the bus voltage distortion caused by feeder harmonics, the increase of transformer open triangle voltage, and the frequent malfunction of the secondary detuning device.
[0124] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.
[0125] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A voltage transformer ferromagnetic resonance detection method, characterized in that: Determine whether there is ferromagnetic resonance based on the voltage transformer's capacitive reactance to ground and the excitation inductive reactance under the rated line voltage. If so, perform the following steps: Collect the zero-sequence voltage signal of the voltage transformer busbar for discretization; The Hanning window is used to perform windowing on discrete signals; Perform fast Fourier transform on the windowed signal to obtain the amplitude distribution of the spectrum signal; The ferromagnetic resonance category is determined based on the frequency spectrum signal amplitude distribution.
2. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: The capacitive reactance of the voltage transformer to ground is obtained by the following formula: In the formula, C represents the capacitance value of the voltage transformer, f represents the frequency of the voltage transformer, and ω represents the angular frequency of the voltage transformer; The excitation inductive reactance at rated line voltage is obtained by the following formula: Where U m Indicates the line voltage of PT operation, I m Indicates the excitation current.
3. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: Determine whether there is ferromagnetic resonance, including: Determine the ferromagnetic resonance threshold range, if X C / X m If the ferromagnetic resonance threshold value is within the ferromagnetic resonance threshold value range, it is determined that the ferromagnetic resonance phenomenon exists; the ferromagnetic resonance threshold value range is: 0.01<X C / X m <2.8 Where, X C It represents the capacitive reactance of voltage transformer to ground, X m It indicates the excitation inductive reactance of the voltage transformer at rated line voltage.
4. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: The sampling frequency of the voltage transformer bus zero-sequence voltage signal is at least 10 times the fundamental frequency of the voltage transformer.
5. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: The signal expression after the discrete signal is windowed using the Hanning window is: x w [n]=x[n]·w(n) In the formula, x[n] represents the discrete signal in the time domain, w(n) represents the window function, M is the total harmonic number contained in the signal, and A is m represents the amplitude of the mth harmonic, f m represents the frequency of the mth harmonic, θ m represents the phase of the mth harmonic; f s is the sampling frequency, and N is the number of sampling points.
6. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: Perform fast Fourier transform on the windowed signal, including: Where x[k] is the kth frequency component of the frequency domain signal, x w [n] is the windowed signal, and N is the number of sampling points.
7. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: After obtaining the amplitude distribution of the spectrum signal, the amplitude and frequency are corrected respectively; among them, The amplitude is corrected using the following formula: Where |x[k0]| is the amplitude to be corrected, k1 and k2 are the discrete spectral lines on the left and right sides of point k0, x[k1]| and |x[k2]| are the amplitudes of the adjacent points on the left and right sides, respectively. And use the following formula to correct the frequency: In the formula, f k0 is the frequency with correction, is the frequency resolution.
8. The voltage transformer ferromagnetic resonance detection method according to claim 1, characterized in that: Determine the type of ferromagnetic resonance based on the spectrum signal amplitude distribution, including: When the spectrum signal amplitude distribution is greater than 50Hz, the ferromagnetic resonance is a high-frequency resonance; When the spectrum signal amplitude distribution is equal to 50Hz, the ferromagnetic resonance is the fundamental frequency resonance; When the spectrum signal amplitude distribution is less than 50Hz, If the peak value of the main peak is much lower than the fundamental frequency, the ferromagnetic resonance is a low-frequency resonance; If the peak value of the main peak is an integer fraction of the fundamental frequency, the ferromagnetic resonance is a fractional frequency resonance.
9. A method for preventing and controlling ferromagnetic resonance of a voltage transformer, characterized in that: The ferromagnetic resonance detection method of a voltage transformer according to any one of claims 1 to 8 is used to detect the ferromagnetic resonance, and prevention and treatment are performed according to the detection result, comprising: To address the frequency division resonance, the neutral point of the primary side of the voltage transformer is grounded via a nonlinear resistor detuning device; To address low-frequency resonance, a damping resistor is added to the open delta winding of the voltage transformer; For fundamental frequency resonance, change the voltage transformer parameters, or connect a damping resistor to the neutral point of the voltage transformer's high voltage measurement; To address high-frequency resonance, add a filter or isolation device to the voltage transformer, or use a large damping resistor.
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