Method for correcting cvt transient measurement errors using digital filter

Abstract

This invention discloses a method for correcting transient measurement errors of CVTs using a digital filter. CVTs, as monitoring devices used to measure grid voltage in power systems, suffer from nonlinear components and are affected by stray capacitance in the windings at high frequencies. This causes oscillating waveforms in the secondary voltage of the CVT during transient processes, disrupting the linear relationship between the steady-state secondary voltage and the primary line voltage. This leads to distortion of the CVT output signal, resulting in a surge in transient voltage measurement errors and reducing the accuracy of the measurement system. Therefore, based on the CVT frequency response curve, an indirect method is used to design a digital filter to correct CVT transient measurement errors. This not only improves the accuracy of transient measurements and suppresses persistent resonance protection measurement systems, but also provides assurance for system relay protection and reliable transient voltage measurement.

Description

Technical Field

[0001] This invention belongs to the field of power quality, and specifically relates to a method for correcting CVT transient measurement errors using a digital filter. Background Technology

[0002] Capacitor voltage transformers (CVTs) have become widely used in power systems for monitoring and metering grid voltage. Under power frequency operation, CVTs can accurately measure and reproduce the primary voltage. When harmonic voltages occur in the system, measurement errors can be corrected based on the CVT's transfer characteristic curve. However, due to the presence of nonlinear components such as compensating reactors, intermediate transformers, and dampers within the CVT, and the influence of stray capacitance in the windings at high frequencies, transient processes can cause oscillating waveforms in the CVT's secondary voltage. Furthermore, excessively high current flowing through the excitation branch can lead to saturation of the CVT's intermediate transformer, causing ferroresonance within the CVT. Because the transient characteristics of the CVT disrupt the linear relationship between the secondary measured voltage and the primary line voltage under steady-state conditions, the CVT output signal becomes distorted, causing a surge in transient voltage measurement errors and reducing the accuracy of the measurement system. If ferroresonance persists, it can also severely damage the measuring instrument, threatening the stable operation of the measurement system.

[0003] Due to the transient characteristics of CVTs, transient voltage measurement errors are relatively large. Existing CVT transient error studies rarely consider the simultaneous effects of CVT transient response characteristics and ferroresonant characteristics. Furthermore, in some transient cases, intermediate transformer saturation leads to further changes in error. Therefore, this study investigates an error correction method for CVT transient measurement to reduce the errors in CVT transient voltage measurement and suppress persistent resonance protection measurement systems, thereby providing assurance for system relay protection and reliable transient voltage measurement. Summary of the Invention

[0004] The purpose of this invention is to provide a method for correcting CVT transient measurements using digital filters, which solves the problem that the transient characteristics of CVT cause distortion of the CVT output signal, resulting in a surge in transient voltage measurement error and reducing the accuracy of the measurement system.

[0005] The technical solution adopted in this invention is a method for correcting CVT transient measurement errors using digital filters. Specifically, it involves constructing an equivalent CVT model, obtaining the CVT frequency response curve using the transfer function method, and based on the CVT frequency response curve, using an indirect digital filter design method to determine the design parameters of the analog filter and design the Butterworth filter parameters to obtain the transfer function of the analog filter. Then, the analog filter is converted into a digital filter using the bilinear transform method to obtain the digital filter transfer function, thus completing the digital filter design and achieving the purpose of correcting CVT transient measurement errors.

[0006] The invention is further characterized in that,

[0007] The designed digital filter can simultaneously suppress the oscillating voltage caused by the transient response and ferromagnetic characteristics of the CVT. In voltage measurement, it can reduce the measurement error caused by the transient characteristics of the CVT. Moreover, this method only requires knowledge of the CVT frequency response curve to design a digital filter suitable for the error correction of the target CVT, making the method more applicable.

[0008] This invention utilizes a digital filter to correct transient measurement errors in CVTs. The specific operation steps are as follows:

[0009] Step 1: Establish an equivalent model based on the CVT structure, and obtain the CVT frequency response curve using the transfer function method;

[0010] Step 2: Determine the design specifications of the analog filter based on the CVT frequency response curve, including the passband cutoff frequency, the passband maximum attenuation, the stopband cutoff frequency, and the stopband minimum attenuation, and design the Butterworth filter parameters to obtain the transfer function of the analog filter.

[0011] Step 3: Use the bilinear transform method to convert the analog filter into a digital filter and obtain the digital filter transfer function;

[0012] Step 4: Use the designed digital filter to process the CVT transient response and the secondary output signal of the ferromagnetic resonance to verify the performance of the designed digital filter.

[0013] Step 1 is implemented as follows: an equivalent model is established based on the CVT structure, and the CVT frequency response curve is obtained by using the transfer function method.

[0014] Based on the CVT structure, an equivalent CVT model is constructed, considering the effects of loss resistance and stray capacitance in each component. Since the transmission error of a CVT to transient signals is determined by its frequency response characteristics, different CVT models have different internal parameters, leading to different frequency response curves. This invention primarily uses the transfer function method to obtain the CVT frequency response curve. To obtain the CVT transfer function, the equivalent CVT model must first undergo impedance equivalence. To obtain the overall CVT transfer function expression, the intermediate transformer is first transformed using a star-delta configuration, yielding its equivalent impedance expression as follows:

[0015]

[0016] Among them, R T1 L T1 R T2 L T2 The resistance and leakage inductance of the primary and secondary windings of the intermediate transformer were measured; R m L m For the magnetizing resistance and inductance of the intermediate transformer; C T1 C T2 C represents the equivalent stray capacitance to ground of the primary and secondary windings of the intermediate transformer; T12 Z represents the coupling stray capacitance between the primary and secondary windings of the intermediate transformer. a Z b Z c Z represents the equivalent impedance between the windings of the intermediate transformer after star-delta transformation. CT1 Z CT2 Z CT12 This refers to the stray capacitance impedance values ​​of the primary winding to ground, the stray capacitance impedance values ​​of the secondary winding to ground, and the coupling capacitance impedance values ​​of the primary and secondary windings of the intermediate transformer. This represents the representation of the s-field, which is also the complex field; Z T1 This refers to the impedance value corresponding to the primary winding of the intermediate transformer, Z. T2 This refers to the impedance value corresponding to the secondary winding of the intermediate transformer, Z. m This represents the impedance value corresponding to the excitation branch of the intermediate transformer.

[0017] The expressions for each impedance are further obtained as follows:

[0018]

[0019] Among them, Z C1 Z is the equivalent impedance of the CVT high-voltage capacitor; C2 Z is the equivalent impedance of the voltage capacitor in the CVT; CS To compensate for the equivalent impedance of the reactor; Z aT Z bT Z cTThe equivalent impedance of the intermediate transformer is to take into account the stray capacitance between each winding;

[0020] Then, the equivalent impedances Z1 to Z6 of each stage port are derived from the secondary side of the CVT, as shown in equation (3):

[0021]

[0022] The ratio of the output and input voltages at each port can be obtained from the equivalent impedance. Multiplying the voltage ratios together gives the overall transfer function expression of the CVT, as shown in equation (4).

[0023]

[0024] Wherein, U1(s) is the input voltage transfer function at port U1(s), and U2(s) is the output voltage transfer function at port U2(s);

[0025] According to equation (4), i.e., the CVT transfer function, the CVT frequency response curve can be obtained. Since the CVT frequency response curve has multiple poles and the overall curve is complex, directly using the overall CVT frequency response curve as the identification target results in a high filter order and significant design difficulty. In filter design, the filter order is the main factor affecting filtering performance; the higher the filter order, the more ideal the frequency response of the designed filter, but the longer the filter delay time. To address the problem of excessively high filter orders, the CVT transfer function can be decomposed into multiple sub-functions to reduce the order of a single filter. Therefore, this invention uses a cascade method to analyze the CVT equivalent circuit, i.e., the CVT equivalent circuit can be considered as a cascade of three parts: a capacitor unit, a compensating reactor, and an intermediate transformer, whose transfer functions are respectively expressed as H... C H L and H T The expression is shown in equation (5).

[0026]

[0027] By representing the CVT as a cascaded three-part system, and using the frequency response curves of the three parts as the design targets for the three digital filters, the filter design order can be effectively reduced, the design difficulty can be lowered, and the filter performance can be improved.

[0028] Step 2 is implemented as follows: Determine the design parameters of the analog filter based on the CVT frequency response curve, including the passband cutoff frequency, the passband maximum attenuation, the stopband cutoff frequency, and the stopband minimum attenuation, and design the Butterworth filter parameters to obtain the transfer function of the analog filter.

[0029] The filter designed in this invention aims to accurately correct the amplitude-frequency characteristics of the CVT output voltage. Therefore, an indirect method is used to design an Infinite Impulse Response (IIR) filter simulation model. First, the design specifications of the digital filter are converted into the design specifications of the analog filter. Then, the analog filter is designed based on the specifications. Finally, the analog filter is converted into a digital filter using the impulse response method or the bilinear transformation method.

[0030] To obtain the design specifications of the analog filter, the CVT frequency response data H needs to be processed. CVT (jω) Amplitude |H CVT (jω)| transformed into logarithmic modulo form:

[0031] |H dB |=20lg|H CVT (jω)| (6)

[0032] In the formula, |H dB This reflects the gain or attenuation of the signal transmitted by the CVT at each frequency.

[0033] The design goal of the analog filter is to filter out |H dB The frequency bands in the curve where the gain is greater than 0 correspond to the filter's stopband. Therefore, according to |H... dB The curve can determine the filter stopband starting angular frequency ω. s1 and cutoff angular frequency ω s2 The first passband cutoff angular frequency ω p1 and the starting angular frequency ω of the second passband p2 and the maximum stopband attenuation A′ s .

[0034] Convert the start and stop angular frequencies into analog filter design specifications, simulating the passband cutoff frequency Ω. p and analog stopband cutoff frequency Ω s The corresponding transformation formula is:

[0035]

[0036]

[0037] In the formula:

[0038] T—Filter sampling frequency;

[0039] To compensate for the nonlinear distortion between the digital angular frequency and the analog frequency, pre-distortion is also required here:

[0040]

[0041]

[0042] The analog filter model used in this invention is a Butterworth filter. When designing a Butterworth filter, the required design specifications include the passband cutoff frequency Ω. pb Maximum passband attenuation A p Stopband cutoff frequency Ω sb and stopband minimum attenuation A s The relationship between the design specifications of the analog filter and the setting parameters of the Butterworth filter is as follows:

[0043]

[0044] Ω sbi =Ω′ si (12)

[0045] A p =1 (13)

[0046] A s =A′ s (14)

[0047] After setting the parameters, the minimum order N of the Butterworth filter can be obtained:

[0048]

[0049]

[0050] And the 3dB cutoff frequency ω of the Butterworth filter n :

[0051]

[0052] Substituting the Butterworth filter parameters into H b From (s), the transfer function of the Butterworth analog filter can be obtained:

[0053]

[0054] Where a0 = 1, k = 1, 2, 3, ..., n, where n is the order of the filter.

[0055] Step 3 is implemented as follows: the analog filter is converted into a digital filter using the bilinear transform method, and the transfer function of the digital filter is obtained.

[0056] The ultimate goal of this invention is to obtain a digital filter. The key to designing a digital filter lies in determining the coefficients of the transfer function. However, identifying multiple variables is quite complex, and the number of coefficients increases with the filter order, making coefficient acquisition even more difficult. Therefore, it is necessary to consider methods for obtaining filter coefficients other than direct identification. Since there is a derivable transformation relationship between the S-plane and the Z-plane, the bilinear transformation method can be used to transform the analog filter into the required digital filter. The transformation relationship is shown in equation (19):

[0057]

[0058] Substituting equation (19) into equation (18), we obtain the transfer function of the digital filter. At this point, the digital filter meets the requirement of filtering out the stopband frequency and has obtained the corresponding minimum filter order.

[0059] Step 4 is implemented as follows: The designed digital filter is used to process the CVT transient response and the secondary output signal of the ferromagnetic resonance to verify the performance of the designed digital filter.

[0060] In step 2, the frequency response curves of the capacitor unit, the compensation reactor, and the intermediate transformer are used as the design targets for three digital filters. Three digital filters are designed to correct CVT transient errors, processing oscillating voltage signals in three frequency bands. During signal processing, the CVT and filters are cascaded; the CVT output voltage is processed by the filters, forming the CVT output signal processing module. The grid voltage u1(t) is input to the CVT as the primary voltage. After transmission by the CVT, its secondary output voltage is sent to the filters for processing. Filter 1 filters for frequencies near frequency range 1, filter 2 filters for frequencies in range 2, and filter 3 filters out frequency-division oscillation components below 50Hz. The output voltage u2(t) of the signal processing module is the voltage signal after CVT transient error correction, verifying the correction of CVT transient response characteristics and ferroresonant characteristics.

[0061] The beneficial effects of this invention are:

[0062] Because the transient characteristics of a CVT disrupt the linear relationship between the secondary measured voltage and the primary line voltage, the CVT output signal becomes distorted, causing a surge in transient voltage measurement errors and reducing the accuracy of the CVT measurement system. Therefore, it is necessary to analyze and correct CVT transient measurement errors. Based on this, an error correction method for CVT transient measurement is invented, which not only reduces CVT transient voltage measurement errors and improves the accuracy of the CVT measurement system, but also provides assurance for system relay protection and reliable transient voltage measurement. Attached Figure Description

[0063] Figure 1This is the equivalent circuit diagram of the CVT of this invention.

[0064] Figure 2 This is the CVT impedance equivalent circuit diagram of the present invention.

[0065] Figure 3 This invention relates to the CVT output voltage processing module.

[0066] Figure 4(a) shows the performance verification results of filter 1 before filtering when the CVT of the present invention undergoes transient response.

[0067] Figure 4(b) shows the performance verification results of filter 1 after filtering when the CVT of the present invention undergoes transient response.

[0068] Figure 5(a) shows the performance verification results of filter 2 before filtering when the CVT of the present invention undergoes transient response.

[0069] Figure 5(b) shows the performance verification results of filter 2 after filtering when the CVT of the present invention undergoes transient response.

[0070] Figure 6(a) shows the performance verification results of filter 3 before filtering when the CVT of the present invention undergoes transient response.

[0071] Figure 6(b) shows the performance verification results of filter 3 after filtering when the CVT of the present invention undergoes transient response.

[0072] Figure 7 This invention compares the transient response output of the CVT with the output of the filter.

[0073] Figure 8(a) shows the performance verification results of filter 1 before filtering when the CVT of the present invention undergoes ferromagnetic resonance.

[0074] Figure 8(b) shows the performance verification results of filter 1 after the CVT of the present invention undergoes ferromagnetic resonance and is filtered.

[0075] Figure 9(a) shows the performance verification results of filter 3 before filtering when the CVT of the present invention undergoes ferromagnetic resonance.

[0076] Figure 9(b) shows the performance verification results of filter 3 after the CVT of the present invention undergoes ferroresonance and is filtered.

[0077] Figure 10 This is a comparison between the output of the CVT when it generates ferroresonance and the output of the filter.

[0078] Figure 11 This is a flowchart of the method of the present invention. Detailed Implementation

[0079] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0080] Example 1

[0081] like Figure 1 The diagram shows the equivalent circuit of the CVT of this invention. C1 and C2 are the high-voltage and medium-voltage capacitors of the CVT, respectively; R1 and R2 are the equivalent loss resistances of the high-voltage and medium-voltage capacitors of the CVT; R... S L S To compensate for the resistance and inductance of the reactor; C S To compensate for the equivalent stray capacitance of the reactor; R T1 L T1 R T2 L T2 The resistance and leakage inductance of the primary and secondary windings of the intermediate transformer were measured; R m L m For the magnetizing resistance and inductance of the intermediate transformer; C T1 C T2 C represents the equivalent stray capacitance to ground of the primary and secondary windings of the intermediate transformer; T12 This refers to the stray capacitance between the primary and secondary windings of the intermediate transformer, and all parameters are referred to the primary side of the intermediate transformer.

[0082] Figure 2 This is the equivalent circuit diagram of the CVT impedance of this invention. Wherein, Z... C1 Z is the equivalent impedance of the CVT high-voltage capacitor; C2 Z is the equivalent impedance of the voltage capacitor in the CVT; CS To compensate for the equivalent impedance of the reactor; Z aT Z bT Z cT The equivalent impedance of the intermediate transformer is considered to account for stray capacitances between windings.

[0083] Example 2

[0084] The present invention provides a method for correcting CVT transient measurement errors using digital filters, such as... Figure 11 As shown, the specific implementation steps are as follows:

[0085] Step 1: Establish an equivalent model based on the CVT structure, obtain the CVT frequency response curve using the transfer function method, and determine the design objectives of the digital filter.

[0086] Based on the CVT structure, an equivalent CVT model is constructed, considering the effects of loss resistance and stray capacitance in each part, such as... Figure 1 The diagram shown is an equivalent circuit diagram of a CVT. Since the transmission error of a CVT to transient signals is determined by its frequency response characteristics, different CVT models have different internal parameters, resulting in different frequency response curves. This invention mainly uses the transfer function method to obtain the CVT frequency response curve. To obtain the CVT's transfer function, the CVT equivalent model must first undergo impedance equivalence. The CVT impedance equivalent circuit diagram is shown below. Figure 2 As shown. To obtain the overall transfer function expression of the CVT, the intermediate transformer is first transformed into a star-delta configuration, resulting in its equivalent impedance expression as follows:

[0087]

[0088] Among them, R T1 L T1 R T2 L T2 The resistance and leakage inductance of the primary and secondary windings of the intermediate transformer were measured; R m L m For the magnetizing resistance and inductance of the intermediate transformer; C T1 C T2 C represents the equivalent stray capacitance to ground of the primary and secondary windings of the intermediate transformer; T12 Z represents the coupling stray capacitance between the primary and secondary windings of the intermediate transformer. a Z b Z c Z represents the equivalent impedance between the windings of the intermediate transformer after star-delta transformation. CT1 Z CT2 Z CT12 This refers to the stray capacitance impedance values ​​of the primary winding to ground, the stray capacitance impedance values ​​of the secondary winding to ground, and the coupling capacitance impedance values ​​of the primary and secondary windings of the intermediate transformer. This represents the representation of the s-field, which is also the complex field; Z T1 This refers to the impedance value corresponding to the primary winding of the intermediate transformer, Z. T2 This refers to the impedance value corresponding to the secondary winding of the intermediate transformer, Z. m This represents the impedance value corresponding to the excitation branch of the intermediate transformer.

[0089] Further obtain Figure 2 The expressions for each impedance are as follows:

[0090]

[0091] Among them, Z C1 Z is the equivalent impedance of the CVT high-voltage capacitor; C2 Z is the equivalent impedance of the voltage capacitor in the CVT; CS To compensate for the equivalent impedance of the reactor; Z aT Z bT Z cT The equivalent impedance of the intermediate transformer is to take into account the stray capacitance between each winding;

[0092] Then, the equivalent impedances Z1 to Z6 of each stage port are derived from the secondary side of the CVT, as shown in equation (3):

[0093]

[0094] The ratio of the output and input voltages at each port can be obtained from the equivalent impedance. Multiplying the voltage ratios together gives the overall transfer function expression of the CVT, as shown in equation (4).

[0095]

[0096] Wherein, U1(s) is the input voltage transfer function at port U1(s), and U2(s) is the output voltage transfer function at port U2(s);

[0097] According to equation (4), i.e., the CVT transfer function, the CVT frequency response curve can be obtained. Since the CVT frequency response curve has multiple poles and the overall curve is complex, directly using the overall CVT frequency response curve as the identification target results in a high filter order and significant design difficulty. In filter design, the filter order is the main factor affecting filtering performance; the higher the filter order, the more ideal the frequency response of the designed filter, but the longer the filter delay time. To address the problem of excessively high filter orders, the CVT transfer function can be decomposed into multiple sub-functions to reduce the order of a single filter. Therefore, this invention uses a cascade method to analyze the CVT equivalent circuit, i.e., the CVT equivalent circuit can be considered as a cascade of three parts: a capacitor unit, a compensating reactor, and an intermediate transformer, whose transfer functions are respectively expressed as H... C H L and H T The expression is shown in equation (5).

[0098]

[0099] By representing the CVT as a cascaded three-part system, and using the frequency response curves of the three parts as the design targets for the three digital filters, the filter design order can be effectively reduced, the design difficulty can be lowered, and the filter performance can be improved.

[0100] Step 2: Determine the design specifications of the analog filter based on the CVT frequency response curve, including the passband cutoff frequency, the passband maximum attenuation, the stopband cutoff frequency, and the stopband minimum attenuation, and design the Butterworth filter parameters to obtain the transfer function of the analog filter.

[0101] The filter designed in this invention aims to accurately correct the amplitude-frequency characteristics of the CVT output voltage. Therefore, an indirect method is used to design an Infinite Impulse Response (IIR) filter simulation model. First, the design specifications of the digital filter are converted into the design specifications of the analog filter. Then, the analog filter is designed based on the specifications. Finally, the analog filter is converted into a digital filter using the impulse response method or the bilinear transformation method.

[0102] To obtain the design specifications of the analog filter, the CVT frequency response data H needs to be processed. CVT(jω) Amplitude |H CVT (jω)| transformed into logarithmic modulo form:

[0103] |H dB |=20lg|H CVT (jω)| (6)

[0104] In the formula, |H dB This reflects the gain or attenuation of the signal transmitted by the CVT at each frequency.

[0105] The design goal of the analog filter is to filter out |H dB The frequency bands in the curve where the gain is greater than 0 correspond to the filter's stopband. Therefore, according to |H... dB The curve can determine the filter stopband starting angular frequency ω. s1 and cutoff angular frequency ω s2 The first passband cutoff angular frequency ω p1 and the starting angular frequency ω of the second passband p2 and the maximum stopband attenuation A′ s .

[0106] Convert the start and stop angular frequencies into analog filter design specifications, simulating the passband cutoff frequency Ω. p and analog stopband cutoff frequency Ω s The corresponding transformation formula is:

[0107]

[0108]

[0109] In the formula:

[0110] T—Filter sampling frequency;

[0111] To compensate for the nonlinear distortion between the digital angular frequency and the analog frequency, pre-distortion is also required here:

[0112]

[0113]

[0114] The analog filter model used in this invention is a Butterworth filter. When designing a Butterworth filter, the required design specifications include the passband cutoff frequency Ω. pb Maximum passband attenuation A p Stopband cutoff frequency Ω sb and stopband minimum attenuation A s The relationship between the design specifications of the analog filter and the setting parameters of the Butterworth filter is as follows:

[0115]

[0116] Ω sbi =Ω′ si (12)

[0117] A p =1 (13)

[0118] A s =A′ s (14)

[0119] After setting the parameters, the minimum order N of the Butterworth filter can be obtained:

[0120]

[0121]

[0122] And the 3dB cutoff frequency ω of the Butterworth filter n :

[0123]

[0124] Substituting the Butterworth filter parameters into H b From (s), the transfer function of the Butterworth analog filter can be obtained:

[0125]

[0126] Where a0 = 1, k = 1, 2, 3, ..., n,

[0127] Step 3: Use the bilinear transform method to convert the analog filter into a digital filter and obtain the digital filter transfer function.

[0128] The ultimate goal of this invention is to obtain a digital filter. The key to designing a digital filter lies in determining the coefficients of the transfer function. However, identifying multiple variables is quite complex, and the number of coefficients increases with the filter order, making coefficient acquisition even more difficult. Therefore, it is necessary to consider methods for obtaining filter coefficients other than direct identification. Since there is a derivable transformation relationship between the S-plane and the Z-plane, the bilinear transformation method can be used to transform the analog filter into the required digital filter. The transformation relationship is shown in equation (19):

[0129]

[0130] Substituting equation (19) into equation (18), we obtain the transfer function of the digital filter. At this point, the digital filter meets the requirement of filtering out the stopband frequency and has obtained the corresponding minimum filter order.

[0131] Step 4: Use the designed digital filter to process the CVT transient response and the secondary output signal of the ferromagnetic resonance to verify the performance of the designed digital filter.

[0132] In step 2, the frequency response curves of the capacitor unit, the compensation reactor, and the intermediate transformer are used as the design targets for three digital filters. Through design, three digital filters are obtained that can be used for CVT transient error correction, processing oscillating voltage signals in three frequency bands respectively. In signal processing, the CVT and the filters are cascaded; the CVT output voltage is processed by the filters, forming a CVT output signal processing module, such as... Figure 3 The diagram shows the CVT output signal processing module. The grid voltage u1(t) is input to the CVT as the primary voltage. After transmission by the CVT, its secondary output voltage is sent to filters for processing. Filter 1 filters the area near frequency range 1, filter 2 filters the area within frequency range 2, and filter 3 filters out frequency-division oscillation components below 50Hz. The output voltage u2(t) of the signal processing module is the voltage signal after CVT transient error correction. The correction of the CVT transient response characteristics and ferroresonant characteristics is verified respectively.

[0133] Example 3

[0134] To verify the accuracy of the CVT transient measurement correction method for digital filters proposed in this invention, a model with the following characteristics was used. CVT was used for simulation verification. Three digital filters were designed according to the invention steps, and their parameters are shown in Table 1.

[0135] Table 1 Digital Filter Parameters

[0136]

[0137]

[0138] The voltage waveforms and spectral characteristics before and after filtering for each filter are as follows: Figures 4(a)-6(b) As shown, specific voltage peak comparisons are shown in Table 2. The waveforms of the CVT output voltage and the filter output voltage are compared as follows: Figure 7 As shown.

[0139] Table 2 Filter input and output voltage results under CVT transient response

[0140]

[0141] From Table 3 and Figures 4(a)-6(b) As can be seen, filter 1 reduced the amplitude of the 167Hz frequency component, filter 2 reduced the amplitude of the 3850Hz frequency component, and filter 3 filtered out noise interference below 50Hz. Ultimately, the filter output approaches 0. Figure 7 The results show that the designed digital filter output corrects the oscillations caused by the CVT transient response.

[0142] In the case of ferromagnetic resonance, the voltage does not contain high-frequency components, so only the performance of filter 1 and filter 3 needs to be verified. The verification results are shown in Table 3. Figures 8(a)-9(b) As shown, filter 1 reduces the amplitude of the 170Hz frequency component, while filter 3 filters out harmonic components below 50Hz. The final output voltage of the filter is the steady-state voltage during normal operation. Figure 10 The results show that the designed digital filter output corrects the oscillations caused by the CVT ferromagnetic resonance.

[0143] Table 3. Filter input and output voltage results under CVT ferromagnetic resonance

[0144]

[0145] In summary, the digital filter designed in this invention can simultaneously suppress the oscillating voltage caused by CVT transient response and ferromagnetic characteristics. In transient voltage measurement, it can reduce the measurement error caused by the transient characteristics of CVT. Furthermore, this method only requires knowledge of the CVT frequency response curve to design a digital filter suitable for error correction of the target CVT, making the method more applicable. It not only reduces the CVT transient voltage measurement error and improves the accuracy of the CVT measurement system, but also provides a guarantee for system relay protection and reliable transient voltage measurement.

Claims

1. A method for correcting CVT transient measurement errors using digital filters, characterized in that, Specifically as follows: An equivalent model is established based on the CVT structure, and the CVT frequency response curve is obtained by the transfer function method. The CVT transfer function is decomposed into multiple sub-functions to reduce the order of individual filters. The cascade method is used to analyze the CVT equivalent circuit, which is considered as a cascaded combination of a capacitor unit, a compensating reactor, and an intermediate transformer. Their transfer functions are expressed as follows: , and The expression is shown in equation (5): （5） in, Z C1 This is the equivalent impedance of the CVT high-voltage capacitor; Z C2 The equivalent impedance of the voltage capacitor in the CVT; Z CS To compensate for the equivalent impedance of the reactor; Z aT , Z bT , Z cT The equivalent impedance of the intermediate transformer is to take into account the stray capacitance between each winding; The frequency response curves of the three parts serve as the design targets for the three digital filters, respectively. An indirect digital filter design method is employed. Based on the CVT frequency response curve, the design specifications of the analog filter are determined, including the passband cutoff frequency, maximum passband attenuation, stopband cutoff frequency, and minimum stopband attenuation. The Butterworth filter parameters are then designed to obtain the transfer function of the analog filter. Details are as follows: First, the design specifications of the digital filter are converted into the design specifications of the analog filter. Then, the analog filter is designed based on the specifications. Finally, the analog filter is converted into a digital filter using the impulse response method or the bilinear transformation method. To obtain the design specifications of the analog filter, the CVT frequency response data is required. Amplitude Transform into logarithmic modulo form: In the formula, This reflects the gain or attenuation of the transmitted signal at each frequency of the CVT; The design goal of analog filters is to filter out The frequency bands in the curve where the gain is greater than 0 correspond to the filter's stopband. Therefore, according to... Curve determines the start angular frequency of the filter stopband and cutoff angular frequency The first passband cutoff angular frequency and the starting angular frequency of the second passband and the maximum attenuation in the stopband. ; Convert the start and stop angular frequencies into analog filter design specifications, simulating the passband cutoff frequency. and analog stopband cutoff frequency The corresponding transformation formula is: In the formula: —Filter sampling frequency; To compensate for the nonlinear distortion between the digital angular frequency and the analog frequency, pre-distortion is also required here: When designing a Butterworth filter, the required design specifications include the passband cutoff frequency. Maximum passband attenuation Stopband cutoff frequency and minimum stopband attenuation The relationship between the design specifications of the analog filter and the setting parameters of the Butterworth filter is as follows: After setting the parameters, the minimum order of the Butterworth filter is obtained. N : and the 3dB cutoff frequency of the Butterworth filter : Substitute the Butterworth filter parameters In this process, the transfer function of the Butterworth analog filter is obtained: in, , The order of the filter; By using the bilinear transform method, the analog filter is converted into a digital filter, the transfer function of the digital filter is obtained, and the design of the digital filter is completed, thereby achieving the purpose of correcting the transient measurement error of CVT. The performance of the designed digital filter was verified by processing the transient response and secondary output signal of the ferromagnetic resonance of the CVT.

2. The method for correcting CVT transient measurement errors using a digital filter according to claim 1, characterized in that, Step 1 is as follows: Based on the CVT structure, an equivalent CVT model is constructed, and the CVT frequency response curve is obtained using the transfer function method. To obtain the CVT transfer function, the equivalent CVT model needs to be impedance equivalently transformed. To obtain the overall CVT transfer function expression, the intermediate transformer is first transformed into a star-delta configuration, resulting in its equivalent impedance expression as follows: （1） in, R T1 , L T1 , R T2 , L T2 Measure the resistance and leakage inductance of the primary and secondary windings of the intermediate transformer; R m , L m The excitation resistance and inductance of the intermediate transformer; C T1 , C T2 This refers to the equivalent stray capacitance to ground of the primary and secondary windings of the intermediate transformer. C T12 This refers to the coupling stray capacitance between the primary and secondary windings of the intermediate transformer. Z a , Z b , Z c This is the equivalent impedance between the windings of the intermediate transformer after star-delta transformation; , , This refers to the stray capacitance impedance values ​​of the primary winding to ground, the stray capacitance impedance values ​​of the secondary winding to ground, and the coupling capacitance impedance values ​​of the primary and secondary windings of the intermediate transformer. express s The field is the way to express the complex number field; This refers to the impedance value corresponding to the primary winding of the intermediate transformer. This refers to the impedance value corresponding to the secondary winding of the intermediate transformer. This represents the impedance value corresponding to the excitation branch of the intermediate transformer. The expressions for each impedance are further obtained as follows: （2） in, Z C1 This is the equivalent impedance of the CVT high-voltage capacitor; Z C2 The equivalent impedance of the voltage capacitor in the CVT; Z CS To compensate for the equivalent impedance of the reactor; Z aT , Z bT , Z cT The equivalent impedance of the intermediate transformer is to take into account the stray capacitance between each winding; Then, the equivalent impedance of each stage port is derived from the secondary side of the CVT. Z 1~ Z 6. As shown in equation (3): （3） The ratio of the output and input voltages at each port is obtained from the equivalent impedance. Multiplying the voltage ratios together yields the overall transfer function expression of the CVT, as shown in equation (4): （4） in, Port input voltage transfer function Port output voltage transfer function.

3. The method for correcting CVT transient measurement errors using a digital filter according to claim 1, characterized in that, Step 3 is as follows: The analog filter is transformed into the required digital filter using the bilinear transform method, and the transformation relationship is shown in equation (19): Substituting equation (19) into equation (18), we obtain the transfer function of the digital filter. At this point, the digital filter meets the requirement of filtering out the stopband frequency and has obtained the corresponding minimum filter order.

4. The method for correcting CVT transient measurement errors using a digital filter according to claim 1, characterized in that, Step 4 is as follows: In step 2, the frequency response curves of the capacitor unit, the compensation reactor, and the intermediate transformer are used as the design targets for three digital filters. Three digital filters for CVT transient error correction are designed to process the oscillating voltage signals in three frequency bands. During signal processing, the CVT and the filters are cascaded; the CVT output voltage is processed by the filters, forming the CVT output signal processing module. (Grid voltage) The primary voltage is input to the CVT, and after transmission by the CVT, its secondary output voltage is sent to filters for processing. Filter 1 filters for the vicinity of frequency range 1, filter 2 filters for the frequency range 2, and filter 3 filters out frequency-divided oscillation components below 50Hz; the signal processing module outputs voltage. The voltage signal after CVT transient error correction is used to verify the correction of CVT transient response characteristics and ferromagnetic resonance characteristics.

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