A method for calculating ultra-low frequency dielectric loss based on nyquist theorem

Abstract

The application relates to a kind of ultra-low frequency insulating medium loss calculation methods based on Nyquist theorem, and the specific steps include: using ultra-low frequency power supply to apply voltage to cable, voltage and current are synchronously sampled in sampling period by data acquisition terminal, and sampling signal is obtained;Utilize fast fourier transform algorithm to filter out other frequencies in sampling signal except specified frequency, and obtain filtered signal;All frequency components higher than Nyquist frequency in filtered signal are filtered out, and filtered frequency domain signal is obtained;Utilize inverse fourier transform to convert filtered frequency domain signal into time domain signal, determine the phase angle difference of voltage and current under time domain signal, and utilize phase angle difference to calculate medium loss value.

Description

Technical Field

[0001] This invention relates to the field of cable insulation defect detection technology, specifically to a method for calculating ultra-low frequency insulation dielectric loss based on the Nyquist theorem. Background Technology

[0002] With the increasing demand for urban development and beautification of cityscapes, cable lines have become increasingly popular. Cross-linked polyethylene (XLPE) cables are easy to lay, require little space, and possess characteristics such as high operating temperature, low dielectric loss, and high electrical strength. However, defects in the cable production and laying process, as well as substandard construction techniques, can compromise the overall insulation level of the cable, seriously affecting the safety of the entire cable line. Therefore, to ensure power supply reliability, necessary handover tests and routine tests help power supply companies understand the insulation level and aging condition of these cables. In 2018, the State Grid Corporation of China began to focus on the field of distribution cable insulation testing technology, and provincial companies conducted technical analysis and evaluation of the insulation status of distribution cables in their respective jurisdictions, mainly using oscillating wave and ultra-low frequency dielectric loss measurement methods.

[0003] As a crucial parameter for high-voltage power equipment, especially capacitive equipment, the dielectric loss angle (DSA) directly reflects the insulation status of the equipment. Accurate measurement of the DSA in high-voltage capacitive equipment allows for monitoring of the insulation status, understanding of physical and chemical changes in the insulation, and timely detection of potential hazards caused by insulation problems, thus preventing accidents. Existing DSA detection methods mainly fall into two categories: hardware-based methods, including the wattmeter method and bridge balancing method, which are cumbersome and inefficient, making them difficult to meet the requirements for automatic DSA detection; and software-based methods, including the correlation function method, sine wave parameter method, harmonic analysis method, and other software calculation methods. Harmonic analysis, based on Fourier transform, is currently the most commonly used method for DSA measurement. However, due to asynchronous sampling, harmonic analysis based on fast Fourier transform suffers from spectral leakage and picket fence effects, leading to significant errors in phase calculation and affecting the accuracy of DSA measurement. On the other hand, for embedded systems, interpolation fitting algorithms are computationally intensive, making it difficult to directly solve for the fitting coefficients in the measurement device. Typically, the fitting coefficients are first solved in the host computer and then imported into the measurement device for measurement, a process that is cumbersome and lacks flexibility. Therefore, developing an efficient and accurate method for calculating dielectric loss is of great significance. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention proposes a method for calculating the loss of ultra-low frequency insulating dielectric based on the Nyquist theorem.

[0005] The technical solution of the present invention is as follows:

[0006] This invention proposes a method for calculating the loss of ultra-low frequency insulating dielectrics based on the Nyquist theorem, the specific steps of which include:

[0007] A voltage is applied to the cable using an ultra-low frequency power supply, and the voltage and current are synchronously sampled within the sampling period using a data acquisition terminal to obtain the sampling signal;

[0008] The Fast Fourier Transform algorithm is used to filter out frequencies other than the specified frequency from the sampled signal to obtain the filtered signal;

[0009] The frequency components above the Nyquist frequency in the filtered signal are all filtered out to obtain the filtered frequency domain signal.

[0010] The filtered frequency domain signal is transformed into a time domain signal using inverse Fourier transform. The phase angle difference between voltage and current is determined in the time domain signal, and the dielectric loss value is calculated using the phase angle difference.

[0011] In a preferred embodiment, the ultra-low frequency power supply generates an ultra-low frequency sinusoidal voltage, with the frequency of the sinusoidal signal between 0.01 and 0.1 Hz.

[0012] In a preferred embodiment, the sampling period is defined as generating a trigger signal at the beginning and end of the period of the ultra-low frequency sinusoidal voltage; the trigger signal at the beginning of the period controls the data acquisition terminal to start acquiring signals, and the trigger signal at the end of the period controls the data acquisition terminal to stop acquiring signals.

[0013] In a preferred embodiment, the sampling frequency of the sampling signal is greater than twice the highest frequency contained in the sampling signal.

[0014] In a preferred embodiment, the Nyquist frequency is half the sampling frequency of the sampled signal.

[0015] As a preferred embodiment, the specific calculation process for the step of filtering out frequencies other than the specified frequency from the sampled signal using the Fast Fourier Transform algorithm is as follows:

[0016] The voltage and current in the sampled signal are subjected to Fast Fourier Transform to generate the spectrum of the sampled signal. The calculation formula is as follows:

[0017] u0(f)=FFT(u0(t))

[0018] i0(f)=FFT(i0(t))

[0019] In the formula, u0(t) and u0(f) represent the time-domain and frequency-domain waveforms of the original voltage signal, respectively, and i0(t) and i0(f) represent the time-domain and frequency-domain waveforms of the original current signal, respectively.

[0020] The frequency sequence in the spectrum of the sampled signal is calculated using the following formula:

[0021] f = n / (N*dt)

[0022] n = 0, 1, 2, ..., N-1

[0023]

[0024]

[0025] In the formula, N is the total number of sampling points, dt is the minimum time interval between sampling points, f is the frequency sequence in the spectrum, f1 and f2 are the upper and lower limits of the filter, and u1(f) and i1(f) are the frequency domain waveforms of the filtered voltage and current.

[0026] Based on the frequency sequence in the spectrum of the sampled signal, filter out frequencies other than the specified frequency in the sampled signal.

[0027] In a preferred embodiment, the step of converting the filtered frequency domain signal into a time domain signal using inverse Fourier transform, determining the phase angle difference between voltage and current in the time domain signal, and calculating the dielectric loss value using the phase angle difference specifically includes:

[0028] The filtered frequency domain signal is converted into a time domain signal using the following formula:

[0029] u2(t) = IFFT(u1(f))

[0030] i2(t) = IFFT(i1(f))

[0031] In the formula, u2(t) and i2(t) are the inverse transformation time-domain signals of voltage and current;

[0032] The phase angle difference between voltage and current in the time domain is calculated using the following formula:

[0033] u3(t)=-|u2(t)|

[0034] i3(t)=-|i2(t)|

[0035] [pksv,locsv]=findpeaks(u3(t))

[0036] [pksc,locsc]=findpeaks(i3(t))

[0037] In the formula, pksv and locsv are the peak voltage and their sampling point indices, and pksc and locsc are the peak current and their sampling point indices.

[0038] Find the relationship between the number of sampling points and the phase angle, and use the number of sampling points to calculate the dielectric loss value. The calculation formula is as follows:

[0039] T=mean(locsv(a:b)-locsv(a-2:b-2))

[0040] θ=mean(locsv(a:b)-locsc(a:b))

[0041] δ=T / 4-θ

[0042] tanδ=tan(2πδ / T)

[0043] In the formula, a and b are the sampling point indices, T is the period of the sinusoidal signal, θ is the number of sampling points between adjacent zero-crossing points of the voltage and current signals, δ is the number of sampling points corresponding to the dielectric loss angle, and tanδ is the dielectric loss value.

[0044] The present invention has the following beneficial effects:

[0045] 1. This invention strictly adheres to whole-cycle sampling when acquiring signals, avoiding the spectral leakage and picket fence effect that exist in the harmonic analysis method based on FFT due to asynchronous sampling in the prior art, which leads to large errors in phase calculation and thus affects the accuracy of dielectric loss angle measurement.

[0046] 2. This invention uses an ultra-low frequency power supply as the signal source for the sampling signal, which has higher stability, higher accuracy of the sampling data, and higher stability and accuracy of the calculated dielectric loss value.

[0047] 3. This invention calculates the dielectric loss value based on the Nyquist sampling theorem, which greatly improves the calculation speed of the dielectric loss value. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the process of the present invention;

[0049] Figure 2 This is a structural diagram of the sampling experimental platform;

[0050] Figure 3 This is a graph showing the result of the sampling signal filtering process;

[0051] Figure 4 A schematic diagram showing the selection of reference points for phase calculation;

[0052] Figure 5 The graph shows the calculation results of the insulating dielectric loss. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0055] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0056] The terms “comprising” and “including” indicate the presence of the described feature, whole, step, operation, element and / or component, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0057] The term “and / or” refers to any combination of one or more of the associated listed items, as well as all possible combinations, and includes these combinations.

[0058] Example 1:

[0059] See Figure 1 A method for calculating the loss of ultra-low frequency insulating dielectrics based on the Nyquist theorem, the specific steps of which include:

[0060] A voltage is applied to the cable using an ultra-low frequency power supply, and the voltage and current are synchronously sampled within the sampling period using a data acquisition terminal to obtain the sampling signal;

[0061] In this embodiment, the experimental platform is set up as follows: Figure 2 As shown, an ultra-low frequency (ULFM) power supply generates an ULFM sinusoidal voltage, which is applied to the cable. The frequency of the ULFM sinusoidal signal is between 0.01 and 0.1 Hz. Voltage signal acquisition is achieved using voltage divider resistors, while current signal acquisition is achieved by connecting a small resistor in series with the cable core. A trigger signal is generated at the beginning and end of each cycle of the sinusoidal voltage waveform. When triggered at the beginning of the cycle, the data acquisition terminal starts acquiring the signal; when triggered at the end of the cycle, the data acquisition terminal stops acquiring the signal, achieving full-cycle sampling. The acquired signal is transmitted to a PC via optical fiber for subsequent data processing.

[0062] In actual operation, signals inevitably contain various high-frequency interferences, including electromagnetic radiation and discharges. According to the Nyquist sampling theorem, to recover the original signal without distortion from the sampled signal, the sampling frequency should be greater than twice the highest frequency of the signal. When the sampling frequency is less than twice the highest frequency of the spectrum, the signal spectrum exhibits aliasing. Theoretically, the "highest frequency" cannot be determined; in engineering, only the main components of the signal are considered. The sampling rate f used in this invention... s 10 KS / s:

[0063] f s =10KS / s

[0064] dt = 1 / f s

[0065] In the formula, dt is the sampling interval.

[0066] The Fast Fourier Transform algorithm is used to filter out frequencies other than the specified frequency from the sampled signal to obtain the filtered signal;

[0067] In this embodiment, the first filtering operation is as follows: Figure 3 As shown, after performing a Fast Fourier Transform (FFT) on the acquired ultra-low frequency sinusoidal voltage and current signal, a spectrum of the sampled signal can be obtained. The spectrum contains various frequency components of the sampled signal, but only some frequency components are effective. Only specified frequency components are retained, while other frequency components are set to zero.

[0068] The voltage and current in the sampled signal are subjected to Fast Fourier Transform to generate the spectrum of the sampled signal. The calculation formula is as follows:

[0069] u0(f)=FFT(u0(t))

[0070] i0(f)=FFT(i0(t))

[0071] In the formula, u0(t) and u0(f) represent the time-domain and frequency-domain waveforms of the original voltage signal, respectively, and i0(t) and i0(f) represent the time-domain and frequency-domain waveforms of the original current signal, respectively.

[0072] The frequency sequence in the spectrum of the sampled signal is calculated using the following formula:

[0073] f = n / (N*dt)

[0074] n = 0, 1, 2, ..., N-1

[0075]

[0076]

[0077] In the formula, N is the total number of sampling points, dt is the minimum time interval between sampling points, f is the frequency sequence in the spectrum, f1 and f2 are the upper and lower limits of the filter, and u1(f) and i1(f) are the frequency domain waveforms of the filtered voltage and current.

[0078] Based on the frequency sequence in the spectrum of the sampled signal, filter out frequencies other than the specified frequency in the sampled signal.

[0079] The frequency components above the Nyquist frequency in the filtered signal are all filtered out to obtain the filtered frequency domain signal.

[0080] In this embodiment, when the sampling frequency f s When the frequency is greater than twice the highest frequency in the signal, the sampled digital signal completely retains the information in the original signal without aliasing. The Nyquist frequency is half the sampling frequency of the discrete signal system. To prevent distortion during signal recovery, the portion of the signal frequency above the Nyquist frequency needs to be set to zero. Since the portion above the Nyquist frequency has already been set to zero during the pre-stage filtering process, no additional operation is required.

[0081] f N =f s / 2 and f2 << f N

[0082] In the formula, f N It is the Nyquist frequency.

[0083] The filtered frequency domain signal is transformed into a time domain signal using inverse Fourier transform. The phase angle difference between voltage and current is determined in the time domain signal, and the dielectric loss value is calculated using the phase angle difference.

[0084] In this embodiment, the filtered Fast Fourier Transform spectrum is subjected to an inverse Fourier transform operation to recover the voltage and current signals in the time domain. The calculation process is as follows:

[0085] u2(t) = IFFT(u1(f))

[0086] i2(t) = IFFT(i1(f))

[0087] In the formula, u2(t) and i2(t) are the inverse transformation time-domain signals of voltage and current.

[0088] When calculating the phase angle difference, the location with the fastest signal change rate should be selected. If other locations are chosen as references, the signal change rate is slow, and the selected reference point may appear multiple times within that time period, causing phase angle measurement errors. From the derivative of a sinusoidal signal, we know that the signal change rate is fastest at the zero-crossing point; therefore, the phase relationship at the zero-crossing points of voltage and current should be found. That is, from max(sin′(m)), we know that m is the zero-crossing point of the sinusoidal signal, and m is the reference point for phase calculation. The process of selecting the reference point is as follows: Figure 4 As shown.

[0089] In practice, finding the position of "zero" is quite difficult. To reduce the complexity of the algorithm, the search for zero-crossing points is transformed into the search for peak points. The calculation process is as follows:

[0090] u3(t)=-|u2(t)|

[0091] i3(t)=-|i2(t)|

[0092] [pksv,locsv]=findpeaks(u3(t))

[0093] [pksc,locsc]=findpeaks(i3(t))

[0094] In the formula, pksv and locsv are the peak voltage values ​​and their sampling point indices, while pksc and locsc are the peak current values ​​and their sampling point indices. By taking the absolute value and inverting the time-domain signal, the zero-crossing points are converted into peak points, which facilitates the algorithm's calculation.

[0095] Find the correspondence between the number of sampling points and the phase angle, and calculate the dielectric loss value using the number of sampling points. The calculation process is as follows:

[0096] T=mean(locsv(a:b)-locsv(a-2:b-2))

[0097] θ=mean(locsv(a:b)-locsc(a:b))

[0098] δ=T / 4-θ

[0099] tanδ=tan(2πδ / T)

[0100] In the formula, a and b are the peak sampling point indices, T is the period of the sinusoidal signal, θ is the number of sampling points between adjacent zero crossings of the voltage and current signals, δ is the number of sampling points corresponding to the dielectric loss angle, and tanδ is the dielectric loss value.

[0101] In publicly available invention patents, due to asynchronous sampling, the harmonic analysis method based on FFT suffers from spectral leakage and the picket fence effect, leading to significant errors in phase calculation and affecting the accuracy of dielectric loss angle measurement. This invention adheres to strict integer-cycle sampling during signal acquisition, fundamentally improving the accuracy of dielectric loss calculation. Furthermore, it proposes a dielectric loss calculation method based on the Nyquist sampling theorem, greatly improving the speed and accuracy of dielectric loss calculation. The stability and accuracy of the algorithm were analyzed through experimental testing. An ultra-low frequency sinusoidal voltage of 9kV was applied to the cable using an ultra-low frequency power supply. The data acquisition terminal simultaneously acquired voltage and current signals while ensuring integer-cycle sampling. The data was synchronously sent to a PC, where dielectric loss calculation was performed. The calculation results are as follows: Figure 5 As shown, the standard deviation of the data obtained by the algorithm is 0.000593191, indicating a concentrated data distribution and good stability. Figure 5 It can be seen that the dielectric loss value obtained by this algorithm is stable and highly accurate.

[0102] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for calculating the loss of ultra-low frequency insulating dielectrics based on the Nyquist theorem, characterized in that, The specific steps include: A voltage is applied to the cable using an ultra-low frequency power supply, and the voltage and current are synchronously sampled within the sampling period using a data acquisition terminal to obtain the sampling signal; The Fast Fourier Transform algorithm is used to filter out frequencies other than the specified frequency from the sampled signal to obtain the filtered signal; The specific calculation process for filtering out frequencies other than the specified frequency from the sampled signal using the Fast Fourier Transform algorithm is as follows: Perform a Fast Fourier Transform on the voltage and current in the sampled signal to generate the spectrum of the sampled signal. The calculation formula is as follows: In the formula, u 0( t ), u 0( f The numbers () represent the time-domain and frequency-domain waveforms of the original voltage signal, respectively. i 0( t ), i 0( f () represent the time-domain and frequency-domain waveforms of the original current signal, respectively; The frequency sequence in the spectrum of the sampled signal is calculated using the following formula: In the formula, N The total number of sampling points. dt The minimum time interval between sampling points. f The frequency sequence in the spectrum. f 1 、f 2 represents the upper and lower limits of the filter, u 1( f ), i 1( f () represents the filtered voltage and current frequency domain waveforms; Based on the frequency sequence in the spectrum of the sampled signal, filter out other frequencies in the sampled signal except for the specified frequency; The frequency components above the Nyquist frequency in the filtered signal are all filtered out to obtain the filtered frequency domain signal. The filtered frequency domain signal is transformed into a time domain signal using inverse Fourier transform. The phase angle difference between voltage and current is determined in the time domain signal, and the dielectric loss value is calculated using the phase angle difference. The steps of converting the filtered frequency domain signal into a time domain signal using inverse Fourier transform, determining the phase angle difference between voltage and current in the time domain signal, and calculating the dielectric loss value using the phase angle difference are as follows: The filtered frequency domain signal is converted into a time domain signal using the following formula: In the formula, u 2( t ), i 2( t () represents the inverse transform time-domain signal of voltage and current; The phase angle difference between voltage and current in the time domain is calculated using the following formula: In the formula, pksv and locsv are the peak voltage and their sampling point indices, and pksc and locsc are the peak current and their sampling point indices. Find the relationship between the number of sampling points and the phase angle, and use the number of sampling points to calculate the dielectric loss value. The calculation formula is as follows: In the formula, a , b For sampling point index, T For the period of a sinusoidal signal, θ This represents the number of sampling points between adjacent zero-crossing points of the voltage and current signals. This represents the number of sampling points corresponding to the dielectric loss angle; This represents the dielectric loss value.

2. The method for calculating the loss of ultra-low frequency insulating dielectric based on the Nyquist theorem according to claim 1, characterized in that, The ultra-low frequency power supply generates an ultra-low frequency sinusoidal voltage, with the frequency of the sinusoidal signal between 0.01 and 0.1 Hz.

3. The method for calculating the loss of ultra-low frequency insulating dielectric based on the Nyquist theorem according to claim 1, characterized in that, The sampling period is defined by generating a trigger signal at the beginning and end of the ultra-low frequency sinusoidal voltage period. The trigger signal at the beginning of the period controls the data acquisition terminal to start acquiring signals, and the trigger signal at the end of the period controls the data acquisition terminal to stop acquiring signals.

4. The method for calculating the loss of ultra-low frequency insulating dielectric based on the Nyquist theorem according to claim 1, characterized in that, The sampling frequency of the sampled signal is greater than twice the highest frequency contained in the sampled signal.

5. The method for calculating the loss of ultra-low frequency insulating dielectric based on the Nyquist theorem according to claim 1, characterized in that, The Nyquist frequency is half the sampling frequency of the sampled signal.

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