CN103576002B - A kind of computing method of capacitive insulator arrangement dielectric loss angle - Google Patents

Abstract

The invention discloses the computing method of a kind of capacitive insulator arrangement dielectric loss angle of monitoring technical field.Its technical scheme is, first builds Blackman self-convolution window, and gathers electric current and the voltage signal of Devices to test, and carries out discrete sampling to electric current and voltage signal; Secondly adopt the Blackman self-convolution window built to carry out windowing to discrete signal sequence to block, obtain the discrete spectrum function that rear discrete signal is blocked in windowing; Then the discrete spectrum function that rear discrete signal is blocked in windowing is analyzed, obtain main lobe width and sidelobe performance; Four spectral line interpolation revised theories are finally adopted to solve voltage, current first harmonics signal phase angle and then obtain Dielectric loss angle.The suppression spectral leakage effect that the present invention utilizes Blackman self-convolution window fabulous, utilizes four spectral line interpolations to carry out Spectrum Correction, and based on the Dielectric Loss Angle error of FFT theory under solution non-synchronous sampling, measuring accuracy is high, and hardware requirement is little.

Description

Capacitive insulation equipment dielectric loss angle calculation method

Technical Field

The invention belongs to the technical field of monitoring, and particularly relates to a method for calculating a dielectric loss angle of capacitive insulation equipment.

Background

The devices of the capacitive type insulation structure are most commonly used in high voltage power equipment, classified by the insulation structure. The dielectric loss angle (dielectric loss angle for short) is an important parameter for measuring the insulation performance of electrical equipment, and can accurately reflect the overall insulation performance. The accurate monitoring of the dielectric loss angle can provide reliable basis for the fault diagnosis of the electrical equipment and provide important guarantee for the safe and stable operation of the power system.

Normally, the dielectric loss angle is a very small value, about 0.001 to 0.02rad, and the true value is too small in actual measurement, so that the dielectric loss angle is easily annihilated by errors. At present, the common dielectric loss monitoring methods mainly comprise a hardware method and a software method. The hardware method mainly comprises a penicillin bridge method and a digital zero-crossing method, and the calculation speed of measuring the dielectric loss angle based on the hardware method is high, but the hardware method has the defects of poor anti-interference capability, low measurement precision, large accumulated error and the like. The analysis and processing of the signal to be measured based on the software method has become the main method of the present dielectric loss monitoring, and the method mainly comprises the methods of a correlation function method, a sine fitting method, a neuron self-adaptive measurement method, a wavelet theory and an improved analysis method thereof, a Hilbert-Huang transformation method and the like in summary, and the methods have the defects of large calculated amount, complex hardware requirement and the like, and have poor capability of resisting noise interference.

The harmonic analysis method (FFT and its improved algorithm) is a method which is widely applied in the aspect of dielectric loss angle measurement at present, the algorithm is easy to implement, and is little interfered by direct current components and harmonics, however, because the frequency of the power system often fluctuates, it is difficult to ensure that signals to be analyzed are accurately sampled synchronously or cut off in a whole period, so that the FFT has frequency spectrum leakage and fence effect, the analysis result, especially the phase result, has large error, and it is difficult to directly apply Fourier analysis to the measurement of the dielectric loss angle. The windowing subsection is carried out on the basis of the existing common window function to analyze signals, the capability of inhibiting the frequency spectrum leakage is limited, and the small frequency spectrum leakage interference can generate large influence on the dielectric loss angle measurement result. After windowing, due to the fence effect, the fundamental accurate spectral line is often in the middle of two discrete spectral lines, and the calculation results of the commonly used spectrum correction algorithms have certain deviation. The reasons all limit the improvement of the calculation result precision of the traditional dielectric loss angle calculation method based on the FFT theory.

Disclosure of Invention

The invention provides a method for calculating a dielectric loss angle of capacitive insulation equipment, which aims to solve the problems of poor interference resistance, low measurement precision and large accumulated error of the conventional dielectric loss angle measurement method in the background art.

A method for calculating a dielectric loss angle of capacitive insulation equipment is characterized by specifically comprising the following steps of:

step 1: constructing a Blackman self-convolution window;

step 2: collecting current and voltage signals of equipment to be tested, and performing discrete sampling on the current and voltage signals to obtain a discrete digital signal sequence of the current and voltage signals;

and step 3: windowing and truncating the discrete signal sequence by adopting the Blackman self-convolution window constructed in the step 1, and performing Fast Fourier Transform (FFT), thereby obtaining a discrete spectrum function of the discrete signal after windowing and truncation;

and 4, step 4: on the basis of the step 3, analyzing the discrete spectrum function of the discrete signal after windowing truncation to obtain the main lobe width and the side lobe characteristics;

and 5: analyzing discrete spectrum of windowed truncated signals after FFT, comparing and finding out four spectral lines with maximum amplitude of all discrete spectral lines near the accurate position of a fundamental frequency point, solving a voltage and current fundamental signal phase angle by adopting a four-spectral-line interpolation correction theory to further solve a dielectric loss angle;

the specific process in the step 3 is as follows:

step 301: after the current and voltage discrete sequence is windowed and cut off, the windowed cut-off signal is as follows:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}\underset{n=0}{\overset{N-1}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h)W_{BP}\left(n\right)$

wherein A is_hIs the amplitude of the h harmonic component; f. of_sIs the sampling frequency; phi is a_hIs the initial phase angle of the h harmonic component; f. of₀Is the fundamental frequency; h is the highest harmonic frequency which can be collected; n is the length of the discrete Blackman self-convolution window; w_BP(n) is a frequency characteristic function of a P-order Blackman self-convolution window;

step 302: according to the basic property of fast Fourier transform FFT, after the windowing truncated signal is subjected to FFT, the discrete frequency spectrum is as follows:

$X\left(k\right)=\underset{h=1}{\overset{H}{\Σ}}\frac{1}{2j}(A_h{e}^{{\mathrm{j\φ}}_m}{W}_{BP}(k-{\mathrm{hk}}_0)+A_h{e}^{-{\mathrm{j\φ}}_h}{W}_{BP}(k+{\mathrm{hk}}_0))$

wherein k is₀＝f₀N/f_sThe accurate position of the fundamental frequency point is obtained;

step 303: according to the basic property of discrete Fourier transform, the discrete spectrum function of a P-order Blackman self-convolution window with the length of N is as follows:

$W_{BP}\left(k\right)={\left\{sin\left(\frac{k}{P}\mathrm{\π}\right)e^{-j\frac{k\mathrm{\π}}{P}}\underset{h=0}{\overset{2}{\Σ}}\frac{{(-1)}^h{a}_{h}sin\frac{2\mathrm{\π}k}{N}}{2sin\[\mathrm{\π}(\frac{k}{N}-\frac{h}{M})\]sin\[\mathrm{\π}(\frac{k}{N}+\frac{h}{M})\]}\right\}}^P$

wherein M is the length of the original Blackman window.

The process for constructing the Blackman self-convolution window comprises the following steps:

step 101: defining a P-order Blackman self-convolution window according to a discrete Blackman window with the length of M;

wherein, $w_B\left(n\right)=0.42-0.5cos\left(\frac{2\mathrm{\π}}{M}n\right)+0.08cos\left(\frac{4\mathrm{\π}}{M}n\right);n=0,1,...,M-1;$

step 102: according to the self-convolution property, a sequence with the length of M is subjected to one-time self-convolution to obtain a new sequence with the length of 2M-1, and after a Blackman window with the length of M is subjected to P-order self-convolution window, the obtained new sequence has the length: MP- (P-1);

step 103: after P-order self-convolution window is carried out on the Blackman window with the length of M, zero is filled at the tail of the convolution sequence, and the discrete Blackman self-convolution window with the length of N-MP is obtained:

in step 2, the current and voltage signals are:

$x\left(t\right)=\underset{h=1}{\overset{H}{\Σ}}{A}_{h}sin(2{\mathrm{\πhf}}_{0}t+{\mathrm{\φ}}_h)$

wherein A is_hIs the amplitude of the h harmonic component, t is the time, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The fundamental frequency, H is the highest harmonic order that can be collected.

The discrete digital signal sequence of the current and voltage signals is:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h);$

wherein A is_hIs the amplitude of the h harmonic component, f_sFor the sampling frequency, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The fundamental frequency, H is the highest harmonic order that can be collected.

In step 4, on the basis of step 3, the discrete spectrum function of the discrete signal after windowing truncation is analyzed, and the width of the main lobe is obtained as follows:

B_W＝12Pπ/N＝12π/M

wherein M is the length of the original Blackman window; p is the self convolution order; and N is the length of the p-order Blackman self-convolution window.

In the step 5, the process of solving the phase angle of the voltage and current signals by adopting a four-spectral-line interpolation correction theory to further solve the dielectric loss angle is as follows:

step 501: setting fundamental wave frequency point accurate position k₀The four maximum spectral lines with nearby amplitudes are respectively k₁、k₂、k₃、k₄(ii) a And the accurate position k of the fundamental wave frequency point₀At k₂、k₃And has k₁＝k₂-1，k₂＝k₃-1，k₃＝k₄-1，k₂≤k₀≤k₃(ii) a When calculating, k₀＝f₀N/f_s；

Step 502: according to the set spectral line ratio

$\begin{array}{c}\mathrm{\β}=f\left(\mathrm{\λ}\right)==\frac{(y_3+y_4)-(y_1+y_2)}{(y_3+y_4)+(y_1+y_2)}=\frac{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)-\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)+\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}\\ =\frac{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)-\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)+\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}\end{array},$

λ＝k₀-k₂0.5, λ ∈ [ -0.5,0.5 [ ]]And obtaining a four spectral line difference value correction formula:

$\mathrm{\β}=\frac{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)-\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)+\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}$

step 503: solving the inverse function lambda f of the four spectral line difference correction formula^-1(β) performing polynomial fitting on the inverse function of the equation by using a least square method to obtain lambda;

step 504: calculating the initial phase angle of the fundamental wave signal according to the discrete spectrum function obtained after the Blackman self-convolution window windowing and cutting and the result obtained in the step 503:

φ＝arg[X_W(k₂)]-arg[W_BP(-λ-0.5)]+π/2

wherein arg [ alpha ], [ alpha ]]Representing the phase angle; w_BPIs a function of the frequency characteristic of the order Blackman self-convolution window;

step 505: respectively calculating the phase angle phi of the current and voltage signals of the capacitive electrical equipment to be tested according to the initial phase angle of the fundamental wave signal obtained in the step 504_u1,φ_i1(ii) a The dielectric loss angle is then:

＝π/2-|φ_u1-φ_i1|。

the method has the advantages that the Blackman self-convolution window is utilized to well inhibit the spectrum leakage effect, the four-spectral-line interpolation is utilized to carry out spectrum correction, dielectric loss angle measurement errors based on the FFT theory under asynchronous sampling are solved, the measurement precision is high, and the hardware requirement is low.

Drawings

FIG. 1 is a graph of a 4-order Blackman self-convolution window discrete time domain characteristic;

FIG. 2 is a graph of the amplitude-frequency characteristics of a 4-order Blackman self-convolution window;

FIG. 3 is a schematic diagram of 4-line interpolation based on Blackman self-convolution windows;

FIG. 4 is a flow chart of a dielectric loss angle measurement algorithm;

fig. 5 is an equivalent circuit model of a capacitive isolation device.

Detailed Description

The preferred embodiments will be described in detail below with reference to the accompanying drawings. It should be emphasized that the following description is merely exemplary in nature and is not intended to limit the scope of the invention or its application.

A method for calculating a dielectric loss angle of capacitive insulation equipment is characterized by specifically comprising the following steps, as shown in FIG. 4:

step 1: constructing a Blackman self-convolution window; the process for constructing the Blackman self-convolution window comprises the following steps:

step 101: defining a P-order Blackman self-convolution window according to a discrete Blackman window with the length of M;

wherein, $w_B\left(n\right)=0.42-0.5cos\left(\frac{2\mathrm{\π}}{M}n\right)+0.08cos\left(\frac{4\mathrm{\π}}{M}n\right);n=0,1,...,M-1;$

step 102: according to the self-convolution property, a sequence with the length of M is subjected to one-time self-convolution to obtain a new sequence with the length of 2M-1, and after a Blackman window with the length of M is subjected to P-order self-convolution window, the obtained new sequence has the length: MP- (P-1);

step 103: after P-order self-convolution window is carried out on the Blackman window with the length of M, zero is filled at the tail of the convolution sequence, and the discrete Blackman self-convolution window with the length of N-MP is obtained:

step 2: collecting current and voltage signals of equipment to be tested, and performing discrete sampling on the current and voltage signals to obtain a discrete digital signal sequence of the current and voltage signals;

the current and voltage signals are:

$x\left(t\right)=\underset{h=1}{\overset{H}{\Σ}}{A}_{h}sin(2{\mathrm{\πhf}}_{0}t+{\mathrm{\φ}}_h)$

wherein A is_hIs the amplitude of the h harmonic component, t is the time, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The frequency is the fundamental frequency, and H is the highest harmonic frequency which can be collected;

the discrete digital signal sequence of the current and voltage signals is:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h);$

wherein A is_hIs the amplitude of the h harmonic component, f_sFor the sampling frequency, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The frequency is the fundamental frequency, and H is the highest harmonic frequency which can be collected;

and step 3: windowing and truncating the discrete signal sequence by adopting the Blackman self-convolution window constructed in the step 1, and performing Fast Fourier Transform (FFT), thereby obtaining a discrete spectrum function of the discrete signal after windowing and truncation; the specific process is as follows:

step 301: after the current and voltage discrete sequence is windowed and cut off, the windowed cut-off signal is as follows:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}\underset{n=0}{\overset{N-1}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h)W_{BP}\left(n\right)$

wherein A is_hIs the amplitude of the h harmonic component; f. of_sIs the sampling frequency; phi is a_hIs the initial phase angle of the h harmonic component; f. of₀Is the fundamental frequency; h is the highest harmonic frequency which can be collected; n is the length of the discrete Blackman self-convolution window; w_BP(n) is a frequency characteristic function of a P-order Blackman self-convolution window;

step 302: according to the basic property of fast Fourier transform FFT, after the windowing truncated signal is subjected to FFT, the discrete frequency spectrum is as follows:

$X\left(k\right)=\underset{h=1}{\overset{H}{\Σ}}\frac{1}{2j}(A_h{e}^{{\mathrm{j\φ}}_m}{W}_{BP}(k-{\mathrm{hk}}_0)+A_h{e}^{-{\mathrm{j\φ}}_h}{W}_{BP}(k+{\mathrm{hk}}_0))---\left(1\right)$

wherein k is₀＝f₀N/f_sThe accurate position of the fundamental frequency point is obtained;

step 303: according to the basic property of discrete Fourier transform, the discrete spectrum function of a P-order Blackman self-convolution window with the length of N is as follows:

$W_{BP}\left(k\right)={\left\{sin\left(\frac{k}{P}\mathrm{\π}\right)e^{-j\frac{k\mathrm{\π}}{P}}\underset{h=0}{\overset{2}{\Σ}}\frac{{(-1)}^h{a}_{h}sin\frac{2\mathrm{\π}k}{N}}{2sin\[\mathrm{\π}(\frac{k}{N}-\frac{h}{M})\]sin\[\mathrm{\π}(\frac{k}{N}+\frac{h}{M})\]}\right\}}^P$

wherein M is the length of the original Blackman window;

and 4, step 4: on the basis of the step 3, analyzing the discrete spectrum function of the discrete signal after windowing truncation to obtain the main lobe width and the side lobe characteristics; the specific process is as follows:

let | W_BP(k) If 0, then:

$\{\begin{array}{c}\frac{k\mathrm{\π}}{P}=m\mathrm{\π}\\ \mathrm{\π}(\frac{k}{N}\±\frac{h}{M})\≠m\mathrm{\π},h=0,1,2,\end{array},m\∈Z$

k＝(3+τ)N_Pthe above formula is true when/N, τ is 0,1, …, M-4;

when tau is 0, k is the first zero crossing point on the right side of the central frequency point,at this time, k is 3P, so the distance between the center frequency point and the first frequency zero crossing point on the right side is 6P pi/N_PAccording to the basic property of discrete Fourier transform, the frequency distribution is symmetrical about a central frequency point; therefore, the main lobe width is:

B_W＝12Pπ/N＝12π/M(2)

wherein M is the length of the original Blackman window; p is the self convolution order; n is the length of the p-order Blackman self-convolution window;

when τ is the second zero crossing point on the right side of the center frequency point, and k is (3+0.5) N/M is 3.5P, the maximum side lobe value is obtained, and the side lobe peak level b (db) of the Blackman self-convolution window is:

$B=20lg\frac{\left|W_{BP}\left(3.5P\right)\right|}{\left|W_{BP}\left(0\right)\right|}=-59P---\left(3\right)$

the sidelobe attenuation rate V (dB/oct) of the Blackman self-convolution window is defined as the decibel number of the ratio of the sidelobe values of the octave and is defined as:

$V=20log\frac{\left|W_{BP}\left(3.5P\right)\right|}{\left|W_{BP}\left(7P\right)\right|}=18P---\left(4\right)$

the sidelobe peak level and the sidelobe attenuation rate of the Blackman self-convolution window are in direct proportion to the self-convolution order, the higher the self-convolution order is, the more excellent the sidelobe performance is, and the stronger the capability of inhibiting spectrum leakage is; therefore, after the discrete signal is cut off by the Blackman self-convolution window, the frequency spectrum leakage effect can be effectively inhibited.

When the length N is larger after the signal is windowed and cut off, k₀The Blackman self-convolution window has excellent side lobe performance, and the frequency spectrum leakage influence effect of the negative frequency component can be ignored, so the formula (1) can be changed into

$X\left(k\right)=\underset{h=1}{\overset{H}{\Σ}}\frac{1}{2j}\left(A_h{e}^{{\mathrm{j\φ}}_m}{W}_{BP}(k-{\mathrm{hk}}_0)\right)---\left(5\right)$

For the fundamental component, its discrete spectrum is

$X_0\left(k\right)=\frac{1}{2j}\left(A_0{e}^{{\mathrm{j\φ}}_0}{W}_{BP}(k-k_0)\right)---\left(6\right)$

According to the formula (2), when the length of the original Blackman window is fixed, the higher the self-convolution order is, the wider the width of the obtained Blackman self-convolution window main lobe is. More fundamental frequency spectrum information is distributed among main lobes, and a large amount of useful information is leaked by using a double spectral line ratio method of general windowed signal frequency spectrum correction to cause errors.

And 5: the process of solving the phase angle of the voltage and current fundamental wave signal and further solving the dielectric loss angle by analyzing the discrete spectrum of the windowed cut-off signal after FFT, comparing and finding out four spectral lines with the maximum amplitude values of all the discrete spectral lines near the accurate position of the fundamental wave frequency point and adopting the four spectral line interpolation correction theory is as follows:

step 501: setting fundamental wave frequency point accurate position k₀The four maximum spectral lines with nearby amplitudes are respectively k₁、k₂、k₃、k₄(ii) a And the accurate position k of the fundamental wave frequency point₀At k₂、k₃And has k₁＝k₂-1，k₂＝k₃-1，k₃＝k₄-1，k₂≤k₀≤k₃(ii) a When calculating, k₀＝f₀N/f_s，f₀50Hz can be taken;

step 502: according to the set spectral line ratio

$\begin{array}{c}\mathrm{\β}=f\left(\mathrm{\λ}\right)==\frac{(y_3+y_4)-(y_1+y_2)}{(y_3+y_4)+(y_1+y_2)}=\frac{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)-\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)+\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}\\ =\frac{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)-\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)+\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}\end{array},$

λ＝k₀-k₂0.5, λ ∈ [ -0.5,0.5 [ ]]And obtaining a four spectral line difference value correction formula:

$\mathrm{\β}=\frac{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)-\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)+\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}$

step 503: solving the inverse function lambda f of the four spectral line difference correction formula^-1(β) performing polynomial fitting on the inverse function of the equation by using a least square method to obtain lambda;

step 504: calculating the initial phase angle of the fundamental wave signal according to the discrete spectrum function obtained after the Blackman self-convolution window windowing and cutting and the result obtained in the step 503:

φ＝arg[X_W(k₂)]-arg[W_BP(-λ-0.5)]+π/2

wherein arg [ alpha ], [ alpha ]]Representing the phase angle; w_BPIs a function of the frequency characteristic of the order Blackman self-convolution window;

step 505: respectively calculating the phase angle phi of the current and voltage signals of the capacitive electrical equipment to be tested according to the initial phase angle of the fundamental wave signal obtained in the step 504_u1,φ_i1(ii) a The dielectric loss angle is then:

＝π/2-|φ_u1-φ_i1|。

examples

The capacitive insulation device in the embodiment is designed to adopt a resistor and capacitor series equivalent model as shown in fig. 5; the capacitance C is 591.02pF, and the resistance values are 5k Ω, 10k Ω, 20k Ω, 22.67k Ω, 30k Ω, 40k Ω, 50k Ω, and 110k Ω, respectively. The calculation formula of the dielectric loss angle true value is as follows: 2 pi f₀RC。

(1) Discrete sampling and analog-to-digital conversion link

The high-speed analog-to-digital converter converts the analog signals of the measured current and voltage into digital quantity, and the sampling frequency fs is 2000 Hz.

(2) Constructing discrete Blackman self-convolution window and windowing and cutting signal

Selecting a Blackman window with the original length of 64 to construct a 4-order Blackman self-convolution window, wherein the length of the Blackman window is 256, and the discrete time domain characteristics of the 4-order Blackman self-convolution window are shown in figure 1; FFT calculation is carried out through a computer, and a 4-order Blackman self-convolution window amplitude-frequency characteristic diagram is shown in figure 2; the attenuation rate of the side lobe is 72dB/oct, and the peak level of the side lobe is-236 dB. And windowing and cutting the voltage discrete signal and the current discrete signal.

(3) And (4) performing frequency spectrum correction by using a four-spectral-line interpolation correction method to obtain initial phases of the voltage and current signals.

Finding out 4 spectral lines with maximum spectral lines according to the FFT operation result in the step (2), and obtaining the FFT output value according to the value [11 ]]β is obtained from the equation [11 ]]The formula is complex in form, the inverse function is difficult to directly obtain, polynomial fitting can be carried out on the inverse function by using the least square method theory, the inverse function does not contain even-order terms because β (f (lambda)) is an odd function, a 4-spectral line interpolation diagram based on a Blackman self-convolution window under a 4-order Blackman self-convolution window is shown in figure 3, and a four-spectral line interpolation fitting formula is that lambda (7.28548466271 + 1.829851746056)³+0.919004861172⁵+0.580921289900⁷

(4) Calculating the dielectric loss angle

And (4) according to the calculation result in the step (3), calculating the initial phases of the voltage signal and the current signal by the equation [13] and calculating the dielectric loss angle by the equation [14 ].

In this example, the equivalent model resistance value of the capacitive insulation device is 22.67 k.OMEGA., and the dielectric loss angle measurement results are shown in Table 1 when the fundamental frequency is varied from 49.6Hz to 50.4Hz (wherein aEb represents a × 10^b)

TABLE 1 measurement of dielectric loss angle at fundamental change

Frequency f/Hz	δ true value/rad	δ Absolute error/rad	Relative error/%)
				49.6	0.004176	1.29E-10	3.09E-08
49.7	0.004184	8.70E-11	2.08E-08
				49.8	0.004192	5.71E-11	1.36E-08
49.9	0.004201	3.62E-11	8.61E-09
				50.0	0.004209	2.17E-11	5.15E-09
50.1	0.004218	1.18E-11	2.79E-09
				50.2	0.004226	5.21E-12	1.23E-09
50.3	0.004234	1.05E-12	2.47E-10
				50.4	0.004243	-1.35E-12	-3.18E-10

In this example, the change of the resistance R in the equivalent model of the capacitive insulation device can change the true value of the dielectric loss value, and when the resistance is different values and the fundamental frequency is 50.1Hz, the measurement result of the dielectric loss angle is shown in table 2:

TABLE 2 measurement results of true value variation of dielectric loss angle

Resistance R/k omega	δ true value/rad	δ Absolute error/rad	Relative error/%)
				5	0.00093	1.14E-11	1.22E-08
10	0.00186	1.15E-11	6.17E-09
				20	0.00372	1.17E-11	3.15E-09
30	0.00558	1.19E-11	2.14E-09
				40	0.00744	1.22E-11	1.64E-09
50	0.00930	1.24E-11	1.33E-09
				110	0.02046	3.78E-12	6.73E-10

In this example, when the resistance value of the equivalent model of the capacitive insulation device is 22.67k Ω, the fundamental frequency is 49.9Hz, and the ratio of the third harmonic to the fundamental changes, the measurement result of the dielectric loss angle is shown in table 3:

TABLE 3 dielectric loss angle measurement results for third harmonic ratio variation

Third harmonic in fundamental proportion	δ Absolute error/rad	Relative error/%)
			10％	3.32E-11	7.91E-09
8％	3.38E-11	8.05E-09
			6％	3.44E-11	8.19E-09
4％	3.50E-11	8.33E-09
			2％	3.56E-11	8.47E-09
0％	3.62E-11	8.61E-09

The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (6)

1. A method for calculating a dielectric loss angle of capacitive insulation equipment is characterized by specifically comprising the following steps of:

step 1: constructing a Blackman self-convolution window;

step 2: collecting current and voltage signals of equipment to be tested, and performing discrete sampling on the current and voltage signals to obtain a discrete digital signal sequence of the current and voltage signals;

and step 3: windowing and truncating the discrete signal sequence by adopting the Blackman self-convolution window constructed in the step 1, and performing Fast Fourier Transform (FFT), thereby obtaining a discrete spectrum function of the discrete signal after windowing and truncation;

and 4, step 4: on the basis of the step 3, analyzing the discrete spectrum function of the discrete signal after windowing truncation to obtain the main lobe width and the side lobe characteristics;

and 5: analyzing discrete spectrum of windowed truncated signals after FFT, comparing and finding out four spectral lines with maximum amplitude of all discrete spectral lines near the accurate position of a fundamental frequency point, solving a voltage and current fundamental signal phase angle by adopting a four-spectral-line interpolation correction theory to further solve a dielectric loss angle;

the specific process in the step 3 is as follows:

step 301: after the current and voltage discrete sequence is windowed and cut off, the windowed cut-off signal is as follows:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}\underset{n=0}{\overset{N-1}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h)W_{BP}\left(n\right)$

wherein A is_hIs the amplitude of the h harmonic component; f. of_sIs the sampling frequency; phi is a_hIs the initial phase angle of the h harmonic component; f. of₀Is the fundamental frequency; h is the highest harmonic frequency which can be collected; n is the length of the discrete Blackman self-convolution window; w_BP(n) is a frequency characteristic function of a P-order Blackman self-convolution window;

step 302: according to the basic property of fast Fourier transform FFT, after the windowing truncated signal is subjected to FFT, the discrete frequency spectrum is as follows:

$X\left(k\right)=\underset{h=1}{\overset{H}{\Σ}}\frac{1}{2j}\left(A_h{e}^{{\mathrm{j\φ}}_m}{W}_{BP}\right(k-{\mathrm{hk}}_0)+A_h{e}^{-{\mathrm{j\φ}}_h}{W}_{BP}(k+{\mathrm{hk}}_0\left)\right)$

wherein k is₀＝f₀N/f_sThe accurate position of the fundamental frequency point is obtained;

step 303: according to the basic property of discrete Fourier transform, the discrete spectrum function of a P-order Blackman self-convolution window with the length of N is as follows:

$W_{BP}\left(k\right)={\left\{sin\left(\frac{k}{P}\mathrm{\π}\right)e^{-j\frac{k\mathrm{\π}}{P}}\underset{h=0}{\overset{2}{\Σ}}\frac{{(-1)}^h{a}_{h}sin\frac{2\mathrm{\π}k}{N}}{2sin\[\mathrm{\π}(\frac{k}{N}-\frac{h}{M})\]sin\[\mathrm{\π}(\frac{k}{N}+\frac{h}{M})\]}\right\}}^P$

wherein M is the length of the original Blackman window.

2. The method of claim 1, wherein the process of constructing the Blackman self-convolution window is:

step 101: defining a P-order Blackman self-convolution window according to a discrete Blackman window with the length of M;

wherein, $w_B\left(n\right)=0.42-0.5cos\left(\frac{2\mathrm{\π}}{M}n\right)+0.08cos\left(\frac{4\mathrm{\π}}{M}n\right);n=0,1,...,M-1;$

step 102: according to the self-convolution property, a sequence with the length of M is subjected to one-time self-convolution to obtain a new sequence with the length of 2M-1, and after a Blackman window with the length of M is subjected to P-order self-convolution window, the obtained new sequence has the length: MP- (P-1);

step 103: after P-order self-convolution window is carried out on the Blackman window with the length of M, zero is filled at the tail of the convolution sequence, and the discrete Blackman self-convolution window with the length of N-MP is obtained:

3. the method of claim 1, wherein in step 2, the current and voltage signals are:

$x\left(t\right)=\underset{h=1}{\overset{H}{\Σ}}{A}_{h}sin(2{\mathrm{\πhf}}_{0}t+{\mathrm{\φ}}_h)$

wherein A is_hIs the amplitude of the h harmonic component, t is the time, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The fundamental frequency, H is the highest harmonic order that can be collected.

4. The method of claim 1, wherein the discrete digital signal sequence of current and voltage signals is:

$x\left(n\right)=\underset{h=0}{\overset{H}{\Σ}}{A}_{h}sin(2\mathrm{\π}\frac{h\·f_0}{f_s}n+{\mathrm{\φ}}_h);$

wherein A is_hIs the amplitude of the h harmonic component, f_sFor the sampling frequency, phi_hIs the initial phase angle, f, of the h-th harmonic component₀The fundamental frequency, H is the highest harmonic order that can be collected.

5. The method according to claim 1, wherein in step 4, on the basis of step 3, the discrete spectrum function of the windowed and truncated discrete signal is analyzed to obtain a main lobe width as follows:

B_W＝12Pπ/N＝12π/M

wherein M is the length of the original Blackman window; p is the self convolution order; and N is the length of the p-order Blackman self-convolution window.

6. The method according to claim 1, wherein in the step 5, the process of solving the phase angles of the voltage and current signals by using the four-spectral line interpolation correction theory to further solve the dielectric loss angle is as follows:

step 501: setting fundamental wave frequency point accurate position k₀The four maximum spectral lines with nearby amplitudes are respectively k₁、k₂、k₃、k₄(ii) a And the accurate position k of the fundamental wave frequency point₀At k₂、k₃And has k₁＝k₂-1，k₂＝k₃-1，k₃＝k₄-1，k₂≤k₀≤k₃(ii) a When calculating, k₀＝f₀N/f_s；

Step 502: according to the set spectral line ratio

$\begin{array}{c}\mathrm{\β}=f\left(\mathrm{\λ}\right)=\frac{(y_3+y_4)-(y_1+y_2)}{(y_3+y_4)+(y_1+y_2)}=\frac{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)-\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}{\left(\right|X_0\left(k_3\right)|+|X_0\left(k_4\right)\left|\right)+\left(\right|X_0\left(k_1\right)|+|X_0\left(k_2\right)\left|\right)}\\ =\frac{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)-\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}{\left(\right|W_{BP}\left(k_3\right)|+|W_{BP}\left(k_4\right)\left|\right)+\left(\right|W_{BP}\left(k_1\right)|+|W_{BP}\left(k_2\right)\left|\right)}\end{array},$

λ＝k₀-k₂0.5, λ ∈ [ -0.5,0.5 [ ]]And obtaining a four spectral line difference value correction formula:

$\mathrm{\β}=\frac{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)-\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}{\left(\right|W_{BP}(-\mathrm{\λ}+1.5)|+|W_{BP}(-\mathrm{\λ}+1.5)\left|\right)+\left(\right|W_{BP}(-\mathrm{\λ}-0.5)|+|W_{BP}(-\mathrm{\λ}-1.5)\left|\right)}$

step 503: solving the inverse function lambda f of the four spectral line difference correction formula^-1(β) performing polynomial fitting on the inverse function of the equation by using a least square method to obtain lambda;

step 504: calculating the initial phase angle of the fundamental wave signal according to the discrete spectrum function obtained after the Blackman self-convolution window windowing and cutting and the result obtained in the step 503:

φ＝arg[X_W(k₂)]-arg[W_BP(-λ-0.5)]+π/2

wherein arg [ alpha ], [ alpha ]]Representing the phase angle; w_BPIs a function of the frequency characteristic of the order Blackman self-convolution window;

step 505: respectively calculating the phase angle phi of the current and voltage signals of the capacitive electrical equipment to be tested according to the initial phase angle of the fundamental wave signal obtained in the step 504_u1,φ_i1(ii) a The dielectric loss angle is then:

＝π/2-|φ_u1-φ_i1|。