CN102156250A - Dielectric loss factor measurement method based on equivalent model - Google Patents

Abstract

The invention discloses a dielectric loss factor measurement method based on an equivalent model, belonging to the technical field of electrical equipment test. The method comprises the following steps: measuring a voltage signal and a current signal on equipment insulation to obtain signal frequency and subharmonic waves; and calculating the dielectric loss factor in that way that the insulation is equivalent to two models, namely parallel connection of a resistor and a capacitor and series connection of a resistor and a capacitor. By the method, the signal frequency fluctuation and the measurement error of the dielectric loss factor caused by the existence of the harmonic wave can be inhibited; and the method has strong anti-interfere capacity and high calculation accuracy.

Description

A Measurement Method of Dielectric Loss Factor Based on Equivalent Model

technical field

The invention belongs to the technical field of electrical equipment testing, in particular to a method for measuring dielectric loss factor based on an equivalent model.

Background technique

The dielectric loss factor is the ratio of the total active power to the total reactive power of the medium under the action of a sinusoidal alternating electric field. The active power is usually composed of losses caused by lossy polarization and insulation resistance. If the insulation of electrical equipment is damp, Penetrating conductive channels, bubble ionization, delamination, shelling, aging, deterioration, etc., at this time, the insulation resistance of the dielectric decreases, the lossy polarization increases, and the corresponding dielectric loss will increase. Therefore, measuring the dielectric loss factor can effectively reflect the insulation condition of electrical equipment. For high-voltage electrical equipment, insulation damage is the main reason for its failure. According to statistics, the power grid accidents directly caused by the damage of electrical equipment insulation account for about 23.1% of the total accidents. Therefore, the detection of the dielectric loss factor of electrical equipment has great theoretical significance and economic value for the safe operation of the power system.

Under normal circumstances, the loss in the insulation of electrical equipment is very small relative to the reactive power, so the value of the dielectric loss factor is small, so the external interference is easy to affect the measurement results, and the influence of frequency fluctuation is more prominent. According to the regulations of the power system, the frequency of the signal is allowed to change within the range of 49.5-50.5 Hz. If the frequency information cannot be obtained and the frequency deviates from 50 Hz to a certain extent, the conventional Fourier algorithm, etc. have large problems in calculating the dielectric loss factor. error.

Contents of the invention

Aiming at the deficiency that the existing calculation dielectric loss factor method mentioned in the above-mentioned background technology has large calculation errors due to frequency fluctuations, the present invention proposes a dielectric loss factor measurement method based on an equivalent model.

The technical scheme of the present invention is, the dielectric dissipation factor measurement method based on equivalent model, it is characterized in that described method comprises the following steps:

Step 1: Obtain the voltage signal and current signal on the insulation of the equipment;

Step 2: According to the data in step 1, obtain the frequency and harmonics of the voltage signal and current signal;

Step 3: Consider the equipment insulation as an equivalent circuit model, use the linear least squares algorithm to obtain the resistance and capacitance parameters in the model, and then directly calculate the dielectric loss factor.

The voltage signal is obtained through a voltage transformer or a capacitive voltage divider.

The current signal is obtained through a through-hole current sensor or a series-connected current sensor.

The process of obtaining the signal frequency and each harmonic of the signal is as follows:

First use the Hanning window interpolation Fourier algorithm to obtain the signal frequency, if the signal frequency is in the range of 49.9-50.1 Hz, then use the fast Fourier algorithm to obtain the harmonics of the voltage signal and current signal; otherwise, according to the obtained signal The frequency is obtained by correcting the ideal sampling frequency method to obtain the harmonics of the signal.

The equivalent circuit model is a parallel connection of a resistor and a capacitor.

The equivalent circuit model is a series connection of a resistor and a capacitor.

The formula for calculating the dielectric loss factor is:

When the resistance and capacitance are connected in parallel, the calculation formula is: tgδ=1/ωRC;

Among them: tgδ is the dielectric loss factor; ω is the angular frequency; R is the equivalent resistance of the insulation; C is the equivalent capacitance of the insulation.

The formula for calculating the dielectric loss factor is:

When the resistor and capacitor are connected in series, the calculation formula is: tgδ=ωRC.

The beneficial effects of the present invention include:

(1) High accuracy

Because the method of the present invention not only considers the fundamental wave components of voltage and current signals, but also considers each harmonic component when calculating the dielectric loss factor, which reduces the calculation error caused by not considering the harmonic components, and the obtained results are more accurate and reliable;

(2) The equivalent resistance and capacitance can be obtained accurately

The resistance and capacitance of capacitive equipment insulation are also important parameters. Obtaining the resistance value and capacitance value helps to monitor the insulation state of capacitive equipment to better maintain its operation;

(3) Strong ability to resist frequency fluctuation and harmonic interference

Since the Fourier algorithm with window interpolation is used when the frequency deviates from the ideal value, the present invention can suppress the error caused by the signal frequency fluctuation and harmonics to the dielectric loss factor measurement, and has stronger anti-interference ability.

Description of drawings

Fig. 1 is a flowchart of the present invention;

Fig. 2 is the fitting result of the casing leakage current with the simplified series model;

Figure 3 shows the fitting results of the bushing leakage current with a parallel simplified model.

Detailed ways

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

Step of the present invention is as shown in accompanying drawing 1:

1. Use a voltage transformer or a capacitive voltage divider to obtain the voltage signal applied to the insulation of the capacitive equipment, and use a through-hole current sensor or a series current sensor to obtain the current signal flowing through the insulation of the capacitive equipment.

2. Use the windowed interpolation Fourier algorithm to obtain the signal frequency, and then use the fast Fourier algorithm or the method of correcting the ideal sampling frequency to obtain the harmonics of the signal.

2.1 Obtain the frequency of the signal

This method uses the Hanning window interpolation Fourier algorithm to obtain the signal frequency, the principle is as follows:

Let the result of the discrete Fourier transform DFT (Discrete Fourier Transformer) of the signal x(n) be X(n), then the result of the discrete Fourier transform DFT of the signal after adding the Hanning window is:

${\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

If the frequency resolution is Δf, then the fundamental frequency f can be expressed as:

f＝(k+Δk)Δf (2)

In the formula: k is an integer; Δk is a decimal.

The approximate calculation of Δk is as follows:

The obtained frequency can be calculated according to formula (2). Because the sampling frequency is usually a fixed value, it is not an integer multiple of the signal frequency, and it cannot be directly intercepted according to the sampled signal to obtain the entire period part to obtain the harmonics;

2.2 Obtaining harmonics of voltage and current signals

Discrete Fourier transform processes the signal after adding a rectangular window. According to the principle of Fourier transform, the time domain product is equal to the frequency domain convolution, which causes the signal spectrum to leak to other frequency bands, which is spectrum leakage. When the frequency of the signal is not at the frequency resolution point of the discrete Fourier transform, the result obtained by direct Fourier transform is different from the original signal, which is the fence effect. In the case of synchronous sampling, the frequency corresponding to the result of Fourier transform is exactly the frequency of the signal, and the spectrum leakage and fence effect just do not appear. In non-synchronous sampling, the frequency obtained by Fourier transform is not the actual frequency of the signal, resulting in spectrum leakage and fence effect.

$\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;t</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

In the formula: N is the highest harmonic order; s _k is the amplitude of the kth harmonic; ω is the fundamental angular frequency of the signal; θ _k is the initial phase angle of the kth harmonic.

According to the Taylor series expansion:

sin(kωt+θ _k )=sin(kωt ₀ +θ _k )+kω(tt ₀ )cos(kωt ₀ +θ _k )+o ¹ (tt ₀ )(5)

When the sampling frequency is larger than the highest harmonic frequency, 0 ¹ (tt ₀ ) is small and negligible, and formula (5) becomes:

sin(kωt+θ _k )＝sin(kωt ₀ +θ _k )+kω(tt ₀ )cos(kωt ₀ +θ _k )

so,

s(t)=s(t ₀ )+a(tt ₀ ) (6)

In the formula:

$\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}\mathrm{<span\; class="notranslate">\; k\&omega;</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

When o ¹ (tt ₀ ) is small and negligible, it can be considered that s(t) obeys the distribution of formula (6) in a small range around t ₀ , since the harmonic components of each order are not known, it can be obtained by linear fitting method The value of a in formula (6), and then according to formula (6), the value of the adjacent point of t ₀ can be obtained.

After determining the interpolation formula, it is necessary to obtain the corrected sampling frequency and number of sampling points, so that the original signal sequence can be corrected to a sequence that meets the requirements of synchronous sampling. Let f _r be the actual fundamental frequency of the signal; f _s is the actual sampling frequency; f _si is the ideal sampling frequency; N is the actual number of sampling points; N _i is the number of ideal sampling points, f _si and N _i need to satisfy the following two formulas In order to meet the requirements of synchronous sampling:

f _si =k ₁ f _r (8)

N _i =k ₂ f _si /f _r (9)

In the formula: k ₁ and k ₂ are positive integers; at the same time, f _si and N _i are required to be as close as possible to f _s and N.

The invention adopts linear interpolation to obtain the signal value corresponding to the approximate ideal sampling frequency point, and then uses Fourier transform to obtain each harmonic.

3. Obtaining dielectric loss factor

In this method, the equivalent resistance and equivalent capacitance of the insulation are considered in two cases:

3.1 Least squares model of resistance-capacitance parallel connection

Assume that the resistance and capacitance in the parallel model are R and C respectively, and the voltage and current signals applied to the insulation are discretized as u(n), i(n), n=0, 1,..., N- 1. The fundamental angular frequency of the signal is ω. When the fundamental frequency is close to 50 Hz, use the Fourier algorithm to obtain the harmonic component of the signal directly. Otherwise, use the method of correcting the ideal sampling frequency. Get the direct current, fundamental wave and second harmonic of the voltage signal and current signal, until the M order harmonic components are U(n) and I(n), n=0, 1, 2,..., M, then the following Equation holds:

U(n)(1/R+jnωC)=I(n), n=0, 1, 2,..., M (10)

The real and imaginary parts on the left and right sides of formula (10) should be equal respectively, then:

$\frac{\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; n\&omega;imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$\frac{\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; n\&omega;\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 11</span>}<span\; class="notranslate">\; )</span>$

In the formula: n=0, 1, 2, ..., M, real and imag respectively obtain the real part and the imaginary part of the complex number.

According to the principle of least squares:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; n\&omega;imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

$<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; n\&omega;\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

In the formula: resistance R and capacitance C are variables to be fitted.

The above formula is a nonlinear function of R and C, which belongs to the nonlinear least squares problem, and can be optimized by using the Levenberg-Marquardt algorithm (Levenberg-Marquardt), but the calculation amount is relatively large. But if 1/R is regarded as a variable, the above formula is a linear least squares problem, thus avoiding the iterative calculation process required by the nonlinear least squares method, greatly speeding up the calculation speed and reducing the difficulty of programming.

After formula (11) is transformed into a matrix form:

U _M Z = I _M (12)

In the formula:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 0</span>}\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&omega;\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&omega;imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&omega;\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; m</span>}& \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& <span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; M\&omega;imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; M\&omega;\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; ;</span>$ $\mathrm{<span\; class="notranslate">\; Z</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}\\ \mathrm{<span\; class="notranslate">\; C</span>}\end{array}\right]<span\; class="notranslate">\; ;</span>$ ${\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; m</span>}\\ \mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; .</span>$

In the above formula, Z is a variable. According to the principle of linear least squares, the optimal solution of resistance and capacitance is:

Z＝(U _M ^T U _M ) ^-1 U _M ^T I _M (13)

Resistance and capacitance solution are R=1/Z(1), C=Z(2). Suppose the sampling time series t(n)=n/f _s , n=0, 1, ..., N-1, f _s is the sampling frequency, then the current signal obtained by fitting according to the resistance, capacitance and voltage signals is:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k\&omega;\; Creal</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k\&omega;\; Cimag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 14</span>}<span\; class="notranslate">\; )</span>$

The resulting dielectric loss factor is:

tgδ＝1/ωRC (15)

3.2 Least squares model of resistance-capacitance series connection

According to the series equivalent model, the following formula holds:

I(n)(R-j/(nωC))=U(n), n=0, 1, 2,..., M (16)

According to the real part and imaginary part in the above formula, we have:

$\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; n\&omega;C</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 17</span>}<span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; n\&omega;C</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

In the formula: n=0, 1, 2, ..., M.

After formula (17) is transformed into a matrix form:

I _M Z = U _M (18)

In the formula: $I_m=\left[\begin{array}{cc}\mathrm{real}\left(I\left(1\right)\right)& \frac{\mathrm{imag}\left(I\left(1\right)\right)}{\mathrm{\&omega;}}\\ \mathrm{imag}\left(I\left(1\right)\right)& -\frac{\mathrm{real}\left(I\left(1\right)\right)}{\mathrm{\&omega;}}\\ \mathrm{real}\left(I\left(2\right)\right)& \frac{\mathrm{imag}\left(I\left(2\right)\right)}{2\mathrm{\&omega;}}\\ \mathrm{imag}\left(I\left(2\right)\right)& -\frac{\mathrm{real}\left(I\left(2\right)\right)}{2\mathrm{\&omega;}}\\ m& m\\ \mathrm{real}\left(I\left(m\right)\right)& \frac{\mathrm{imag}\left(I\left(m\right)\right)}{\mathrm{M\&omega;}}\\ \mathrm{imag}\left(I\left(m\right)\right)& -\frac{\mathrm{real}\left(I\left(m\right)\right)}{\mathrm{M\&omega;}}\end{array}\right];$ $Z=\left[\begin{array}{c}R\\ \frac{1}{C}\end{array}\right];$ $u_m=\left[\begin{array}{c}\mathrm{real}\left(u\left(1\right)\right)\\ \mathrm{imag}\left(u\left(1\right)\right)\\ \mathrm{real}\left(u\left(2\right)\right)\\ \mathrm{imag}\left(u\left(2\right)\right)\\ m\\ \mathrm{real}\left(u\left(m\right)\right)\\ \mathrm{imag}\left(u\left(m\right)\right)\end{array}\right].$

In the above formula, Z is the variable to be optimized. If 1/C instead of C is regarded as a variable, then formula (18) becomes a linear least squares problem, and the optimal solution of resistance and capacitance is:

Z＝(I _M ^T I _M ) ^-1 I _M ^T U _M (19)

Then the solution of resistance and capacitance is R=Z(1), C=1/Z(2). The current signal obtained by fitting according to the resistance, capacitance, and voltage signals is:

${\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k\&omega;C</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;RC</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; R</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;C</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;RC</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; R</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;C</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;RC</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; real</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; k\&omega;C</span>}}{\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;RC</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; imag</span>}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k\&omega;t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 20</span>}<span\; class="notranslate">\; )</span>$

The resulting dielectric loss factor is:

tgδ＝ωRC (21)

Experimental verification:

A 110 kV bushing insulation is applied with an effective value of 10 kV power frequency voltage, the voltage signal is obtained through a capacitor voltage divider, and the current signal in the insulation is passed through the non-inductive connection between the low voltage end of the bushing and the ground wire. The resistance is obtained, and the obtained two signals are connected to the Tektronix TDS2024 oscilloscope. Choose a group of collected voltage and current signals, and use the simplified dielectric equivalent circuit model of resistors and capacitors connected in series and parallel to fit them. The original current signal and the fitted current signal are shown in Figure 2 and Figure 3, respectively.

Note: The solid/dotted lines in Fig. 2(1) and Fig. 3(1) represent the measured/fitted current signals.

It can be seen from Fig. 2 and Fig. 3 that both the RC series equivalent model and the RC parallel equivalent model can better fit the current signal on the bushing insulation, but in comparison, the parallel model fitting accuracy slightly higher than the series model. The fitting of the leakage current of other electrical equipment insulation, such as the leakage current of insulators under dry conditions, also verified the above analysis, and a good fitting effect laid the foundation for the accurate calculation of the subsequent dielectric loss factor.

27 sets of voltage and leakage current data were measured. The parallel model obtained the average values of equivalent resistance and equivalent capacitance of 160.7 megaohms and 144.6 picofarads, respectively, and the standard deviations were 0.6 megaohms and 0.07 picofarads; the series model obtained equivalent resistance The mean values of the equivalent capacitance and the equivalent capacitance are 2.87 megaohms and 147.6 picofarads respectively, and the standard deviations are 9153 ohms and 0.09 picofarads respectively, and the stability is very high. Generally, the insulation resistance of the insulation decreases after being damp, has penetrating conductive channels or discharge, and the capacitance will increase after being damp, so the equivalent resistance and capacitance can be used as a reference for the insulation condition.

Taking the dielectric non-simplified circuit model to simulate the insulation of capacitive equipment as an example, the discrete voltage and current signals are generated by simulation, and the real value of the dielectric loss factor at 50 Hz is 1.16×10 ^-2 (the frequency changes within the range of 49.5 to 50.5 Hz When the real value of the dielectric loss factor changes less than 1%), the amplitude ratio of the 2nd and 3rd harmonics of the voltage signal to the fundamental wave is 0.03, 0.04, and the signal frequency takes 5 points from the range of 49.5 to 50.5 Hz, and the sampling frequency is selected as 5 kilohertz, the sampling time length is 0.1 second, and the number of digits for quantization is 14, and the dielectric loss factor is calculated based on the Fourier algorithm and the method of the present invention, and the error of the gained dielectric loss factor is shown in the table below.

Table 1 Absolute value of errors obtained by the two methods at different frequencies/10 ^-5

It can be seen from Table 1 that with the increase of the frequency deviation of 50 Hz, the error of the Fourier algorithm increases, the maximum error can reach 1064×10 ^-5 , and the average error can reach 579×10 ^-5 when the frequency deviation is 0.5 Hz. The error is likely to be greater than the dielectric loss factor value allowed by current capacitive devices. The resistance-capacitance series/parallel model proposed by the present invention has high accuracy. The maximum error of the parallel model method is 12×10 ^-5 , and the series model method has a maximum error value of 26.5×10 ^-5 , which is higher than that of the real medium. The loss factor values are much smaller, and the accuracy should be able to meet the requirements. For signals at different frequencies and initial phases, the average values of the equivalent resistance and equivalent capacitance obtained by the parallel model are 1001 MΩ and 272.0 picofarads, respectively, and the standard deviations are 6.73 MΩ and 0.01 picofarads respectively; the series model obtains the equivalent resistance and The average values of the equivalent capacitance are 0.13 megaohm and 272.0 picofarads, and the standard deviations are 1231 ohms and 2.01 picofarads respectively, all of which have good stability.

Taking resistance and capacitance components connected in series to simulate capacitive equipment as an example, an arbitrary waveform generator Agilent33120A generates a sinusoidal voltage with a peak value of about 10 volts and a frequency of 49.5 to 50.5 Hz. Each frequency point measures 10 groups of signals with a sampling frequency of 25 k Hz, the number of sampling points is 2500, and the dielectric loss factor obtained by the Fourier algorithm and the method of the present invention varies with frequency as follows.

Table 2 Calculation results of the dielectric loss factor of the measured signal/10 ^-2

From the data in Table 2, it can be found that the results obtained by the three methods at 50 Hz are similar and relatively reliable. However, as the frequency deviation increases, the Fourier algorithm error also gradually increases. The dielectric loss factor obtained at 49.5 Hz is close to three times the original value, and even negative values will appear at 50.5 Hz. Obviously, when the frequency deviation is serious When the Fourier algorithm result error is too large. And no matter the present invention adopts the equivalent model of resistance-capacitance parallel connection or resistance-capacitance series connection, the obtained dielectric loss factor maintains high stability in the frequency range of 49.5-50.5 Hz, and the result fluctuates very little with the frequency change, and the two equivalent The dielectric loss factor obtained by the model is also very similar. 50 groups of signals with different frequencies were measured. The average values of the equivalent resistance and equivalent capacitance obtained by the parallel model were 26.0 kohms and 23.3 microfarads respectively, and the standard deviations were 2644 ohms and 29.5 nanofarads respectively; the series model obtained the equivalent resistance and equivalent The average values of capacitance were 0.72 ohms and 23.3 microfarads, and the standard deviations were 0.07 ohms and 0.24 microfarads, respectively.

The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed in the present invention can easily think of changes or Replacement should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be determined by the protection scope of the claims.

Claims (8)

1. the dielectric dissipation factor measuring method based on equivalent model is characterized in that described method comprises the following steps:

Step 1: obtain voltage signal and current signal on apparatus insulated;

Step 2:, obtain the frequency and the signal each harmonic of voltage signal and current signal according to the data of step 1;

Step 3: with the apparatus insulated equivalent-circuit model that is thought of as, utilize the linear least-squares algorithm to obtain the resistance in the model, capacitance parameter, directly calculate then and obtain dielectric dissipation factor.

2. according to the described a kind of dielectric dissipation factor measuring method of claim 1, it is characterized in that described voltage signal obtains by voltage transformer (VT) or capacitive divider based on equivalent model.

3. according to the described a kind of dielectric dissipation factor measuring method of claim 1, it is characterized in that described current signal is by the centre path current sensor or seal in the formula current sensor and obtain based on equivalent model.

4. according to the described a kind of dielectric dissipation factor measuring method of claim 1, it is characterized in that the process of described picked up signal frequency and signal each harmonic is based on equivalent model:

Earlier with adding Hanning window interpolation Fourier algorithm picked up signal frequency, if signal frequency in 49.9～50.1 hertz of scopes, then obtains the each harmonic of voltage signal and current signal with fast Fourier algorithm; Otherwise according to the each harmonic of the signal frequency that obtains with the desirable sample frequency method picked up signal of correction.

5. according to the described a kind of dielectric dissipation factor measuring method of claim 1, it is characterized in that described equivalent-circuit model is resistance and electric capacity parallel connection based on equivalent model.

6. according to the described a kind of dielectric dissipation factor measuring method of claim 1, it is characterized in that described equivalent-circuit model is resistance and capacitances in series based on equivalent model.

7. according to the described a kind of dielectric dissipation factor measuring method of claim 5, it is characterized in that the computing formula of dielectric dissipation factor was when described resistance and electric capacity were in parallel based on equivalent model:

tgδ＝1/ωRC

Wherein: tg δ is a dielectric dissipation factor; ω is an angular frequency; R is the equivalent resistance of insulation; C is the equivalent capacity of insulation.

8. according to the described a kind of dielectric dissipation factor measuring method based on equivalent model of claim 6, the computing formula of dielectric dissipation factor is when it is characterized in that described resistance and capacitances in series:

tgδ＝ωRC。

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