CN103616553A - Short circuit large current waveform fitting method - Google Patents

Abstract

The invention discloses a short circuit large current waveform fitting method. Firstly, the waveform of a testing short circuit current is recorded through a digital recording instrument; secondly, the waveform is processed, specifically, in a half wave, the midpoint between two current zero crossing points serves as a center, 0.5-fold half wavelength time serves as a time window, parabola fitting is carried out on sampling points in the window, and a rough peak point time tP is solved; the tP serves as a center, 0.1-fold half wavelength time serves as a time window, parabola fitting is carried out on sampling points in the window, accurate peak point coordinates tPN and iPN are solved; a peak point is solved for a positive half wave; a valley point is solved for a negative half wave; the expression of an upper envelope line is solved for all peak points; the expression of a lower envelope line is solved for all valley points; the expression of a direct current component is solved, four parameters including a peak value, an effective value, a direct current component and a power factor are worked out. According to the short circuit large current waveform fitting method, very high precision and an anti-noise ability are achieved, and the actual engineering application demands can be met.

Description

Short-Circuit High Current waveform fitting method

Technical field

The present invention relates to a kind of Short-Circuit High Current waveform fitting method, a kind of test waveform that recovers during for the large capacity short-circuit test of electric equipment specifically, calculates the method for current parameters, belongs to electrical apparatus test technical field.

Background technology

The equipment such as transformer, switch, isolating switch, relay and fuse all will carry out Short-Circuit High Current test before dropping into operation of power networks, and large Laboratory need to bear the ability of short-circuit current to these equipment, the ability etc. that switches on and off short-circuit current is tested.When testing, waveform parameter how correctly to extract the short-circuit test electric current that testing equipment produces is extremely important.These parameters comprise peak value, effective value, DC component and power factor etc.Traditional computing method are to adopt image method, first find out figure peak value, then with straight line, adjacent peak value are connected to calculate corresponding effective value and DC component.The advantage of this method is directly perceived and easily operation, but is difficult to obtain enough accurate result of calculation.

Along with improving constantly of digital measuring instrument and computer measurement analytical technology level, the extraction replacement classic method that Digital Signal Processing is used for to waveform parameter has become developing direction.Existing document proposition polynomial expression, for example Chebyshev polynomials, carry out the method for short-circuit current envelope matching and obtain each parameter value.The present invention proposes a kind ofly with para-curve quadratic fit, to ask for peak, valley point, respectively near segment of curve peak, valley point is carried out to matching and obtains upper and lower envelope expression formula, and then obtain the method for each waveform parameter by the method for double exponential fitting.

Summary of the invention

The present invention proposes a kind of Short-Circuit High Current waveform fitting method, and the method can calculate peak value, effective value, DC component and four parameters of power factor of Short-Circuit High Current waveform.The inventive method has very high precision and antimierophonic ability, can meet practical engineering application requirement.

Technical solution of the present invention is as follows:

A kind of method of Short-Circuit High Current waveform fitting, its feature is, first the method uses the waveform of digital recorder (as oscillograph) record test short-circuit current, then this Wave data is processed to (referring to process flow diagram and the example of the measured waveform shown in Fig. 2 of Fig. 1) according to following steps:

1) in a half-wave, with the mid point t of two current zero-crossing points _acentered by, the half-wavelength time of 0.5 times is time window (referring to Fig. 3), and the sampled point in window is done to the Parabolic Fit based on least square method, obtains rough peak point time t _p;

2) with t _pcentered by, the half-wavelength time of 0.1 times is time window (referring to Fig. 4), and the sampled point in window is carried out to Parabolic Fit, obtains peak point coordinate t accurately _pN, i _pN;

3) to each half-wave repeating step 1) and step 2) process, to all positive half-waves, obtain peak point; To all negative half-waves, obtain valley point;

4) all peak points are carried out to double exponential fitting, obtain the expression formula (referring to Fig. 5) of coenvelope line;

5) all valley points are carried out to double exponential fitting, obtain the expression formula of lower envelope line;

6) according to coenvelope line expression formula and lower envelope line expression formula, obtain the expression formula of DC component, calculate peak value, effective value, DC component and four parameters of power factor.

The sampling rate of described digital recorder is not less than 10k/s.

Technique effect of the present invention:

The present invention utilizes the method for para-curve twice fitting to ask for peak, valley point, by the method for double exponential fitting envelope, when calculating effective value, DC component and power factor, all has very high precision and antimierophonic ability, can meet practical engineering application requirement.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of the inventive method.

Fig. 2 is an actual measurement short-circuit current waveform.

Fig. 3 is the schematic diagram of asking for the rough peak point time.

Fig. 4 is the schematic diagram of asking for accurate peak point coordinate.

Fig. 5 is the schematic diagram of asking for effective value, DC component and power factor.

Embodiment

Below embodiments of the invention are elaborated.

Fig. 1 is the process flow diagram of the inventive method.The method is first with the waveform of digital recorder record test short-circuit current, and Fig. 2 is the embodiment of the present invention: the short-circuit current waveform of an actual measurement, and the sampling rate of described digital recorder is 20k/s, shunt sensitivity is 0.25V/kA.Then this Wave data is processed according to following steps:

1) half cycle that Fig. 3 is short-circuit current, t _land t _htime value while being respectively its current value zero crossing, t _at _land t _hmid point, with t _acentered by be a 0.5*(t _h-t _l) time window, within guaranteeing that like this peak point necessarily drops on window ranges.Sampled point in window is done to the Parabolic Fit based on principle of least square method, obtain peak point time t _p; Now required time point is rough, is to choose sample window during for Parabolic Fit for the second time to do a center reference;

2) determine rough peak point time t _pafter, do Parabolic Fit for the second time, ask for the coordinate of peak point.Specific practice is with t _pcentered by be a 0.1*(t _h-t _l) time window, as shown in Figure 4, can make so required peak point among window, can guarantee to ask for again the accuracy of peak point.Sampled point in window ranges is done to Parabolic Fit again based on principle of least square method, ask for extreme point, obtain peak point coordinate (t _pN, i _pN);

3) to each half-wave repeating step 1), 2) process.To all positive half-waves, obtain peak point; To all negative half-waves, obtain valley point;

4) all peak points of step 3) being obtained carry out double exponential fitting, obtain coenvelope line f(t as shown in Figure 5) expression formula;

5) all valley points of step 3) being obtained carry out double exponential fitting, obtain lower envelope line g(t as shown in Figure 5) expression formula;

6) the upper and lower envelope expression formula f(t obtaining according to step 4) and step 5)) and g(t), both arithmetic mean

be the DC component expression formula of short-circuit current.The effective value of each corresponding point and DC component, the effective value of locating waveform as DD ' is

dC component is

then, according to DC component expression formula i (t), ask for power factor

as shown in Figure 5, some A and some C are respectively first and second electric current peak dot of the measured current waveform of trying to achieve in step 3), and its corresponding peak dot time is respectively t ₁with t ₂, corresponding DC component is respectively i _d1with i _d2,

${\mathrm{<figure-callout\; id="1"\; label="i\; d"\; filenames="HDA0000431243000000031.png"\; state="\{\{state\}\}">i</figure-callout>}}_d=I_{d0}{e}^{-\frac{t_1}{T}}---\left(1\right)$

$i_{d2}=I_{d0}{e}^{-\frac{t_2}{T}}---\left(2\right)$

Above-mentioned two formulas are divided by and are arranged, can obtain:

$T=\frac{t_2-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="HDA0000431243000000031.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{\ln (I_{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="HDA0000431243000000031.png"\; state="\{\{state\}\}">d</figure-callout>}1}/I_{d2})}---\left(3\right)$

Power factor can be expressed as:

In formula, f is supply frequency.

Table 1 is to implement the result that the inventive method is asked for peak value, valley, effective value, DC component and the power factor of this measured waveform.

Each parameter value of measured waveform that table 1 the inventive method is calculated

Implementation result for explanation the inventive method, using below and there is the international short circuit of the STL(alliance of comparability) the TDG(test data generator that provides) in curve 1 as calculated example (each parameter reference value and power factor that this curve is given are as shown in table 2 below), relatively the inventive method and existing methodical implementation result.

The reference value of the curve 1 that table 2STL-TDG provides

On the method calculated curve 1 proposing with the present invention and curve 1, add after 2% noise, calculate gained each parameter as shown in table 3 and table 4.

The parameter value of the curve 1 that table 3 is tried to achieve by the inventive method

Table 4 curve 1 adds the parameter value of trying to achieve by the inventive method again after 2% noise

By above result of calculation, can find out, the reference value providing with STL-TDG is compared, and the relative error of the peak value of the curve 1 calculating by the inventive method, effective value, DC component, power factor is respectively within 0%, 0.16%, 0.38% and 0.19%; On curve 1, add the relative error of the peak value that calculates gained after 2% noise, effective value, DC component, power factor respectively within 0.63%, 0.25%, 1.01% and 1.27%.Compare with the existing method with Chebyshev polynomials matching, the comparison of the relative error between the reference value that the inventive method and existing method fitting result and STL-TDG provide is in Table 5.Visible the inventive method is in noiseless and noisy situation, and fitting result is better than now methodical fitting result comprehensively.

The relative error (%) of table 5 the inventive method and existing method acquired results and reference waveform parameter comparison

Claims (2)

1. a Short-Circuit High Current waveform fitting method, is characterized in that, first the method with the waveform of digital recorder record test short-circuit current, is then processed according to following steps this waveform:

1) in a half-wave, centered by the mid point of two current zero-crossing points, the half-wavelength time of 0.5 times is time window, and the sampled point in window is done to the Parabolic Fit based on least square method, obtains rough peak point time t _p;

2) with t _pcentered by, the half-wavelength time of 0.1 times is time window, and the sampled point in window is carried out to Parabolic Fit, obtains peak point coordinate t accurately _pN, i _pN;

3) to each half-wave repeating step 1) and step 2) process, to all positive half-waves, obtain peak point; To all negative half-waves, obtain valley point;

4) all peak points are carried out to double exponential fitting, obtain the expression formula of coenvelope line;

5) all valley points are carried out to double exponential fitting, obtain the expression formula of lower envelope line;

6) according to coenvelope line expression formula and lower envelope line expression formula, obtain the expression formula of DC component, calculate peak value, effective value, DC component and four parameters of power factor.

2. the method for claim 1, is characterized in that, the sampling rate of described digital recorder is not less than 10k/s.

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