Application of Matlab language in harmonic analysis of power supply system

introduction

The load of the power supply system is transitioning from traditional linear loads, such as motors, heat radiation electric lighting, and electric heating equipment, to nonlinear loads, such as frequency converters, electric vehicle chargers, gas discharge lighting, and household appliances with rectifiers. The high-order harmonics caused by these nonlinear loads seriously pollute the power supply environment and seriously reduce the quality of power. The prevention, detection, and control of high-order harmonics rely on the detection of instantaneous currents in the power supply system and harmonic analysis. For a 50 Hz industrial frequency current, the frequency of its 32nd harmonic is 1 600 Hz. According to Shannon's theorem, in order to maintain signal fidelity, the sampling frequency must be at least 3 200 times/s, which limits the acquisition and calculation of current signals to the use of computers, and the current and voltage detection signals obtained are discrete information streams.

This paper uses Matlab language to compile a subroutine for harmonic analysis of current and voltage signals. Users can call this subroutine after obtaining the current or voltage signal. The subroutine will return the amplitude and phase of the DC component, fundamental wave, 2~256 harmonics in a few seconds. At the same time, it gives the waveform of the signal, the amplitude and phase distribution diagram of DC, fundamental wave, each harmonic, and the original signal waveform recombined according to the Fourier transform result. This subroutine is very simple and practical for power supply system harmonic researchers.

1 Operating Environment

This subroutine can run on Matlab7.0, Matlab2012a, and Matlab2012b versions.

The current or voltage signal/(l) to be subjected to harmonic analysis is a periodic function.

Its period is 2m. The time period of power frequency voltage in China is 70= =0.02 s, but it is not constant and will fluctuate with the changes in grid load and prime mover output. Once the power frequency changes, the frequencies of its harmonics will also change, which brings difficulties to the calibration of each harmonic. Therefore, this paper selects the phase angle ol as the independent variable, and its period is o070=2m/070=2m, so that the period of the 2nd harmonic is m, and the period of the kth harmonic is . It is no longer affected by the load fluctuation of the power system, which improves the calculation accuracy. The discussion process and conclusions are also suitable for the situation of foreign countries/0=60 Hz.

This paper agrees to sample 512 times in one cycle, that is, 29 times. The discrete Fourier transform requires the sampling frequency to satisfy Shannon's theorem, that is, the sampling frequency must be greater than twice the highest frequency of the signal. Therefore, 512 samplings can ensure that harmonics below 256 are true.

2 Calculating harmonics in Matlab

In the power supply system, the periodic function can be expanded into:

In Matlab, let the signal of the closed interval [0, 2m] on the phase axis be x(k), k=l,2,…, N is a discrete periodic signal with a period of 2m and a sampling interval of

, the number of samples in the whole cycle is N=5l2, then the discrete Fourier series expression is:

Where WN=eN. Here X(k)=a(k)+ib(k) is the Fourier coefficient returned by Matlab, which is a complex variable. The original signal can be combined from the Fourier coefficients obtained:

It can be seen that the DC component of the current and voltage of the power supply system is , the amplitude and phase angle of the fundamental wave are respectively and small l, and the amplitude and phase angle of each harmonic are respectively and small k, k=2,3, …,N/2.

3 Application Examples

Taking half-wave rectification as an example, assuming that the input voltage of the half-wave rectifier is AC single-phase 220 V, it is turned on when the positive half-cycle voltage is higher than the charged battery voltage of 200 V and the forward conduction voltage of the rectifier tube is 0.7 V. The current depends on the loop resistance of the rectifier circuit, 0.5 Q.

The specific procedures are as follows:

Harmonic Analysis of Current Signal in Half-wave Rectification Circuit

clear:clc:close:

R=0.5: Set the resistance of the charging circuit to 0.5 Q

omigat=linspace(0)2*pi)5l2): Sample 5l2 times per cycle y=sqrt(2)*220*sin(omigat): Rated 220 V voltage waveform iout=zeros(size(y)):

fori=l:5l2:

ify(i)<0.7

y(i)=0: remove the negative half wave

else

y(i)=y(i)-0.7: minus the forward voltage drop of the rectifier diode

end:

ify(i)>vout

iout(i)=(y(i)-vout)/R; calculate the current in the conduction area

end;end;

y=funcanaly(iout,-80,240); Call the harmonic analysis function disp(y(:, 1:33)); format short Display the amplitude and phase of the first 32 harmonics saveeⅩm 2 54.daty -ascii; Create a data file

The operation results are shown in Figure 1 and Table 1. The original time domain waveform in Figure 1 is the current waveform at the entrance of the rectifier. The verification time domain waveform contains waveforms of fundamental wave, 2~4 harmonics, 1~32 harmonic combination and waveforms of harmonic combination below 256. Compared with the original waveform, the verification time domain waveform is basically indistinguishable, indicating that the harmonics below 32 can be restored to the original waveform quite accurately. Figure 1 (b) is the amplitude and phase of DC, fundamental wave and harmonics below 32. Table 1 lists the amplitude and phase of harmonics below 32 in digital form. It can be seen from the table that the half-wave rectifier will produce even and odd harmonics, and the amplitude of the harmonics produced is gradually reduced.

Figure 1 Harmonic analysis of half-wave rectified current waveform

4 Conclusion

The current and voltage signals in the power supply system are continuous signals. When converting them into sampled signals for analysis on Matlab, it is necessary to solve the problems of the number of input data of the sampling frequency and the number of returned harmonics. The harmonic analysis results cannot be obtained directly from the fast Fourier transform. This paper studies the relationship between Fourier coefficients and power system harmonics, and proposes a subroutine that can be directly called, which has certain practical value for studying power system harmonics.