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Frequency Spectrum Generated by Thyristor Control J Electrocomponent Science and Technology (C) Gordon and Breach Science Publishers Ltd. 1974, Vol. 1, pp. 43-49 Printed in Great Britain FREQUENCY SPECTRUM GENERATED BY THYRISTOR CONTROL J. K. HALL and N. C. JONES Loughborough University of Technology, Loughborough, Leics. U.K. (Received October 30, 1973; in final form December 19, 1973) This paper describes the measured harmonics in the load currents of thyristor circuits and shows that with firing angle control the harmonic amplitudes decrease sharply with increasing harmonic frequency, but that they extend to very high harmonic orders of around 6000. The amplitudes of the harmonics are a maximum for a firing delay angle of around 90 Integral cycle control produces only low order harmonics and sub-harmonics. It is also shown that with firing angle control apparently random inter-harmonic noise is present and that the harmonics fall below this noise level at frequencies of approximately 250 KHz for a switched 50 Hz waveform and for the resistive load used. The noise amplitude decreases with increasing frequency and is a maximum with 90 firing delay. INTRODUCTION inductance. 6,7 Literature on the subject tends to assume that noise is due to the high frequency Thyristors are now widely used for control of power harmonics generated by thyristor switch-on and the in both d.c. and a.c. circuits. The advantages of design of suppression components is based on this. relatively small size, low losses and fast switching This investigation has been performed in order to speeds have contributed to the vast growth in establish the validity of this assumption, since it is application since their introduction, when they were believed that there may be a number of perhaps basically a solid-state replacement for mercury-arc separate sources of noise in thyristor circuits. Four rectifier devices. As a result, attention has been well-known circuits have been examined, both focussed on the inherent problems produced by experimentally using a spectrum analyser and by a thyristor control, some of which are a perpetuation theoretical analysis of the waveforms to define the of those with mercury-arc rectifiers. These are now harmonic spectrum expected. The presence of giving cause for greater concern owing to the scale of random noise, in addition to the expected harmonics, usage. The majority of applications utilise a.c. line is demonstrated. commutation and only these are considered here. The switching action of the thyristors (or triac) results in non-sinusoidal currents being drawn from 2 EXPERIMENTAL DETAILS the a.c. supply system. Harmonics and noise are thereby injected into the power supply and give rise, The four single-phase circuits investigated were a to conducted interference with other electronic and single-thyristor half-wave rectifier, a triac a.c. con- communications equipment.2-4 Unless the apparatus troller with firing angle control, a thyristor full-wave is screened, radiated interference also occurs. The rectifier bridge, and a triac a.c. controller with effects of interference are varied, from malfunctioning integral cycle control. The triac functions as two of low-level micrologic circuits and triggering of other thyristors in anti-parallel, but has a single gate separately-controlled thyristors to disturbance of electrode. The load current waveforms were ex- radio and T.V. reception, s The elimination of these amined and these have the form shown in Figure 1. effects is an important objective. Ways of suppressing From the conducted interference viewpoint, the the harmonics and noise have been devised using, on supply current is of interest. The supply current is the the one hand, greatly improved discrete components same as the load current in all circuits except the and on the other, composite devices containing rectifier bridge, in which case it has the same form as within one component resistance, capacitance and that of the triac with firing angle control. 43 44 J.K. HALL tesistive Lc load Mains Thyristor circuit Sampling resitor No counter __r-t,, i o oooro00 Frequency analy=er FIGURE 2 Basic measuring circuit. (d) A typical trace is shown in Figure 3, where the individual harmonics at 50 Hz intervals can easily be ((1} Single thyristor, hall-wave rectifier. seen. Controls on the analyser enable the bandwidth b) Variable a.c. by trioc with firing angle control. of the filter, the swept frequency limits and sweep (c) Thyristor bridge, full-wove rectifier. time to be controlled. A variable attenuator adjusts the (d) Variable a.c. by triac with integral cycle control. input signal appropriately. The frequency counter (Figure 2) gives a direct indication of the frequency FIGURE Output waveforms for the circuits examined. band being swept, thus enabling the specific harmonic frequencies displayed to be interpreted. It should be noted that the spectrum analyser indicates the The basic measuring circuit is shown in Figure 2. magnitudes of the harmonics present in the wave- This consists of a resistive load of low inductance form, but not their phase in relation to the supplied from single-phase a.c. mains through the fundamental. thyristor controller. In series with the load is a sampling resistor of very low inductance, across which a voltage proportional to load current is taken. This is fed to a Hewlett-Packard spectrum analyser8 and an oscilloscope. This arrangement is more suit- able for study of the low frequency harmonics, since combined symmetrical and asymmetrical radio- frequency components are indicated. For detailed study of the radio-frequency voltages, the techniques of BS 8009 are more appropriate. The complete test circuit is installed in a screened room in order to reduce external interference. The principle of the spectrum analyser is that the waveform under examination is swept by a narrow- band filter (10 Hz minimum bandwidth) controlled Zdro Harmonic by a variable frequency oscillator. The output is frequency, frequency .('500 HZ/C rn,) displayed on a storage tube whose vertical axis FIGURE 3 Harmonic spectrum trace from the represents amplitude, and horizontal axis frequency. spectrum analyser. THYRISTOR FREQUENCY SPECTRUM 45 3 THEORETICAL CONSIDERATIONS B1 rr--&+ 2n 2 The current waveforms of Figure can be resolved into the harmonic components present by use of the where a is the firing delay angle, general Fourier Series:- and ] is the peak value of the sinusoidal current. n--c fit) Ao + E Cn sin(not. + n) b) Triac with firing delay: n:l nth harmonic of the supply frequency (n 3,5,7,...): where is the waveform function under consideration, f(t) 2 n is the harmonic order- 1,2,3 cos(n-1)a An Ao is the direct component 7r][cos(n+l)tn+l n-1 n2-1 ] is of the nth harmonic Cn the amplitude 1)o n is the phase of the nth harmonic. nl[sin(n+n+l sin(n-1)o]n-1 The expansion is calculated from: 2 Even harmonics are absent, since An Bn 0 th Cn (An + Bn n 2,4,6,... during the derivation. where d.c. component: fit) cos n cot d(cot) Ao 0 fundament: and ] fit) sin n cot d(ot) [cos2-l]2 sin An B1 tan -1 [ 22a] n Bn c) Full-wave rectifier: The mean or d.c. level is given by: nth harmonic of the supply frequency (n 2,4,6,...): 2r cos(1-2n)a 2 Ao | fit) dt An + + 2n o rr [cos(l+2n)al+2n 1-2n 1-4nz ] The constants An, Bn and Ao for each waveform are [sin(1 + 2n)a sin(1 2n)a] as follows: n k i +2n 1- a) Half-wave rectifier: Odd harmonics are absent, since An Bn 0 with nth harmonic of the supply frequency (n 2,3,4,...): n 3,5,7, during the derivation. 1" [cos(1 + n)ot cos(1 n)ot 2(-1)n] d.c. conponent: An + + 27r [ + n n n] ] + n)a sin(1 Ao [1 + cos a] [sin( -nn)a] Bn=- -+n fundamental: d.c. component: A1 =B1 =0 Ao (cos ot + 1) d) Triac with &tegral-cycle control: 2r nth harmonic of the output waveform (n 1,2,3,... fundamental: T, 3T, 5T,...): iT (2nrrN) cos A An 2 2r [cos rr(n T2) [ T ] 46 J.K. HALL TABLE Measured harmonic amplitudes (as a % of mains) with varying firing angle for the half-wave rectifier circuit. Firing angle a Amplitude at the stated harmonic frequency (Hz) 50 100 150 500 1000 2000 (Degrees) (fundamental) (2nd) (3rd) (10th) (20th) (40th) 18 50.0 22.0 1.4 1.0 0.4 0.20 54 43.0 27.0 10.0 2.4 1.0 0.45 90 28.0 23.0 15.0 3.0 1.2 0.60 126 11.0 10.0 9.0 2.5 1.0 0.45 162 1.3 1.5 1.8 1.0 0.4 0.20 iT (2nrN) a) Thyristor Half-Wave Rectifier Bn sin rr(n 2 T2) T The results of measurements of specific low frequency harmonics generated with the single Putting n the gives coefficients for the funda- thyristor control are given in Table I. They are shown mental frequency at the that the load; is, lowest as a function of firing angle and it is apparent that the subharmonic of the x supply frequency (= 1/T supply harmonics are a maximum with a firing delay of 90 frequency). Other coefficients are for fre- given A detailed representation of the harmonics present up quencies up to that of the The coef- supply voltage. to 1900 Hz with a firing delay of 90 is shown in ficients for the supply frequency harmonic of the Figure 4.
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