Self-commutated thyristor inverter
Abstract Generated abstract
This paper analyzes a self-commutated thyristor inverter based on a parallel independent inverter circuit without a separate master oscillator, intended primarily for fluorescent lighting supplies. It describes the operating sequence, commutation process, and control-current formation, deriving expressions for load voltage, operating limits, recovery time, external characteristics, and output frequency under aperiodic and oscillatory capacitor-recharge conditions. The authors argue that aperiodic recharging is preferable because oscillatory operation can produce damaging current and voltage surges, and they propose the use of a saturable choke with a rectangular hysteresis loop to shape control pulses and stabilize frequency. Experimental converter variants built for 27 V to 115 V at 500 Hz and 110 V to 127 V at 50 Hz reportedly achieved about ±5 percent frequency stability with compensation for load current and supply-voltage variation.
Full Text
SELF-COMMUTATED THYRISTOR INVERTER
T. K. KOBZEVA, S. I. KOROLEV, B. P. SOUSTIN
(Presented by the scientific and technical seminar of the Department of Electrical Equipment)
The intensive development of semiconductor devices with high operating qualities gives reason to hope that the main part of inverters will be made with thyristors. The circuit under consideration is built on these elements on the basis of a parallel independent inverter without a special circuit for the master oscillator (Fig. 1). The frequency-setting elements are the additional winding \(W_y\) of the output transformer \(Tr\ 1\), together with the inductance of the winding \(W_d\) of the saturating choke \(DN\) and the shaping circuit \(R_y C_y\). The operation
Fig. 1
of the circuit in Fig. 1 is analogous to the operation of a transistor multivibrator with magnetic coupling; however, in this case the output transformer is not saturated.
When the power supply is switched on, the starting circuit, consisting of capacitor \(C_z\) and transformer \(Tr2\), operates and turns on thyristor 1. In all windings of transformer \(Tr1\) an emf of the sign indicated in Fig. 1 is induced. In this case the voltage on the control electrode of thyristor 2 is positive, and that of thyristor 1 is negative. However, thyristor 2 cannot turn on instantaneously, since inductances are included in the control-electrode circuits and the control current increases according to a certain law. The voltage on the capacitor rises to twice the supply voltage \(2U_=\). When the current through the control electrode of thyristor 2 reaches a value equal to the trigger current, thyristor 2 turns on, and the discharge of capacitor \(C_k\) turns thyristor 1 off. In the windings of the output transformer the polarity of the voltage changes, and in the control circuit of thyristor 1 the current will flow according to the same law. The frequency of the output voltage will be determined by the parameters of the transformer, by the load resistance, and by the circuit \(R_y, C_y\), and \(W_d\). With complete identity of the parameters of the thyristor control circuits, the rise time of the control current in both circuits will be the same, and a symmetrical voltage will appear at the output of transformer \(Tr1\). The voltage waveform depends on \(L_d, C_k, Z_n\), as follows from the general theory of inverters.
Uncontrolled diodes in the control circuits are necessary to prevent reverse current from flowing through the control electrode, as required by the technical specifications of the thyristor.
When considering the electromagnetic processes in the self-controlled inverter, it is assumed that \(\cos\varphi_N \geq 0.95\), i.e., the load may be taken as purely active, the smoothing inductance \(L_d \ne \infty\), the inverter transformer is ideal with a transformation ratio of \(1:1\), there is no forward voltage drop across the conducting thyristors, and the reverse resistance of a blocked thyristor is equal to infinity. Then, for steady-state operation of the inverter, one may represent the equivalent circuit of Fig. 2 for the instant when valve 2 has turned on and 1 is already turned off; capacitor \(C_k\) retains its initial charge.
Fig. 2
In Fig. 2,
\[ C=\left(\frac{w_1' + w_1''}{w_1'}\right) C_k = 4C_k \]
is the referred capacitance,
\[ R=\frac{R_A}{(w_2/w_1)^2}=R_n \]
is the referred resistance.
The current through the inductance \(L_d\) at the instant \(t=0\) will be determined by the magnitude of the load,
\[ I_0=\frac{U_=}{R}. \tag{1} \]
The voltage across capacitor \(C\) at the instant of switching will be equal to the voltage of the power supply. The equations of the loop currents are written as
\[ \left. \begin{aligned} U_=L_d\frac{di_1(t)}{dt}+i_1(t)R-i_2(t)R,\\ 0&=U_c(t)+i_2(t)R-i_1(t)R. \end{aligned} \right\} \tag{2} \]
The voltage across the load will have the form
\[ U_{\mathrm{n}}(t)=U_{=}\left[1+\frac{1-4a^{2}}{4a}\left(e^{-b(1-2a)t}-e^{-b(1+2a)t}\right)\right], \tag{3} \]
where
\[ a=\sqrt{\frac{1}{4}-\frac{T_c}{T_L}};\qquad b=\frac{1}{2T_c};\qquad T_c=RC;\qquad T_L=\frac{L_d}{R}, \]
For \(T_L>4T_c\) the nature of the voltage variation will be aperiodic; for \(T_L<4T_c\), oscillatory. For the oscillatory case, the voltage across the load is
\[ U_{\mathrm{n}}(t)=U_{=}\left[1+2\sqrt{\frac{T_c}{T_L}}\,d\,e^{-bt}\sin(2bdt-\operatorname{arctg}2d)\right], \tag{4} \]
where
\[ d=\sqrt{\frac{T_c}{T_L}-\frac{1}{4}}. \]
For normal operation it is necessary that, in mode (4), the thyristors not turn off earlier than a half-period of the output voltage and that they retain conductivity. For this purpose, the minimum of the first derivative of the current is found; hence
\[ I_{1\min}(t_{\min})=\frac{U_{=}}{R}\left(1-\frac{1+4d^2}{2d}e^{-\frac{3\pi}{4d}}\right). \tag{5} \]
If the condition
\[ I_{1\min}(t_{\min})>0, \tag{6} \]
is imposed, then
\[ 0.25<\frac{T_c}{T_L}<3.28. \]
The expression for the external characteristic of the inverter for an aperiodic variation of the voltage on the capacitor has the form
\[ \frac{U_{\mathrm{n}}}{U_{=}} = 1+\frac{2A_1}{B_1}(4+A_1)\left(e^{-\frac{B_1}{4}}-1\right) +\frac{2A_2}{B_2}(4+A_2)\left(e^{-\frac{B_2}{4}}-1\right) + \]
\[ +\,2A_1A_2\frac{f}{b}\left(1-e^{-\frac{2b}{f}}\right). \tag{7} \]
where
\[ A_1=\frac{2e^{\frac{b}{4f}}}{e^{-\frac{3\kappa}{4}}(1-e^{\kappa})}; \qquad A_2=\frac{2e^{\frac{b}{4f}}}{e^{-\frac{\kappa}{4}}(e^{\kappa}-1)}; \qquad B_1=\frac{b}{2f}-\frac{\kappa}{2}; \]
\[ B_2=\frac{b}{2f}+\frac{\kappa}{2}; \qquad \kappa=\frac{1}{2f}\sqrt{4b^2-\frac{1}{CL_d}}. \]
From expressions (4) and (5) it is evident that, with an oscillatory nature, large surges of current and voltage arise in the circuit, which may disable the thyristor. Therefore, the most desirable mode of operation of the self-commutated inverter is with aperiodic recharging of the capacitor. If, according to the operating conditions, an oscillatory mode is mandatory, then the thyristors must be selected with the necessary margin. In this case, the time allowed for recovery of the control ...
properties is found from the condition \(U_c(t)=0\), and it must satisfy the requirement \(0.5T_c \ge t_b\). The time allowed for the thyristor to recover its control properties has a complicated expression; however, if during the commutation interval the current \(i_1=\mathrm{const}\), i.e., \(L_{\mathrm{n}}\ne 0\), then
\[ t_b=\sqrt{L_d C}\,\operatorname{arctg} \frac{ \sqrt{3U_=^{4}C^{2}+4U_=^{2}i_1^{2}L_d C} +U_= i_1\sqrt{L_d C} }{ \sqrt{3U_=^{2}i_1^{2}L_d C+4i_1^{4}L_d^{2}} -U_=\sqrt{C} }. \tag{8} \]
To determine the parameters of the control circuit it is necessary to consider the electromagnetic processes in these circuits. From Fig. 1 it is seen that, when thyristor 1 is opened, current through the control electrode of thyristor 2 does not begin to flow immediately, but only after the voltage on capacitor \(C_k\) reaches the opposite polarity. It is assumed here that the power of the source \(U_c(t)\) is sufficiently large that its internal resistance may be neglected.
In determining the control current, a differential equation is solved that is written for an equivalent circuit in which the voltage varies according to (3) or (4), referred to the control winding \(\omega_y\). However, this solution proves complicated and unsuitable for practice. If it is assumed that a rectangular voltage is induced in the control winding \(\omega_y\), and that the inductance of the control circuit is constant, then the current in the control electrode will have the form
\[ i_y(t)=\frac{2U_{\mathrm{ct}}}{R_y} \left[ \frac{R_y}{R_y+R_{yk}} + A_3 e^{-\left(g+\frac{a}{T_1}\right)t} \sin\left(\frac{a}{T_1}t+\gamma\right) \right], \tag{9} \]
where
\[ A_3= \sqrt{ \left(\frac{R_y+R_{yk}}{R_y}\right)^2 + \frac{(T_1T_2+2T_1T_3-T_2T_3)^2} {8g(2-d)T_1^2T_2^2(T_2+T_3)^2} }; \]
\[ \gamma=\operatorname{arctg} \frac{ 8R_yT_1T_2(T_2+T_3)^2\sqrt{2g(2-g)} }{ (R_y+R_{yk})(T_1T_2+2T_1T_3-T_2T_3)^2 }; \]
\[ g=\frac{(T_1+T_3)^2}{2T_1T_3}; \]
\[ T_1=R_yC_y; \]
\[ T_2=\frac{L_y}{R_y}; \]
\[ T_3=\frac{L_y}{R_{yk}}. \]
Here \(U_{\mathrm{ct}}\) is the amplitude of the rectangular voltage referred to the control winding \(i_y(t)\);
\(R_{yk}\) is the resistance of the control-electrode-to-cathode junction. This quantity is not constant and changes when \(i_y(t)\) changes. If \(R_y \gg R_{yk}\) is chosen, then \(R_{yk}\) may be neglected, which considerably simplifies expression (9). However, with constant inductance, the current in the control circuit (9) increases smoothly, which is undesirable for the valves and for the inverter as a whole, since the output frequency will vary additionally with the thyristor temperature.
As practice has shown, the shaping circuit \(R_yC_y\) is not needed, and a saturation choke DN, made on iron with a rectangular hysteresis loop, successfully accomplishes the task of shaping the control-current pulse.
With idealization of the magnetization curve of the core of the MS, the time during which the induction changes from \(-B_0\) to \(+B_s\) can be found from the expression
\[ \int_{0}^{T'} U_c(t)\,dt = \int_{-B_0}^{+B_s} w_1 s\,dB = w_1 s (B_s + B_0), \tag{10} \]
Fig. 3. Time dependences of the voltages on the inverter elements:
a) voltage on the thyristor; b) current through the control electrode; c) voltage on the load;
d) current in the dc circuit. \(U_= = 27\ \mathrm{V};\ f = 400\ \mathrm{Hz};\)
\(U_n = 115\ \mathrm{V},\ i_{ym} = 70\ \mathrm{mA}\).
where \(U_c(t)\) is found from (3) or (4). For a rectangular waveform of the output voltage, the output frequency is determined by the expression
\[ f_{\mathrm{out}} = \frac{2U_{\mathrm{dc}}}{(B_s + B_0) w_1 s}. \tag{11} \]
Here \(w_1\) and \(s\) are the number of turns of the working winding of the MS and the cross section of the steel. From (11) it is seen that, when the load changes, the frequency will change. However, if \(B_0\) is varied, it is possible to obtain \(f = \mathrm{const}\) when chang-
…varying load current and supply voltage. The initial induction must vary according to the law
\[ B_0=-\left[B_s-\frac{2\left(k_{\mathrm{v}} I_{\mathrm{n}}\pm \Delta U_{=}\right)}{f_{\mathrm{out}} w_{\mathrm{d}} S}\right], \tag{12} \]
where \(k_{\mathrm{v}}\) is the tangent of the slope angle of the external characteristic (7).
At the Tomsk Polytechnic Institute, two variants of such converters were built: from a DC voltage of \(27\ \mathrm{V}\) to an AC voltage of \(115\ \mathrm{V}\) at a frequency of \(500\ \mathrm{Hz}\), and from a DC voltage of \(110\ \mathrm{V}\) to an AC voltage of \(127\ \mathrm{V}\) at a frequency of \(50\ \mathrm{Hz}\), using VKU-20 thyristors.
Standard saturable reactors on toroidal cores with a rectangular hysteresis loop were used as the \(DN\).
The waveforms of the voltages and currents in individual sections of the circuit are shown in Fig. 3.
The frequency stability when (12) was satisfied, i.e., when additional control windings of the \(DN\) were connected according to the load current and the supply voltage, was \(\pm 5\%\). The circuit of the self-commutated inverter is most applicable up to \(2\text{–}5\ \mathrm{kW}\) at a high inverted voltage, when an additional power supply is needed to implement the control circuit. The inverter is intended for fluorescent lighting.
References
- W. Schilling, Steurung und Kommutierung bei statischen selbstgeführten Wechselrichtern mit Thyristoren. Electrotechnik und Maschinenbau, 1966, 83, No. 10.