Forced Commutation in a Pulse Slip Regulator of an Induction Motor with Antiparallel-Connected Thyristors
Abstract Generated abstract
The paper addresses forced commutation in pulse slip regulation of an induction motor using antiparallel-connected thyristors, with the aim of reducing the number of commutation devices. It proposes a regulator circuit with a single common series-type forced-commutation unit and analyzes the quasi-steady commutation process by dividing it into stages and deriving relations for capacitor voltage, currents, recovery times, voltage stresses, and average currents in auxiliary elements. The resulting formulas provide design conditions for selecting the commutating capacitor, inductances, and resistances, including requirements for resonant recharging and reliable turn-off of the power thyristors. The proposed circuit is presented as advantageous for drives with frequent starts and a wide range of shaft load variation.
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Forced Commutation in a Pulse Slip Regulator of an Induction Motor with Antiparallel-Connected Thyristors
Yu. P. Kostyukov, O. G. Makarenko
(Presented by the scientific and technical seminar of the Scientific Research Institute of AEM)
Reducing the number of forced-commutation devices with antiparallel-connected valves is possible by switching off all power thyristors with a single forced-commutation unit. However, such circuits have not been considered in the literature, which is explained by the difficulty of creating forced-commutation circuits with antiparallel-connected valves. Therefore, the development of new forced-commutation circuits and the improvement of known ones is a topical and important task.
Figure 1 shows a developed circuit of pulse regulation with a common forced-commutation unit of the series type. The distinguishing feature of the circuit is that the commutating inductance $L_1$ is connected between like-named electrodes of the controlled valves T1, T2 and T3, T4; and, in order to create a path for the reverse current to flow through the power thyristors at the moment of their turn-off and to provide circuit symmetry, the common point of the auxiliary resistances $R_1$ and $R_2$ is connected to the midpoint of the resistance $R_3$, which is connected in parallel with the commutating inductance $L_1$, with
\[ R_3 = 4R_1 = 4R_2. \]
It is not difficult to show that during the slip-frequency period there are six time intervals, in each of which, during the pulse (the power thyristors are on), the structure of the power circuit remains unchanged.
Let us analyze the quasi-steady processes occurring in the circuit under consideration over one commutation period; for this purpose we shall divide the whole process into stages. The first stage begins at the moment the auxiliary thyristor T5 is switched on and is characterized by the flow of a reverse-current pulse through the power thyristors that are in the conducting state. This time, owing to the negligible inductance of the circuit—the commutating capacitor—thyristors, is negligibly small. Then the second stage begins, during which the commutating capacitor is resonantly recharged to the maximum negative voltage (interval $t_1$–$t_4$, Fig. 2), the rotor current passes into the auxiliary resistances, and the power thyristors turn off. In the third stage, the commutating capacitor, under the action of its own voltage and the voltage of the supply source, is charged to the voltage $U_0$. In this process the auxiliary thyristor T5 turns off, and part of the electromagnetic energy stored in the inductance $L_1$ is dissipated in the auxiliary resistance $R_3$.
Fig. 1
Fig. 2
We shall begin the consideration of the quasi-steady-state mode in the forced-commutation device from the second stage, under the following assumptions:
- The turn-on time of the thyristors and the action time of the reverse current are negligibly small,
- The voltage drop across the thyristors and diodes is equal to zero.
- The parameters of the circuits \(L_1, L_2, C, R\) are constant.
In this case the characteristic equation has the form
\[ F(p)=R_3L_1Cp^2+L_1p+R_3=0. \tag{1} \]
Solving equation (1) under the initial conditions
\[ u_c(t_1)=U_0,\quad i_{L_1}(t_1)=I_0, \tag{2} \]
we obtain expressions for the voltage across the capacitance and the current
\[ u_c=-u_{R_3}=u_{L_1}=-e^{-bt}\left[U_0\frac{\omega}{\omega_0}\sin(\omega_0t-\psi_0)+\frac{I_0}{\omega_0C}\sin\omega_0t\right]; \tag{3} \]
\[ i_c=-e^{-bt}\left[\frac{U_0}{R_3}\left(\cos\omega_0t+\frac{\omega_0^2-b^2}{2b\omega_0}\sin\omega_0t\right)-I_0\frac{\omega}{\omega_0}\sin(\omega_0t-\psi_0)\right], \tag{4} \]
where \(\psi_0=\operatorname{arctg}\dfrac{\omega_0}{b}\) is the phase-shift angle between the current \(i\) and the voltage \(u_c\);
\[ b=\frac{1}{2R_3C} \]
is the damping decrement of the circuit;
\(\omega_0\) is the natural angular frequency of the commutating circuit, taking damping into account;
\(\omega\) is the same, without taking damping into account.
To ensure resonant recharging of the commutating capacitor, the condition
\[ R_3>\frac{1}{2}\sqrt{\frac{L_1}{C}}. \tag{5} \]
must be satisfied.
The time \(t_{\mathrm{v}1}\), provided by the forced-commutation circuit to the power thyristors for recovery of their blocking properties, is determined from expression (3) and the relation
\[ 2IR_1-u_c=0, \tag{6} \]
then, after simple transformations, we find
\[ e^{bt_{\mathrm{v}1}}=-\frac{2b}{\omega_0}(2+\kappa)\sin\omega_0t_{\mathrm{v}1}+2\kappa\cos\omega_0t_{\mathrm{v}1}, \tag{7} \]
where \(\kappa=\dfrac{U_0}{IR_3}\) is the voltage multiplication factor in the \(C\)—\(R_3\) circuit.
The resulting relation (7) is transcendental with respect to the circuit parameters and is solved only by numerical or graphical methods. Introducing a linear approximation of the voltage on the commutating capacitor in the interval \(t_1\)—\(t_3\), we obtain a simpler expression for the time \(t_{\mathrm{v}1}\).
\[ t_{\mathrm{v}1}=\left(1-\frac{1}{2\kappa}\right)\frac{1}{\omega_0}\operatorname{arctg}\frac{\omega_0}{b\left(1+\dfrac{2}{\kappa}\right)}. \tag{8} \]
The duration of the second stage can be determined from equation (4), with \(i_c=0\).
\[ \omega_0 t_0=\pi-\operatorname{arctg} \frac{2(\kappa+1)} {-\dfrac{b}{\omega_0}(\kappa+2)+\dfrac{\omega_0}{b}\kappa}. \tag{9} \]
The maximum forward voltage on the auxiliary thyristor T5 is equal to \(U_0\), and the maximum reverse voltage is obtained from equation (3), when \(t=t_0\),
\[ U_{\mathrm{rev}\,T5} = -e^{-bt_0} \left[ U_0\frac{\omega}{\omega_0}\sin(\omega_0t_0-\psi_0) + \frac{I_0}{\omega_0 C}\sin\omega_0t_0 \right]. \tag{10} \]
The recovery time of the blocking properties of the auxiliary thyristor is
\[ t_{\mathrm{v}}=\frac{1}{\omega_{02}}\arccos\frac{U_1}{U_1+U_{C2}}. \tag{11} \]
The value of the charging inductance \(L_2\) is selected according to the condition
\[ L_2> \frac{(t_{\mathrm{v}2})^2} {C\left(\arccos\dfrac{U_1}{U_1+U_{C2}}\right)^2}. \tag{12} \]
The average value of the current through the auxiliary thyristor T5 and diode D1 is determined as follows:
\[ I_{\mathrm{avg}\,T5} = \frac{C}{T} \left\{ U_0 \left[ 1-e^{-bt_0} \left( \cos\omega_0t_0-\frac{b}{\omega_0}\sin\omega_0t_0 \right) \right] + \frac{I_0}{\omega_0 C}\sin\omega_0t_0\cdot e^{-bt_0} \right\}, \tag{13} \]
\[ I_{\mathrm{avg}\,D1} = \frac{C}{T}(U_1+U_{C2})\cdot \left(1+e^{-\pi\frac{b_2}{\omega_{02}}}\right). \tag{14} \]
The dependences obtained make it possible to select the elements of the forced-commutation circuit. For normal operation of the circuit it is necessary that the initial voltage on the capacitor be
\[ U_0>I_m\cdot 3R_1, \tag{15} \]
where \(I_m\) is the maximum current to be switched off in the power thyristor.
Knowing the value of the turn-on current, from expression (15) we determine the initial voltage on the commutating capacitor. The capacitance of the commutating capacitor is preliminarily selected from the condition for switching off the maximum current in the power thyristor
\[ C> \frac{k_z t_{\mathrm{v.p}} I_m} {(U_0-I_m2R_1)}, \tag{16} \]
where
\(k_z\) — safety factor with respect to recovery time
\(t_{\mathrm{v.p}}\) — rated recovery time of the thyristor’s controllability.
For a specified recovery time \(t_{\mathrm{v.p}}\), using expression (8) or (7), we find the required value of \(\omega_0\), from which we determine the value of the commutating inductance
\[ L_1=\frac{1}{C(\omega_0^2+b^2)}. \tag{17} \]
The selected values of the capacitance \(C\) and the inductance \(L_1\) are then checked according to condition (5).
The merit of the proposed pulse-control circuit lies in the presence of a single common forced-commutation unit and in the low installed power of the power thyristors. This circuit is recommended for electric drives with frequent starts and wide limits of variation of the load on the motor shaft.