Thyristor Chopper with Nonlinear Inductance in the Accelerated Recharge Circuit
Abstract Generated abstract
This paper analyzes a DC thyristor chopper using forced capacitive commutation in which the thyristor switch is shunted by an accelerated recharge branch containing an oppositely connected diode and a nonlinear inductance with a rectangular hysteresis loop. Under idealized assumptions for the valves, source voltage, load current, and magnetic core, the authors derive expressions for capacitor voltage, core induction, saturation conditions, delay time before accelerated recharge, and the resulting commutation interval. The analysis shows that once the nonlinear choke saturates, the commutating capacitor is recharged through an oscillatory circuit, improving commutation capability. It also indicates that the output voltage waveform area increases with load current, giving the converter a load-current-dependent average voltage regulation effect that may be used as positive feedback.
Full Text
THYRISTOR CHOPPER WITH NONLINEAR INDUCTANCE IN THE ACCELERATED RECHARGE CIRCUIT
V. N. MISHIN, V. P. LAIER
(Presented by the Scientific and Technical Seminar of the Nuclear Research Institute)
The use of an accelerated recharge circuit in converter devices employing a thyristor switch with forced capacitive commutation to regulate the voltage at the converter output makes it possible to reduce the dependence of the recharge time of the commutating capacitor on the load current [1, 2, 3].
This article analyzes the operation of a DC converter [4] when the thyristor switch is shunted by a circuit consisting of an oppositely connected diode and a nonlinear inductance (Fig. 1). The nonlinear inductance \(L_2\) is implemented on a core with a rectangular hysteresis loop.
In analyzing the processes in the converter, losses in the steel of the core are not taken into account; the squareness coefficient of the hysteresis loop is taken as equal to 1; the valves have ideal characteristics; and the voltage at the source terminals and the load current during the interval of commutation processes are constant.
Fig. 1
Fig. 2
Taking into account that the additional elements of the circuit in Fig. 2, \(R\), \(D_3\), \(L_2\), affect the operation of the converter only from the moment the power thyristor \(T1\) is turned off, we shall begin consideration of the processes in the converter from this same moment. The equivalent circuit of the converter is shown in Fig. 2.
The equation of the core dynamics may be written in the form [5]
\[ i=I_0+\frac{u_{L_2}}{R(B)}, \tag{1} \]
where \(I_0=\dfrac{H_0 l}{N_2}\) is the component of the choke current determined by the threshold field strength \(H_0\) of the core material;
\(l\) is the length of the mean magnetic line of force of the core with cross section \(S\);
\(N_2\) is the number of turns of choke \(L_2\);
\(R(B)\) is the nonlinear resistance of inductance \(L_2\);
\(U_{L_2}=-e_L=N_2S\dfrac{dB}{dt}\) is the voltage across the choke.
In the absence of core saturation, \(R(B)\approx\infty\); therefore, for inductions \(|B|<B_s\), the nonlinear inductance is a current limiter (CL). For inductions \(|B|=B_s\), \(R(B)=0\), and the circuit \(C\)—\(L_2\)—\(D_3\)—\(C\) is formed for accelerated recharge of the commutating capacitance.
Taking into account the adopted assumptions, at \(|B|<B_s\) the capacitor, after turn-off of the power thyristor T1, is recharged by the load current \(I\) in accordance with the expression
\[ U_c(t)=-U_k+\frac{It}{C}, \tag{2} \]
where \(U_k\) is the voltage across the capacitor at the moment the thyristor is turned off. Taking into account that, for a lossless circuit,
\[ U_{L_2}=N_2S\frac{dB}{dt}=U_c(t), \tag{3} \]
we determine from (3) the induction for \(B(0)=B_0\)
\[ B=B_0-\frac{U_k t}{N_2S}+\frac{It^2}{2N_2SC}; \tag{4} \]
the core remagnetization time in accordance with (4) is
\[ t=\frac{CU_k}{I} \left[ 1-\left( 1-\frac{2\Delta B N_2SI}{CU_k^2} \right)^{\frac{1}{2}} \right], \tag{5} \]
where \(\Delta B=B-B_0\) is the change in the core induction.
With the corresponding choice of the parameters of the saturating choke and of resistor \(R\) of the initial bias of the induction \(B_0\), it is possible to ensure saturation of the core \(B=-B_s\) before the voltage across the capacitor changes its sign. Then the delay time of the forced (accelerated) recharge of the capacitor is
\[ t_3=\frac{CU_k}{I} \left[ 1-\left( 1-\frac{2(B_0+B_s)N_2SI}{CU_k^2} \right)^{\frac{1}{2}} \right]. \tag{6} \]
It is evident from (6) that the maximum delay can be achieved at the initial induction \(B_0=-B_s\).
The conditions for ensuring saturation of the core can be obtained from (6), i.e.
\[ |B|=B_s \text{ when } \begin{cases} U_k \ge U_s=\left[\dfrac{2(B_0+B_s)N_2Sl}{C}\right]^{\frac12},\\[6pt] I \le I_s=\dfrac{CU_k^2}{2(B_0+B_s)N_2S}. \end{cases} \]
After the core reaches saturation, a circuit of accelerated recharge of the commutating capacitance is formed, the processes in which are described by the equation
\[ L_{2s}C\dfrac{d^2U_c}{dt^2}+U_c=0. \tag{9} \]
The solution of (9) for the voltage across the capacitance, under the initial conditions
\[ U_{c(0)}=U_3=U_k-\dfrac{It_3}{C} \quad \text{and} \quad i_{c(0)}=I, \]
has the form
\[ U_c=-U_3\cos \omega t+\dfrac{I}{C\omega}\sin \omega t, \tag{10} \]
Fig. 3
where \(L_{2s}\) is the leakage inductance of the saturated choke \(L_2\);
\[ \omega=\dfrac{1}{\sqrt{L_{2s}C}} \]
is the angular frequency of the accelerated-recharge circuit.
The time allowed for extinguishing the thyristor is determined as the sum of the delay time and the time of accelerated discharge of the capacitor to zero, i.e., taking (10) into account,
\[ t_v=t_3+\sqrt{L_{2s}C}\cdot \operatorname{arctg} \dfrac{U_k-\dfrac{It_3}{C}}{I\rho}, \tag{11} \]
where
\[ \rho=\sqrt{\dfrac{L_{2s}}{C}} \]
is the characteristic impedance of the accelerated-recharge circuit.
The accelerated recharge of the capacitor will end when the current in the inductance \(L_2\) is equal to zero, i.e., when \(i=i_c-I=0\). The total time of oscillatory recharge is
\[ t_k \approx \pi\sqrt{L_{2s}C}. \]
The time for recharging the commutating capacitance to the source voltage \(E\).
\[ t=\frac{C(E-U_3)}{I}. \]
Time diagrams of the variation of the voltage at the converter output for different values of the load current are presented in Fig. 3.
The volt-second area bounded by the curve of the variation of the voltage at the converter output increases with increasing load current; that is, a converter with an accelerated-recharge circuit using a nonlinear inductance has the property of regulating the average voltage when the load current changes. Consequently, the use of an accelerated-recharge circuit with a diode and nonlinear inductance makes it possible to obtain a converter with high commutation capability, while the property of the circuit to regulate the average voltage at the converter output under fluctuations of the load current makes it possible to use it as positive feedback with respect to load current.
REFERENCES
-
R. Wagnet. Anordnung zur Impulssteuerung der Spannung eines Gleichstromverbrauchers. FRG Patent, No. 1242289, 1967.
-
G. N. Buslaev, G. K. Shvarts. Evaluation of capacitor arrangements for locking thyristors. Elektrichestvo, 1968, No. 6.
-
V. A. Labuntsov, G. A. Belov. Comparative analysis of thyristor pulse DC-voltage converters. Collection of reports of MEI for 1968–1969, pp. 38–51.
-
DC-voltage converter. Patent 43—562, 56AO, Japan, published 10/I 1968.
-
M. A. Rosenblat. Magnetic Elements of Automation and Computing Technology. Moscow, Nauka, 1966.