Selection of Switching Frequency in TRShIP-D Electric Drives
Abstract Generated abstract
This paper examines how to select and regulate the switching frequency in DC electric drives using thyristor reversible pulse-width converters. It argues that frequency choice should not be based only on minimizing additional losses, but must also account for thyristor turn-off time, voltage utilization of the supply, and the need to maintain continuous armature current for sufficiently stiff mechanical characteristics. The authors derive frequency-selection conditions from the voltage utilization factor and from the boundary of continuous current, and propose regulating switching frequency as a function of the control parameter so that current pulsations and additional motor losses remain constant under unchanged load. They conclude that the allowable upper frequency is limited by thyristor commutation capability, while the lower limit is set by the required source voltage utilization factor.
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SELECTION OF SWITCHING FREQUENCY IN TRShIP-D ELECTRIC DRIVES
V. A. Beinarovich, L. S. Udut, V. S. Fadeev
(Presented by the scientific and technical seminar of the NII AEM)
DC electric drives with thyristor reversible pulse-width converters (TRShIP) make it possible to ensure maximum speed of response, determined only by the properties of the motor. However, the practical application of such systems is limited by a number of difficulties, associated mainly with the complexity of their implementation and the insufficient reliability of the forced-commutation devices of TRShIP. In [1] it is shown that the implementation of TRShIP can be simplified by using symmetric separate control of the bridge arms, which, in comparison with joint control, has a simpler circuit implementation and ensures higher reliability of converter operation. On the other hand, the methods of joint and separate symmetric control are completely equivalent in the region of continuous currents, while in the zone of discontinuous currents the characteristics of the actuating motor in both cases are soft and nonlinear [2].
Improvement of the performance of a drive with TRShIP can be obtained by a rational choice of the switching frequency. Usually the switching frequency is chosen from the condition of minimizing additional losses [3, 4]. However, when designing systems it is also necessary to take into account the possibilities of practical realization of the required frequency and the voltage utilization factor of the source.
The maximum realizable switching frequency of TRShIP, \(f_{\mathrm{M}}\), is limited by the thyristor turn-off time \(t_{\mathrm{off}}\) indicated in their nameplate data. As the switching frequency \(f=\frac{1}{T}\) is increased, the voltage utilization factor of the source, \(K_{\mathrm{u}}\), decreases; it is equal to the ratio of the maximum output voltage to the supply-source voltage.
\[ K_{\mathrm{u}}=\frac{U_{\mathrm{pm}}}{U}=1-\frac{2t_{\mathrm{off}}}{T}. \tag{1} \]
From (1) the required switching frequency \(f_{\mathrm{n}}\), ensuring attainment of a specified voltage utilization factor of the source, can be determined.
From the condition for obtaining continuous currents over a specified range of load variation, using the expression obtained in [2],
\[ I_{\mathrm{gr}}= \frac{ U\left[\tau_1-\tau_1^2\left(\frac{\tau_1-1}{2\tau_{\mathrm{ya}}-1}\right)\right](2-\tau_1) - U\tau_1^2\left(1+\frac{\tau_1-1}{2\tau_{\mathrm{ya}}-1}\right)(1-\tau_1)^2 }{ R_{\mathrm{ya}}\tau_{\mathrm{ya}} } \tag{2} \]
by substituting the minimum continuous armature current \(I_{\min}=I_{\mathrm{gr}}\), we obtain the law of variation of the switching frequency
\[ f= \frac{ U\left[\tau_1-\tau_1^2\left(\frac{\tau_1-1}{2\tau_{\mathrm{ya}}-1}\right)\right](2-\tau_1) - U\tau_1^2\left(1+\frac{\tau_1-1}{2\tau_{\mathrm{ya}}-1}\right)(1-\tau_1)^2 }{ I_{\mathrm{gr}}L_{\mathrm{ya}} }. \tag{3} \]
With such frequency regulation, the amplitude of the current pulsations and the additional losses in the motor remain constant over the entire speed-control range at unchanged load.
For \(\gamma=0.5\), from (3) we obtain the value of the maximum switching frequency \(f_t\) from the condition of continuous current.
From the condition of minimizing the total additional losses in the motor and the TRShIP, the optimum frequency \(f_{\mathrm{opt}}\) is determined as a function of \(\gamma\) [3, 4]; it also has its greatest value at \(\gamma=0.5\).
Thus, the switching frequency should be regulated as a function of \(\gamma\), both according to the conditions for obtaining stiff mechanical characteristics in the continuous-current mode (3) and according to the conditions for minimizing total losses [3, 4].
The upper limit of frequency regulation in the TRShIP is in any case restricted by the permissible switching frequency \(f_m\), determined by the turn-off time of the thyristors. In the case when \(f_{\mathrm{opt}}\ne f_t\) at \(\gamma=0.5\), and both of these frequencies are less than \(f_m\), the larger of the two obtained values, \(f_{\mathrm{opt}}\) or \(f_t\), should be selected as the maximum switching frequency.
The lower limit of frequency regulation is determined from (1) for the specified value of the voltage utilization factor of the source.
LITERATURE
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V. A. Beinarovich, L. S. Udut, V. S. Fadeev, N. G. Volkov. Methods for controlling reversible pulse-width converters. Proceedings of the VII Scientific and Technical Conference “Static Converters in Automation and Electric Drive.” Tomsk, 1972.
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L. S. Udut, V. S. Fadeev, V. A. Beinarovich. Calculation of the mechanical characteristics of electric motors when supplied from thyristor TRShIP with symmetrical control. Present collection.
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G. A. Glazenko. Pulse Semiconductor Amplifiers in Electric Drives. Energiya, 1965.
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M. I. Kraitsberg, E. V. Shikut. Pulse Methods for Regulating DC Circuits by Means of Thyristors. Energiya, 1969.