External Characteristics of a Compensating Converter with Two-Stage Artificial Commutation
Abstract Generated abstract
This paper analyzes the external characteristics of a six-phase compensating converter with an equalizing reactor and a two-stage forced-commutation unit, a configuration intended to improve the power factor of valve converters. By separating the rectified-voltage period into intervals with one and two conducting power valves, the author derives a system of equations relating load current, commutation duration, capacitor parameters, extinction angle, and rectified voltage. Approximate boundary expressions for minimum and maximum load current show that increasing the extinction angle increases the slope of the external characteristic, while at small extinction angles the characteristic may be stiffer than that of a naturally commutated converter. The comparison of calculated characteristics indicates that the forced-commutated compensating converter can maintain higher rectified voltage than a naturally commutated converter at the same extinction angle.
Full Text
External Characteristics of a Compensating Converter with Two-Stage Forced Commutation
A. A. Kuvshinov
(Presented by the Scientific and Technical Seminar of the Scientific Research Institute of AEM)
To increase the power factor of valve converters, forced commutation has recently been used ever more widely. The simplest unit of two-stage forced commutation for a six-phase converter with an equalizing reactor is the unit shown in Fig. 1. This article considers the external characteristics of such a converter.
Fig. 1
Taking as the origin for measuring angles the moment of completion of the first commutation (turning off of the next valve), we divide one period of the rectified voltage into two intervals.
- An interval of duration \(\vartheta_n\), when one power valve is on. During this time the rectified voltage is equal to the sum of the voltage of the operating phase of the anode transformer and the voltage across the corresponding half of the equalizing reactor.
\[ U_{d1} = U_m \cos(\vartheta_g-\gamma_1-\vartheta) + \frac{1}{2} \left( U_{ck1} - \frac{U_{ck1}+U_{ck2}}{\vartheta_n}\,\vartheta \right), \tag{1} \]
where \(0<\vartheta<\vartheta_p\),
\(U_{ck1}\) is the voltage on the commutating capacitor at the end of the first commutation [1],
\(U_{ck2}\) is the voltage on the commutating capacitor at the beginning of the second commutation [1],
\(U_m\) is the amplitude of the secondary voltage of the power transformer,
\(\vartheta_r\) is the extinction angle, measured to the left from the point of natural firing of the valves,
\(\gamma_1\) is the duration of the first commutation.
- An interval of duration \(\dfrac{\pi}{3}-\vartheta_p\), when two power valves are switched on. The rectified voltage at this time, as in an ordinary converter, is equal to the half-sum of the rectified voltages of the three-phase groups
\[ U_{d2}=\frac{\sqrt{3}}{2}U_m\sin\left(\frac{\pi}{3}-\vartheta_r+\gamma_1+\vartheta\right), \tag{2} \]
where \(\vartheta_p<\vartheta<\dfrac{\pi}{3}\).
Having integrated expressions (1) and (2) over the corresponding limits and having added equations (15) and (16) from [1] for determining the durations of the first commutation and of the switched-on state of one power valve \(\vartheta_p\), we obtain a system of equations describing the external characteristic of the compensating converter:
\[ \left\{ \begin{aligned} I_d\frac{1-\sin \varepsilon\gamma_1}{\sin \varepsilon\gamma_1} &=4\varepsilon\omega C U_m \cos\left(\vartheta_r-\frac{\gamma_1+\vartheta_p}{2}\right) \sin\left(\frac{\pi}{6}-\frac{\gamma_1+\vartheta_p}{2}\right),\\[6pt] I_d\frac{\varepsilon\vartheta_p\,\tg \varepsilon\gamma_1-1}{\tg \varepsilon\gamma_1} &=4\varepsilon\omega C U_m \sin\left(\vartheta_r-\frac{\gamma_1+\vartheta_p}{2}\right) \cos\left(\frac{\pi}{6}-\frac{\gamma_1+\vartheta_p}{2}\right),\\[6pt] U_d&=\frac{3}{\pi}U_m\left[ \frac{\vartheta_p}{2} -\frac{\sqrt{2}\cos\left(\frac{\pi}{4}-\varepsilon\gamma_1\right)-1}{1-\sin\varepsilon\gamma_1} \cos\left(\vartheta_r-\frac{\gamma_1+\vartheta_p}{2}\right) \sin\left(\frac{\pi}{6}-\frac{\gamma_1+\vartheta_p}{2}\right)\right.\\ &\qquad\left. +\cos\left(\vartheta_r-\gamma_1-\frac{\vartheta_p}{2}\right) \sin\left(\frac{\pi}{3}+\frac{\vartheta_p}{2}\right) \right]-\Delta U_R-\Delta U_B, \end{aligned} \right. \tag{3} \]
where
\[ \varepsilon=\frac{1}{\omega\sqrt{2LC}}, \]
\(I_d\) is the converter load current,
\(C\) is the capacitance of the commutating capacitor,
\(\Delta U_R\) is the voltage drop across the active resistances of the circuit,
\(\Delta U_B\) is the voltage drop in the valves,
\(L\) is the inductance of one transformer phase, referred to the secondary circuit.
In order to estimate approximately the steepness of the external characteristics of the compensating converter, let us determine the values of the rectified voltage at the boundaries of the external characteristic, neglecting the quantities \(\Delta U_R\) and \(\Delta U_B\).
- Operating mode with the minimum possible load current.
As the converter load current decreases, the duration of the first commutation is shortened, while the duration of the on-state of the power valve increases and, for a sufficiently small value of the commutating-capacitor capacitance, will approach \(\pi/3\).
Consequently, the rectified voltage in this mode is equal to
\[ U_{d\max}=\frac{3}{\pi}\,U_m\cos\left(\vartheta_{\mathrm{g}}-\frac{\pi}{6}\right). \tag{4} \]
Formula (4) is the well-known expression for the no-load voltage of a six-phase converter with neutral terminal, operating at a control angle \(\alpha=\vartheta_{\mathrm{g}}-\gamma_1\).
- The operating mode with the maximum load current for which the compensating converter is designed.
In this mode, the time during which one power valve is in the on-state may be neglected, and then
\[ U_{d\min}=\frac{3\sqrt{3}}{2\pi}U_m\cos(\vartheta_{\mathrm{g}}-\gamma_1), \tag{5} \]
that is, the rectified voltage in this mode is equal to the no-load voltage of an ordinary six-phase converter with an equalizing reactor at a control angle \(\alpha=\vartheta-\gamma_1\).
From a comparison of expressions (4) and (5) for the values of the rectified voltage at the boundaries of the external characteristic, it is seen that, as the extinction angle increases, the slope of the external characteristic increases.
At small extinction angles \((\vartheta_{\mathrm{g}}<30^\circ)\), the external characteristic of the compensating converter may be stiffer than the external characteristic of a converter with natural commutation, owing to the fact that the duration of the first commutation, with the appropriate choice of the commutating capacitance, may be much shorter than the duration of commutation in a conventional converter.
An approximate value of the rectified voltage of the compensating converter can be obtained from expression (26) [1], if it is assumed that there are no losses in the converter and that the active power on the alternating-current side is equal to the load power,
\[ U_d \approx \frac{3}{\pi}U_m \cos\left(\vartheta_{\mathrm{g}}-\frac{\vartheta_{\mathrm{n}}}{2}-\frac{3\gamma_1+\gamma_2}{4}\right) \sin\left(-\frac{\pi}{3}+\frac{\vartheta_{\mathrm{n}}}{2}+\frac{\gamma_1+\gamma_2}{2}\right). \tag{6} \]
From expressions (4)—(6) it is seen that the rectified voltage of a compensating converter with two-stage forced commutation is always higher than the voltage of a converter with natural commutation operating with a control angle \(\alpha\) equal to the extinction angle \(\vartheta_{\mathrm{g}}\), because during part of the period the converter operates according to the “delta—six-phase star” circuit.
Fig. 2
In Fig. 2 the external characteristics of the compensating converter are plotted for various extinction angles and two values of the commutating-capacitor capacitances. Also plotted here are the external characteristics of a converter with natural commutation (dashed lines) for firing angles \(\alpha\) equal to the extinction angles.
A comparison of these characteristics shows that, both in terms of the magnitude of the load-current variation range and in terms of the stiffness of the external characteristics, preference should be given to thyristor converters.
REFERENCES
- A. I. Zaitsev, A. A. Kuvshinov. On the calculation of a six-phase converter with an equalizing reactor with a forced-commutation unit. Reports to the VI Scientific and Technical Conference on Problems of Production Automation, vol. 1, Tomsk, 1969.