CONVERTER DEVICES WITH A SHIFT COEFFICIENT EQUAL TO UNITY

A. I. ZAITSEV, V. N. MISHIN, V. L. KUZMIN

(Presented by the scientific and technical seminar of the Scientific Research Institute of Electrical Machines)

Compensating converters make it possible to compensate reactive power in the network while simultaneously supplying the load with rectified current [1–2]. However, the magnitude of the generated power is a function of the control angle and the load, which is not always desirable in practice. For a direct-current electric drive with a wide range of speed regulation and a sharply varying load, it is expedient for the converter to operate with $\cos\varphi = 1$ independently of the depth of regulation, which will relieve the network of reactive-power dips and surges.

Let us consider variants of regulating converters while satisfying the condition $\cos\varphi = 1$, using as an example a bridge three-phase converter under the assumption of instantaneous commutation.

I. A converter with commutation of unlike groups (the linear diagram is presented in Fig. 1). In the case under consideration, one group of valves operates with artificial commutation and leading control angles $(\alpha_i)$, while the other operates with natural commutation of the valves and lagging control angles $(\alpha_e)$, with $|\alpha_i| = |\alpha_e| = \alpha$.

Depending on the magnitude of the control angles, two modes are possible in the converter under consideration:

\[ \text{a) } \quad 0 \leq \alpha \leq \frac{\pi}{6}; \qquad \frac{5\pi}{6} \leq \alpha \leq \pi . \]

The rectified voltage is determined by the expression

\[ u_d = \frac{3\sqrt{2}}{\pi} u_{\text{н}} \left[ \sqrt{3}\sin\left(\frac{\pi}{6}+\alpha\right) + \sin\left(\frac{\pi}{3}-2\alpha\right)\cos\alpha \right], \tag{1} \]

where $U_{\text{н}}$ is the rms value of the phase voltage at the converter input.

The distortion coefficient is

\[ \nu = \frac{I_{(1)}}{I_d} = \frac{3}{2\pi} \sqrt{ 2+\sqrt{3}\cos\left(\frac{\pi}{6}+2\alpha\right) +\sin\left(\frac{\pi}{6}+2\alpha\right) }, \tag{2} \]

where $I_d, I_{(1)}$ are the rms values of the line current and of its first harmonic, respectively.

b)
\[ \frac{\pi}{6} \leqslant \alpha \leqslant \frac{5\pi}{6}, \]

\[ u_d=\frac{3\sqrt{6}}{\pi}u_{\text{н}}\cos\alpha, \tag{3} \]

\[ \nu= \frac{0.5\sqrt{6}} {\sqrt{\pi^2\left(1-\frac{2\alpha}{\pi}\right)}} \sqrt{ 2+\sqrt{3}\cos\left(\frac{\pi}{6}+2\alpha\right) +\sin\left(\frac{\pi}{6}+2\alpha\right) }. \tag{4} \]

As follows from Fig. 1 and expressions (1, 2, 3, 4), the case under consideration is characterized by a high content of higher harmonics in the primary-current curve (Fig. 5, curve I) and by significant pulsations of the rectified voltage.

Fig. 1

II. A converter with symmetrical “rectification” of the half-waves of the line voltage relative to the amplitude value (Fig. 2). With this method of control, the duration of the current pulses through the bridge valves is equal to \(\lambda=\frac{2\pi}{3}-2\alpha\); therefore, for \(\alpha>0\), the load current flows through the zero valve during part of the period. The mean value of the rectified voltage is

\[ u_d=\frac{6\sqrt{6}}{\pi}u_{\text{н}}\sin\left(\frac{\pi}{2}-\alpha\right), \tag{5} \]

and the distortion coefficient is

\[ \nu=3\sqrt{ \frac{2-\cos 2\alpha-\sqrt{3}\sin 2\alpha} {\pi^2-6\alpha\pi} }. \tag{6} \]

For this variant, a considerable distortion of the phase current is also characteristic (Fig. 5, curve II), as are substantial pulsations of the rectified voltage.

III. The content of higher harmonics in the curve of the current drawn from the supply, and the pulsations of the rectified voltage, can be reduced by using a converter with buffer valves (Fig. 3) and symmet-

partial “rectification” of the half-waves of the phase voltage. The expression for the rectified voltage has the following form:

\[ u_d=\frac{6\sqrt{2}}{\pi}u_{\text{n}}\sin\left(\frac{\pi}{3}-\alpha\right). \tag{7} \]

The distortion factor is

\[ \nu=\sqrt{\frac{6\left[1+\sin\left(\frac{\pi}{6}-2\alpha\right)\right]}{\pi(\pi-3\alpha)}}. \tag{8} \]

Fig. 2

The distortion factor in this control variant is maximal (Fig. 5, curve III), while the current pulsations in the load are minimal. All three variants, despite the fact that for them \(\cos\varphi=1\), are distinguished by a large distortion of the phase current and by significant pulsations of the output voltage.

Fig. 3

IV. To a large extent these drawbacks are eliminated if compensating and ordinary bridge converters, connected in parallel or in series, operate into a common load (Fig. 4). The rectified voltage in such a system is determined by the expression

\[ u_d=\frac{6\sqrt{6}}{\pi}u_{\mathrm{н}}\cos\alpha . \tag{9} \]

The distortion coefficient is described by three equations corresponding to different ranges of variation of the control angle:

\[ 0\leq \alpha \leq \frac{\pi}{6}; \qquad \frac{5\pi}{6}\leq \alpha \leq \pi; \tag{10} \]

\[ \nu= \frac{ \sqrt{\,6\left[2+\sqrt{3}\sin\left(\frac{\pi}{3}-2\alpha\right)+\sin\left(\frac{\pi}{6}+2\alpha\right)\right]\,} }{ 2\pi\sqrt{\frac{2}{3}-\frac{\alpha}{\pi}} }; \tag{11} \]

Fig. 4

\[ \frac{\pi}{6}\leq \alpha \leq \frac{\pi}{3}; \qquad \frac{2\pi}{3}\leq \alpha \leq \frac{5\pi}{6}; \tag{12} \]

\[ \nu= \sqrt{ \frac{ 3\left[6+3\sqrt{3}\cos\left(\frac{\pi}{6}+2\alpha\right)+3\sin\left(\frac{\pi}{6}+2\alpha\right)\right] }{ \pi(5\pi-12\alpha) } }; \tag{13} \]

\[ \frac{\pi}{3}\leq \alpha \leq \frac{2\pi}{3}; \tag{14} \]

\[ \nu= \frac{ \sqrt{ \pi\left[6+3\sqrt{3}\cos\left(\frac{\pi}{6}+2\alpha\right)+3\sin\left(\frac{\pi}{6}+2\alpha\right)\right] } }{ \pi\sqrt{\pi-2\alpha} }. \tag{15} \]

The dependence of the distortion coefficient on the depth of regulation of the output voltage is presented in Fig. 5 (curve IV). The distortion of the phase current here begins to increase in the range of variation of the control angle from \(\frac{\pi}{3}\) to \(\frac{\pi}{2}\). The pulsations of the rectified voltage are minimal and do not depend on the regulation range.

Curve V (Fig. 5) shows the variation of the power factor of a conventional converter with natural commutation as a function of the depth of regulation of the rectified voltage.

Thus, among the converter-device variants considered with $\cos \varphi = 1$, the most expedient appears to be a combination composed of compensating and conventional converters, connected in series or in parallel and connected to a

Fig. 5

common load. The use of such devices in reversible systems makes it possible to obtain ideal matching of the characteristics of the sets, which will allow equalizing reactors to be dispensed with [3].

REFERENCES

1. A. I. Zaitsev, V. N. Mishin. Thyristor converters with artificial commutation. Report at a scientific and technical conference. Status and prospects for the development of the production and implementation of power semiconductor valves and converter devices based on them. VNIIEM, Moscow, 1966.

2. A. I. Zaitsev, V. N. Mishin, N. N. Mishina. Characteristics of one class of compensating converters. In: Converter-Engineering Devices, issue 1. Kiev, 1969.

3. G. G. Magazinnik, I. V. Dudchenko, V. A. Tikhomirov. Some features of the statics and dynamics of compensated thyristor converters for DC drives. Reports of the VII Scientific and Technical Conference, Static Converters in Automation and Electric Drives, Tomsk, 1971.