Single-Phase Thyristor Inverter with Sinusoidal Output Voltage
Abstract Generated abstract
This paper examines a single-phase parallel thyristor inverter intended to produce an approximately sinusoidal 50 Hz output voltage. It argues that, for a fixed output frequency, the practical way to reduce distortion is to connect series resonant L-C filter sections tuned to suppress selected odd harmonics of the rectangular inverter voltage, especially the 3rd, 5th, and 7th components. The analysis derives the fundamental-frequency impedance of the filter sections and shows that, for typical harmonic orders, their effect is approximately inductive. The paper concludes that removing the main lower harmonics, and potentially the 9th as well, can keep the residual higher-harmonic content near a level acceptable for most consumers, provided the inverter frequency is well stabilized.
Full Text
Single-Phase Thyristor Inverter with Sinusoidal Output Voltage
V. P. Petrovich
(Presented by the scientific and technical seminar of the Department of Electrical Equipment)
The mastery by domestic industry of the production of silicon controlled valves—thyristors—has made it possible in a number of cases to replace electromechanical versions of converters with static converters. One of the main disadvantages of static voltage converters is the difficulty of obtaining a voltage of sinusoidal form. In the case of a fixed output-voltage frequency, the simplest and most accessible method of obtaining a sinusoidal voltage is the use of multi-link \(L—C\) filters, which make it possible to isolate the first harmonic component of the output voltage and suppress the higher harmonic components. Let us consider a single-phase parallel thyristor inverter with resonant circuits connected at the output in series with the load, shown in Fig. 1. The inverter frequency, determined by the frequency of the master oscillator, is constant and equal to 50 Hz.
Fig. 1
As is known, the rectangular output voltage of a single-phase parallel inverter contains only odd harmonics. By tuning the \(L—C\) circuits connected in series
into resonance at the 3rd, 5th, 7th, etc. harmonics, one can obtain at the load a voltage arbitrarily close to sinusoidal. In practice, for most consumers, a deviation of the output voltage from a sinusoidal waveform within 10–15% is permissible. This can be achieved by suppressing the 3rd, 5th, and 7th harmonics [1]. The resonance condition is
\[ m\omega = \frac{1}{\sqrt{L_m C_m}}, \]
where \(m\) is the number of the corresponding harmonic to which the circuit is tuned; \(\omega\) is the angular frequency of the fundamental harmonic.
The admittance of the \(m\)-th filter section for the fundamental harmonic, neglecting the active resistance of the inductance winding, is
\[ Y_{1m} = -j\left(\frac{1}{\omega L_m} - \omega C_m\right) = -j \frac{1}{\omega L_m}\left(1 - \omega^2 C_m L_m\right). \]
Substituting \(L_m C_m = \dfrac{1}{m^2\omega^2}\) and \(\omega L_m = X_{Lm}\), we obtain
\[ Y_{1m} = -j \frac{1}{X_{Lm}}\left(1 - \frac{1}{m^2}\right). \]
The impedance of the \(m\)-th filter section for the fundamental harmonic is
\[ Z_{1m} = \frac{1}{Y_{1m}} = jX_{Lm}\frac{m^2}{m^2 - 1}. \]
Taking into account that \(m \ge 3\), the unity in the denominator may be neglected in comparison with \(m^2\); then
\[ Z_{1m} \approx jX_{Lm} = j\omega L_m. \]
The impedance of each filter section for the fundamental harmonic will have an inductive character and will be approximately equal to the inductive reactance of the section. With a purely active load \(R_{\mathrm{n}}\), the total impedance at the inverter output will be
\[ Z_{\mathrm{n}1} = R_{\mathrm{n}} + j \sum_{1}^{n} X_{Lm} = R_{\mathrm{n}} + j\omega \sum_{1}^{n} L_m. \]
With an active-inductive load,
\[ Z_{\mathrm{n}2} = R_{\mathrm{n}} + j\left(X_{\mathrm{n}} + \sum_{1}^{n} X_{Lm}\right) = R_{\mathrm{n}} + j\omega\left(L_{\mathrm{n}} + \sum_{1}^{n} L_m\right), \]
where \(R_{\mathrm{n}}\) and \(L_{\mathrm{n}}\) are the load parameters.
The influence of various loads on inverter operation has been examined fairly fully in the literature [2–4]. From the standpoint of filtering, a change in the load has little effect on the operation of the converter; however, high filter efficiency can be achieved only at a constant output-voltage frequency. For rigid frequency stabilization when external conditions change, or when the load current changes in the case where the driving device and the inverter are supplied from a single power source, measures have been taken to stabilize the supply voltage of the driving device within a range of \(\pm 1\%\).
In the absence of the 3rd, 5th, 7th, and 9th harmonics, the ratio of the rms value of the remaining higher harmonic components to the rms value of the fundamental harmonic is
\[ \frac{\sqrt{U_{11}^{2}+U_{13}^{2}+\ldots}}{\sqrt{U_{1}^{2}}} = \frac{\sqrt{\left(\frac{1}{11}\right)^{2}+\left(\frac{1}{13}\right)^{2}}}{1} \approx 0.11, \]
which is quite acceptable for most consumers.
REFERENCES
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I. V. Nezhdanov. Thyristor Inverters. “Energiya,” Moscow, 1965.
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V. A. Labuntsov, G. A. Rivkin, G. I. Shevchenko. Autonomous Thyristor Inverters. “Energiya,” Moscow, 1967.