Dependence of the steady-state current magnitude in the control winding of the BEMU-RCh on the frequency of control signals
Abstract Generated abstract
The paper analyzes how the steady-state current in the control winding of a regulated-frequency brushless electric-machine amplifier with a thyristor controlled commutator depends on the repetition frequency of control pulses. Using a staged commutation model, the authors derive expressions for the current at successive points in the cycle, obtain a formula for the average steady-state current and its sinusoidal modulation, and relate these quantities to winding, commutating-capacitor, supply, and switching-frequency parameters. Experiments on a prototype BEMU-RF show good agreement with the theoretical frequency characteristics, indicating that at constant dc supply voltage the control current decreases as switching frequency rises and that reducing the ratio of commutated-section inductance to parallel-branch inductance can improve the characteristic.
Full Text
DEPENDENCE OF THE MAGNITUDE OF THE STEADY-STATE CURRENT IN THE CONTROL WINDING OF THE BEMU-RF ON THE FREQUENCY OF CONTROL SIGNALS
A. I. SKOROSPESHKIN, B. E. TROFIMENKO
(Recommended by the seminar of the departments of electrical machines and general electrical engineering)
In [1] we investigated the commutation process in the control winding of a regulated-frequency electromachine amplifier equipped with a thyristor controlled commutator (Fig. 1). The expressions obtained determine the magnitude and the nature of the change in current in the commutated section and in the parallel branch of the winding.
Fig. 1. Diagram of a thyristor UPM with a control winding
In practice it was found that the current established in the control winding, at a constant supply-source voltage, depends strongly on the frequency of the control signals. In connection with this, it is necessary to establish the relation between the steady-state current of the control winding \(I_{\text{st}}\) and the repetition frequency of the switching pulses of the UPM cells \(f_{\text{p}}\).
The current oscillations in the control winding are due to the following causes:
a. The first stage of commutation is characterized by the discharge of the commutating capacitors into the control winding (Fig. 2). Since \(U_c \gg E_y\), the current in the winding increases from \(I_1\) to \(I_2\) (Fig. 3). The current continues to increase until the commutating capacitors have discharged to zero.
Fig. 2. Equivalent circuit of the first stage of commutation
b. In the second stage of commutation, each parallel branch of the control winding is connected to the supply source \(E_y\) through the commutated section \(W_s\) and the commutating capacitor \(C\) connected in parallel with it (Fig. 4), with the initial data for this stage being
\[ i_s = -i_0; \qquad U_c = 0. \]
During this stage of commutation, the current in the control winding decreases to the value \(I_3\), after which it increases according to an exponential law to the value \(I_1\) over the time \(t_e = T_{\mathrm{p}} - t_{\mathrm{k}}\) (Fig. 3), where
\[ T_{\mathrm{p}} \]
is the repetition period of the control pulses,
\[ t_{\mathrm{k}} \]
is the full commutation period, equal to
\[ t_{\mathrm{k}} = L_y \frac{\sqrt{L_s \cdot C}}{2L_s + L_y} + \frac{\pi}{2}\sqrt{L_s \cdot C}. \tag{1} \]
Let us assume that the current in the control winding before the commutation process is equal to \(I_1\); then, according to [1],
\[ I_2 = \frac{E_y + 4U_c}{2L_y \cdot \omega_y}\sin \omega_y \cdot t_1 + I_1 \cos \omega_y t_1; \tag{2} \]
Fig. 3. Character of variation of the control-winding current
Fig. 4. Equivalent circuit of the second commutation stage
\[ t_1 = L_y \frac{\sqrt{L_s \cdot C}}{2L_s + L_y}; \]
\[ I_3 = I_2 \left( 1 + \frac{2L_s}{L_o} \right); \tag{4} \]
\[ I_y = I_3 + \left( \frac{E_y}{r_y} - I_3 \right) \cdot \left( 1 - e^{-\frac{r_y}{L_y} t_3} \right). \tag{5} \]
Designations in (2, 3, 4, 5):
\(E_y\) — emf of the power-supply source;
\(U_c\) — voltage on the commutating capacitor before the commutation process;
\(L_s\) — inductance of section \(W_s\).
\(L_0\) is the inductance of the parallel branch of winding \(W_0\), without the commutated section;
\(L_y\) is the inductance of the control winding;
\(r_y\) is the active resistance of the control winding;
\(C\) is the commutating capacitor;
\[ \omega_y=\sqrt{\frac{2}{L_y C}} . \]
The process in the winding will become steady when the current \(I_y\), according to (5), has increased by the beginning of the next commutation cycle to the value \(I_1\). Equating \(I_y=I_1\) and solving the system of equations (2, 4, 5), we obtain
\[ I_1=\frac{E_y}{r_y}\cdot \left( \frac{ e^{\frac{t_e}{\tau_y}}-1 }{ e^{\frac{t_e}{\tau_y}}-K } \right), \tag{6} \]
where
\[ K=\left(1-\frac{2L_s}{L_0}\right) \left( \sqrt{\frac{2L_s}{L_y}}\cdot \sin\frac{\sqrt{2L_s L_y}}{2L_s+L_y} + \cos\frac{\sqrt{2L_s L_y}}{2L_s+L_y} \right). \tag{7} \]
The average value of the steady-state current in the control winding is equal to
\[ I_{\mathrm{avg}}=\frac{I_3+I_1}{2}=I_1\frac{K+1}{2}. \tag{8} \]
The current surges in the first commutation period up to the value \(I_2\) occur in a relatively short time; therefore we do not take them into account in determining \(I_{\mathrm{avg}}\).
In accordance with Fig. 3, without significant error it may be assumed that a current equal to \(I_{\mathrm{avg}}\) flows through the control winding, modulated by a sinusoid with period
\[ T_p=\frac{1}{f_p} \]
and amplitude
\[ I_{mf}=\frac{I_1}{2}(1-K). \tag{9} \]
Finally, the magnitude of the current and the law of its variation in the control winding, depending on the parameters of the UPS—control winding system and on the frequency of the control signals, are written in the form:
\[ I_y=\frac{E_y}{r_y} \frac{ e^{\frac{t_e}{\tau_y}}-1 }{ e^{\frac{t_e}{\tau_y}}-K } \left[(1+K)+(1-K)\sin 2\pi f_p t\right]. \tag{10} \]
An experiment was carried out on a prototype BEMU-RF having a thyristor UPS of the type shown in Fig. 1, with a control winding having the following parameters: \(L_y=52.5\cdot10^{-3}\ \mathrm{H}\); \(L_0=36\cdot10^{-3}\ \mathrm{H}\); \(L_s=2.6\cdot10^{-3}\ \mathrm{H}\); \(r_y=1\ \Omega\); \(C=10\ \mu\mathrm{F}\).
Figure 5 presents curves of the dependence of the control current on the switching-signal frequency for three supply voltages \(E_{y1}\), \(E_{y2}\), \(E_{y3}\).
The graphs show good agreement between the theoretical and experimental data. The discrepancy can be explained by the assumption, made by us in [1], that there are no losses in the steel of the magnetic core.
Fig. 5. Dependence of the control-winding current
on the repetition frequency of the switching signals.
— experimental curve,
— x — x — x — theoretical curve
Conclusions
-
The thyristor control power converter of the type shown in Fig. 1, for supplying an armature-type control winding, has a characteristic feature: with a constant d.c. source voltage \(E_y\), the control current decreases as the switching frequency increases.
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The control-winding current contains a dc component and an ac component.
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To improve the characteristic \(I_y=f(f_p)\), it is necessary to decrease the ratio
\[ \frac{L_s}{L_0}, \]
or, equivalently, to increase the number of taps from the control winding.
References
- A. I. Skorospeshkin, B. E. Trofimenko. Investigation of the commutation process in the control winding of a brushless electric-machine amplifier of adjustable frequency. Izvestiya TPI, vol. 172, 1967.