Effect of Capacitances on the Main Characteristics of a Brushless Electric Machine Amplifier
Abstract Generated abstract
This paper examines how capacitors connected in parallel with the output load affect the performance of a brushless electric machine amplifier. Using characteristic curves, experimental external characteristics, feedback compensation schemes, and time constant measurements, it analyzes changes in control current, gain, voltage stiffness, controllability, and response speed. The study finds that parallel capacitance can reduce the required control current, increase gain, and improve response speed when combined with suitable feedback, but it also increases nonlinearity and can cause loss of machine control at certain capacitance and feedback values.
Full Text
INFLUENCE OF CAPACITANCES ON THE MAIN CHARACTERISTICS OF A BRUSHLESS EMA
A. I. Skorospeshkin, E. N. Podborskii, E. F. Obergan
(Recommended by the scientific seminar of the departments of electrical machines and general electrical engineering.)
When capacitances are connected in parallel with the output winding of the stator, the amplifier is loaded with a capacitive load; in this case the armature reaction is magnetizing, and the voltage at the output will be greater than the emf without capacitances.
In Fig. 1 the characteristic of the capacitances is plotted on the scale of the control m.m.f.
Fig. 1. No-load characteristic of the BEMA and volt-ampere characteristic of the capacitances on the scale of the control m.m.f.
control. The dashed line shows the volt-ampere characteristic of the capacitors under self-excitation up to point \(A\).
From these curves it is seen that the control m.m.f. when capacitors are connected at the output is reduced by as many times as \(BC\) is smaller than \(OC\). In practice, the control current can be reduced by a factor of 2–3 while maintaining control of the machine.
The gain factor at the same output power increases correspondingly by a factor of 4–9.
The capacitances can be selected according to the following formula
\[ C=\frac{1}{1.25\omega Xps}, \tag{1} \]
where \(\omega\) is the angular frequency;
\(1.25\) is a coefficient allowing for the necessary margin to prevent self-excitation.
External Characteristics and Compensation
With capacitors connected in parallel, the external characteristics of a brushless electric-machine amplifier (BEMA) without feedback have a very large slope. Therefore this mode is of no interest.
Positive current feedback makes it possible to increase the stiffness of the external characteristics. Experimentally obtained absolutely stiff external characteristics with capacitors connected in parallel at the output were recorded.
In addition, in investigating a BEMA with capacitors connected in parallel at the output, linear load-current feedback was used, making it possible to increase substantially the stiffness of the external characteristics. The linear feedback was implemented by means of current transformers whose primary windings are connected in series with the load. The ends of their secondary windings are star-connected, and the beginnings are connected to a three-phase rectifier assembled according to the Larionov circuit. At the rectifier output a feedback winding is connected, hereinafter called the compensating winding. It is shunted by a variable resistor. The compensating winding is placed in the stator slots according to the same scheme as the control winding.
A direct current flows through the compensating winding; its magnitude is proportional to the load current, since the current transformers have an unsaturated magnetic system. An additional e.m.f. in the output winding increases directly in proportion to the load current.
For this case, Fig. 2 gives the external characteristics obtained experimentally at various feedback coefficients. From these curves it is seen that the external characteristics are nonlinear. Moreover, the nonlinearity of the external characteristics is more pronounced here than in an amplifier with linear feedback without capacitors.
In a brushless EMA with linear feedback and without capacitors, it is possible to compensate the demagnetizing action of the armature reaction only at one value of the load current \(I_{s1}\). At a current value less than \(I_{s1}\), overcompensation occurs, while at a current greater than \(I_{s1}\), undercompensation is observed; that is, the external characteristic is nonlinear.
Capacitors connected in parallel with the load intensify the nonlinearity of the external characteristics under linear feedback in the following manner.
With overcompensation, the voltage under load is greater than at no load; therefore an additional current flows in the capacitors, which additionally magnetizes the machine. With undercompensation, the current in the capacitors decreases as the load increases, which leads to an additional reduction in voltage.
Fig. 2. External characteristics of the amplifier with linear feedback and capacitors connected in parallel with the load.
It should be noted that, when a BEMU operates with capacitors at the output and with linear feedback, cases of loss of control of the machine are possible. The conditions for the occurrence of this phenomenon depend on the feedback coefficient and on the magnitude of the capacitance at the output. As the feedback coefficient increases, the probability of loss of control increases.
The external characteristics shown in Fig. 2 correspond to the region of stable operation of the amplifier. The external characteristic that passes above the others corresponds to the boundary of the control zone, i.e., to the critical feedback coefficient. With a further increase in the feedback coefficient, loss of control of the amplifier is observed.
Gain coefficient
The dependences of the gain coefficient on the load current, for capacitors connected in parallel and obtained for absolutely rigid external characteristics, are linear in nature. In addition, dependences of the gain coefficient on the load current have been obtained for a BEMU
with linear feedback, with different feedback coefficients (shown in Fig. 3). From these curves it is seen that the gain coefficient increases with increasing load current only up to its maximum value, and then begins to decrease because of the sharp drop in the output voltage. In testing a brushless EMA with capacitors connected in parallel with the load and with linear current feedback, the largest gain coefficient obtained was \(K_{y\max} = 12500\). A higher gain coefficient could not be obtained: the amplifier lost controllability.
Fig. 3. Dependence of the gain coefficient on the load current of a brushless EMA with linear feedback and capacitors connected in parallel with the load.
Speed of response
Speed of response characterizes the responsiveness of the amplifier to a change in the input signal. For automatic-control systems, the conversion time of a low-power input signal is of great importance. This time is determined by the time constants of the amplification stages.
In a BEMA there are two amplification stages. The input amplification stage is the control winding—a two-pole rotor winding; the output stage is the four-pole rotor winding—the output winding of the BEMA.
The time constant of the control circuit is equal to
\[ T = \frac{l_y}{r_y}, \tag{2} \]
where \(L_y\) is the inductance of the control winding;
\(r_y\) is the active resistance of the control winding.
The time constant of the four-pole winding is equal to
\[ T_{p2} = \frac{l_{p2}}{r_{p2}}, \tag{3} \]
where \(L_{p2}\) is the inductance of the four-pole rotor winding;
\(r_{p2}\) is the active resistance of the four-pole winding.
The time constant of the machine can, with sufficient accuracy, be taken as equal to the sum of the time constants of the stages.
\[ T = T_y + T_{p2}. \tag{4} \]
It follows from the formulas that the speed of response improves as the active resistance of the circuits is increased.
The time constants of the circuits can be calculated from the data obtained by measuring the total resistance to alternating current and the active resistance of the circuit under consideration, or they can be determined directly by the oscillographic method.
The time constant of the control circuit is determined from the oscillogram of the rise of the control current when the control winding is connected to a constant voltage.
Table 1
| \(T_y\) | 0.01 |
| \(T_{p2}\) | 0.015 |
| \(T\) | 0.125 |
| \(T_y + T_{p2}\) | 0.025 |
The time constant of the four-pole winding is determined by the same method; in this case the rise curve of the current of the four-pole winding is oscillographed when it is connected to a constant voltage.
The overall speed of response of the two stages is determined by oscillographing the rise of the emf of the output winding of the brushless EMA.
The time constants determined from oscillograms for the brushless EMA are presented in Table 1.
As can be seen from the table, the sum of the time constants \(T_y\) and \(T_{p2}\) is not equal to \(T\). This is explained by the fact that, when determining the speed of response by stages, not all feedbacks acting in the amplifier and affecting its speed of response are taken into account.
A comparison of the time constants of the brushless amplifier and of the commutator EMA-12A showed that they have approximately the same speed of response.
When capacitances are connected in parallel with the load, the speed of response of the amplifier is substantially improved. Experimentally it proved possible to reduce by a factor of two the time constant of the amplifier when capacitances were connected in parallel with the load.
Conclusions
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Connecting capacitances in parallel with the load, with proper feedback, substantially improves the main characteristics of the amplifier—the gain coefficient and the speed of response.
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When the brushless EMA operates in the external-characteristic mode with feedback, cases are possible in which control of the machine is lost at certain values of the feedback coefficient and of the capacitance values.