Asynchronous Valve Cascade with Pulse Control
Abstract Generated abstract
This paper examines pulse speed control for wound-rotor asynchronous motors in valve cascade systems, motivated by the possibility of using thyristor switching to reduce converter power and improve regulation compared with rheostatic methods. It argues for a commutation law with constant thyristor off-time and variable frequency, especially for fan-type loads, and derives steady-state expressions for rectified rotor-current ripple, average current, speed characteristics, and torque under stated simplifying assumptions. The analysis indicates how permissible current pulsations determine the required circuit time constant and smoothing inductance, and shows that motor speed can be regulated through the relative thyristor conduction duration. Experiments on a 4 kW induction motor produced speed and mechanical characteristics agreeing with calculated values within about 10 to 15 percent, which the authors regard as acceptable for engineering practice.
Full Text
ASYNCHRONOUS VALVE CASCADE WITH PULSE CONTROL
A. I. ZAITSEV, Yu. P. KOSTYUKOV
(Recommended by the scientific seminar of the Electromechanical Faculty)
Speed regulation of asynchronous motors with a wound rotor is carried out by introducing additional resistance into the rotor circuit and by cascade schemes. The limited use of rheostatic control is determined by energy losses in the rotor circuit and by the stepwise nature of regulation; however, this method is used in drives with fan-type loads.
Speed regulation of asynchronous motors by cascade schemes is at present becoming increasingly widespread. A promising system is one in which the rotor slip energy, through an uncontrolled rectifier and a valve or machine converter, is returned to the network.
Recent achievements of domestic industry in the field of thyristors open up the possibility of applying a pulse method of speed regulation for asynchronous motors.
The principle of constructing systems with pulse regulation is as follows: into the rotor direct-current circuit (Fig. 1), in parallel with the converter device (P) or with an additional resistance, an artificial turn-off circuit IV for the power thyristor is inserted, consisting of capacitive commutation elements. Such a circuit makes it possible, by changing the relative duration of conduction of the power thyristor, to regulate the rotational speed of the motor. Rectifier V is assembled according to a three-phase bridge circuit; smoothing reactor R reduces current pulsations. To avoid a short circuit of the converter, a protective diode D is included in its circuit.
Fig. 1.
The use of pulse control makes it possible to reduce the rated power of converter devices and is especially expedient in drives with fan-type loads, for which the converter power over any control range will be insignificant. It should be noted that the converter can be used to improve the overall power factor and can be common to several cascades.
For circuits with pulse-controlled resistance, the principal drawback of the rheostatic method—the stepwise nature of control—is eliminated.
CHOICE OF THE COMMUTATION LAW. For pulse control of electric machines, systems with pulse-width modulation and systems with variable commutation frequency have found the widest application [1].
Control in such circuits is carried out by changing the relative on-duration, which is equal to:
\[ \bar{t}=\frac{T-t_u}{T}, \tag{1} \]
where \(T\) is the pulse repetition period,
\(t_u\) is the pulse duration corresponding to the off-state time of the power thyristor.
The repetition period is limited by the frequency properties and by the magnitude of the limiting power dissipated by the thyristor.
Other conditions being equal, the switching losses depend only on frequency and current [2].
For systems with pulse-width modulation, a characteristic feature is the constancy of the commutation frequency of the power thyristor. The case corresponding to maximum load and on-duration is the most severe thermal regime for thyristors with constant commutation frequency.
The use of duration modulators with variable commutation frequency substantially eases the thermal regime of the thyristors and increases the efficiency of the pulse circuit. For the commutation law under consideration, \(t_u=\mathrm{const}\) is characteristic. The system parameter in this case is the quantity
\[ a=\frac{t_u}{T_2}, \tag{2} \]
where \(T_2\) is the time constant during the second commutation interval.
The quantity \(a=\frac{t_u}{T_2}\) must be chosen depending on the permissible value of losses and pulsations in the DC rotor circuit. In systems with variable commutation frequency, switching losses decrease in proportion to the increase in the relative on-duration. Under this commutation law, the most severe operating mode of the thyristors is the mode corresponding to the maximum commutation frequency (that is, the minimum rotational speed of the motor) and the greatest load. With a wide range of speed control of asynchronous motors with a phase-wound rotor, the current and voltage in the rotor circuit reach maximum values at different slips; usually, at small slips the voltage is low and the current is large, and conversely; the latter is especially characteristic of drives with fan-type loads. Consequently, under pulse-
... in speed control of asynchronous motors with a phase-wound rotor, the switching losses are not always maximal at the lowest rotational speed. In this case, in order to obtain small values of \(\gamma\), it is quite permissible to overstate the operating frequency of the power thyristor in comparison with its rated value, since, in order to reduce current pulsations, it is desirable to choose \(t_u\) as small as possible. At the same time it should be stipulated that the overstatement of the operating frequency must be chosen for each specific case depending on the nature of the load. On the basis of the considerations indicated above, in pulse speed control of asynchronous motors with a phase-wound rotor it is advisable to use a commutation law with a constant time of the disconnected state of the power thyristor and a variable frequency, since it has substantial advantages in comparison with pulse-width modulation, especially in drives with fan-type loads.
Determination of Current Pulsations
Below is a derivation of the basic relationships characterizing the operation of an asynchronous motor with a phase-wound rotor under pulse speed control in the steady-state mode.
Obviously, the basic assumptions specific to valve systems [3, 4, 6] will also be valid in our case.
It is assumed here that the average value of the internal emf of the asynchronous motor is proportional only to the amplitude of the rotor line voltage at standstill
\[ \left| E = \frac{3}{\pi} E_p \right| \]
and to the slip. The decrease in the internal emf due to the overlap of the valves is approximately accounted for by the voltage drop in an equivalent ohmic resistance proportional to the leakage reactance of the phase of the asynchronous motor
\[ \left| R_e s = \frac{3}{\pi} x_e \right|. \]
We shall assume that the forward voltage drop in the semiconductor valves does not depend on the magnitude of the current, and that the forward voltage drops across the protective diode and the power thyristor are equal and referred to the common dc circuit \((\Delta U = \mathrm{const})\). If the active resistance of the stator is neglected, then the mutual-inductance coefficients between the stator and rotor windings may be considered independent of the relative position of these windings. In this case, in the equivalent circuit we take into account the constant value of the leakage inductance of two phases of the asynchronous motor.
In the rectified-current circuit, in any time interval we shall also take into account the active resistance of two phases of the rotor winding \((R)\), the reactor inductance, and the leakage inductance of two phases of the asynchronous motor \((L)\).
Fig. 2.
In the converter circuit we take into account only the counter e.m.f. of unchanged magnitude \((E_u)\) and the equivalent ohmic resistance \((R_u)\); this case corresponds to the majority of the basic pulse-control circuits described in the literature [7].
We introduce the following restrictions when considering steady-state processes: a) current pulsations with slip frequency are absent; b) the rectified current is continuous; c) the valve overlap angle does not exceed \(60^\circ\); d) the artificial turn-off circuit of the power thyristor is equivalent to an ideal switch.
Under these conditions the equivalent circuit is shown in Fig. 2. The initial equations characterizing the operation of this circuit at an arbitrary slip \(s\) of the asynchronous motor have the form:
1) the time interval during which the power thyristor is on,
\[ 0 \leq t \leq \gamma T \]
\[ i + T_1 \frac{di}{dt} = I', \tag{3} \]
2) the time interval during which the power thyristor is off,
\[ \gamma T \leq t \leq T \]
\[ i + T_2 \frac{di}{dt} = I'', \tag{4} \]
where
\[ I'=\frac{Es-\Delta U}{R_e s+R} \quad\text{— limiting value of the current at the given slip and } \gamma=1; \tag{5} \]
\[ T_1=\frac{L}{R_e s+R} \quad\text{— time constant of the circuit during the first commutation interval;} \tag{6} \]
\[ I''=\frac{Es-\Delta U-E_u}{R_e s+R+R_u} \quad\text{— limiting value of the current at the given slip and } \gamma=0; \tag{7} \]
\[ T_2=\frac{L}{R_e s+R+R_u} \quad\text{— time constant of the circuit during the second commutation interval.} \tag{8} \]
It is necessary to remember that the quantity \(I''\) is negative when \(Es-\Delta U<E_u\).
Introducing a new variable—the relative time
\[ \bar t=\frac{t}{T}, \tag{9} \]
where
\[ T=\frac{t_u}{1-\gamma} \quad\text{— commutation period,} \]
and denoting
\[ \beta'=\frac{T}{T_1}, \qquad \beta''=\frac{T}{T_2}, \tag{10} \]
we represent the circuit equations in the form
\[ \frac{di}{\beta' \, d\bar t}+i=I', \qquad 0\leq \bar t\leq \gamma, \tag{11} \]
\[ \frac{di}{\beta'' \, d\bar t}+i=I'', \qquad \gamma\leq \bar t\leq 1. \tag{12} \]
Solving these equations by the usual methods of pulse engineering [5], we finally obtain expressions for the ripple amplitude and the average current in the steady-state regime.
The current ripple amplitude in the steady-state regime is
\[ \Delta I = \frac{(I' - I'')\left(1 - e^{-\alpha \beta \gamma/(1-\gamma)}\right)\left(1 - e^{-\alpha}\right)} {1 - e^{-\alpha}\cdot e^{-\alpha \beta \gamma/(1-\gamma)}} . \tag{13} \]
where
\[ \beta = \frac{\beta'}{\beta''} = \frac{T_2}{T_1}, \quad \beta \ll 1, \tag{14} \]
\[ \alpha = \frac{t_{\mathrm{u}}}{T_2}. \tag{15} \]
Fig. 3.
The average current in the steady-state regime is
\[ I_{\mathrm{av}} = I'\gamma + I''(1-\gamma) - \Delta I \frac{(1-\gamma)(1-\beta)}{\alpha \beta}. \tag{16} \]
Obviously, the current ripples are maximal at the greatest \(\gamma\) and depend on \(\alpha, \beta\). Expanding the expression for \(\Delta I\) in a Taylor series and retaining only the first two terms, which is entirely permissible for small \(\alpha\), we obtain for the average current
\[ I_{\mathrm{av}} = \frac{ I'\gamma + \dfrac{I''}{\beta}(1-\gamma) }{ \gamma + \dfrac{1}{\beta}(1-\gamma) }. \tag{17} \]
The expression for the ripple amplitude may be rewritten as follows:
\[ \frac{\Delta I}{I_{\mathrm{av}}} = \frac{\left[(Es-\Delta U)(1-\beta)+\beta E_{\mathrm{u}}\right]\gamma \alpha} {Es-\Delta U-E_{\mathrm{u}}(1-\gamma)} . \tag{18} \]
For a pulse-controlled resistance, \(E_u=0\); then
\[ \frac{\Delta I}{I_{\mathrm{cp}}}=(1-\beta)\gamma \alpha . \tag{19} \]
If the permissible current pulsations are specified, then, using the expressions given above, we find the required value of the coefficient \(\alpha\). From the known \(\alpha\) and \(t_u\), one can determine the time constant during the second commutation interval and, if necessary, select the required inductance of the smoothing reactor. For \(\alpha<0.1\), the energy indices of the pulse circuit practically do not differ from those of circuits with continuous control.
SPEED AND MECHANICAL CHARACTERISTICS
Expression (17) for the average value of the current can be reduced to the form
\[ I_{\mathrm{cp}}= \frac{Es-\Delta U-E_u(1-\gamma)} {R_{\mathrm{e}}s+R+R_u(1-\gamma)} . \tag{20} \]
Whence we obtain an approximate equation of the speed characteristic \(n=f(I_{\mathrm{cp}})\) for an asynchronous motor with pulse control,
\[ s= \frac{(E_u+I_{\mathrm{cp}}R_u)(1-\gamma)+\Delta U+I_{\mathrm{cp}}R} {E-I_{\mathrm{cp}}R_{\mathrm{e}}}, \tag{21} \]
or
\[ n=n_0\left[ 1- \frac{(E_u+I_{\mathrm{cp}}R_u)(1-\gamma)+\Delta U+I_{\mathrm{cp}}R} {E-I_{\mathrm{cp}}R_{\mathrm{e}}} \right], \tag{22} \]
where
\(n_0\) is the ideal no-load speed;
\(n\) is the instantaneous value of the rotor speed. It follows from this that \(n\) is proportional to \(\gamma\), i.e., by changing \(\gamma\)—the relative on-duration—we correspondingly change the rotational speed of the asynchronous motor with a phase-wound rotor. Operation at high speed is achieved by increasing the relative on-duration. As \(\gamma\to1\), the speed characteristic approaches the natural one. The lower limit of speed regulation as \(\gamma\to0\) is determined by the internal e.m.f. of the converter; the stiffness of the speed characteristics at small \(\gamma\) deteriorates. For \(R_u=0\), the characteristics are parallel to one another. For a pulse-controlled resistance, \(E_u=0\), and the characteristics have the same form as with rheostatic control. The range of speed control for given \(E_u\), \(R_u\) depends on the change in \(\gamma\). Usually, in order to obtain the upper and lower limits of regulation, it is sufficient to have \(\gamma\) equal respectively to 0.95 and 0.05, since in this case the characteristics practically coincide with the limiting characteristics at \(\gamma=1\) and \(\gamma=0\).
For stabilization of the rotational speed, feedbacks may be applied.
The dependence of the torque of an asynchronous motor on the average value of the current of the rectified circuit is determined by the following expression [4]:
\[ M=\frac{1}{\omega_0}EI_{\mathrm{cp}} \left( 1-\frac{I_{\mathrm{cp}}R_{\mathrm{e}}}{E} \right), \tag{23} \]
where \(\omega_0\) is the synchronous angular velocity of the rotor.
Using formulas (22) and (23), one can construct the speed and mechanical characteristics of an induction motor for an unchanged value of $\gamma$. With pulse control of speed, an induction motor can operate in the same modes as an ordinary cascade.
To verify the initial assumptions and the final formulas presented in the article, the Department of Electric Drive of TPI carried out an experimental study of the pulse circuit on a 4.0 kW induction motor.
Figure 4 shows a family of experimental characteristics $s=f\left(\dfrac{M}{M_{\mathrm{n}}}\right)$ for an induction-valve cascade. At small loads on the motor shaft, a mode of discontinuous currents is possible.
The discrepancy between the experimental and calculated data does not exceed $(10 \div 15\%)$, that is, it lies within the limits permissible for engineering practice.
Fig. 4.
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