Control of Single Phase Induction Motor Using Forced-Commutated

Electric Machines and Power Systems, 27:1201–1214, 1999 Copyright ° c 1999 Taylor & Francis, Inc. 0731-356X / 99 $12.00 + .00

Control of Single Phase Induction M otor Using Forced-Commutated Electronic Switches and Free-W heeling Paths M. A. ABDEL-HALIM, B.Sc., M.Sc., Ph.D. Electrical Engineering Dept. King Saud University P. O. Box 800 Riyadh 11421, Saudi Arabia Single phase induction motors show better performance and have less cost if they are controlled using electronic switches instead of mechanical switches. This paper suggests a semiconductor-based method to start the motor and to control the speed and the direction of rotation. This is achieved by feeding the two stator windings of a split-single-phase motor via two forced-commutated solid-state devices. Meanwhile, each winding is shunted by a free-wheeling path that is controlled as well by a forced-commutated solid-state device. Therefore high starting torques and low starting currents are realized. Speed control is easily achieved at higher motor e ciency, compared with the case of controlling the motor using forced-commutated electronic switches without free-wheeling paths. This paper computes detailed performance characteristics of the motor employing the suggested method. For this purpose, the motor is represented in the dqo reference frame. Then, the performance is described by a developed state space mathematical model taking care of the discontinuities introduced by the electronic switches.

1

List of Symbols H : machine and load inertia constant, seconds i & v : p.u. current and p.u. voltage, respectively p: normalized time operator R & L : p.u. resistance and p.u. inductance, respectively T : torque, p.u. ®: transistor ring angle !o

1.1

& !r : base speed and p.u. rotor speed, respectively

Subscripts 1 & 2: stator- and rotor-side, respectively a & m : auxiliary- and main-winding, respectively d & q : direct- and quadrature-axis, respectively e & l : electrical and load, respectively Manuscript received in nal form January 25, 1999. Address correspondence to M. A. Abdel-halim.

1201

1202

2

M. A. Abdel-halim

Introduction

Single-phase induction motors are started conventionally by [1,2] either phase splitting of the stator winding, using main and auxiliary windings together with capacitors connected to the auxiliary winding, or using commutator winding on the rotor to start it as a repulsion motor. The speed is conventionally controlled using either winding tappings, variac, autotransformer, or series impedance [1–3]. The principle of these methods is to reduce the speed by reducing the motor air gap ux. The direction of rotation of the motor is reversed conventionally by interchanging the terminals of the stator windings [1]. Conventional methods for starting and speed control of single-phase induction motors often need quite expensive external electrical equipment. Moreover, they require mechanical switches that are the most troublesome parts. These switches suŒer from mechanical wear that aŒects the motor performance. Nonconventional methods based on using a triac in series with the stator main winding have been suggested for just controlling the speed of the motor [4–6]. The author has recently suggested [7,8] solid-state–based two methods to start, control the speed, and reverse the direction of rotation of the single-phase induction motors. One of these methods uses a naturally-commutated electronic switch (triac) in each of the main and auxiliary winding, whereas in the other, forced-commutated electronic switches (power transistors) are used. The second method gives higher starting torque compared with the resulting starting torque when naturally-commutated switches are used. On the other hand, speed control performance characteristics regarding the motor e ciency and supply current harmonic contents are better in case of using naturally commutated switches. Concerning the supply displacement factor, natural commutation always gives large lagging input current displacement angles, whereas forced commutation improves the displacement angle to the extent that it may goes in the lead direction. This paper presents and analyzes a developed method for enhanced control of the motor based on using a solid-state AC voltage controller in each winding of a split-phase motor having two identical stator windings. The converter consists mainly of two power transistors integrated in two diode bridges—one in series with the supply, and the other is shunted with the winding to provide a free-wheeling path. The use of such four electronic switches and their control circuits increases the cost of the motor, but the cost of the solid-state devices are rapidly going down, and it is expected to compare favorably with other conventional control equipment in the near future. Power transistors are chosen to employ forced commutation. This enables getting large phase shift between the stator winding currents, whereas the use of free-wheeling paths improves the utilization of the stored energy in the motor inductances. Thus, high starting torques at low supply current, good power factor, low motor harmonic contents, and high motor e ciency are anticipated. Also, the surge voltages that appear across the solid-state devices when the forced commutation is employed are avoided in the present method due to the provided free-wheeling paths. To determine the motor performance characteristics, a mathematical model has been developed. This model is based on using the dqo Kron’s equivalent circuit for induction motor [9]. The eŒect of the incorporated semiconductor devices on the voltages applied on the stator windings has been considered. A computer program has been developed to simulate the system. With the aid of the program, the

Control of Single Phase Induction Motor

1203

Figure 1. Motor schematic diagram. motor steady-state and transient performance characteristics have been computed. The motor performance with the new method has been evaluated through some computed performance factors.

3

Fundamentals of the Proposed M ethod

Figure 1 shows the circuit of a split-phase induction motor with its windings supplied from a single-phase source through the proposed converters. Each transistor has its own control circuit, but the two transistors of any of the two windings are alternatively switched on and oŒ. The impressed voltage upon the winding is equal to the supply voltage when the line transistor in series with it is on. When the free-wheeling path is activated, the impressed voltage is set to zero. The motor draws its current from the supply once the line transistor is turned on. This supply current is forced to reduce to zero when the line transistor is turned oŒ. Therein, the free-wheeling transistor, which is turned on, carries the motor current. To start the motor, the two line transistors are turned on and oŒat two diŒerent angles. The stator currents will have two time-shifted fundamental components. These components produce a component of rotating ux that results in a starting torque. The direction of rotation of the motor is reversed easily by interchanging the ring and extinction orders of the two line transistors. At running condition, only the main winding is excited, and the speed is controlled by controlling the voltage applied on it. This is easily done through the variation of the line transistor ring and extinction angles. Plugging braking is achieved by re-exciting the other winding and interchanging the order of the turning on and the order of the turning oŒangles of the line transistors.

4

Circuit and M athematical M odel

The induction motor is represented in the dqo reference frame by a four-coil generalized machine [9]. As the motor is fed and controlled from the stator side, the

1204

M. A. Abdel-halim

reference frame has been chosen to be attached to the stator member. The mathematical model will be derived based on the following assumptions: iii iii iv -

the saturation eŒects are neglected; the air gap ux space harmonics are neglected; the iron losses are neglected; and the electronic switches are assumed to be ideal.

Utilizing Kron’s model [9] for an induction motor, the following matrix equation using p.u. quantities is applied: 2 3 2 32 3 0 0 u 1d R 1d + X 11d p X 12d p i1d 6u 7 6 76i 7 X 12d p R 2d + X 22d p X 22q!r X 12q!r 6 2d 7 6 7 6 2d 7 (1) 6 7= 6 76 7 4 u 2q 5 4 5 4 i2q 5 X 12d!r X 22d!r R 2q + X 22q p X 12q p u 1q

0

0

R 1q + X 11q p

X 12q p

i1q

u 1d and u1q are set equal to the supply voltage when the associated line transistor

is activated, and is set equal to zero when the associated free-wheeling path is activated. Because the rotor is a squirrel cage type, the two voltages of the rotor in the direct- and quadrature-axis are zeros. Rewriting equation (1) in a split form yields [u ] = [R ][i] + [X ]p[i] + !r [G ][i], (2) where [i] = [i1d , i2d , i2q , i1q ]T , [u] = [u1d , 0, 0, u 1q ]T , [R ] is the resistance matrix, [X ] is the reactance matrix, and [G ] is the rotational voltage coe cient matrix. Rearranging the equation terms, the following state space form is obtained: (3) p[i] = [A ][i] + [B ][u], where [A ] =

[X ]

[B ] = [X ]

1

1

([R ] + !r [G ]) ,

.

The equation for the rotor speed is p!r = 1= (2H ! o )[ T e

Tl ].

(4)

The electrical torque, in p.u., is given by [9]: T e = 2[X 12d i1d i2q + X 22d i2d i2q

X 12q i1q i2d

X 22 i2q i2d ] .

(5)

The supply current is given by i s = F d id + F q iq ,

(6)

where F d and F q are switching functions and take either “ 1” or “ 0” value. The value is “ 1” if the associated line transistor is on; otherwise it is “ 0.”


5

1205

Digital Simulation

A computer program has been developed to determine the performance of the motor. The state-space matrix equation is solved by numerical integration using the fourth-order Runge-Kutta technique [10] with the appropriate initial conditions. During any transient condition, the state space variables are the motor four currents in addition to the rotor speed. These variables are governed by equation (1) to (4). At steady-state conditions, the speed pulsation is neglected, and thus the speed is considered constant. Consequently, the motor currents are the only state variables, and they are governed by equation (1). The steady-state currents are reached after few cycles to allow the transient currents to die out. Once the current wave-forms are obtained, conventional numerical techniques [10] are applied to compute their eŒective (rms) value and fundamental component. Then, the harmonic and power factors in addition to the motor e ciency are calculated.

6

Results and Discussions

A single-phase induction motor having similar main and auxiliary windings has been chosen to apply the proposed method; the specications of the motor are given in [8]. The load is assumed to reect a torque approximately proportional to the speed. The motor full-load torque is about 0.4 p.u. Therefore, the constant of proportionality is adjusted to a value up to 0.4 p.u./ p.u. The motor and load data are fed into the program to compute the transient and steady-state performance. The eŒect of the transistor on angles for a constant conduction angle of 90 degrees upon the motor starting torque is displayed in Figure 2. The gure shows that when the turn-on angle of the main transistor is smaller than that of the auxiliary one, the average developed torque is positive. As the main-winding transistor turn-on angle exceeds that of the auxiliary one, the developed torque reverses its direction. It is clear from the computed results that the starting torque produced by the motor employing the suggested method is higher than the full load torque. Therefore, this method is suitable for starting a motor with loads that

Figure 2. Starting torque of the motor.

1206

M. A. Abdel-halim

Figure 3. The supply starting current of the motor. reect high resistive torque at starting. The starting current variation with the transistor triggering angles is shown in Figure 3. For the sake of comparison, the starting torque and current for both the naturally commutated case and the forced commutation technique without free-wheeling paths are shown in Figures 4 through 7. Starting torques obtained by the proposed method are several times higher than those obtained with natural-commutated electronic switches, and even higher than the method of forced-commutation without free-wheeling paths. This is due to the fact that the phase shift between the two stator-winding fundamental currents attained by the forced commutation technique is larger, compared with that attained by natural commutation. Although higher starting torques are obtained, the start-

Figure 4. Starting torque with naturally commutated switches.


1207

Figure 5. The supply starting current with naturally commutated switches. ing current is, in general, less. For example, the maximum starting torque in case of the proposed method is accompanied by about 2.8 p.u. supply current, whereas for forced commutation it is accompanied by 3.0 p.u. supply current, and for natural commutation it is accompanied by about 4.0 p.u. supply current. The supply current is less in case of forced commutation, as one of the phase currents is forced to lead the voltage while the other lags it. Consequently, the resultant current will have a small fundamental current component nearly in-phase with the voltage. In case of natural commutation, the two currents lag the voltage, and their resultant is a large value having a displacement angle that is enlarged by the phase control.

Figure 6. Starting torque with forced-commutated switches.

1208

M. A. Abdel-halim

Figure 7. The supply starting current with forced-commutated switches.

Figure 8 shows the speed transient of the motor when started at main and auxiliary on angles of 0 and 90 degrees and extinction angles of 90 and 180 degrees, respectively, then plugging braking is employed by interchanging the order of both the on and oŒangles. Speed control of the motor is achieved using three control strategies. The rst is the extinction angle control, where the turn-oŒangle is varied, whereas the turn-on angle is kept constant at zero degree. The second is the symmetrical control, where

Figure 8. Starting followed by plugging braking.


1209

both the turn-on and turn-oŒangles are varied such that ¯ = ¼ ®. The third strategy is the ring angle control where the turn-on angle is varied whereas the turn-oŒangle is kept constant at 180 degrees. The supply current, motor current, harmonic factors, displacement angle, power factor, and motor e ciency curves are shown for the three strategies in Figures 9 through 15. Comparison of the results reveals the following points: i - The ring angle control strategy gives the highest supply current, but the least motor current. It result in the least harmonic contents and an e ciency better than that obtained by the symmetrical control strategy. ii - The extinction angle control helps in decreasing the supply current displacement angle to the extent that it gives leading displacement angles at low speeds. iii - Both the extinction angle and symmetrical angle control give higher power factor than the ring angle control. The motor harmonic factor and e ciency employing the ring angle control strategy when compared with those obtained using variac voltage control, naturally commutated switches, and forced commutated-switches without free-wheeling paths are shown in Figures 16 and 17. Comparing the results it could be concluded that i - The motor e ciency is bad in case of using forced commutation without free-wheeling paths, as the energy stored in the winding is dissipated in a high shunt resistance. ii - Use of free-wheeling paths improves the harmonic factor, but it will not be as much good as the case of naturally-commutated switches.

Figure 9. Supply current variation with the speed.

1210

M. A. Abdel-halim

Figure 10. Motor current variation with the speed.

Figure 11. Supply harmonic factor variation with the speed.


Figure 12. Motor harmonic factor variation with the speed.

Figure 13. Supply displacement angle variation with the speed.

1211

1212

M. A. Abdel-halim

Figure 14. Power factor variation with the speed.

Figure 15. Motor e ciency.


Figure 16. Comparison of the motor harmonic factor.

Figure 17. Comparison of the motor e ciency.

1213

1214

7

M. A. Abdel-halim

Conclusion

Single-phase induction motors can be started, speed-controlled, and reversed using forced-commutated electronic switches in conjunction with free-wheeling paths. This method gives high starting torques at relatively low starting currents. The existence of the free-wheeling paths enables the utilization of the stored energy, thus the e ciency of the motor is improved. The supply displacement angle is smaller than that associated with natural commutation. The power factor, therefore, is better. The free-wheeling paths eliminate the voltage spikes associated with forced commutation. The motor speed could be controlled using diŒerent strategies. Three strategies have been applied; namely, extinction angle control, symmetrical angle control, and ring angle control. The motor and supply performance is greatly aŒected by the chosen control strategy. The motor performance is better with ring angle control, whereas the supply conditions are better with extinction angle control.

References [1] Veinott, C. G., and Martin, J. E., 1986, “ Fractional and Subfractional Horsepower Electrical Motors,” Mcgraw-Hill, Inc. [2] Say, M., 1984, “ Alternating Current Machines,” Pitman, England. [3] Veinott, C. G., 1977, “ Performance Calculation on L - and T -Connected TappedW inding Capacitor Motors,” IEEE Trans. on Power Apparatus and Systems, Vol. PAS96, No. 4, pp. 1137–1144. [4] Cattermole, D. E., Davis, R. M., and Wallace, A. K., 1975, “ The Design Optimization of a Split-Phase Fan Motor with Triac Voltage (Speed) Control,” IEEE Trans., Vol. PAS-94, No. 3, pp. 778–785. [5] Cattermole, D. E., and Davis, R. M., “ A Triac Voltage (Speed) Control for Improved Performance of Split-Phase Fan Motors,” IEEE Trans., Vol. PAS-94, No. 3, pp. 786– 791. [6] Fatih, N., 1988, “ Performance Characteristics of a Triac-Controlled Single-Phase Induction Motor Having Space Harmonics in its Magnetic Field,” Electric Power Systems Research, Vol. 14, pp. 97–102. [7] Abdel-halim, M. A., 1996, “ Solid State Control of Single Phase Induction Motor,” Electrical Machines and Power System Journal, Vol. 24, No. 6, pp. 623–638. [8] Abdel-halim, M. A., 1997, “ Control of Single Phase Induction Motor Using Forcedcommutated Electronic Switches,” Electrical Machines and Power System Journal, Vol. 25, No. 6, pp. 1119–1133. [9] Adkins, B., and Harley, R. G., 1975, “ The General Theory of Alternating Current Machines,” Champman and Hall, London. [10] Ralaston, A., 1965, “ A First Course in Numerical Analysis,” McGraw-Hill, New York.

Biography Dr. Mohammed A. Abdel-halim was born in Cairo in 1951. He graduated at Faculty of Eng., Cairo University, Egypt in 1974. He obtained by M.Sc. from the same institute in 1979, and his Ph.D. degree from Loughborough University of Technology, England, in 1986. Dr. Abdel-halim joined Cairo Univ., Faculty of Eng., as a demonstrator (1974–1979), an assistant lecturer (1979–1982), and an assistant professor (1986–1990). He joined University of Science and Technology, Faculty of Eng., Irbid, Jordan (1990–1993). Currently he is an associate professor at Electrical Eng. Dept., King Saudi Univ., Saudi Arabia. His main research interest is in electrical machines and power electronics.