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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 5, OCTOBER 2004 1081

Space-Vector Modulation in a Two-Phase InductionMotor Drive for Constant-Power Operation

M. A. Jabbar, Senior Member, IEEE, Ashwin M. Khambadkone, Member, IEEE, and Zhang Yanfeng

AbstractIn the paper, a space-vector pulsewidth-modulation(SVPWM) inverter is proposed for constant-power operation of atwo-phase induction motor. The operating principle of SVPWM isdescribed, and the algorithm for constant-power operation is pre-sented. Analysis for dynamic operation using a simple scalar con-trol scheme is carried out and parameters for implementation ofthe scheme are obtained. Experimental investigation of the schemeis carried out and comparative analysis of the performance of thescheme is presented.

Index TermsConstant-power operation, space-vectorpulsewidth modulation (SVPWM), three-phase inverter,two-phase induction motor.

I. INTRODUCTION

MOST domestic appliances, such as portable drills and

vacuum cleaners, need variable-speed constant-power

operation. AC series motors have a natural constant-power op-

eration characteristics and are commonly used for these appli-

cations. However, ac series motors cannot run at high speeds be-

cause of the brush and commutation problems. Significant radio

frequency interference (RFI) problems have to be solved and the

brush wear and noise become excessive.

Permanent-magnet motors along with variable-speed drives

can also be used and are highly efficient. However, costs andmechanical problems such as mounting of magnetic poles in the

rotor at very high speed limit their use. On the other hand, in-

duction machines along with variable-frequency drives can be

used to achieve constant-power operation above rated speed.

Usually, for low-power operation, fractional horsepower mo-

tors are used. They operate from a single-phase supply and uti-

lize a phase-splitting capacitor to develop a rotating field in the

air gap. However, due to an elliptical rotating field, a pulsating

torque is produced that causes higher noise than a three-phase

induction motor.

In recent years various schemes have been proposed for in-

verter-driven two-phase induction motors. In [1] and [2], square

voltage waveforms with quadrature phase shift are supplied to

the two-phase windings of a two-phase induction motor driven

by an inverter. Though this drive is simpler and cheaper, the

control range of speed is limited and the harmonic content of

the output voltage is high. In [3] and [4], phase-difference angle

Manuscript received October 25, 2002; revised March 15, 2004. Abstractpublished on the Internet July 15, 2004.

M. A. Jabbar and A. M. Khambadkone are with the Department of Elec-trical and Computer Engineering, National University of Singapore, Singapore117576 (e-mail: [email protected]).

Z. Yanfeng was with the Singapore Power System, Singapore. He is nowwithManufacturing Integration Technology Ltd., Singapore 569872.

Digital Object Identifier 10.1109/TIE.2004.834969

control of a two-phase induction motor is used which can ex-

tend the speed control range without a substantial increase in

cost of the drive. However, under phase-difference angle con-

trol, the torque pulsation still exists. In [5], rotor-flux-oriented

control is used to eliminate the ac term of the electromagnetic

torque in an unbalanced two-phase motor.

This paper introduces a fractional horsepower variable-speed

drive with a two-phase motor supplied from a voltage-source

inverter. The windings of the motor are symmetrical. To obtain

a rotating magnetic field in the motor, it is supplied from a two-

phase variable-frequency variable-voltage source.The scheme followed in this work is to operate a two-phase

induction motor with space-vector pulsewidth-modulation

(SVPWM) control to mimic the torquespeed characteristic of

an ac series motor and, thus, obtain a constant-power operation

characteristic.

II. DEVELOPMENT OF THE DESIGN

A. System Configuration

Fig. 1 shows the system that uses a domestic single-phase

supply with a rectifier and an inverter to supply the two-phase

motor with V/f control. In this work we have modified an un-balanced two-phase induction motor and rewound it into a sym-

metrical two-phase induction motor.

A two-phase drive can be obtained by using different config-

urations of inverters and windings.

Fig. 2 shows one of the ways of connecting the two-phase

windings. This is a cheaper method because it uses only four

switches. Fig. 2 also shows that two capacitors are connected in

series in the dc link to form a midpoint that is connected to neu-

tral point . In practice, two large resistors are also needed in

parallel with the capacitors to balance the voltage of the capac-

itors. This increases the losses in the system. For an H-bridge

inverter, the maximum output voltage (peak value) of one phaseusing sinusoidal PWM is

(1)

However, at low speed, an H-bridge inverter suffers from un-

balanced operation due to uneven discharging of the dc-link ca-

pacitor [6]. This leads to significant voltage ripple at low speeds.

Moreover, both capacitors in the dc link should be rated for

dc-link voltage and, hence, increase the cost.

The alternative means to connect the neutral point in this

system is to use a three-phase inverter to generate two-phase

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1082 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 5, OCTOBER 2004

Fig. 1. System configuration for constant-power operation.

Fig. 2. H-bridge inverter with phase connections.

output, as shown in Fig. 3. Instead of connecting point to

the dc link, we connect it to one of the inverter outputs which

simplifies the dc-link circuit and eliminates the problems in the

H-bridge inverter.

The three-phase system is used to generate two-phase voltage

outputs in which SPWM was used [6]. The two main legs of

the inverter are controlled using SPWM while the neutral leg

is switched 50% duty cycle to get neutral point . This

method can eliminate the voltage ripple problem in H-bridge

inverters. However, the maximum voltage output is as the same

as (1).

We propose SVPWM method instead of SPWM. As shown in

Fig. 3, this type of inverter is very much like the inverter used in

a three-phase induction motor drive. The only difference is the

magnitude and the location of the basic space vectors, which

is discussed in Section II-B. With this scheme, the maximum

output voltage (peak value) of one phase using SVPWM can be

increased to

(2)

B. Space-Vector Modualtion for the Two-Phase System

SVPWM refers to a special switching sequence of the upperthree power transistors of a three-phase inverter. It has been

Fig. 3. Three-phase inverter with phase connections.

TABLE ISWITCHING PATTERNS AND OUTPUT VOLTAGES

OF A THREE-PHASE POWER INVERTER

shown to generate less harmonic distortion in the output volt-

ages or currents applied to the phases of an ac motor and pro-

vides more efficient use of supply voltage in comparison with

direct sinusoidal modulation technique [7].

As shown in Fig. 3, there are eight possible switching com-

binations for the three upper power transistors that feed the

three-phase power inverter. The switching states of the lower

power transistors are opposite to the upper ones and so are com-

pletely determined once the states of the upper power transistors

are known. The eight combinations and the derived output phase

voltages in terms of dc-link voltages are shown in Table I,

where are the states of the switches and and arethe orthogonal phase voltages.

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JABBAR et al.: SPACE-VECTOR MODULATION IN A TWO-PHASE INDUCTION MOTOR DRIVE FOR CONSTANT-POWER OPERATION. 1083

Fig. 4. Basic space vectors and switch patterns.

Fig. 5. Symmetric space-vector PWM switching pattern.

From Table I, we can get six nonzero vectors and two zero

vectors. In these basic space vectors, and are two

zero space vectors. Thus, SVPWM can be implemented in this

system. Unlike a normal three-phase inverter in which the space

vectors form a symmetric hexagon, the space vectors in this

system form an asymmetric hexagon, as shown in Fig. 4. From

Fig. 4, it is known that the magnitude of must be limited tothe envelope defined by the circle (dashed circle in Fig. 4). This

gives a maximum magnitude of for .

The objective of SVPWM is to approximate the reference

voltage vector by a combination of the eight switching pat-

terns. One simple means of approximation is to require the av-

erage output of the inverter (in a small period, ) to be the

same as the average of in the same period. Supposing that

is located in the sector formed by and , we can get

(3)

where and are the respective durations in time for which

switching patterns and are applied within period .From (3), we can say that for every PWM period, the desired

reference voltage can be approximated by having the power

inverter inswitching patterns and for and durations

of time, respectively. Since the sum of and is less than or

equal to , the rest of the switching period is occupied by

the zero switching state. Therefore, we define as

(4)

By properly calculating , , and , the correct switching

signals can be generated. An example of symmetric SVPWM

waveforms is shown in Fig. 5 where it is assumed that the ref-

erence voltage is in the sector formed by vectors and.

TABLE IIQUANTITIES IN CONSTANT MATRIX

M

FOR EACH SECTOR

Fig. 6. Switching sequence for each sector.

This switching pattern depends on the sector of operation.

The switching sequence is decided to ensure that only one

switch commutates to achieve the transition from one switching

state to another. This ensures a minimum number of com-

mutations. For a given sector the switching sequence can be

generalized as ,

where and are the active vertex vectors of the sector. The

switching state corresponding to for a sector is decided on

the condition that only one commutation is required to transit

from to . Similarly, the choice of for a sector ensures

one commutation to transit from to . Table II defines the

respective and vectors for all six sectors. We can see that

all states require one commutation to and all statesrequire one commutation to the state. In order to maintain

the minimum commutation condition the sequence of switching

will depend on the sector as shown in Fig. 6. For example, in

sector 1, is chosen as , while is chosen as ,

which results in .

We can define that

(5)

(6)

where and stand for the magnitudes of the resulting

switching state vectors and and are their angles measuredin a clockwise direction with respect to the real axis .

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Fig. 7. Switching time ofT

,T

, andT

in one period.

Fig. 8. Simulation phase current and mid-bridge current waveforms.

Based on Fig. 6, the quantities in (5) and (6) for each sector

can be derived, and these are shown in Table II.

Supposing and substituting (5) and (6) into (3),

we can get

(7)

where

(8)

Once the sector of reference is determined, we can com-

pute the matrix using Table II and (8). The actual values of

the components of matrix are either 1, 1, or 0. After is

known, and can be easily calculated by using (7). Fig. 7

shows the switching time of and in one period in which

the switching frequency is set at 10 kHz.

The current of the return bridge in a three-leg topology in-

verter with the SVM scheme is also times phase currents

which can be easily seen from Fig. 8. Thus, when designing

these kinds of inverters, the rated current of the insulated gate

bipolar transistors (IGBTs) in the return bridge should be higher.

C. Comparison of Steady-State Performance

To evaluate the performance of the proposed scheme a com-

parison is given in Table III. The estimated switching losses are

obtained by assuming dc-bus voltage is 325 V, switching fre-quency is 10 kHz, output fundamental frequency is 50 Hz, and

TABLE IIICOMPARISON OF THREE TYPES OF INVERTERS

the load is 375 W. In domestic appliances, normally, a single-

phase supply is used which limits the dc-bus voltage to 325 V

(230-V supply). For the same dc-bus voltage, a higher output

voltage of an inverter means that higher output torque as well as

a larger speed range can be easily obtained. We can see that the

proposed scheme produces 41% more voltage than the H-bridge

configuration with only a 21% increase in losses. On the other

hand, the use of SPWM with 50% duty cycle for the return legproduces higher losses at a lower maximum voltage.

III. CONTROL STRATEGY OF TWO-PHASE INDUCTION MOTORS

FOR CONSTANT-POWER OPERATION

Induction motors can be controlled such that they can produce

low torque at high speeds and vice versa. This would require an

active control of the stator frequency and voltage in accordance

with the change in actual torque and speed of the machine.

By properly setting the frequency and amplitude of the supply

voltage of a two-phase induction machine, it can be operated

at the intersection point of the torquespeed curve of induction

motors and the trajectory of constant-power operation (Fig. 9).When load torque changes, the frequency and amplitude of the

supply voltage of the induction machine are adjusted so that

the machine can operate at another intersection point. If we do

that through the whole speed range, a constant-power operation

can be maintained at every operating point. Thus, a two-phase

induction machine will operate just like a universal motor.

For any kind of electrical machine, the output power can be

expressed as

(9)

To obtain constant-power operation, the product of and

should be a constant. In steady state, the electromagnetic torqueequals the load torque. Thus, we can use the electromagnetic

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Fig. 9. Torquespeed characteristics of a two-phase induction machine withopen-loop V/f control and constant-power operation trajectory.

Fig. 10. Relationship of synchronous speed and desired rotor speed.

torque to obtain the speed command instead of the load torque.Since we need only the average torque for the control, it is ob-

tained from estimating stator-flux vector and current. As a dy-

namic and accurate position of flux is not required, a low-pass

filter is used to obtain the stator-flux vector. The torque calcu-

lated is averaged over five periods of the sampling with the sam-

pling frequency of 10 kHz.

A. Estimation of Slip for Constant-Power Operation

Normally, in medium and large induction motors, the slip is

very small. However, in fractional horsepower induction mo-

tors, the torquespeed characteristic becomes soft, so the slip is

large; in order to operate with constant-power characteristic, thisslip must be compensated. To this end, the torquespeed charac-

teristics of a two-phase induction machine for different frequen-

cies (open-loop V/f control is applied) are measured (Fig. 9).

Secondly, the intersection points of the torquespeed curves

and constant-power operation trajectory are calculated and, at

the same time, the corresponding synchronous speeds are also

recorded. Thus, we get two variables: one is the desired rotor

speed and the other is the corresponding synchronous speed.

Finally, by using an interpolation technique and polynomial

fit, we can obtain the function of synchronous speed and

desired rotor speed as for a given output power

as shown in Fig. 10. Thus, once the desired rotor speed is known,

the corresponding synchronous speed can be determined by thisfunction.

This slip estimation method is easy to implement. Most tasks

can be done offline, which greatly saves the computational time

of the microcontroller.

B. Speed Rate of Change Limitation

An abrupt change of supply frequency will cause transient

current in the motor which should not exceed the rated currentof the inverter. By limiting the step change of supply frequency,

this transient current can be limited in the permitted range.

Let denote the supply frequency at any instant, denote

the rated voltage, and denote the rated angular frequency. It

is assumed that the supply voltage is proportional throughout to

the supply frequency, which maintains the flux in the machine

at a practically constant level. Thus, the supply voltage at can

be defined as

(10)

We rewrite the stator voltage equation in a reference frame ro-tating at the angular velocity with natural (non-p.u.) values

(11)

where is the stator voltage space vector, is the stator current

space vector, isthestator flux-linkage space vector, and is

the stator resistance. Reverting to p.u. form, the above equation

becomes

(12)

Assume that the supply frequency of the machine, previouslya constant at angular velocity , is slightly increased by .

Therefore, we get

(13)

Neglecting second-order quantities, applying Laplace trans-

forms, and making use of (12), the above equation yields

(14)

In these equations, provided that is not less than 0.1, one

may write to a very fair approximation [8], which

modifies the equations as follows:

(15)

The solution of (15) is obtained by inversion to a time function

as

(16)

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Fig. 11. Block diagram of control algorithm.

Fig. 12. Five-step control.

Then, we can get amplitude relationship of and

(17)

This equation indicates that if the stator flux has no change

after an abrupt change of supply frequencies there should be no

inrush current in the stator windings. This can be true if (10) is

maintained. However, beyond the rated angular speed, supply

voltage can no longer increase with frequency. Thus, the flux is

also not a constant so that an inrush current appears. Since the

stator flux is proportional to , we can get

(18)

Substituting (18) in (17), we obtain

(19)

To limit the inrush current to 0.5 p.u., and using (19), we know

that should be limited to 1/9 p.u. .

C. Control Strategy

The entire control block diagram is shown in Fig. 11.

This block diagram can be explained with the five simple

steps shown in Fig. 12.

1) The electromagnetic torque is calculated based on feed-

back voltage and currents.

2) The desired rotor speed is obtained by obtaining the re-quired slip.

Fig. 13. Maximum output voltages of a three-phase inverter with SVPWM.

Fig. 14. Experimental torquespeed characteristic (solid line) and idealconstant-power operation (dashed line).

3) The reference frequency is determined by using the syn-

chronous speed and rotor speed relationship curve shown

in Fig. 10. The maximum rotor speed change given by

(19) is maintained.

4) The reference voltage is obtained from a lookup table

based on voltage and frequency profiles.

5) The desired two-phase voltages are generated by

the SVPWM scheme based on reference voltage

and frequency.

IV. EXPERIMENTAL RESULTS

To verify the proposed space-vector modulation and control

algorithm, the system shown in Fig. 1 was constructed. Thecontrol was implemented on a digital signal processor (DSP)

fixed-point microcontroller TMS320C240. The PWM unit of

the microcontroller was used to implement the SVPWM. The

PWM switching frequency and sample frequency are both set at

10 kHz. In this system, a four-pole two-phase induction motor

was used.

Fig. 13 shows the maximum output voltages (fundamental)

of the inverter. We obtained 40% more voltage output with the

three-phase inverter using space-vector modulation compared to

that of the H-bridge inverter.

Fig. 14 shows the torquespeed characteristic of the proposed

system. The results show a significant constant-power operation

characteristic over a wide speed range. For most domestic ap-pliances such a speed range is satisfactory.

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Fig. 15. Startup of the two-phase induction motor drive system; output power

is set at 10 W.

Fig. 16. Stator current response of constant-power operation to a step change

in the load torque from 0.042 to 0.144 N 1 m; output power is set at 10 W.

V. DYNAMIC PERFORMANCE OF TWO-PHASE INDUCTION

MOTOR DRIVES

In this section, the dynamic performance of two-phase induc-

tion motor drives is presented.

Fig. 15 shows the startup of this two-phase induction motor

drive. At the beginning, the drive starts up with open-loop V/f

control and no-load condition until the drive operates with

50-Hz power supply in the steady state. Then, the closed-loop

constant-power operation control algorithm is applied. Finally,

the drive operates with 10-W power output. The rotor speed is

about 2200 r/min which is limited by the friction torque (about

0.042 N m) of the drive system.

To investigate the robustness of the proposed control algo-

rithm, we analyzed the phase current, flux, and speed response

of the motor drive to step changes in load torque. Figs. 16 18

show the stator current, stator flux, and shaft speed response of

the two-phase induction motor drive to a step change in load

torque from 0.042 N m (friction torque) to 0.144 N m. In Fig. 18

it is shown that in about 4 s the rotor speed of the two-phase

motor changes from 2200 to 670 r/min to keep the output power

as a constant ( 10 W). From Fig. 17 we can see that the stator

flux increases. This is because, above 50 Hz (base frequency),

the amplitude of the two-phase supply is fixed, thus, the stator

flux at higher speed becomes smaller; below 50 Hz, V/f with

drop compensation control is applied, thus, the stator fluxes arealmost constant.

Fig. 17. Stator flux response of constant-power operation to a step change inthe load torque from 0.042 to 0.144 N

1

m: output power is set as 10 W.

Fig. 18. Speed response of constant-power operation to a step change in theload torque from 0.042 N.m to 0.144 N.m: output power is set at 10 W.

From these figures we can see that the response of the drive

system is not very fast. In order to reduce the cost of the system,

the scalar control scheme without speed feedback is used in this

project. To avoid large current and unstable operation, the max-

imum speed change should be limited as given by (19). There-

fore, the fast response performance is sacrificed. However, for

domestic appliances, in most cases, fast response is not critical.

Therefore, such a dynamic performance is still acceptable in do-

mestic appliances.

VI. CONCLUSION

A scheme has been developed to use small two-phase

induction motors with SVPWM inverters in domestic appli-

ances to achieve constant-power operation characteristic. This

scheme eliminates problems generated by ac series motors. A

three-phase inverter topology with SVPWM was used to pro-

duce higher output voltage with lower distortion as compared

to an H-bridge inverter. Off-the-shelf components can be used

for this drive. Hence, the method is simple and cost effective

for high-volume manufacturing.

REFERENCES

[1] L. M. C. Mhango and R. Perryman, Analysis and simulation of ahigh-speed two-phase AC drive for aerospace applications, Proc.

IEEElect. Power Applicat., vol. 144, no. 2, pp. 149157, Mar. 1997.

[2] I. R. Smith, D. Creighton, and L. M. C. Mhango, Analysis and perfor-mance of a novel two-phase drive for fan and water-pumping applica-tions, IEEE Trans. Ind. Electron., vol. 36, pp. 530538, Nov. 1989.

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[3] D. Jang and G. Cha, Phase-difference control of 2-phase inverter-fedinduction motor, in Conf. Rec. IEEE-IAS Annu. Meeting, 1989, pp.377383.

[4] DoHyun and J. S. Won, Voltage, frequency and phase-difference anglecontrolof PWM inverters-fed two-phase induction motors,IEEE Trans.Power Electronics, vol. 9, pp. 377383, July 1994.

[5] C. B. Jacobina, Rotor-flux-oriented control of a single-phase inductionmotor drive, IEEE Trans. Ind. Electron., vol. 47, pp. 832841, Aug.

2000.[6] S. S.Wekhande, B. N. Chaudhari, and S. V. Dhopte, A lowcost inverterdrive for 2-phaseinduction motor, in Proc. IEEE Int.Conf. Power Elec-tronics and Drive Systems, July 1999, pp. 428431.

[7] J. Holtz, Pusle modulation for electric power conversion, Proc. IEEE,vol. 82, pp. 11941214, Aug. 1994.

[8] P. K. Kovacs, Transient Phenomena in Electrical Machines. Ams-terdam, The Netherlands: Elsevier, 1984.

M. A. Jabbar (SM84) was born in Bangladesh.He received the B.Sc. degree in electrical engi-neering from Bangladesh University of Engineering

and Technology, Dhaka, Bangladesh, in 1968, andthe Ph.D. degree from Southampton University,Southampton, U.K., in 1977.

He is currently an Associate Professor in the De-partment of Electrical and Computer Engineering,National University of Singapore, Singapore. Sincereceiving the Ph.D. degree, he has been involvedin teaching and research in the areas of magnetic

systems and small devices. He has worked in industrial research for developing

new types of products for various companies. He spent more than a decade inindustry working in the U.K., Singapore, and Bangladesh. He has been involved

in product design and development since the early 1970s. He has been anacademic, as well, in three different countries. For five years before he joinedthe National University of Singapore in 1992, he was the Head of Research and

Development at Maxtor Corporation, Singapore, a leading American disk drivemanufacturer. He has published very widely in these areas.

Dr. Jabbar was awarded a Commonwealth Scholarship for higher studies in1972. He is a Chartered Engineer in the U.K. and a Corporate Member of theInstitution of Electrical Engineers, U.K. He is also a Fellow of the Institution ofEngineers, Bangladesh.

Ashwin M. Khambadkone (M95) received theDr.-Ing. degree from Wuppertal University, Wup-pertal, Germany, in 1995. He also holds a GraduateCertificate in Education from the University ofQueensland, Brisbane, Australia.

In 1987, he joined the Electrical Machines andDrives Laboratory, Wuppertal University, as a Re-search Assistant. He was involved in research in the

areas of PWM methods, field-oriented control, pa-rameter identification, and sensorless vector control.He was also involved in industrial development of

vector control drives. From 1995 to 1997, he was a Lecturer at the Universityof Queensland. He was also with the Indian Institute of Science, Bangalore,India, in 1998. Since 1998, he has been an Assistant Professor at the NationalUniversity of Singapore, Singapore. His research activities are in the control ofac drives, design and control of power electronic converters, and fuel-cell-basedsystems.

Dr. Khambadkone was the recipient of the Outstanding Paper Award forthe year 1991 and the Best Paper Award for the year 2002 of the IEEETRANSACTIONS ON INDUSTRIAL ELECTRONICS.

Zhang Yanfeng received the M.S. degree fromZhejiang University, Hangzhou, China, in 1999, andthe M.Eng. degree from the National University ofSingapore, Singapore, in 2003.

In 2002, he joined the Singapore Power Systemas an R&D Engineer for voltage dip compensation.In 2003, he joined Manufacturing Integration Tech-nology Ltd., Singapore, as an Electrical Engineer.

He is involved in the development of semiconductorautomation equipment.

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