A Phasor Speed Control of a Single or Two Phase Induction Motor

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Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1283

978-1-4244-1736-0/08/$25.00 2008 IEEE 1

A Phasor Speed Control of a Single or Two PhaseInduction Motor

Manuel Guerreiro, Daniel FoitoEscola Superior de Tecnologia de Setbal

Instituto Politcnico de SetbalSetbal, Portugal

Email: [email protected], dfoito@ est.ips.pt

Armando CordeiroInstituto Superior de Engenharia de Lisboa

Instituto Politcnico de LisboaLisboa, Portugal

Email: [email protected]

Abstract This paper is focused on the speed control of a

single or two phase induction motor using a diametrical inversion(DI) of the stator voltages. The changes in the speed error sign areresponsible for each DI which inverts the stator voltage phasorand its angular velocity. The main and the auxiliary windings arealways connected and thus the speed error sign allows todeterminate the rotating field direction. The motor is fed by arectifier associated with a three-phase inverter. The core of the

drive command its a 16-bit dsPIC device, which receives thespeed error sign and generate the appropriate PWM referencevoltages signs to the three-phase inverter. Simulation andexperimental results allow assume a good performance.

I. INTRODUCTIONSome market researches indicate that the annual commercial

sales volume of capacitor start single-phase induction motors

(SPIM) is approximately 4 million units (approximately 3 % of

the fractional horsepower motors). These motors are used in a

wide variety of commercial and industrial applications, with

the largest being ventilating, air conditioning equipment,

pumping equipment and commercial/industrial heating [1].Most of these types of electrical machines are used in fixed

speed drives [2]. There is wide recognition that energy can be

saved with the installation of adjustable-speed drives and other

devices to control motor systems, particularly in HVAC fans

and industrial pumps [1].Efforts have been made in single phase adjustable speed

drives with different kinds of PWM strategies, like SPWM andSpace Vector PWM, to perform better motor utilization withhigher efficiency [3].

This paper proposes a speed control strategy for SPIM orTwo-Phase Induction Motors (TPIM) using diametricalinversion in which the two winding voltages are PWM

modulated using a 16-bit dsPIC device. The motor is fed by athree-phase inverter.

II. COMMAND ACTIONSAn induction motor can be regarded as a complex system

consisting of two interconnected subsystems that are an

electromagnetic subsystem and a mechanical subsystem.

The mathematical model of the electromagnetic subsystem is

generally made up of four first order differential equations and

a fifth equation [4] which reflects the generation of an

electromagnetic torque. Applying on the motor a voltage (one

or more phases depending on type of the motor) the currents

and fluxes are modified and their resulting interaction causes

the development of an electromagnetic torque.

Electromagnetic

subsystem

Mechanical

subsystem

V

V

Te

m

Fig. 1 The induction motor seen as two interconnected subsystems

So the input, or command action, of this subsystem is a

voltage and the electromagnetic torque is its output.

In turn, this electromagnetic torque ( eT ) is the input of themechanical subsystem and it changes the position or the speed

(m

) of the rotor with a load torque (L

T ). The rotational

dynamic of the system with a friction coefficient (D) and a

moment of inertia (J) can be described by (1).

( )1

m m e L

DT T

J J + = (1)

Any significant delay in the control process, between the

applied voltage and the resulting electromagnetic torque, can

lead to an undesirable oscillatory response. To assure an

accurate speed control of a motor rotor it is necessary that thecommand actions applied on it leads to a fast direction change

of the electromagnetic torque. Then, the motor response will

can be a fast brake or acceleration very convenient to set

against to the actual error.

A SPIM has generally two accessible windings that can be

fed by two independent voltages. The centrifugal switch or

capacitor, if any, shall be short-circuited or removed. As the


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Proceedings of the 2008 International Conference on Electrical Machines

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axes of those windings are displaced 90 one of another it is

possible to provide the machine with a phasorial control.

A spatial voltage phasor can be defined on a complex plane

as:

sV V jV = + (2)

where V and V are the voltages applied on main andauxiliary windings.

Both, Quadrature Inversion (QI) and Diametrical Inversion

(DI), are command actions which were developed in the scope

of the rotor position control applied on a three-phase induction

motor [5,6].

The QI technique consists of substituting the actual stator

voltage phasor by another which has a displacement of 90

with the rotor flux phasor. The new voltage phasor will rotate

in the opposite direction of the previous one. This action

provokes the greatest variation of the torque derivative and so

it will presumably lead to the fastest change of the torque sign

[6].

The QI requires the rotor flux position determination inevery instant. It would be possible to construct a rotor flux

observer, however, in this work, the adopted way, was to

replace the QI by another command action. The QI can be

simplified and substituted by the diametrical inversion (DI).

The DI consists of replacing the voltage phasor 1( )s tV by

another one which is, as the name suggests, diametricallyopposed ( )s tV . The direction of the angular velocity must also

be reversed (fig. 2). The phasor angular speed is .

t

t-1

0

t-1

t

V

V

( )1tS

V

( )t

SV

Fig.2 The DI substitutes the1( )s tV by diametrically opposed ( )s tV .

III. CONTROLLER SCHEMEA voltage phasor SV can be represented in time domain by

V and V voltages. To obtain these voltages will be previously

generate their reference voltages, Vrefand Vref , respectively.

Using the projections ofs

V on the , axis it easy to

conclude that the desirable voltages are:

=

=

sin

cos

max

max

VV

VV

ref

ref (3)

The voltages to apply to the motor are reproduced from thereference voltages using the motor control PWM of a dsPICdevice connected to a three-phase inverter (fig.3). Obviously,in such a drive, it is advisable to use a low cost three-phaseinverter to reduce the final cost.

Vmax

. cos

Vmax

.sin

PWM

Inverter

M

nref

n

+

/2 Energy

+1

-1

V ref

V ref

Fig.3 Adopted controller scheme for SPIM speed control.

Although the actual speed can be obtained using anestimator or observer, in this work, a speed sensor (a small DCgenerator) was used. The sign of the speed error determines,through a hysteretic comparator, the convenient direction ofthe voltage phasor. The hysteretic width is directly related withthe switching frequency of the semiconductors. Obviously,increasing the hysteretic bandwidth the drive performance candiminish, and, consequently, it needs to attain a compromise.

The speed error is defined by the difference between the

reference speed and the actual speed (4)

n ref e n n= (4)

Every change of the sign of the speed error provokes an

angular jump of rad in the angle. This jump is acharacteristic of the diametrical inversions.

The successive DI allow that the magnetic field of the motor

accelerate or decelerate, on average values, as necessary to

guarantee that the rotor speed reaches and follows the

reference speed.

To feed the motor was used a low cost three-phase PWMinverter. A DC source, or a AC source with a simple bridge

rectifier provides the needed energy to the inverter.

Since there are two voltages the controller can be applied on

a single-phase induction motor with two windings permanently

connected or on a two phase induction motor.

The core of the drive command is a dsPIC30F4011 device.

The fundamental input of this device is the speed error sign.

Internally, an appropriated loop provides the integration, and it


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3

provokes, if necessary, the discontinuities, generating the

necessary angle. A sinusoidal table is included and it isshared by the sine and cosine functions.

The outputs of the dsPIC device are the PWM command

signals to the semiconductors of the inverter legs. The

converter topology is shown in fig 4. It consists of a simple

bridge rectifier and a three-phase PWM inverter. Two winding

single-phase induction motor connected to three-phase

inverter.

Auxiliary

Main

S1

S3

S5

S2

S4

S6

UDC

UAC

Controller and Semiconductor Drives

Fig.4 Adopted converter topology in the experimental tests.

IV. DRIVE RESULTSThe simulation tests were implemented in Matlab/Simulink

software using the Power System Blockset. Different types of

speed references and load conditions were simulated. Some

experimental results were also obtained. Fig 5 represents the

drive response simulation to a step speed reference.

0 0.5 1 1.5

0

1000

n(rpm)

0 0.5 1 1.5-10

0

10

20

t (s)

Te(Nm)

Tr

Tr

Fig.5 Simulation results obtained with a step speed reference of 1000 rpm. Atorque disturbance was introduced at t=1s. The rotor speed and the

electromagnetic torque are also represented.

In this conditions, the unloaded motor rotation starts freely.

The diametrical inversions are unnecessary and all the

available power is used to accelerate the motor and also to

compensate the rotational losses. After, there is an equilibrium

zone. A convenient DI sequence is applied. The

electromagnetic torque is oscillatory and it has a small average

value to just compensate the rotational losses. At t = 1 s, the

motor is hardly loaded with a step torque. The electromagnetic

torque response is fast and the speed change is insignificant.

The successive DI sequence creates a voltage which, in

average, has a non null rms value. This is the adequate value to

create the opposed electromagnetic torque against the load

torque.

Fig. 6 shows a step from 600 rpm to -600rpm. In this

simulation test, the motor is loaded with 1 Nm. The direction

of the load torque is opposite to the positive direction of therotor speed and, for that reason the speed of the rotor took

almost as long to reach the 600 rpm from zero as the change

from 600 to -600 rpm.

The electromagnetic torque has two starting regions and two

situations of constant speed. In the starting regions the

dynamics of the electromagnetic torque is similar to normal

and non-controlled starting. In the constant speed regions, the

rotor speed follows its reference and the average value of the

electromagnetic torque is the needed to support the opposite

rotational torque and the load torque.

The currents of the main and the auxiliary windings are also

shown in Fig. 6. It is clearly visible the differences between the

starting region or speed reference inversion region and those

with constant speed.

-600

0

600

n(rpm)

-10

0

10

Te(Nm)

-20

0

20

Im(A)

0 0.5 1 1.5 2

-20

0

20

t(s)

Ia(A)

Fig.6 Simulation results obtained with a step speed reference of 600 to -600 rpm. The motor is loaded with 1 Nm. The rotor speed, the

electromagnetic torque, the currents of the main and the auxiliary winding

are represented.

Fig. 7 shows a command signal with two levels. When alevel is substituted by the other one, there is a DI. Thereference voltages are described by (5).

Fig. 8 represents the same situation but it was obtainedexperimentally using a dsPIC30F4011 device and athree-phase inverter.


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4

( )

( )

max

max

cos2

sin2

ref

ref

V V dt

V V dt

=

=

(5)

The reference voltages Vref and Vref suffer discontinuities.The phases sequence, after and before, a DI are different, this

is, if after a DI Vrefleads Vrefbefore Vreflags Vref.

errorsign

Valfa

0 0.02 0.04 0.06 0.08 0.1

t(s)

Vbeta

Fig.7 . Diametrical inversions caused by the changes of error sign. Simulationresult.

V

V

en

Fig.8 . Diametrical inversions caused by the changes of error sign.Experimental result.

An experimental result of the drive response can be seen in

Fig. 9. The first and second curves are the reference and actual

speed, respectively, and third and fourth are the main and

auxiliary windings currents.

Imain

Nref

Iaux

Nm

Fig.9 . Speed control. The curves are: reference speed, actual

speed motor and main and auxiliary currents. Experimental results.

V. CONCLUSIONSA new approach to control the speed of a single or two phase

induction motor drive was presented and its effectiveness was

analyzed by several simulation and experimental tests.

In this new approach the diametrical inversion was used,

avoiding the rotor flux position determination in every instant.

With this command action the applied voltage phasor can be

inverted and rotate in the opposite direction depending on the

speed error sign. As consequence, the torque direction can

change very quickly and the drive will have a good

performance. Hence, the motor speed can be easily adjusted.

The results revealed that the rotor speed reaches the

reference speed without relevant damping or overshoot in

loaded or unloaded conditions.

The results also revealed that the speed control presents high

robustness against external torque disturbances. The 16-bit

dsPIC device as core of the drive command revealed

acceptable results.

REFERENCES

[1] Analysis of Energy Conservation Standards for Small Electric Motors,Building Technologies, Office of Energy Efficiency and RenewableEnergy, U.S. Department of Energy, June 2003.

[2] Blaabjerg, F.; Lungeanu, F.; Skaug, K.; Tonnes, M.; Two-PhaseInduction Motor Drives,IEEE 2004 ISBN 1077-2618/04.

[3] Ba-thunya, Ali S.; Khopkar, R.; Wei, K.; Toliyat, H. A.; Single PhaseInduction Motor Drives A Literature Survey, IEEE 2001 ISBN 0-7803-7091-0/01.

[4] Kim, S., E. Benedict, F. Fatehi, , N. Patel, A. Homaifar, T.A Lipo,Adjustable Speed Drive Control Based on Random Pulse WidthModulation, CPES Annual Meeting, Apr. 2000, pp. 202-209.

[5] M. Guerreiro, F. Silva, A New Position Controller For Induction Machi-nes: Diametrical Inversion of the Stator Voltage, ISIE97, Guimares,Portugal, July 1997.

[6] M. Guerreiro, F.Silva, Rotor Position Control for Induction MachinesUsing Diametrical Inversion of Stator Voltage, IEE Proceedings ElectricPower Applications, Vol. 147, Nr. 2, pp. 99-106, Maro, 2000.

[7] Young, C. M; Liu, C. C; Liu, C. H; New Inverter-driven design andcontrol method for two-phase induction motor drives, IEEE Proc.

Electr. Power Appl. Vol. 143, N6, November 1996.[8] Caisse, A.; Richardson, D.; Rotating Electric Machinery and

Transformer Technology, 4th ed., Prentice Hall, 1997 ISBN 0-13-409649-1.

[9] Toro, V.; Basic Electric Machines, Prentice Hall, 1990 ISBN 0-13-0601462.

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A Phasor Speed Control of a Single or Two Phase Induction Motor