effect of large induction motors on the

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Fig. 1. Dynamic model of induction motor

Fig. 2. Detailed induction motor model

the system increases the voltage recovery time which varies in

proportion to the fault clearing time. During the fault the

induction motor decelerates and to reaccelerate it needs to

absorb lagging VAR [6]. Since the torque produced by the

induction motor varies as the square of voltage, the torque will

reduce. The retardation is less for induction motors with large

inertia making it easy to reaccelerate to its normal speed after

the fault is cleared.

2. Transient characteristics of the induction motor

During the fault, the voltage at the terminals of the

induction motor drops and the induction motor feeds into the

fault, reducing the lagging MVAR taken from the system.

Rapidly decaying transients are produced which reduce

stability drastically. Torques with negative peaks of five times

per unit torque and currents peaks of ten times the per unit

current are produced [6].

3. Proximity of the induction motor to the fault location.

The location of the induction motor has a profound effect

on the stability of the system. If the induction motor is located

near an accelerating generator, the excess power generated

after the fault is cleared can be taken up by the induction motor

and helps in attaining a stable point more rapidly.

4. Load characteristics of the induction motor Loads with low inertia constants will rapidly decelerate

and the continuity of the output may be lost. High inertia loads

with the load torque varying as some function of speed, may

undergo a limited amount of retardation and may be able to

reaccelerate on voltage recovery.

5. System stability

Stability of a physical system is its ability to return to its

original position or another equilibrium point on occurrence of

a disturbance. If a power system can regain its synchronous

speed after a small disturbance it is called steady state stability

and if it regains synchronous speed after a large disturbance it

is called transient stability. The transient stability is a fast

phenomenon. The action of voltage regulators and turbine

governors is not included in the transient stability studiesbecause they are too slow to act.

III. MODELING AND APPLICATION

Static and dynamic load models are implemented in this

paper. Static load model expresses the active and reactive

power at any instant of time in terms of bus voltage and

frequency at that instant. Dynamic load model takes the past

instants of time into account while expressing active and

reactive power as a function of bus voltage and frequency [4].

A. Induction motor

The dynamic model used for synchronous motors is shown

in Fig. 1. Here,

r 1 , r 2 = stator resistance and rotor resistance respectively.

x1 , x2 = stator reactance and rotor reactance respectively.

xm = magnetizing reactance.

s = slip of the induction motor.

Fig. 2 shows a more detailed model. Here,

Rs, Lls = stator resistance and leakage inductance.

R' r ,L' lr = rotor resistance and leakage inductance

referred to the stator.

Lm = magnetizing inductance.

V' qr ,V qs = q axis rotor voltage referred to stator and stator

voltage.

V' dr, V ds = d axis rotor voltage referred to the stator and

stator voltage.

r = electrical angular velocity.

ds , qs = stator d and q axis fluxes.

J = combined rotor and load viscous friction

coefficient.

T e,

T m

= Electromagnetic and shaft mechanical torque

respectively.

The distribution of current in the rotor conductors is

different at high and low rotor frequencies and hence the rotor

resistance varies significantly over the speed range. So the

simplest model using only the flux dynamics does not represent

an accurate model. A dynamic model including the mechanical

dynamics, rotor flux dynamics and stator flux dynamics should

be considered [6]. The mechanical system of the induction

motor is modeled as shown.

1

2m e m m

d T F T

d t H

m m

d

d t

B. Synchronous generator

The test system takes into account the dynamics of the

stator, field and damper windings. Equivalent circuit of the

synchronous machine is as shown in Fig. 3.

224 2007 39th North American Power Symposium (NAPS 2007)



Fig.4. Test system configuration

Fig. 3. Synchronous generator model

Fig. 5. Speed response of generator 2, using dynamic and constant

impedance model, fault clearing time 5 cycles

Here,

Rs , L l = stator resistance and leakage inductance.

Lmq , Lmd = q axis and d axis magnetizing inductance. R' kq1 , L' lkq1 , R' kq2 , L' lkq2 = q axis resistances and leakage

inductances referred to the stator.

R' fd , L' lfd = d axis field resistance and leakage

inductances referred to the stator.

R' kd , L' lkd = d axis resistance and leakage inductance

referred to the stator.

r = electrical angular velocity

d , q = d and q axis fluxes.

C. Induction motor load

In general, depending on the type of load on the motor, the

load torque and power model can be represented in the

following form.

21 2 3mT k k k ; 2 31 2 3mP T k k k

In the work reported in this paper, the constants have been

used: k 1 = k 3 = 0, k 2 = 4.482 NMs.

D. Tests

The test system shown in Fig. 4 is simulated in MatLab

and its responses for a three phase fault are observed for

different fault locations, induction motor loads, and fault

clearing times. The simulated responses of the two load models

are compared for varying induction motor loads. The

comparison is based on the speed variation of the generators

and the critical clearing time of the system. This indicates the

relative stability of the system.

IV. DEMONSTRATION

A. Load models of an induction motor

Induction motor is represented with its dynamic model

and constant impedance load models and both the responsesare compared. The effect of induction motor on the stability of

the system is analyzed by changing the fault clearing time. Fig.

5 shows the speed variations of generator 2 in constant

impedance and dynamic load models for a fault at bus3 and a

fault clearing time of 5cycles. It is observed that the speed of

generator 1 is not affected by the fault. Comparing the plots, it

is observed that

1. Both the peak overshoots are higher in the dynamic model

than in the constant impedance representation;

2. First zero crossing takes less time in the dynamic

representation;

3. In the dynamic representation the system comes back to its

normal state more quickly when the induction motor is in

the system, i.e., induction motor improves damping.The above observations hold true even for a fault with a

fault clearing time of 10 cycles. In all the simulations that were

carried out, it was found out that when the fault clearing time is

in the range of 1 to 10 cycles for 1000 HP motor load, the

system attains the stable point more rapidly when the induction

motor is in the system.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.985

0.99

0.995

1

1.005

1.01

1.015

Time (sec)

S p e e d ( p u )

Fig. 6. Speed response of generator 2, with and without ride-

through, fault clearing time 5 cycles

2007 39th North American Power Symposium (NAPS 2007) 225



Table 5: Critical Clearing Time, Motor Near Generator, Fault at

Bus 3

No of 1000 HP motors CCT for IM, in seconds

1 0.876

2 0.238

3 0.172

Table 1: Critical Clearing Time, Fault at Bus 1

No of 1000

HP motors

CCT for IM (dynamic

model) in seconds

CCT for (constant

impedance model)

in seconds

1 0.509 >2

2 0.184 >2

3 0.117 0.7


No of 1000HP motors

CCT for IM (dynamicmodel) in seconds

CCT for (constant

impedance model)

in seconds

1 0.473 >2

2 0.168 >2

3 0.11 0.69


No of 1000

HP motors

CCT for IM (dynamic

model) in seconds

CCT for (constant

impedance model)

in seconds

1 0.808 >2

2 0.268 >2

3 0.13 1.3


No of 1000HP motors

CCT for IM (dynamicmodel) in seconds

CCT for (constantimpedance model)

in seconds

1 0.49 >2

2 0.183 >2

3 0.118 0.98

Table 6: Critical Clearing Time, Motor Tripped at 70% of the

Terminal Voltage, Fault at Bus 3

No of

1000HPMotors

CCT for IM

(Tripping) inseconds

CCT for (Ride

Through) in seconds

1 2.06 0.808

2 1.98 0.268

3 0.214 0.13

B. Effect of the induction motor location with respect to the

fault

The critical clearing time is obtained for different fault

locations. If the fault is at a remote location in comparison to

the induction motor, then the voltage at the terminal of the

induction motor will be reduced by a certain extent. But this

reduction will not have much effect on the system and the

induction motor should reaccelerate such that the system

attains stable state.

1. Fault occurs at bus 1

Comparing the critical clearing time of the system in Table

1 between the dynamic representation and the constant

impedance representation, the dynamic representation shows

lower system stability than the constant impedance

representation, in terms of lower critical clearing time. Thus a

constant impedance representation gives optimistic results. The

dynamic representation of induction motor incorporates the

changes in the speed. So, small changes in the slip change the

net output of the induction motor, and the power absorbed by

the induction motor during the fault and post fault conditions

change. This results in lower critical clearing time. With

reacceleration of the motor, load current becomes very high

resulting in further low voltage and the system becomes

unstable. Larger the induction motor load, the more unstablethe system will be. It is observed that the critical clearing time

goes down as the load increases.

2. Fault occurs at bus 2

The critical clearing time in Table 2 verifies that the

dynamic representation of an induction motor worsens the

stability of the system. It is observed that the fault clearing

time depends on the electrical distance between fault and the

induction motor. The fault clearing time is minimum for this

case when compared to all other cases as the electrical distance

between the motor and the fault is the least. Since the fault is at

the terminals of the induction motor, the induction motor will

decelerate quickly because of the reduction in motor torque.

The slip will rise with a further increase in the line currents.

Since the line currents can reach a very high value depending

on speed loss, the system will be more unstable. It is alsoobserved that as the induction motor load increases, the system

becomes more unstable.

3. Fault occurs at bus3

The electrical distance between the fault and the induction

motor is the largest in this case and so is the critical clearing

time. The dynamic representation of the induction motor

results in lower critical clearing time compared to the constant

impedance model and hence worsens the stability of the

system. It is also observed that higher the induction motor

load, the more unstable the system will be. The higher critical

clearing time can be explained by the argument that since the

fault is closer to the induction motor, the voltage at the

terminal of the induction motor drops down to a low value, but

not as low as when the fault is at its terminals. When theinduction motor reaccelerates, it will draw high load current

resulting in low voltage. Since the system cannot sustain the

larger load current, it becomes unstable more quickly.

Similar conclusions can be made for a fault at bus 4.

C. Presence of induction motor near the generator (Fault

occurs at bus 3)

In this topology the induction motor and the generator are

located on the same bus. This was done by changing the

impedance of the transmission line between bus 2 and bus 4 to

zero. The critical clearing time is more in this case; this can be

attributed to the transient characteristics of the induction

motor. The presence of an induction motor helps in stabilizing

the power system in this case.

D. Effect of induction motor ride through

The induction motor is tripped when the voltage at the

terminal of the induction motor drops to 70 percent of the rated




Table 8: Transmission Line Specifications

From To R(pu) X1(pu) Xc(pu)

1 2 0.1216 0.7234 0.0073

1 3 0.1216 0.7234 0.0073

2 3 0.1216 0.7234 0.0073

Table 7: Induction Motor Specifications

Parameters Values

Nomi nal P ower 7 46 kW

Rated Voltage(L-L) 2.4 kV

Stator Resistance 29 m

Stator Inductance 0.5 mH

Rotor Resistance 40 m

Rotor Inductance 0.5 mH

Inertia 63.87 kg.m

2

Table 9: System Data

Bus No Pg Pd Qg Qd Type

1 – – – – Swing

2 0 0.2238 0 0.0148 (lag) PQ

3 0 0 0 0.005 (lead) PQ

4 0.03 0 0.03 0.005 (lead) PQ

voltage [2]. As expected when induction motor is taken out of

the network, the critical clearing time of the system increases.

The results are shown in Table 6.

V. DISCUSSION AND CONCLUSIONS

The following conclusions can be drawn from the studies

described in this paper.

1. The presence of induction motors in the system does not

improve stability except when the fault is far away from the

induction motor.

2. The first zero crossing of the dynamic model in the

presence of the induction motor takes less time when

compared to the constant impedance model and motor

tripped case. It helps in stability.

3. The dynamic model of the induction motor provides more

realistic results than the constant impedance model,

requiring higher critical clearing times.

4. For the same capacity of generators and induction motor,

system stability is less at higher loads.

When the transient fault is at a remote location with

respect to the induction motor, it is recommended to keep the

induction motor in the system because voltage at the terminal

of the induction motor will not be very low and the likelihood

of an induction motor recovering its steady state is higher. The

motor’s inertia and characteristics help to attain a stable state

more rapidly.

Further research on identifying conditions where the

presence of induction motors is beneficial to system stability is

in progress, and results will be reported in due course.

VI. REFERENCES

[1] T. S. Key, “Predicting behavior of induction motors during severe faults

and interruptions,” IEEE Industry Applications Magazine, Jan/Feb

1995.

[2] J. C. Das, “Effects of momentary voltage dips on the operation of

induction and synchronous motors,” IEEE Transactions on Industry

Applications, vol. 26, no. 4, July/Aug 1990, pp. 711–718.

[3] M. J. Bollen, “The influence of motor reacceleration on the voltage

sags,” IEEE Transactions on Industry Applications, vol. 31, no. 4,July/Aug 1995, pp 667–674

[4] J. C. Gomez, M. M. Morcos, C. Reineri, and G. Campetelli, “Induction

motor behavior under short interruptions and voltage sags,” IEEE Power

Engineering Review, Feb 2001, pp. 11-15.

[5] G. W. Bottrell and L. Y. Yu, “Motor behavior through power system

disturbances,” IEEE Transactions on Industry Applications, vol. 16, no.

5, Sep/Oct 1980, pp. 600–604.

[6] .IEEE Task Force on Load Representation for Dynamic Performance,

“Load representation for dynamic performance analysis,” IEEE

Transaction on Power Systems, vol. 8, no. 2, May 1993, pp 472–482

[7] P. Kundur, Power System Stability and Control, McGraw Hill, 1994.

VII. APPENDIX

The system data used in the demonstration cases reported

in section IV are shown below, in Tables 7–9. Fig. 7 shows the

MatLab-SimuLink model used in this work.

2007 39th North American Power Symposium (NAPS 2007) 227



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effect of large induction motors on the

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