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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)
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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
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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
Table 2: Critical Clearing Time, Fault at Bus 2
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
Table 3: Critical Clearing Time, Fault at Bus 3
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
Table 4: Critical Clearing Time, Fault at Bus 4
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
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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.
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228 2007 39th North American Power Symposium (NAPS 2007)