INTRODUCTION
Many studies and investigations have been carried out to assess, satisfy and
enhance the power quality of the electric power system (Souto
et al., 1998). It is well known that around 80% of electrical industrial
loads consist of three phase induction motors. Induction motors need a high
current and reactive power at starting. Starting of a large electrical motors
connected to a bus with small short circuit power, will produce disturbance
for supply network and local consumers. This disturbance generally is in the
form of voltage dip and will cause power quality of the network to decrease.
Furthermore abatement of voltage will result in reduction of starting torque
and consequently time of motor speeding up will be increased (Hedayati
and Oraee, 2005). Consequently, any power quality and energy resource survey
approach should take into consideration the behavior and performance of these
devices under ideal and nonideal supply conditions.
To compensate the disturbance during the starting, it is proposed to use Shunt
FACTS devices such as SVC or STATCOM. These types of compensators increase the
motor speeding up and improve the voltage profile. The fundamental difference
in operation principle between SVC and STATCOM is that STATCOM is a converterbased
var generation function as shuntconnected synchronous voltage source; whereas
SVC is thyristor controlled reactors and thyristor switched capacitors, function
as a shunt connected controlled reactive admittance. In addition to that, STATCOM
has the ability to exchange real power from the system if it is equipped with
an energy storage element at its dc terminal. Major advantages of STATCOM over
the conventional SVC are significant size reduction, reduced number of passive
elements due to the development of capacitor technology, ability to supply required
reactive power even at low bus voltage, better control stability and lower harmonics
(Song and Johns, 1999; Hingorani and
Gyugyi, 2000).
Power quality that is concerned with variations of the voltage from its ideal
waveform, affect the dynamic behavior of induction motors. Power quality occurrence
includes the small deviations from the rated or preferred value called voltage
variations and immediate deviations from its standard or ideal wave form are
called events. One of the most popular events in the power system is voltage
sags. Voltage sags are short period lessening of rms voltage, caused by short
circuits, over loads and starting of large motor (Bollen, 2000).
In this study, comprehensive assessment of the effects of STATCOM and SVC controllers
has been carried out for dynamic behaviors of induction motor starting under
ideal supply conditions. Also, the performances of induction motor operations
with shunt FACTS under symmetrical and unsymmetrical voltage sags are investigated.
SYSTEM MODELING
The system under study is the machine, a network and infinite bus where FACTS device (e.g., STATCOM or SVC) is installed on the terminal of the induction motors. Figure 1 shows the system modeling with a SVC which consists of fixed shunt Capacitor (FC) and Thyristor Controlled Reactor (TCR), while Fig. 2 shows with a STATCOM which consists of DC capacitor, a three phase GTO based Voltage Source Converter (VSC) and a step down transformer.

Fig. 1: 
System modeling with a SVC 

Fig. 2: 
System modeling with a STATCOM 
Motor model: In this study, the induction motor will be presented by
Park model. The complete electro mechanical equations are as follows (Hedayati
and Oraee, 2005):
Where:
and
The expressions for the electromagnetic torque and inertia coefficient respectively
are:
A list of symbols is given in the Appendix A.
SVC model: As mentioned, the model of SVC in this studyis FCTCR. The
dynamic equations of SVC which are presented by Park model are as follows (Hedayati
and Oraee, 2005):
where:
α is firing angle of thyristor.
STATCOM model: The STATCOM is modeled as a voltagesourced converter
behind a step down transformer as shown in Fig. 2. The STATCOM
generates a controllable AC voltage source V_{out}(t) = V_{0}
sin (ωt  ψ) behind the leakage reactance. The voltage difference
between the STATCOM bus AC voltage and V_{out}(t) produces active and
reactive power exchange between the STATCOM and the power system (Hedayati
and Oraee, 2005; Rahim and Kandlawala, 2004; Wang,
1999; Seyed et al., 2005).
From Fig. 2 we have:
The DC voltage V_{DC} is governed by:
where, C_{DC} the dc capacitor is value and I_{DC} is the capacitor current. The output voltage phasor is:
For the PWM inverter; c = mk and k is the ratio between AC and DC voltage; m is the modulation ratio defined by PWM and φ is phase angle defined by the PWM. From Fig. 2:
that:
Substituting Eq. 6 into Eq. 9 gives:
From the above, it can be shown that I_{Loq} and I_{Lod} equations are written as:
Transmission line model: It is possible to model a short transmission
line as a constant resistance and reactance. The dynamic model of transmission
line presented by Park model is for Fig. 1 as:
And the model can also be expressed for Fig. 2 as:
The relationship between stator currents and flux linkages of quadrate and
direct axes components are written as (Rahim and BaberAbbas,
2007):
Linearized model: In the design of electromechanical mode damping controllers, the linearized incremental model around a nominal operation point is usually employed. Linearizing the expressions of V_{sqm} and V_{dsm} and substituting into the linear form of (1)(11) yield the following lineraized model for SVC:
And for STATCOM expressed as:
In short:
where, A and B are constant linearization matrices and C represents the relation between state vector and the chosen output.
DESIGN OF CONTROLLER
In this study, PI controller is used to control the thyristor firing angle
(α) of SVC or phase angle (φ) of STATCOM. α (or φ) adjust
according to variation in terminal voltage v_{t} and angular speed ω.
The block diagram of SVC and STATCOM controllers is shown in Fig.
3. The PI controllers are normally located in the feedback route. An extra
washout block is embraced in series with the controller to remove any undesirable
signal in the steady state (Rahim and BaberAbbas, 2007).
The function of controller in the feedback loop is composed as a pole placement
method was used to specify perfect gain settings, K_{P} and K_{I}
of the controller. The control signal from the PI can be represented by:
It is easy to see that the characteristic equation of the close loop system is:
If λ is the system eigen value to be assigned, we have:
Assume that the value of T_{ω} is given, we need to assign a pair
of eigen values to obtain the values of K_{P} and K_{I} (Hedayati,
2002):

Fig. 3: 
PI controller configuration of SVC and STATCOM 
SIMULATION RESULTS
Study of different shunt FACTS effects: The results of simulation for starting of induction motor in MATLAB programme are shown on Fig. 4 and 5. Figure 4 displays the rotor speed of the motor and Fig. 5 shows the terminal voltage of the motor for three cases: without any compensator, using SVC and using STATCOM model based on Fig. 1 and 2. The values of K_{P} and K_{I} are 50 and 0.00145, respectively. The parameters of the system are given in Appendix B. It is clear that the time of motor speeding up is lower when the STATCOM is used; besides the dip of voltage without using any compensator is almost 20%; using SVC the voltage profile is improved and declined around 10%. With utilization the STATCOM, voltage dip is decreased considerably less than 5%.
Power quality problem: Power quality context that influence the dynamic
behavior of induction motor, include non ideal conditions such as harmonics,
interruptions, voltage unbalance and voltage sags. Between these conditions,
the voltage sags and short interruptions are very important because the voltage
sags are the main cause of disturbances in distribution systems (Gomez
and Morcos, 2002).

Fig. 4: 
Rotor speed of motor under ideal supply condition 

Fig. 5: 
Terminal voltage of motor under ideal supply condition 
Table 1: 
Definition of symmetrical and unsymmetrical voltage sags 


Fig. 6: 
Terminal voltage of motor under symmetrical voltage sag without
compensator 
Voltage sags (or voltage dips) are unexpected reduction on the rms voltage
that may lead to deficiency or crashing of responsive equipment frequently used
in industrial applications (Bollen, 2000; Juarez
et al., 2009). On the other hand, voltage sag is defined as decreasing
in rms supply voltage between 0.1 and 0.9 p.u. with duration of 0.5 cycles to
1 min (Dugan et al., 1996).
Due to dissimilar types of faults in power systems, dissimilar types of voltage
sag can be constructed. Different kinds of connection of transformers in power
grid will produce different types of voltage sags. Voltage sags are divided
to seven categories; but one type is symmetrical and between other types that
are known unsymmetrical voltage sags, one type has the serious effect on the
performance of the system (Guasch et al., 2004).
Table 1 shows the definition of the symmetrical and unsymmetrical
voltage sags.
The effects of SVC and STATCOM on dynamic performances of starting of induction
motor under symmetrical voltage sag are specified on Fig. 6.
The duration of voltage sag is 0.2 sec, starting at t_{onsag} = 4.5
sec and stopping at t_{offsag} =4.7 sec. Sag magnitude is 90% (h =
0.1). Figure 6 shows the terminal voltage of motor without
compensator, so Fig. 7 and 8 display the
voltage of terminal using the SVC and STATCOM respectively. It is shown that
the transient of voltage after stopping the voltage sag is lower with applying
of shunt FACTS. Utilization of STATCOM is very effectual, because the transient
of voltage is remarkably receded and the profile of voltage has better dynamic
performance.

Fig. 7: 
Terminal voltage of motor under symmetrical voltage sag with
SVC 

Fig. 8: 
Terminal voltage of motor under symmetrical voltage sag with
STATCOM 

Fig. 9: 
Terminal voltage of motor under unsymmetrical voltage sag
without compensator 
Figure 9 shows the terminal voltage of motor without using
any compensator. Figure 10 and 11 display
the terminal voltage of motor with SVC and STATCOM when unsymmetrical voltage
sag is applied. Lower voltage transients and better dynamic behavior is observed
when using STATCOM over SVC.

Fig. 10: 
Terminal voltage of motor under unsymmetrical voltage sag
with SVC 

Fig. 11: 
Terminal voltage of motor under unsymmetrical voltage sag
with STATCOM 
CONCLUSION
In this study, the application o shunt FACTS installed on terminals of induction motor are presented and compared together. The results of simulations show that these devices are useful for increasing motor speeding up and getting better voltage profile. Computer test results prove this point that STATCOM is more effectual than SVC for compensation disturbances and improving dynamic behavior of large induction motor under ideal supply condition. Whereas voltage sags is one of the most conventional power quality contexts in power systems, the performances of the system under symmetrical and unsymmetrical voltage sags are investigated. The results show that utilization of STATCOM is considerably forceful and is more suitable than SVC for decreasing transients and amending the voltage profile.
APPENDIX A: NOMENCLATURE
X_{L} 
= 
Transmission line reactance 
R_{L} 
= 
Transmission line resistance 
X_{SDT} 
= 
Leakage Reactance of step down Transformer 
X_{ls}, X'_{lr} 
= 
Leakage reactance of the stator and rotor windings 
X_{M} 
= 
Magnetizing reactance of the windings 
R_{S}, R'_{r} 
= 
Resistance of stator and rotor windings 
H_{M}, D 
= 
Inertia and damping coefficients 
J_{M} 
= 
Inertia of rotor 
ω_{b}, ω_{d} 
= 
Base electrical angular velocity, reference frame speed 
ω_{rm} 
= 
Rotor angular velocity 
ψ_{qsm}, ψ_{dsm} 
= 
Flux linkages of stator along qd axes 
ψ_{qrm}, ψ_{drm} 
= 
Flux linkages of Armature along qd axes 
V_{qsm}, V_{dsm} 
= 
Stator voltages in qd axes 
V'_{qsm}, V'_{dsm} 
= 
Armature voltages in qd axes 
P_{m} 
= 
Number of poles 
P_{B} 
= 
Base rated power 
T_{em}, T_{LM} 
= 
Electromagnetic torque, Load torque 
i_{qsm}, i_{dsm} 
= 
Stator currents along qd axes 
i_{Lq}, i_{Ld} 
= 
Quadrate and direct axes components of inductance branch of SVC current 
i_{Cq}, i_{Cd} 
= 
Quadrate and direct axes components of capacitance branch of SVC current 
i_{Loq}, i_{Lod} 
= 
Quadrate and direct axes components of STATCOM current I_{Lo} 
V_{q∞}, V_{d∞} 
= 
Infinite bus voltage along qd axes 
V_{M} 
= 
STATCOM bus voltage 
APPENDIX B
Parameters of Drive system and Induction motor for comparing SVC and VSI: V_{lineline} = 575 v, 200 Hp, f = 60 Hz, Rs = 0.011 (p.u), R’r = 0.006(p.u), Xls = 0.0048 (p.u), X’lr = 0.00483 (pu), XM = 2.424 (p.u), J = 2.6 (kg.m^ 2), P = 4
Parameters of induction motor for comparing SVC and STATCOM:
V_{lineline} = 2300 v, 2250 Hp, f = 60 Hz,
Rs = 0.00919 (p.u), R’r = 0.00697 (p.u),
Xls = . 0.0716 (p.u), X’lr = 0.0716 (p.u), XM = 4.13 (p.u), J = 63.87 (kg.m^2),
P = 4
Parameters of transmission line: x_{L} = 0.04 (p.u), R_{L} = 0
Parameters of SVC and STATCOM: Xc = 0.5 (p.u), Xin = 0.335 (p.u), C = 1, x_{SDT} = 0.025(p.u), V_{DC0} = 1,
Parameters of PI controller: K_{P} = 50, K_{I} = 0.00145, T_{W} = 0.008.