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Critical Clearing Time and Transient Stability
Analysis of SCIG based Wind Farm
P.Sravanthi, K. Radha Rani, Dr. J. Amarnath, Dr. S.Kamakshaiah
Abstract—In recent years generation of electricity using wind
power has received considerable attention worldwide. Induction
machines are mostly used as generators in wind power based
generations. Since induction machines have a stability problem
as they draw very large reactive currents during fault condition,
reactive power compensation can be provided to improve
stability. This paper deals with the Impact of STATCOM on the
Wind Farm performance. The essential feature of the
STATCOM is that it has the ability to absorb or inject fastly the
reactive power with power grid entirely by means of electronic
processing of the voltage and current waveforms in a voltage
source converter (VSC). This function is identical to the
synchronous condenser with rotating mass. In the present work
transient stability improvement and critical clearing time(CCT)
analysis using STATCOM under faults is proposed.
Improvement of transient stability with and without STATCOM
and reactive power injection by STATCOM is studied.
Simulation results are given, commented and discussed. The test
results prove the effectiveness of the proposed STATCOM
controller in terms of fast damping the power system oscillations
and restoring the power system stability.
Index Terms-- Transient Stability, Critical Clearing Time,
Active Power, Reactive Power, FACTS, STATCOM and Wind

ith the increase in demand of power and decrease of
fossil fuels, mankind has been forced to search
alternative sources for the generation of electricity[1].
Nowadays wind as a significant proportion of non-pollutant
energy generation, is widely used[2]. Wind power in spite of
being stochastic in nature has proved itself as a viable solution
to this problem. As the wind turbine technology is developing
at a good pace, more and more wind power plants are being
integrated with the conventional form of generation.
With the increase in the ratio of wind generation to
conventional generation, several problems related with
integration of wind farms have emerged[1]. In addition, power
transmission and distribution systems face increasing demands
for more power, better quality and higher reliability at lower
cost, as well as low environmental effect. Under these
conditions, transmission networks are called upon to operate
at high transmission levels, and thus power engineers have
had to confront some major operating problems such as
transient stability, damping of oscillations and voltage
regulation etc [3].These problems are due to distinct properties
of the generators used with the conventional form (Thermal &
Hydro) of generation and wind based generation. In thermal
and hydro power based generation synchronous generators are


used while in wind based generation mostly induction
generators are used[1].
One of the simple methods of running a wind generating
system is to use the induction generator connected directly to
the grid system The induction generator has inherent
advantages of cost effectiveness and robustness. However
induction generators require reactive power for magnetization.
When the generated active power of an induction generator is
varied due to wind, absorbed reactive power and terminal
voltage of an induction generator can be significantly affected
Flexible AC Transmission Systems are represented by a
group of power electronic devices. This technology was
developed to perform the same functions as traditional power
system controllers such as transformer tap changers, phase
shifting transformers, passive reactive compensators,
synchronous condensers, etc. Particularly FACTS devices
allow controlling all parameters that determine active and
reactive power transmission, nodal voltages magnitudes,
phase angles and line reactance. Replacement of the
mechanical switches by semi conductor switches allowed
much faster response times without the need for limiting
number of control actions. However, FACTS technology is
much more expensive from the mechanical one. FACTS
devices can be divided into two generations. Older generation
bases on the thyristor valve, where newer uses Voltage Source
Converters (VSC)[5].
Flexible AC Transmission Systems (FACTS) are used
extensively in power systems because of their ability to
provide flexible power control. Examples of such devices are
the Static Synchronous Compensator (STATCOM) and the
Unified Power Flow Controller (UPFC). STATCOM is
preferred in wind farms due to its ability to provide bus bar
voltage support either by supplying and/or absorbing reactive
power in to the system[6].
A. Squirrel Cage Induction Generator
The fixed speed wind generator systems have been used
with a multiple-stage gearbox and a SCIG directly connected
to the grid through a transformer. Therefore, rotor speed
variations are very small, because the only speed variations
that can occur are changes in the rotor slip, because the
operating slip variation is generally less than 1%, this type of
wind generation is normally referred to as fixed speed. A
SCIG consumes reactive power. Therefore, in case of large

978-1-4799-4103-2/14/$31.00©2014 IEEE

wind turbines and/or weak grids, often capacitors are added to
generate the induction generator magnetizing current, thus
improving the power factor of the system as a whole. The slip
is generally considered positive in the motor operation mode
and negative in the generator mode. In both operation modes,
higher rotor slips result in higher current in the rotor and
higher electromechanical power conversion. If the machine is
operated at slips greater than unity by turning it backwards, it
absorbs power without delivering anything out i.e. it works as
a brake[3]
The block diagram of wind turbine induction generator is
shown in Fig 1. The stator winding is connected directly to the
60 HZ grid and the rotor is driven by a variable-pitch wind
turbine. The power captured by the wind turbine is converted
into electrical power by the induction generator and is
transmitted to the grid by the stator winding. The pitch angle
is controlled in order to limit the generator output power to its
nominal value for high wind speeds. In order to generate
power the induction generator speed must be slightly above
the synchronous speed. The pitch angle controller regulates
the wind turbine blade pitch angle β, according to the wind
speed variations. A Proportional-Integral (PI) controller is
used to control the blade pitch angle in order to limit the
electric output power to the nominal mechanical power. The
pitch angle is kept constant at zero degree when the measured
electric output power is under its nominal value. When it
increases above its nominal value the PI controller increases
the pitch angle to bring back the measured power to its
nominal value. The pitch angle control system is illustrated in
the Fig 2.[7]

turbine is aggregated with these quantities of the electric
generator coupled with the turbine [3].

Here Pm= mechanical power developed by the wind
turbine, Cp= power coefficient of the turbine, ρ is the density
of air striking the turbine blades (kg/m3, A is the swept area of
the rotor blades of the turbine (m2), λ is the tip-speed ratio, β
is the pitch angle (degrees)[1] ,[2], [3], [7], [8].

The relation between Cp, β and λ is shown in Fig 3.

Fig. 3. Aerodynamic power coefficient variation Cp_ against tip speedratio λ
and pitch angle β.

B. Induction Machine
In the present study, the electrical part of the machine is
represented by a fourth-order state-space model and the
mechanical part by a second-order system. All electrical
variables and parameters are referred to the stator. All stator
and rotor quantities are in the arbitrary two-axis reference
frame (d-q frame).
Fig. 1. Wind Turbine Induction Generator

Fig. 2. Control System for pitch angle control

The model of wind turbine used for the purpose of
simulation is a per unit model based on the steady state power
equation of a wind turbine. The gear train used for coupling
the generator with the grid is assumed to have infinite stiffness
while the friction factor component and the inertia of the

Shunt compensators are primarily used for bus voltage
regulation by means of providing or absorbing reactive power.
They are effective for damping electromechanical oscillations.
Different kinds of shunt compensators are currently being
used in power systems, of which the most popular ones are
Static Var Compensator SVC and STATCOM . In this work,
only the STATCOM, which has a more complicated topology
than SVC, is studied. Static Synchronous Compensator
(STATCOM) is a shunt controller mainly used to regulate
voltage by generating/absorbing reactive power. The
schematic diagram of STATCOM is shown in Fig 4.

transformer and VSC losses and to keep the capacitor
B. V-I Characteristics of STATCOM


A. Operating Principle of STATCOM
Fig. 6. V-I Characteristics of STATCOM

Fig. 5. Operating Principle of STATCOM

The resulting STATCOM can inject or absorb reactive
power to or from the bus to which it is connected and thus
regulate bus voltage magnitudes. The main advantage of a
STATCOM over SVC is its reduced size, which results from
the elimination of ac capacitor banks and reactors; moreover,
STATCOM response is about 10 times faster than that of SVC
due to its turn-on and turn-off capabilities. The active and
reactive power exchange between the VSC and the system is
shown in Fig 5 are a function of the converter output voltage
denoted as Vout, i.e,

V1=line to line voltage of source V1
V2=line to line voltage of V2
X=Reactance of interconnection Transformer and filters
δ= angle of V1 with respect to V2
In steady state operation, the voltage V2 generated by the
VSC is in phase with V1 (=0), so that only reactive power is
flowing (P=0). If V2 is lower than V1, Q is flowing from V1
to V2 (STATCOM is absorbing reactive power).
On the reverse, if V2 is higher than V1, Q is flowing from
V2 to V1 (STATCOM is generating reactive power). The
amount of reactive power is given by
A capacitor connected on the DC side of the VSC acts as a
DC voltage source. In steady state the voltage V2 has to be
phase shifted slightly behind V1 in order to compensate for

As long as the reactive current stays within the minimum
and minimum current values (-Imax, Imax) imposed by the
converter rating, the voltage is regulated at the reference
voltage Vref. However, a voltage droop is normally used
(usually between 1% and 4% at maximum reactive power
output), and the V-I characteristic has the slope indicated in
the fig 6. In the voltage regulation mode, the V-I characteristic
is described by the following equation:
V=Vref + Xs I
Where V : Positive Sequence Voltage (pu)
I : Reactive Current (I>0 indicates an Inductive Current)
Xs: Slope or Droop Reactance[9]
The following definitions from[8] provide the foundation
for transient stability and small-signal stability analysis.
1) Disturbance in a Power System. A disturbance in a
power system is a sudden change or a sequence of changes in
one or more of the operating parameters of the system, or in
one or more of the operating quantities.
2) Small Disturbance in a Power System. A small
disturbance is disturbance for which the equations that
describe the dynamics of the power system may be linearized
for the purpose of analysis.
3) Large Disturbance in a Power System. A large
disturbance is a disturbance for which the equations that
describe the dynamics of the power system cannot be
linearized for the purpose of analysis.
4) Steady-State Stability of a Power System. A power
system is steady-state stable for a particular steady-state
operating condition if, following any small disturbance, it
reaches a steady-state operating condition which is identical or
close to the pre-disturbance operating condition. This is also
known as small disturbance stability of a power system.
5) Transient Stability of a Power System. A power system
is transiently stable for a particular steady-state operating
condition and for a particular disturbance if, following that
disturbance, it reaches an acceptable steady-state operating
From the above definitions, one observes that the transient
stability problem encompasses the small-disturbance stability
problem. The transient stability analysis involves more

detailed non linear models, solution techniques, and includes
steady-state stability analysis of the operating condition that
will be reached following the transient. The stability problem
is concerned with the behavior of the synchronous machines
after a disturbance. For convenience of analysis, stability
problems are generally divided into two major categoriessteady state stability and transient state stability[9].
A. Swing Equation
The relative position of the resultant magnetic field axis
and rotor axis is fixed under normal conditions. Power angle
and torque angle are the angle between the two axes. During
disturbance, a relative motion begins because of the
deceleration or acceleration with respect to the synchronously
rotating air gap mmf. Swing equation is the mathematical
structure to describe relative motion.






= P


− P


Runge-Kutta method

The swing equation can be transformed into state variable
form as[9]

= Δω
dΔω πf o

Now apply modified Euler’s method to the above equations
as below



Δω pi +1

δ ip+1

= Δω pi +1, where Δω pi +1 = Δω i +


πf 0

δ ip+1

δ ip+1

dΔ ω

= δi +





Then the average value of the two derivatives is used to
find the corrected values.

Swing equation in terms of inertial constant M ,



Relationship between electrical power angle δ and
mechanical power angle δm and electrical speed &
mechanical speed of synchronous machine ,
Where P is the pole number.
Swing equation in terms of electrical power angle δ :

The transient stability studies involve the determination of
whether or not synchronism is maintained after the machine
has been subjected to severe disturbance. This may be sudden
application of load, loss of generation, loss of large load, or a
fault on the system. In most disturbances, oscillations are of
such magnitude that linearization is not permissible and the
nonlinear swing equation must be solved.
A. Numerical Solution of Swing Equation
The transient stability analysis requires the solution of a
system of coupled non-linear differential equations. In
general, no analytical solution of these equations exists.
However, techniques are available to obtain approximate
solution of such differential equations by numerical methods
and one must therefore resort to numerical computation
techniques commonly known as digital simulation. Some of
the commonly used numerical techniques for the solution of
the swing equation are:
Point by point method
Euler modified method


⎛ dδ
= δi + ⎜⎜
⎝ dt


⎛ dΔω

⎜ dt
p ⎟Δt, Δωi +1 = Δωi +
Δωi ⎟


δi +




B. Point by Point Method
It is always required to know the critical clearing time
corresponding to critical clearing angle so as to design the
operating times of the relay and circuit breaker so that time
taken by them should be less than the critical clearing time for
stable operation of the system.
So the point-by-point method is used for the solution of
critical clearing time associated with critical clearing angle
and also for the solution of multi machine system. The stepby-step or point-by-point method is the conventional,
approximate but proven method. This involves the calculation
of the rotor angle as time is incremented. The accuracy of the
solution depends upon the time increment used in the analysis.
The following parameters are evaluated for each interval (n)
The accelerating power Pa (n-1)=Ps - Pe(n-1)
From the swing equation α(n-1)=Pa(n-1)/M


CCT is defined as maximal fault duration for which the
system remains transiently stable. Mathematically, CCT is a
complex function of pre-fault system conditions(operating
point, topology, system parameters), fault structure (type and
location) and post fault conditions that themselves depend on
the protective relaying plan employed. It would be highly
desirable to define this relation analytically. But, diversity of
variables involved makes this task extremely complicated.
In practice, CCT can be obtained in one of two ways: by
trial and error analysis of system post disturbance equations or
by integrating fault-on equations and checking the value of
Lyapunov energy function until it reaches a previously
determined critical level. For the first approach, many
integration processes are necessary. But, for the second
approach we can evaluate the CCT in just one integration
process. The major problem for the second approach is to find
an analytical energy function which considers a precise model
of generator and the effect of new Flexible AC Transmission
System (FACTS) devices added to improve the transient
behaviour of power system like STATCOM.
The CCT With the continuous increase in the diffusion of
the wind farms in the electric systems is important to be
analyzed.. During severe faults as a three phase fault, the
electromagnetic torque decrease when the mechanical torque
related to wind speed is considered to be constant. In this case
the rotor shaft accelerates; hence it is important to analyze the
speed impact. Critical clearing time CCT and critical speed
The slip factor determines the wind generator stability.
During faults, the increase in slip point at which the
electromagnetic torque corresponds to the same amount as
before disturbance is known as the critical slip. If the
disturbance is cleared beyond the stable point, a continuous
increase in the rotor speed will be encountered whereas, the
electromagnetic torque decreases. In this case runaway slip is
denoted. The time duration starting from the fault time until
the critical slip point is the CCT. Hence the CCT can be
determined from the torque and rotor speed characteristic of
the induction machine. For this purpose, the CCT of a single
induction generator wind turbine was simulated using

Fig. 7. Test System

The first objective of this paper is to evaluate the specific
needs of the system to restore to its initial state as quickly as
possible after fault clearing.
A. Effect of Phase-Phase to Ground Fault on Wind Turbine2
The effect of a phase-Phase to ground fault at Wind
Turbine2 is studied. The ground fault is initiated at t=15s and
cleared at t=15.1s. The system is studied under different
conditions at the load bus as chosen below.

Without Statcom:
Fig 8(a) and 9(a) shows the active and reactive power at the
load bus, it can be seen that the active power curve reached
8.5MW in transient state operation and with the presence of
fault both the curves takes more time to reach stable state of
Fig 10(a) and 11(a) shows the active and reactive power of
each wind turbine. It is clear according to these results that the
active and reactive power of wind farm takes more oscillations
to reach stable state of operation with the appearance of fault.

With Statcom:
According to the previous simulation results, STATCOM
at bus2 is added to view the STATCOM effects.
Fig 8(b) and 9(b) shows the active and reactive power at
the load bus, it can be seen that in both the curves the active
and reactive powers are stabilized faster with less oscillations
compared with the preceding case in the transient state and
even after the fault.
Fig 10(b) and 11(b) shows the active and reactive power
for each wind turbine. According to the simulation results, the
curves presented below shows the importance of the
compensation when the wind farm recovers its operation after
the fault and takes its stability with some oscillation by the
intervention of STATCOM at bus bar 2.

The proposed test system has a wind farm of three wind
turbiness each having two equal wind turbines connected to a
network of 2 bus bars. The type of generator is a Squirrel
Cage Induction Generator(SCIG). Under normal operating
conditions, the wind farm provide 9MW, the bank condenser
used to offer a reactive power to the IG, as presents in the
following Fig 7.

Fig. 8(a). Without STATCOM


Fig. 8(b). With STATCOM
Fig. 8. Active power at 33kv bus2

Fig. 11(b). With STATCOM
Fig. 11. Reactive Power of Wind Farm

B. Effect of Three Phase To Ground Fault on Wind Turbine2

Fig. 9(a). Without STATCOM

Without Statcom:
Fig 12(a) and 13(a) shows the active and reactive power at
the load bus, it can be seen that the active power curve
reached 8.5MW in transient state operation and with the
presence of fault both the curves takes more time to reach
stable state of operation.
Fig 14(a) and 15(a) shows the active and reactive power of
each wind turbine. It is clear according to these results that the
active and reactive power of wind farm takes more oscillations
to reach stable state of operation with the appearance of fault.

Fig. 9(b). With STATCOM
Fig. 9. Reactive power at 33kv bus2

With Statcom:
According to the previous simulation results, STATCOM
at bus2 is added to view the STATCOM effects.
Fig 12(b) and 13(b) shows the active and reactive power at
the load bus, it can be seen that in both the curves the active
and reactive powers are stabilized faster with less oscillations
compared with the preceding case in the transient state and
even after the fault.
Fig 14(b) and 15(b) shows the active and reactive power
for each wind turbine. According to the simulation results, the
curves presented below shows the importance of the
compensation when the wind farm recovers its operation after
the fault and takes its stability with some oscillation by the
intervention of STATCOM at bus bar 2.

Fig. 10(a). Without STATCOM

Fig. 10(b). With STATCOM
Fig. 10. Active Power of Wind Farm

Fig. 12(a). Without STATCOM

Fig. 12(b). With STATCOM
Fig. 12. Active Power at 33kv bus2
Fig. 11(a). Without STATCOM


Fig. 13(a). Without STATCOM

Fig. 13(b). With STATCOM
Fig. 13. Reactive Power at 33kv bus2

Fig. 14(a). Without STATCOM

Fig. 14(b). With STATCOM

C. Transient Stability Criteria
The wind farm delivers 9MW output power at
steady-state. A phase-phase ground fault was induced at wind
turbine2. The STATCOM is disconnected. The simulation
time is 20seconds which is enough to investigate the transient
behavior of the rotor speed.
Fault is induced at t=15sec and the rotor speed is
shown in pu for various fault clearance time t= 15.1 s, 15.4 s
and 15.41 s. Fig. 16(a), (b), (c). Shows the response on the
rotor speed for phase-phase fault induced at the terminal of the
wind turbine2 and cleared for different time. It is obvious
from the Fig. 16(c) at the fault clearing t=15.41s the machine
is unable to remain stable. Thus, the CCT is 0.41seconds.
Above this critical point the rotor will continue to accelerate
indicating a runaway slip. This means that the CCT of an
induction generator can be calculated, which will be useful to
increase the transient stability criteria.

Fig. 16(a). Rotor Speed vs. Time for Fault Clearing Time t=15.1s

Fig. 16(b). Rotor Speed vs. Time for Fault Clearing Time t=15.4s

Fig. 14. Active Power of Wind Farm

Fig. 16(c). Rotor Speed vs. Time for Fault Clearing Time t=15.41s
Fig. 15(a). Without STATCOM

Fig. 15(b). With STATCOM
Fig. 15. Reactive Power of Wind Farm

The simulation is repeated when the STATCOM is
connected in order to investigate its impact on the transient
stability margin.
To observe the effect of the STATCOM on the critical
clearing time (CCT), the STATCOM is connected and the
phase-phase fault was induced at bus2. By investigating the
fault clearing time it is found that when the STATCOM is
connected, the CCT becomes CCT=0.5sec. It is obvious that
the STATCOM had increased the critical clearing time CCT
by 90ms. Hence giving the machine more time to right
through fault and remains connected and re-establish a stable
operating point after the fault is cleared.

power swings damping, voltage regulation, increase of power
transmission and chiefly as a supplier of controllable reactive
power to accelerate voltage recovery after fault occurrence.

Fig. 16(c). Rotor Speed vs. Time for Fault Clearing Time t=15.5s


During fault, the STATCOM have the capacity to control
the reactive power transfer at its terminal. Hence it achieves a
voltage regulation mode. Fig 17. shows the voltage at
STATCOM’s terminal (top) and the reactive power generated
by the STATCOM all along the simulation (bottom).



Fig. 17. Voltage and generated reactive power by STATCOM

FACTS devices are power electronics based reactive
compensators that are connected in a power system and are
capable of improving the power system transient performance
and the quality of supply. In this paper system stability of
SCIG wind farms has been investigated. Power system with
wind farms performance can be improved using FACTS
devices such as STATCOM. The dynamic model of the
studied power system is simulated using Simulink Matlab
package software. Wind farm is compared with and without
the presence of STATCOM under various faults like phasephase to ground fault and three phase to ground fault. Test
system contains three wind farms, each wind farm has two
equal wind turbines. To validate the effect of the STATCOM
controller of power system operation , the system is subjected
to different disturbances such as faults and power operating
Solutions for enhancing transient stability margin or
increasing the CCT were proposed. Simulation results proved
that the SATCOM can increase the CCT. Moreover, the
STATCOM contributed in restoring the voltage to its initial
reference point following a disturbance. However, power
electronics converters that use forced-commutated electronic
devices implemented succeed in controlling the voltage and
the reactive power remarkably.
The digital results prove the powerfulness of the proposed
STATCOM controller in terms of stability improvement,

Rajiv Singh, “Transient Stability Improvement of a FSIG Based Grid
Connected wind Farm with the help of a SVC and a STATCOM:A
Comparison”, International Journal of Computer and Electrical
Engineering, Vol.4, No.1, February 2012.
G. Elsady, “STATCOM for Improved Dynamic Performance of Wind
Farms in Power Grid” , 14th International Middle East Power Systems
Conference (MEPCON’10), Cairo University, Egypt, December 19-21,
Bouhadouza Boubekeur, “Application of STATCOM to Increase
Transient Stability of Wind Farm”, American Journal of Electrical
Power and Energy Systems. Vol. 2, No. 2, 2013.
CH.AppalaNarayana, “Application of STATCOM for Transient
Stability Improvement and Performance Enhancement for a Wind
Turbine Based Induction Generator” , International Journal of Soft
Computing and Engineering (IJSCE) ISSN: 2231-2307, Volume-2,
Issue-6, January 2013.
Naimul Hasan , “ Dynamic Performance Analysis Of DFIG Bases Wind
Farm with Statcom and SVC” ,International Journal of Emerging
Technology and Advanced Engineering.
Valarmathi, “Power Quality Analysis in 6 MW Wind Turbine Using
Static Synchronous Compensator” , American Journal of Applied
Sciences 9 (1): 111-116, 2012.
Pradeep Kumar, “Dynamic Performance of STATCOM on the Induction
Generator based Wind Farm”, International Conference on Global
Scenario in Environment and Energy ICGSEE-2013[14th – 16th March
Amit Garg, “Dynamic Performance Analysis of IG based Wind Farm
with STATCOM and SVC in MATLAB / SIMULINK”, International
Journal of Computer Applications Volume 71– No.23, June 2013.
K. Radha Rani, J. Amarnath, S. Kamakshaiah, “Transient Stability and
Contingency Analysis of Power System in Deregulated Environment” in
International Review on Modelling and Simulations (IREMOS), Vol.4,
N.3, June 2011, pp.1257-1265.
P.Sravanthi has obtained B.Tech degree in Electrical
& Electronics Engineering from Malineni Lakshmaiah
Women’s Engineering college ,Guntur, A.P, India in
the year 2012.She is presently a post graduate student
in Power System Engineering at R.V.R & J.C. College
of Engineering, Guntur, Andhra Pradesh, India.

K. Radha Rani has obtained B.Tech degree in
Electrical & Electronics Engineering from JNTU
College of Engineering, Kakinada, A.P, India in the
year 1998 and Post Graduation M.E. Electrical Power
Engineering from, Vadodara in the year
2001. She has submitted Ph.D. thesis in EE Dept. at
JNTU, Hyderabad and currently associated with
R.V.R&J.C. College of Engineering, Guntur, Andhra Pradesh, India. Her
research interests include power system security and control, FACTS.

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