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Titre: Impact of static synchronous compensator on the stability of a wind farm: Case study of wind farm in Tunisia
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WIE0010.1177/0309524X16671193Wind EngineeringKaroui et al.
Impact of static synchronous
compensator on the stability of
a wind farm: Case study of wind
farm in Tunisia
© The Author(s) 2016
Reprints and permissions:
Ridha Karoui1, Abdelkarim Aouiti2, Maha Zoghlami2
and Faouzi Bacha2
The static synchronous compensator is one of the FACTS (Flexible Alternating Current Transmission System) device capable of
maintaining the stability of wind turbines during a sudden default. Among these faults, the voltage drops at the connection bus wind
turbines. For this fault case, the static synchronous compensator intervenes by injection of the reactive power to compensate the
voltage drop. In this article, as application case, we study the wind farm of Bizerte (north of Tunisia). This farm is composed of fixed
speed aero-generators using squirrel cage induction generators. Our study begins with modeling the wind system. Next, we describe
the technical requirements for connection of a wind energy system to the grid and outfit at the voltage dips (low-voltage ride through)
according to STEG (Tunisian Company of Electricity and Gas). We also present the structure of static synchronous compensator.
Finally, we present the simulation results of the wind farm under low-voltage ride through with and without static synchronous
Wind farm, asynchronous generator, voltage control, grid code, static synchronous compensator
The wind energy has now become one of the sources of energy that finds an important place in the electrical networks for
many countries of the world, particularly in Europe and China. These energy sources are submitted as for the case of conventional sources to several types of disturbances, particularly the sudden variation of the voltage at the connection bus.
The persistence and severity of these variations can cause the disconnection of these sources (action protection system). In
such cases, we can attend to an imbalance of energy balance (if power generated by the wind farm is important) that can
spread into the grid and causes a collapse of the voltage. To not be in such a situation, it is essential to use devices that are
capable of rapidly reducing these variations and thus preserve the continuity of the power system operation. These devices
are the FACTS (Flexible Alternating Current Transmission System) based on power electronics. Among these devices,
the static synchronous compensator (STATCOM), also known as the static synchronous condenser, is a regulating device
used on alternating current electricity transmission networks. It allows to stabilize the voltage by injection/absorption of
the reactive power. Many authors have studied the impact of STATCOM controllers on the voltage at the connection bus
of the wind farm (Patel et al., 2012; Qiao et al., 2008; Tahrani and Bandaghiri, 2014).
In this article, we study the impact of a STATCOM on Bizerte wind farm (north of Tunisia) (Kardous et al., 2013;
Kumar et al., 2013). This wind farm uses fixed speed wind turbines based on squirrel cage induction generators (SCIG)
directly connected to grid via a soft start system.
Laboratory for Industrial Systems (LISI), National Institute of Applied Sciences and Technology (INSAT), University of Carthage, Tunis,
2Computer Laboratory for Industrial Systems (LISI), Tunis University, Tunis, Tunisia
Ridha Karoui, Computer Laboratory for Industrial Systems (LISI), National Institute of Applied Sciences and Technology (INSAT), University of
Carthage, Zone urbaine Nord, BP 676, Tunis 1080, Tunisia.
The remaining of this article is organized as follows. Section “Presentation of the wind farm of Bizerte” begins with a
representation of the wind farm of Bizerte and then the modeling of wind system; thereafter, we represented the technical
requirements of wind generator connection and held to the voltage dips (low-voltage ride through (LVRT)) according to
STEG (Tunisian Company of Electricity and Gas). In section “STATCOM modeling and control,” we describe a simple
structure of a STATCOM, its equivalent circuit, and its control system. Section “Simulation results” is dedicated to the
simulation results which are performed under MATLAB/SIMULINK software. Finally, we finish this work by a conclusion.
Presentation of the wind farm of Bizerte
The wind farm of Bizerte (north of the country) is spread over two sites (Metline and Kchabta). This farm has been operational since end of 2012. The climate in this region is Mediterranean. The annual average wind speed is between 7 and
10 m/s. Prevailing winds are from west to northwest and windiest seasons are in winter and spring (Figure 1).
Figure 1. Tunisia wind farm location (Ounissa et al., 2013).
Wind turbines of wind farm Bizerte are of AE61 type manufactured by the Spanish company MADE. This type of wind
turbine is based on induction machines. These two plants have a total capacity of 190 MW, and they are performed in two
steps as follows (Kardous et al., 2013; Patel et al., 2012) (Figure 2):
Figure 2. Connection system of wind farm to network.
Karoui et al.
•• Step 1. Begin in 2011 (120 MW)
•• Step 2. Begin in 2012 (70 MW)
The power supplied by each site is as follows:
•• Metline: 72 WT type AE61 (1320 KW) ⇒ 95.04 MW
•• Kchabta: 71 WT type AE61 (1320 KW) ⇒ 93.72 MW
Wind turbine model
Our work is based on the use of fixed speed wind turbines whose production systems are SCIGs. The advantage of this
wind turbine is its robustness and electrical simplicity. The rotor speed of generator is fixed independently of the wind
speed and it is determined by the frequency imposed by the electrical grid, the gear ratio, and generator conception
(Boubekeur et al., 2013). The machine magnetization is ensured by a capacitor battery. The disadvantage of these generators is that the power exchanged with the electrical grid is not controllable (Figure 3).
Figure 3. Structure of the fixed speed wind turbine connected to the grid.
The mechanical power on the wind turbine shaft is a function of the wind speed vw and the performance coefficient C p
3 C (λ , β )
Pt = ρ π R 2 vw
where β is the pitch angle and λ is the tip–speed ratio whose expression is as follows
where Ωt is the velocity of turbine (blades) and R is the radius of the turbine blades. The performance coefficient is
C p (λ , β ) = 0.5176 116 −0.4 β −5 e Λ + 0.0068λ (3)
λ + 0.08β β 3 + 1
The developed torque by the turbine is given by the following expression
Tt = t (5)
For the fixed speed wind turbine, the tip–speed ratio is at its optimum value λopt corresponding to the maximum performance coefficient C p max of wind turbine for any wind speed. Figure 4 gives the power coefficient variation under tip
ratio and pitch angle variation.
Figure 4. Aerodynamic performance coefficient variation C p against tip–speed ratio λ and pitch angle β .
The maximum performance coefficient ( C p max = 0.48 ) corresponds to pitch angle β = 0° and λnom = λopt 8.1
The voltage equations for the stator and rotor of the generator in the arbitrary reference frame and in per unit system is
= Rs ids − ϕqs +
= Rs iqs + ϕds +
1 d ϕds
1 d ϕdr
= Rr idr − s.ϕqr +
= Rr iqr + s.ϕdr +
where ( ϕds , ϕqs ) and ( ϕdr , ϕqr ) are, respectively, the stator and rotor flux. Their expressions are given as follows
= Ls ids + Lsr idr
= Ls iqs + Lsr iqr
= Lr idr + Lsr idr (7)
= Lr iqr + Lsr iqs
where Ls and Lr are the cyclic inductances of stator and rotor, respectively; Lsr is the cyclic mutual inductance of the
stator to rotor; and s is the slip of the induction machine.
The electromechanical torque developed by the asynchronous machine in per unit system is given by the following
Te = (ϕds iqs − ϕqs ids ) (8)
The mechanical equations are as follows
(Tm − Te )
s = 1 − ω
Karoui et al.
Figure 5. Torque–speed characteristics of an induction machine.
where ωr is the rotor speed in pu, Tm is the mechanical torque in pu, Te is the electromagnetic torque in pu, H is the
combined inertia constant of the wind turbine generator (WTG) system in seconds, and s is the slip in pu.
The operating point of the induction generator is obtained when the mechanical torque intersects the electrical torque
curve. In this point, the two torques are equal and we can write
− Te ) = 0 ⇒ ωr =Cst
The power generated by the induction generator is then
Ps = Te Ω r = Tm Ω r (11)
During a voltage drop at the terminals of the generator, the mechanical torque Tm is practically unchanged, but the
electrical torque will be reduced since it is proportional to the square of terminal voltage. This means that the resulted
overspeed is a function of the inertia constant H of the generator, the duration of the fault, and the severity of the fault.
If the voltage is not restored quickly, the over-speed protection system (related to voltage drop) is activated and the wind
turbines would be disconnected from the grid thus causing an energy imbalance and the instability of the power system.
To stabilize the voltage variation and maintain the wind farm connected to the network, an alternative is to use a static
compensator of reactive power as the STATCOM.
Figure 5 shows the characteristics of the electrical and mechanical torque as a function of the rotor speed in the steady
state for nominal voltage and during a voltage drop.
We noted a right shift of operating point which is caused by the acceleration of the rotation speed of the rotor.
Critical time of stability of the induction generator
During the occurrence of short circuits in the network, induction generators tend to accelerate and there exists a critical
point corresponding to a critical velocity and critical time after which the system is destabilized (Kanabar and Khaparde,
The large disturbance stability of an induction generator can be determined by analyzing the response in the time of the
rotor speed after the short-circuit application.
By integrating the mechanical equation (9), we get
Figure 6. Steady-state equivalent circuit of an induction generator: (a) complete circuit and (b) reduced circuit.
Tm − T e
It has been assumed that during the fault, Te − Tm remains approximately constant, and we will have
(ωcri − ω0 ) (13)
Te − Tm
where tcri is the critical clearing time, ω0 is the initial rotor speed (before fault), and ωcri is the critical rotor speed (during the fault).
If the fault duration is longer and not cleared before time t = tcri , the rotor speed ( ωr ) reaches a speed greater than ωcri .
If the fault is not eliminated, the operating point will move more to the right (Figure 5), then ωr will continue to increase,
making the system unstable (Kanabar and Khaparde, 2008) and the wind farm can be disconnected from the network
under the action of security system.
Starting from the equation that links the slip to the rotor speed (equation (9)), we can write
ω0 = 1 − s0
ωcri = 1 − scri
To calculate basic and critical slip value, we will use a simple system consisting of an induction generator directly connected to an infinite bus (without capacitor bank and coupling transformer) represented in Figure 6.
From Figure 6(a), we will give the Thevenin equivalent circuit seen from the rotor
V Th =
Zm + Zs
Z Th = Z + Z = RTh + jX Th
where Z m = jX m and Z s = Rs + jX s , with Z eq = Z Th + Z r .
Karoui et al.
Figure 7. Voltage profile according to the requirements of LVRT capability of wind turbine connected to the grid.
The rotor’s current magnitude is as follows
( RTh + Rr / s ) 2 + ( X Th + X r ) 2
The electrical torque Te can be calculated by
Rr / s
( RTh + Rr / s ) + ( X Th + X r )
The stable and unstable equilibrium points can be determined by making Te = Tm . Thus, we have
+ ( X Th r + X r ) 2 ) s 2 + Rr (2 RTh − VTh2 / Tm ) s + Rr2 = 0 (18)
Equation (18) can be written as
a s 2 + b s + c = 0 (19)
The resolution of equation (19) allows us to find the value of the initial speed of the rotor (before fault) and the critical
speed during fault.
ω0 = 1 −
ω = 1 − b + ∆
Requirements during the voltage drop
The technical requirement of the connection of wind generators to the grid is the capability to remain connected to the grid
under voltage dips (LVRT) (Malia et al., 2013). The grid code requires that wind farms must be able to stay connected to
the network during a voltage dip. Figure 7 shows the shape of a voltage dip according to STEG, December 2015.
The technical requirements according to STEG are given in Table 1, where the normal and abnormal voltages with
maximum operating periods are given.
The voltage regulation in a wind power plant can be carried out by the generating unit (pitch control) or by means of
other equipment added to the plant by the power company (e.g. static VAR compensator [SVC] and STATCOM). In all
cases, the supplied voltage performance by a wind power plant control must be similar to that of a power plant of the same
capacity equipped with conventional synchronous generators.
Table 1. Normal and abnormal voltage ranges.
Maximum operating period
Figure 8. STATCOM connection.
STATCOM modeling and control
The STATCOM belongs to the family of FACTS that are developed to maintain the voltage within acceptable limits and to
limit the reactive power flows. It is a shunt compensator composed of a voltage-sourced converter (VSC) based on power
electronic devices (gate turn-off thyristors [GTOs], insulated gate bipolar transistors [IGBTs], integrated gate-commutated
thyristors [IGCTs], etc.) and a capacitor as a DC power source. Figure 8 gives the STATCOM connection to the grid.
The STATCOM generates a three-phase alternating voltage in phase with the grid voltage from a DC voltage source
by generation/absorption of reactive power (Boubekeur et al., 2013; Ounissa et al., 2013). The amplitude of the generated
voltage is controllable (by controlling the state of switches) in order to adjust the amount of reactive power exchanged
with the grid.
The STATCOM is seen as an adjustable voltage source behind a reactance. Figure 9 gives the equivalent circuit of the
The transfer of the reactive power (Figure 9) is between the grid (connection bus) and the STATCOM. V t is the voltage
to be controlled and Vsh is the voltage generated by the STATCOM. The power relations are described by the following
expression (Mineski et al., 2004; Patel et al., 2012; Tahrani and Bandaghiri, 2014)
Vt Vsh sin(δ )
Vt (Vt − Vsh cos(δ ))
where δ = θ S − θ sh , phase shift angle is between V sh and V S , and X t is the equivalent reactance of the transformer.
The STATCOM should not exchange the active power with the grid. According to this hypothesis, the voltage delivered
by the STATCOM must be in phase with the voltage of connection bus that allows us to write
θt − θ sh = 0 ⇒ Psh =
Vt Vsh sin(δ )
= 0 (22)
Karoui et al.
Figure 9. Equivalent circuit of STATCOM.
Assuming that Vsh voltage is on the axis “d” =
and Vshd V=
sh ; Vshq 0
We also have
V − Vt
I sh = I shq = sh
Reactive power is given by the following equation
Qsh = Vsh I shq = sh
Using equation (24), we can distinguish the three modes of STATCOM operation (Ounissa et al., 2013; Tahrani and
•• Vsh = VS ⇒ Qsh = 0: no energy transfer (stabilized voltage).
•• Vsh > VS and Qsh > 0: the STATCOM operates in capacitive mode and provides reactive power to the grid (case of
a voltage drop).
•• Vsh < VS and Qsh < 0: the STATCOM operates in inductive mode and absorbs reactive power from the network
(case of a voltage boost).
The more efficient method of controlling the STATCOM is by the synchronous reference frame strategy, which uses
ordinate transformations to generate the current reference. It uses the Clarke and Park transformation, well known for this
purpose (Figure 10). The control is based on discrete pulse width modulation (PWM) and requires the measurement of
the terminal voltage of wind farm, the AC current, and the DC voltage of the STATCOM. The phase-locked loops (PLL)
allow synchronizing the positive sequence component of the three-phase primary voltage Vt . The direct and inverse axis
components of the three-phase voltages and current are Vd , Vq , id , and iq , computed using the d–q transformation. The
outputs of the VRMS voltage regulator and Vdc voltage regulator (namely, id∗ and iq∗ ) act as reference currents for the current regulator. The inner loop of regulation is based on the control of the magnitude and phase of the voltage generated
by the PWM converter.
The current loops are performed on the three phases, whose outputs provide the voltage command values Vabc
PWM converter. Figure 11 shows the block diagram of the current control in closed loop.
As an application, we simulate the impact of STATCOM on the wind farm of Bizerte (north of Tunisia). This wind farm
is distributed over two sites (Metline and Kchabta) and composed of fixed-speed wind turbine based on squirrel cage
induction generators (SCIG) (Kardous et al., 2013). Our study is localized on part of wind farm composed of seven wind
Figure 10. STATCOM control block.
Figure 11. Current control loop.
Figure 12. System diagram on MATLAB/SIMULINK.
turbines connected to the bus voltage (30 kV). This part is related to the transformer (30/90 kV) by an underground cable
of length 0.84 km (see Appendix I). The nominal power generated by these turbines is 10 MW for a nominal wind speed
16 m/s (Kumar et al., 2013).
The STATCOM is connected to the common bus of wind turbines. Figure 12 shows the implantation of our system
under MATLAB/SIMULINK software (Malarvizhi and Baskaran, 2010; Patel et al., 2012).
In what follows, we will proceed to simulations with and without STATCOM for a voltage drop.
Karoui et al.
Voltage at the connection bus of wind farm
Figure 13 shows the voltage level at the point of connection of wind turbines with and without STATCOM (no fault).
The STATCOM always tends to maintain the voltage at the reference value 1 pu ( Vref ) at the connection bus of the
Figure 13. Voltage at the connection bus of wind turbines with and without STATCOM.
(Figure 14. Continued)
Figure 14. Simulation with and without STATCOM.
Simulation of a voltage drop with and without STATCOM
We have applied a voltage drop (−0.2 pu) during 0.5 s (5–5.5 s) and then two successive voltage drops during 0.8 s (−0.2
and −0.15 pu) to the bus level 90 kV.
Figure 14 shows the simulation results of some mechanical and electric variables of studied system with and without
During the voltage drop in the connection bus of wind farm, the electrical and mechanical variables of the wind system
have changed (reduction in active power, increase in current, and acceleration the rotors of wind turbines). The acceleration of the rotor speed of generators due to the voltage drop may cause the disconnection of the wind farm if the fault is
not eliminated in a time required by the network code and we can have an unstable power system.
The STATCOM, by its contribution in reactive energy, contributed to maintaining of the voltage at a level near to the
equilibrium value; consequently, the stability of the various variables and in particular the speeds of the rotors of the wind
turbines allows maintaining the wind turbines connected to the grid, thereby avoiding the imbalance of electrical grid.
This article shows the effect of a voltage drop (to the connection node) on electrical and mechanical variables of a wind
farm, particularly the rotor speed of induction generator. The duration and severity of the voltage drop may cause disconnection of the wind farm which can cause energy imbalance of power system. To stabilize the wind turbines, a system
FACTS based on power electronics is used. This system is the STATCOM which is a static compensator for reactive
power. By injection of reactive power, the STATCOM helps to stabilize a voltage at a relatively constant value. It can
avoid disconnection of a wind farm. It was shown by simulation results that the voltage at the connection bus between
wind farm and the grid fluctuated less in the presence of a STATCOM; therefore, the rotor speed of wind turbines maintains near values of their initial value before fault.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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Table 2. Wind turbine parameters.
Nominal wind speed
Wind turbine bus voltage
Stator leakage reactance
Rotor leakage Reactance
ν n (m/s)
x s (pu)
x r (pu)
X m (pu)
Table 3. Transformer parameters.
Primary leakage inductance
Secondary leakage inductance
Résistance of Iron losses transformer
T (MV) (0.69/30 kV)
T (HV) (30/90 kV)
Table 4. Line parameters.
Line resistance BT
Line reactance BT
Line resistance HT
Line reactance HT
Line section length
X MV (H/Km)
X HV (H/km)
Table 5. Characteristic parameters of STATCOM.
DC link nominal voltage