Electrical Power and Energy Systems 33 (2011) 1172–1184

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Impact of FACTS controllers on the stability of power systems connectedwith doubly fed induction generators

N. Senthil Kumar ⇑, J. GokulakrishnanDepartment of Electrical and Electronics Engineering, B.S. Abdur Rahman University (Formerly B.S.A. Crescent Engineering College), GST Road, Vandalur, Chennai, Tamilnadu, India

a r t i c l e i n f o

Article history:Received 16 April 2008Received in revised form 7 January 2011Accepted 28 January 2011Available online 30 March 2011

Keywords:Wind energy conversion systemsDoubly fed induction generatorsFlexible alternating current transmissionsystemsRotor angle stabilityRotor speed stability

0142-0615/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.ijepes.2011.01.031

⇑ Corresponding author.E-mail address: senthilkumarsaieshwar@gmail.com

a b s t r a c t

The increasing power demand has led to the growth of new technologies that play an integral role inshaping the future energy market. Keeping in view of the environmental constraints, grid connected windturbines are promising in increasing system reliability. This paper presents the impact of FACTS control-lers on the stability of power systems connected with wind energy conversion systems. The wind gener-ator model considered is a variable speed doubly fed induction generator model. The stability assessmentis made first for a three phase short circuit without FACTS controllers in the power network and then withthe FACTS controllers. The dynamic simulation results yield information on (i) the impact of faults on theperformance of induction generators/wind turbines, (ii) transient rating of the FACTS controllers forenhancement of rotor speed stability of induction generators and angle stability of synchronous genera-tors. EUROSTAG is used for executing the dynamic simulations.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction energy capture (ii) improved power quality and (iii) reduced

As power systems became interconnected, areas of generationwere found to be prone to electromechanical oscillations. Theseoscillations have been observed in many power systems world-wide. As the level of power transmission rose, largely throughexisting interconnections, which were becoming relatively weakand inadequate, load characteristics added to the problem causingspontaneous oscillations. The oscillations may be local to a singlegenerator or generator plant (local oscillations, 1.0–2 Hz), or theymay involve a number of generators widely separated geographi-cally (interarea oscillations 0.2–0.8 Hz). If not controlled, theseoscillations may lead to total or partial power interruption [1].Wind energy development is consumer and environment friendly,requires shorter construction time and is cost competitive. It be-comes one of the most competitive sources of renewable energy.However, wind power has some disadvantages. Mostly, wind pow-ered generators are induction generators. The induction generatorabsorbs reactive power during its normal operating condition. Thismay create low voltage and dynamic instability in the system [2].There are two major types of wind generator models, which areused very widely. The first one is the squirrel cage induction gen-erator and the second one doubly fed induction generator. For thepresent work doubly fed induction generator model is used forexecuting dynamic simulations as they possess several advantagesthan fixed speed induction generators which are (i) advanced

ll rights reserved.

(N. Senthil Kumar).

mechanical stress. The dynamic stability of a single wind turbinegenerator supplying an infinite bus through a transmission linewas studied by developing the linearized model of the power sys-tem under different loading conditions [3]. The effect of wind tur-bines on the transient fault behavior of the nordic power systemwas investigated for different faults in [4]. A new definition on ro-tor speed stability of fixed speed induction generators is proposedin [5]. This manuscript examines the dynamic behavior of the dou-bly fed induction generator in line with Ref. [5]. The impact of highwind power penetration on power system oscillation stability isinvestigated in [6]. The effect of wind power on the oscillationsis investigated by gradually replacing the power generated bythe synchronous generators in the system by power from eitherconstant or variable speed turbines.

An efficient reduced order model of DFIG is proposed for rotorand grid side converters for all the four operating modes in [7].The rotor current controller model developed in Ref. [7] is usedto control the DFIG in this paper. The application of voltage sourceconverter (VSC) based transmission controllers for wind energyconversion systems are discussed in [8]. The application of a STAT-COM with battery energy storage to smooth the line power of windfarm consisting of a fixed speed wind farm was discussed in Ref.[9]. The modeling of large offshore wind farms for voltage stabilityanalysis using PSS/E and voltage stability enhancement using SVCwas discussed in [10]. The dynamic behavior of DFIG and the effectof fault ride through of DFIG wind turbines are studied in [11]. Thedynamic behavior of DFIG wind turbines during grid faults issimulated and assessed using the DIgSILENT.

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1173

The objective of the present work is to study the impact ofFACTS controllers on the dynamic performance of the power sys-tem connected with a doubly fed induction generator to the windfarm. The dynamic stability of the system is studied by runningtime domain simulations using the EUROSTAG software [12] withand without FACTS controllers. The following FACTS controllers aretaken up for the dynamic analysis.

(i) Static var compensator (SVC).(ii) Static compensator (STATCOM).

(iii) Thyristor controlled series capacitor (TCSC).(iv) Unified power flow controller (UPFC).

This paper is organized as follows Section 2 presents the mod-eling of power system and wind turbine along with FACTS control-lers. Section 3 presents the dynamic simulation results obtained fora three phase transient fault on the system with and withoutFACTS controllers. Section 4 presents results and discussion onthe simulation results obtained. Section 5 presents the conclusion.

2. Modeling of the power system and wind turbine

In general for the purpose of dynamic analysis power systemsare modeled by a set of differential and algebraic equations(DAE), that is:

_x ¼ f ðx; y; k;pÞ0 ¼ gðx; y; k; pÞ

ð1Þ

where x e Rn is a vector of state variables associated with the dy-namic states of generators, loads and other system controllers.y e Rm is a vector of algebraic variables associated with steady statevariables resulting from neglecting fast dynamics (e.g., most loadvoltage phasor magnitudes and angles); k e Rl is a set of uncontrol-lable parameters, such as variations in active and reactive power ofloads; p e Rk is a set of controllable parameters such as transformertap, AVR settings and FACTS controller reference voltages.

2.1. Wind turbine concepts and modeling

Normally a wind turbine creates mechanical torque on a rotat-ing shaft, while an electrical generator on the same rotating shaft iscontrolled to produce an opposing electromagnetic torque. Thepower and torque equations for the wind turbine are as follows:

Pitch Reference PowerRefer

Main Controller

PITCH CONTROLLER

GEAR BOX

Rotor

Wind

Fig. 1. Wind energy conversion sche

P ¼ ðq=2Þ�Cpðk; hÞAV3 ð2Þ

Tm ¼Px

ð3Þ

where q is the density of air (1.22 kg/m3); A is the swept area of theblade in m2. Cp is the performance co-efficient which represents therotor efficiency of the turbine (captured power/wind power); V isthe wind speed (m/s); P is the output power of the turbine; x isthe rotor speed of wind turbine; k is the tip speed ratio Vt/V, the ra-tio between blade tip speed Vt and wind speed upstream the rotor V(m/s); h is the pitch angle in degrees.

The parameters of the modeled system are given in theAppendix.

The wind turbine and its associated controls are modeled usingthe EUROSTAG software [12] (Tractable Engineering, 2004) and themain control units modeled are shown in Fig. 1. The main control-ler manages the overall control functions, whereas pitch and powercontroller are subordinate units.

The wind energy conversion scheme used for simulation con-sists of a doubly fed induction generator (rotor circuit connectedto the grid through power electronic converter). The converter ad-justs the frequency of the rotor feeding current to enable variablespeed operation (Fig. 2).

2.2. Doubly fed induction generator model

The doubly fed induction generator is the most commonly usedmachine for wind power generation. The rotor terminals are fedwith a symmetrical three-phase voltage of variable frequencyand amplitude. Using the generator convention, the following setof dynamic equations results:

Vds ¼ �Rsids �xswqs þ dwds=dt ð4ÞVqs ¼ �Rsiqs þxswds þ dwqs=dt ð5ÞVdr ¼ �Ridr � sxswqr þ dwdr=dt ð6ÞVqs ¼ �Rriqr þ sxswdr þ dwqr=dt ð7Þ

where v is the voltage in (V), R is the resistance in (X), i the currentin (A) and xs the stator electrical frequency in (rad/s), w the fluxlinkage (Vs) and s the rotor slip [13].

From the above set of dynamic equations d and q indicate thedirect and quadrature axis components and s and r indicate statorand rotor quantities. The d–q reference frame is rotating at

PeDFIG

Pref

ence

POWER ELECTRONIC CONVERTER

POWER CONTROLLER

me and its associated controls.

1174 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

synchronous speed with the q-axis 90� ahead of the d-axis.The fluxlinkages in Eq. (7) can be calculated using the following set ofequations in per unit:

wds ¼ �ðLs þ LmÞids � Lmidr

wqs ¼ �ðLs þ LmÞiqs � Lmiqr

wdr ¼ �ðLr þ LmÞidr � Lmids

wqr ¼ �ðLr þ LmÞiqr � Lmiqs

ð8Þ

with Lm is the mutual inductance and Ls and Lr, are the stator androtor leakage inductances respectively in (8).

The changes in generator speed that result from a difference inelectrical and mechanical torque can be calculated using generatorequation of motion

dxs

dt¼ 1

2HðTm � TeÞ ð9Þ

where H is the inertia constant (seconds) and Tm is the mechanicaltorque.

Te is the electro mechanical torque generated by the DFIG:

Te ¼ wdriqr � wqridr ð10Þ

The converters are represented as current sources, and there-fore the current set points equal rotor currents. The current setpoints are derived from the set points for active and reactivepower. The active power set point is generated by the rotor speedcontroller, based on the actual rotor speed value. The reactive

Wind Farm DFIG

Wind

GEAR BOX

VSC

Fig. 2. Structure of the doubly fed Induction

Washout Block

+

Vref +

_

Bus Voltage Vmeas

K/ (1+sT

sTw/ (1+sTw)

Fig. 3. Structure of SVC contro

power set point is generated by the terminal voltage controlleror power factor controller, based on the actual value of the termi-nal voltage or the power factor.

2.3. Synchronous generators

The synchronous generator model used for this dynamic analy-sis is the two axis model with four state variables [14]:

_E0di ¼1

s0qoi

ð�E0di � ðxqi � x0qiÞIqiÞ

_E0qi ¼1

s0doi

ðEFDi � E0qi þ ðxdi � x0diÞIdiÞ

_xi ¼1sjiðTmi � Dxi � TeiÞ

_di ¼ xi

i ¼ 1;2; . . . ;n

ð11Þ

where the state variables are E0d is the direct axis component of volt-age behind transient reactance, E0q is the quadrature axis componentof voltage behind transient reactance, x is the angular velocity ofrotor, d is rotor angle

2.4. Static var compensators (SVC)

SVC is basically a shunt connected static var generator/absorberwhose output is adjusted to exchange capacitive or inductive cur-rent so as to maintain or control specific power system variables;

to Power grid

DC LINK

1 VSC 2

generator based wind turbine system.

SVC bus Voltage deviations

Bmax

Bsvc

Bmin

)

ller with stabilizing loop.

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1175

typically, the controlled variable is the SVC bus voltage. One of themajor reasons for installing an SVC is to improve dynamic voltagecontrol, and thus, increase system loadability. An additional stabi-lizing signal, and supplementary control superimposed on the volt-age control loop of an SVC can provide damping of systemoscillations during transient faults and disturbances (Fig. 3) [16].The state equation for SVC can be written as:

BSVC ¼KTðV ref � Vmeas þ uÞ � 1

TBSVC ð12Þ

where BSVC the SVC susceptance, u is the stabilizing loop output.Here, Vref is chosen as 1.0 per-unit and Vmeas is the PCC voltage.

2.5. STATCOM

The STATCOM resembles in many respects a synchronous com-pensator, but without inertia. The basic electronic block of a STAT-COM is the voltage source converter (VSC), which in generalconverts an input dc voltage into a three-phase output voltage atfundamental frequency, with rapidly controllable amplitude andphase. a is the phase shift between the controller VSC AC voltageand its bus voltage V. Vref is the reference voltage setting.[15]

The dynamic equations include the differential equations forthe voltage magnitude controller, phase angle controller and STAT-COM power balance. The following differential equations (in per-unit) can be written from the block diagrams given in Figs. 4aand 4b:

Vx ¼½KMac V � Vx�

TMac

ð13Þ

Fig. 4a. PWM voltage magnitude controller of STATCOM.

GAIN

LEANET

WASHOUTBUS VOLTAGEDEVIATIONS

V

1+s1+s

sTw1+sTwKstab

V

Fig. 4b. PI phase angle con

msh ¼½kVy þ KT1 Vy�KDmsh�

T2ð14Þ

Vdcx ¼½KMdc

Vdc � Vdcx�TMdc

ð15Þ

Da ¼ KPVdcy þ KIVdcy ð16Þ

where, Vx is the output of AC voltage measuring circuit; Vdcx is out-put of DC voltage measuring circuit; Da is the output of phase anglecontroller block; msh can be obtained from, KMac and TMac are thegain and time constant of the ac voltage measuring circuit respec-tively. Vdcy is the input to the PI controller in DC voltage measuringcircuit.

k ¼ffiffiffi38

rðm0 þmshÞ ð17Þ

Here, k is the proportionality constant of STATCOM PWM VSC out-put voltage and

m0 ¼ffiffiffi83

rVref

Vdc

� �ð18Þ

2.6. Thyristor controlled series capacitors (TCSC)

Thyristor controlled series capacitor schemes typically use athyristor controlled reactor in parallel with a capacitor to varythe effective compensating reactance. For the purpose of analysis,the TCSC, regardless of its practical implementation, can be consid-ered simply as a continually variable capacitor whose reactance iscontrollable in the range of 0 6 Xc 6 Xcmax. The single line diagramof the TCSC is shown in Fig. 5. The variable reactance model of TCSCis as shown in Fig. 6. The reference value of the TCSC reactance Xref

is fixed based on the degree of compensation required. For thepresent work the value of Xref is chosen as half of the line inductivereactance. XC is the variable reactance inserted by the TCSC moduleinto the line [16].

XC ¼ðXref � Xmeas þ UÞK � XC

Tð19Þ

Xref is the reference value of TCSC reactance to be inserted in theline; Xmeas is the measured reactance; U is the stabilizing signal; Tis the time constant of the controller; Xmax and Xmin is the maxi-mum and minimum limits of reactance.

Kp+KI/s+ -

D/LAGWORK

+

+ +

U

dcref

Vdc

Vdcy

Vdcx

T1T2

KMdc1+sTM

Δα

δ

α

troller for STATCOM.

1176 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

2.7. Unified power flow controllers (UPFC)

The UPFC is the most versatile FACTS controller developed sofar, with all encompassing capabilities of voltage regulation, seriescompensation, and phase shifting. It comprises of two voltagesource converters coupled through a common DC link. The singleline diagram is shown in Fig. 7.

The active and reactive power flow control loops of the UPFC isshown in Figs. 8 and 9. The stabilizing signal for the unified powerflow controller is derived from a power oscillation-damping block,which uses active power flow (Pflow) as the input signal. Pflow Ref isthe reference value of active power flow in the line on which UPFCis connected. This value is obtained after running a power flow inthe line on which UPFC is to be connected. Vseq is the component ofseries injected voltage in quadrature with the line current. Qref isthe reference setting for reactive power flow in the UPFC connectedline and Qflow is the actual reactive power flow in the line and Vsep

is the component of AC voltage injected in phase with the linecurrent.

2.7.1. Parameter tuning of FACTS controllersThe parameter tuning of FACTS controllers is an important

problem as the stabilizing effect will depend on the gain of the con-trollers. The tuning is posed as an optimization problem with theobjective as minimizing the oscillations of PCC voltage from the de-sired value and is given by:

XL

Xc

Fig. 5. Thyristor controlled series capacitor.

+

-

+U

STABILIZINGSIGNAL

Xref

Xmeas

K/(1+

Fig. 6. Dynamic m

I

Vt

VDC

Vs

VSC1

k

SHUNT TRANSFORMER

Fig. 7. Single line di

Minimize : PI ¼X

k

½ðV ref � VkÞ2 þ ðxref �xkÞ2� ð20Þ

Kmin 6 K 6 Kmax

where Vref = 1.0 per-unit and PI is the sum squared deviation indexof the PCC voltage.

The optimization problem is solved using sequential quadraticprograming in MATLAB.

3. Dynamic simulation results and stability investigation

The single line diagram of the test system with the wind tur-bine connected is shown in Fig. 10. The test system consists of asix bus system with two synchronous generators G1 and G2. Thedoubly fed induction generator (IG) is connected to the gridthrough a two winding transformer. IG denotes the inductiongenerator terminal node. The two synchronous generators arerated at 1100 MW (G1) and 5500 MW (G2). The wind farm isrepresented by an aggregated model consisting of 10 wind tur-bines of each 2 MW. The induction generator is injecting5.5 MW in the steady state. The total system load at bus 4 and5 is 1500 MW which corresponds to nominal operatingcondition.

5 and 4 are load buses. At bus 5 the load is represented as acombination of Impedance and voltage frequency dependant loadin the dynamic simulation. The dynamic simulation is carried outfor a three phase fault on line 1–2 in the second line. The threephase fault is cleared in five cycles. The shunt connected FACTScontrollers (SVC and STATCOM) are located near bus 2 and the ser-ies connected FACTS controllers are located in one of the 2–3 lines.

3.1. Rotor angle deviations of synchronous generators without windfarm, with wind farm and with FACTS controllers

Fig. 11 shows the rotor angle response of the synchronous gen-erators without the wind farm in the network. From Fig. 11 it can

sT)

XMIN

XMAX

XC

odel of TCSC.

VSE

SERIES TRANSFORMER

VSC2

i

agram of UPFC.

P flow ref

u- Stabilizing Signal

∑ Kp+ (KI/s)

Pflow

++

Vseq

-

Fig. 8. Active power flow control loop.

∑Kq+ (KI/s)

Qref

+

−

Vsep

Qflow

Fig. 9. Reactive power flow control loop.

Fig. 10. Single line diagram of the power system with DFIG.

0 2 4 6 8 10

48

50

52

54

56

58

60

62

64

s

deg

[faultcleared] MACHINE : GEN ANGULAR POSITION Unit : deg[faultcleared] MACHINE : GENEQ ANGULAR POSITION Unit : deg

ROTOR ANGLE RESPONSE WITHOUT WIND FARM

Fig. 11. Rotor angle response without wind farm.

0 2 4 6 8 1040

45

50

55

60

65

70

75

80

85

Time (Sec)

G1

G2

Rotor angle (Deg)

Fig. 12. Rotor angle response with wind farm – High load operating condition.

0 2 4 6 8 1040

45

50

55

60

65

70

75

80

Rotor Angle (Deg)

Time (Sec)

SVC

STATCOM

Fig. 13. Rotor angle response of synchronous machine G1 with wind farm – Effectof SVC and STATCOM – High load operating condition.

0 2 4 6 8 10 40

45

50

55

60

65

70

75

80

TCSC

UPFC

Rotor Angle (Deg)

Time (Sec)

Fig. 14. Rotor angle response of synchronous machine G1 with wind farm – Effectof TCSC and UPFC – High loading condition.

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1177

be observed that after the fault the generator rotor angle of G1deviates slightly but after the fault clearance the system returnsto a new post equilibrium rotor angle value. Generator G2, whichsupplies a local load, lies far away from the transient fault andhence is left unperturbed. Fig. 12 shows the rotor angle responseof the synchronous generators with wind farm included in thenetwork.

From Fig. 12 it can be observed that the rotor angle of synchro-nous generator G1 oscillates indefinitely. This leads to dynamicinstability (sustained oscillations of rotor angle) in the system. Figs.13 and 14 show the rotor angle response of synchronous genera-tors with shunt and series controllers included in the transmissionline network. Responses shown in Figs. 13 and 14 correspond tothe high load operating condition where the total system load is in-creased by 40%. The controller parameters of the static var com-pensator/STATCOM are tuned to stabilize the oscillations as givenby the objective function of Eq. (12).

1178 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

From Fig. 13 it can be observed that rotor angle oscillations set-tle down after 4 s with the SVC controller included in the network.The oscillations settle down in 2 s with STATCOM.

0 2 4 6 8 10

10

15

20

25

30

35

40

45

50

55

60

65

Rotor angle (Deg)

Time (Sec)

Without FACTS

SVC

STATCOM

Fig. 15. Rotor angle response of synchronous machine G1 with wind farm – Effectof SVC and STATCOM – Nominal loading condition.

0 2 4

10

15

20

25

30

35

40

45

50

55

60

65

Rotor angle (Deg)

Fig. 16. Rotor angle response of synchronous machine G1 with wind

1.10

1.14

1.16

1.18

1.20

1.22

1.12

2 4

Rotor Speed (p.u.)

T

Fig. 17a. Rotor speed response of DFIG – Effect of

This may be attributed due to the fact that STATCOM (A voltagesource converter based FACTS controller) has a faster transient re-sponse compared to static var compensator (a passive thyristorswitched reactor/capacitor). From Fig. 14 it can be observed thatthere are no oscillations in the rotor angles of synchronous gener-ator with UPFC in the network. Figs. 15 and 16 shows the rotor an-gle response of synchronous generators with shunt and seriescontrollers in the network when the system load level is at itsnominal value as specified in Section 3.

The parameters of both TCSC and UPFC controllers are opti-mized to enhance system damping. From Fig. 15 it can be observedthat the rotor angle oscillations settle down in 7 s and with UPFC(Fig. 16) the oscillations settle down in 5 s. This is due the fact thatUPFC contributes reactive power to the network after the distur-bance from its shunt branch.

3.2. Rotor speed deviation of DFIG – Effect of FACTS controllers

Fig. 17a demonstrates the effect of FACTS devices on the rotorspeed response of DFIG after the disturbance. The speed of theinduction generator tends to increase towards its maximum valueset (1.2 per-unit) in the dynamic simulation without FACTS con-trollers in the network After the clearance of the fault it is observedthat the speed of the wind turbine does not reach its prefault stea-

6 8 10

UPFC

Without FACTS

TCSC

Time (Sec)

farm – Effect of TCSC and UPFC – Nominal operating condition.

10 8

SVC

STATCOM

TCSC

6

Without FACTS

ime (Sec)

FACTS devices. High load operating condition.

0 2 4 6 8 10

1.096

1.097

1.098

1.099

1.100

1.101

1.102

1.103

1.104

Rotor Speed (p.u.)

Time (Sec)

Without FACTS

SVC

STATCOM

Fig. 17b. Rotor speed response of DFIG – Effect of FACTS devices nominal operatingcondition.

0 2 4 6 8 10

1.096

1.097

1.098

1.099

1.100

1.101

1.102

1.103

1.104

Rotor Speed (p.u.)

Time in Sec

UPFC

TCSC

Fig. 17c. Rotor speed response of DFIG – Effect of FACTS devices nominal operatingcondition.

0.0 0.5

1.086

1.088

1.090

1.092

1.094

1.096

1.098

1.100

1.102

Rotor speed (p.u)

Fig. 17d. Effect of rotor speed stability following the outag

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1179

dy state value of 1.1 p.u. This post fault rotor speed deviation of theasynchronous generator causes rotor speed instability as discussedin Ref. [6].

However with the SVC additional dynamic reactive power sup-port and the stabilizing signal provided suppresses the rotor speedoscillations of the asynchronous generators. From Figs. 17a–17d itcan be inferred that there are no appreciable speed deviations withUPFC controller in the network. This is due to the effectiveness ofUPFC damping controller attached with its power flow controllerand also due to the shunt reactive support provided by the UPFC(Figs. 8 and 9). Hence it can be concluded that UPFC damps outrotor speed/rotor angle oscillations of asynchronous and synchro-nous generators more effectively. The impact of FACTS controllerson the rotor speed stability following the outage of generator G1 isshown in Fig. 17(d), with and without SVC in the network.

The effect of the fault ride through attached with rotor side con-verter of DFIG has a very minimal effect following a contingency(generator outage) which causes the rotor speed of the inductiongenerator to deviation from its steady state.

3.3. Active power injected by the DFIG – Effect of FACTS controllers

Fig. 18 shows the active power injected by the wind turbine intothe grid following the three phase fault carried on one of the linesnear bus 3. The stator protection system associated with the induc-tion generator disconnects the stator from the grid if the terminalvoltage of the induction generator is less than 0.75 p.u. for a periodof 0.08 s, hence the stator active power delivered comes down tozero after the fault. The active power injected comes down to zerofrom its initial value of 5.5 MW specified in the load flow.

The power calculation according to Eq. (2) is based on a singlewind speed. However, in reality, the wind speed may differ slightlyin direction and intensity across the area traversed by the blades.To consider this effect, the wind speed is supplied through a lagblock to the power conversion equation. This creates a slightchange in the active power delivered to the grid before the distur-bance at 1 s. Fig. 19 shows the wind speed block given as input tothe algebraic equation of power. [7].

1.0 1.5 2.0

Time (Sec)

WITHOUT FACTS

SVC

e of Synchronous generator G1 with and without SVC.

00

2 4 6 8 10

1

2

3

4

5

6

7

8

Active Power Injected, MW

Time (Sec)

Fig. 18. Active power Injected by the wind farm without FACTS devices.

1

1+sTw

Wind speed

V

Fig. 19. Wind speed supplied through lag block.

T0 2 4

-2

-1

0

1

2

3

4

5

6

7

8

9

Power Injected (MW)

Fig. 20. Active power injected by w

Ti0 2 4

0

1

2

3

4

5

6

7

Active Power Injected (MW)

Fig. 21. Active power Injected by the w

1180 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

Fig. 20 shows the active power injected by the wind turbine intothe grid following the transient fault with SVC/TCSC. It can be ob-served that after the fault the active power injected oscillatesaround the steady state power injection value of 5.5 MW and theMW injection into the grid does not become zero with SVC. Thisis due to the dynamic reactive power support provided by theSVC/TCSC in addition to the fault ride through capability of the in-verter associated with DFIG rotor.

ime (Sec) 6 8 10

SVC

TCSC

ind farm with SVC and TCSC.

me (Sec) 6 8 10

STATCOM

UPFC

ind farm with STATCOM and UPFC.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Time (sec)

Terminal Voltage (p.u.)

Fig. 22. Induction generator terminal voltage without FACTS.

0.85

0.90

0.95

1.00

1.05

0 1 2 3 4 5

Time (sec)

SVC TCSC

Terminal Voltage (p.u)

Fig. 23. Induction generator terminal voltage – Effect of SVC and TCSC.

Time (Sec)

0.92

0.94

0.96

0.98

1.00

1.02

0 1 2 3 4 5

STATCOM UPFC

Terminal Voltage (p.u)

Fig. 24. Induction generator terminal voltage – Effect of STATCOM and UPFC.

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1181

Fig. 21 shows the active power injected by the wind farm fol-lowing the transient fault with STATCOM/UPFC. It can be ob-served that due to the fast transient response of the STATCOMthe active power injected comes to the steady state of 5.5 MWwithin 2 s. It can be observed that there are no appreciable oscil-lations or power fluctuations in the induction generator terminalafter the disturbance. This is due to the reactive power supportprovided by the series converter and shunt converters of UPFCin addition to the fault ride through capabilities of the rotor sideconverter of DFIG.

3.4. Induction generator terminal voltage – Effect of FACTS controllers

The response in induction generator terminal voltage followingthe transient fault is shown in Fig. 22, without FACTS controllers inthe network. The under voltage protection system associated withthe wind turbine disconnects the stator from the network if thevoltage at its stator terminals is less than 0.75 p.u. for a period of0.08 s.

Figs. 23 and 24 show the response of the induction generatorterminal voltage with SVC/TCSC and STATCOM/UPFC.

Time (Sec)

0 2 4 6 8 10

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

MVAr Injected, SVC

Fig. 25. Dynamic reactive compensation – SVC.

Time (Sec) 0 2 4 6 8 10

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

MVAr Injected, STATCOM

Fig. 26. Dynamic reactive compensation – STATCOM.

Time (Sec)

0 2 4 6 8 10-400

-300

-200

-100

0

100

200

300

MVArInjected, TCSC

Fig. 27. Dynamic reactive compensation – TCSC.

1182 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

It can be concluded that terminal voltage of the DFIG is above0.75 p.u. after 0.1 s.

Comparing Figs. 22–24 it can be concluded that the UPFC im-proves the fault ride through capability of the DFIG very effectively.

3.5. Dynamic reactive compensations of the FACTS controllers

Dynamic reactive compensation of the wind farm can be orga-nized in several ways. This depends on (i) the demand of reactivecompensation for voltage reestablishing (ii) controllability of theequipment and (iii) Cost. When the success criterion is to get thevoltage reestablishing within the predefined range, e.g., avoiduncontrollable as well as over-voltages in the grid, the dynamic

reactive compensation can be capacitive or inductive. So long asno disconnection of the wind turbines occurs and the grid con-nected induction generators absorb reactive power during voltagereestablishing process, the dynamic reactive compensation shouldbe capacitive.

The dynamic reactive compensation of the FACTS controllers,play a major key role in controlling the transients on rotor speedoscillations of the asynchronous generator.

The reactive power compensation provided by shunt FACTSControllers are shown in Figs. 25 and 26. Comparing the figures,it can be observed that the compensation of the SVC swings from�60 MVAr to 50 MVAr for stabilizing the rotor speed oscillations.Use of an SVC with a less capacity results in uncontrollable voltage

Time (Sec) 0 2 4 6 8 10

-300-200-100

0100200300400500600700

MVArInjected, UPFC

Fig. 28. Dynamic reactive compensation – UPFC.

N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184 1183

decay or in sufficiently damped voltage oscillations. The dynamicreactive power compensation of STATCOM for achieving the samecontrol objective is only 0.8 MVAr. Hence it can be concluded that aSTATCOM is cost effective when compared to SVC for stabilizingrotor speed oscillations of the induction generator.

Figs. 27 and 28 compare the dynamic reactive compensations ofTCSC and UPFC following the disturbance. From Fig. 27 it can beobserved that the MVAr injected by the TCSC branch swings fromits steady state value of 50–300 MVAr. It can be observed thatthe series converter reactive power rating of UPFC swings from400 MVAr to 800 MVAr following the disturbance. This high tran-sient reactive power requirement results in increased cost of ser-ies/shunt converters.

4. Results and discussion

For the simulation study the gains and time constants of theFACTS controllers are tuned using a conventional optimization pro-gram, which minimizes the voltage/rotor speed oscillations of theinduction generator. From the results we conclude that amongshunt connected FACTS controllers the STATCOM provides betterdamping the oscillations compared to that of the SVC. Also, the dy-namic reactive compensation (Transient Rating) required by theSTATCOM is lesser than SVC. This is due to the fact that a STATCOMis basically voltage sourced converter based shunt controller andSVC is a shunt connected thyristor switched capacitor/reactor.Among series connected FACTS controllers the UPFC damps bothrotor angle oscillations of synchronous generators and rotor speedoscillations of induction generator very effectively when comparedwith TCSC. This is due to the reactive support provided by theshunt branch of the UPFC following the disturbance. Howeverthe reactive power rating of UPFC is very high compared to thatof the TCSC. It is suggested that a STATCOM of suitable ratingmay be installed at the point of common coupling (PCC) with orwithout a capacitor may be used for stabilizing rotor speed oscilla-tions associated with doubly fed variable speed induction genera-tors following transient faults and disturbances.

5. Conclusion

The development of wind turbine and wind farm models is vitalbecause as the level of wind penetration increases it poses dynamicstability problems in the power system. For the present work wehave taken a doubly fed induction generator model and illustratedthe presence of sustained oscillations with wind farms. SuitableFlexible AC Transmission Systems controllers are modeled usingthe non-linear simulation models and the transient ratings of theFACTS controller are obtained to stabilize the rotor speed/rotor an-gle oscillations in a DFIG based wind energy conversion scheme.

The rotor speed stability of the DFIG based system following a gen-erator outage is studied. It can be observed that the effect of lowvoltage ride through (LVRT) is very minimum following the contin-gency and the presence of a FACTS device like the SVC improvesthe rotor speed stability.

Acknowledgements

The first author (Dr. N. Senthil Kumar) would like to thank hisfather Mr. S.K. Natarajan and wife Mrs. Bhuvana who consistentlysupported and encouraged him a lot during his research workmorally.

Appendix A. Doubly fed induction generator dynamic data

A.1. Parameters

Base values for the per unit system conversion.Base power: 100 MVABase voltage: 0.69 kV for low voltage bus bar, 150 kV for highvoltage busbar.

B. Line data

From

To R X Transformer tap

1

2 0.000185 0.00769 1.0526 2 3 0.00208 0.02285 – 2 3(2) 0.00208 0.02285 – 3 4 0.00208 0.02285 – 3 5 0.00185 0.00769 –

Load data

Load bus

PD (MW) QD (MVAr)

4

5000 2000 5 500 175

Appendix B. Dynamic data of generators

B.1. Doubly fed induction generator

Rated apparent power MVA: 20 MVA.Rotor inertia: 3.527 MW s/MVA.Rs (p.u.) = 0.0693.Xs (p.u.) = 0.080823.

1184 N. Senthil Kumar, J. Gokulakrishnan / Electrical Power and Energy Systems 33 (2011) 1172–1184

Rr (p.u.) = 0.00906.Xr (p.u) = 0.09935.Xm (p.u.) = 3.29.Rotor speed for synchronization: 0.9 p.u.Minimum rotor speed: 0.56 p.u.Maximum rotor speed: 1.122 p.u.

B.2. Gains of FACTS controllers

Gain parameters

Tuned gains

SVC

K 48.2 STATCOM K 47.3 TCSC K 41.1 UPFC K 40

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Dr. N. Senthil Kumar is presently working as an assistant professor (selectiongrade) in the Department of Electrical and Electronics Engineering at B.S. AbdurRahman University. His area of research includes modeling of FACTS devices forpower system stability studies. Modeling of wind energy conversion systems forpower system stability analysis.

Mr. J. Gokulakrishnan is a post graduate student in M.E. (Power System Engi-neering) in the Department of Electrical and Electronics Engineering in B.S. AbdurRahman University.