1

Mitigation of Subsynchronous Oscillations in a

Series Compensated Wind Farm with
Thyristor Controlled Series Capacitor (TCSC)
Rajiv. K. Varma, Member, IEEE, Ysni Semsedini, Non Member and Soubhik Auddy, Student
Member, IEEE

Abstract— Wind power penetration is rapidly growing all over It will be further necessary to transmit the generated power
the world as the alternative, renewable and environment friendly through transmission networks that can sustain large power
resource of energy production. With this rapid growth of wind flows. It is well known that series compensation is an effective
power, the power systems of future will likely see the integration means of increasing power transfer capability of an existing
of large wind farms with electrical networks that are series transmission network.
compensated for ensuring stable transmission of bulk power. This
may potentially lead to subsynchronous resonance (SSR) issues. However, series compensation is shown to cause a highly
Although SSR is a well-understood phenomenon that can be detrimental phenomenon called Subsynchronous Resonance
mitigated with FACTS devices, scant information is available on (SSR) in electrical networks. SSR manifests itself in two ways:
the SSR problem in a series compensated wind farm. This paper
the induction generator (IG) effect and torsional interaction
reports the occurrence and mitigation of SSR caused by induction
generator (IG) effect as well as torsional interactions (TI), in a (TI). The induction generator effect is caused by the interplay
series compensated wind farm. SSR suppression is achieved as an of the series compensated network and the generator stator
added advantage of a Thyristor Controlled Series Capacitor circuit. Meanwhile, torsional interaction is caused by the
(TCSC) actually installed to increase the power transfer interaction of the mechanical/torsional system and the
capability of the transmission line. In this study, a wind farm electrical network. Flexible AC Transmission Systems
employing self-excited induction generator (SEIG) is connected to (FACTS) can provide an effective solution to mitigate SSR [1-
the grid through a series compensated line. A Thyristor 3].
Controlled Series Capacitor (TCSC) is shown to damp A vast body of literature is available on the mitigation of
subsynchronous oscillations when provided with closed loop
subsynchronous resonance in a conventional thermal power
current control. Extensive simulations have been carried out
using EMTDC/PSCAD to validate the performance of TCSC in plant [1]. However, very little information is presented on the
damping SSR. subsynchronous resonance issues in a series compensated wind
farm [2]. The major difference between WECS and
Index Terms—Wind power systems, FACTS, Self-excited conventional power plants is that WECS uses induction
Induction Generator (SEIG), Series Compensation, generators as opposed to synchronous generators. In this
Subsynchronous Resonance (SSR), Thyristor Controlled paper, it is shown that induction generators are also prone to
Series Capacitors (TCSC), Open Loop Control, Closed SSR interplay. Growing subsynchronous oscillations both due
loop Current Control. to induction generator (IG) effect as well as torsional
interaction (TI) are shown to be the cause of system instability
in a series compensated wind farm.
I. INTRODUCTION A thyristor controlled series capacitor (TCSC) is employed

W ind Energy Conversion System (WECS) is an emerging

means of energy production throughout the globe. Wind
in place of fixed series capacitors to mitigate the
subsynchronous oscillations, in addition to providing stability
enhancement. It is reported in [3, 4] that a TCSC with an open
generating capacities have increased from negligible levels in
the early nineties to over 50 GW today. This shift to wind loop firing angle control when employed in a transmission
energy will inevitably lead to large wind turbine generators system supplied with conventional steam turbine-driven
(WTG) being integrated into electric power grids. synchronous generators, offers more resistance at increased
levels of series compensation at subsynchronous frequencies
while at fundamental frequency the same TCSC offers
Rajiv K. Varma and Soubhik Auddy are Associate Professor and Ph.D. capacitive reactance enhancing the power flow through the
student, respectively, in Electrical & Computer Engineering Dept., University transmission line. This shows that TCSC has an inherent
of Western Ontario, London, ON, N6A5B9, CANADA (e-mails:
rkvarma@uwo.ca, sauddy@uwo.ca). capability of damping SSR while increasing the power transfer
Y. Semsedini is in London Hydro, London, ON (e-mail: capability of a transmission line.
Semsediy@londonhydro.com ) This paper reports the effectiveness of a TCSC with a
closed loop current control mode to damp the SSR in a wind
 2

farm. The wind farm is connected to the grid through a series Ns − N r (3)
s=
compensated transmission network. The study system is Ns
derived from the IEEE First Benchmark Model (FBM) and the
wind farm is modeled by a group of coherent induction
When the magnitude of this resistance exceeds the sum of the
generators with shunt capacitance. The entire mechanical
armature and network resistances at a resonant frequency,
system, comprising the gear train, rotor blades and tower, of
the wind turbine is modeled by a single mass, as their there will be self-excitation.
individual natural resonant frequencies are very close.
Nonlinear time domain simulations of fault studies are carried The induction generator effect can be explained in case of a
out using EMTDC/PSCAD. wind farm comprising induction generator from its equivalent
circuit drawn in Fig. 1.
The organization of the paper is as follows. The two
mechanisms of SSR - induction generator (IG) effect and R1 jX1 jX2
torsional interaction (TI) are briefly described in section II.
Section III outlines the study system configuration; section IV
proves the potential occurrence of SSR both due to IG effect
and TI interactions in a series compensated wind farm. Rc jXm R2/s
Section V covers the selection of TCSC parameters. The
performance of the TCSC in mitigating SSR is shown in
section VI; finally section VII concludes the paper.

Fig. 1 Equivalent circuit diagram of an induction machine

II. SUBSYNCHRONOUS RESONANCE R1 = stator resistance; X1 = stator leakage reactance; R2 = rotor resistance
referred to stator; X2 = rotor leakage reactance referred to stator; Rc = core-
Subsynchronous resonance occurs in a power system loss resistance; Xm = magnetizing reactance;
network when the mechanical system of the generator
exchanges energy with the electrical network [1, 5]. Series
compensation in the line results in excitation of B. Torsional Interactions
subsynchronous currents at electrical frequency This form of self excitation involves both the electrical and
XC mechanical dynamics. This may occur when the electrical
fe = f 0 (1) resonant frequency fe is near the complement of a torsional
XL
resonant frequency fn of the turbine-generator shaft system [1,
5]. The torques at rotor torsional frequencies may then get
Where XC = reactance of the series compensator; XL = amplified and potentially lead to shaft failure.
reactance of the line including generator and transformer; and
f0 = the nominal frequency of the power system.
C. Transient SSR
These currents result in rotor torques and currents at the Transient SSR generally refers to transient torques on
complementary frequency: segments of the T-G shaft resulting from subsynchronous
oscillating currents in the network caused by faults or
fr = f 0 − fe (2) switching operations. This usually occurs when the
complement of the electrical network resonant frequency gets
closely aligned with one of the torsional natural frequencies.
These rotor currents result in subsynchronous armature voltage
components which may enhance subsynchronous armature III. SYSTEM CONFIGURATION
currents to produce SSR. There are two aspects of the SSR:
(a) Self excitation involving both Induction generator
effect and Torsional Interaction The study system is derived essentially from the IEEE first
(b) Transient torque (also called as transient SSR) benchmark model of SSR studies [10]. A TCSC is replaced
with the fixed series compensator in the system shown in Fig.
A. Induction Generator Effect 2. The capacitive reactance of the TCSC is the same as
Self-excitation of the electrical system alone is caused by variable line series compensation and the inductive reactance
induction generator effect. As the rotating MMF produced by is chosen as to avoid multiple resonant peaks or infinite
the subsynchronous frequency armature currents is moving impedance offered by TCSC in its impedance-firing angle
slower than the speed of the rotor, the resistance of the rotor characteristics [3]. Section V describes it in more detail. The
(at the subsynchronous frequency viewed from the armature detailed system data can be found in Appendix.
terminals) is negative as the slip s of the induction generator is
negative, as depicted in the equivalent circuit shown in Fig. 1.
 3

Machine Terminal Voltage (p.u.)

0.9

0.8

0.7

0.6
Fig. 2 Wind generator study system with TCSC
0.5

0.4
IV. SSR IN SERIES COMPENSATED WIND FARM
In this section both the induction generator self excitation 4 4.5 5 5.5 6
and torsional interaction effects are studied in the study system Time (s)
Fig. 4 Generator terminal voltage for 100 MW power transfer for 90% series
depicted in Fig. 2. The firing angle control of the TCSC is
compensation
blocked so that the possibility of SSR can be examined in a
non-FACTS equipped series compensated wind farm. A three
phase to ground fault is implemented to study potential of both 1.07

self excitation and transient torque SSR. The power flow 1.06

Generator Rotor Speed (p.u.)

studies are conducted using the DSA Power Tools software
1.05
[11] and the electromagnetic time domain simulations are
performed with the PSCAD/EMTDC software [12] 1.04

1.03
A. Induction Generator Self-excitation Effect
1.02

Studies reported in this section show that there are two 1.01

factors which influence the self-excitation phenomenon of an

1
induction generator. These are: 4 4.5 5
Time (s)
5.5 6

• Power transfer level. Fig. 5 Generator rotor speed for 100 MW power transfer for 90% series
• Level of series compensation. compensation
These factors are addressed separately.
The generator power output is now increased to 500 MW.
For a power transfer of 100 MW, the induction generator At this high power level, the induction generator is operated at
self excitation effect is not seen to be so prominent. Even a much higher speed over the synchronous speed. This
though oscillations are visible in the electromagnetic torque, increased power transfer makes the apparent negative rotor
machine terminal voltage and rotor speed, they are seen to resistance exceed the sum of total armature and network
decay with time. This is depicted in Fig. 3 - Fig. 5. If the line resistance. Thus giving rise to subsynchronous oscillations.
resistance is decreased, these oscillations become larger and The dominant electrical mode in this case is 20.54 Hz.
continue for a longer duration which is expected of induction
generator self excitation oscillations. However, the line Next, the series compensation level is varied for 500 MW
resistance reduction is not a realistic option and is hence not generator power output. It is observed that with increasing
reported here. series compensation levels the oscillations due to induction
generator self excitation get enhanced making the system
eventually unstable. The electromagnetic torque is depicted for
1
50%, 65% and 90% in Fig. 6, 7 and 8, respectively. The
0.5 electrical frequencies fe in the electromagnetic torque increases
Electromagnetic Torque (p.u.)

0
according to (1) and consequently, the rotor torque frequency
fr decreases as in (2).
-0.5

-1

-1.5

-2

-2.5
4 4.5 5 5.5 6
Time (s)
Fig. 3 Electromagnetic torque for 100 MW power transfer for 90% series
compensation
 4

1
It is observed that with increasing series compensation
0.5
levels the oscillations due to torsional interaction also get
Electromagnetic torque (p.u.)
0 enhanced making the system eventually unstable. The
-0.5
mechanical torque between Mass 1 and Mass 2 is depicted for
50%, 65% and 90% in Fig. 9, 10 and 11 respectively.
-1

-1.5 2

-2

Mechanical torque between

Mass 1 and Mass 2 (p.u.)
1.5
-2.5
4 4.5 5 5.5 6
Time (s)
1
Fig. 6 Electromagnetic torque for 50% series compensation
1 0.5

0.5
Electromagnetic torque (p.u.)

0
0

-0.5
-0.5
0 5 10 15 20
-1 Time (s)
-1.5 Fig. 9 Mechanical torque between mass 1 and 2 (T12) for 50% series
compensation and fr = 0.8 Hz
-2
3
-2.5

Mechanical torque between

-3

Mass 1 and Mass 2 (p.u.)

2
4 4.5 5 5.5 6
Time (s)
Fig. 7 Electromagnetic torque for 65% series compensation 1

4
0
Electromagnetic torque (p.u.)

2
-1

0
-2
5 10 15 20
-2 Time (s)
Fig. 10 Mechanical torque between mass 1 and 2 (T12) for 65% series
compensation and fn = 0.8 Hz
-4
4
-6
4 4.5 5 5.5 6 3
Mechanical Torque between
Mass 1 and Mass 2 (p.u.)

Time (s)
Fig. 8 Electromagnetic torque for 90% series compensation 2

B. Torsional Interactions 0

A very high level of series compensation is typically needed -1

as indicated by (1) and (2) to generate a rotor torque at a
-2
frequency in the close vicinity of the resonant frequency of the
wind turbine mechanical system (comprising rotor blades and -3
5 10 15 20
gear train). There are in fact two typical resonant frequencies Time (s)
[7-8]: Fig. 11 Mechanical torque between mass 1 and 2 (T12) for 90% series
• 1.1 Hz corresponding to the tower side ways compensation and fn = 0.8 Hz
oscillations.
• 2.5 Hz relating to mechanical system.
V. SELECTION OF TCSC PARAMETERS
A two-mass torsional system model is added to the The thyristor controlled series capacitor (TCSC) increases
induction generator model. Since both the frequencies are very the power transfer capability of a transmission network in
close, only one torsional frequency is considered to represent addition to several other functions [3]. It provides a rapid,
the effect of both these natural frequencies. Hence, Mass 1 continuous control of the transmission line series
models the combined tower and wind turbine mechanical compensation level thus dynamically controlling the power
system and Mass 2 represents the inertia of the generator. flow in the line.
 5

α
In this application, the TCSC is assumed to be primarily
employed in the network for controlling line reactance and
hence control of power flow. The SSR damping function is
added through constant current control for this study. It is
reported [4] that a TCSC when operating at fundamental
frequency offers a pure capacitive reactance to increase the
power transfer capability of the network. On the other hand the
same TCSC offers resistive impedance at subsynchronous Fig. 13 TCSC Constant Current Controller
frequencies which need to be damped. The resistive impedance
of the TCSC increases with the increased boost factor which is Here Iref is the pre-fault or pre-contingency current
the ratio of the capacitive reactance offered by the TCSC and calculated from EMTDC/PSCAD line-current phasor. The
the total line reactance. Hence, the TCSC also provides a main current controller is a PI Controller. The parameters of
resistive damping to the subsynchronous oscillations. this controller are also adjusted systematically through
electromagnetic transient simulation studies by hit-trial to get
the minimum settling time or fastest damping criterion.
The general configuration of a TCSC is shown below:

VI. PERFORMANCE OF TCSC IN THE MITIGATION OF SSR

A TCSC is already installed to improve the power transfer

capability of the transmission network of the study system
shown in Fig 2. The damping performance of this TCSC in
mitigating SSR is examined in this section. Here the TCSC is
Fig. 12 General configuration of a TCSC
operating in a closed-loop current control mode.
For this configuration the equivalent TCSC reactance is
computed as per the following equation: A. Damping performance of TCSC for IG effect

X C2 2β + sin2β 4X C2 cos 2 β ktankβ − tanβ In this case also, the damping performance of the TCSC is
X TCSC = X C − +
XC − XL π XC − XL k 2 − 1 π shown for the worst possible operating condition of 500 MW
(4) power flow and 90% series compensation. The signals
reported to show the damping performance of TCSC are:
where β = angle of advance (before the forward voltage
becomes zero) = π-α; α is the firing angle of the thyristors. It
Electromagnetic torque of the generator (Te)
is noted from (4) that a parallel resonance is created between
Generator rotor speed (Wr)
XC and XL at the fundamental frequency, corresponding to the
Generator terminal voltage (Vt)
values of firing angle αres, given by:
πω Fig. 14, 15 and 16 display the generator electromagnetic-
α res = π - (2m - 1) (5) torque, generator rotor speed, machine terminal voltage,
2ω r
respectively.
3
The different resonances can be reduced to one by proper Without TCSC
choice of k = ωr/ω = √ XC/ XL in the range of 900 < α < 1800. 2 With TCSC CC
Electromagnetic torque (p.u.)

As XC is known, XL could eventually be calculated once a 1

proper value of k is chosen to ensure a single resonant peak. 0

Once the XC and XL values of the TCSC are calculated, a -1
closed loop current control scheme is employed for proposed
-2
application. The functional block diagram of TCSC closed
-3
loop current control is depicted in Fig. 13.
-4

-5
4 5 6 7 8 9 10
Time(s)
Fig. 14 Damping of SSO in the electromagnetic torque
 6

1.08 1.6
Without TCSC Without TCSC
With TCSC CC 1.5 With TCSC CC

Generator Rotor Speed (p.u.)

Generator rotor speed (p.u.) 1.06

1.4
1.04
1.3
1.02
1.2
1
1.1

0.98 1

0.96 0.9
4 5 6 7 8 9 10 5 10 15 20
Time(s) Time(s)
Fig. 15 Damping of SSO in the generator speed Fig. 18 Damping of SSO in the rotor speed by TCSC
1.6
Without TCSC
Generator terminal voltage (p.u.)

380
1.4 With TCSC CC

1.2
375
1

Xtcsc (Ohm)
0.8
370
0.6

0.4 365

0.2
4 5 6 7 8 9 10
Time(s) 360
5 10 15 20
Fig. 16 Damping of SSO in the generator terminal voltage Time(s)
Fig. 19 Variation of TCSC reactance in damping of SSO
B. Damping performance of TCSC for TI

Finally the damping of TCSC in mitigating torsional VII. CONCLUSION

interaction is investigated. The signals examined are:

Mechanical torque between Mass 1 and Mass 2. With the rapid growth of wind power penetration into the
power system grid, wind farms will likely be evacuating bulk

Generator rotor speed (Wr)
power through series compensated networks. This will render

TCSC reactance (XTCSC)
the power system vulnerable to SSR. In this paper a thyristor
controlled series capacitor is applied to damp SSR in such a
Fig 17, 18 and 19 demonstrate mechanical torque between series compensated wind farm. The following conclusions are
Mass 1 and 2, generator rotor speed and TCSC susceptance drawn from extensive electromagnetic transient simulation
respectively. It is apparent from the figures that TCSC closed- studies over widely varying levels of series compensation:
loop current control effectively damps the SSO due to TI
effect.
SSR is a potential threat in series compensated wind
4 farms even at realistic levels of series compensation.
Without FACTS
With TCSC CC

A TCSC which is originally employed to improve
3
power transfer capability of the transmission line is
Mechanical Torque between
Mass 1 and Mass 2 (p.u.)

2 sufficient to damp SSR provided it is equipped with

1
proper control scheme.

Closed loop current control of TCSC is found to be
0 effective in damping subsynchronous oscillations both
-1 due to torsional interaction and induction generator
effects, even when the system is subjected to a severe
-2
fault.
-3
5 10 15 20
Time (s)
Fig. 17 Damping of SSO in the mechanical torque between Mass 1 and
Mass 2 by TCSC
 7

Rajiv K. Varma (Member 1996) obtained B.Tech. and

Ph.D. degrees in Electrical Engineering from Indian
Institute of Technology (IIT), Kanpur, India, in 1980
and 1988, respectively. He is currently an Associate
VIII. APPENDIX Professor and Associate Chair-Graduate at the
University of Western Ontario (UWO), Canada. Prior to
A. Generator Data: this position, he was a faculty member in the Electrical
Engineering Department at IIT Kanpur, India, from
Power Rating = 1000 HP; VLL = 26.0 KV; 1989-2001. While in India, he was awarded the
Rs = 0.015 p. u; XLs = 0.091p.u; Rr1 = 0.0507 p. u; Government of India BOYSCAST Young Scientist Fellowship in 1992-93 to
Rr2 = 0.0095 p. u; XL1 = 0.0 p. u; XL2 = 0.0539 p. u; conduct research on Flexible AC Transmission System (FACTS) at the
University of Western Ontario (UWO). He also received the Fulbright grant
Xm12 = 0.1418; HG = 0.5 of the U.S. Educational Foundation in India, to conduct research in FACTS at
B. Torsional System Data: Bonneville Power Administration (B.P.A.), Portland, Oregon, USA, during
May-Aug. 1998. He is the Chair of IEEE Working Group on "FACTS and
HVDC Bibliography" and is active on a number of other IEEE working
Power= 100MW; HT = 12.5 pu; HG = 0.5 pu; KGT = 0.15 pu groups. He has received several Teaching Excellence awards at the Faculty of
Engineering and University level at UWO. His research interests include
FACTS, Power systems stability, Wind power generation systems and
C. TCSC Data: Distribution Automation.

K = Percentage series compensation XC/X∑ =90%, 65%, 50%; Ysni Semsedini received his B. Sc and M. Sc degrees in
XL = Calculated from (4) to avoid multiple resonant peaks in Electrical and Computer Engineering from the University
of Western Ontario, London, Ontario, Canada in 2003 and
TCSC reactance-firing angle characteristics. TCSC Current 2006 respectively. He was a distribution engineer in
Controller: KP = 0.0; KI = 200; Kitchener – Wilmot Hydro, Kitchener, Ontario, Canada
from 2003 to 2004. Currently he is working in London
REFERENCES Hydro, London, ON. His research interests include
modeling and performance studies of wind farms and
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[11] DSA Power Tools User manual, Power Tech Lab, Surrey, BC, 2005
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