64 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO.

1, FEBRUARY 2013

Damping of SSR Using Subsynchronous

Current Suppressor With SSSC
R. Thirumalaivasan, Member, IEEE, M. Janaki, Member, IEEE, and Nagesh Prabhu, Member, IEEE

Abstract—Hybrid series compensation using static synchronous SSSC is a voltage source converter (VSC) based FACTS con-
series compensator (SSSC) and passive series capacitor can im- troller, and has one degree of freedom (i.e., reactive voltage
prove the stability of the system, increases the power transfer control) injects controllable reactive voltage in quadrature with
capability and is useful for the fast control of power flow. This
paper analyzes the subsynchronous resonance (SSR) character- the line current. The risk of SSR can be minimized by a suit-
istics of the hybrid series compensated power system in detail able combination of hybrid series compensation consisting of
and proposes a simple method for the extraction of subsyn- passive components and VSC based FACTS controllers such
chronous components of line current using filter. The extracted as STATCOM or SSSC. The advantage of hybrid compensa-
subsynchronous frequency component of line current is used to tion is reported in [5] and shown that reactive voltage control
inject a proportional subsynchronous voltage in series with the
transmission line which suppresses subsynchronous current in mode of SSSC reduces the potential risk of SSR by detuning
the transmission network. This novel technique is termed as sub- the network resonance. The SSR characteristics of TCSC and
synchronous current suppressor. The design of subsynchronous SSSC are compared in [6] and studies indicate that vernier op-
current suppressor is based on damping torque analysis and using eration of TCSC is often adequate to damp SSR whereas a sub-
genetic algorithm. A novel graphical representation of series synchronous damping controller (SSDC) with SSSC is desired
resonance condition when SSSC is incorporated in the system
is presented. The detailed study of SSR is carried out based on for damping critical torsional modes when the line resistance is
eigenvalue analysis, transient simulation and damping torque low. A method for online estimation of subsynchronous voltage
analysis. The results of the case study on a system adapted from components in power systems is described in [7] and used for
IEEE First Benchmark Model demonstrates the effectiveness and the mitigation of SSR [8]. The damping of SSR using single
robust performance of subsynchronous current suppressor in phase VSC based SSSC is reported in [9].
damping of SSR under various system operating conditions.
Linear analysis is performed on D-Q model of the system with In this paper, the analysis and simulation of a hybrid series
SSSC and the results are tested by executing transient simulation compensated system with SSSC based on three-level 24-pulse
based on detailed nonlinear three-phase model. [10] VSC is presented. The major objective is to investigate SSR
Index Terms—Damping torque, eigenvalue, FACTS, genetic al- characteristics of the hybrid series compensated power system
gorithm (GA), static synchronous series compensator (SSSC), sub- in detail using both linear analysis, nonlinear transient simula-
synchronous resonance (SSR), torsional interaction (TI), voltage tion and propose a simple method for the extraction of subsyn-
source converter (VSC). chronous component of line current using filter. The extracted
subsynchronous frequency component of line current is used to
inject a proportional subsynchronous voltage in series with the
I. INTRODUCTION
transmission line which suppresses subsynchronous current in
the transmission network. This novel technique is termed as sub-

S ERIES compensation is an economic solution to improve

the stability of transmission system and increases the
power transfer capability. However, the potential inherent
synchronous current suppressor and effectively mitigates SSR.
The study system is adapted from IEEE FBM and the anal-
ysis is executed based on damping torque analysis, eigenvalue
problem in series compensated transmission lines connected to
analysis, and transient simulation. The paper is organized as fol-
turbo generators is subsynchronous resonance (SSR) leading
lows: In Section II, modeling of SSSC and the different methods
to adverse torsional interactions [1]–[4] which results in shaft
of analysis of SSR are given. Section III gives a case study and
failure of mechanical system.
highlights the importance of filters to damp SSR under varying
The onset of series connected FACTS controllers, like
system parameters. Performance evaluation and the design of
thyristor controlled series capacitor (TCSC) and static Syn-
subsynchronous current suppressor is given in Section IV. Con-
chronous series compensator (SSSC), has made it possible not
clusions drawn based on case studies are given in Section V.
only to regulate power flow in critical lines and also to counter
the problem of SSR. SSSC has several advantages over TCSC.
II. MODELING OF SSSC AND ANALYSIS OF SSR
Manuscript received March 20, 2011; revised August 27, 2011, December The converter circuit of SSSC is usually a multi-pulse and/or
22, 2011, and February 09, 2012; accepted March 23, 2012. Date of publication
multilevel configuration. In this work, SSSC is modeled by
May 30, 2012; date of current version January 17, 2013. Paper no. TPWRS-
00242-2011. a combination of three-level, 24-pulse configuration with
R. Thirumalaivasan and M. Janaki are with the School of Electrical Engi- TYPE-1 controllers [11]. In three-level converter topology the
neering, VIT University, Vellore-632014, India.
magnitude of converter output voltage is controlled by varying
N. Prabhu is with Canara Engineering College, Benjanapadavu, Bantwal,
Mangalore-574219, India (e-mail: prabhunagesh@rediffmail.com). dead angle with fundamental switching frequency [5], [12],
Digital Object Identifier 10.1109/TPWRS.2012.2193905 [13]. With the help of Type-1 controller, both the magnitude

0885-8950/$31.00 © 2012 IEEE

THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 65

where , 5, 7, 11, 13 and is the dead angle (period)

during which the converter pole output voltage is zero. We can
eliminate the 5th and 7th harmonics by using a twelve-pulse
VSC, which combines the output of two six-pulse converters
using transformers.
The switching functions for first twelve-pulse converter are
given by

where

(4)

The switching functions for second twelve-pulse converter are

given by
Fig. 1. Switching function for a three-level converter.

and phase angle of converter output voltage can be controlled

and the converter pole voltage is zero for the time duration
of per cycle. The harmonic distortion on the ac side is
greatly reduced by using three-level converter.
In this paper, the detailed three-phase model of SSSC is de- where
veloped by modelling the converter operation using switching
functions. The switching function for phase “a” is shown
in Fig. 1.
The switching functions of phase b and c are similar but phase (5)
shifted successively by 120 in terms of the fundamental fre-
quency. Assuming that the dc capacitor voltages The switching functions for a 24-pulse converter are given by
, the converter terminal voltages with respect to the mid
point of dc side “N” can be obtained as (6)

The two 12-pulse converters are interfaced to obtain three-level

(1) 24-pulse VSC based SSSC. The converter output voltage are
given by

and the converter output voltages with respect to the neutral of (7)
transformer can be expressed as
where .
If the switching functions are approximated by their funda-
(2) mental components (neglecting harmonics) for a 24-pulse three-
level converter, we get

where (8)
is the switching function for phase “a” of a six-pulse three-level
VSC. Similarly for phase “b”, and for phase “c”, can and , are phase shifted successively by 120 .
be derived. The peak value of the fundamental and harmonics The line current is given by
in the phase voltage are found by applying Fourier analysis and are phase shifted successively by 120 . Note that
on the phase voltage and can be expressed as is the angle by which the fundamental component of converter
output voltage leads the line current. It should be noted that is
(3) nearly equal to depending upon whether SSSC injects
66 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013

Fig. 2. Switching function of 24-pulse three-level converter analogous to a

48-pulse converter when .

Fig. 4. Phasor diagram of SSSC.

where is the modulation index [5]. For a 24-pulse three-level

converter the modulation index is a function of dead angle and
Fig. 3. Schematic representation of SSSC. is given by . is the transformation ratio of SSSC
interfacing transformer. From the control point of view it is con-
venient to define the real voltage and reactive voltage
inductive or capacitive voltage. Neglecting converter losses we which are the components of in phase and quadrature with
can get the expression for dc capacitor current as line current , respectively, and the phasor diagram is shown in
Fig. 4. and in terms of variables in D-Q frame ( and
(9) ) are obtained as

(13)
A particular harmonic reaches zero, when . (14)
At , the switching function for phase “a” is
shown in Fig. 2 and indicates that 24-pulse three-level converter
behaves like a 48-pulse converter when as 23rd and Here, positive indicates inductive mode of operation of
25th harmonics are negligibly small. SSSC and positive indicates that SSSC absorbs active power
from the line.
A. Mathematical Model of SSSC in D-Q Frame of Reference The dc side capacitor is described by the dynamical equation
When switching functions are approximated by their funda- as
mental frequency components, neglecting harmonics, SSSC can
be modeled by transforming the three-phase voltages and cur- (15)
rents to D-Q variables using Kron’s transformation [15]. The
SSSC can be represented functionally as shown in Fig. 3. where ,
In Fig. 3, and are the resistance and reactance of the , ( —base frequency), —susceptance of dc side capac-
interfacing transformer of VSC. The magnitude control of con- itor, —conductance which accounts for losses.
verter output voltage is achieved by modulating the conduc- and are the D-Q components of the line current .
tion period affected by dead angle of a converter while the dc is the phase angle of line current and is the angle by which
voltage is maintained constant. converter output voltage leads the line current.
The converter output voltage can be represented in the D-Q
frame of reference as B. SSSC Voltage Control (Three-Level VSC)
In Type-1 controller both magnitude (modulation index )
(10) and phase angle of converter output voltage are controlled.
The dc side capacitor voltage is maintained at a constant
where and are the D and Q components of SSSC injected voltage by controlling real voltage . The real voltage refer-
voltage and are defined as follows: ence is obtained as the output of dc voltage controller.
The reactive voltage reference may be kept constant
(11) or obtained from a power scheduling controller. However, for
(12) the SSR analysis constant reactive voltage control is considered.
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 67

Fig. 5. Type-1 controller for SSSC.

It should be noted that harmonic content of the SSSC injected

voltage would vary depending upon the operating point since
magnitude control will also govern the switching.
The dc capacitor voltage reference can be varied (depending Fig. 6. Modified IEEE First Benchmark Model with SSSC.
on reactive voltage reference) so as to give optimum harmonic
performance. In three-level 24-pulse converter, dc voltage ref-
erence may be adjusted by a slow controller to get optimum har- 1) The generator supplies power of 0.9 p.u. to the trans-
monic performance at in steady state. mission line.
The structure of type-1 controller for SSSC is given in Fig. 5. 2) The mechanical input power to the turbine is made con-
In this figure, and are calculated as stant.
3) The total series compensation is kept at 0.76 p.u. The study
is carried out for the following cases
(16) Case-1:Without SSSC Case-2:With SSSC In Case-1, Fixed
capacitor alone is used for the series compensation with
and in Case-2, hybrid compensa-
(17)
tion is used wherein 0.25 p.u. of series compensation is met
by SSSC and the remaining compensa-
tion is provided by fixed capacitor .
4) In transient simulation, a small mechanical disturbance of
C. Analysis of Subsynchronous Resonance 10% step decrease in mechanical input torque is applied at
0.5 s and restored at 1 s1 s is considered. To validate the
The SSR is analyzed based on damping torque, eigenvalue effectiveness of SSSC under severe fault, a three-phase to
analysis and transient simulation [14]. The steady-state SSR is ground fault applied at generator terminal at 1 s and cleared
analyzed based on damping torque and eigenvalue analysis with after three cycles is considered.
linearized models at the operating point. The transient SSR is
analyzed by transient simulation with nonlinear model of the
system, where the generator stator transients are taken into ac- A. Eigenvalue Analysis
count with the detailed generator model (2.2) [15]. The trans- The eigenvalues of the system matrix for the linearized
mission line is modeled by lumped resistance and inductance to system about an operating point are given in Table I for case
consider the effect of line transients. 1 and case 2. It should be noted that, without SSSC, i.e.,
The graphical representation of resonance condition using in case-1, mode-1 becomes unstable at the operating point
impedance function of SSSC on single phase basis is presented considered. It is to be noted that with the inclusion of SSSC,
in this paper in Section III and is a novel representation to val- (case-2) undamping of mode-1 is reduced and the frequency of
idate the results of damping torque and eigenvalue analysis. It network mode (sub) is increased to 128.4 rad/s. This network
shows the variation of inductive and capacitive reactances with mode closely matches with torsional mode-2 and it turns out
frequency varied from 10–300 rad/s. This graphical represen- to be unstable. This indicates that the introduction of SSSC for
tation presents a clear picture of possible SSR condition in the series compensation increases and shifts the network resonant
system. frequency.

III. CASE STUDY B. Transient Simulation

The system under study is adapted from IEEE FBM [16] The transient simulation is carried out for the combined non-
which consists of a turbine, generator (2.2 model), series com- linear system which includes SSSC represented by both D-Q
pensated long transmission line and SSSC injecting a series and three-phase model using MATLAB-SIMULINK [17].
voltage in the transmission line is shown in Fig. 6. The transient simulation results for a step change of 10% de-
The analysis is carried out by considering the following as- crease in the mechanical input torque applied at 0.5 s and re-
sumptions and initial operating condition. stored at 1 s with three-phase model of three-level VSC based
68 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013

TABLE I
EIGENVALUES OF THE COMBINED SYSTEM WITH AND WITHOUT SSSC

Fig. 8. Variation of damping torque with and without SSSC.

of SSSC, the peak negative damping is significantly reduced

and shifts the network mode frequency (subsynchronous) and
hence undamping of torsional mode-1 is also reduced. The
shifted subsynchronous electrical frequency matches with
mode-2 torsional frequency (127 rad/s) and the corresponding
torsional mode becomes unstable. These results are consistent
with eigenvalue analysis.
2) Graphical Representation of Resonance Condition: The
representation of impedance function of SSSC in single phase
basis from that of D-Q axis is given below.
To obtain , the SSSC equations (along with controller) are
linearized at the operating point and expressed as

(18)

(19)
Fig. 7. Variation of rotor angle and LPA-LPB section torque for step change
in input mechanical torque with three-phase model of three-level VSC based
SSSC. (20)

where
SSSC is shown in Fig. 7. It is clear from Fig. 7 that the system
is unstable as the LPA-LPB section torque grows with time.

C. Discussion
The SSR problems under various operating conditions can is identity matrix.
be predicted by using damping torque analysis. The correla-
tion of damping torque analysis and eigenvalue results in pre-
dicting torsional mode stability is discussed in detail in [18]
which demonstrates the importance of damping torque analysis
to determine the torsional mode stability.
1) Damping Torque Analysis With Linearized Model of
SSSC: Variation of damping torque is shown in Fig. 8 for case (21)
1 and 2. It is to be noted that without SSSC (case-1), damping
torque goes maximum negative at a frequency of about 98 The resistance and the emulated reactance of SSSC
rad/s and matches with torsional mode-1 frequency and severe on single phase basis as a function of frequency is computed
torsional interactions are expected. In case-2 with the inclusion for case-2 with . It is found that, the resistance
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 69

subsynchronous frequency components using filters and miti-

gation of SSR using subsynchronous current suppressor is pre-
sented in the following section.

IV. DESIGN OF SUBSYNCHRONOUS CURRENT SUPPRESSOR

Damping of SSR can be obtained by designing a subsyn-
chronous damping controller (SSDC) which provides positive
damping in the range of critical torsional mode of frequencies
[14]. Damping of SSR using STATCOM is achieved by SSDC
which takes Thevenin voltage signal (a synthesized voltage)
[19] using locally available STATCOM bus voltage and is
used to modulate the reactive reference current to improve the
damping of unstable torsional modes. The present work pro-
poses the improvement of damping of critical torsional modes
by extracting subsynchronous components of line current and
injecting a proportional voltage to suppress the subsynchronous
frequency currents. This is a simple method which reduces the
Fig. 9. Graphical representation of resonance conditions with and without
SSSC. magnitude of subsynchronous currents flowing through the
generator and is termed as subsynchronous current suppressor
(SSCS).
The extraction of subsynchronous frequency current com-
is negligible while the emulated reactance is
ponent is achieved by band-pass filters operate in rotating
practically constant with frequency as shown in Fig. 9.
D-Q coordinates. Accordingly the tuning of filters depends on
The graphical representation of resonance frequency is
the multimass turbine-generator shaft torsional frequencies.
shown in Fig. 9 for cases 1 and 2. It shows the variation of
Hence it is adequate to design filter based on the knowledge
inductive and capacitive reactances with frequency varied from
of torsional mode frequencies to extract the subsynchronous
10–300 rad/s. In case-1, when the fixed capacitor provides
frequency components to damp SSR. In this paper, the IEEE
76% of compensation the resonance oc-
FBM with six mass mechanical system is considered, which has
curs at , where . In case-2,
five natural torsional mode frequencies [4]. The torsional mode
where compensation of 76% is met by and
frequency is taken as the center frequency and the pass band of
, the effective capacitive reactance
filter is chosen from the eigen value analysis in which torsional
is obtained by adding the constant reactance offered by
mode is unstable for the band of subsynchronous network mode
SSSC to that offered by fixed capacitor . The variation of
frequencies closer to that of critical torsional frequency. The
effective capacitive reactance with frequency is
frequency response of band-pass filters for all critical torsional
also shown in Fig. 9. Now the resonance occurs at a frequency
modes are shown in Fig. 10. This method of filter design is
of , where and this is
also valid for any transmission network topologies as only the
consistent with the subsynchronous network mode frequency
complement of network resonance frequencies
as obtained by
matches with torsional frequencies cause SSR. The
eigenvalue analysis and about 127 rad/s obtained by damping
block diagram of subsynchronous current suppressor to extract
torque analysis with SSSC.
subsynchronous frequency components from the line current is
The effect of additional series compensation by SSSC to sup-
shown in Fig. 11. Two band-pass filters (in D-Q frame) are used
plement the existing fixed capacitor is to increase the elec-
to extract each torsional frequency component and
trical resonance frequency of the network. However, this in-
from the line current and . Each filter set is effective only
crease in frequency is not significant as compared to that ob-
for their corresponding torsional mode frequency and improve
tained with the equivalent fixed capacitor offering additional
the damping of respective torsional modes by reducing the
compensation (case-1, in this case). This
negative damping. Subsynchronous current suppressor extracts
illustrates that the SSSC is not strictly SSR neutral however, it
subsynchronous frequency currents corresponding to modes
offers a reactance which remain practically constant with fre-
1, 2, 3, and 4 passed through appropriate gains to for
quency.
obtaining and and sum up the signal to obtain
Hence it is obvious that, to mitigate SSR, the damping of crit-
and as mentioned in the following:
ical torsional modes should be improved by reducing the neg-
ative damping. This paper investigates the application of sub-
synchronous current suppressor for damping SSR. The subsyn-
chronous components of line current can be extracted from the
network using filters with narrow pass band. The extracted sub-
synchronous line current components are used to inject propor-
tional voltages by SSSC to suppress the subsynchronous cur-
rents flowing in the generator. A systematic method to extract where is the torsional mode ( , 2, 3, and 4).
70 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013

Fig. 12. Type-1 controller for SSSC with extracted subsynchronous frequency
components from subsynchronous current suppressor.

A. Application of Genetic Algorithm for Optimization of

Subsynchronous Current Suppressor Parameters
Fig. 10. Frequency response of band-pass filters. The objective of subsynchronous current suppressor is to en-
hance the damping torque by reducing the negative damping at
critical torsional mode frequencies. The synchronizing torque at
torsional frequencies are not significantly affected by the elec-
trical network (with or without damping controller [14]), hence
it is simpler to design subsynchronous current suppressor by op-
timizing the gains to with the objective to minimize the
deviations between the desired damping torque and
actual damping torque to reduce the negative damping in
the range of all torsional mode frequencies. Genetic algorithm
is adopted for optimizing the gains of subsynchronous current
suppressor to ensure the stability in the complete range of all
critical torsional mode frequencies.
On the basis of these facts, the objective function is defined
as

minimize (22)

where , is the p.u.

deviation in generator rotor speed and is the p.u. change
in electric torque, is the summation of squared error over
Fig. 11. Block diagram of subsynchronous current suppressor. the range of series compensation ( to 0.75 p.u and
, and ) up to 100%. To
ensure the stability of the system, the objective function is sub-
Since modal inertia of torsional mode 5 is very high, mode 5 jected to the constraint that
is never excited and filter to extract mode 5 frequency compo- Real part of all eigenvalues (23)
nent is not desired. The extracted subsynchronous voltage or-
ders and (in D-Q frame of reference) are transformed In order that subsynchronous current suppressor minimizes the
to inphase and quadrature components and , re- negative damping, the desired damping torque is taken as pos-
spectively, and are used to modulate the in phase and quadrature itive while ensuring all eigenvalues to have negative real parts.
voltage orders and of SSSC as shown in Fig. 12. However, it was noticed that, when the value of is
The subsynchronous frequency components of various large positive, network mode becomes unstable. Here, the de-
modes extracted from line current are passed through a suitable sired damping torque is taken as 8 p.u. for the entire
gains to and the damping of critical torsional modes are range of torsional frequencies. The outcome of GA optimiza-
improved by properly tuning to using GA making use tion is the gains to which remain unchanged at various
of damping torque analysis. Genetic algorithm has been used operating conditions while ensuring system stability.
to optimize the parameters of control system that are complex
and difficult to solve by conventional optimization methods B. Analysis of SSR With Subsynchronous Current Suppressor
[20]. In the following section optimization of subsynchronous The analysis is performed based on eigenvalue analysis,
current suppressor parameters based on damping torque using damping torque analysis and transient simulation. D-Q model
GA is presented. of SSSC is considered for damping torque and eigenvalue
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 71

Fig. 13. Damping torque with SSSC and SSCS. Fig. 14. Variation of real part of eigenvalue of torsional modes with compen-
sation level with SSSC and SSCS.

analysis and the detailed three-phase model of SSSC is used

for transient simulation.
1) Damping Torque Analysis: The damping torque with
SSSC and GA optimized subsynchronous current suppressor
(case-3) is shown in Fig. 13. It is to be noted that, the peak
negative damping is greatly reduced with subsynchronous
current suppressor.
The negative damping is negligible in the range of torsional
frequencies (60–300 rad/s) and the system is expected to be
stable with the intrinsic mechanical damping and the transmis-
sion line resistance. The variation of real part of eigenvalue of
all torsional modes with compensation level is shown in Fig. 14
when the mechanical damping is neglected. Referring to Fig. 14,
it is observed that all the torsional modes are stable with the pro-
posed subsynchronous current suppressor using optimal param-
eters when the hybrid compensation is varied from 0.3 p.u. to 1
p.u. This demonstrates the robustness of the designed subsyn-
chronous current suppressor in damping subsynchronous oscil- Fig. 15. Variation of emulated reactance of SSSC with SSCS.
lations in the range of series compensation.
The variation of total effective capacitive reactance incor-
TABLE II
porating subsynchronous current suppressor is EIGENVALUES OF THE COMBINED SYSTEM WITH SSSC AND SSCS
shown in Fig. 15 (case-3), it is observed that is not constant
with frequency due to the presence of filters used in subsyn-
chronous current suppressor. The total effective capacitive reac-
tance incorporating subsynchronous current suppressor
never becomes equal to in the frequency range of
50–275 rad/s. It is to be noted that between 275 to 300 rad/s, the
effective capacitive reactance is equal to at two frequencies,
which are close to torsional mode-5. Since the modal inertia of
mode-5 is high, it is unaffected and remain stable as shown in
Fig. 14. All other torsional modes (1–4) and swing mode (0)
are also found to be stable when hybrid compensation is varied
from 0.3 p.u. to 1 p.u. This clearly indicates that the designed
subsynchronous current suppressor ensures that the series com-
pensated power system is free from SSR.
2) Eigenvalue Analysis: The eigenvalues of the system with presence of both SSSC and subsynchronous current suppressor
three-level VSC-based SSSC and SSCS are shown in Table II. (Table II), the following observations can be made.
Comparing the eigenvalue results of with SSSC and without 1) With subsynchronous current suppressor, the damping of
subsynchronous current suppressor (Table I, col-2) and with the torsional modes 1 and 2 has significantly improved.
72 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013

2) The damping of torsional mode-3 and mode-4 is margin-

ally increased with subsynchronous current suppressor.
3) Damping of mode-0 is marginally decreased.
4) Modal inertia of Mode-5 is very high and hence is not ex-
cited.
5) The damping of subsynchronous network mode is signifi-
cantly increased with subsynchronous current suppressor.
3) Transient Simulation: The transient simulation has been
carried out for the overall system including SSSC with sub-
synchronous current suppressor using MATLAB-SIMULINK
[17]. Fig. 16 shows the simulation results for full load of
with the step change of 10% decrease in the input me-
chanical torque applied at 0.5 s and removed at 1 s and sub-
synchronous current suppressor is activated at . It is ob-
served that the section torque is growing with time until ,
when subsynchronous current suppressor is activated at ,
the oscillations of shaft section torque decays with time. The
Fig. 16. Variation of rotor angle oscillation and LPA-LPB section torque for
FFT analysis of the LPA-LPB section torque is performed be- step change in mechanical input torque with SSSC and subsynchronous current
tween 3–8 s with the time spread of 1 s and is shown in Fig. 17. suppressor is activated at .
Referring to Fig. 17, it is observed that in the time span of 3–5 s,
the mode-1 component is predominant and increases with time.
When SSCS is activated at 5 s, the mode-1 component decays
with time and demonstrates the effectiveness of subsynchronous
current suppressor to suppress the subsynchronous frequency
components in the line. Transient simulation for three-phase
fault at generator terminal with fault impedance as given in
IEEE FBM [16] is applied at 1 s cleared after three cycles with
and are shown in Figs. 18 and 19,
respectively. The SSCS gain values to remain unchanged
in all operating points and is observed that with SSCS the os-
cillations of section torque decay with time. The line current
and D-Q components of subsynchronous current when
and following three-phase fault at generator terminals
with SSCS are shown in Fig. 20. It shows that SSCS extracts
subsynchronous frequency components even when the funda-
mental frequency line current is zero . It is to be
noted that, under disturbance conditions the line is expected to
carry currents due to energy exchange between mechanical and
Fig. 17. FFT analysis of LPA-LPB section torque for case-3 (
electrical system at their natural frequencies. As a result, the and , SSCS activated at 5 s).
transmission line carries both subsynchronous and supersyn-
chronous frequency current components . The su-
persynchronous frequency currents in the network contributes C. Discussion
positive damping torque [4]. It is the subsynchronous frequency
component of network currents that cause negative damping. We propose a novel method to extract the subsynchronous
Under disturbances, torsional mode-1 (98 rad/s) gets excited for frequency components from the line current using filters. The
the operating points considered which is most severe torsional design of subsynchronous current suppressor is based on the
mode and contributes maximum negative damping. The FFT damping torque method [18], and genetic algorithm is adopted
analysis of phase “a” line current is performed in the time span for optimizing subsynchronous current suppressor filter gains.
of 1–1.4 s and 2–4 s as shown in Fig. 21 and it is interesting to The results demonstrate the robust performance of the system
note that the subsynchronous network frequency compo- in the entire compensation level and for the different operating
nents of line current decreases with time. From the result of FFT conditions.
analysis of phase “a” of line current, it is evident that the SSCS is In the present work, hybrid compensation is used. While
effective in extracting and suppressing the subsynchronous fre- the series active compensation is provided by the VSC based
quency components of line current even when the fundamental SSSC for the enhancement of power transfer capability, the
frequency line current is zero. This clearly demonstrates the ef- use of subsynchronous current suppressor mitigates the SSR.
fectiveness and robust performance of the proposed SSCS in The damping of all torsional modes in the entire range of
mitigating SSR while to gain values remain unchanged compensation level is improved without the risk of SSR by
under varying operating conditions. employing subsynchronous current suppressor.
THIRUMALAIVASAN et al.: DAMPING OF SSR USING SUBSYNCHRONOUS CURRENT SUPPRESSOR WITH SSSC 73

Fig. 18. Variation of rotor angle and LPA-LPB section torque for three-phase
fault at generator terminal with SSSC and subsynchronous current suppressor Fig. 20. Line current magnitude and D-Q components of subsynchronous cur-
when . rent for three-phase fault at generator terminal when .

Fig. 19. Variation of rotor angle and LPA-LPB section torque for three-phase
fault at generator terminal with SSSC and subsynchronous current suppressor Fig. 21. FFT analysis of line current in phase “a” when .
when .

2) The inclusion of SSSC reduces the risk of SSR by detuning

V. CONCLUSION
the network resonant frequency. Although the introduc-
In this paper, the characteristics of a hybrid compensated tion of SSSC reduces the peak negative damping, properly
transmission line with series capacitor and SSSC is analyzed. designed subsynchronous current suppressor improves the
The converters are modeled using switching functions. The damping of all the critical torsional modes.
time invariant model is derived based on D-Q variables. The 3) The subsynchronous current suppressor effectively im-
predictions about the stability of torsional modes using various proves the damping of torsional modes in the entire range
methods of analysis shows good agreement. A simple technique of compensation level and for the different operating
for the extraction of subsynchronous frequency components conditions.
using filters is proposed. Filter gains are optimized using GA 4) The SSCS is effective in extracting and suppressing the
and is based on damping torque analysis. subsynchronous frequency components of line current
The following points emerge based on the results of the case under various disturbances even when the operating point
study. fundamental frequency line current is zero.
1) The SSSC is not strictly SSR neutral, however it offers a re- 5) The risk of SSR is totally eliminated with the inclusion of
actance which remains practically constant with frequency subsynchronous current suppressor as electrical resonance
and increases the electrical resonant frequency of the net- condition is eliminated in the practical range of series com-
work when constant reactive voltage control is adopted. pensation levels.
74 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 28, NO. 1, FEBRUARY 2013

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