a comparative study of damping subsysnchronous resonance using tcsc and imdu

1. 978-1-4673-0766-6/12/$31.00 ©2012 IEEE
A Comparative Study of Damping Subsynchronous
Resonance Using TCSC and IMDU
Prakash Chittora
Electrical Department
Delhi Technological University
Delhi, India
prakashchittora@gmail.com
Narendra Kumar
Electrical Department
Delhi Technological University
Delhi, India
Dnk_1963@yahoo.com
Abstract— Damping SSR oscillation has been a topic of great
interest and research. The advent of series FACTS controllers,
e.g. Thyristor Controlled Series Capacitor (TCSC) and Static
Synchronous Series Compensator (SSSC) has made it possible
not only for the fast control of power flow in a transmission line,
but also for the mitigation of Subsynchronous Resonance (SSR)
in the presence of fixed series capacitors. An idea is presented in
this paper for damping of subsynchronous resonance with TCSC
and its comparison with IMDU in which no controllers is needed.
The IEEE First Benchmark Model for subsynchronous
resonance studies is used to conduct eigenvalue analysis. The
time domain simulation study under large disturbance condition
is carried out with IMDU located at the HP turbine end of T-G
shaft and TCSC connected along the transmission line. This
paper presents a simple design for TCSC scheme in which
constant firing angle model is used. This paper shows that
damping characteristics obtained by using IMDU are better than
TCSC; But TCSC can be used for damping SSR as well as
controlling the active power flow. The results are obtained by
modelling a linearized system in MATLAB.
Keywords— Induction machine damping unit (IMDU),
subsynchronous resonance (SSR), Thyristor controlled switched
capacitor (TCSC), modelling, IEEE first benchmark model,
eigenvalue analysis, SSR
I. INTRODUCTION
Growth of electric power transmission facilities is restricted
despite the fact that bulk power transfers and use of
transmission systems by third parties are increasing.
Transmission bottlenecks, non-uniform utilization of facilities
and unwanted parallel path or loop flows are not uncommon.
Transmission system expansion is needed, but not easily
accomplished. Factors that contribute to this situation include
a variety of environmental, land-use and regulatory
requirements. As a result, the utility industry is facing the
challenge of the efficient utilization of the existing AC
transmission lines.
Flexible AC Transmission Systems (FACTS) technology
is an important tool for permitting existing transmission
facilities to be loaded, at least under contingency situations, up
to their thermal limits without degrading system security [1-4].
The most striking feature is the ability to directly control
transmission line flows by structurally changing parameters of
the grid and to implement high-gain type controllers, based on
fast switching.
A problem of interest in the power industry in which
FACTS controllers could play a major role is the mitigation of
Subsynchronous Resonance (SSR) oscillations. SSR is a
dynamic phenomenon in the power system which has certain
special characteristics. Numerous modelling techniques and
improvements on these schemes have also been given [5-6].
The use of stored magnetic energy has been published in [7].
The idea of the induction machine damping unit (IMDU) to
supress the SSR was introduced in [8] and extended in [9].
IEEE second benchmark model [13] for subsynchronous
resonance was used in [10] to analyse the damping properties
of an IMDU.
The main emphasis of this paper is to test the effectiveness
of IMDU and TCSC for damping SSR in a series compensated
system and compare their results. This paper also present a
simple design for TCSC scheme in which constant firing angle
model is used. The paper shows that damping characteristics
obtained by using IMDU are better than TCSC, But TCSC can
be used for damping SSR as well as Controlling the active
power flow. The IEEE First Benchmark Models [11] for
subsynchronous studies is used to conduct eigenvalue analyses
and time domain simulations.
II. SYSTEM DESCRIPTION
A. Synchronous Machine Model
We have use Model 1.1 (Field circuit with one
equivalent damper on q-axis) published By IEEE task force, of
synchronous machine for modelling.
The electrical dynamic equations of the synchronous
machine are presented below [12]:
1) Stator Equation:
(1)qadm
q
q iRS
dt
d
v
B
−Ψ+−
Ψ
−= )1(
1
ω

2. Fig.1. A series capacitor compensated network model
(2)
2) Rotor Equations:
(3)
(4)
B. Network Model
Fig.1. shows that a series capacitor-compensated
transmission line may be represented by the RLC circuit [12]
III. SYSTEM MODELLING FOR EIGENVALUE ANALYSIS
We shall now demonstrate the damping effects of IMDU
and TCSC through eigenvalue analysis. To do this, we have to
develop a linear model of the overall system. The linearized
models for the generator and shaft system for IEEE first
benchmark model are well documented. Here, we use the
approach given in [10].
A. Combined Generator and Shaft System Model
The linearized state equations are given by:
(5)
(6)
Where the state vector GxΔ , input vector guΔ and output
vector GyΔ are given by
B. Modelling the Transmission Line
The differential equations for the circuit elements, after
applying Park’s transformation, can be expressed in the d-q
reference frame as following
The voltage across the capacitor(12):
(7)
The above equations can be represented in state space
model as:
(8)
Where state vector NxΔ and Input vector 1NuΔ are
Fig.2. IMDU connected to the system
daqm
d
d iRS
dt
d
v
B
−Ψ+−
Ψ
−= )1(
1
ω
[ ]qqqd
qo
d
ixxE
Tdt
dE
)'('
'
1'
−−−=
[ ]fddddq
do
q
EixxE
Tdt
dE
+−+−= )'('
'
1'
[ ] [ ] [ ] fdGgGGGG EBuBxAx 21 +Δ+Δ=Δ
•
[ ] GGG xCy Δ=Δ
ΔΔ=Δ me
t
G xxx
=Δ LPBLBGGENGEEXCGEN
t
m STSTSx δ
HPHIIPILALPALAB STSTST
ΔΔΔΨΔΨ=Δ '' qdqd
t
e EEx
[ ]QD iiy
t
G ΔΔ=Δ
Δ
Δ
+
Δ
Δ−
=
Δ
Δ
•
•
Q
D
CB
CB
Q
D
B
B
CQ
CD
i
i
X
X
Vc
Vc
V
V
ω
ω
ω
ω
0
0
0
0
[ ] [ ] [ ] 2211 NNNNNNN uBuBxAx Δ+Δ+Δ=Δ
•
[ ] ΔΔ=Δ CQCD
t
VVxN
[ ]
Δ
Δ
=Δ
Q
D
N
i
i
U 1

3. C. Modelling the Induction Machine Damping Unit
Fig.2. shows IMDU connected to system. For the
eigenvalue analysis, the torque-speed characteristics of an
induction machine, with small rotor resistance, to be used as
IMDU can be considered linear between synchronous speed
and the critical slip (maximum torque) when operated at
constant terminal voltage and frequency. Therefore, the torque
of the damping unit can be modelled as being proportional to
speed deviation, (deviation from synchronous speed). The
slope of the torque-speed characteristic as follows [10]:
The field exciter dynamics is not modelled and the
excitation is held constant at 1 pu. The time constant of the
mechanical system is very large when compared to the
electrical system, and hence, the speed governor dynamics are
not included, keeping the input power to the turbines constant.
Variables torque produced in the different shaft section, which
are functions of the difference of the slip at the ends of the
shaft. The differential equations governing the IMDU model
are as follows [10]:
(9)
(10)
D. Modelling TCSC unit
The TCSC is modelled [14] in detail taking into
consideration of the switching action of thyristors for transient
simulation. The eigenvalue analysis is based on the dynamic
phasor model of TCSC given in reference, where the TCSC is
modelled as a variable capacitor.
The equations of TCSC in D-Q frame of reference can be
given as [14]
(11)
(12)
Where
Where
(13)
The prevailing conduction angle can be approximated as
(14)
Where is the conduction angle reference .
E. Combined System Model Including IMDU only
On combining generator, network and IMDU equations
(5), (6), (8), (9), (10) The final system state space model
equations are
(15)
Where
F. Combined System Model Including TCSC only
On combining generator, network and TCSC equations
(5),(6),(8),(11),(12), the final system state space model
equations are
(16)
Where
IM
IMT
k
ωΔ
Δ
=
[ ]
[ ] [ ] [ ]
[ ] [ ]
+
=
NGN
GGGI
TI
ACB
HBHFBA
A
1
111
ΔΔ=Δ NGITI xxx
t
ctc
B
tCQCeffD
tCD
b
VbI
dt
dV ω
)( −=
ctc
B
tCDCeffQ
tCQ
b
VbI
dt
dV ω
)( +=
[ ] [ ] [ ] 221 NTfdTT uBEBxAx TT Δ+Δ+Δ=Δ
•
ΔΔΔ=Δ TCSCNG
t
xxxxT
ΔΔ=Δ me
t
G xxx
IM
PI
IM
IM
IM
IM
H
T
S
H
kD
S
22
−
−
−=
•
( )HPIMIMPI SSKT −=
•
[ ] [ ] [ ] 221 NTfdTTI uBEBxAx TITI Δ+Δ+Δ=Δ
•
.).(
1
.).(.).( up
X
upCupb
tc
tcctc ==
.).(.).( upCupb effCeff =
.).(.).( upXupL tltl =
1
2
2
2
)
2
tan()
2
tan()
2
(cos
1
2
)sin(
21
1
2
1
41
)(
−
−
−
−
+
+
−
−=
σσσω
σσ
π
σ
t
t
t
ttLr
ttC
tC
eff
k
k
k
SkL
kC
C
C
tLtC
r
LC
1
=ω
2
1
1
−
−
=
tk
S
tL
tC
t
X
X
k =
φσσ 2*
+=
]arg[2*
tCVjI−+≈ σ
)]()arg[(2*
tCDDtCQQtCDQtCQD VIVIjVIVI −−−+= σ
**
2απσ −=

4. Where
TABLE I EIGEN VALUES OF SYSTEM IN DFFERENT CASES
S.No. Without IMDU
P=0.7 ,P.F.=0.9,
Xc=0.35
With IMDU Only
P=0.7 ,P.F.=0.9
Xc=0.35
With TCSC Only
P=0.7 ,P.F.=0.9
Xc=0.35,XTCSC=0.20
Comments
1 -0.46505 + j10.128
-0.46505 – j10.128
-1.88054 + j10.081
-1.88054 – j10.081
-1.0409 + j14.162
-1.0409 - j14.162
Torsional
Mode #0
2 0.043375 + j99.574
0.043375 – j99.574
-2.33 + j96.698
-2.33 – j96.698
-0.25793 + j98.237
-0.25793 – j98.237
Torsional
Mode #1
3 0.028616 + j127.13
0.028616 – j127.13
-0.59096 + j126.27
-0.59096 – j126.27
-1.316 + j126.98
-1.316 – j126.98
Torsional
Mode #2
4 0.03606 + j160.34
0.03606 – j160.34
-5.0673 + j147.1
-5.0673 – j147.1
-0.33452 + j160.54
-0.33452 – j160.54
Torsional
Mode #3
5 0.001427 + j202.85
0.001427 – j202.85
-0.27956 + j201.61
-0.27956 – j201.61
-0.085585 + j202.9
-0.085585 – j202.9
Torsional
Mode #4
6 -2.879e-07 + j298.18
-2.879e-07 - j298.18
-2.1094 + j286.73
-2.1094 – j286.73
-0.36358 + j298.18
-0.36358 – j298.18
Torsional
Mode #5
7 -3.3979 + j141.26
-3.3979 – j141.26
-2.7704 + j142.04
-2.7704 - j142.04
-1.8704 + j67.84
-1.8704 – j67.84
Network
Mode #1
8 -4.4197 + j612.42
-4.4197 – j612.42
-4.4197 + j612.42
-4.4197 - j612.42
-0.48833 + j497.65
-0.48833 – j497.65
Network
Mode #2
9 -0.083245 -0.082673 -6.1563
10 -4.0937 -4.0916 -0.1718
11 -23.67 + j737.19
-23.67 – j737.19
-3.8336+ j733.5
-3.8336 - j733.5
[ ]
[ ] [ ] [ ] [ ]
[ ]
+
=
21
21
1111
0* FCF
BACB
HBHBHFBA
A
G
NNGN
GGGG
T
[ ] [ ] [ ]+
=
0
212
1
GGG
B
L
G
T
BHCB
X
B
B ω
[ ]
[ ]
[ ]
=
2
1
2
N
G
T
B
HB
B
=
ctc
B
ctc
B
b
b
F
ω
ω
0
0
1
−
=
0
0
2
B
ctc
Ceff
B
ctc
Ceff
b
b
b
b
F
ω
ω
=Δ LPBLBGGENGEEXCGEN
t
m STSTSx δ HPHIIPILALPALAB STSTST
ΔΔΔΨΔΨ=Δ '' qdqd
t
e EEx
ΔΔ=Δ tCQtCD
t
TCSC vvx

5. IV.SYSTEM STUDIES
The system considered is the IEEE first benchmark model
for SSR analysis [11]. The FBS system is simulated with the
help of MATLAB. The Network parameter are based on
generator base of 892.4 MVA are given in [12] .The
Synchronous M/C data are given in [12].The shaft inertia and
spring constant are given in [12]. There are six inertia
corresponding to six rotors, which are four turbines, one
generator and one rotating exciter. Inertia constant of IMDU is
0.034248645 sec.
A steady-state operating point is chosen in which the
machine operates with a power factor of 0.9 while delivering a
power of 0.7 p.u. Self-damping of 0.1 is added to the shaft. No
mutual damping is assumed. Constant field voltage is also
assumed. Infinite bus voltage is 481.33 kV.
For TCSC we assume XC=0.35, which is the compensation
level of system and XTCSC=0.20, with vernier ratio
XTCSC/Xtl=1.25
Table I shows eigenvalues of system with and without
IMDU and TCSC. As we can see that on adding IMDU and
TCSC, the system eigenvalues have real negative parts. This
indicates that system has reached in stable configuration.
V. TIME DOMAIN ANALYSIS
A digital computer simulation study, using a linearized
system model, has been carried out to demonstrate the
effectiveness of the proposed controllers. The MATLAB
SIMULINK model was used to obtain time domain simulation
under large disturbances. The IMDU is coupled to HP and
electrical connected to System. The TCSC is connected in the
network. The SIMULINK model is run for 10 seconds and
various shaft torques and power angle delta response were
obtained. Fig.3. (a,d,g,j,m,p) shows the response obtained
without IMDU. Fig.3. (b,e,h,k,n,q) the same responses when
IMDU is connected to the system. Fig. 3.(c,f,i,l,o,r) shows the
responses when TCSC connected to the system. We see that
SSR is effectively damped out by using IMDU and TCSC.
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(j) (k) (l)
Gen-Exc Torque (pu)
1.0
0.5
0.0
-0.5
-1.0
Time, s
Gen-LPB torque (pu)4.0
2.0
0.0
-2.0
-4.0
Time, s
Gen-LPB torque (pu)4.0
2.0
0.0
-2.0
-4.0
Time, s
LPA-LPB torque (pu)
4.0
2.0
0.0
-2.0
-4.0
Time, s
0.2
0.1
0.0
-0.1
-0.2
Gen-Exc Torque (pu)
Time, s
Gen-LPB torque (pu)
6.0
3.0
0.0
-3.0
-6.0
Time, s
Time, s
LPA-LPB torque (pu)
5.0
2.5
0.0
-2.5
-5.0
LPA-HI torque (pu)
Time, s
3.0
1.5
0.0
-1.5
-3.0
LPA-HI torque (pu)
Time, s
3.0
1.5
0.0
-1.5
-3.0 Time, s
LPA-HI torque (pu)
1.6
0.8
0.0
-0.8
-1.6
Gen-Exc Torque (pu)
1.0
0.5
0.0
-0.5
-1.0
Time, s
LPA-LPB torque (pu)
4.0
2.0
0.0
-2.0
-4.0
Time, s

6. Power angle
Time, s
2.0
1.0
0.0
-1.0
-2.0
(m) (n) (o)
(p) (q) (r)
Fig.3. (a) Generator exciter torque oscillations with fixed capacitor, (b) Generator exciter torque oscillations with IMDU, (c) Generator exciter torque
oscillations with TCSC, (d) Generator LPB shaft torque oscillations with fixed capacitor, (e) Generator LPB shaft torque oscillations with IMDU, (f) Generator
LPB shaft torque oscillations with TCSC, (g) LPA-LPB shaft torque oscillations with fixed capacitor, (h) LPA-LPB shaft torque oscillations with IMDU,
(i) LPA-LPB shaft torque oscillations with TCSC (j) LPA-HI shaft torque oscillations with fixed capacitor, (k) LPA-HI shaft torque oscillations with IMDU,
(l) LPA-HI shaft torque oscillations with TCSC, (m) HI shaft torque oscillations with fixed capacitor, (n) HI shaft torque oscillations with IMDU (o) HI shaft
torque oscillations with TCSC, (p) Power angle oscillations with fixed capacitor, (q) Power angle oscillations with IMDU, (r) Power angle oscillations with
TCSC
VI. CONCLUSIONS
Eigenvalue studies and time domain simulations conducted
on the IEEE First Benchmark Models show the damping
benefits on SSR of IMDU and TCSC the major findings of the
study are as follows.
1) The inclusion of the IMDU on the T-G shaft can damp
torsional interaction type of SSR oscillations without
the aid of any other controller.
2) The TCSC also damp SSR to a great extent. Besides
damping SSR, it also works as to control active power
flow. So TCSC is much more effective than IMDU
3) In case of IMDU there is no need of any external
controller so design difficulties reduces to a much low
level as compared to TCSC where there need extra
effort to design a suitable controller.
4) The IMDU is a small-size high power and low energy
induction machine connected in mechanical system of
Machine, whereas TCSC is connected in network
system.
5) The IMDU can be switched on only after a disturbance
is detected.
6) TCSC are already installed and working well whereas
IMDU is a new concept to damp SSR.
7) The range of value of K (Slope of torque-speed
characteristics) found to be lye between 3 to 5.
So overall we can say that SSR damping using IMDU has
greatest advantage of being independent of any external
controller but limit is also that it has to be mechanically
connected to generator as compared to TCSC where it can be
installed anywhere in the line and also has extra role of being
able to control active power flow as well.
REFERENCES
[1] Song, Y. H. and Johns, A. T., Flexible AC transmission systems
(FACTS), London, Institution of Electrical Engineers, 1999.
[2] Hingorani, N. G. and Gyugyi, L., Understanding FACTS: concepts and
technology of flexible AC transmission systems, New York, IEEE Press,
2000.
[3] Acha, E., FACTS: modelling and simulation in power networks,
Chichester, Wiley, 2004.
[4] Mathur, R. M. and Verma, R. K., Thyristor-based FACTS controllers
for electrical transmission systems, Piscataway, NJ, IEEE, 2002.
[5] B. K. Perkins and M. R. Iravani, “Dynamic modeling of a TCSC with
application to SSR analysis,” IEEE Trans. Power Syst., vol. 12, no.
4,pp. 1619–1625, Nov. 1997.
[6] X. Zhao and C. Chen, “Damping subsynchronous resonance using an
improved NGH SSR damping scheme,” in Proc. IEEE Power Eng. Soc.
Summer Meeting, Jul. 1999, vol. 2, pp. 780–785.
[7] W. Li, L. Shin-Muh, and H. Ching-Lien, “Damping subsynchronous
resonance Using superconducting magnetic energy storage unit,” IEEE
Trans. Energy Convers., vol. 9, no. 4, pp. 770–777, Dec. 1994.
[8] S. K. Gupta, A. K. Gupta, and N. Kumar, “Damping subsynchronous
resonance in power systems,” Proc. Inst. Elect. Eng., Gen.,
Transm.,Distrib., vol. 149, no. 6, pp. 679–688, Nov. 2002.
[9] K. Narendra, “Damping SSR in a series compensated power system,”
in Proc. IEEE Power India Conf., 2006, p. 7.
[10] S. Purushothaman, “Eliminating Subsynchronous oscillations with an
Induction Machine Damping Unit (IMDU)” IEEE Trans. On Power
System, vol. 26, No. 1,Feb. 2011.
[11] IEEE Subsynchronous Resonance Task Force, “First benchmark model
for Computer simulation of subsynchronous resonance,” IEEE Trans.
Power App. Syst., vol. PAS-96, no. 5, pp. 1565–1572, Sep. 1977.
[12] K. R. Padiyar, Power System Dynamics stability and control, BS
Publication, second Edition, 2008.
[13] IEEE Subsynchronous Resonance Working Group, “Second
benchmark model for computer simulation of subsynchronous
resonance,” IEEE Trans. Power App. Syst., vol. PAS-104, no. 5, pp.
1057–1066, May 1985.
[14] Paolo Mattavelli, Alexander M Stankovic and George C
Verghese, .SSR Analysis with Dynamic Phasor Model of Thyristor
Controlled Series Capacitor ., IEEE Transactions on Power Systems,
Vol. 14, No. 1, pp. 200-208, February 1999.
HI shaft torque (pu)
Time, s
2.0
1.0
0.0
-1.0
-2.0
HI shaft torque (pu)
Time, s
2.0
1.0
0.0
-1.0
-2.0
Time, s
0.6
0.3
0.0
-0.3
-0.6
HI shaft torque (pu)
Time, s
3.0
1.5
0.0
-1.5
-3.0
Power anglePower angle
Time, s
2.0
1.0
0.0
-1.0
-2.0