Engineering, 2013, 5, 180-184
doi:10.4236/eng.2013.51b033 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Application of STATCOM for Damping Subsynchronous
Resonance in a Multi-machine System
Yanlong Sun, Liangeng Ban, Daye Yang, Yizhen Wang
China Electric Power Research Institute, Beijing, China
Abstract
Results of an investigation on the application of STATCOM for damping subsynchronous resonance (SSR) in a mul-
ti-machine system is presented in this paper. For a multi-machine system which has a set of identical parallel tur-
bine-ge nerato rs or no n-identical turbine-generators having torsional modes of the same frequenc y, generators may suf-
fer from the same mode of torsional interaction corresponding to a certain series compensation degrees. Generators in
such system ma y have different oscillation beha viors when they are unequally loaded or have different shaft and elec-
trical parameters. Serving as the grid-side equipment, the reactive power output of a STAT COM could have an impact
on all generators electrical distance nearby. Thus a single STATCOM could be used to damp torsional interactions of
multi-generators when additional proper control strategy is supplemented. In this paper, control strategy of using
STATCO M to damp SSR in a multi-mac hine sys tem is de signed and its effec tiveness is validated based on a modified
IEEE second benchmark model.
Keywords: subsynchronous resonance (SSR); multi-machine system; STATCOM; mode partition controller (MPC).
1. Introduction
Areas that have an uneven distribution of energy and
load need transmission of bulk power over long distance
to realize the op timal arrangement of resources. For s uch
long distance transmission systems, steady state stability
limit is often the bottleneck factor that constrains the
transmission capability of the system. Use of series ca-
pacitor compensation could reduce the equivalent reac-
tance of the transmission line and significantly improve
steady state stability limit of the system. Thus, series
compensation has been widely used worldwide as a
cost-effective measure to improve the transmission capa-
bility. However, transmission systems with series com-
pensation may have an electromechanical coupling with
the nearby turbine-generators, causing subsynchronous
resonance (SSR) and cause loss to the fatigue life of the
generator shaft.
For transmission systems with series compensation, its
sendi ng end genera lly ha s mor e than one unit, often with
multiple units of a power plant or several power plants
having short electrical distance from each other. Thus a
system of multi-machine delivered through series com-
pensation line is formed. For systems that have parallel
identical turb ine-ge nerato rs or non -identical units having
torsional modes of the same frequency, generators may
suffer from the same mode of torsional interaction at a
certain series compensation degrees. Reference [2, 3]
conducted a research on the SSR characteristics of two
kinds of multi-machine system. Results show that oscil-
lation behaviors of unequally-loaded parallel identical
generators and non-identical units having torsional mod-
es of the same frequency may have different amplitude
and phase, relating to their output level or modal para-
meter differences.
As a new type of reactive power compensation FACTS
device, STATCOM has a fast and smooth control per-
formance. By applying appropriate control strategies,
STATCOM could b e used to damp SSR . Taki ng gener a-
tor speed as the input signal, [4] propose a way to excite
additional electromagnetic torq ue at the modal frequenc y
by injecting controllable compensation current into the
generator using STATCOM, thus to damp torsional inte-
raction of the generator. Reference [5] take local voltage
as input signal and damp SSR by modulating the reactive
current reference of STATCOM. By monitoring subsyn-
chronous frequency current component in the transmis-
sion line and injecting corresponding compensation cur-
rent into the grid using STATCOM, these current com-
ponents could be prevented from flowing into the gene-
rator set, so as to achieve the intention of damping SSR
[6].
Various control strategies have been designed to damp
SSR using STATCOM in above references, but all these
researches are based on the single-machine system,

Y. L. S UN ET AL.
181
making these control strategies ap plicable only for sin-
gle-machine system and parallel identical generators
with same operating conditions [7]. For multi-machine
system in which generators have different oscillation
behavior, a STATCOM control strategy is proposed in
this paper to damp torsional oscillatio ns of all gener ator s.
All generator s’ spee d is needed as the input signal to the
STATCOM and a reactive power reference is generated
through moda l partition controller . Time do main si mula-
tions based on a modified IEEE second benchmark mod-
el are carried out to validate the effectiveness of the pro-
posed strategy.
2. System Modeling
In multi machine system, torsional interaction occurs
onl y bet we en t ho se un its t ha t ha ve t o rsi ona l mod es of t he
same frequency. EPRI suggests that if corresponding
torsional vibration frequencies of the units are different
from each other more than 1%, the original mul-
ti-machine system could be simplified into a sin-
gle-machine system by reserving the unit concerned,
while replacing other units by its subtransient reactance
and a fixed voltage source. In addition, parallel identical
generators with same operating conditions can be studied
as an equivalent single unit. Therefore, in the study of
the multi-machine system SSR, only unequally-loaded
parallel identical generators and non-identical units hav-
ing torsional modes of the same frequency are consi-
dered in this paper.
System Ⅱ of the IEEE second benchmark model
represents a system in which two non-identical genera-
tors that both have a torsional mode of 24.65Hz deliver
power through a series compensated line [8]. In order to
incorporate unequally-loaded parallel identical genera-
tors into the model, an additional generator with the
same parameters as the original 700MVA unit in [8] is
added to the high-voltage bus in the power plant. Fig. 1
sho ws the o ne-line diagram of the modified IEEE second
benchmark model, with STATCOM connected at the
high-voltage b us in the po wer pl ant.
In fig.1, gen 1 has a capacity of 600MVA and its me-
chanical system comprises four masses, i.e., the
high-pressure turbine (HP ), the low-pressure turbine (LP),
the generator (GEN), and the exciter (EXC), with three
subsynchronous torsional oscillation modes of
24.65Hz、32.39Hz and 51.1Hz; gen 2 has a capacity of
700MVA and its mechanical system comprises three
masses, i.e., the high-pressure turbine (HP), the
low-pressure turbine (LP), and the generator (GEN), with
two subsynchronous torsional oscillation modes of
24.65Hz and 44.9 9H z.
By adjusting gen 2 and gen 3 to different output level,
this model comprises both unequally-loaded parallel
identical generators and non-identical units having tor-
sional modes of the same frequency. Thus it could
represent various kinds of multi-machine system that we
concern about. The STATCOM is adjusted to work at
constant reactive power control.
R
L
jX
L
-jX
C
Gen 1 600MVA
R
1
，X
1
R
2
，X
2
R
2
，X
2
STATCOM
VSC
Gen 2 700MVA
Gen 3 700MVA
Fig. 1 Modified IEEE second benchmark model with STATCOM
3. STATCOM Controller Design
As mentioned in part 1, STATCOM could be applied
to damp SSR of a single-machine system under a variety
of co ntrol strategies, but not all these strategies can adapt
to the damp of SSR in multi-machine system. Output of
the generators will have a corresponding change when
volta ge of its export bus is modula ted through the contro l
of the reactive power output of the STATCOM, thus a
controllable additional electromagnetic torque is induced
on the ge nera tor sha ft. W ith pro per p hase adjustment, t his
additional torque could be used to damp the torsional
oscill ation of the generator shaft. Since gener ators in most
multi-mac hine system connect to a co mmon sendi ng bus,
volta ge modulation of the common bus using STAT COM
could have an impact on all the generators. If the
STAT COM is control led based on the synthetic consider-
ation of the different oscillation behaviors of all genera-
tors, SSR in multi-machine system could be damped us-
ing STATCOM installed o n the common bus.
3.1. Modal partition controller
In order to damp SSR, STATCOM’s reactive power
output should use the generator speed as a reference.
For single generator suffered from SSR, when its shaft
speed rises, the STATCOM should be controlled to
improve the bus voltage. Consequently, output of the
generator as well as the electromagnetic torque on the
shaft would increase. Under the condition of constant
mechanical torque input on the shaft, STATCOM’s

Y. L. S UN ET AL.
182
regulation would play an decelerate effect on the ge-
nerator. For condition that shaft speed decreases, the
above process would be the opposite. Since STAT-
COM could regulate its reactive power output rapidly,
it could be used to damp SSR.
Generator shaft usually has more than one torsional
vibration mode. In order to avoid reciprocal influence
between different mode control loops, structure of
mode partition shown in Fig. 2 is used.
ω
0
ω
+
-
ssr
Q
band pass
filter
(mode n)
proportional
(mode n)
phase
compensation
(mode n)
band pass
filter
(mode 1)
proportional
(mode 1)
phase
compensation
(mode 1)
band pass
filter
(mode 2)
proportional
(mode 2)
phase
compensation
(mode 2)
… … …
+
++
Fig. 2 Mode partition controller
The input signal of the mode partition controller (MPC)
is the generator speed ω. Speed deviation could be ob-
tai ned b y d ifferencing ω and the synchronous speed ω0.
Speed signal o f each torsiona l mode could b e separated
from the speed deviation using specially designed high
qual ity facto r ba nd -pass filter, which has a same center
frequency as the corresponding torsional mode. Pa ra-
meters of proportional and phase compensation com-
ponent for each torsional mode could be designed in-
dependently due to the use of a parallel multi-channel
controller structure. Summation of the output of each
channel yields the reactive power reference QSSR for
the STATCOM to damp SSR. In order to avoid unex-
pected overregulation, limitation components are used
at the end of each channel and the final output of the
contro ller.
3.2. Phase compensation component design
The most critical part in the MPC design process is the
determination of the phase compensation parameter for
each mode channel. With inappropriate phase compensa-
tion, STAT COM may s ti mula te SSR rat her t han d a mp it.
According to the complex torque coefficient method [9,
10], STATCOM can damp SSR when the phase differ-
ence between the additional electromagnetic torque
caused by the control of STATCOM and the modal
speed of the gener ator is in the range of -90°~+90°.
Fig. 3 shows the overall flow diagram of damping SSR
using STATCOM. Process from the additional reactive
power reference Qref_SSR to the additional electromagnetic
torque ∆T e_SSR may cause some phase shift, depending
on the phase characteristics of STATCOM and transmis-
sion system. In order to damp SSR, some phase com-
pensation components are needed in the MPC to adjust
the phase difference between ∆T e_SSR and ∆ω m into the
range of -90°~ +90°. With other components stay the
same, maximum damping can be get when ∆ω m is in
phase wit h ∆Te_SSR.
damp
mode speed
Δω
m
ΔT
e_SSR
mode
partition
controller
generate Q
ref_SSR
STATCOM
reactive power
output
system
characteristic
Fig. 3 overall flow diagram of damping SSR using STATCOM
Specific frequency signal can be used to calculate the
phase difference needed to be compensated by MPC.
When applying a sinusoidal reactive power instruction
Qtest at a torsional frequency at STATCOM, corres-
ponding additional electro-magnetic torque will emerge
on the shaft. The corresponding frequency electromag-
netic torque component ∆Te_test can be separated using
Fourier analysis. Phase difference Δφsys between Qtest
and ∆Te_test is just the total phase deviation of STAT-
COM and the transmission system at this particular fre-
quency, thus MPC needs to compensate a phase in the
range of -Δφsys±90° in this mo de channel.
3.3. STATCOM Controller for Multi-machine
System
In the control strategy described above, output of
STATCOM will affect the torsional frequency of the
shaft slightly besides it s damp of the torsional oscillatio n
when phase difference between ∆Te _SSR and ∆ωm is
not 0°. If only one generator speed is taken as the input
signal in a multi-machine system, only this generator’s
torsional oscillation could be damped. Although the
initial phase difference between its mode speed and
additional ele ctro magneti c t orq ue is i n t he r a nge o f -90°~
+90°, torsional oscillation still couldn’t be damped due
to the influence of STATCOM on the torsional
frequency of its shaft for other generators. This
phenomena has been verified by [2] based on a
dual-machine system with SVC.
MPC
gen 1
+-
1G
ω
2G
ω
GN
ω
0
ω
MPC
gen 2
+-
0
ω
MPC
gen N
+-
0
ω
… …
limitation
1ssr
Q
2ssr
Q
ssrN
Q
Σ
ssr
Q
total
reactive power
reference
Fig. 4 STATCOM controller for Multi-machine system

Y. L. S UN ET AL.
183
Different oscillation behaviors of multiple generators
must be taken into consideration in the design of control
strategy for damping SSR in a multi-machi ne s yste m. B y
designing independent MPC for each generator and tak-
ing all generators’ speed as input signal, a total reactive
power reference can be synthesized for STATCOM to
damp torsiona l oscillatio ns of all generators.
4. Digital Simulation
To demonstrate the effectiveness of proposed control
strategy for damping SSR in multi-machine system, the
EMTDC/PSCAD program is used to do a simulation on
the dynamic performance of the system modeled in sec-
tion Ⅱ. The analysis is carried based on the following
initial operating condition and assumptions.
012345678
-20
0
20 gen 1
012345678
-10
0
10 gen 2
Speed deviation （ r ad/s ）
012345678
-20
0
20 gen 3
Time（sec）
Fig. 5 System responses without SSR damping controller
05 10 15 20 25 30
-2
0
2gen 1
0510 15 20 25 30
-1
0
1gen 2
Speed deviation （ r ad/s ）
05 10 15 20 25 30
-1
0
1gen 3
Time（sec）
Fig. 6 System responses with SSR damping controller
1. Gen1, gen2, and gen3 deliver 0.9 p.u., 0.9 p.u.,
and 0.1 p.u. power to the transmission line re-
spectively.
2. The input mechanical power to the three genera-
tors’ turbine is co nstant.
3. The compensation level provided by the series
capacitor is 47% of the line reactance XL.
4. A three phase line-to-ground instantaneous fault
is applied at the infinite bus at 2.5 sec and re-
moved 0.01 sec later.
At a compensation level of 47%, the electric system has
a negative damping at the common torsional frequency
of the three generators. Without SSR damping control,
the system is unstable after the fault is cleared. Speed
deviation curve of the three unit obtained by transient
simul ation is shown in Fig. 5. It can also be seen from
Fig. 5 that although the three units are oscillating at the
same frequency, their amplitude are different as a result
of different shaft parameter and output level.
Fig. 6 shows the si mulatio n result of the speed d eviatio n
curve of the three units when multi -machine SSR damp-
ing controller is added to STATCOM. It can be seen
from Fig. 6 that damping of the system has been greatly
enhanced. The oscillations of all the three units’ shaft
decay with time, indicating the effectiveness of the mul-
ti-mac hi ne SS R damping co ntr olle r.
5. Conclusion
This paper proposed a control strategy of using STAT-
COM to damp SSR in multi-machine system. The strat-
egy is verified by time domain simulation of a mul-
ti-machine system modified based on IEEE second
benchmark model. Dynamic response of the three gene-
rators’ speed deviation without and with the SSR damp-
ing controller is presented. The simulation result reveals
that by taking all generators’ speed as input signal and
with proper phase compensation, SSR in a mul-
ti-machine system can be damped using STATCOM.
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