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Published in IET Generation, Transmission & Distribution
Received on 29th August 2011
Revised on 10th January 2012
doi: 10.1049/iet-gtd.2011.0625
ISSN 1751-8687
Damping of subsynchronous oscillations in power
system using static synchronous series compensator
M. Farahani
Department of Electrical Engineering, Bu-Ali Sina University, Hamedan, Iran
E-mail: m.farahani@basu.ac.ir
Abstract: In this study, a static synchronous series compensator (SSSC) is used to damp the subsynchronous oscillation in a
power system compensated by the series capacitor. In order to achieve an effective damping, a supplementary
subsynchronous damping controller (SSDC) is added to the SSSC. The only input signal for the SSDC is the rotor speed
deviation to generate the modulation index for controlling the injected voltage of the voltage-sourced converter (VSC). Also,
the chaotic optimisation algorithm is employed to tune the parameter of SSDC. The design objective is to suppress the
subsynchronous resonance (SSR) caused by the series capacitor. By using the SSDC, the SSSC connected at the transmission
line is able to damp the SSR. The first system of IEEE second benchmark model is used to evaluate the effective of SSDC on
the torsional oscillations. The several simulations are used to demonstrate the ability of SSDC in damping the SSR.
1
Introduction
The use of series capacitor is a conventional method for
reducing high reactance of long transmission lines. This
method has some advantages such as increase in transient
stability, improvement of load carrying of transmission lines
and by controlling this reactance, they allow better control
over load sharing between parallel transmission lines.
However, despite these benefits, these series capacitors can
increase the risk of interaction between electrical power
systems and turbine – generators’ rotor torsional system.
This problem is known as subsynchronous resonance (SSR)
or subsynchronous oscillations. ‘Subsynchronous oscillation
is an electric power system condition where the electric
network exchanges significant energy with a turbine –
generator at one or more of the natural frequencies of the
combined system below the synchronous frequency of the
system following a disturbance from equilibrium’ [1].
The researchers have used many techniques to overcome
this problem and proposed many controllers in the literatures.
In general, most of these techniques can be divided into two
main groups. The first one contains the controllers based on
the excitation system of generator [2–4]. The second one
consists of the flexible AC transmission systems (FACTS)
devices.
The FACTS devices provide a powerful mechanism in
order to control the reactive power and voltage in power
systems. Besides these abilities, the different types of these
devices can be used in improving the stability of system. A
lot of articles have been published about the use of these
devices in damping the SSR [5 – 13].
In this paper, a static synchronous series compensator
(SSSC) along with the supplementary subsynchronous
damping controller (SSDC) connected at the transmission
IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539– 544
doi: 10.1049/iet-gtd.2011.0625
line is used to damp the SSR. The parameters of SSDC are
tuned by the chaotic optimisation algorithm to achieve an
effective damping. The SSSC is used as a voltage source in
series with a fixed capacitor. So, this combination can
prevent the subsynchronous oscillations that may be caused
by conventional fixed capacitor. This factor, along with the
simple control method, makes the proposed configuration
highly effective in damping the SSR.
2
System under study
In this study, the first system of IEEE second benchmark
model shown in Fig. 1 is used to evaluate and analyse the
risk of SSR [14]. In this model, a 600-MVA synchronous
generator via two 500-kV transmission lines is connected to
a large grid which is approximated by an infinite bus. The
turbine – generator system as shown in Fig. 2 is modelled by
four masses.
As seen in Fig. 1, the SSSC injects a voltage Vs in series
with the transmission line where it is connected. Voltagesourced converter (VSC) using insulated gate bipolar
transistor (IGBT)-based pulse width modulation (PWM)
inverters is used in this study. However, as details of the
inverter and harmonics are not represented in the SSR
studies, the same model can be used to represent a gate turn
off (GTO)-based model. The overall performance of SSSC
is completely explained in [10 – 11].
3
3.1
Proposed approach
Structure of control for the SSSC
An SSSC has an inherent damping capability and that only
under certain circumstances it may be not sufficient [11],
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in the system power. Therefore the SSDC uses the rotor
speed deviation to modulate the SSSC-injected voltage Vq
to improve the damping of the unstable torsional modes. In
Fig. 3, Vqref represents the reference injected voltage as
desired by the steady-state power flow control loop. The
steady-state power flow loop acts quite slowly in practice
and hence, in the present study Vqref is assumed to be
constant during the disturbance period. In the control
system block diagram, Vd_conv and Vq_conv designate the
components of converter voltage Vconv which are,
respectively, in phase and in quadrature with current.
The control system consists of
Fig. 1 IEEE second benchmark model along with SSSC
Fig. 2 Modelling of the turbine–generator system
thereby to achieve an effective damping, an SSDC must be
designed and added to the SSSC. The structure shown in
Fig. 3 is selected in this study in order to control the power
flow. In this structure, there are two basic controllers
implemented in SSSC, a Vq voltage regulator and a DC
voltage regulator. The principal strategy in controlling
SSSC for damping the SSR oscillations is to use simple
stabilising signals. The rotor speed deviation of generator
Dv contains components of all the torsional modes.
Consequently, if the rotor speed deviation is used to control
SSSC, all the torsional modes, in addition to the mode
corresponding to the generator mass will be affected. As
seen in Fig. 3, the SSDC input selected is the rotor speed
deviation of generator. The input after passing through a
washout filter excites the derivative gain Kd . The output
signal of derivative gain signifies the existence of the SSR
† A phase-locked loop (PLL) which synchronises on the
positive-sequence component of the current I. The output of
the PLL (angle u ¼ vt) is used to compute the direct-axis
and quadrature-axis components of the AC three-phase
voltages and currents (labelled as Vd , Vq or Id , Iq on the
diagram shown in Fig. 3).
† Measurement systems measuring the q components of AC
positive-sequence of voltages V1 and V2 (V1q and V2q) as well
as the DC voltage Vdc .
† AC and DC voltage regulators that compute the two
components of the converter voltage (Vd_conv and Vq_conv)
are required to obtain the desired DC voltage (Vdcref ) and
the injected voltage (Vqref ). The Vq voltage regulator is
assisted by a feed-forward-type regulator which predicts the
Vconv voltage (the injected voltage on the VSC side of the
transformer) from the Id current measurement.
3.2
Problem formulation
The transfer function of SSDC is
y=
TW s
DvKd s
1 + TW s
(1)
Although local control signals can easily be obtained, they
may not consist of the oscillation modes. By considering
the recent advances in optical fibre communication and
global positioning system, the rotor speed deviation can be
measured and deliver to the control centre [10].
Fig. 3 Block diagram of power flow control of the SSSC along with SSDC
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doi: 10.1049/iet-gtd.2011.0625
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In the SSDC, the signal washout block serves as a highpass filter, with the time constant TW, high enough to allow
signals associated with oscillations in input signal to pass
unchanged. The washout time constant TW is usually prespecified [10]. In this paper, TW is taken as 10 s. In order to
achieve a satisfactory damping, the derivative gain Kd must
be determined. Under steady-state conditions, the SSDC
output and Vqref are constant values. During the dynamic
and transient conditions the series injected voltage Vq is
modulated to suppress the subsynchronous oscillations.
3.3
Optimisation problem
It is worth mentioning that the SSDC is designed to minimise
the modes oscillation. So, the objective can be formulated as
the minimisation of objective function f given by
f =
t=tsim
t|Dv| dt
(2)
t=0
where tsim is the simulation time and Dv is the rotor speed
deviation. For objective function calculation, the time-domain
simulation of the system model incorporating all saturation
limits of control signals is carried out for the simulation
period. The purpose is to minimise this objective function to
damp the torsional oscillations. The design problem can be
formulated as the following constrained optimisation
problem, where the constraint is the SSDC parameter bounds
Kdmin ≤ Kd ≤ Kdmax
(3)
In this paper, the chaotic optimisation algorithm (COA) is used
to solve this optimisation problem and search for the optimal
parameter. The implementation of optimisation algorithm is
summarised in Fig. 4.
3.4
Chaotic optimisation algorithm
In this paper, the COA based on the Lozi map is implemented
and used. The Lozi map is as follows [15]
y1 (k) = 1 − a|y1 (k − 1)| + y(k − 1)
(4)
y(k) = b y1 (k − 1)
(5)
z(k) =
y(k) − a
b−a
(6)
where k is the iteration number. In this work, the values of y
are normalised in the range [0, 1] to each decision variable in
the n-dimensional space of optimisation problem. Thus,
y [ [20.6418, 0.6716] and [a, b] ¼ (20.6418, 0.6716).
Many unconstrained optimisation problems with continuous
variables can be formulated as the following functional
optimisation problem.
Find X to minimise f (X ), X ¼ [x1 , x2 , . . ., xn], where f and
X are the objective function and the decision solution vector,
respectively. The decision solution vector consists of n
variables xi that are bounded by lower (Li) and upper limits
(Ui). The COA based on the Lozi map is shown as follows
[15] (Fig. 5):
Where Mg , Ml , f∗ and X∗ are number of iterations of the
chaotic global and local searches, the best objective function
and the best solution of the current run of the chaotic search,
respectively. The impact of the current best solution on the
generating of a new trial solution is controlled by the step
size l. A small l tends to perform exploitation to refine
results by local search, whereas a large one tends to facilitate
a global exploration of search space. In this study, we have
n ¼ 1 and X ¼ [x1] ¼ [Kd]. The COA based on the Lozi
map is completely explained in [15].
4
Simulations and results
The optimisation of SSDC parameter is carried out based on
the following initial operating condition and assumptions:
1. The generator delivers 1 p.u. power to the transmission
system and the magnitude of the generator and infinite bus
voltages are adjusted at 1.00 p.u.
2. The compensation level provided by the series capacitor is
set at 55%
3. It is assumed that three-line-to-ground fault is occurred at
the beginning of the line 2.
In order to acquire better performance, 2000 and 500
iterations are considered for the global search and the local
search, respectively. It should be noted that the COA is run
several times and then the optimal parameter of SSDC is
chosen. The final value of SSDC parameter is Kd ¼ 0.839.
To show the effectiveness of SSSC with the proposed
SSDC, three simulations are carried out using MATLAB/
SIMULINK.
4.1
Fig. 4 Flowchart of optimisation
IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539– 544
doi: 10.1049/iet-gtd.2011.0625
Increase in input mechanical power
As the first test case, a 10% decrease in input mechanical
power is applied to the generator at t ¼ 0.5 s and removed
at t ¼ 1 s. Also, the compensation of the line 1 and the
operating conditions are 55% and P ¼ 0.85 p.u.,
Vt ¼ 1 p.u., respectively. The rotor speed deviation of
generator Dv as shown in Fig. 6 is well controlled and the
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Fig. 5 COA based on the Lozi map
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IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539 –544
doi: 10.1049/iet-gtd.2011.0625
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Fig. 6 Rotor speed deviation during and after a small disturbance
Fig. 7 Torque of Gen-LP section during and after a small disturbance
oscillations amplitude is clearly decreased by the SSSC.
Fig. 7 illustrates the torsional oscillation on the shaft in
generator-low pressure turbine (Gen-LP) section. It is
observed that in the absence of SSSC, increase of the
oscillation amplitude indicates that the generator have a
growing torsional vibration, which would probably lead to
great damage on the shaft. When the SSSC is applied to the
system, the subsynchronous oscillation is successfully
damped out.
4.2
Disconnection of the line 2
For the second simulation, it is assumed that the transmission
line 2 is tripped out at t ¼ 1 s and again reclosed at t ¼ 4 s.
Also, the compensation of the line 1 and the operating
conditions are 55% and P ¼ 0.9 p.u., Vt ¼ 0.95 p.u.,
respectively. Fig. 8 shows the rotor speed deviation. It is
Fig. 8 Rotor speed deviation during and after the disconnection of
line 2
IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539– 544
doi: 10.1049/iet-gtd.2011.0625
clear that in this disturbance, the SSSC’s performance is
still satisfactory. The torsional oscillations on the shaft in
Gen-LP section is depicted in Fig. 9. As the SSDC
parameter is tuned under heavy operating conditions and
with a large disturbance, the SSSC with the SSDC show a
proper performance in other operating conditions and with
different disturbances.
4.3
Three-line-to-ground fault
For completeness, the performance of SSSC is also
investigated under a large disturbance. To demonstrate the
robustness of SSSC with the proposed SSDC, the
performance of SSSC is evaluated in different operating
conditions. For this purpose, it is assumed that a serious
three-phase short-circuit fault occurs at the beginning of
line 2 and the compensation of the line 1 and the operating
Fig. 9 Torque of Gen-LP section during and after the
disconnection of line 2
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Fig. 10 Rotor speed deviation during and after a large
disturbance
controller called SSDC is designed and added to the SSSC.
A simple structure is proposed for the SSDC. The COA is
used to tune the parameter of SSDC in order to minimise
the oscillation amplitude. A simple signal is chosen as the
input of SSDC. This signal contains all the torsional modes
so that the SSSC with the proposed SSDC can improve the
stability of system. The SSSC is used as a voltage source in
series with a fixed capacitor. So, this combination can
prevent the subsynchronous oscillations that may be caused
by conventional fixed capacitor. This factor along with
simple control method, make the proposed configuration
highly effective in damping the SSR. Some simulations are
used to demonstrate the ability of the SSSC with the
proposed SSDC.
6
Fig. 11 Torque of Gen-LP section during and after a large
disturbance
conditions are 55% and P ¼ 0.95 p.u., Vt ¼ 1.05 p.u.,
respectively. The rotor speed deviation is depicted in
Fig. 10. It is clear that the proposed controller is robust and
provides efficient damping even under large disturbance
conditions. The torsional oscillation on the shaft in Gen-LP
section is shown in Fig. 11. For short time after the fault
(about ,1 s), the magnitude of the oscillations is large,
because of the severe impact of the fault. The SSSC with
the proposed SSDC is clearly able to decrease during the
short time so that the severe vibration on the shaft is
quickly debilitated.
In addition to these simulations, sufficient simulations have
been carried out for other operating conditions and with large
but different disturbances. Totally, SSSC’s performance is
good in damping all the torsional modes and can
satisfactorily weaken the vibrations caused by SSR in
disturbances.
5
Conclusion
In this paper, an SSSC is proposed to dampen the SSR. In
order to achieve an effective damping, an auxiliary
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IET Gener. Transm. Distrib., 2012, Vol. 6, Iss. 6, pp. 539 –544
doi: 10.1049/iet-gtd.2011.0625