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APPLICATIONS OF CONTROLLABLE SERIES CAPACITORS FOR DAMPING OF POWER
SWINGS*
M. Noroozian P. Halvarsson
Reactive Power Compensation Division
ABB Power Systems
S-721 64 Västerås, Sweden
Abstract fast studies of networks and relate the results to the
This paper examines the use of controllable series capacitors development of the associated CSC control algorithms. Also
for damping of electromechanical oscillations. The the controls system for the CSC has improved with high
fundamental input signal for damping of power swings is computational possibilities and digital signal processors
discussed based on the study of eigenvalues of a linearized making it possible to optimize the control algorithm of each
power system. The impact of a CSC on damping of a power installation.
system is shown through an analytical approach. Use of A problem of much interest in the study of power systems is
appropriate locally measurable input signals are investigated the elimination of low frequency oscillations which might arise
for two power systems. The performance of CSC for damping between coherent areas within a power network. Application of
of power swings is compared with that of a PSS. It is shown s)
power system stabilisers (PSS’ has been one of the first
that a CSC can be a very effective device for damping of power measures to offset the negative damping effect of voltage
swings using locally measurable input signals. regulators and improve system damping in general. The basic
Keywords: FACTS, CSC, power oscillation damping, function of a power system stabiliser is to extend stability
eigenvalue sensitivity, local variables, PSS limits by modulating generator excitation to provide damping
to the oscillation of synchronous machine [1]. But with
increasing transmission line loading over long distances, the
1. INTRODUCTION use of conventional power system stabilisers may in some
cases, not provide sufficient damping for inter-area power
In recent years, progress in the field of high power electronics, swings [2]. In these cases, other effective solutions are needed
has made it possible to build converters placed on high to be studied.
potential. This technology can be used to perform different
tasks such as thyristor controlled series capacitors. The The early work in the study of applications of series capacitor
development of direct light triggered thyristors (LTT) has was initiated in 1966 by Kimbark [3]. The work showed that
made it possible to design reliable converters using minimum the transient stability of an electric power system can be
of components on potential. Several demonstration projects improved by switched series capacitors. Later work has
have shown that the use of semiconductors on high potential explored the benefits of the controllable series capacitor for
are a reliable and today feasible technology. Demonstration improving small disturbance stability [4]. Recent studies show
projects have been in service for several years. that series reactive compensation is more efficient than shunt
reactive compensation for damping of power swings. For
Recent work has described control algorithms for CSC
example, in [5]and [6], the damping effects of shunt reactive
changing its impedance in the sub-harmonic frequency range.
compensation and series reactive compensation are compared.
Using the synchronous voltage reversal (SVR) control
It is shown that CSC offers a better economic solution than
algorithm eliminates the problems associated with sub
SVC.
synchronous resonance problems when series compensation at
high levels are introduced in networks close to thermal
This paper is organised as follows:
generating units using units with long shafts.
Section 2 derives the fundamental signal for damping of power
Further improvements has been made in the field of swings in a power system. Section 3 explains the contribution
computation tools for network studies that together with the of a CSC on damping of power swings. Section 4 examines the
powerful hardware development, makes it possible to perform use of locally measurable input signals for damping using a
CSC. The performance of a PSS on damping of power swing is
compared with that of a CSC in Section 5.
* Presented at the 5th Symposium of Specialists in Electric and Expansion Planning (V SEPOPE), May 19-24, 1996, Brazil
1
2. DAMPING OF POWER SWINGS 3. DAMPING OF POWER SWINGS BY CSC
In this section the fundamental control signal required for The power system representation in Fig. 3-1 is used to model
damping of electromechanical oscillations is discussed. To an inter-connected system. It is assumed that a CSC is located
facilitate the analysis, a one-machine infinite-bus system is on the intertie for damping of power swings.
considered and the classical model for synchronous machine
is used. E∠δ VA∠θ A V∠0
′
Xd XC XL
E∠δ VA∠θ A V∠0
′
Xd XL
M
ω
M
ω Fig. 3-1: study of CSC for damping control
Fig. 2-1: System for study of damping control
No damping torques are assumed in the system, which means
Assuming a constant mechanical power, the linearized that the transmission system will oscillate by itself without
equation of the system in the state space form is: damping and only CSC can contribute to the damping. The
control signal is selected as the difference between the speed of
∆ω 0
& K S ∆ω the machine and the infinite bus. For the reason discussed in
∆δ =
& M ∆δ the previous section, this signal is appropriate for damping of
1 0
power swings. Thus the control law is:
∆X C = K C ∆ω
where KS is the synchronising coefficient:
VE
KS = cos δ where K C is a gain. The lineraized machine equations are:
Xd + X L
′
M∆ω = − ∆P
&
which shows that with this model the system response is purely
&
∆δ= ω
oscillatory. To damp the power oscillations, a supplementary
power is needed to modulate the generated power. If the 1
where P = bEV sinδ with b= . The
modulated power is selected as: ′
X L − X C + Xd
linearized controlled system matrix is:
∆
∆P = K ω ∆ω + K δ δ
− K C b 2 E sin δ − bE cos δ ∆ω
the controlled matrix is: ∆ω
&
∆δ =
& M M ∆δ
K S + K δ ∆ω 1 0
∆ω ω
& K
&
∆δ =M M
1 ∆δ It is seen the damping term depends both on K C and sin δ.
0
This reveals the following conclusions:
The system has at most two distinct eigenvalues and in the
case of an oscillatory response: • A CSC can enhance the damping of electromechanical
oscillations.
1
Kω 4( KS + Kδ) K 2 2 • The damping effect of a CSC increases with transmission
λ1,2 = ± j − ω
line loading. This is a very important feature of a CSC,
M M M 2
since the damping of the system normally is lower at
heavily loaded lines.
Equation above shows that only the component of ∆ω
contributes to damping and ∆δ affects only the frequency of Further it can be shown that the damping effect of a CSC is
oscillation (synchronising torque). not sensitive to the load characteristics [ .
5]
2
4. NUMERICAL EXAMPLES
It is assumed that a CSC is located between Bus A and Bus B.
In this section, the application of a CSC is demonstrated
The CSC consists of a fixed capacitor (FC) and a thyristor
through model power systems. The method of analysis is based
controlled series capacitor (TCSC). The FC is used to share an
on eigenvalue analysis of the linearized power system.
equal loading between the two lines. The TCSC is used for
damping of power swings. Fig. 4.3 shows the CSC
4.1 Regulator Design
configuration.
A linear control design method based on the sensitivity of the
eigenvalues is used for design of the regulator to damp the
electromechanical oscillations. Two local input signals are
examined:
• PE : active power flow through the line.
• VA : Voltage at the node near to CSC
Fig. 4.3: CSC scheme
Fig 4-1 shows the structure of the selected CSC regulator.
The regulator parameters are designed for the three inputs and
∆XCmax
PE
sT 1 + sT1 1 + sT3 ∆XC are given in Table 2.
w
VA K
1+ sTw 1 + sT2 1 + sT4 ∆XCmin
Input K T1 T2 T3 T4
Fig. 4.1: CSC regulator PE 4.75 0.0806 0.2925 0.0806 0.2925
4.2. Two Machines System VA 3.0 0.2502 0.0942 0.2502 0.0942
In Fig. 4.2 two systems are connected via an intertie. The
length of the lines are shown in the figure. The total power Table 2: Parameters of CSC regulators
flow through the intertie is 2100 MW. The machines are
modelled with field windings and the influence of exciters are The system eigenvalues with the TCSC operation are given in
included. No damper windings are modelled. Table 3:
PE VA
Eigenvalue 1/s Hz 1/s Hz
1 -1.00 0.00 -1.00 0.00
2 -16.47 0.00 -16.71 0.00
3 -10.52 0.75 -7.24 1.64
4 -10.52 -0.75 -7.24 -1.64
Fig. 4.2.: 500 kV test power system 5 -6.00 0.67 -8.74 0.63
6 -6.00 -0.67 -8.74 -0.63
The eigenvalues of the system without the active control of 7 -0.61 0.95 -3.07 0.85
TCSC are shown in Table 1 (The electromecanical modes are 8 -0.61 -0.95 -3.07 -0.85
shown with double frame). 9 -2.92 0.00 -3.06 0.00
10 -0.018 0.00 -0.080 0.00
Eigenvalue 1/s Hz 11 -0.012 0.00 -0.012 0.00
1 -16.475 0
2 -10.483 0.749 Table 3: Eigenvalues with TCSC operation
3 -10.483 -0.749
4 -0.130 1.037 It is seen that the CSC has contributed to the damping of the
5 -0.130 -1.037 electromechanical oscillations considerably. It is interesting to
6 -0.013 0 note that the performance of the controller is better when the
7 -3.090 0 the capacitor node voltage (VA ) is used as input signal. It is to
be noted that this result is only valid for this network structure
Table 1: Eigenvalues of the two-machine system
3
and for other topologies,other signals might yield a better • VA : Voltage at Bus A
performance.
4.3. Four-Machine System
The regulator parameters are designed for the two inputs and
Fig. 4.4 shows a two area system connected via an intertie. are given in Table 5.
The data of the network is given in [7].
Input K T1 T2 T3 T4
VA 0.14 0.1274 0.5907 0.1274 0.5907
TCSC
PE -0.28 0.1410 0.5682 0.1410 0.5682
Gen1
L1 C1 C2 L2 Gen3
Gen2 Gen4
Table 5: Parameters of the CSC regulator
Fig. 4.4: Four-machine system The impact of CSC on damping of electromechanical modes
are shown in Tables 6 and 7 for the two input signals:
The two area system exhibits three electromechanical
oscillation modes: Eigenvalue Damping
Mode 1/s Hz ratio (%)
• An inter-area mode with a frequency of 0.56 Hz in which Inter-area -0.41 0.57 11.51
the generating units in one area oscillate against those in
the other area. Local G1, G2 -0.66 1.07 9.81
• A local mode in area 1, with a frequency of 1.07 Hz, in Local G3, G4 -0.70 1.11 10.08
which generator G1 and G2 oscillate against each other.
• A local mode in area 2, with a frequency of 1.11 Hz, in Table 6.: Damping of Electromechanical modes with VA
which generator G3 and G4 oscillate against each other.
as input signal
The eigenvalues related to the electromechanical modes are
shown in Table 4.
Eigenvalue Damping
Mode 1/s Hz ratio (%)
Eigenvalue Damping
Inter-area -0.89 0.47 28.75
Mode 1/s Hz ratio (%)
Local G1, G2 -0.68 1.07 10.08
Inter-area -0.18 0.56 5.18
Local G3, G4 -0.71 1.11 10.11
Local G1, G2 -0.67 1.07 9.83
Local G3, G4 -0.70 1.11 10.03
Table 7.: Damping of Electromechanical modes with PE
Table 4.: Damping of Electromechanical modes as input signal
It is seen that the while the damping of local modes are rather The simulation results show that a CSC can contribute to the
good, inter-area mode has a poor damping. A controllable damping of the power swings in complex systems where many
series capacitor is assumed to be located on the inter-tie to modes are present. In this example, the regulator has been
enhance the damping of the inter-area mode. The local designed to damp the inter-area mode. It is noted that the
variables based on the principles discussed in Section 4.1, are damping of the local modes are not degraded but increased a
used for input signals. The following input signals are little. The other interesting result is that in this network the
selected: intertie power flow is a better signal than the node voltage.
• PE : active power flow through the line.
4
5. COMPARISON WITH PSS 6. CONCLUSIONS
In this section , the damping effect of power sytem stabilisers This paper has examined the use of controllable series
are examined for the power systems discussed in Section 4. capacitor for damping of electromechanical oscillations. Based
The PSS design is based on the eigenvalue sensitivity on the study of the eigenvalues of a linearized power system,
approach. In each system , the best placement for provision of the following conclusions were obtained:
a PSS is determined. After the allocation of the first PSS, the
second one is designed. • With an appropriate control strategy, a CSC enhances the
power swing damping. This contribution is an increasing
5.1 Two Machine System function of transmission line loading.
The eigenvalue analysis shows that G1 has a higher damping • Locally measurable input signals can be used with a CSC
effect for placement of the PSS. Table 8 shows the regulator to effectively damp the power swings.
electromechanical modes after PSS installation.
• The contribution of a CSC to damping of power swings is
Eigenvalue Damping higher than a PSS.
Location 1/s Hz ratio (%)
ACKNOWLEDGEMENTS
G1 -1.30 1.02 19.83
G1+G2 -1.42 1.02 21.49
The authors wish to thank Mikael Halonen, Lennart Ängquist
and Prof. Göran Andersson for contribution to this work.
Table 8.: Damping of Electromechanical modes with PSS for
two machine system
REFERENCES
5.2 Four Machine System [1]. E.V. Larsen and D.A.Swan. "Applying Power System
Stabilizers", IEEE Transactions on Power Apparatus and
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higher damping effect. The next best placement for PSS is on
[2]. J.F. Hauer, “Reactive Power Control as a Means for
s
G1. Table 9 shows the impact of PSS’ on damping of the
Enhanced Inter-Area Damping in the Western U.S. Power
inter-area mode and local modes.
System, A Frequency-domain Perspective Considering
Robustness Needs”, IEEE Tuotorial Course 87THO187-5-
PWR, 1987
Eigenvalue Damping [3]. E.W. Kimbark. "Improvement of System Stability by
Switched Series Capacitors. " IEEE Transactions on Power
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G4 Local G1-G2 -0.67 1.07 9.83 Capacity by Thyristor Control Reactive Power ". IEEE
Local G3-G4 -0.71 1.11 10.12 Transactions on Power Apparatus and Systems, PAS-100(8),
Aug. 1981, pages 3933-3939.
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[5]. M. Noroozian and G. Andersson. "Damping of Power
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Compensation”, IEEE Transactions on Power Systems, May
1993, pp. 687-700
This table shows that the impact of PSS´s on damping of local [7] M. Klein, et al., “Analytical Investigation of Factors
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