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
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

             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
 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:
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
          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 [ .

               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
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

• 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
                sT        1 + sT1   1 + sT3              ∆XC         are given in Table 2.
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

and for other topologies,other signals might yield a better               • VA : Voltage at Bus A
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
                                                                           PE       -0.28       0.1410         0.5682      0.1410      0.5682
                 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.

               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 (%)
              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
5.2 Four Machine System                                                [1]. E.V. Larsen and D.A.Swan. "Applying Power System
                                                                       Stabilizers", IEEE Transactions on Power Apparatus and
For the four-machine system the PSS located at G4 has a                Systems, PAS-100(6), June 1981, pp. 3017-3046.
higher damping effect. The next best placement for PSS is on
                                                                       [2]. J.F. Hauer, “Reactive Power Control as a Means for
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
   Location          Mode           1/s      Hz       ratio (%)        Apparatus and Systems, PAS-85(2), Feb. 1966, pp. 180-188.
                   Inter-area       -0.20    0.56          5.69        [4]. Å. Ölwegård, et. al. "Improvement of Transmission
      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.
                   Inter-area       -0.21    0.56          5.80
                                                                       [5]. M. Noroozian and G. Andersson. "Damping of Power
    G1+G4       Local G1-G2         -0.67    1.07          9.87        System Oscillations by Controllable Components". IEEE
                Local G3-G4         -0.71    1.11          10.12       Transaction on Power Delivery, vol 9, No. 4, Oct. 1994, pages
Table 9.: Damping of Electromechanical modes with PSS for              [6] L. Ängquist, B. Lundin and J. Samuelsson, “Power
four-machine system                                                    Osillation Damping Using Controlled Reactive Power
                                                                       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
modes are rather good but the damping of inter-area mode is            Influencing Power System Stabilizers Performance”, IEEE
not sufficient.                                                        Transactions on Energy Conversion, Vol. 7, No. 3, September
                                                                       1993, pp. 382-390


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