APPLICATIONS OF CONTROLLABLE SERIES CAPACITORS FOR DAMPING OF POWER SWINGS *

Transcription

1 APPLICATIONS OF CONTROLLABLE SERIES CAPACITORS FOR DAPING OF POWER SWINGS *. Noroozian P. Halvarsson Reactive Power Compensation Division ABB Power Systems S-7 64 Västerås, Sweden Abstract This paper examines the use of controllable series capacitors for damping of electromechanical oscillations. The fundamental input signal for damping of power swings is discussed based on the study of eigenvalues of a linearized power system. The impact of a CSC on damping of a power system is shown through an analytical approach. Use of appropriate locally measurable input signals are investigated for two power systems. The performance of CSC for damping of power swings is compared with that of a PSS. It is shown that a CSC can be a very effective device for damping of power swings using locally measurable input signals. eywords: FACTS, CSC, power oscillation damping, eigenvalue sensitivity, local variables, PSS. INTRODUCTION In recent years, progress in the field of high power electronics, has made it possible to build converters placed on high potential. This technology can be used to perform different tasks such as thyristor controlled series capacitors. The development of direct light triggered thyristors (LTT) has made it possible to design reliable converters using minimum of components on potential. Several demonstration projects have shown that the use of semiconductors on high potential are a reliable and today feasible technology. Demonstration projects have been in service for several years. Recent work has described control algorithms for CSC changing its impedance in the sub-harmonic frequency range. Using the synchronous voltage reversal (SVR) control algorithm eliminates the problems associated with sub synchronous resonance problems when series compensation at high levels are introduced in networks close to thermal generating units using units with long shafts. Further improvements has been made in the field of computation tools for network studies that together with the powerful hardware development, makes it possible to perform fast studies of networks and relate the results to the development of the associated CSC control algorithms. Also the controls system for the CSC has improved with high computational possibilities and digital signal processors making it possible to optimize the control algorithm of each installation. A problem of much interest in the study of power systems is the elimination of low frequency oscillations which might arise between coherent areas within a power network. Application of power system stabilisers (PSS s) has been one of the first measures to offset the negative damping effect of voltage regulators and improve system damping in general. The basic function of a power system stabiliser is to extend stability limits by modulating generator excitation to provide damping to the oscillation of synchronous machine []. But with increasing transmission line loading over long distances, the use of conventional power system stabilisers may in some cases, not provide sufficient damping for inter-area power swings []. In these cases, other effective solutions are needed to be studied. The early work in the study of applications of series capacitor was initiated in 966 by imbark [3]. The work showed that the transient stability of an electric power system can be improved by switched series capacitors. Later work has explored the benefits of the controllable series capacitor for improving small disturbance stability [4]. Recent studies show that series reactive compensation is more efficient than shunt reactive compensation for damping of power swings. For example, in [5]and [6], the damping effects of shunt reactive compensation and series reactive compensation are compared. It is shown that CSC offers a better economic solution than SVC. This paper is organised as follows: Section derives the fundamental signal for damping of power swings in a power system. Section 3 explains the contribution of a CSC on damping of power swings. Section 4 examines the 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), ay 9-4, 996, Brazil

2 . DAPING OF POWER SWINGS In this section the fundamental control signal required for damping of electromechanical oscillations is discussed. To facilitate the analysis, a one-machine infinite-bus system is considered and the classical model for synchronous machine is used. E δ V A θ A X d X L V 0 Fig. -: System for study of damping control Assuming a constant mechanical power, the linearized equation of the system in the state space form is: & = S 0 δ 0 where S is the synchronising coefficient: S VE = X + X d L cosδ which shows that with this model the system response is purely oscillatory. To damp the power oscillations, a supplementary power is needed to modulate the generated power. If the modulated power is selected as: P = + δ δ the controlled matrix is: & + = S 0 δ δ The system has at most two distinct eigenvalues and in the case of an oscillatory response: 4( + ) j S δ λ, = ± Equation above shows that only the component of contributes to damping and δ affects only the frequency of oscillation (synchronising torque). 3. DAPING OF POWER SWINGS BY CSC The power system representation in Fig. 3- is used to model an inter-connected system. It is assumed that a CSC is located on the intertie for damping of power swings. E δ V A θ A X d X C X L Fig. 3-: study of CSC for damping control V 0 No damping torques are assumed in the system, which means that the transmission system will oscillate by itself without damping and only CSC can contribute to the damping. The control signal is selected as the difference between the speed of the machine and the infinite bus. For the reason discussed in the previous section, this signal is appropriate for damping of power swings. Thus the control law is: XC = C where C is a gain. The lineraized machine equations are: & = P = where P = bev sinδ with b =. The X X + X linearized controlled system matrix is: & sinδ cosδ δ & = Cb E be δ 0 L C d It is seen the damping term depends both on C and sinδ. This reveals the following conclusions: A CSC can enhance the damping of electromechanical oscillations. The damping effect of a CSC increases with transmission line loading. This is a very important feature of a CSC, since the damping of the system normally is lower at heavily loaded lines. Further it can be shown that the damping effect of a CSC is not sensitive to the load characteristics [5].

3 4. NUERICAL EXAPLES In this section, the application of a CSC is demonstrated through model power systems. The method of analysis is based on eigenvalue analysis of the linearized power system. 4. 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 examined: P E : active power flow through the line. V A : Voltage at the node near to CSC Fig 4- shows the structure of the selected CSC regulator. PE VA st w stw st st 4.. Two achines System st3 st4 Fig. 4.: CSC regulator X Cmax X Cmin X C In Fig. 4. two systems are connected via an intertie. The length of the lines are shown in the figure. The total power flow through the intertie is 00W. The machines are modelled with field windings and the influence of exciters are included. No damper windings are modelled. It is assumed that a CSC is located between Bus A and Bus B. The CSC consists of a fixed capacitor (FC) and a thyristor controlled series capacitor (TCSC). The FC is used to share an equal loading between the two lines. The TCSC is used for damping of power swings. Fig. 4.3 shows the CSC configuration. Fig. 4.3: CSC scheme The regulator parameters are designed for the three inputs and are given in Table. Input T T T 3 T 4 P E V A Table : Parameters of CSC regulators The system eigenvalues with the TCSC operation are given in Table 3: P E V A Fig. 4..: 500 kv test power system The eigenvalues of the system without the active control of TCSC are shown in Table (The electromecanical modes are shown with double frame). /s Hz Table : s of the two-machine system /s Hz /s Hz Table 3: s with TCSC operation It is seen that the CSC has contributed to the damping of the electromechanical oscillations considerably. It is interesting to note that the performance of the controller is better when the the capacitor node voltage ( V A ) is used as input signal. It is to be noted that this result is only valid for this network structure 3

4 and for other topologies,other signals might yield a better performance Four-achine System Fig. 4.4 shows a two area system connected via an intertie. The data of the network is given in [7]. V A : Voltage at Bus A The regulator parameters are designed for the two inputs and are given in Table 5. Input T T T 3 T 4 V A Gen Gen TCSC L C C L Gen4 Gen3 P E 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: An inter-area mode with a frequency of 0.56 Hz in which the generating units in one area oscillate against those in the other area. A local mode in area, with a frequency of.07 Hz, in which generator G and G oscillate against each other. A local mode in area, with a frequency of. Hz, in which generator G3 and G4 oscillate against each other. The eigenvalues related to the electromechanical modes are shown in Table 4. ode /s Hz ratio (%) Inter-area Local G, G Local G3, G Table 4.: of Electromechanical modes It is seen that the while the damping of local modes are rather good, inter-area mode has a poor damping. A controllable series capacitor is assumed to be located on the inter-tie to enhance the damping of the inter-area mode. The local variables based on the principles discussed in Section 4., are used for input signals. The following input signals are selected: ode /s Hz ratio (%) Inter-area Local G, G Local G3, G Table 6.: of Electromechanical modes with V A as input signal ode /s Hz ratio (%) Inter-area Local G, G Local G3, G Table 7.: of Electromechanical modes with P E as input signal The simulation results show that a CSC can contribute to the damping of the power swings in complex systems where many modes are present. In this example, the regulator has been designed to damp the inter-area mode. It is noted that the damping of the local modes are not degraded but increased a little. The other interesting result is that in this network the intertie power flow is a better signal than the node voltage. P E : active power flow through the line. 4

5 5. COPARISON WITH PSS In this section, the damping effect of power sytem stabilisers are examined for the power systems discussed in Section 4. The PSS design is based on the eigenvalue sensitivity approach. In each system, the best placement for provision of a PSS is determined. After the allocation of the first PSS, the second one is designed. 5. Two achine System The eigenvalue analysis shows that G has a higher damping effect for placement of the PSS. Table 8 shows the electromechanical modes after PSS installation. Location /s Hz ratio (%) G GG Table 8.: of Electromechanical modes with PSS for two machine system 5. Four achine System For the four-machine system the PSS located at G4 has a higher damping effect. The next best placement for PSS is on G. Table 9 shows the impact of PSS s on damping of the inter-area mode and local modes. Location ode /s Hz ratio (%) Inter-area G4 Local G-G Local G3-G Inter-area GG4 Local G-G Local G3-G Table 9.: of Electromechanical modes with PSS for four-machine system This table shows that the impact of PSS s on damping of local modes are rather good but the damping of inter-area mode is not sufficient. 6. CONCLUSIONS This paper has examined the use of controllable series capacitor for damping of electromechanical oscillations. Based on the study of the eigenvalues of a linearized power system, the following conclusions were obtained: With an appropriate control strategy, a CSC enhances the power swing damping. This contribution is an increasing function of transmission line loading. Locally measurable input signals can be used with a CSC regulator to effectively damp the power swings. The contribution of a CSC to damping of power swings is higher than a PSS. ACNOWLEDGEENTS The authors wish to thank ikael Halonen, Lennart Ängquist and Prof. Göran Andersson for contribution to this work. REFERENCES []. E.V. Larsen and D.A.Swan. "Applying Power System Stabilizers", IEEE Transactions on Power Apparatus and Systems, PAS-00(6), June 98, pp []. J.F. Hauer, Reactive Power Control as a eans for Enhanced Inter-Area in the Western U.S. Power System, A Frequency-domain Perspective Considering Robustness Needs, IEEE Tuotorial Course 87THO87-5- PWR, 987 [3]. E.W. imbark. "Improvement of System Stability by Switched Series Capacitors. " IEEE Transactions on Power Apparatus and Systems, PAS-85(), Feb. 966, pp [4]. Å. Ölwegård, et. al. "Improvement of Transmission Capacity by Thyristor Control Reactive Power ". IEEE Transactions on Power Apparatus and Systems, PAS-00(8), Aug. 98, pages [5].. Noroozian and G. Andersson. " of Power System Oscillations by Controllable Components". IEEE Transaction on Power Delivery, vol 9, No. 4, Oct. 994, pages [6] L. Ängquist, B. Lundin and J. Samuelsson, Power Osillation Using Controlled Reactive Power Compensation, IEEE Transactions on Power Systems, ay 993, pp [7]. lein, et al., Analytical Investigation of Factors Influencing Power System Stabilizers Performance, IEEE Transactions on Energy Conversion, Vol. 7, No. 3, September 993, pp