Tuning, Performance and Interactions of PSS and ... - Semantic Scholar

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Tuning, Performance and Interactions of PSS and FACTS Controllers N. Mithulananthan, Student Member, IEEE, Claudio A Cañizares, Senior Member, IEEE, and John Reeve, Fellow, IEEE

AbstractThis paper discusses issues of tuning, performance and interactions of PSS and FACTS controllers in a test power system. The controllers are placed in the system to control electromechanical oscillations (Hopf bifurcations) and the corresponding gains are tuned to observe their effect on oscillatory modes and overall system performance. Studies are carried out to compare performances of these controllers in a wide variety of operating and fault conditions. The damping introduced by individual controllers is compared with the combined performance of multiple controllers, showing possible negative interactions among them. Index TermsElectromechanical oscillation, FACTS controllers, PSS, Hopf bifurcations, interactions, performance, PSS, tuning.

I. INTRODUCTION

P

ower system controllers play a vital role in stabilizing power systems, especially after critical faults by adding damping to weak electromechanical modes [1], [2], [3], [4]. The controllers may be tuned to bring the system back to stable operating conditions, as seen in real power system incidents [5]. For example, in the case of the onset of an oscillatory instability, which can be associated with a Hopf Bifurcation [6], tuning may restore the complex mode to the open left-half plane. While a Power System Stabilizer (PSS) can be considered an economical option to add damping on critical electromechanical modes [1], [2], the placement may be problematical due to generator ownership in a deregulated environment. Other alternatives are Flexible AC Transmission System (FACTS) controllers [3], [7], [8], which can be designed to use a variety of control signals and, in principle, can be placed at any location in the transmission system to achieve the best possible damping. The tuning of one controller could affect another controller that may be located in the same region [9]; these interactions may enhance or adversely affect some oscillatory modes in the system [10]. On applying root locus techniques to PSS tuning, increasing the gain could improve the damping of one electromechanical mode but degrade the damping of another mode associated with a FACTS controller; this could be interpreted as an interaction between the FACTS controller This work was partially supported by NSERC, Canada, and the Ontario Graduate Scholarship (OGS) program. The authors are with the Department of Electrical & Computer Engineering, University of Waterloo, ON, Canada, N2L-3G1, [email protected].

and the PSS. It is not feasible using root locus analysis to determine the reason for these interactions as pointed out in [9]; however, sensitivity based techniques are proposed in [10] to study this problem. In the current paper, the effect of different controllers gain at a Hopf bifurcation point and the performance at different loading levels for various cases are studied using the IEEE 14bus test system. The effect of an additional SVC control loop for oscillation damping on the dynamic loading margin is discussed here as well. Finally, controller interaction studies are presented for the same test system. Section II introduces some concepts in electromechanical oscillations in power systems, power system controllers, the analytical tools and test system used in this paper. Simulation results, including tuning, performance and interactions of the controllers are discussed in Section III. Section IV summarizes the main contributions presented in this paper and indicates future research directions. II. MAIN CONCEPTS, MODELS, TOOLS AND TEST SYSTEM A. Electromechanical Oscillations Electromechanical oscillation problems are characterized by sustained or growing oscillations of system frequency and power flows due to a loss of synchronizing torque [1]. A pair of eigenvalues of system equilibria (operating points) typically move from the left complex-plane to the right half-plane, after system contingencies (e.g. line outages). By slowly varying parameters like system loading, these oscillations can be associated with a Hopf Bifurcation (HB) problem [4]. In this paper, PSS, SVC and TCSC controllers are employed, placing them to give maximum damping to the oscillatory mode associated with the HB. B. Power System Stabilizers (PSS) A PSS can be viewed as an additional block of a generator excitation control or Automatic Voltage Regulator (AVR), added to improve the overall power system dynamic performance, and especially control electromechanical oscillations. This is a very effective method of enhancing small-signal stability performance on a power system network. Figure 1 depicts the PSS controller model used in this paper. C. Static Var Compensator (SVC) A SVC is basically a shunt connected static var generator/load whose output is adjusted to exchange capacitive or inductive current so as to maintain or control specific power

2 V smax

Lead / Lag

Washout Filter

Gain

13

G GENERATORS

Rotor Speed Deviation

K

ST W

PSS

1 +

1 + ST1 1 + ST2

STW

Vs

1 + ST3 1 + ST4 V smin

C

SYNCHRONOUS COMPENSATORS

Gen. 1

Fig. 1. PSS controller.

12

14 11

10 9

PSS G

Gen. 4 1

V ref

Gen. 5 C

6

7

C

8 4

SC

TC Vsvc +

-

+ K

+

1 + ST 1

+ SVC 1 + ST 5

1 + ST 3

+

1 + ST 2 ST 7 1 + ST 7

+

1 + ST 6

SD2

1 + ST 4 -

5

B svc

SVC

Additional Signal

Ka SVC

2

Fig. 2. A SVC controller with additional oscillation damping control.

G

3

Gen. 2 C

1.0

Gen. 3

Input Signal K

T TCSC

W

1 + ST W

1 1 + ST1

1 + ST 2 1 + ST 3

K2

S TCR

SD2

Fig. 4. Test system with different power system controllers.

B (p.u.)

0

Fig. 3. A TCSC controller for oscillation damping.

Base Case Line 2−4 Outage Line 2−3 Outage

Operating Points (λ=0.4 p.u.)

1

HB

D. Thyristor Controlled Series Compensator (TCSC) A TCSC is a controller specifically designed to be connected in series with tie lines to control their impedance. These types of controllers can be used for oscillation damping (both subsynchronous and electromechanical), when properly modeled and controlled. Figure 3 shows the TCSC used in this paper for oscillation damping. In Figs. 2 and 3, SD2 is a nonlinear function representing the Thyristor Control Reactor and Fixed Capacitor elements that are an integral part of a SVC and a TCSC, respectively [7], [8]. E. Analytical Tools PV curves and, hence, the maximum loading margins were obtained with UWPFLOW [12]. Eigenvalue analysis and time domain simulations were carried out using the MASS and ETMSP tools of PSAPAC [13]. UWPFLOW is a research tool that has been designed to determine maximum loadability margins in power systems associated with saddle-node and limit-induced bifurcations. It has detailed static models of various power system elements such as generators, loads, HVDC links, and various FACTS controllers, particularly SVC, TCSC and STATCOM controllers. The program generates a variety of outputs that allow for further analyses, such as left and right eigenvectors associated with the smallest real Jacobian eigenvalue, power flow solutions at different loading levels, PV curves, etc.

HB 0.8

Voltage (p.u.)

system variables. Typically, the controlled variable is the SVC bus voltage; however, an additional stabilizing signal, and supplementary control, superimposed on the voltage control loop of a SVC can also provide oscillation damping as discussed in [4], [11]. The SVC model used in this paper is depicted in Fig. 2.

HB

0.6

0.4

0.2

0 260

280

300

320

340 360 Total Load. (MW)

380

400

420

440

Fig. 5. PV curves and HB points for various operating conditions.

MASS is part of EPRI's Power System Analysis Package (PSAPAC). It can be used to analyze the steady state stability of a power system by calculating all its eigenvalues. It also yields several outputs such as the system state matrix, the participation matrix, left and right eigenvectors, etc. ETMSP is also part of the PSAPAC software, developed to perform timedomain simulations for stability analysis of large interconnected power systems. This program combines multiple numerical integration methods and advanced modeling of a variety of devices and controllers for transient and mid-term stability analyses. F. Test System A one-line diagram of the IEEE 14-bus test system with the addition of controllers is given in the Fig. 4. It consists of 5 generators with IEEE Type 1 exciters, 3 transformers, 14 buses and 21 lines. There are 11 loads in the system with total real and reactive loads of 259 MW and 81.3 Mvar, respectively. The power flow data for this system can be found in the archives of the University of Washington; the corresponding dynamic data for generators and exciters were chosen from [14].

3 80

70

Ka

SVC

Ka

=0.26

SVC

=0.27

60

Imaginary

50

40

30

20

KaSVC =0 10

KaSVC =0.27 0 −0.5

Fig. 6. HB induceed oscillation triggered by line 2-4 outage no controller (λ=0.4 p.u.).

−0.3

−0.2

−0.1 Real

0

0.1

0.2

0.3

Fig. 8. Locus of some eigenvalues vs. SVC additional controller gain KaSVC at HB point for the base case (KaSVC=0-0.27).

9

K

−0.4

=0

pss

8

12

K

=7.8

TCSC

7

Kpss=61

10

5

=7.0

KTCSC=0.1

8

K 4

K

TCSC

Kpss=0

=61

Imaginary

Imaginary

6

pss

KTCSC=7.8

6

3

4

2

1

0 −0.45

Kpss=61

Kpss=0 −0.4

−0.35

−0.3

−0.25

−0.2

−0.15

2 −0.1

−0.05

0

0.05

Real

Fig. 7. Locus of some eigenvalues vs. PSS gain Kpss, at HB point for the base case (Kpss=0-61).

0

−1.2

−1

−0.8

−0.6 Real

−0.4

−0.2

0

Fig. 9. Locus of some eigenvalues vs. TCSC gain KTCSC at HB point for the base case (KTCSC=0-7.8).

III. SIMULATION RESULTS Figure 5 shows the PV curves for the test system including bifurcation points for various cases. All the loads in the system were modeled as constant PQ loads and varied in the same ratio according to the following equation: PL = Po (1 + λ ) Q L = Qo (1 + λ )

(1)

where Po and Qo correspond to the base loading conditions and λ is the loading factor. As shown in Fig. 5, HB points were detected in all the cases, including two critical outages chosen to simulate contingencies that lead to oscillatory instabilities. Time domain simulations confirmed that the line 2-4 outage leads to an oscillatory unstable condition, as shown in Fig. 6. Participation factor analysis indicated that the dominant state variables associated with the HB mode were the rotor angle δ and angular speed ω of Gen. 3. From trial tests, the most effective damping of critical modes was achieved with the PSS, SVC and TCSC located as shown in Fig. 4. A PSS placed at Gen. 3 was not effective in removing the HB.

A. Tuning Figure 7 shows the locus of some critical eigenvalue of the system for a variation in the PSS gain. Observe that HB mode moves to the left, and that for a PSS gain KPSS=60 another HB mode associated with Gen. 1 appears, as confirmed through time domain simulations for a line 2-4 outage (the circuit breakers opened at both ends of the line). Figure 8 shows the locus of the system eigenvalues with respect to the additional SVC controller gain KaSVC. The HB associated with the Gen. 3 moves to the left and a complex mode associated with the SVC controller itself crosses the imaginary axis for KaSVC=0.27, which was confirmed through time domain simulations. It was also observed that the system critical eigenvalues, especially the electromechanical modes, move to the left with an increase in the main SVC controller gain KSVC. As in the previous cases, the TCSC controller also removes the HB. However, a controller gain KTCSC=7.8 is problematical, as a pair of complex eigenvalues associated with the controller itself cross the imaginary axis as shown in Fig. 9; time domain simulations confirm these results.

4

Fig. 10. Oscillation damping with PSS for line 2-4 outage (λ=0.4 p.u.). Fig. 12. Oscillation damping with TCSC for line 2-4 outage (λ=0.4 p.u.). TABLE I STATIC AND DYNAMIC LOADING MARGINS WITH AND WITHOUT CONTROLLERS

S L M (MW)

Fig. 11. Oscillation damping with SVC for line 2-4 outage (λ=0.4 p.u.).

B. Performance Using the gain settings that yield the maximum damping of the critical modes, some further studies were carried out to explore and compare the performance for each controller under a wide variety of operating conditions. Figures 10, 11 and 12 show the time domain simulation for a line 2-4 outage at the operating point given by λ=0.4 (Total Load = 363 MW) for the various controllers. All the controllers remove the oscillation problem due to the HB as triggered by the line 2-4 outage; the best damping is obtained with the PSS (Fig. 10), followed by the TCSC (Fig. 12). The TCSC controller could not eliminate the HB problem completely as a HB appears at increased loading conditions. Static loading margin (SLM) and dynamic loading margin (DLM) of the system with and without various controllers are given in Table I. The DLM is defined as the distance between the base load (λ=0 or 259 MW) and the closest HB point, whereas the SLM is the distance between the base load and the tip of the nose curve. Both the PSS and SVC remove the HB as DLM=SLM. It is important to notice that the additional SVC control loop significantly increases the DLM as shown in Table II, for various operating conditions. Supplementary benefits of the controllers on voltage profiles during the transient period for a line 2-4 outage are shown in Figs. 13, 14 and 15. Observe that the best voltage profiles are obtained with the SVC, as expected (Fig. 14); comparable

D L M (MW)

No. cont. PSS SVC TCSC No. cont. PSS SVC TCSC

Base Case 176 176 212 192 122 176 212 176

Line 2-4 Outage 132 132 168 161 90 132 168 142

Line 2-3 Outage 65 65 98 88 36 65 98 83

TABLE II DYNAMIC LOADING MARGINS WITH SVC

Dynamic Loading Margins (MW)

Base Case Line 2-4 Outage Line 2-3 Outage

No. Add. Control 186 148 80

Add. Control 212 168 98

results were obtained for the TCSC (Fig. 15). With the PSS, voltage profiles at some buses drop about 10-15 percent, before they recover. Performance of these controllers with respect to a threephase fault and a sudden load change were also studied at the HB point for the base case. Table III shows the maximum sudden load increase (SLI) that the system can withstand at bus 9, which is the 5th weakest bus in the system, before losing stability as a percentage of the load at that bus. This table also shows the maximum fault clearing time (MFCT) for a threephase fault at the middle of the line 2-4 for various controllers. These faults were cleared by removing line 2-4 completely. The SLI studies were carried out for different load buses, but only the worst case scenario results are reported here. From these results, both PSS and SVC are less susceptible to sudden load changes and three phase faults in the system.

5 9

8

with PSS with SVC with PSS & SVC

7

Imaginary

6

5

4

3

2

1

Fig. 13. Voltage profiles for line 2-4 outage with PSS (λ=0.4 p.u.).

0 −1.4

−1.2

−1

−0.8

−0.6 Real

−0.4

−0.2

0

0.2

Fig. 16. Some eigenvalues with PSS, SVC and PSS and SVC combined at HB point for the base case. 9

8

Kpss=10 7

K

=80

pss

6

Imaginary

Kpss=10 5

4

KPSS=80

3

2

Fig. 14. Voltage profiles for line 2-4 outage with SVC (λ=0.4 p.u.). 1

K

K

=80

pss

=10

pss

0

−1.2

−1

−0.8

−0.6 Real

−0.4

−0.2

0

0.2

Fig. 17. Locus of some eigenvalues of the system with PSS and SVC for variations in the PSS controller gain. TABLE III SUSCEPTIBILITY OF DIFFERENT CONTROLLERS

Controller PSS SVC TCSC

Fig. 15. Voltage profiles for a line 2-4 outage with TCSC (λ=0.4 p.u.).

C. Interactions Several studies were performed with two controllers in the system, i.e. PSS and SVC, PSS and TCSC, and SVC and TCSC. Figure 16 shows some system eigenvalues for each PSS and SVC and both combined. Observe that the introduction of the SVC in the system with PSS degrades the damping on several electromechanical modes, and most noticeably on the two modes on the top right-hand corner of Fig. 16.

SLI (%) 110 110 25

MFCT (Cycles) 18 15 3

Tuning of the controller gains was carried out to study possible interactions. The tuning of the SVC controller main KSVC gain did not create any problems in the system; as the controller gain increased, most of the electromechanical modes moved to the left. Tuning of additional controller gain KaSVC produced the same result as obtained in the tuning section. However, the tuning of PSS controller gain KPSS yielded a different result. With the SVC controller in the system, there is more room to tune the PSS controller gain as shown in Fig. 17. Notice that the complex mode associated with Gen. 1 crosses the imaginary axis for KPSS=80, which is an increase with respect to the results obtained with the PSS alone (Fig. 7).

6 10

9

9

8

7

with PSS with TCSC with PSS & TCSC

with TCSC with SVC with TCSC & SVC

8

7

6

Imaginary

Imaginary

6

5

4

5

4

3

3

2

2

1

1

0 −1.4

−1.2

−1

−0.8

−0.6 Real

−0.4

−0.2

0

0.2

Fig. 18. Some eigenvalues with PSS, TCSC and PSS and TCSC combined at HB point for the base case.

0 −1.4

−1.2

−1

−0.8

−0.6 Real

−0.4

−0.2

0

0.2

Fig. 20. Some eigenvalues with SVC, TCSC and SVC and TCSC combined at HB point for the base case.

9 10

K

8

=10

pss

9

7

K

=50

pss

7

Kpss=10

KaSVC=0.06 6

5 Imaginary

Imaginary

6

Kasvc= 0.86

KaSVC=0.06

8

4

Ka

svc

= 0.86

5

4

3

K

=50

pss

3

2 2

Kpss=50

1

1

Kpss=10 0 −1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

Ka

0.2

Real

0 −0.8

−0.7

−0.6

−0.5

−0.4

−0.3 Real

−0.2

−0.1

=0.06

SVC

Kasvc= 0.86 0

0

0.1

0.2

Fig. 19. Locus of some eigenvalues of the system with PSS and TCSC for variations in the PSS controller gain.

Fig. 21. Locus of some eigenvalues of the system with SVC and TCSC for variations in the additional SVC controller gain.

Conversely the tunable range of KPSS is reduced when a TCSC is combined with a PSS, as can be seen in Figs. 18 and 19, where it can be observed that the TCSC enhances the damping of most of the electromechanical modes except for the one associated with Gen. 1 (bottom right-hand corner in Fig. 18, next to the null eigenvalue associated with the system reference). In this case, the complex mode associated with Gen. 1 crosses the imaginary axis at KPSS=45; this was confirmed through time domain simulations. These results show the possible negative effects of the interaction between the PSS and the TCSC. Finally, in Fig. 20 it is shown that the combination of an SVC with a TCSC degrades the damping on two of the electromechanical modes. Furthermore, the electromechanical mode associated with Gen. 4 crosses the imaginary axis following an increase in KaSVC as shown in Fig. 21 due to the interaction of the two controllers; this was not observed when each controller was acting alone in the system.

However, care must be taken when tuning these controllers to avoid instability at certain gains. The most effective damping was observed with a PSS; however, the SVC and TCSC controllers not only increased the dynamic loading margins of the system but also the static loading margins, thus yielding a better voltage profile during post fault transients. Dynamic loading margin of the system with a SVC greatly improved with an additional control loop. Finally, the PSS and SVC controllers show less susceptibility to sudden load changes and three phase faults. This paper demonstrates that installing multiple controllers on the system may not improve the dynamic performance due to undesirable interactions. The tuning of one controller may affect other controllers and thus lead to unstable conditions. These issues should be taken into consideration when designing systems with multiple controllers. The implementation of a coordinated controller tuning procedure to avoid undesirable interactions in power system, and thus improve overall dynamic performance is under study.

IV. CONCLUSIONS This paper demonstrates that PSS, SVC and TCSC controllers with appropriate gain settings alleviate the oscillation problem associated with Hopf bifurcations.

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V. REFERENCES [1] [2] [3]

[4]

[5]

[6]

[7] [8]

[9] [10]

[11]

[12] [13] [14]

P. Kundur, Power System Stability and Control, McGraw Hill, New York, 1994. G. Rogers, Power System Oscillations, Kluwer, Norwell, MA 2000. E. Uzunovic, C. A. Cañizares, and J. Reeve, , "EMTP Studies of UPFC Power Oscillation Damping," Proc. of NAPS’99, pp. 405-410, San Luis Obispo, CA, Oct. 1999. Available: http://www.power.uwaterloo.ca. N. Mithulannathan, C. A. Cañizares, and J. Reeve, "Hopf Bifurcation Control in Power System using Power System Stabilizers and Static Var Compensators," Proc. of NAPS’99, pp. 155-163, San Luis Obispo, California, October 1999, Available at http://www.power.uwaterloo.ca. C. Alsberg, "WSCC issues Preliminary Report on August Power Outgae," press release, WSCC, Sept. 1996. Available at http://www.wscc.com. E. H. Abed and P. P. Varaiya, "Nonlinear Oscillation in Power Systems," Int. J. Electric Power and Energy Systems, Vol. 6, pp. 37-43, 1984. N. G. Hingorani, "Flexible AC Transmission Systems," IEEE Spectrum, pp. 40-45, April 1993. C. A. Cañizares, " Power Flow and Transient Stability Models of FACTS Controllers for Voltage and Angle Stability Studies," Proc. 2000 IEEE/PES Winter Meeting, Singapore, Jan. 2000. Available at http://www.power.uwaterloo.ca. "Impact of Interactions among Power System Controllers," CIGRE, November 1999. M. J. Gibbard, D. J. Vowles, and P. Pourbeik, "Interactions Between, and Effectiveness of, Power System Stabilizers and FACTS Device Stabilizers in Multimachine Systems," IEEE Trans. Power Systems, Vol. 15, No. 2, pp. 748-755, May 2000. M. J. Lautenberg, M. A. Pai, and Padiyar . "Hopf Bifurcation Control in Power System with Static Var Compensators," Int. J. Electric Power and Energy Systems, Vol. 19, No. 5, pp. 339-347, 1997. C. A. Cañizares, "UWPFLOW," University of Waterloo, June 2001. Available at http://www.power.uwaterloo.ca. "Small Signal Stability Analysis Program Ver. 3.1: User’s Manual," EPRI, TR-101850-V2R1, May 1994. P. M. Anderson and A. A. Fouad, Power System Control and Stability, IEEE Press, 1994.

VI. BIOGRAPHIES Nadarajah Mithulananthan was born in Sri Lanka. He received his B.Sc. (Eng.) and M.Eng. degrees from the University of Peradeniya, Sri Lanka, and the Asian Institute of Technology, Thailand, in May 1993 and August 1997, respectively. Mr. Mithulananthan has worked as an Electrical Engineer at the Generation Planning Branch of the Ceylon Electricity Board, and as a Researcher at Chulalongkorn University, Thailand. He is currently a Ph.D. candidate at the University of Waterloo working on applications and control design of FACTS controllers. Claudio A. Cañizares received in April 1984 the Electrical Engineer diploma from the Escuela Politécnica Nacional (EPN), Quito-Ecuador, where he held different teaching and administrative positions from 1983 to 1993. His M.Sc. (1988) and Ph.D. (1991) degrees in Electrical Engineering are from the University of Wisconsin-Madison. Dr. Canizares is currently an Associate Professor and Associate Chair of Graduate Studies at E&CE Department of the University of Waterloo, and his research activities mostly concentrate on studying stability, modeling and computational issues in ac/dc/FACTS systems. John Reeve received the B.Sc., M.Sc., Ph.D. and D.Sc. degrees from the University of Manchester (UMIST). After employment in the development of protective relays for English Electric, Stafford, between 1958 and 1961, he was a lecturer at UMIST until joining the University of Waterloo in 1967, where he is currently an Adjunct Professor in the Department of Electrical & Computer Engineering. He was a project manager at EPRI, 1980-81, and was with IREQ, 1989-1990. His research interests since 1961 have been HVDC transmission and high power electronics. He is the President of John Reeve Consultants Limited. Dr. Reeve was chair of the IEEE DC Transmission Subcommittee for 8 years, and is a member of several IEEE and CIGRE Committees on dc transmission and FACTS. He was awarded the IEEE Uno Lamm High Voltage Direct Current Award in 1996.