IEEE Power System Paper-Design and Performance Evaluation of Subsynchronous Damping Controller With STATCOM

1398 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 21, NO. 3, JULY 2006

Design and Performance Evaluationof Subsynchronous Damping Controller

With STATCOMK. R. Padiyar, Senior Member, IEEE, and Nagesh Prabhu

AbstractA long transmission line needs controllable series aswell as shunt compensation for power flow control and voltageregulation. This can be achieved by suitable combination of pas-sive elements and active FACTS controllers. In this paper, seriespassive compensation and shunt active compensation providedby a static synchronous compensator (STATCOM) connected atthe electrical center of the transmission line are considered. Itis possible to damp subsynchronous resonance (SSR) caused byseries capacitors with the help of an auxiliary subsynchronousdamping controller (SSDC) on STATCOM. The objective of thispaper is to investigate the SSR characteristics of the system andpropose a new design procedure for SSDC based on nonlinearoptimization to meet the specifications on the damping torquein the range of critical torsional frequencies. The SSDC uses theThevenin voltage signal to modulate the reactive current referenceof STATCOM. The Thevenin voltage signal is derived from thelocally available STATCOM bus voltage and reactive currentsignals. The STATCOM configurations considered in this paperare 12 pulse, two- and three-level voltage source converter withType-2 and Type-1 control, respectively. The controller regulateseither reactive current (supplied by the STATCOM) or the busvoltage. The 3-phase model of the STATCOM is based on switchingfunctions. By neglecting harmonics in the switching function, D-Qmodel is derived which is combined with similar models of theother system components for linear analysis. The results of thelinear analysis are validated by carrying out transient simulationbased on the detailed nonlinear models. The study is performedon the system adapted from the IEEE First Benchmark Model.

Index TermsDamping torque, eigenvalue, FACTS, static syn-chronous compensator (STATCOM), subsynchronous dampingcontroller (SSDC), subsynchronous resonance (SSR), torsionalinteraction (TI), voltage source converter (VSC).

I. INTRODUCTION

THE increase of power transfer capability of long transmis-sion lines can be achieved by reducing the effective linereactance, providing dynamic voltage support by static var com-pensators and by static phase shifters. Series compensation oflong lines is an economic solution to the problem of enhancingpower transfer and improving system stability. However, se-ries-compensated transmission lines connected to turbogener-ators can result in subsynchronous resonance (SSR), leading toadverse torsional interactions [1][4].

Manuscript received January 19, 2005; revised July 1, 2005. Paper no.TPWRD-00028-2005.

The authors are with the Department of Electrical Engineering, IndianInstitute of Science, Bangalore 560 012, India (e-mail: [email protected]).

Digital Object Identifier 10.1109/TPWRD.2005.861332

The power transfer capability enhancement can also beachieved by suitable combination of passive elements andactive FACTS controllers. In this paper, series passive com-pensation and shunt active compensation provided by staticsynchronous compensator (STATCOM) connected at theelectrical center of the transmission line are considered forthe analysis. Both two-level and three-level, 12-pulse voltagesource converters (VSCs) are considered for STATCOM con-figuration with Type-2 and Type-1 controllers, respectively[5], [6]. The controller can regulate either bus voltage or thereactive current output of STATCOM. The reactive current canalso be modulated by the output of a subsynchronous dampingcontroller (SSDC) which uses the Thevenin voltage signal. TheThevenin voltage signal is derived from the locally availableSTATCOM bus voltage and reactive current signals.

The IEEE FBM is considered for the analysis of SSR. Thestudy is carried out based on damping torque analysis, eigen-value analysis, and transient simulation. The paper is organizedas follows. Section II describes the modeling of STATCOM.The different methods of analysis of SSR are discussed in Sec-tion III. Section IV describes a case study and highlights theneed of a SSDC for damping of SSR. The design of SSDC andthe evaluation of its performance is presented in Section V. Themajor conclusions of the paper are given in Section VI.

II. MODELLING OF STATCOM WITH TWO- ANDTHREE-LEVEL VSC

In the power circuit of a STATCOM, the converter haseither a multi-pulse and/or a multilevel configuration. Herethe STATCOM is realized by a combination of 12-pulse andtwo-/three-level configuration. When the dc voltage is constant,the magnitude of ac output voltage of the converter can bechanged by pulsewidth modulation (PWM) with two-leveltopology which demands higher switching frequency andleads to increased losses. The three-level converter topologycan achieve the goal by varying dead angle with funda-mental switching frequency [7], [8]. The time period in a cycleduring which the converter pole voltage is zero is . Thethree-level converter topology greatly reduces the harmonicdistortion on the ac side [6], [8][10].

The detailed three-phase model of a STATCOM is developedby modeling the converter operation by switching functions [7],[11]. The modeling of two- and three-level VSC are discussedin detail in [12] and [7], respectively, and is not repeated here.

0885-8977/$20.00 2006 IEEE

Authorized licensed use limited to: UNIVERSITATSBIBLIOTHEK DORTMUND. Downloaded on September 10, 2009 at 15:54 from IEEE Xplore. Restrictions apply.

PADIYAR AND PRABHU: DESIGN AND PERFORMANCE EVALUATION OF SSDC WITH STATCOM 1399

Fig. 1. STATCOM as a shunt FACTS controller.

A. Mathematical Model of STATCOM in D-Q Frame of [11]and [12]

When switching functions are approximated by theirfundamental frequency components neglecting harmonics,STATCOM can be modeled by transforming the three-phasevoltages and currents to D-Q variables using Krons transfor-mation [13]. The STATCOM can be represented functionally,as shown in Fig. 1.

The magnitude control of converter output voltage isachieved by modulating the conduction period affected bydead angle of a converter while the dc voltage is maintainedconstant.

The converter output voltage can be represented in the D-Qframe of reference as

(1)

(2)

(3)

The following equations in the D-Q variables can be given fordescribing STATCOM:

(4)

(5)

(6)

where

, D-Q components of STATCOM current.is modulation index and for a two-level converter,

(a constant), for a 12 pulse converter. is theangle by which the fundamental component of converter outputvoltage leads the STATCOM bus voltage . For a three-levelconverter, the modulation index is a function of dead angleand is given as .

B. STATCOM Current Control (Two-Level VSC)

With a 2-level VSC, the reactive current control can beachieved by varying alone (refer Fig. 2). In this controller,the modulation index is constant. The capacitor voltage is

Fig. 2. Type-2 controller for 2-level VSC-based STATCOM.

Fig. 3. Type-1 controller for STATCOM.

not regulated but depends upon the phase difference betweenthe converter output voltage and the bus voltage. The reactivecurrent control is effected by converter output voltage magni-tude(which is a function of dc voltage control) and achieved byphase angle control [5]. This causes the variation of capacitorvoltage over a small range with change in operating point.

C. STATCOM Current Control (Three-Level VSC)

The real current drawn by the VSC is controlled by phaseangle and reactive current by modulating the converter outputvoltage magnitude as a function of . The Fig. 3 shows theschematic representation of TYPE-1 controller for STATCOMcurrent control. The reactive current reference of STATCOMcan be kept constant or regulated to maintain bus voltage mag-nitude at the specified value.

In Fig. 3, real and reactive currents are defined as

(7)

(8)

and and are calculated as

(9)

(10)

Equations (7) and (8) result in positive values when theSTATCOM is absorbing power and reactive power. It is to be



Fig. 4. Interaction between mechanical and electrical system.

noted that is the output of the auxiliary controller such asSSDC.

III. ANALYSIS OF SSR

The two aspects of SSR are [4]: 1) steady state SSR [(induc-tion generator effect (IGE) and torsional interaction(TI)] and2) transient torques. The analysis of steady-state SSR can bedone by linearized models at the operating point and includedamping torque analysis and eigenvalue analysis. The analysisof transient SSR requires transient simulation of the nonlinearmodel of the system. For the analysis of SSR, it is adequate tomodel the transmission line by lumped resistance and induc-tance where the line transients are also considered. The gener-ator stator transients are also considered by using detailed (2.2)model of the generator [13].

The analysis of SSR with STATCOM is carried out basedon damping torque analysis, eigenvalue analysis, and transientsimulation.

A. Damping Torque Analysis

Damping torque analysis is a frequency domain methodwhich can be used to screen the system conditions that give riseto potential SSR problems. The significance of this approach isthat it enables the planners to decide upon a suitable counter-measure for the mitigation of the detrimental effects of SSR.Damping torque method gives a quick check to determine thetorsional mode stability. The system is assumed to be stable ifthe net damping torque at any of the torsional mode frequencyis positive [14].

The interaction between the electrical and mechanical systemcan be represented by the block diagram shown in Fig. 4.

At any given oscillation frequency of the generator rotor, thecomponent of electrical torque ( ) in phase with the rotorspeed ( ) is termed as damping torque. When the IGE isneglected (as it does not have significant effect on the predictionof torsional mode stability), the generator can be represented bythe classical model [15].

B. Eigenvalue Analysis

In this analysis, the detailed generator model (2.2) [13] is con-sidered. The electromechanical system consists the multi-massmechanical system, the generator, the excitation system, powersystem stabilizer (PSS), torsional filter, and the transmission line

Fig. 5. Modified IEEE first benchmark model with STATCOM.

with STATCOM. The STATCOM (1)(10) along with the equa-tions representing electromechanical system [4], [13] (in D-Qvariables), are linearized at the operating point and eigenvaluesof system matrix are computed. The stability of the system isdetermined by the location of the eigenvalues of system matrix.The system is stable if the eigenvalues have negative real parts.

C. Transient Simulation

The eigenvalue analysis uses equations in D-Q variableswhere the switching functions are approximated by their fun-damental frequency components (converter switchings areneglected). To validate the results obtained from dampingtorque and eigenvalue analysis, the transient simulation shouldbe carried out using detailed nonlinear three-phase model ofSTATCOM which considers the switching in the three-phaseconverters.

IV. A CASE STUDY

The system considered is a modified IEEE FBM [16]. Thesystem is represented schematically in Fig. 5, which consistsof a generator, turbine, series compensated long transmissionline and STATCOM connected at the electrical center of thetransmission line.

The modeling aspects of the electromechanical system com-prising the generator, the mass-spring mechanical system, theexcitation system, power system stabilizer (PSS) with torsionalfilter, the transmission line containing the conventional seriescapacitor are discussed in [4].

The Analysis is carried out based on the following initial op-erating condition and assumptions.

1) The generator delivers 0.9 p.u. power to the transmissionsystem.

2) The dynamics of the turbine-governor systems are ne-glected and the input mechanical power to the turbine isassumed constant.

3) The compensation level provided by the series capacitoris set at 0.6 p.u.

4) The dynamic voltage support at the mid point of the trans-mission line is provided by STATCOM. The results ofload flow indicated that, the reactive power requirementat the mid point of transmission varies from 75 to 375Mvar from light to full load conditions of the generator.In order to effectively utilize the symmetric capability ofSTATCOM in both inductive as well as capacitive range,



TABLE ITORSIONAL MODE EIGENVALUES OF THE SYSTEM WITH TWO-LEVEL VSC-BASED STATCOM

TABLE IITORSIONAL MODE EIGENVALUES OF THE SYSTEM WITH

THREE-LEVEL VSC-BASED STATCOM

a fixed shunt capacitor is also used at the STATCOM buswhich provides a reactive power of 225 Mvar. The ratingof STATCOM is selected as . At the operatingpoint considered, the STATCOM supplies 99 Mvar andthe fixed capacitor supplies 225 Mvar to maintain a busvoltage of 1.015 p.u.

5) For the case studies without STATCOM, the value of fixedshunt capacitor is selected such that, the midpoint voltageis set at 1.015 p.u. in steady state.

A. Eigenvalue Analysis

In this analysis, the turbine-generator mechanical dampingis considered and generator is modeled with the (2.2) model(as indicated in Section III-B). The overall system is linearizedabout an operating point and the eigenvalues of the system ma-trix [A] are given in Tables I and II for two-level and three-levelVSC-based STATCOM, respectively.

Table II shows that mode-2 is unstable at the operating pointconsidered. The voltage control reduces the undamping of crit-ical torsional mode-2 and improves the damping of swing mode.Mode-5 is not affected with the inclusion of STATCOM as itsmodal inertia is very high. In general, voltage controller reducesthe damping of torsional modes except the critical mode-2. Thedamping of subsynchronous network mode is increased withmarginal increase in the frequency for voltage control. Com-paring the results of Tables I and II, it is observed that, thedamping of critical torsional mode-2 is improved with a three-level VSC-based STATCOM while it is reduced marginally forother torsional modes. The improvement in the damping of crit-ical torsional mode-2 with three-level VSC-based STATCOM

Fig. 6. Variation of rotor angle and LPA-LPB section torque for pulse changein input mechanical torque (D-Q model of three-level VSC-based STATCOM(with voltage control)).

is due to the fact that, the frequency of the network mode (sub-synchronous) does not exactly match with that of the torsionalmode-2. There is no significant difference between the dampingof torsional modes with two-level and three-level converters.

B. Transient Simulation

The transient simulation of the combined nonlinear systemincluding STATCOM (with voltage control) is carried out usingboth D-Q and 3-phase model using MATLAB-SIMULINK [17].

The simulation results for 10% decrease in the input mechan-ical torque applied at 0.5 s and removed at 1 s with D-Q modelof three-level STATCOM is shown in Fig. 6.

The simulation results with 3-phase model of a three-levelSTATCOM is shown in Fig. 7.

It is clear from Figs. 6 and 7 that, the system is unstable asthe oscillations in rotor angle and LPA-LPB section torque growwith time. The results for two-level VSC-based STATCOM aresimilar and not shown here.

The FFT analysis of the LPA-LPB section torque (variationare obtained with 3-phase model of three-level STATCOM) isperformed between 610 s with the time spread of 1 s. Theresults of fast Fourier transform (FFT) analysis are shown inFig. 8.

Referring to Fig. 8, it is observed that as the time progresses,mode-2 component increases while all other torsional modecomponents (particularly mode-1) decay. The decrement factor



Fig. 7. Variation of rotor angle and LPA-LPB section torque for pulsechange in input mechanical torque [3-phase model of three-level VSC-basedSTATCOM (with voltage control)].

Fig. 8. FFT analysis of LPA-LPB section torque (3-phase model of three-levelVSC-based STATCOM (with voltage control)).

of mode-2 calculated from FFT analysis is found to be0.2787 and is comparable to the real part of eigenvalue (0.28)corresponding to mode-2 given in Table II. Accuracy of theD-Q model is also obvious from comparing Figs. 6 and 7.

It is observed that, the STATCOM requires a SSDC fordamping of the unstable torsional mode.

C. Discussion

The damping torque method involves less computationalburden and is a convenient tool for analyzing the SSR charac-teristics of the electrical network. Damping torque analysis canbe used to predict the potential SSR problems under varioussystem operating conditions.

1) Damping Torque Analysis With Detailed D-Q Model ofSTATCOM: The damping torque is evaluated in the range offrequency of 0300 rad/s for the following cases

1) With STATCOM reactive current control.2) With STATCOM reactive current reference obtained from

voltage controller.and compared with the damping torque results withoutSTATCOM (Here, the fixed shunt capacitor value is selected

Fig. 9. Variation of damping torque with detailed D-Q model of three-levelVSC-based STATCOM.

such that the midpoint voltage is 1.015 p.u.). The variation ofdamping torque with frequency with detailed D-Q model ofthree-level VSC-based STATCOM (Type-1 controller is usedfor reactive power control) is shown in Fig. 9.

The voltage control reduces the peak negative damping andmarginally increases the resonance frequency. It is interesting tonote that, the reactive current control marginally increases theundamping compared to the case without STATCOM. This isnot surprising, as the contribution of positive supersynchronousdamping torque due to shunt capacitor has reduced with thelesser value of shunt capacitor used. It is also observed that thevoltage control increases the negative damping of the torsionalmodes particularly in the range of frequencies greater than 130rad/s.

It should be noted that the inclusion of STATCOM with reac-tive current control does not change the damping characteristicsof the network significantly. Although the voltage control re-duces the peak negative damping at the critical torsional modefrequency, the system is unstable as there is a sharp dip nearabout 127 rad/s, which matches with mode-2 of IEEE FBM.

It is reported in [4] and [18] that, SVC and STATCOM candestabilize the torsional mode with voltage control. Such a be-havior is also observed in the present analysis. The reductionof damping of torsional modes with voltage control in the fre-quency range of 130300 rad/s can be observed in Fig. 9.

Although the damping torque analysis is approximate, it canbe used as a fast screening tool. A systematic method for thedesign of SSDC based on damping torque method is presentedin Section V.

V. DESIGN OF SSDC

Improvement of the damping of SSR modes can be achievedby SSDC. The Thevenin voltage signal ( ) de-rived from the locally available STATCOM bus voltage ( ) andthe reactive current ( ) is used for damping of power swingsin [19], [20]. Here the SSDC (represented by a transfer func-tion ) which takes the Thevenin voltage signal as input isused to modulate the reactive current reference to improve the



Fig. 10. Block diagram of SSDC for STATCOM.

damping of the unstable torsional mode. The block diagram ofSSDC is shown in Fig. 10.

A. Design of SSDC Based on Parameter Optimization of theTransfer Function

The objective of SSDC is to enhance the damping torqueat the critical range of torsional frequencies such that the netdamping torque is positive. The critical range of frequencies isdecided by the negative damping introduced by the electricalsystem in the absence of SSDC. The SSDC should not signifi-cantly affect the synchronizing torque, similar to the action of aPSS.

The preliminary studies involving curve fitting (in the criticalrange of torsional frequencies) by specifying desired values ofthe damping torque (without affecting the synchronizing torque)resulted in a SSDC transfer function of second order. The initialdesign of the SSDC based on transfer function fitting improvedthe damping of torsional modes however, the performance wasfound to be not entirely satisfactory.

Since the synchronizing torque at torsional frequenciesare not significantly affected by the electrical network (withor without SSDC), it is simpler to design the SSDC transferfunction by parameter optimization with the objective of min-imizing the deviations between the desired damping torque( ) and the actual damping torque ( ).

For the design of SSDC ( ) based on parameter optimiza-tion, the structure of the transfer function is assumed as

(11)

The objective for optimizing of the parameters ( , , , and) of the transfer function is to

Minimize

subjected to

The constraints ensure that the poles of the transfer functionare complex and have negative real parts.

It order that, the SSDC contributes to the positive dampingthe is taken to be positive. However, it was observedthat, with large positive value for causes the networkmode unstable. In the frequency range of 110135 rad/s, max-imum possible positive value for is selected withoutcausing the network mode to become unstable. Here, the de-sired damping torque is taken as 1 (p.u.) for

. and are taken to be 110 rad/s and 135rad/s (the critical frequency range).

Fig. 11. Variation of damping torque with detailed D-Q model of three-levelVSC-based STATCOM and SSDC.

The optimization routine fmincon of MATLAB is used forthe solution. The designed value of (SSDC) is obtained as

The is Thevenin reactance (a tunable parameter) andselected so as to maximize the damping torque of the overallsystem computed with the designed transfer function .

B. Analysis of SSR With SSDC

The analysis with SSDC is carried out based on dampingtorque analysis, eigenvalue analysis and transient simulation.While damping torque and eigenvalue analysis considers D-Qmodel of STATCOM, the transient simulation considers the de-tailed 3-phase models of STATCOM.

1) Damping Torque Analysis: The damping torque with de-tailed D-Q model three-level VSC-based STATCOMs is shownin Fig. 11.

It is seen that, the peak negative damping is significantly re-duced with SSDC and occurs at a lower frequency of about 52rad/s. Since this frequency does not match with any of the tor-sional modes, the system is expected to be stable. It should benoted that the damping torque is positive with SSDC in the crit-ical range of torsional mode frequencies.

2) Eigenvalue Analysis: The eigenvalues of the overallsystem for two-level and three-level VSC-based STATCOM onvoltage control and SSDC are shown in Table III.

Comparing the eigenvalue results without SSDC (referTable II) and with SSDC (Table III), the following observationscan be made.

1) The damping of critical mode-2 has significantly im-proved with SSDC.

2) The damping of all torsional modes is increased withSSDC.

3) Mode-5 is not affected as its modal inertia is very high.4) The damping of subsynchronous network mode is re-

duced with SSDC.



TABLE IIITORSIONAL MODE EIGENVALUES OF THE SYSTEM WITH

STATCOM AND SSDC

Fig. 12. Variation of rotor angle and LPA-LPB section torque for pulse changein input mechanical torque (with 3-phase model of three-level VSC-basedSTATCOM with SSDC).

3) Transient Simulation: The transient simulation of theoverall system including STATCOM with SSDC has been car-ried out with the 3-phase model using MATLAB-SIMULINK[17].

The simulation results for 10% decrease in the input mechan-ical torque applied at 0.5 s and removed at 1 s with three-levelVSC-based STATCOM along with SSDC are shown in Fig. 12.

The results show that the SSDC is effective in stabilizing thecritical torsional modes.

C. Discussion

While the design of SSDC based on the damping torque anal-ysis is not new [21], we propose a new algorithm for the designwhich results in better performance. According to the proce-dure in [21], the desired transfer function is speci-fied as a function of frequency. This implies specifying the syn-chronizing torque in addition to the damping torque. Based onthis ideal transfer function, it is possible to synthesize the fre-quency response of the SSDC if simplified models of the device(STATCOM in our case) and the system are employed. How-ever, the practical implementation is problematic for any arbi-trary frequency response, and hence curve fitting, by physically

realizable transfer function is required. The approximations in-troduced by this step can affect considerably the damping torquein the critical torsional frequency range. A better procedure asexplained in Section V-A ensures that the damping torque ismaintained close to the specification. There is no need to specifythe synchronizing torque (In any case, the electrical system hasvery little influence on the frequencies of the torsional modes).Also, there is no need to simplify the device and system modelsto obtain the transfer function of the SSDC.

The results of the SSDC design procedure proposed in Sec-tion V-A are compared with those obtained from the curve fit-ting procedure similar to that outlined in [21]. Fig. 11 shows thecomparison which clearly indicates the improved performanceof the new design procedure. The design is also robust as thedip in the damping torque is less and frequency at which it oc-curs is much below the first torsional mode frequency. It is alsointeresting to observe that, the swing mode (mode zero) is notdestabilized by SSDC, rather the SSDC marginally improves thedamping.

It is possible to improve the performance of the SSDC byadjusting the specifications (altering the frequency range of in-terest). However, this is not investigated here.

Using a lead-lag network for SSDC, [22] investigates the ef-fect of various control signals for damping torsional oscillations.While the frequency of the synthesized voltage is consideredin [22], this paper considers the magnitude of the synthesizedvoltage (termed as Thevenin voltage).

VI. CONCLUSION

In this paper, we have studied the characteristics of atransmission line compensated by series capacitor with theSTATCOM provided at the electrical center of the transmis-sion line. The modeling of two-level and three-level 12-pulseVSCs along with their controllers are presented in detail. Theconverters are modeled using switching functions. Neglectingharmonics in the switching functions enables the derivation oftime invariant models based on D-Q variables. The predictionsabout the torsional mode stability using the various methods ofanalysis show good agreement.

The following points emerge based on the results of the casestudy.

1) The inclusion of STATCOM does not change the SSRcharacteristics of the network significantly.

2) Although the voltage control reduces the peak negativedamping, a properly designed SSDC is required fordamping of the critical torsional mode.

3) A simple and new technique for the design of SSDC byparameter tuning based on damping torque method is pro-posed. The SSDC parameters are tuned to get optimumperformance to provide positive damping in a range oftorsional frequencies. The case study to illustrate the tech-nique indicates that the results are satisfactory.

4) The D-Q model of STATCOM is found quite accurate inpredicting the system performance.



REFERENCES

[1] M. C. Hall and D. A. Hodges, Experience with 500 kV subsynchronousresonance and resulting turbine generator shaft damage at Mohave gen-erating station, in Analysis and Control of Subsynchronous Resonance,1976, IEEE Publ. 76 CH 1066-O-PWR.

[2] C. E. J. Bowler, D. N. Ewart, and C. Concordia, Self excited torsionalfrequency oscillations with series capacitors, IEEE Trans. Power App.Syst., vol. PAS-92, pp. 16881695, 1973.

[3] L. A. Kilgore, D. G. Ramey, and M. C. Hall, Simplified transmis-sion and generation system analysis procedures for subsynchronousresonance problems, IEEE Trans. Power App. Syst., vol. PAS-96, pp.18401846, Nov./Dec. 1977.

[4] K. R. Padiyar, Analysis of Subsynchronous Resonance in Power Sys-tems. Boston, MA: Kluwer, 1999.

[5] Schauder and Mehta, Vector analysis and control of advanced staticVAR compensators, Proc. Inst. Elect. Eng. C, vol. 140, no. 4, pp.299306, Jul. 1993.

[6] N. G. Hingorani and L. Gyugyi, Understanding FACTS. New York:IEEE Press, 2000.

[7] K. R. Padiyar and N. Prabhu, Analysis of subsynchronous reso-nance with three level twelve-pulse VSC based SSSC, in Proc. IEEETENCON-2003, Oct. 1417, 2003.

[8] K. K. Sen and E. J. Stacy, UPFC- Unified power flow controller:Theory,modeling and applications, IEEE Trans. Power Del., vol. 13,no. 5, pp. 14531460, Oct. 1998.

[9] R. W. Menzis and Y. Zhuang, Advanced static compensation using amultilevel GTO thyristor inverter, IEEE Trans. Power Del., vol. 10, no.2, pp. 732738, Apr. 1995.

[10] J. B. Ekanayake and N. Jenkins, Mathematical models of a three leveladvanced static var compensator, Proc. Inst. Elect. Eng., Gen. Transm.Distrib., vol. 144, no. 2, Mar. 1997.

[11] N. Prabhu, Analysis of SubSynchronous Resonance with VoltageSource Converter based FACTS and HVDC Controllers, Ph.D. disser-tation, Indian Inst. of Sci., Bangalore, India, Sep. 2004.

[12] K. R. Padiyar and A. M. Kulkarni, Design of reactive current andvoltage controller of static condenser, Int. J. Electr. Power EnergySyst., vol. 19, no. 6, pp. 397410, 1997.

[13] K. R. Padiyar, Power System Dynamics Stability and Control- SecondEdition. Hyderabad, India: B.S. Publications, 2000.

[14] I. M. Canay, A novel approach to the torsional interaction and elec-trical damping of the synchronous machine, Part-I: Theory, Part-II: Ap-plication to an arbitrary network, IEEE Trans. Power App. Syst., vol.PAS-101, pp. 36303647, 1982.

[15] K. R. Padiyar and N. Prabhu, Investigation of SSR characteristics ofunified power flow controller, Electr. Power Syst. Res., vol. 74, pp.211221, 2005.

[16] IEEE committee report, First bench mark model for computer sim-ulation of subsynchronous resonance, IEEE Trans. Power App. Syst.,vol. PAS-96, pp. 15651572, Sep./Oct. 1977.

[17] Using MATLAB-SIMULINK, The Math Works, Inc., Natick, MA, 1999.[18] N. Rostomkolai, R. J. Piwko, E. V. Larsen, D. A. Fischer, M. A. Mo-

barak, and A. E. Poitras, Subsynchronous torsional interactions withSVCS Concepts and practical implications, IEEE Trans. Power Syst.,vol. 5, no. 4, pp. 13241332, Nov. 1990.

[19] A. M. Kulkarni and K. R. Padiyar, Damping of power swings usingshunt FACTS controllers, in Proc. 4th Workshop on EHV Technology,Bangalore, India, Jul. 1998.

[20] K. R. Padiyar and V. Swayam Prakash, Tuning and performance evalu-ation of damping controller for a STATCOM, Int. J. Electr. Power andEnergy Syst., vol. 25, pp. 155166, 2003.

[21] R. J. Piwko and E. V. Larsen, HVDC system control for damping ofsubsynchronous oscillations, IEEE Trans. Power App. Syst., vol. PAS-101, pp. 22032210, Jul. 1982.

[22] K. R. Padiyar and R. K. Varma, Static VAR system auxiliary controllersfor damping torsional oscillations, Int. J. Electr. Power Energy Syst.,vol. 12, no. 4, pp. 271286, 1988.

K. R. Padiyar (SM91) received the B.E. degree in electrical engineering fromPoona University, Poona, India, in 1962, the M.E. degree from the Indian Insti-tute of Science (I.I.Sc.), Bangalore, India, in 1964, and the Ph.D. degree fromthe University of Waterloo, Waterloo, ON, Canada, in 1972.

He is an Honorary Professor of Electrical Engineering at I.I.Sc. Banga-lore. He was with the Indian Institute of Technology, Kanpur, India, from19761987, prior to joining I.I.Sc. His research interests are in the area ofHVDC and FACTS, system dynamics, and control. He has authored threebooks and over 200 papers.

Dr. Padiyar is a Fellow of Indian National Academy of Engineering.

Nagesh Prabhu received the Dipl. Elect. Eng. from Karnataka Polytechnic,Mangalore, India, in 1986. He graduated in electrical engineering from the In-stitution of Engineers, India, in 1991 and received the M.Tech. degree in powerand energy systems from N.I.T. Karnataka, India (formerly Karnataka RegionalEngineering College), in 1995, and the Ph.D. degree from the Indian Instituteof Science, Bangalore, India, in 2005.

He was with N.M.A.M. Institute of Technology, Nitte, India, from 1986 to1998 prior to joining the J.N.N. College of Engineering, Shimoga, India. Hisresearch interests are in the areas of power system dynamics and control, HVDCand FACTS.


tocDesign and Performance Evaluation of Subsynchronous Damping ContK. R. Padiyar, Senior Member, IEEE, and Nagesh PrabhuI. I NTRODUCTIONII. M ODELLING OF STATCOM W ITH T WO- AND T HREE -L EVEL VSC

Fig.1. STATCOM as a shunt FACTS controller.A. Mathematical Model of STATCOM in D-Q Frame of [ 11 ] and [ 12B. STATCOM Current Control (Two-Level VSC)

Fig.2. Type-2 controller for 2-level VSC-based STATCOM.Fig.3. Type-1 controller for STATCOM.C. STATCOM Current Control (Three-Level VSC)

Fig.4. Interaction between mechanical and electrical system.III. A NALYSIS OF SSRA. Damping Torque AnalysisB. Eigenvalue Analysis

Fig.5. Modified IEEE first benchmark model with STATCOM.C. Transient SimulationIV. A C ASE S TUDY

TABLE I T ORSIONAL M ODE E IGENVALUES OF THE S YSTEM W ITH T WO TABLE II T ORSIONAL M ODE E IGENVALUES OF THE S YSTEM W ITH T HRA. Eigenvalue Analysis

Fig.6. Variation of rotor angle and LPA-LPB section torque for B. Transient Simulation

Fig.7. Variation of rotor angle and LPA-LPB section torque for Fig.8. FFT analysis of LPA-LPB section torque (3-phase model ofC. Discussion1) Damping Torque Analysis With Detailed D-Q Model of STATCOM: T

Fig.9. Variation of damping torque with detailed D-Q model of tV. D ESIGN OF SSDC

Fig.10. Block diagram of SSDC for STATCOM.A. Design of SSDC Based on Parameter Optimization of the Transfe

Fig.11. Variation of damping torque with detailed D-Q model of B. Analysis of SSR With SSDC1) Damping Torque Analysis: The damping torque with detailed D-Q2) Eigenvalue Analysis: The eigenvalues of the overall system fo

TABLE III T ORSIONAL M ODE E IGENVALUES OF THE S YSTEM W ITH STAFig.12. Variation of rotor angle and LPA-LPB section torque for3) Transient Simulation: The transient simulation of the overallC. DiscussionVI. C ONCLUSIONM. C. Hall and D. A. Hodges, Experience with 500 kV subsynchronoC. E. J. Bowler, D. N. Ewart, and C. Concordia, Self excited torL. A. Kilgore, D. G. Ramey, and M. C. Hall, Simplified transmissK. R. Padiyar, Analysis of Subsynchronous Resonance in Power SysSchauder and Mehta, Vector analysis and control of advanced statN. G. Hingorani and L. Gyugyi, Understanding FACTS . New York: IK. R. Padiyar and N. Prabhu, Analysis of subsynchronous resonancK. K. Sen and E. J. Stacy, UPFC- Unified power flow controller: R. W. Menzis and Y. Zhuang, Advanced static compensation using aJ. B. Ekanayake and N. Jenkins, Mathematical models of a three lN. Prabhu, Analysis of SubSynchronous Resonance with Voltage SouK. R. Padiyar and A. M. Kulkarni, Design of reactive current andK. R. Padiyar, Power System Dynamics Stability and Control- SecoI. M. Canay, A novel approach to the torsional interaction and eK. R. Padiyar and N. Prabhu, Investigation of SSR characteristic

IEEE committee report, First bench mark model for computer simulUsing MATLAB-SIMULINK, The Math Works, Inc., Natick, MA, 1999.N. Rostomkolai, R. J. Piwko, E. V. Larsen, D. A. Fischer, M. A. A. M. Kulkarni and K. R. Padiyar, Damping of power swings using K. R. Padiyar and V. Swayam Prakash, Tuning and performance evalR. J. Piwko and E. V. Larsen, HVDC system control for damping ofK. R. Padiyar and R. K. Varma, Static VAR system auxiliary contr

Documents

IEEE Power System Paper-Design and Performance Evaluation of Subsynchronous Damping Controller With STATCOM