InvestigationofSSRCharacteristicsofHybridSeries ...downloads.hindawi.com/journals/ape/2011/621818.pdfThe advent of series FACTS controllers, thyristor controlled series capacitor (TCSC)

Hindawi Publishing CorporationAdvances in Power ElectronicsVolume 2011, Article ID 621818, 8 pagesdoi:10.1155/2011/621818

Research Article

Investigation of SSR Characteristics of Hybrid SeriesCompensated Power System with SSSC

R. Thirumalaivasan,1 M. Janaki,1 and Nagesh Prabhu2

1 School of Electrical Engineering, VIT University, Vellore 632014, India2 Canara Engineering College, Benjanapadavu, Bantwal, Mangalore 574219, India

Correspondence should be addressed to R. Thirumalaivasan, [email protected]

Received 2 November 2010; Accepted 13 March 2011

Academic Editor: Henry S. H. Chung

Copyright © 2011 R. Thirumalaivasan et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The advent of series FACTS controllers, thyristor controlled series capacitor (TCSC) and static synchronous Series Compensator(SSSC) has made it possible not only for the fast control of power flow in a transmission line, but also for the mitigation ofsubsynchronous resonance (SSR) in the presence of fixed series capacitors. SSSC is an emerging controller and this paper presentsSSR characteristics of a series compensated system with SSSC. The study system is adapted from IEEE first benchmark model(FBM). The active series compensation is provided by a three-level twenty four-pulse SSSC. The modeling and control detailsof a three level voltage source converter-(VSC)-based SSSC are discussed. The SSR characteristics of the combined system withconstant reactive voltage control mode in SSSC has been investigated. It is shown that the constant reactive voltage control ofSSSC has the effect of reducing the electrical resonance frequency, which detunes the SSR. The analysis of SSR with SSSC is carriedout based on frequency domain method, eigenvalue analysis and transient simulation. While the eigenvalue and damping torqueanalysis are based on linearizing the D-Q model of SSSC, the transient simulation considers both D-Q and detailed three phasenonlinear system model using switching functions.

1. Introduction

Power transfer capability of long transmission line is limitedby the transient stability limit. The first swing stability limitof a single machine infinite bus system can be determinedthrough well-known equal-area criterion [1, 2]. Duringfaulted period, the electrical output power of the machinedecreases drastically while the input mechanical powerremains more or less constant. Thus, the machine acquiresexcess energy and is used to accelerate the machine. Theexcess energy during faulted period can be represented byan area called accelerating area. To maintain stability, themachine must return the excess energy once the fault iscleared. The excess energy returning capability of themachine in postfault period is represented by another areacalled decelerating area. Thus, the stability of the system canbe improved by enlarging the decelerating area, and itrequires raising the power-angle curve of the system. FlexibleAC transmission systems (FACTS) devices are found to bevery effective in improving both stability and damping of

a power system by dynamically controlling the power-anglecurve of the system [1, 2]. With SSSC, working in capacitivemode, net reactance is reduced, and, during the firstswing, sufficient decelerating area is introduced to count-erbalance the accelerating area. However, in the subsequentswings, the SSSC provides better damping than that of theSTATCOM when supplementary modulation controllers areincorporated [3].

The series capacitor compensation for long-distancepower transmission line helps in enhancing power transferand is an economical solution to improve the system stabilitycompared to addition of new lines. A series capacitorcompensated line exhibits a resonant minimum in itsimpedance at a frequency fer = f0 =

√XC/XL, where XC is

the capacitive compensating reactance, XL is inductive linereactance, and f0 is the synchronous frequency of the powersystem. The resonant frequency fer of the compensatedline depends on the level of compensation of the lineinductance but is always subsynchronous since, in practice,the compensation ratio is less than unity. It is the coupling of

2 Advances in Power Electronics

this subsynchronous electrical transmission line resonance tothe mechanical resonances of a multistage turbine-generatorthat gives rise to the phenomenon of SSR. The problem ofself-excited torsional frequency oscillations (due to torsionalinteractions) was experienced at Mohave power station inUSA. in December 1970 and October 1971 [3, 4].

The hybrid compensation consisting of suitable combi-nation of passive elements and active FACTS controller suchas TCSC or SSSC can be used to mitigate SSR [5]. SSSCis a new generation series FACTS controller based on VSCand has several advantages over TCSC based on thyristorcontrollers. An ideal SSSC is essentially a pure sinusoidalAC voltage source at the system fundamental frequency. Thevoltage is always injected in quadrature with the line current,thereby emulating an inductive or a capacitive reactance inseries with the transmission line [3]. SSSC output impedanceat other frequencies is ideally zero. Thus, SSSC does notresonate with the inductive line impedance to initiate sub-synchronous resonance oscillations. However, in hybridseries compensation, fixed capacitor element contributes forseries resonance.

The SSSC has only one degree of freedom (i.e, reactivevoltage control, unless there is an energy source connectedon the DC side of VSC which allow for real power exchange)which is used to control active power flow in the line [3].The VSC based on three-level converter topology greatlyreduces the harmonic distortion on the AC side [3, 6, 7].In this paper fixed series capacitor and active compensationprovided by three-level twenty four-pulse VSC-based SSSCare considered. The constant reactive voltage control of SSSCis considered. The major objective is to investigate SSR char-acteristics of the series compensated system with SSSC usingboth linear analysis and nonlinear transient simulation. Itis shown that the constant reactive voltage control of SSSChas the effect of reducing the electrical resonance frequency,which detunes SSR.

The study is carried out based on frequency domainmethod, eigenvalue analysis and transient simulation [8].The modelling of the system neglecting VSC is detailed(including network transients) and can be expressed in DQvariables or (three) phase variables. The modeling of VSCis based on (1) DQ variables (neglecting harmonics in theoutput voltages of the converters) and (2) phase variables andthe use of switching functions. The damping torque analysis,eigenvalue analysis, and the controller design is based onthe DQ model while the transient simulation considersboth models of VSC. The results based on linear analysisare validated using transient simulation based on nonlinearsystem model.

The paper is organized as follows. Section 2 describes themodelling of SSSC whereas the different methods of analysisof SSR are discussed in Section 3. Section 4 describes a casestudy and investigates the SSR characteristics with SSSC. Themajor conclusions of the paper are given in Section 5.

2. Modelling of SSSC with Three-Level VSC

Figure 1 shows the schematic representation of SSSC. In thepower circuit of an SSSC, the converter is usually either

Vi+ i

VSC

idc

vdc

+

bc

gc

Figure 1: Schematic representation of SSSC.

a multipulse or a multilevel configuration. The eliminationof voltage harmonics requires multi-pulse configuration ofVSC. The multi-pulse converters are generally of TYPE-2where only the phase angle of converter output voltage canbe controlled and modulation index of the converter remainsfixed [3].

When the DC voltage is constant, the magnitude of acoutput voltage of the converter can be changed by PulseWidth Modulation (PWM) with two-level topology whichdemands higher switching frequency and leads to increasedlosses. In three level converter topology, both the magni-tude and phase angle of converter output voltage can becontrolled. This converter is classified as TYPE-1 converter[9], where DC bus voltage is maintained constant andthe magnitude of converter output voltage is controlled byvarying dead angle β with fundamental switching frequencymodulation [3, 10]. The harmonics are dependent on thecapacitance and the operating point of the SSSC. The detailedthree-phase model of SSSC is developed by modelling theconverter operation by switching functions. The switchingfunction for phase “a” is shown in Figure 2.

The switching functions of phases b and c are similarbut phase shifted successively by 120◦ in terms of thefundamental frequency. Assuming that the dc capacitorvoltagesVdc1 = Vdc2 = Vdc/2, the converter terminal voltageswith respect to the midpoint of dc side “N” can be obtainedas

⎡

⎢⎢⎢⎣

ViaN

VibN

VicN

⎤

⎥⎥⎥⎦=

⎡

⎢⎢⎢⎣

Pa(t)

Pb(t)

Pc(t)

⎤

⎥⎥⎥⎦Vdc

2, (1)

Advances in Power Electronics 3

0.450.4450.440.4350.430.4250.42

Time (s)

−1.5

−1

−0.5

0

0.5

1

1.5

Pa(t

)

Pa(t)

2β

Line current ia(t)

Figure 2: Switching function for a three level converter.

and the converter output voltages with respect to the neutralof transformer can be expressed as

⎡

⎢⎢⎢⎣

Vian

V ibn

V icn

⎤

⎥⎥⎥⎦=

⎡

⎢⎢⎢⎣

Sa(t)

Sb(t)

Sc(t)

⎤

⎥⎥⎥⎦Vdc , (2)

where

Sa(t) = Pa(t)2

−[Pa(t) + Pb(t) + Pc(t)

6

]. (3)

Sa(t) is the switching function for phase “a” of a 6-pulse 3-level VSC. Similarly for phase “b”, Sb(t), and for phase “c”,Sc(t) can be derived. The peak value of the fundamental andharmonics in the phase voltage Vi

an are found by applyingFourier analysis on the phase voltage and can be expressed as

Vian(h) =

2hπ

Vdc cos(hβ), (4)

where, h = 1, 5, 7, 11, 13, and β is the dead angle (period)during which the converter pole output voltage is zero. Wecan eliminate the 5th and 7th harmonics by using a twelve-pulse VSC, which combines the output of two six-pulse con-verters using transformers.

The switching functions for first twelve-pulse converterare given by

S121a(t) = S1a(t) +

1√3

(S′1a(t)− S′1c(t)

),

S121b(t) = S1b(t) +

1√3

(S′1b(t)− S′1a(t)

),

S121c(t) = S1c(t) +

1√3

(S′1c(t)− S′1b(t)

),

(5)

where

S′1x(t) = S1x

[

t +2πωo

112

]

S1x(t) = Sx

[t +

π

ωo

124

], x = a,b, c.

(6)

The switching functions for second twelve-pulse converterare given by

S122a(t) = S2a(t) +

1√3

(S′2a(t)− S′2c(t)

),

S122b(t) = S2b(t) +

1√3

(S′2b(t)− S′2a(t)

),

S122c(t) = S2c(t) +

1√3

(S′2c(t)− S′2b(t)

),

(7)

where

S′2x(t) = S2x

[t +

2πωo

112

]

S2x(t) = Sx

[t − π

ωo

124

], x = a,b, c.

(8)

The switching functions for a twenty four-pulse con-verter are given by

S24x (t) = S12

1x(t) + S122x(t), x = a,b, and c. (9)

If the switching functions are approximated by their fun-damental components (neglecting harmonics) for a 24-pulsethree level converter, we get

Vian =

8πVdc cos

(β)

sin(ωot + φ + γ

), (10)

and Vibn, Vi

cn are phase shifted successively by 120◦.The line current is given by ia =

√2/3Ia sin(ωo + φ) and

ib, ic are phase shifted successively by 120◦. Note that γ isthe angle by which the fundamental component of converteroutput voltage leads the line current. It should be noted thatγ is nearly equal to±π/2 depending on whether SSSC injectsinductive or capacitive voltage. Neglecting converter losses,we can get the expression for dc capacitor current as

[idc

]= −

[S24a (t) S24

b (t) S24c (t)

]

⎡

⎢⎢⎢⎣

ia

ib

ic

⎤

⎥⎥⎥⎦. (11)

A particular harmonic reaches zero when 2β = 180◦/h. Atβoptimum = 3.75◦, the three level 24-pulse converter behavesnearly like a two-level 48-pulse converter as 23th and 25thharmonics are negligibly small.

2.1. Modelling of SSSC in D-Q Variables. When switchingfunctions are approximated by their fundamental frequencycomponents, neglecting harmonics, SSSC can be modelledby transforming the three-phase voltages and currents to D-Q variables using Kron’s transformation [2]. The SSSC canbe represented functionally as shown in Figure 3.


I∠φ+

Rst Xst

Vi∠φ + γ

Figure 3: Equivalent circuit of SSSC as viewed from AC side.

In Figure 3, Rst and Xst are the resistance and reactance ofthe interfacing transformer of VSC. The magnitude controlof converter output voltage Vi is achieved by modulating theconduction period affected by dead angle of converter whiledc voltage is maintained constant.

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

Vi =√

ViD

2+Vi

Q2,

ViD = kmVdc sin

(φ + γ

),

ViQ = kmVdc cos

(φ + γ

),

(12)

where km = kρ cosβse; k = 4√

6/π for a 24-pulse converter. ρis the transformation ratio of the interfacing transformer.

From a control point of view, it is convenient to define theactive voltage (VP(se)) and reactive (VR(se)) voltage injectedby SSSC in terms of variables in D-Q frame (Vi

D and ViQ) as

follows

VR(se) = ViD cosφ−Vi

Q sinφ,

VP(se) = ViD sinφ +Vi

Q cosφ.(13)

Here, positive VR(se) implies that SSSC injects inductive volt-age and positive VP(se) implies that it draws real power tomeet losses.

The dc side capacitor is described by the dynamical equa-tion as

dVdc

dt= −gcωb

bcVdc − idc

ωbbc

, (14)

where idc = −[km sin(φ + γ)ID + km cos(φ + γ)IQ], ID and IQare the D-Q components of the line current.

2.2. Type-1 Controller. In this type of controller, both mag-nitude (modulation index km) and phase angle of converteroutput voltage (γ) are controlled. The capacitor voltage ismaintained at a constant voltage by controlling the activecomponent of the injected voltage VP(se). The real voltagereference VP(se)(ord) is obtained as the output of DC voltagecontroller. The reactive voltage reference VR(se)(ord) maybe kept constant or obtained from a power schedulingcontroller. However, for the SSR analysis, constant reactivevoltage control is considered.

It should be noted that harmonic content of the SSSC-injected voltage would vary depending upon the operatingpoint since magnitude control will also govern the switching.The capacitor voltage reference can be varied (depending onreactive voltage reference) so as to give optimum harmonic

vdc ref

+Σ−

Kp

Kis

+

+Σ

VP(se)(ord)

VR(se)(ord)

γ

βsevdc

11 + sTmd

γ and βse

calculator

Figure 4: Type-1 controller for SSSC.

ΔTm +Σ

−ΔTe

ΔSmMechanical system

G(s)

Electrical system

KH(s)

Figure 5: Interaction between mechanical and electrical system.

performance. In three level 24-pulse converter, dc voltage ref-erence may be adjusted by a slow controller to get optimumharmonic performance at βse = 3.75◦ in steady state.

The structure of type-1 controller for SSSC is given inFigure 4. In Figure 4, γ and βse are calculated as

γ = tan-1

[VR(se)(ord)

VP(se)(ord)

]

,

βse = cos−1

⎡

⎣

√V 2P(se)(ord) +V 2

R(se)(ord)

kmVdc

⎤

⎦ .

(15)

3. Analysis of SSR

The two aspects of SSR are [4](i) steady-state SSR (inductiongenerator effect (IGE) and torsional interaction (TI)) (ii)shaft torque amplification due to transients. The analysis ofsteady-state SSR can be done by linearized models at theoperating point and include damping torque analysis andeigenvalue analysis. The analysis of shaft torque amplificationdue to transients requires transient simulation of the nonlin-ear model of the system. For the analysis of SSR, it is adequateto model the transmission line by lumped resistance andinductance where the line transients are also considered.The generator stator transients are also considered by usingdetailed (2.2) model of the generator.

The analysis of SSR is carried out based on dampingtorque analysis, eigenvalue analysis, and transient simula-tion.

3.1. Damping Torque Analysis. Damping torque analysis is afrequency domain method which can be used to screen thesystem conditions that give rise to potential SSR problemsinvolving torsional interactions. It also enables the plannersto decide on a suitable countermeasure for the mitigation ofthe detrimental effects of SSR. Damping torque method gives


Generator

Vg∠θg

RT XT

XCRL XL

i

VSC

XSYS

SSSC

+

+ bc

gc

Eb∠0

(a) Electrical System

HP IP LPA LPB GEN EXC

Teω

(b) Six mass mechanical system

Figure 6: Modified IEEE first benchmark model with SSSC.

350300250200150100500

Frequency (rad/s)

−60

−50

−40

−30

−20

−10

0

10

Tde

With SSSC

Without SSSC

Figure 7: Damping torque with admittance function in D-Q axes.

a quick check to determine the torsional mode stability. Thesystem is assumed to be stable if the net damping (includingelectrical and mechanical) at any of the torsional modefrequency is positive.

The interaction between the electrical and mechanicalsystem can be represented by the block diagram shown inFigure 5. (ΔSm) is the p.u. deviation in generator rotor speed,and (ΔTe) is the p.u. change in electric torque [11].

The transfer function relating (ΔTe) to (ΔSm) is KH(s).At any given oscillation frequency of the generator rotor, thecomponent of electrical torque (ΔTe) in phase with the rotorspeed (ΔSm) is termed as damping torque. The dampingtorque coefficient (Tde(ω)) is defined as follows:

Tde(ω) = �[ΔTe

(jω)

ΔSm(jω)

]

= �[H( jω)]K=1. (16)

In obtaining (16), it is necessary to express the impedancefunction [Zs] of SSSC in D-Q frame [8].

3.2. Eigenvalue Analysis. In this analysis, the detailed gen-erator model (2.2) [2] is considered. The electromechanicalsystem consists of the multimass mechanical system, the gen-erator, the excitation system, power system stabilizer (PSS),

torsional filter, and the transmission line with SSSC. TheSSSC equations (12)–(14) along with the equations repre-senting electromechanical system [2, 4] (in D-Q variables),are linearized at the operating point, and eigenvalues ofsystem matrix are computed. The stability of the systemis determined by the location of the eigenvalues of systemmatrix. The system is stable if the eigenvalues have negativereal parts.

3.3. Transient Simulation. The eigenvalue analysis uses equa-tions in D-Q variables neglecting the harmonics. To validatethe results obtained from damping torque and eigenvalueanalysis, the transient simulation should be carried out usingdetailed nonlinear three-phase model of SSSC which con-siders the switching in the thyristors/three-phase converters.The actual converter switching of the SSSC based on threelevel 24-pulse converter is modelled by generating switchingfunctions.

4. A Case Study

The system considered is a modified IEEE FBM [12]. Thecomplete electromechanical system is represented schemat-ically in Figure 6, which consists of a generator, turbine, andseries compensated long transmission line with SSSC inject-ing a reactive voltage in series with the line. The electricalsystem data is taken from [8].

The modelling aspects of the electromechanical systemcomprising the generator, and the mass-spring mechanicalsystem, the excitation system, power system stabilizer (PSS)with torsional filter, and the transmission line containingthe conventional series capacitor are discussed in [4]. Theanalysis is carried out on the IEEE FBM based on thefollowing initial operating condition and assumptions.

(1) The generator delivers 0.9 p.u. power to the transmis-sion system.

(2) The input mechanical power to the turbine is as-sumed constant.

(3) The total series compensation level is set at 0.6 p.u.

(4) For transient simulation, a step decrease of 10% me-chanical input torque applied at 0.5 sec and removedat 1 sec is considered in all case studies.


109876543210

Time (s)

70

75

80

85δ

(deg

)

(a)

109876543210

Time (s)

−0.5

0

0.5

1

1.5

2

LPA

-LP

Bto

rqu

e(p

.u)

(b)

Figure 8: System response without SSSC.

4.1. Damping Torque Analysis. The damping torque due toelectrical network is evaluated in the range of frequency of10–360 rad/sec for the following cases using (14).

(1) Without SSSC,

(2) With SSSC.

In case (1), the series compensation of 60% is completelymet by fixed capacitor and in case (2), hybrid compensationis used wherein 45% of compensation is met by fixed capac-itor and the remaining 15% by SSSC. The variation ofdamping torque with frequency for both cases is shown inFigure 7.

It is to be noted that, in case (1), the damping torqueis maximum negative at a frequency of around 127 rad/secwhich matches with the natural frequency of torsionalmode-2 and adverse torsional interactions are expected. Incase (2), maximum undamping occurs at a frequency ofabout 150 rad/sec. Since this network frequency mode is notcoinciding with any of the torsional modes, the system isstable.

4.2. Eigenvalue Analysis. In this analysis, generator model(2.2) is considered. The SSSC equations along with the equa-tions representing electromechanical system consideringmechanical damping are linearized at the operating point.The eigenvalues of system matrix are computed and are givenin Table 1. It is to be noted that inclusion of SSSC leads to astable system and reduces the potential risk of SSR problem.

4.3. Transient Simulation. The eigenvalue analysis uses equa-tions in D-Q variables where the switching functions areapproximated by their fundamental components (converterswitchings are neglected). To validate the results obtainedfrom damping torque and eigenvalue analysis, the transientsimulation should be carried out using detailed model ofSSSC which considers the switching of three-phase converter.Hence, the three level 24-pulse converter is modelled bygenerating switching functions. The transient simulation ofthe combined system with detailed three-phase model of

Table 1: Eigen values of the combined system.

Torsional modeEigenvalue

Without SSSC With SSSC

0−1.7366± j

8.9279−1.2987± j 8.1094

1 −0.2143± j 99.4580 −0.2132± j 99.135

2 0.6658± j 127.000 −0.0695± j 127.050

3 −0.6459± j 160.420 −0.6438± j 160.210

4 −0.3646± j 202.820 −0.3694± j 202.800

5 −1.8504± j 298.170 −1.8504± j 298.170

Network mode −1.9029± j 126.950 −1.4918± j 149.980

Network mode −2.9906± j 626.790 −2.4803± j 582.980

SSSC has been carried out using MATLAB-SIMULINK [13].The system response for simulation without SSSC is shownin Figure 8. The simulation results of combined system withdetailed three phase model of SSSC is shown in Figure 9. Itis to be noted that the system is stable with the inclusion ofSSSC for the constant reactive voltage control.

4.4. Discussion. The representation of impedance functionof SSSC in single-phase basis (Zs(1ph)( jω)) from that of D-Qaxes [Zs] [8] is approximate and is given below

Zs(1ph) = 12

[{ZsDD

(j(ω− ω0)

)+ ZsQQ

(j(ω −ω0)

)}

+ j{ZsDQ

(j(ω −ω0)

)− ZsQD(j(ω − ω0)

)}].

(17)

The resistance Rse and reactance Xse of SSSC on singlephase basis as a function of frequency ωer are computed forXsssc = 0.15 with constant reactive voltage control. It is foundthat the resistance is negligible while the reactance Xse ispractically constant with frequency.

The effect of inclusion of SSSC on the resonancefrequency is shown in Figure 10 for cases 1 and 2.


109876543210

Time (s)

70

75

80

85δ

(deg

)

(a)

109876543210

Time (s)

0.55

0.6

0.65

0.7

0.75

0.8

LPA

-LP

Bto

rqu

e(p

.u)

(b)

Figure 9: System response with detailed three phase model of SSSC.

35030025020015010050

ωer (rad/s)

−0.5

0

0.5

1

1.5

2

2.5

3

3.5

Rea

ctan

ce

−(XC + Xse)

−XCXL

Xse216 227

Figure 10: Graphical representation of resonance conditions withand without SSSC.

When the fixed capacitor provides 45% compensation,the resonance occurs at ωer = 216 rad/sec where XC =XL. When the additional compensation of 15% is providedby SSSC, the effective capacitive reactance (XC + Xse) isobtained by adding the constant reactance offered by SSSCto that offered by fixed capacitor. The variation of effectivecapacitive reactance (XC + Xse) with frequency is alsoshown in Figure 10. Now, the resonance occurs at a higherfrequency of ωer = 227 rad/sec where (XC + Xse) = XL andthis is consistent with the subsynchronous network modefrequency (ω0-ωer = 377-227 = 150) of about 150 rad/secas obtained with damping torque analysis with SSSC.

The effect of providing additional series compensation bySSSC to supplement the existing fixed capacitor is to increasethe electrical resonance frequency of the network. However,this increase in frequency is not significant as compared tothat obtained with the equivalent fixed capacitor offeringadditional compensation (case 1) ωer = 250 rad/sec in thiscase. This indicates that the SSSC is not strictly SSR neutral

however, it offers a reactance which remains practically con-stant with frequency.

5. Conclusion

In this paper, we have presented the analysis and simulationof a hybrid series compensated system with SSSC. Themodelling details of 24-pulse three level VSC-based SSSC ispresented. The application of D-Q model is validated by thetransient simulation of the three-phase model of SSSC.

There is no appreciable difference in the resonancefrequency of the electrical network as the total series com-pensation (in a hybrid compensation scheme) is increased byincreasing the series reactive voltage injected, instead of theseries capacitor. This reduces the risk of SSR as the fixedcapacitor can be chosen such that the electrical resonancefrequency does not coincide with the complement of thetorsional modal frequency (which is practically independentof the electrical network). It is observed that the injectedreactive voltage can be adjusted to detune the SSR. The casestudies indicated that the SSSC is not strictly SSR neutralhowever, it offers a reactance which remains practicallyconstant with frequency.

References

[1] N. G. Hingorani and L. Gyugyi, Understanding FACTS, IEEEPress, New York, NY, USA, 2000.

[2] K. R. Padiyar, Power System Dynamics—Stability and Control,B.S.Publications, Hyderabad, India, 2nd edition, 2002.

[3] K. R. Padiyar, FACTS Controllers in Power Transmission andDistribution, New Age International (P) Limited, New Delhi,India, 2007.

[4] K. R. Padiyar, Analysis of Subsynchronous Resonance in PowerSystems, Kluwer Academic Publishers, Boston, Mass, USA,1999.

[5] K. R. Padiyar and N. Prabhu, “Analysis of SSR with three-leveltwelve-pulse VSC-based interline power-flow controller,” IEEETransactions on Power Delivery, vol. 22, no. 3, pp. 1688–1695,2007.


[6] R. W. Menzis and Y. Zhuang, “Advanced static compensa-tionusing a multilevel GTO thyristor inverter,” IEEE Transac-tions on PowerDelivery, vol. 10, no. 2, 1995.

[7] J. B. Ekanayake and N. Jenkins, “Mathematical models of athree-level advanced static VAr compensator,” IEE Proceedings,vol. 144, no. 2, pp. 201–206.

[8] K. R. Padiyar and N. Prabhu, “Analysis of subsynchronousresonance with three level twelve-pulse VSC based SSSC,” inProceedings of the IEEE Confernce on Covergent Technologiesfor the Asia-Pacific Region (TENCON ’03), pp. 76–80, October2003.

[9] C. Schauder and H. Mehta, “Vector analysis and control ofadvanced static VAR compensators,” IEE Proceedings C, vol.140, no. 4, pp. 299–306, 1993.

[10] K. K. Sen and E. J. Stacey, “UPFC—Unified Power Flow Con-troller: theory, modeling, and applications,” IEEE Transactionson Power Delivery, vol. 13, no. 4, pp. 1453–1460, 1998.

[11] N. Prabhu and K. R. Padiyar, “Investigation of subsyn-chronous resonance with VSC-based HVDC transmissionsystems,” IEEE Transactions on Power Delivery, vol. 24, no. 1,pp. 433–440, 2009.

[12] IEEE Subsynchronous Resonance Task Force, “First benchmark model for computer simulation of Subsynchronous res-onance,” IEEE Transactions on Power Apparatus and Systems,vol. 96, no. 5, pp. 1565–1572, 1977.

[13] The Math works Inc, “Using MATLAB-SIMULINK,” 1999.

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

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InvestigationofSSRCharacteristicsofHybridSeries ...downloads.hindawi.com/journals/ape/2011/621818.pdfThe advent of series FACTS controllers, thyristor controlled series capacitor (TCSC)

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