Ghosh Tuesday July 24 2003

8/20/2019 Ghosh Tuesday July 24 2003

1/71

DayDay--22

Series Compensation &Series Compensation &Other FACTS ControllersOther FACTS Controllers

Arindam GhoshArindam Ghosh

Dept. of Electrical EngineeringDept. of Electrical EngineeringIndian Institute of TechnologyIndian Institute of Technology

KanpurKanpur, India, IndiaEE--mail:mail: aghoshaghosh@@iitkiitk.ac.in.ac.in


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Series Compensation ofSeries Compensation of

Transmission SystemsTransmission SystemsA device that is connected in series with theA device that is connected in series with the

transmission line is called atransmission line is called a seriesseriescompensator compensator . In the analysis given below,. In the analysis given below,we shall investigate the effect of thewe shall investigate the effect of the

series compensator onseries compensator on•• the voltage profilethe voltage profile

•• the powerthe power--angle characteristicsangle characteristics•• the stability marginthe stability margin•• the damping of power oscillationsthe damping of power oscillations


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Ideal Series CompensatorIdeal Series Compensator

•• The ideal series compensator is represented byThe ideal series compensator is represented bya voltage source that only supplies reactivea voltage source that only supplies reactivepower and no real power.power and no real power.

•• The location of the series compensator is notThe location of the series compensator is notcrucial, and it can be placed anywhere along thecrucial, and it can be placed anywhere along thetransmission line.transmission line.


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Voltage Profile Voltage Profile

•• The series voltage must be injected in suchThe series voltage must be injected in sucha way that the series compensator does nota way that the series compensator does not

absorb any real power in the steady state.absorb any real power in the steady state.The injected voltage is thenThe injected voltage is then

°

= 90~~ jS Q e I V

µ

λ wherewhere λ λ is a proportionality constant.is a proportionality constant.

•• The ratioThe ratio λ λ //X X is called theis called the compensationcompensationlevel level . For example, we call the compensation. For example, we call the compensationlevel to be 50% whenlevel to be 50% when λ λ == X X /2./2.


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Voltage Profile Voltage Profile

( )λ

δ

µ X j

V V

jX

V V V I

Q RS

S

−∠=

−−=

~~~~

The choice of sign of the injected voltageThe choice of sign of the injected voltage visvis--

àà--visvis that of the current plays an importantthat of the current plays an importantrole in the operation of the seriesrole in the operation of the seriescompensator.compensator.

Let us assumeLet us assume.0

~,

~°∠=∠= V V V V RS δ

ThenThen


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Mode of OperationMode of Operation

( )λ λ

−−∠=⇒=− °−

X jV V I e I V S

j

S Q~~~ 90:1Case

The above choice corresponds to the voltageThe above choice corresponds to the voltagesource acting as a pure capacitor. Hence we callsource acting as a pure capacitor. Hence we callthis as thethis as the capacitive mode of operation capacitive mode of operation ..

( )λ

δ λ

+

−∠=⇒=− °+

X j

V V I e I V S

j

S Q

~~~: 902Case

Since the voltage source in this case acts as aSince the voltage source in this case acts as apure inductor, we call this as thepure inductor, we call this as the inductiveinductive

mode of operation mode of operation ..


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An Example An Example

Consider a system with sending and receivingConsider a system with sending and receivingend voltages being 1end voltages being 1∠∠3030ºº and 1and 1∠∠ 00ºº per unitper unitrespectively,respectively, X X = 0.5 per unit and= 0.5 per unit and λ λ = 0.15= 0.15per unit. Let us assume that the seriesper unit. Let us assume that the series

compensator operates in the capacitivecompensator operates in the capacitivemode. Then we havemode. Then we have

unit per752248.0~ unit per15479.1

~

°−∠=°∠=

Q

S

V I


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Example (Continued)Example (Continued)

TheThe phasorphasor diagram isdiagram isgiven left. Let us nowgiven left. Let us nowinvestigate theinvestigate the

impact of theimpact of thelocation compensatorlocation compensatorplacement on theplacement on the

voltage profile. Wevoltage profile. Weshall denote theshall denote thevoltage on the left ofvoltage on the left of

the compensator bythe compensator byV V QL QL and on the rightand on the rightof the compensatorof the compensator

byby V V QR QR ..


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CaseCase--1: Compensator1: Compensator

in middlein middle

•• The seriesThe seriescompensator iscompensator isplaced in theplaced in the

middle.middle.•• The worst voltageThe worst voltage

sag occurs atsag occurs at

each side of theeach side of theseriesseriescompensatorcompensator

where the voltagewhere the voltagevector aligns withvector aligns withthe currentthe current

vector.vector.


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CaseCase--2: Compensator2: Compensator

before the infinite busbefore the infinite bus

•• The seriesThe seriescompensator iscompensator is

placed justplaced justbefore thebefore theinfinite bus.infinite bus.

•• The maximumThe maximumvoltage risevoltage riseoccurs justoccurs just

before thebefore thecompensator.compensator.

•• The worst voltage sag still occurs where theThe worst voltage sag still occurs where the

voltage vector aligns with the current vector.voltage vector aligns with the current vector.


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PowerPower-- Angle Curve Angle Curve

The real and reactive powers at the sendingThe real and reactive powers at the sendingand receiving end are given byand receiving end are given by

( )

( )

λ

δ

λ

δ

λ δ

λ δ

µµ

µµ

X

V j X

V jQ P

X V j

X V jQ P

R R

S S

1cossin

cos1sin

22

22

−+=+

−+=+

The real power flow is thenThe real power flow is then

λ

δ

µ X

V P P P RS e

sin2===


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Reactive PowerReactive Power

Since the injected voltage and line current areSince the injected voltage and line current areinin quadraturequadrature,,

•• the real power supplied by the compensatorthe real power supplied by the compensatoris zero.is zero.

•• the reactive power supplied by thethe reactive power supplied by thecompensator operating in the capacitivecompensator operating in the capacitivemode ismode is

( )( )

( )1cos2~~Im2

2

−−

== ∗ δ λ

λ

X

V j I V Q S QQ


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Reactive PowerReactive Power

Both the realBoth the realpowerpowertransfer andtransfer andthe reactivethe reactiveinjectioninjection

requirementrequirementincrease withincrease withthe increasethe increase

in thein thecompensationcompensationlevel (level (λ λ //X X ).).

l h d f


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Alternate Method of Alternate Method of

Voltage Injection Voltage Injection•• The series compensator injects a voltage thatThe series compensator injects a voltage that

is inis in quadraturequadrature with the line current.with the line current.•• So far we have assumed that the injectedSo far we have assumed that the injectedvoltage magnitude is proportional to thevoltage magnitude is proportional to the

magnitude of the line current.magnitude of the line current.•• If we now relax the assumption, then theIf we now relax the assumption, then themagnitude of the injected voltage is given bymagnitude of the injected voltage is given by

°= 90~~~ j

S

S Q e

I

I V µ


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PhasorPhasor DiagramsDiagrams

Capacitive Operation Inductive OperationCapacitive Operation Inductive Operation

Note that it is assumed thatNote that it is assumed that

δ ∠=°∠= V V V V S R

~,0

~


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Expression for PowerExpression for Power

For the capacitive operationFor the capacitive operation

( )2sin2~~

δ V V I X QS +=

The power flow is then given byThe power flow is then given by

( )2cos~

sin2

δ δ Qe V X

V

X

V P ±=

For the inductive operationFor the inductive operation

( )2sin2~~ δ V V I X QS +−=


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PowerPower-- Angle Curve Angle Curve

i


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Series CompensatorSeries Compensator

Modes of OperationModes of OperationWith appropriate control, the seriesWith appropriate control, the series

compensator operates in two modes:compensator operates in two modes:•• Constant ReactanceConstant Reactance

°

= 90~~ jS Q e I V

µ

λ •• Constant VoltageConstant Voltage

°= 90~

~~ j

S

S Q e

I I V µ


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Comparison Between theComparison Between the

Modes of OperationModes of Operation

•• The two curves matchThe two curves matchatat π π /2/2..

•• The maximum powerThe maximum powerfor constant voltagefor constant voltagecase occurs earliercase occurs earlierthanthan π π /2./2.

•• The power transfer forThe power transfer for

constant voltage caseconstant voltage caseforfor δ δ = 0= 0 is greateris greaterthan zero.than zero.


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Comparison Between theComparison Between the

Modes of OperationModes of Operation

•• The increase in lineThe increase in linecurrent in eithercurrent in eithercase is monotonic.case is monotonic.

•• However the rate ofHowever the rate ofrise in the constantrise in the constant

voltage mode is lowervoltage mode is lowerthan constantthan constantreactance mode.reactance mode.

•• Constant voltage isConstant voltage isthe more desirablethe more desirablemode of operationmode of operation

P Fl C t l dP Fl C t l d


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Power Flow Control andPower Flow Control and

Power Swing DampingPower Swing DampingLet us consider an example to illustrateLet us consider an example to illustrate

•• the power flow control andthe power flow control and

•• The power swing dampingThe power swing damping

capabilities of ideal series compensator.capabilities of ideal series compensator.The system containsThe system contains

•• a double circuit transmission linea double circuit transmission line•• one of the two lines compensated by anone of the two lines compensated by an

ideal series compensator.ideal series compensator.

l


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An Example An Example

pu43.2 pu,43.1 pu,0.1

pu15.0withmodereactanceConstant30 pu,5.0 pu,1.0

~~

021

0

===

=°====

mee

RS

P P P

X V V λ δ


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For any increase or decrease in the powerFor any increase or decrease in the powerflow, the series compensator can beflow, the series compensator can becontrolled in one of the following twocontrolled in one of the following two

modes.modes.•• Regulating Control Regulating Control : Channeling the increase: Channeling the increase

(or decrease) in power through line(or decrease) in power through line--1. In1. In

this case the series compensator holds thethis case the series compensator holds thepower flow over linepower flow over line--2 constant.2 constant.

•• Tracking Control Tracking Control : Channeling the increase: Channeling the increase

(or decrease) in power through line(or decrease) in power through line--2. In2. Inthis case the series compensator helps inthis case the series compensator helps inholding constant the power flow over lineholding constant the power flow over line--1.1.

E l (C i d)


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•• The input to the control system is the powerThe input to the control system is the powerflow over lineflow over line--2 (2 (P P e e 22).).•• P P e e 22 is compared with the reference valueis compared with the reference value P P ref ref

and the error is passed through a PI controller.and the error is passed through a PI controller.•• In addition, a damping controller is also addedIn addition, a damping controller is also added

to the feedback loop.to the feedback loop.

•• The output of the controllerThe output of the controller is theis thecompensation levelcompensation level C C I I (=(=λ λ //X X ).).

( ) ( ) dt d

C dt P P K P P K C P eref I eref P I δ ∆

+−+−= ∫ 22

TheThe controller parameters arecontroller parameters are

75and1,1.0 === P I P C K K


Example:Example:


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Example:Example:

Regulating ControlRegulating Control

•• The system is in the nominal steady state withThe system is in the nominal steady state withP P m m 00 = 2.43 per unit.= 2.43 per unit.

•• The mechanical power input is suddenly raisedThe mechanical power input is suddenly raised

by 10% (i.e., 0.243 per unit).by 10% (i.e., 0.243 per unit).•• It is expected that the series compensatorIt is expected that the series compensator

will hold the power through linewill hold the power through line--2 constant at2 constant atP P e e 22 such that entire power increase issuch that entire power increase ischanneled through linechanneled through line--1.1.

•• We then expect that the powerWe then expect that the power P P e e 11

willwillincrease to 1.243 per unit and the load angle toincrease to 1.243 per unit and the load angle togo up to 0.67go up to 0.67 radrad..

•• The compensation level will then change to 13%.The compensation level will then change to 13%.

Example:Example:


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Example:Example:

Regulating ControlRegulating Control

E ampleExample:


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Example:Example:

Tracking ControlTracking Control

•• The system is in the nominal steady state withThe system is in the nominal steady state withP P m m 00 = 2.43 per unit.= 2.43 per unit.

•• The mechanical power input is suddenly raisedThe mechanical power input is suddenly raisedby 25% (i.e., 0.6 perby 25% (i.e., 0.6 per untiunti).).•• It is expected that the series compensatorIt is expected that the series compensator

will make the entire power increase to flowwill make the entire power increase to flowthrough linethrough line--2.2.•• Then bothThen both P P e e 11 and load angle are maintainedand load angle are maintained

constant at their nominal values.constant at their nominal values.•• The power,The power, P P e e 22, through line, through line--2 will then2 will thenincrease to about 2.04 per unit and theincrease to about 2.04 per unit and the

compensation level will change to 51%.compensation level will change to 51%.

Example:Example:


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Example:Example:

Tracking ControlTracking Control


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Practical Series CompensatorPractical Series Compensator

•• The series compensator structure assumedThe series compensator structure assumedthroughout this section is essentially that ofthroughout this section is essentially that ofaa static synchronous series compensator static synchronous series compensator ororSSSC SSSC . Like in the case of STATCOM, the. Like in the case of STATCOM, theSSSC includes an SVS (supplied by a dcSSSC includes an SVS (supplied by a dc

capacitor) and a coupling transformer.capacitor) and a coupling transformer.•• AA thyristor controlled series compensator thyristor controlled series compensator

oror TCSC TCSC is an older thyristor and passiveis an older thyristor and passiveelement based devices that controls theelement based devices that controls thefundamental reactance. We shall discuss itfundamental reactance. We shall discuss itfirst.first.

ThyristorThyristor Controlled SeriesControlled Series


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ThyristorThyristor Controlled SeriesControlled Series

Compensator (TCSC)Compensator (TCSC)

Equivalent CircuitEquivalent Circuit VoltageVoltage--CurrentCurrent

WaveformsWaveforms


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TCSCTCSC -- Circuit EquationsCircuit Equations

The TCSC voltage and currents are combinationThe TCSC voltage and currents are combinationof two piecewise linear models. Let theof two piecewise linear models. Let the

system state vector besystem state vector be x x T T

= [= [v v c c i i P P ]. Then when]. Then whenthe thyristor is onthe thyristor is on

LiC x

L

C x

+

−=

0

1

01

10&

TCSCTCSC Ci it E tiCi it E ti


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TCSCTCSC -- Circuit EquationsCircuit Equations

Similarly when the thyristor is offSimilarly when the thyristor is off

LiC x x

+

=

0

1

00

00

&

The waveform ofThe waveform of v v C C is a combination of theis a combination of thesolution of these two state equations andsolution of these two state equations andtherefore is not a smooth sinusoidal function.therefore is not a smooth sinusoidal function.

Therefore both the inductor current andTherefore both the inductor current andcapacitor voltage are the solutions of twocapacitor voltage are the solutions of twopiecepiece--wise linear models.wise linear models.

TCSCTCSC -- FundamentalFundamental


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CSC u da e taCharacteristicsCharacteristics

•• A TCSC is a parallel combination of a fixedA TCSC is a parallel combination of a fixedcapacitor and a thyristor controlled reactor.capacitor and a thyristor controlled reactor.

•• Therefore the steady state fundamentalTherefore the steady state fundamentalimpedance of the TCSC is given byimpedance of the TCSC is given by

( )

( )α P C

P C

TCSC X X

X X

X −=

•• We can therefore see that by varying theWe can therefore see that by varying the

conduction angle, the fundamental frequencyconduction angle, the fundamental frequencyreactance of the TCSC can be made inductivereactance of the TCSC can be made inductiveor capacitive.or capacitive.



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ReactanceReactance

The fundamental reactance of the TCSC is given byThe fundamental reactance of the TCSC is given by

( ) ( )

( )[ ] ( ) ( ) P

P

C

P C

P C

X

X

X

X X

X X

π

α π β β α π α π β β β

β β π

α π α π β

−=−−−=

=−

=−+−

=

222

5334

321

cos4,tantan

,,2sin2

( ) C C TCSC X X X −−+= 5421 β β β β

•• α α is the firing angleis the firing angle•• X X C C andand X X P P respectively are therespectively are the reactancesreactances ofof

the capacitor and parallel inductor.the capacitor and parallel inductor.



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TCSC FundamentalReactance PlotReactance Plot


I d Pl t f Fi it QI d Pl t f Fi it Q


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Impedance Plots for Finite QImpedance Plots for Finite Q

•• The fundamental reactance and resistanceThe fundamental reactance and resistancechange with the quality factor of the coil.change with the quality factor of the coil.

•• The above design curves can be used forThe above design curves can be used for

characterizing the TCSC.characterizing the TCSC.

TCSC Waveforms forTCSC Waveforms for


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TCSC Waveforms forTCSC Waveforms for

Finite Q FactorFinite Q Factor

TCSC ControlTCSC Control


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A TCSC can be controlled in three modes.A TCSC can be controlled in three modes.Blocking Mode:Blocking Mode:•• TheThe thyristorsthyristors are not gated (i.e., the TCR isare not gated (i.e., the TCR is

blocked).blocked).•• The line current passes through the capacitor.The line current passes through the capacitor.•• The TCSC performs the task of a fixed seriesThe TCSC performs the task of a fixed series

capacitor.capacitor.Bypass Mode:Bypass Mode:

•• The thyristors are gated for full conductionThe thyristors are gated for full conductionof inductor current.of inductor current.•• The TCSC behaves as a parallel of fixedThe TCSC behaves as a parallel of fixed

capacitor and inductor.capacitor and inductor.



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Bypass Mode (continued):Bypass Mode (continued):•• The capacitor voltage is less for a given lineThe capacitor voltage is less for a given line

current.current.

•• Therefore this mode is utilized to reduceTherefore this mode is utilized to reducecapacitor stress during faults.capacitor stress during faults.

VernierVernier Control Mode:Control Mode:

•• The conducting angle of the TCSC isThe conducting angle of the TCSC iscontinuously varied to operate in eithercontinuously varied to operate in eithercapacitive boost or inductive boost modes.capacitive boost or inductive boost modes.

•• In this mode the TCSC follows theIn this mode the TCSC follows thefundamental reactance curve shown earlier.fundamental reactance curve shown earlier.

Static Synchronous SeriesStatic Synchronous Series


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yy

Compensator (SSSC)Compensator (SSSC)•• An SSSC contains anAn SSSC contains an

SVS and a couplingSVS and a couplingtransformer that istransformer that isconnected in seriesconnected in series

with the line.with the line.•• The SSSC is operatedThe SSSC is operated

such that the injectedsuch that the injectedvoltage is almost involtage is almost inphasephase quadraturequadrature withwith

the line current.the line current.

Equivalent Circuit of SSSCEquivalent Circuit of SSSC


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Compensated SystemCompensated System

•• In the equivalent circuit of an SSSCIn the equivalent circuit of an SSSCcompensated system, the SSSC is representedcompensated system, the SSSC is representedby a voltage source and impedance (by a voltage source and impedance (L L

r r

,,R R r r

).).•• The SSSC is connected between buses 1 and 2.The SSSC is connected between buses 1 and 2.•• The pair (The pair (L L 11,,R R ) represent the line and) represent the line and L L 22

represents a transformer.represents a transformer.

SSSC ControlSSSC Control


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•• An instantaneous 3An instantaneous 3--phase set of line voltagesphase set of line voltagesat bus 1 is used to calculate the angleat bus 1 is used to calculate the angle θ θ thatthatis phase locked to the phaseis phase locked to the phase--a of the linea of the line

voltage.voltage.•• An instantaneous 3An instantaneous 3--phase set of measured linephase set of measured line

currents is first decomposed into real andcurrents is first decomposed into real and

reactive components.reactive components.•• The amplitude and the relative angle of theThe amplitude and the relative angle of the

line currentline current θ θ ir ir are then calculated.are then calculated.

•• The phase locked angleThe phase locked angle θ θ p p andand θ θ ir ir are added toare added toobtain the angleobtain the angle θ θ l l which is the angle of thewhich is the angle of theline current.line current.



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•• The are two control loops.The are two control loops.•• Since the SSSC voltage must lag the line currentSince the SSSC voltage must lag the line current

by 90by 90ºº, a fixed angle equal to, a fixed angle equal to --9090ºº is added tois added to θ θ l l to obtainto obtain θ θ

fref fref in the main loop.in the main loop.

•• In the auxiliary loop, the reactance demandIn the auxiliary loop, the reactance demand X X tref tref is added tois added to X X r r of SSSC.of SSSC.

•• The sum is multiplied by the magnitude of theThe sum is multiplied by the magnitude of theline current and a constant to obtainline current and a constant to obtain V V dcref dcref ..

•• The error betweenThe error between V V dcref dcref

and theand the actual value ofactual value ofV V dc dc is passed through a PI controller to obtainis passed through a PI controller to obtain θ θ d d ..

•• This quantity is then added toThis quantity is then added to θ θ fref fref to obtainto obtain θ θ f f

of the inverter.of the inverter.



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•• The PI controller retains the charge on the dcThe PI controller retains the charge on the dccapacitor by injecting a voltage nearly incapacitor by injecting a voltage nearly inquadraturequadrature with the line current.with the line current.

•• The real power exchange between the ac systemThe real power exchange between the ac systemand SSSC takes place if the injected voltage isand SSSC takes place if the injected voltage is

not innot in quadraturequadrature with the line current, whichwith the line current, whicheither charges or discharges the dc capacitor.either charges or discharges the dc capacitor.

•• The PI controller then advances or retards theThe PI controller then advances or retards the

phase of the injected voltage relative to linephase of the injected voltage relative to linecurrent in order to adjust the power at accurrent in order to adjust the power at acterminals and keep the dc voltage constant.terminals and keep the dc voltage constant.

Comparison Between SSSC and TCSCComparison Between SSSC and TCSC


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Comparison (Continued)Comparison (Continued)


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Comparison (Continued)Comparison (Continued)


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Other FACTS ControllersOther FACTS Controllers


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Other FACTS ControllersOther FACTS Controllers

There are many other FACTS controllers thatThere are many other FACTS controllers thatuse the power electronic technology. Weuse the power electronic technology. Weshall briefly discuss the following:shall briefly discuss the following:

•• Interline Power Flow Controller (IPFC)Interline Power Flow Controller (IPFC)

•• ThyristorThyristor Controlled Braking ResistorControlled Braking Resistor(TCBR)(TCBR)

•• ThyristorThyristor Controlled Phase Angle RegulatorControlled Phase Angle Regulator(TCPAR)(TCPAR)

•• Unified Power Flow Controller (UPFC)Unified Power Flow Controller (UPFC)

Interline Power FlowInterline Power Flow


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Controller (IPFC)Controller (IPFC)

An IPFC contains two or moreAn IPFC contains two or more SSSCsSSSCs that arethat areconnected to a common dc bus to facilitateconnected to a common dc bus to facilitate

real power exchange between them.real power exchange between them.

IPFC (Continued)IPFC (Continued)


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•• Each individual SSSC can provide controllableEach individual SSSC can provide controllableseries compensation to the line it is connected.series compensation to the line it is connected.•• In addition, it can also exchange powerIn addition, it can also exchange power

between them.between them.•• Example: Assume that LineExample: Assume that Line--1 is lightly loaded1 is lightly loaded

while Linewhile Line--2 is heavily loaded.2 is heavily loaded.

•• SSSCSSSC--1 then absorbs power to charge the dc1 then absorbs power to charge the dccapacitor.capacitor.

•• SSSCSSSC--2 is then supplied real power by the dc2 is then supplied real power by the dccapacitor.capacitor.

•• In this way the load sharing between the linesIn this way the load sharing between the lines

can be equalized.can be equalized.

ThyristorThyristor ControlledControlled


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y

Braking ResistorBraking ResistorThis is a shunt connectedThis is a shunt connected thyristorthyristor switchedswitched

resistor, which is used for minimizing theresistor, which is used for minimizing thepower acceleration during a fault.power acceleration during a fault.

•• In the schematicIn the schematic

diagram, thediagram, thethyristorsthyristors areareusually blocked.usually blocked.

•• They areThey areswitched on whenswitched on whena fault isa fault is

detected.detected.

Braking ResistorBraking Resistor


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For the system shown above, the criticalFor the system shown above, the critical

clearing angle is computed to be 52.24º.clearing angle is computed to be 52.24º.We shall now place a dynamic brake at theWe shall now place a dynamic brake at thegenerator terminals.generator terminals.



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( ){ } R

E I E P e10

Re2

′≈∠′= ∗δ

We assume that theWe assume that thebraking resistor isbraking resistor ispressed intopressed intoservice as soon asservice as soon asthe fault occursthe fault occurs

and is removed asand is removed assoon as the fault issoon as the fault iscleared. Thencleared. Then



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It can be seen that the critical clearing angleIt can be seen that the critical clearing angleincreases with the increase in the value ofincreases with the increase in the value ofthe resistor.the resistor.

Phase Angle Regulator (PAR)Phase Angle Regulator (PAR)


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Phase Angle Regulator (PAR)Phase Angle Regulator (PAR)

PARPAR -- OperationOperation


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•• The PAR is inserted between the sending endThe PAR is inserted between the sending endand transmission line.and transmission line.•• It is a sinusoidal voltage source withIt is a sinusoidal voltage source with

controllable amplitude.controllable amplitude.•• For an ideal PAR the angle of theFor an ideal PAR the angle of the phasorphasor V V σ σ isisstipulated to vary such that the magnitude ofstipulated to vary such that the magnitude of

V V seffseff remains constant.remains constant.

PARPAR -- PowerPower-- Angle Curve Angle Curve


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PARPAR -- Phase ShiftingPhase Shifting


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Assume that a resistive load is connected at theAssume that a resistive load is connected at the

output.output.



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The voltages obtained at the lower and upperThe voltages obtained at the lower and uppertaps aretaps are v v 11 andand v v 22 respectively.respectively.

•• At the zero crossing of these voltages, theAt the zero crossing of these voltages, theswitchswitch Sw Sw 11 is turned on.is turned on.•• AtAt α α the switchthe switch Sw Sw 22 is turned on.is turned on.

•• This commutates the current ofThis commutates the current of Sw Sw 11 bybyforcing a negative anode to cathode voltageforcing a negative anode to cathode voltageacross it, thereby making the voltage acrossacross it, thereby making the voltage across

the loadthe load v v 22..•• The switchThe switch Sw Sw 22 turns off when the currentturns off when the currentthrough it reverses.through it reverses.



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The voltage thus obtained contains harmonics.The voltage thus obtained contains harmonics.The fundamental component of the voltageThe fundamental component of the voltageis given byis given by

( )

+−

−+=−

−=

∠+= −

2

2sin

2

~~~

,12cos2

~~

tan~

12

1

12

122

0

α α π

π α

π

V V V b

V V a

b

abaV

We can therefore vary the fundamental voltageWe can therefore vary the fundamental voltageby varying the delay angleby varying the delay angle α α ..

Unified Power FlowUnified Power Flow


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Controller (UPFC)Controller (UPFC)A UPFC contains aA UPFC contains a

shunt SVS and ashunt SVS and aseries SVS thatseries SVS that

are connected toare connected toa common dc busa common dc bussuch that realsuch that real

power exchangepower exchangecan take placecan take placebetween them.between them.

UPFCUPFC -- Equivalent CircuitEquivalent Circuit


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The termThe term P P pq pq

indicatesindicatesreal powerreal powerexchangeexchange

betweenbetweenthe shuntthe shuntand seriesand series

branches.branches.

UPFCUPFC -- PhasorPhasor DiagramsDiagrams


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(a) Voltage Regulation, (b) Line impedance compensation,(a) Voltage Regulation, (b) Line impedance compensation,(c) Phase shifting and (d) simultaneous control.(c) Phase shifting and (d) simultaneous control.

UPFCUPFC -- Real & Reactive PowerReal & Reactive Power


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LetLet ρ δ −∠=−∠=°∠= pq pq RS V V V V V V

~,

~,0

~

Then for the uncompensated system (Then for the uncompensated system (V V pq pq = 0)= 0)we havewe have

( )1cos

sin

2

0

2

0

−=−=

==

δ

δ

X

V QQ

X

V P P

R



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For the compensated systemFor the compensated system∗

−∠+−∠−

−∠=− jX

V V V

V jQ P pq

R

ρ δ

δ

Solving we getSolving we get

( )

( ) ρ δ

ρ δ

−−=

−−=

cos

sin

0

0

X

VV QQ

X

VV P P

pq

R

pq



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ThenThen

•• This is the equation of circle with its centerThis is the equation of circle with its center

atat P P 00,,Q Q 00 and radius ofand radius of VV VV pq pq //X X ..•• SupposeSuppose V V 22//X X = 1.0 and= 1.0 and V V pq pq = 0.5= 0.5V V ..

•• ThenThen VV VV pq pq //X X = 0.5.= 0.5.

( ) ( )2

2

0

2

0

=−+−

X

VV QQ P P

pq

R

Real Versus Reactive PowerReal Versus Reactive Power


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Even though theEven though theuncompensateduncompensatedsystem cannotsystem cannottransfer anytransfer anypower in thispower in this

case, the UPFCcase, the UPFCis capable ofis capable oftransmittingtransmitting

power in eitherpower in eitherdirection.direction.

Real Versus Reactive PowerReal Versus Reactive Power


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RealReal vsvs Reactive PowerReactive Power


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•• The figures show that the UPFC has theThe figures show that the UPFC has theunique capability to control independentlyunique capability to control independentlythe real and reactive power flow at anythe real and reactive power flow at any

transmission angle.transmission angle.•• It is however assumed here that theIt is however assumed here that the

sending and receiving end voltages aresending and receiving end voltages are

provided by independent power systemsprovided by independent power systemswhich are able to supply and absorb realwhich are able to supply and absorb realpower without any internal angular change.power without any internal angular change.

•• In practice the situation will be differentIn practice the situation will be differentdepending on the change in load angle.depending on the change in load angle.

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Ghosh Tuesday July 24 2003