Flexible AC Transmission Systems FACTS 7

7/29/2019 Flexible AC Transmission Systems FACTS 7

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Distributed Power and FACTS

Static Shunt Compensators: SVC and STATCOM

Voltage compensation with a shunt connected device

Consider a lossless transmission system with a shunt connectedcompensator at the centre of the transmission line, as shown inFigure 1. Without compensation we have the following relationshipsfor the real and reactive power at the receiving and sending lineterminations R and S. Given the ideal situation where the terminalsare at rated voltage

S RV V V

Then2

sin( )S R

VP P

X (1)

2

1 cos( )S RV

Q QX

(2)

SM MR I I I (3)

Figure 1 Lossless transmission line with shunt compensationproviding voltage VM and current IM at the centre

The phasor diagram for the non-compensated transmission line isas given in Figure 2 .

ISM

VMVS

jX/2IMR

VR

jX/2

IM

ImaginaryVS

jXI

I

/2

/2

VR

Real

= /2

VM


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Figure 2 Phasor diagram for non-compensated losslesstransmission lineFor shunt compensation at the centre of the lossless transmissionline so that centre is at rated voltage. We have a phasor diagram asgiven in Figure 3.

Figure 3. Phasor diagram for a compensated losslesstransmission line where the centre and terminals of the

transmission line is at rated voltage

For the compensated transmission line the phasor diagram depictedin Figure 3. represents the transmission line split into two sections

of impedancejX/2 and wqe have the following relationships

S R MV V V V

and from (1) and (2)

2

2sin

2SM MRV

P PX

(4)

2

21 cos

2MS MR

VQ Q

X

(5)

From Kirchhoffs current law we have

M SM MR I I I (6)

The compensator current IM is depicted inFigure 3. Notice that thecompensator current is in quadrature with the compensator voltage(IM, Vm) so that no real power is injected on the system but from(5) the total reactive power provided by the compensator is

24

1 cos2MS MR

VQ Q Q

X

(7)

Imaginary

VS

jXISM /2

IMR

/2

/2

VR

RealVM

ISM

IM

jXIMR

/2


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Equation (7) can be used to define the MVA rating required for thecompensator. The variation of power transfer with load angle forthe compensated and uncompensated case is given in Figure. 4. Byimproving the voltage level at the midpoint of the transmissionsystem we have also allowed an increase in the transfer of real

power.

P uncompensated

P compensated

Q

Figure 4 variation of real power transferred and compensatorreactive power demand with load angle

If we assume that the total MVA on the transmission line can notexceed rated MVA (|S|=1) and the terminal voltages are all at ratedvoltage (V=1) then

2 21SP Q (8)

2 sin( )2

PX

(9)

2 1 cos( )2S RQ Q

X

(10)

Therefore, by combining equations(9) and (10)

2 24

2 1 1 4comp S R S

P X

Q Q Q Q X

(11)

Equations (8) and (11) then give

2 2(1 )2

1 14

SS

Q XQ

X

(12)

Therefore this gives

4S

XQ (13)

From (11) the rated per unit value of the shunt compensator must then be

2comp XQ (14)

/2 load angle

4V /X

2V2/X

V2/X


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The above analysis is only valid for transmission between two pointsthat each have voltage support as can be found on transmissionsystems or distribution systems with distributed generation. If thesystem is radial with one end terminated with a passive load thenthe best location for the shunt compensation is at the load end

rather than the centre where load voltage support can be provided.Figure 5 shows the ideal arrangement for a radial system.

In order to ensure rated voltage at the load end the compensatormust compensate the load reactive power QL and provide thetransmission reactive power QT as indicated in Figure 5. Fromequations (1) and (2) we can write that for rated load voltage (V=1)

21 1 1 ( )S RQ Q PX X

(8)

Figure 6 shows the relationship between transmitted real power andtransmission reactive powerQT necessary for voltage support for

rated voltage. It can be seen that in general the reactive power is alot less than the real power so that the shunt controller VA will notbe relatively that large. For transmission lines the thermal limit willbe a lot less than the maximum power ofV2/X.

E V

IA QT QL

SA

Source Load

A B

Z

Figure 5 Shunt compensation on a radialdistributionsystem

Var

Comp


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0 0.5 1 1.5 20

0.5

1

1.5

2

Real Power

ReactivePower

Figure 6 Relationship between real and reactive transmissionpower for good load voltage support for a system impedancej0.5 pu.


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undamped

damped

Angle

time

Q

compensator

undamped

damped

time

Power

Figure 8 Damping of power swings through compensatorcontrol


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FACTS shunt controllers

Shunt controllers are required to maintain synchronous operationwith the ac system under all operating conditions, regulate the busvoltage and dampen power swings. In the past shunt compensation

has been mainly achieved with shunt reactors comprising capacitorbanks and inductors. In the past 30 years control of these reactorshas either been achieved through simple circuit breaker operation(switching devices online or off line) or by gate turn-off thyristors.These devices are collectively known as static var generators (SVG).

Flexible reactive power generation can be achieved throughthyristor switching and the common form of shunt devices is asdepicted in Figure 9.

Figure 7 Conventional Facts controller designs. a) Thyristor controlled reactor

(TCR) b) Thyristor switched capacitor (TSC) c) Fixed capacitor thyristor

controlled reactor (FC-TCR).

The use of thyristor switching gives more flexibility but at the

expense of increased injected harmonics. The capacitor can only beswitched at voltage zeros to limit the current. Both the shuntinductor and capacitor reactive power is also related to the linevoltage and therefore not completely controllable.

For a bidirectional thyristor valve controlled reactor of inductance Lthe fundamental current I1is related to the thyristor gate switchingangel and is given by

1

2 1( ) 1 sin(2 )

VI

L

(9)

a) b) c)


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which implies the fundamental admittance Y1is

1

1 2 1( ) 1 sin(2 )Y

L

(10)

The harmonic currents drawn are given by

2

4 sin cos( ) cos sin( )( )

( 1)n

V n n nI

L n n

(11)

These characteristics can be seen in figure 8. Note that 3rd and 9thharmonics are absent in three phase balanced connections (star ordelta) and a 12 puls arrangement eliminates 5th and 7th harmonics.

0 20 40 60 80 100

0.05

0.1

0.15

3rd

5th

7th

9th

11th

13th

Fundamental/10

Delay angle (deg)

pu

Figure 8 Amplitude of the harmonic currents drawn by a TCRagainst thyristor delay angle.

From figure 8 it can be seen that the relative current harmonics canbe quiet high and as the system impedance usually increases withfrequency (inductive) then the higher harmonics may createsignificant system voltage distortion. Filters can be added if

necessary but this will increase the losses.


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The fundamental current drawn by a TCR is limited by themaximum TCR admittance (=0) so that the V-I operating region is

as given in Figure 9.

Figure 9 Operating region for a TCR

Thyristor switched reactors are often used for shunt capacitanceshowever they are not as flexible as Fixed capacitor thyristorcontrolled reactor (FC-TCR) which has more controllability and thecapacitor can be replaced by a harmonic filter with the fundamentalreactance. The operating region for a FC-TCR is as shown infigure 10.

Vtcr

Itcr

Ymax


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Figure 10 Operating region for a FC-TCR

Static Synchronous Compensator (STATCOM)

Static var compensators (SVC) can only be adjusted via adjustmentof their admittance in a step like manner. By using modernconvertor technology a synchronous shunt device can be used withfar more controllability. The usual static synchronous compensator

arrangement is for a voltage sourced converter to feed a step downtransformer as depicted in Figure 8. By arranging the convertervoltage to be in phase with the line voltage reactive power can becontrolled by adjusting the converter voltage amplitude to be eithergreater of less than the line voltage as reflected at the transformersecondary terminals. From considering the pu phasor diagramsgiven in Figure 9 it can be seen that if the converter voltage isgreater than the line voltage (as is reflected on the transformersecondary circuit) then the compensator acts as a reactive powersource (capacitor) and if the converter voltage is less than the linevoltage (as is reflected on the secondary circuit of the step downtransformer) then the compensator acts as a reactive power load(inductor) as.

LjX

0

V VI (12)

V

IC IL

YLmax

YCmax


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Figure 11 Typical STATCOM arrangement using a voltagesourced convertor

Figure 12. pu phasor diagrams for different STATCOMconditions. a) converter voltage and line voltage identicalgiving no injected current b) converter voltage greater thanline voltage creating a leading current c) converter voltageless than the line voltage creating a lagging current.

STATCOM is a far more flexible device and the operating region islimited only by its maximum VA. The operating region of a

controller Voltage

sourced

converter

settings

busbar

Step down transformer

with leakage reactanceXL

potential

transformer

I V

V0

V

V0V = V0 , I = 0

a)

V

V0

jXLII

Leading I capacitor

b)

V

V0 jXLI

Lagging I inductor

c)

I


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STATCOM is as shown in figure 13. These devices are very fastacting with negligible delay.

Figure 10 Operating region for a STATCOM

Because the STATCOM can provide rated current I0 for all voltage

levels as apposed to SVC which are limited by maximum reactanceYmax the STATCOM of comparable rating will provide an increased

stability margin for power swings. This can be seen by comparingthe transmitted power verses load angle of the STATCOM and SVClocated at the midpoint of a transmission line as shown in Figure 1.Up until the rated current of the devices is exceeded both deviceswill behave ideally. For the STATCOM the maximum current will belimited to I0 thus by considering the real and reactive power into the

mid point gives

2 cos 22

2

m s mm o

V V VV IjQ

X

(13)

Then

0

cos2

4

sm

VV I

X X

(14)

Hence

2 02 sin sinsin2 22

S m SSV V I V V

PX X

(15)

V

IC IL

YLmax

YCmax


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For the SVC the maximum admittance will be limited to Ymax thus by

considering the real and reactive power into the mid point gives

22max

cos2

22

m s mm

V V VV YjQ

X

(16)

Then max

cos2

14

s

m

V

VY X

(17)

Hence

2

max

2 sin sin2

14

S m SV V V

PY XX

X

(18)

The performance of STACOM and SVC shunt compensators of 1 purating are compared in figure 11.

P uncompensated

P compensated

P STATCOM

P SVC

Figure 11 variation of real power transferred for SVC andSTATCOM compensators of 1 pu rating with load angle

2V /X

V2/X

/2 load angle

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Flexible AC Transmission Systems FACTS 7