TSA8

7/27/2019 TSA8

http://slidepdf.com/reader/full/tsa8 1/6

7/27/2019 TSA8


The apparent impedance seen by animpedance relay at C looking towards the

line is given by 0 E E

E Z Z

I ~

I ~

Z E ~

I ~

E ~

Z

B A

AT A

AAC C

∠∠∠∠−

−−−∠

∠∠∠

∠∠∠∠++++−−−−====

−−−−========

δ δδ δ

δ δδ δ

−−−−∠∠∠∠−−−−∠∠∠∠++++−−−−====

10 1

Z Z Z T

AC δ δδ δ

If EA=EB=1.0 pu

(((( ))))(((( ))))

−−−−

−−−−====

++++−−−−++++−−−−====

++++++++++++−−−−====

++++∠∠∠∠++++∠∠∠∠−−−−∠∠∠∠−−−−∠∠∠∠

++++∠∠∠∠++++∠∠∠∠++++−−−−====

2 cot

2 Z j Z

2 Z

sin 2

cos 1 j

2

1Z Z

sin j 2

sin j cos 1Z Z

10 110 1

10 1

Z Z

T A

T

T A

T A

T A

δ δδ δ

δ δδ δ

δ δδ δ

δ δδ δ

δ δδ δ δ δδ δ

δ δδ δ δ δδ δ

7/27/2019 TSA8


During a swing, the angle δ changes.Fig. 13.37 shows the locus of Z C as a

function of δ on an R-X diagram, whenEA=EB

Fig. 13.37 Locus of Z C as a function of δδδδ, with E A=E B

7/27/2019 TSA8


• When E A and E B are equal, the locus of Z C is seen to be a straight line which is theperpendicular bisector of the total system impedance between A and B, i.e., of theimpedance ZT

– the angle formed by lines from A and B to

any point on the locus is equal to thecorresponding angle δ

• When δ=0, the current I is zero and Z C is infinite

• When δ=180°, the voltage at the electrical centre is zero

– the relay at C in effect will see a 3-phasefault at the electrical centre. The electricalcentre and impedance centre coincide inthis case.

• If E A is not equal to E B , the apparent impedance loci are circles, with their centres onextensions of the impedance line AB

• When E A>E B , the electrical centre will be above the impedance centre; when E A<E B ,

the electrical centre will be below the impedance centre. Fig. 13.38 illustrates theshape of the apparent impedance loci for three different values of the ratio E A / E B .

7/27/2019 TSA8


Fig. 13.38 Loci of ZC with different values of EA/EB

7/27/2019 TSA8


• For generators connected to the main system through a weak transmission system (high external impedance), the electrical centre may appear on the transmission line

• When a generator is connected to the main system through a strong transmission system , the electrical centre will be in the step up transformer or possibly within the

generator itself• Electrical centres in effect are not fixed points: effective machine reactance and the

magnitudes of internal voltages vary during dynamic conditions.

• Voltage at the electrical centre drops to zero as δ increases to 180°and thenincreases in magnitude as δ increases further until it reaches 360°

– when δ reaches 180 , the generator willhave slipped a pole ; when δ reaches theinitial value where the swing started, one

slip cycle will have been completed.

Documents

TSA8