Knee point calculation for 765kV CT's

CT Ratio :3000-2000-1000-500/lACT Class :PS

Secondary Winding Resistance:· 15 ohm at 3000 tap· 10 ohm at 2000 tap. 5 ohm at 1000 tap. 2.5 ohm at 500 tap

Length of line assumed =25 kms.

Where IF= Max. secondary fault current at zone-l reachpoint.X/R = Primary system reactance/resistance ratio

System short circuit Fault Calculations

System Impedance,Zs =Vs/ IF

765xl03

- ,J3x40x 103

IF = 40 kA(Fault Level)

=11.042 ohms -.

Line parameters are

Rr. = 1.9513 X 10-6 Pu/kM/Ckt] On a 100 MVA ,765 kV BaseXL= 4.475 X 10-5pu/kM/ckt

XL _ 4.475xlO-s

RL -1.9513x10-6

=22.93

=23

e=tan-I

(

4.475XlO-S

)1.953 x 1O-{i

= 87.5°

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Knee point calculation for 765kV CT's

Therefore

('Xs = Zs sin 87.5°

= 11.042 X 0.999 = 11.031 ohmsRs = Zs cos 87.5°= 11.042 X 0.0436 = 0.481 ohms

Zs = 0.481 + j11.031

Line Impedance:

Rr.= 1.9513 X 10-6 pulkM/ckt.:XL=4.475 X 10-5pu/kM/ckt :

On a 100MVA ,765 kV Base

Therefore

Base Impedance =765 X 765/100 = 5852.25 ohms

Rr.= 1.9513 X 10-6X 5852.25 = 0.01142 ohmslkMXL= 4.475 X 10-5X 5852.25 = 0.2619 ohmslkM

For a Line length of25 kMs (zone-1 reach=20 kMs)

Rr.' = 0.01142 X 20 = 0.2284 ohmsXL'= 0.2619 X 20 = 5.238 ohms

Therefore

Total Fault Impedance upto zone-1 reach point

R= Rr.'+ Rs = 0.2284+0.481 = 0.7902 ohmsX=Xs+ XL'

= 11.031+ 5.238 = 16.269 ohms

Z = 0.7094 + j 16.269Z = 16.284 ohms

Therefore Fault current at zone-1 reach= IF'

765x103

- J3 x16.284

= 27123.12 A

IF'= 27.12 kA (fault level at zone-1 reach point)

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Knee point calculation for 765kV CT's

Lead Burden:

Cable Length= 800 mLead resistance = 8.71 ohms/kM( x 2.5 mm2 copper cable is used)

Therefore

2R = 2x 800x 8.71 = 6.968L 2 1000

= 7.0ohmsCT secondaryresistance, Rcr = 15.00 at 3000/1 A tap

Knee point voltage requirement

VK~0.6IF( 1+;)Rcr +RL)

Relay burden is negligible .Therefore Rrelay=0.27120

VK~ 0.6x-(1 +23)(15 +7.0)3000

For 3000/1 A tap

VK~ 2863.87Vat30001lTap

Selected knee point voltage for 3000/1 A tap =6000 V(plese see note below)

RCf ~15.00hm Imag < 20mAatVK

"For 2000 A tap,

27120VK(2000)=0.6x-x(I+23)(10+7.0)2000

= 3319.5 V

Selected knee point voltage for 2000/1 A tap =4000V(same as that for 400 kV CTs)

Note:

1. Since the requirement at 2000/1 A tap is 2V per turn,the selected knee point voltagefor 3000/1 A tap is 6000V.This is in line with the knee point voltage requirementbeing specified for 400 kV CT's .

2. It is intended to use only 3000/1 A or 000/1 A taps for 765 kV line protection.

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Knee point calculation for 765kV CT's

3. 1000/1 A and 500/1 A taps shall be used for Generator circuits (Protection OverallDifferential,Overhead Line Differential).

CT requirement for busbar protection

IF =40 kA

VK~2IF(RCT+RL)

For 3000 A tapRcr = 15.0ohmsRr.= 7.0 ohms

40000VK~2x-x(15.0+7.0)3000

Selected VK at 3000/1 A tap = 3000V

For 2000 A tapRcr = 10.0 ohmsRr.= 7.0 ohms

40000VK~2x-x(IO.0+7.0)2000

Selected VK at 2000/1 A tap = 2000V

VK~ 680V

For 1000 A tapRcr = 5.0 ohmsRr.= 7.0 ohms

40000VK~2x-x(5.0+7.0)1000

Selected VK at 1000/1 A tap = 1000V

Note:1. 500/1 A tap shall not be used for bus-bar protection.2. 500/1 A tap shall be used for Generator circuit protection(Overall Differential,

Overhead Line Differential)

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