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Application Notes P54x/EN AP/Ja4

MiCOM P543, P544, P545 & P546 (AP) 6-85

AP

6.7 Worked example for CT requirements

The Power system and the line parameters (Line length: 100 km) as given in section 3.2 isused here to calculate CT requirements.

6.7.1 Important notes to be considered

Current differential Both If and X/R are to be calculated for a through fault

Distance Zone1 reach point case Both If and X/R are to be calculated for a fault atZone1 reach point

For calculating the CT requirements, the bus bar short time symmetrical fault rating shallbe considered as the bus fault level.

When there are only indicative X/Rs available, then the circuit breakers dc breakingcapacity shall be used to arrive at the primary time constant (and hence the primarysystem X/R). The derivation shall be obtained from the circuit breaker manufacturer;practical primary time constants arrived in such a way vary between 50 ms (applicablefor 66 kV and 132 kV breakers) and 120 ms (applicable for 220 kV and 400 kVbreakers). 150 ms is a practical figure for generator circuit breakers.

6.7.2 System data

In the following example, the following parameters have been considered for the CTcalculations:

System voltage - 230 kV

System frequency - 50 Hz

System grounding - solid

Single circuit operation between Green Valley and Blue River

CT ratio - 1200/1

Line length - 100 kms

Line positive sequence impedance Z1 = 0.089 + j 0.476 ohm / km

Bus fault level - 40 kA

Primary time constant = 120 ms

6.7.3 Calculation of Primary X/R

Primary X/R till the Green Valley bus = 2 * pi * f * primary time constant in s

= 2 * pi * 50 * 0.12

Primary X/R till the bus = 37.7

6.7.4 Calculation of Source Impedance Zs

Source Impedance Zs = 230 kV / (1.732 * 40 kA)= 3.32 ohms

Source angle = tan-1 (X/R)

= tan-1 (37.7)= 88.48 deg

Hence, Zs = 0.088 + j 3.317 ohms

7/23/2019 p54x_en_m_ka4+kb4

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P54x/EN AP/Ja4 Application Notes

(AP) 6-86 MiCOM P543, P544, P545 & P546

AP

6.7.5 Calculation of full line impedance (full 100 kms)

Z1 = 0.089 + j 0.476 ohm / km

ZL = 8.9 + j 47.6 ohms

ZL = 48.42 ohms with an angle 79.4 deg

6.7.6 Calculation of total impedance till remote bus bar

ZT = Zs + ZL = 8.988 + j 50.917 ohms

= 51.7 ohms with an angle of 80 deg

6.7.7 Calculation of through fault X/R

X/R thro = 50.917 / 8.988

= 5.66

6.7.8 Calculation of through fault If

If thro = 230kV / (1.732 * 51.7 )

= 2568.5 A primary

= 2.14 A (secondary)

6.7.9 Calculation of line impedance till Zone1 reach point (80kms)

Zzone1 = 0.8 * ZL = 7.12 + j 38.08 ohms

= 38.73 ohms with an angle of 79.4 deg

6.7.10 Calculation of total impedance till Zone1 reach point

ZTzone1 = Zs + Zzone1

= 7.208 + j 41.397 ohms

= 42.019 ohms with an angle of 80 deg

6.7.11 Calculation of X/R till Zone1 reach point

X/R zone1 = 41.397 / 7.208

= 5.74

6.7.12 Calculation of fault current till Zone1 reach point

If zone1 = 230 kV / (1.732 * 42.019)

= 3160.34 A (primary) = 2.63 A (secondary)