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Find the base impedance for a 10 kV, 10 MVA 3-Phase system
- a)5 ohms
- b)7 ohms
- c)10 ohms
- d)1 kilo ohms
Correct answer is option 'C'. Can you explain this answer?
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Find the base impedance for a 10 kV, 10 MVA 3-Phase systema)5 ohmsb)7 ...
Base Impedance Calculation for a 3-Phase System
To calculate the base impedance for a 3-phase system, we need to use the following formula:
Zbase = Vbase^2 / Sbase
Where,
Vbase = Phase-to-phase voltage of the system
Sbase = Apparent power of the system
Given data:
Phase-to-phase voltage, V = 10 kV
Apparent power, S = 10 MVA
Step 1: Calculate the base apparent power (Sbase)
Sbase = 10 MVA / 3
Sbase = 3.33 MVA
Step 2: Calculate the base voltage (Vbase)
Vbase = 10 kV / √3
Vbase = 5.77 kV
Step 3: Calculate the base impedance (Zbase)
Zbase = Vbase^2 / Sbase
Zbase = (5.77 kV)^2 / 3.33 MVA
Zbase = 10 ohms
Therefore, the correct answer is option (c) 10 ohms.
To calculate the base impedance for a 3-phase system, we need to use the following formula:
Zbase = Vbase^2 / Sbase
Where,
Vbase = Phase-to-phase voltage of the system
Sbase = Apparent power of the system
Given data:
Phase-to-phase voltage, V = 10 kV
Apparent power, S = 10 MVA
Step 1: Calculate the base apparent power (Sbase)
Sbase = 10 MVA / 3
Sbase = 3.33 MVA
Step 2: Calculate the base voltage (Vbase)
Vbase = 10 kV / √3
Vbase = 5.77 kV
Step 3: Calculate the base impedance (Zbase)
Zbase = Vbase^2 / Sbase
Zbase = (5.77 kV)^2 / 3.33 MVA
Zbase = 10 ohms
Therefore, the correct answer is option (c) 10 ohms.
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Find the base impedance for a 10 kV, 10 MVA 3-Phase systema)5 ohmsb)7 ...
Per Unit System:
- The per-unit value of any quantity is defined as the ratio of actual value in any unit to the base or reference value in the same unit.
- Any quantity is converted into per unit quantity by dividing the numeral value by the chosen base value of the same dimension. The per-unit value is dimensionless.
PU Value (PU) = A/B
Here, A is the actual value in any unit
B is the Base or reference value in the same unit
B is the Base or reference value in the same unit
Consider the base value of voltage is (kVB), the Base value of current is (IB) and the base value of apparent power is (kVAB)
And, Base value of current (IB)
Now, the Base value of the impedance (ZB) will be the ratio of the base value of voltage to the current.
From equation (1),
Hence, per unit value of impedance can be written as if Z is the actual value of impedance,
Since the above expression is given infraction of 1000 units,
Hence per unit value will be given as,
Calculation:
And, Base value of current (IB)
Now, the Base value of the impedance (ZB) will be the ratio of the base value of voltage to the current.
From equation (1),
Hence, per unit value of impedance can be written as if Z is the actual value of impedance,
Since the above expression is given infraction of 1000 units,
Hence per unit value will be given as,
Calculation:
We have,
kVB = 10 kV,
MVAB = 10 MVA
Hence,
ZB = 102/10 = 10 ohms
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