A 60kW 2,2kW three-phase star-connected alternator supplies a load operating at a power factor of 0,8 lagging. If the alternator at an efficiency of 85%, calculate
a) The phase voltage of the alternator
b) the phase current of the alternator
c) the mechanical power needed to drive the alternator
a) The apparent power of the load can be calculated as the real power divided by the power factor:
Apparent power = Real power / Power factor = 60kW / 0.8 = 75kVA
In a three-phase system, the apparent power is equal to the line voltage multiplied by the line current:
Apparent power = √3 x Line voltage x Line current
We can rearrange this equation to solve for the line voltage:
Line voltage = Apparent power / (√3 x Line current)
Since the alternator is star-connected, the phase voltage is equal to the line voltage. Therefore, the phase voltage is:
Phase voltage = 75kVA / (√3 x Line current)
b) To calculate the phase current of the alternator, we can rearrange the equation above:
Line current = Apparent power / (√3 x Line voltage)
Given that the apparent power is 75kVA and the line voltage is the same as the phase voltage, the line current is:
Line current = 75kVA / (√3 x Phase voltage)
c) The electrical power input to the alternator can be calculated as the real power divided by the efficiency:
Electrical power input = Real power / Efficiency = 60kW / 0.85 = 70.5882kW
Since the mechanical power needed to drive the alternator is equal to the electrical power input, the mechanical power required is:
Mechanical power = 70.5882kW