A 60kW 2,2kW three-phase star connected alternator supplies a load at a power factor of 0,8 lagging. If the alternator is operating 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) To calculate the phase voltage of the alternator, we need to use the formula for apparent power:
Apparent Power (S) = √3 * Phase Voltage (V) * Phase Current (I)
The apparent power is given by 60kW, so we can rearrange the formula to solve for the phase voltage:
√3 * Phase Voltage (V) * Phase Current (I) = 60kW
Phase Voltage (V) = 60kW / (√3 * Phase Current (I))
b) The power factor (pf) is given as 0.8 lagging. Power factor is defined as the ratio of real power to apparent power. Real power (P) is given by the formula:
Real Power (P) = Apparent Power (S) * Power Factor (pf)
Real Power (P) = 60kW * 0.8 = 48kW
We can use the formula for real power to calculate the phase current:
Real Power (P) = √3 * Phase Voltage (V) * Phase Current (I) * Power Factor (pf)
48kW = √3 * Phase Voltage (V) * Phase Current (I) * 0.8
Phase Current (I) = 48kW / (√3 * Phase Voltage (V) * Power Factor (pf))
c) The mechanical power needed to drive the alternator can be calculated using the formula for efficiency:
Efficiency = Real Power (P) / Mechanical Power
Rearranging the formula, we can solve for Mechanical Power:
Mechanical Power = Real Power (P) / Efficiency
Mechanical Power = 48kW / 0.85
Note: Convert the efficiency from percentage to decimal form by dividing by 100.
Let's calculate the phase voltage and phase current first:
a) Phase Voltage (V) = 60kW / (√3 * Phase Current (I))
b) Phase Current (I) = 48kW / (√3 * Phase Voltage (V) * Power Factor (pf))
Then we can calculate the mechanical power needed to drive the alternator:
c) Mechanical Power = 48kW / 0.85