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
To solve this problem, we can use the following formulas and equations:
a) The apparent power (S) is given by S = P / power factor, where P is the real power supplied by the alternator. In this case, P = 60 kW. So,
S = 60 kW / 0.8 = 75 kVA
b) The apparent power (S) is also given by S = √3 * V * I, where V is the phase voltage and I is the phase current. Rearranging this equation, we get:
I = S / (√3 * V)
To find I, we need to calculate V first. The power (P) is also given by P = √3 * V * I * power factor. Rearranging this equation, we get:
V = P / (√3 * I * power factor)
Substituting the known values, we have:
V = 60 kW / (√3 * I * 0.8)
Since the efficiency of the alternator is 85%, the real power (P) is given by P = efficiency * apparent power. Rearranging this equation, we have:
P = 0.85 * 75 kVA = 63.75 kVA
Substituting this value back into the previous equation, we have:
V = 63.75 kVA / (√3 * I * 0.8)
c) The mechanical power (Pm) needed to drive the alternator is given by Pm = P / efficiency, where P is the real power supplied by the alternator. Substituting the known value, we have:
Pm = 60 kW / 0.85 = 70.59 kW
Now, we can solve the equations to find V and I:
V = 63.75 kVA / (√3 * I * 0.8)
Substituting V in the equation:
60 kW = (√3 * V * I * 0.8)
Plugging in the known values:
60 kW = (√3 * (63.75 kVA / (√3 * I * 0.8)) * I * 0.8)
Simplifying the equation:
60,000 = (63.75 / 0.8) * I
I = 60,000 * 0.8 / 63.75 = 750 A
Finally, substituting I back into the equation for V:
V = (63.75 kVA) / (√3 * 750 A * 0.8)
V ≈ 60.78 V
Therefore,
a) the phase voltage of the alternator is approximately 60.78 V.
b) the phase current of the alternator is approximately 750 A.
c) the mechanical power needed to drive the alternator is approximately 70.59 kW.