Final answer:
To estimate the starting line current for a 10 H.P. 3-phase induction motor with a star-delta starter, you must calculate the full load current and then adjust it by multiplying by 3.5 and dividing by √3 to account for the starting current and voltage reduction respectively.
Step-by-step explanation:
Estimating the Line Current at Motor Start
To estimate the line current at the instant of starting the motor using a star-delta starter, we must consider the reduction in voltage that occurs due to the star-delta configuration. A star-delta starter reduces the starting voltage to √3 or approximately 58% of the full line voltage. The short circuit current is given as 3.5 times the full load current.
First, we must calculate the full load current of the motor using the formula:
- Full Load Power (P) = 10 H.P. (Horsepower)
- Full Load Efficiency (η) = 0.83
- Power Factor (p.f.) = 0.8
- Supply Voltage (V) = 500 V
The full load current (IFL) can be calculated from the power formula for three-phase systems:
P = √3 V IFL p.f. η
After calculating IFL, we multiply it by the starting current factor (3.5 times IFL) and adjust for the star-delta reduction to find the starting current, Istart:
Istart = (3.5 IFL) / √3
Finally, the estimated starting line current is obtained.