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A 400 V, 3-phase synchronous motor has armature current of 150 A. It has synchronous resistance and reactance of 0.4 тДж and 4 тДж per phase, respectively. If the power developed is 130 kW and the iron and friction losses are 1 kW, then the efficiency of the motor will be ____________.
60%
81.6%
91.6%
75%
81.6%
The efficiency of a synchronous motor is the ratio of output power to input power. The input power includes the power developed (mechanical output plus internal losses) plus the electrical losses (I2R losses) and the constant losses (iron and friction).
The efficiency of a synchronous motor is the ratio of output power to input power. The input power includes the power developed (mechanical output plus internal losses) plus the electrical losses (I2R losses) and the constant losses (iron and friction).
PcuтАЛ=3Ia2тАЛRaтАЛ тАФ Copper losses in a 3-phase motor
╬╖=PdevтАЛ+PcuтАЛPdevтАЛтИТPcfтАЛтАЛ├Ч100% тАФ Efficiency calculation formula
The input power PinтАЛ is the sum of the power developed PdevтАЛ and the copper losses PcuтАЛ, plus the constant iron and friction losses PcfтАЛ. Given VLтАЛ=400┬аV, IaтАЛ=150┬аA, RaтАЛ=0.4┬а╬й, PdevтАЛ=130┬аkW, and PcfтАЛ=1┬аkW, we calculate copper loss as 3├ЧIa2тАЛ├ЧRaтАЛ=3├Ч1502├Ч0.4=27┬аkW. The total output power is PoutтАЛ=PdevтАЛтИТPcfтАЛ=130тИТ1=129┬аkW. The input power is PinтАЛ=PdevтАЛ+PcuтАЛ=130+27=157┬аkW. The efficiency ╬╖ is PinтАЛPoutтАЛтАЛ├Ч100%.
Copper losses in a 3-phase system are calculated using the formula 3I2R.
Power developed represents the mechanical power produced by the machine, but not the final shaft output.
Efficiency accounts for all losses, including constant losses like iron and friction, and variable losses like I2R.
Constant speed operation
Power factor improvement
Requires DC excitation
Not self-starting
Power factor correction
Constant speed industrial drives
Calculation: ╬╖=158129тАЛ├Ч100тЙИ81.64%.
Option B is the correct result of the calculation based on the power flow balance.
B is correct тАФ The efficiency is calculated by dividing the actual shaft output by the total electrical input power, resulting in approximately 81.6%.
Always ensure you distinguish between power developed (internal) and output power (shaft) when dealing with efficiency problems in rotating machines.