Determining Synchronous Motor Power Factor and kVA Rating

What are the specific loads available for calculation?

The following loads are available for calculation:

• i) Induction motors: 900 hp with 0.75 power factor, 90% average efficiency.
• ii) Lighting and heating loads: 110 kW
• iii) Synchronous motor: Consumes 400 hp.

Determining the kVA Rating of Synchronous Motor

a) To determine the kVA rating of the synchronous motor, we need to consider the power factor. The power factor is the cosine of the angle between the current and voltage waveforms. In this case, we have an initial power factor of 0.75 and we want to increase it to 0.92.

First, we need to calculate the apparent power (S) of the synchronous motor using the initial power factor:

S_initial = P / power factor_initial

Where P is the real power (400 hp in this case). So,

S_initial = 400 hp / 0.75 = 533.33 kVA

Next, we can calculate the new apparent power (S_new) using the desired power factor:

S_new = P / power factor_new

S_new = 400 hp / 0.92 = 434.78 kVA

Therefore, the kVA rating of the synchronous motor should be 434.78 kVA to achieve a power factor of 0.92.

Determining the Power Factor of Synchronous Motor

b) To determine the power factor of the synchronous motor, we can rearrange the formula for apparent power:

power factor = P / S

Where P is the real power and S is the apparent power. In this case, the real power is 400 hp and the apparent power is 434.78 kVA.

power factor = 400 hp / 434.78 kVA

power factor = 0.92

Therefore, the power factor of the synchronous motor is 0.92.