A manufacturing plant with several heavy machines requires significant power supplied by a balanced three-phase system.

To determine the instantaneous power absorbed by the plant's load, the analysis is performed on a Y-connected time-domain circuit.

The phase voltages have a phase difference of 120 degrees and the square root of two is used to convert peak voltages to RMS values for accurate power analysis.

When a machine operates, it draws current from the power supply, leading to a phase lag between phase currents and their corresponding phase voltages.

The total instantaneous power drawn by the machine's load is calculated by summing the instantaneous power in each of the three phases.

The obtained total instantaneous power remains nearly constant and does not change with time. This allows for the calculation of active, reactive, and apparent power per phase.

The total active power is the sum of the active powers in three phases. Similarly, the total reactive and apparent power is calculated.

These results hold true for both Y- and delta-connected loads.