8.8:
Power in a Three-Phase Circuit
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Three-phase systems have two configurations: the wye and delta. A star configuration can be three or four wires; in a delta configuration, the components are connected in a closed loop. Instantaneous power refers to the power value at a precise moment, and in a balanced three-phase system, it is constant. This is because the sum of the instantaneous powers in the three phases remains steady over time, despite individual fluctuations, due to the symmetry and phase relationship. The total instantaneous power in a balanced three-phase system is constant and does not fluctuate over time.
Active, Reactive, and Complex Power:
The average power per phase is one-third of the total average power in a balanced three-phase system. Similarly, the reactive power per phase is one-third of the total reactive power in the system. The complex power, which combines both active and reactive power per phase, is also one-third of the total complex power.
Equivalence in Power Calculations:
The Delta and Wye configurations have voltages and currents in all phases and lines. In these configurations, the loads are connected to each phase at the load end. The power consumed by the load and the equivalence between wye and delta configurations extends to power calculations. Whether in a wye-connected or a delta-connected system, the total power is the sum of the power in each of the three phases. This can be calculated using the relationships between line and phase voltages and currents. For a wye-connected system and a delta-connected system:
