Salt Lake City, Utah
June 20, 2004
June 20, 2004
June 23, 2004
9.957.1 - 9.957.12
On Three-Phase Reactive Power
Brian Manhire Ohio University
It is well known that in single-phase alternating current (AC) electric power systems, both aver- age power and reactive power, which are the real and imaginary parts of single-phase complex power, can be made to appear explicitly in the time-domain formulation of sinusoidal instantane- ous power. However, unlike the single-phase case, in three-phase electric power systems, only (constant) three-phase average power appears in the three-phase instantaneous power counterpart. The mathematical reasons for this are explained and an algebraic reformulation of three-phase instantaneous power is contrived to unify complex power and instantaneous power across both cases.
I. Single-Phase Steady-State Power
Consider the single-phase steady-state sinusoidal inductive electric circuit of Figure 1.
Figure 1. Single-phase steady-state sinusoidal inductive electric circuit
Let the ideal sinusoidal voltage source be:
van(t) = Vpeakcos(ω t ) V (1)
where: Vpeak is the peak value of the sinusoidal voltage (in volts), ω is the radian fre- quency of the voltage in radians per second, t is time in seconds and the units of resistance R and inductance L are in ohms and henries, respectively.
The current is:1
ia(t) = Ipeakcos(ω t - θ) A (2)
Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education
Manhire, B. (2004, June), On Three Phase Reactive Power Paper presented at 2004 Annual Conference, Salt Lake City, Utah. https://peer.asee.org/13798
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