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Session 1793

On Three-Phase Reactive Power

Brian Manhire Ohio University

Abstract

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

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Manhire, B. (2004, June), On Three Phase Reactive Power Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--13798