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On Three Phase Reactive Power

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2004 Annual Conference


Salt Lake City, Utah

Publication Date

June 20, 2004

Start Date

June 20, 2004

End Date

June 23, 2004



Conference Session

Emerging Trends in Engineering Education

Page Count


Page Numbers

9.957.1 - 9.957.12



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Paper Authors

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Brian Manhire

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

Session 1793

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. 10.18260/1-2--13798

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