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. 10.18260/1-2--13798
ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2004 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015