这几天在Power Globe 上看到对无功功率的一些讨论，把一些比较好的解释放到这里。正如Charles A. Gross 所说，这些解释都（部分地）正确地揭示或说明了无功功率，但也都不是一个完美或根本的解释，其中的一个原因是我们在尝试为一个非物理或抽象的量提供物理解释。

It’s been fun reading all the explanations.  One of my favorites  is “Q is the foam on the beer…”.They all have elements of truth, but never the whole truth and nothing but the truth.  Hence, none really explain what Q is.The reason that we are having so much trouble coming up with a physical explanation for Q is that Q is non-physical, as are  many concepts in engineering. --Charles A. Gross, PE, PhD, FIEEE

Reactive power is a measure of the back and forth flow between energy

in magnetic and electric fields in components. The reactive power value

measures the magnitude of the instantaneous flow between these fields.

---B.Ross

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The answer to your question requires some understanding of ac circuits.

Ac voltages (V) and currents(I) vary sinusoidally in time and have three basic properties:  strength (RMS magnitude, V in volts, I in amperes); frequency (e.g. 60 Hz); and phase.  Phase involves two quantities (V and I, in this case) .  

V and I are said to be “in phase”, if they both peak at the same instant; are zero at the same instant; reverse polarity/direction at same instant; etc.

V and I are said to be “out of phase”, if when V peaks, I is zero, and vice versa.  More precisely we really should say “V and I are 90 degrees out of phase”. [ one “cycle” of ac V or I is 360 degrees; hence 90 degrees is equivalent to ¼ cycle, so it would be also correct to say “V and I are ¼ cycle out of phase”].

Now general, V and I are not in phase or 90 degrees out of phase but somewhere in between.  It is possible to divide the current (I) into two components:

the in-phase component or “active current”  (IA) and

the (90 deg) out-of-phase component or “reactive current” (IR)

Correspondingly, there are two kinds of power:

Active Power (P) = V*IA,  which we say is measured in watts

Reactive Power (Q) = V*IR, which we say is measured in volt-amperes reactive, or “vars”

There is also a third kind of power in ac circuits:

Apparent Power (S) = V*I, which we say is measured in volt-amperes , or “VA”.

These three are related:  S = sqrt[sqr(P) + sqr(Q)] as are the currents.

I = sqrt[sqr(IA) + sqr(IR)]  

How much of “I” is “IA” is communicated thru something called the power factor (pf), such that

IA = I*pf  and P = S*pf

An Example:  A 120 V ac source supplies 10 A at a pf = 0.8 lagging. The term lagging means that the current trails the voltage in time. Find S, P, and Q.

S = V*I = 120(10) = 1200 VA

P = S*pf = 1200(0.8) = 960 W

Q= sqrt(1200^2-960^2)= 720 var

I = 10 A

IA = I*pf = 10(0.8) = 8 A

IR = sqrt(10^2-80^2)= 6 A

Now that we know what Q is, at least in terms of V, I, and phase, what is it physically?

There are three passive circuit elements:  R,L,C

R, and only R, dissipates active power (P).

L and C are called “reactive elements” in that they do not dissipate energy, but they do store it an internal magnetic field (L), or electric field (C).  This field energy” is constantly flowing into and out of L and C and the source, and  over an ac cycle, averages to zero.  This energy exchange requires a current component that is necessarily  90 deg out of phase with the voltage (IR), and hence a corresponding power component Q = V*IR.  

            --- Charles A. Gross, PE, PhD, FIEEE

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Reactive power is a myth and a delusion. It is no more than a mathematical coincidence. It can be extremely useful, but it is without foundation.

You know the math: it is just a matter of using a sine or a cosine term to switch between real and reactive power. It is just the difference between the one side or the other of a right-angle triangle. But think! That right triangle does not represent a phasor. The 90-degree rotation business of phasors does not apply because power is not a phasor.

A few years ago, NIST did a survey of the way this thing called reactive power was being measured, and found there were at least nine different methods that would give nine different results, depending on how far the waveform was from sinusoidal. It became a NEMA report: NEMA C12.24 TR-2011, Definitions for Calculations of VA, VAh, VAR, and VARh for Poly-Phase Electricity Meters, registered with ANSI May 2011.

Over a hundred years ago, we engineers were asking whether it was possible to measure something that was not real, and whether the fact that you could measure something meant that it was real. The digital revolution in measurements has firmly answered that it is possible to measure something that is not real, because the number-crunching part of measurement is no more than data compression. The ways we measure reactive power underlines that. Today, you can buy equipment that will let you choose whose definition you use in the measurement.

That is not to say the idea of reactive power is not useful. It has simplified thinking about voltage management in the power system. It has led to some interesting solutions in that area: SVCs for example. But once you get away from the simplified notion of a perfect sine-wave, you enter undefined territory, the realm of imagination.

Power factor is in the same boat. Another calculation of very great value and usefulness, and yet not defined for waves that are not sinusoidal.

We will, of course, continue to use these terms: they are much too useful to abandon. But we should be aware of their limited meaning, and sometimes we are not. See, for example, Berrisford, A.J., “Smart Meters should be smarter”, presented at the IEEE PES General Meeting, San Diego, CA July 2012. DOI 10.1109/PESGM.2012.6345146

           --- Harold Kirkham,Staff Scientist,Pacific Northwest National Laboratory.