A far as a “true RMS” power definition—voltamperes are the product of RMS current and RMS voltage measured over at least one full AC electrical cycle. Regardless of the shape of the voltage and current waveforms, their ‘DC thermal equivalent’ can be accurately measured and yield precise apparent power, and, time integrated, apparent energy. The ability to slice up AC waves accurately, fast enough and in real time (much less in places where meters get installed) has only been possible about the last 15 years. Once a periodic wave is reduced to a stream of bits, calculating various quantities becomes duck soup.
Watts are the product of instantaneous voltage and instantaneous current, summed through many slices or fractions of of a cycle. These definitions are inherently wide-band and not frequency dependent. There is not any significant disagreement on how to measure real and apparent quantities. Note the term ‘RMS watts’ is contradictory and inappropriate.
Search on NRC Canada, power measurement and authors Arseneau and Filipski.
However reactive power is defined or measured, the Pythagorean relationship for apparent, real and reactive power does not necessarily hold. What to call the “leftover” power is a subject of wide debate, and has tended to be conveniently defined based on the capabilities of various meter designs.
Reactive power and distortion components get screwed up, because of the 90° phase shift needed for measurement (¼ of an electrical cycle) can’t be done for two or more simultaneous frequencies; making the fundamental definition of reactive power frequency dependent.
In the late 1980s, Arseneau and Filipski captured nasty in-the-field [like arc furnaces] voltage and current waveforms [up to 47% THD current] and extensively tested electromechanical and solid-state meters to observe what distortion’s effect had on registration.
Voltampere demand measures everything—as long as it is periodic—it doesn’t matter how awful the waveform looks. So right now it is the fairest way to quantify power and energy at a given point; i.e., at the ‘meter,’ which is usually also the ‘point of common coupling.’ With all the dsp stuff, meter users, standards folks and manufacturers will hammer out new algorithms that more closely represent an accurate and fair way to buy and sell electricity. A big step has been IEEE 1459-2000 DESCRIPTION at