Grid Connected Photovoltaics

Power Quality Concepts

RMS value (Root Mean Square)

It is the square root of the mean-square value and represents the effective value of a wave. For a sinusoidal wave: rms value = Valuemax/sqrt(2) For any type of wave: (with harmonics)
rms value = sqrt[1/T*int{f(t)^2 dt}]
= sqrt[(dc)^2 + sum (rmsn^2)]
= sqrt[(Mean value)^2 + 1/2 (sum of the squares of harmonic amplitudes)]

THD (Total Harmonic Distortion)

As a mesure of the amount of distortion of a wave related to perfect sine one, a figure of merit called Total Harmonic Distortion is used. It is defined like the ratio of the root-mean-square (RMS) of the harmonic content to the root-mean-square value of the fundamental quantity, expressed as a percent of the fundamental.
THD = RMS value of wave form without the DC and the fundamental / RMS value of fundamental
The lower distortion, the more the output looks like a sine wave, and hence the smaller are the higher harmonic amplitudes and correspondingly the THD.

Fourier series and applications

Any periodic wave which is single-valued and continuous except for a finite number of finite discontinuities, and which does not have an infinite number of maxima or minima in the neighborhood of any point, may be represented by the sum of a number of sine waves of different frequencies. Except in special cases an infinite number of components are theoretically required. Practically, however, only a few terms are necessary in most instances because of the relatively small effect of the terms of higher frequency.

The Fourier series representation can be used in linear networks to obtain steady-state responses to periodic excitations. Most of the non-sinusoidal waves found in electrical engineering can be expressed in terms of sine-wave components of different frequencies. Under these conditions each sine component may be handled according to the laws governing the calculations of sine waves. The results of all component analyses are combined according to certain laws to form the composite or final analysis. Superposition principle is applied in this case.

Superposition

It is possible to calculate responses in simple circuits when one source (or a combination of sources equivalently represented as a single source) excites a network. When more than one source excites a linear network, the resulting response may be obtained as the sum of individual responses caused by each source acting alone while all other sources are made zero.
Thus adding the responses due to sources applied one at a time, we can obtain the response due to all sources acting together. In using the superposition principle, all sources other than the one under consideration are set to zero. Setting a voltage source to zero means Vs=0, which is equivalent to replacing the voltage source vs with a short circuit. Setting a current source to zero means making Is=0, which is equivalent to replacing the current source is with an open circuit. The process of setting sources to zero is referred to as killing the sources.

Further information on power quality concepts: Glossary of Power Quality Terms