Harmonics in Different Three-phase Systems

(i) All third harmonics are equal in all phases of the circuit i.e. they are in time phase.

(ii) Fifth harmonics in the three phases have a negative phase sequence of R, B, Y because the fifth harmonic of blue phase reaches its maximum value before that in the yellow phase.

(iii) All harmonics which are not multiples of three, have a phase displacement of 120º so that they can be dealt with in the usual manner.

(iv) At any instant, all the e.m.fs. have the same direction which means that in the case of a Y-connected system they are directed either away from or towards the neutral point and in the case of Δ- connected system, they flow in the same direction.

Main points can be summarized as below :

(i) all triple-n harmonics i.e. 3rd, 9th, 15th etc. are in phase,
(ii) the 7th, 13th and 19th harmonics have positive phase rotation of R, Y, B.
(iii) the 5th, 11th and 17th harmonics have a negative phase sequence of R, B, Y.

Contents

Harmonic Analysis

By harmonic analysis is meant the process of determining the magnitude, order and phase of
the several harmonics present in a complex periodic wave.

For carrying out this analysis, the following methods are available which are all based on
Fourier theorem:

(i) Analytical Method–the standard Fourier Analysis
(ii) Graphical Method– (a) by Superposition Method (Wedgemore’ Method) (b) Twenty four
Ordinate Method
(iii) Electronic Method–by using a special instrument called ‘harmonic analyser’
We will consider the first and third methods only.

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