Abstract
New terminology is introduced to make clear the relationship between harmonics and symmetrical components. Three-phase sets are classiﬁed in terms of symmetrical sets and asymmetrical sets. Subclasses are introduced with the names symmetrical balanced sets, symmetrical unbalanced sets, asymmetrical balanced sets and asymmetrical unbalanced sets to show that a threephase set can resolve to either one, two or three symmetrical component sets.

The results from four case studies show that these subclasses and their resolution to symmetrical component sets improve understanding of harmonic analysis of systems having balanced and unbalanced harmonic sources and loads.

Conclusions
The table and paragraph given in Ref. 1 does not adequately describe the relationship between harmonics and symmetrical components, especially harmonic sources and does not cover unbalanced loads.

In general authors of power system literature ignore the symmetrical set concept as opposed to the asymmetrical set. The role that the symmetrical set plays in harmonic analysis and in the modelling of harmonic sources should not be ignored.

Classically, positive, negative and zero sequence components have the same frequency. The positive, negative and zero sequence symmetrical components injected by an unbalanced harmonic source have different frequencies.

The new terminology/subclasses of three-phase sets introduced distinguish balanced and unbalanced harmonic sources from each other and are found suitable for comparing injections to harmonic ﬂows in systems in terms of symmetrical components.

The results show that what is injected in terms of symmetrical component sets by a harmonic source is not necessarily received by the system, i.e. the harmonic ﬂows may resolve to one, two or three symmetrical component sets and this depends upon the type of three-phase set found at a given point/node in a system.

The results show that if the harmonic source and the load is balanced, the line voltages and 6k ± 1 harmonic currents in the motor section are symmetrical sets. Only one SCS per harmonic frequency is applied to the motor.

If the harmonic source is unbalanced and the load remains balanced the line voltages and currents in the motor section are unaffected by the injected triplen harmonics.

If the source is balanced and the load unbalanced, the 6k ± 1 harmonics in the line voltages and currents are asymmetrical balanced sets, therefore two SCSs per harmonic frequency (a positive and a negative sequence symmetrical component set) is applied to the motor.

If the source and load are both unbalanced, the heating effect on the motor is further increased as triplen harmonics as asymmetrical balanced sets, are added to the 6k ± 1 harmonic asymmetrical balanced sets resulting in the motor being subjected to two SCSs per harmonic frequency (a positive and a negative sequence symmetrical component set) at triplen and 6k ± 1 harmonic frequencies adding to the decline in the life expectancy of the motor.

The results show that triplen harmonics as ﬂows act like 6k ± 1 harmonics and are not purely zero sequence, as is commonly believed, but resolve to two SCSs per harmonic frequency (a positive and a negative sequence symmetrical component set) in the three-wire sections and to three SCSs per harmonic frequency (a positive, a negative and a zero sequence symmetrical component set) in the four-wire sections when the source and load are unbalanced.

The results show that both symmetrical sets and asymmetrical sets and their resolution to symmetrical component sets are important analytical tools for harmonic analysis of systems having balanced and unbalanced harmonic sources and loads.

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