Fundamentals of Harmonics

Overviews Definitions and Nonlinear Loads Harmonics Power Quantities Harmonic Sequences Triplen Harmonics Harmonics Indices Harmonic Sources Classical Sources and Power Electronics Locating Harmonic Sources Impacts of Harmonics Interharmonics

1.1 Nonlinear Loads Fundamentals of Nonlinear Loads Fourier representation

1.2 Harmonic Phenomena Harmonics in voltage and current CAUSE: Current Effect: Voltage

Examples of Harmonics I

Examples of Harmonics II

Examples of Harmonics III

Harmonics versus Transients

Power Factor Consider first a sinusoidal voltage and current

RMS In case of harmonics,

Harmonic Phase Sequences In a balanced three-phase circuit: the fundamental defines the positive phase sequence (or rotation) such as ABC or xyz or 321, and the 4th, 7th, 10th, …, are also positive sequence the 2nd, 5th, 8th, 11th ,…, are negative sequence (eg CBA) the 3rd, 6th, 9th, …, are zero seq (all in phase)

1 + 2 - 3 4 5 6 7 8 9 10 1 + 3 5 - 7 9 11 13 15 17 19

Triplen harmonics Harmonic order h values that are multiples of 3 are called triplen harmonics If the three phase circuit is balanced, the triplen harmonics are all in phase (zero sequence) triplen harmonic line currents will be additive at the neutral of a wye circuit by KCL (zero triplens if three-wire ungrounded wye or if delta) triplen harmonic line-line voltages will be zero by KVL

Transformer

Harmonic Indices Total harmonic distortion = THD

Harmonic Indices Total demand distortion = TDD

Harmonics Sources Conventional Sources Industrial Sources Single-phase power supplies Fluorescent lighting ASD for HVAC and elevators Industrial Sources Power converters DC and AC drives Saturable devices

4.1.1 SMPS

4.1.2 Fluorescent lighting

Power Converter