App-11
IM WT310E-01EN
Appendix
App
Harmonics
Harmonics refer to all sine waves whose frequency is an integer multiple of the fundamental wave 
(normallya50Hzor60Hzsinusoidalpowerlinesignal)exceptforthefundamentalwaveitself.The
input currents that flow through the power rectification circuits, phase control circuits, and other circuits 
used in various kinds of electrical equipment generate harmonic currents and voltages in power lines. 
When the fundamental wave and harmonic waves are combined, waveforms become distorted, and 
interference sometimes occurs in equipment connected to the power line.
Terminology
The terminology related to harmonics is described below.
• Fundamentalwave(fundamentalcomponent)
  The sine wave with the longest period among the different sine waves contained in a periodic 
complex wave. Or the sine wave that has the fundamental frequency within the components of the 
complex wave.
• Fundamentalfrequency
  The frequency corresponding to the longest period in a periodic complex wave. The frequency of 
the fundamental wave.
• Distorted wave
  A wave that differs from the fundamental wave.
• Higher harmonic
  A sine wave with a frequency that is an integer multiple (twice or more) of the fundamental 
frequency.
• Harmoniccomponent
  A waveform component with a frequency that is an integer multiple (twice or more) of the 
fundamental frequency.
• Harmonicdistortionfactor
  The ratio of the rms value of the specified nth order harmonic contained in the distorted wave to the 
rms value of the fundamental wave (or all signals).
• Harmonicorder
  The integer ratio of the harmonic frequency with respect to the fundamental frequency.
• Total harmonic distortion
  The ratio of the rms value of all harmonics to the rms value of the fundamental wave (or all signals).
Interference Caused by Harmonics
Some of the effects of harmonics on electrical devices and equipment are explained in the list below.
• Synchronizationcapacitorsandseriesreactors
  Harmonic current reduces circuit impedance. This causes excessive current flow, which can result 
in vibration, humming, overheat, or burnout.
• Cables
  Harmonic current flow through the neutral line of a three-phase, four-wire system will cause the 
neutral line to overheat.
• Voltagetransformers
  Harmonics cause magnetostrictive noise in the iron core and increase iron and copper loss.
• Breakersandfuses
  Excessive harmonic current can cause erroneous operation and blow fuses.
• Communicationcables
  The electromagnetic induction caused by harmonics creates noise voltage.
• Controldevices
  Harmonic distortion of control signals can lead to erroneous operation.
• Audiovisualdevices
  Harmonics can cause degradation of performance and service life, noise-related video flickering, 
and damaged parts.
Appendix 2  Power Basics (Power, harmonics, and AC RLC circuits)