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1 Origin of harmonics1.1 Current drawn by non-linear loadsHarmonic currents are generated by non-linearloads, ie. loads which draw a current with adifferent form from the voltage which powersthem. The most common loads of this type arethose based on rectifier circuits.A typical non-linear load, such as that shown infigure 1, draws a current containing all harmonicorders, both odd and even. The appearance ofthe current drawn, which has two differenthalf-waves, and its harmonic spectrum areshown in figures 2 and 3.(A)6420-2-4t(s)0 0.020.04Fig. 2: Appearance of the current drawn10090807060(%) 5040302010Fig. 1: Example of a typical non-linear load(non-symmetrical)01 3 5 7 9 11 13 15 17 19Harmonic orderFig. 3: Spectrum of the current drawn1.2 Symmetrical non-linear loadsHowever, the majority of loads connected to thenetwork are symmetrical, ie. the currenthalf-waves are equal and opposing. This can beexpressed mathematically by the equation:f( ωt + π) = − f( ωt)In this case, the even order harmonics arezero. Assuming that the current includes asecond order harmonic, it is possible to write, forexample:This gives:I( ωt + π) = I sin ( ωt + π) + I sin 2( ωt + π)1 2I( ωt + π) = − I sin ωt + I sin2 ωt1 2This can only be equal to − I( ωt ) if I 2(magnitude of the second harmonic) is zero.This reasoning can be extended to all evenorder harmonics.I( ωt) = I sin ωt + I sin 2ωt1 2Cahier Technique Schneider Electric no. 202 / p.4