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1.3 3-phase loadsConsider a symmetrical, balanced, non-linear3-phase load without neutral connection, asshown in figure 4.Assuming that the currents drawn by this loadinclude the third harmonic, the third orderharmonic currents of each phase can be writtenas follows:i r3 = I 3 sin 3ωt⎛ 2π⎞i s3 = I3 sin 3 ⎜ωt− ⎟ = I sin ( 3 t − 2 ) = i⎝r33 ⎠ 3 ω π⎛ 4π⎞i t3 = I3 sin 3 ⎜ωt− ⎟ = I sin ( 3 t − 4 ) = i⎝r33 ⎠ 3 ω πir3 = i s3 = i t3The third order harmonic currents of all threephases are therefore equal.However, if there is no neutral conductor,ir + is + it = 0.The sum of the third order harmonic currents inparticular should be zero, which is only possibleif each of the components is zero.Symmetrical, balanced, 3-phase loads do nottherefore generate a third harmonic.This reasoning can be extended to all harmonicorders which are multiples of 3.Harmonic currents which are not zero aretherefore of the order 5, 7, 11, 13, etc, ie. theytake the form 6k ± 1.This can be demonstrated for any systemincorporating rectifiers, whether controlled ornot. We can therefore demonstrate thatharmonic orders are written h = (nxp) ± 1, wheren is an integer (1, 2, 3, 4, 5, etc) and p thenumber of rectifiers which make up the device.For example, a circuit which only includes onerectifier (half-wave rectification) has harmonicsof the order n ± 1 and presents all possibleharmonics, starting with 0 which is the directcurrent.For a bridge consisting of 4 diodes, the firstharmonic is of order 3, as demonstrated insection 1.2.Fig. 4: 3-phase loadirisitThis result is illustrated by the diagramconsisting of a diode rectifier with capacitivefiltering (see fig. 5), where the current drawn isrepresented by the curve in figure 6 and itsspectrum in figure 7.Fig. 5: 3-phase rectifier bridge with capacitive filtering3002001000-100-200-300Network voltage (V)Line current (A)0 0.020.04Fig. 6: Appearance of the current drawn by the circuitin figure 510090807060(%) 50403020100t(s)1 3 5 7 9 11 13 15 17 19 21 23 25Harmonic orderFig. 7: Harmonic spectrum of the current drawn by thecircuit in figure 5Cahier Technique Schneider Electric no. 202 / p.5