1、24.437 Power Electronics Sinusoidal Pulse width modulation The switches in the voltage source inverter(See Fig.1)can be turned on and off as required.In the simplest approach,the top switch is turned on If turned on and off only once in each cycle,a square wave waveform results.However,if turned on
2、several times in a cycle an improved har- monic profile may be achieved. Fig 1:Simple Voltage Sourced In the most straightforward implementation,generation of the desired output voltage is achieved by comparing the desired reference waveform(modulating signal)with a high-frequency triangu- larcarrie
3、rwave as depicted schematically in Fig.2.Depending on whether the signal voltage is larger or smaller than the carrier waveform,either the positive or negative dc bus voltage is applied at the output.Note that over the period of one triangle wave,the average voltage applied to the load is proportion
4、al to the amplitude of the signal(assumed constant)during this period. The resulting chopped square waveform contains a replica of the desired waveform in its low fre- quency components,with the higher frequency components being at frequencies of an close to the carrier frequency.Notice that the roo
5、t mean square value of the ac voltage waveform is still equal to the dc bus voltage,and hence the total harmonic distortion is not affected by the PWM process. The harmonic components are merely shifted into the higher frequency range and are automati- cally filtered due to inductances in the ac sys
6、tem. When the modulating signal is a sinusoid of amplitude Am,and the amplitude of the triangular carrier is Ac,the ratio m=Am/Ac is known as the modulation index.Note that controlling the modulation index therefor controls the amplitude of the applied output voltage.With a sufficiently high carrier
7、 frequency(see Fig.3 drawn for fc/fm=21 and t=L/R=T/3；T=period of funda- mental),the high frequency components do not propagate significantly in the ac network(or load) due the presence of the inductive elements.However,a higher carrier frequency does result in a larger number of switchings per cycl
8、e and hence in an increased power loss.Typically switching frequencies in the 2-15 kHz range are considered adequate for power systems applications.Also in three-phase systems it is advisable to use s so that all three waveforms are symmetric. Fig 2:Principal of Pulse Width Modulation Fig.3:SPWM wit
9、h fc/fm=48,L/R=T/3 Note that the process works well for m 1.For m 1,there are periods of the triangle wave in which there is no intersection of the carrier and the signal as in Fig.4.However,a certain amount of this“overmodulation”is often allowed in the interest of obtaining a larger ac voltage mag
10、ni- tude even though the spectral content of the voltage is rendered somewhat poorer. Note that with an odd ratio for fc/fm,the waveform is anti-symmetric over a 360 degree cycle. With an even number,there are harmonics of even order,but in particular also a small dc compo- nent.Hence an even number is not recommended for single phase inverters,particularly for smal ratios of fc/fm.
