《电力电子技术》课程教学课件（PPT讲稿）Topic 12 AC square waveforms inverter、Theorem of SPWM（2）

Topic 12Main contentsLast lecture reviewAC square waveforms inverterTheorem of SPWM (2)

Main contents • Last lecture review • AC square waveforms inverter • Theorem of SPWM (2) Topic 12

1.1 Square wave and sinusoidal waveFourierSeriesdl.Such a periodic arbitrary function01can be expanded in an infinitela/2series of exponential timefunctions called the Fourier series ,u (t)- + [a, cos(no,t) +b, sin(no,t)]2n=1x(t)dtwhereao2x(t) sin(n o,t)dtx(t)cos(n ,t)dt6a.nTT.JOE-mail:

E-mail: xjhuang@bjtu.edu.cn 1.1 Square wave and sinusoidal wave U1, f1 v1 t Fourier Series Such a periodic arbitrary function can be expanded in an infinite series of exponential time functions called the Fourier series , 1 1 2 n n [a cos(n b sin(nt)]  n=1 u (t)= a0 +  t) + where  T 0 T x(t)dt 0 a = 2  T n T 0 1 a = x(t) cos(n 2  t)dt  T n T 0 1 b = x(t)sin(n 2  t)dt

U1if1dlExpressionofsguarewaveinFourierseriesformotVal2≥ u= msi(,)= /2y sin(0,) = si(a,) /元uu10.512-2-1C5

1 1 1 sin( 2 2V Vd sin( 4  u  u1 = V1m sin(1 t)=  t) =  t)  U1, f1 v1 t Expression of square wave in Fourier series form

Expressionof squarewave inFourier series formotu = Vim sin( /,t) + V3m sin(3 /t)Vu/4=[sin(α,t) + = sin(3 ,t)]3元2

U1, f1 v 1  t 1 1 [ s i n ( sin(3 13 d 2 4 V  u  V1m sin(  1 t) + V3m sin(3 1t) =  t ) +  t)]  Expression of square wave in Fourier series form

Expressionofsguarewave inFourierseriesformotu = Vm sin(@,t)+ V3m sin(30,t)+ Vsm sin(50t)Vu/-[sin(αt) += sin(3の,t) += sin(5@ t)].L35元0.5-112-2C

U1, f1 v1 t 1 1 1 [sin( 2 3 5 Vd 4 1 1  u V1m sin(1 t)+V3m sin(31 t)+V5m sin(51 t) = t) + sin(3 t) + sin(5 t)] Expression of square wave in Fourier series form

ValExpressionofsguarewaveinFourierseriesformotu ~ Vm sin(@,t) + V3m sin(30,t)+ Vsm sin(50,t)+ Vrm sin(70,t) sin(3,t) += sin(5 の,t) += sin(7 0,t)].[sin(ot) += s3元0.512-2-1

v1 U1, f1 t 1 1 1 1 [sin( 2 3 5 7 Vd 4 1 1 1  u V1m sin(1 t) +V3m sin(31 t)+V5m sin(51 t) +V7m sin(71 t) = t) + sin(3 t) + sin(5t) + sin(7 t)] Expression of square wave in Fourier series form

U1.f1ValExpressionofsguarewaveinFourierseriesformotu ~ Vim sin(Oit) + V3m sin(30;t)+ Vsm sin(50,t)+..... +Vnm sin(nO;t)三[sin(,) + ↓ sin(30,) + sin(50,) .+ in(n,)] Va/35元?u0.5-22-44-6-0.5

v1 U1, f1 t 1 1 1 1 [sin( 2 3 5 Vd n 4 1 1 1  = u V1m sin(1 t) +V3m sin(31 t)+V5m sin(51 t)++Vnm sin(n1 t) t) + sin(3 t) + sin(5t) ++ sin(nt)] Expression of square wave in Fourier series form

ValExpressionofsguarewaveinFourierseriesformotu = Vim sin(O,t)+ V3m sin(3,t)+ Vsm sin(5O,t)+ ...... + Vnm sin(nOit)+=[sin(0,t) + = sin(30 ,t) += sin(5α,t) + ...+- sin(no,t)+...]. 'a3元n

v1 U1, f1 t 1 1 1 1 [sin( 3 5 d 2 V n 4 1 1 1  = u =V1m sin(1 t)+V3m sin(31 t)+V5m sin(51 t)++Vnm sin(n1 t)+ t) + sin(3 t) + sin(5 t) ++ sin(n t) +] Expression of square wave in Fourier series form

1.2Conceptsof non-sinusoidal waveformU1, f11) Fundamental and harmonics01 is called fundamental frequency.no1 is called harmonic frequency or harmonicswhere n>1.V1m is the peak amplitude of fundamental componentVnm is the peak amplitude of harmonics componentwhere n>1

1.2 Concepts of non-sinusoidal waveform v1 U1, f1 t 1 is called fundamental frequency. n1 is called harmonic frequency or harmonics, where n>1. V1m is the peak amplitude of fundamental component. Vnm is the peak amplitude of harmonics component, where n>1. 1) Fundamental and harmonics

2)RMS (Root Mean Square)0Definition:u?dtU = Us = Urms In square wave on this page, we haveU = U, = Urms = JJ u2dt="/nnJJ vansin2(nwit)=/zm-1

U1, f1 v1 t Definition: 2) RMS (Root Mean Square) In square wave on this page, we have