《电力电子技术》课程教学课件（PPT讲稿）Topic 14 Line-Frequency Diode Rectifiers

Maycausingresonance conditionsbetweenthecapacitive reactance of the shunt capacitors and theinductive reactance of the transmission lines.VOverloading the shunt capacitors used by utilities forvoltage support.VMaycausingEMlidCdROther equipmentFigure5-25 Line-voltage notching and distortionFigure5-26Voltage waveform at thepoint of common coupling in thecircuit of Fig.5-25

17 ✓May causing resonance conditions between the capacitive reactance of the shunt capacitors and the inductive reactance of the transmission lines. ✓Overloading the shunt capacitors used by utilities for voltage support. ✓ May causing EMI

Example5-AAcurrentisof sguarewaveform is showninfollowing Figure. Calculate and plot its fundamental frequencycomponent and its distortion component. What is the THDassociated with this waveform?isa0Solution411元tortion

Example 5-A A current is of square waveform is shown in following Figure. Calculate and plot its fundamental frequency component and its distortion component. What is the THD associated with this waveform? Solution

Solution: From Fourier analysis, By choosing the time origirnas shown in Figure, is(t) can be expressed as:-sin o.t=sin 50,+Sin+35元aOsin 7o,t +...Ti41/元b= 0.911S12, = /12 -(0.91)2 = 0.4361distortion0.4361%THD = 100× ldistorion = 100×48.4%0.9115

Solution: From Fourier analysis, By choosing the time origin as shown in Figure, is (t) can be expressed as: 7 3 5 1 s 1 1 1 + 1 sin 7 t +.) i = 4 I(sint + 1 sin 3t + 1 sin 5 t  0.9I = 100 0.436I = 48.4% I = 0.436I 2 2 = − I 2 = −(0.9I ) 2 I 2 I I = 0.9I Is1 %THD =100 Idistortion distortion s s1 Is1 = (4  )

4lmportantCalculatingEguations(1) Sinusoidals of different frequency are orthogonal.2元If mtnsin(mot) sin(not + d)d(ot) = 0(2) Sin. and cosine are orthogonal.2元sin ot cosotd (ot) = 0Josin( ot) sin(ot + d)d (ot)(3) In generalCOS2元J02☆TheseEquations will beusefulforcalculatingpower,etc

If m≠n 0 sin(mt) sin(nt +)d (t) = 0 2 4 Important Calculating Equations (1) Sinusoidals of different frequency are orthogonal. (3) In general cos 1 2 sin( 1 2 2 0 t)sin(t +)d (t) = 0 sint costd (t) = 0 2 (2) Sin. and cosine are orthogonal. ☆These Equations will be useful for calculating power, etc

(4) Obtaining Harmonic Components by Fourier AnalysisO0g(t) = G + Zgh(t)=G。 + Z(an cos(hot)+ b, sin(hot)h=1h=1一2元g(t)·d(ot)2元g(t)cos(hot)d(ot)h =1,2,..,oo元g(t)sin(hot)d(ot)h=1,2,...,00TJOVa,+betan dG,=G,L0an200G21ZG0E-mail:xjhuarh=1

E-mail: xjhuang@bjtu.edu.cn 21 (4) Obtaining Harmonic Components by Fourier Analysis