Single Phase Line Frequency Uncontrolled Rectifiers
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1 Single Phae Line Frequency Unconrolle Recifier Kevin Gaughan 24-Nov-03 Single Phae Unconrolle Recifier 1
2 Topic Baic operaion an Waveform (nucive Loa) Power Facor Calculaion Supply curren Harmonic an Th Effec of Source nucance Operaion wih Conan DC Volage (Capaciive Loa) Volage Doubler Configuraion Effec of Non-linear loa on Neural curren 24-Nov-03 Single Phae Unconrolle Recifier 2
3 Single Phae Brige Recifier i = i i 1 v v V o 24-Nov-03 Single Phae Unconrolle Recifier 3
4 Aumpion eal Dioe Zero ource impeance Highly inucive loa L/R >>T => DC oupu curren oe no vary over coure of cycle) Coninuou inucor curren ( nucor Curren oe no go o zero uring cycle) 24-Nov-03 Single Phae Unconrolle Recifier 4
5 Recifier Waveform 2.V 2.V v T/2 T i 1 i 3 i 24-Nov-03 Single Phae Unconrolle Recifier 5 -
6 Recifier Relaionhip DC Oupu Volage T / 2 2. V.in(. ) Vo = v = =. V = 0. 9V T / 2 RMS Supply Curren T ( i ( )) 2. 0 = = T Real Power an Apparen Power Auming lo-le componen Real AC power in = DC power ou: 2. 2 P = Vo. =. V. = 0.9V. Apparen power by efiniion i V rm. rm : S = V.. 24-Nov-03 Single Phae Unconrolle Recifier 6
7 24-Nov-03 Single Phae Unconrolle Recifier 7 Harmonic Analyi The Supply Curren can be expree a a Fourier Serie: ( ) + = + = 1 0 ).in( ).co( ) ( n n n n b n a i where = ). (. 2 1 i = 0 (No DC componen) 0. ) co(. ) co(. 1 ) co( ). ( = + = = n n n i a n (No Coine componen) n n n n i b n 4 ) in(. ) in(.. 1 ) in( ). ( = + = = b n = 0 for n = 2,4,6... n b n 4 = for n = 1,3, 5... (No Even Harmonic) ubiuing for a n an b n : =... 5 ) 5 in( 3 ) 3 in( 1 ) in( 4 ) ( i
8 Exracing he Harmonic The funamenal componen of curren i 1 i he Fourier componen ha i a he ame frequency a he volage. i 1( 1 1 ) = a.co( ) + b.in( ) We can ue a phaor iagram o a hee wo componen remembering ha co() lea in() by 90 i 1 () a 1 co() φ 1 b 1 in() i 1 ()= 2. 1 in(+φ 1 ) where 1 i he rm of he funaemanal = a b =. = a1 1 0 an φ 1 i he phae hif of he funamenal = an ( ) = an ( ) = 0 b 1 1 Error in MUR eqn 3-27 Noe any oher harmonic componen n an f n be calculae in he ame way. 24-Nov-03 Single Phae Unconrolle Recifier 8
9 Power Facor wih non-inuoial curren Curren i no a inewave => Power facor i no merely co(φ) Can ue he more general efiniion of power facor PF= Real Power / Apparen Power = P/S For recifier ecribe above: PF = P S 2 2 V. = V. = 2 2 = Nov-03 Single Phae Unconrolle Recifier 9
10 Diplacemen Power Facor The iplacemen power facor (DPF) i he power facor ha woul arie from he phae hif of he funamenal DPF = co(f 1 ) For he recifier we are looking a DPF = co(0)=1 f he volage i a pure inewave hen only he funamenal componen of curren give real power an he overall power facor (PF) in he preence of harmonic i lower by he raio of he rm of he funamenal o he overall rm. PF=P/S=DPF. 1 / For he recifier we are looking a PF = 1x0.9 / =0.9 o all of he power facor reucion in hi cae come from harmonic 24-Nov-03 Single Phae Unconrolle Recifier 10
11 A ueful rick wih rm quaniie We can expre a repeiive waveform a he um of harmonic componen: i ( 2 ) = in( + φ1 ) in( + φ ) +... f we quare an inegrae on he way o geing he rm ( ) he cro prouc erm inegrae o zero. So he overall rm become: = Thi i uually expree a : = c i The above i an exremely ueful equaion relaing he rm, he c componen, he funamenal an he iorion of a waveform 24-Nov-03 Single Phae Unconrolle Recifier 11
12 Toal Harmonic Diorion Toal harmonic iorion (THD) i an inex ue o quanify he amoun of iorion in a waveform THD i efine a THD =.100% f he waveform ha no c componen hen THD can be calculae a: THD = f he volage i inuoial hen only he funamenal componen of curren give rie o ueful power. The harmonic componen give rie o exce heaing in cable an may inerfere wih oher equipmen. eally THD houl be a cloe o 0% a poible. The recifer wwe have examine ha a THD of 2 2 i THD = % ( ).100% = 48% 24-Nov-03 Single Phae Unconrolle Recifier 12
13 Effec of Source nucance i V L v V 24-Nov-03 Single Phae Unconrolle Recifier 13
14 Source nucance Waveform v A µ 0 µ i 0 µ v l 0 µ i 1 µ 0 24-Nov-03 Single Phae Unconrolle Recifier 14
15 Effec of ource inucance ake ime for he curren in L o revere. During he commuaion inerval µ (in raian) he volage v clampe o zero. Effec of ource inucance: Average oupu volage i reuce Diplacemen power facor i i-improve THD i uually improve 24-Nov-03 Single Phae Unconrolle Recifier 15
16 Equaion During Commuaion v = 0 o v l = v an he curren i in L mu change from - o +. i L. 1 = µ ( ) µ vl = v L. i = v. =. v. = A µ bu i =2 o A µ =2..L. olving he inegral equaion we can how ha L co( µ ) = 1 2. V The oupu volage V i ill he average of v bu hi ime i v ha a chunk equal o A µ aken ou once every raian. V = V o A 2 2. V 2. L. µ = 24-Nov-03 Single Phae Unconrolle Recifier 16
17 Problem 3 One of he ioe in a brige recifier ha faile open circui. You may aume ha all componen are ieal. The loa i highly inucive an ource inucance may be neglece 1. Plo he circui waveform (v (), i (), ioe curren, v ()) 2. Derive expreion for oupu DC volage (V ), npu Power facor (PF), Diplacemen power facor (DPF) an oal harmonic iorion (THD) 3. Buil a pice moel of he circui an ue i o verify your anwer. Hin: a) The circui will behave like a half wave recifier. b) 2 = c i 2 c) Suggee value for imulaion v (): 100V peak (70Vrm), 50Hz L 1 =100H, R loa = Nov-03 Single Phae Unconrolle Recifier 17
18 Brige Recifier wih Capaciive Loa 24-Nov-03 Single Phae Unconrolle Recifier 18
19 Aumpion eal Dioe Highly Capaciive RC >>T => Capacior volage no vary over coure of cycle =>Like a conan volage ource loa Curren i zero prior o every zero croing of volage => Commuaion inerval i zero. 24-Nov-03 Single Phae Unconrolle Recifier 19
20 Recifier wih Conan volage Source Loa i i 24-Nov-03 Single Phae Unconrolle Recifier 20
21 Recifier wih a cie volage 24-Nov-03 Single Phae Unconrolle Recifier 21
22 DC-Sie Volage an Curren Relaionhip Zero curren correpon o c volage equal o he peak of he inpu ac volage 24-Nov-03 Single Phae Unconrolle Recifier 22
23 Effec of DC-Sie Curren on THD, PF an DPF Very high THD a low curren value 24-Nov-03 Single Phae Unconrolle Recifier 23
24 Cre Facor veru he Curren Loaing The Cre Facor i very high a low value of curren 24-Nov-03 Single Phae Unconrolle Recifier 24
25 Dioe-Recifier wih a Capacior Filer Power elecronic loa i repreene by an equivalen loa reiance 24-Nov-03 Single Phae Unconrolle Recifier 25
26 Line-Volage Diorion PCC i he poin of common coupling 24-Nov-03 Single Phae Unconrolle Recifier 26
27 Line Volage Diorion Real Life AC line ha ome ource impeance ( uually inucive L 1 ) The harmonic curren componen will caue a harmonic volage o appear acro hi impeance = v The harmonic componen of v pcc i: v in ( vpcc) i = L1 n 1 Noe ha he inucive naure of ource impeance will en o amplify he effec of harmonic a higher frequencie L pcc 1 i 24-Nov-03 Single Phae Unconrolle Recifier 27
28 Line-Volage Diorion Diorion in volage upplie o oher loa 24-Nov-03 Single Phae Unconrolle Recifier 28
29 Volage Doubler Recifier n 115-V poiion, one capacior a-a-ime i charge from he inpu. 24-Nov-03 Single Phae Unconrolle Recifier 29
30 Effec of Harmonic on Neural Curren Three Phae yem normally expec phae curren o um o zero o no neural or a very ligh neural wire i require Bu if here are a lo of ingle phae recifier on each of he phae Triplen Harmonic a cumulaively o neural wire can carry a ignifican 3 r harmonic componen See MUR ecion 5-5 for example. 24-Nov-03 Single Phae Unconrolle Recifier 30
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