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+=R
VI mavgo F٣ J٣E
אאאאאא'Im'W
)cos1.(2)( απ
+= II mavgo F٣ J٤E
ImאאאVm/R K
א٢٦١ א א א
אאא א
- ٣٩ -
٣ J٢ J٢אאאR.M.S. value of the load voltage and current אאאאאאאאF٣ J٢E
W
)2
2sin1(.2)( π
απα+−=VV m
rmso F٣ J٥E אאאאאאW
)2
2sin1(.2)( π
απα+−= II m
rmso F٣ J٦E
אאאאאאאFαEאאFαEאאאFαEאK
אא(Vdo)א)0( =α אF٣ J١EVdoW
πVV m
do = F٣ J٧E
אאאVo אאאאאאא
אאאK
٣ J٢ J٣אא(Power Factor) אא'PF'אאא'P'אאא'S'אW
SPPF = F٣ J٨E
אאאאאאאא
RIP rmso2= F٣ J٩E
RIP rmsS2= F٣ J١٠E
rmsSrmso II =
א٢٦١ א א א
אאא א
- ٤٠ -
אאאאאאF٣ J٩EF٣ J١٠EאF٣ J٨EW
s
rmso
VRI
PF )(= F٣ J١١E
אאאאאאאא'R'אF٣ J٦EאF٣ J١١EW
)2
2sin1.(21
πα
πα+−=PF F٣ J١٢E
٣ J١W
אאאאא120
VKאאא10 Ω،אאא'Vo'א'PL'אאאW
FE α = 0o FEα = 45o FEα = 90o FEα = 135o FEα = 180o
אW
אאאא'Vm'W 7.16921202 ===VV sm
V
אא'Vo(avg)'א'PL'אאF٣ J١EF٣ J٩EW
)cos1.(2)(
απ
+=VV mavgo
RIP rmsoL2
)(=
FEאאα = 0oאאW 54)0cos1.(
27.169
)( =+= oavgoV π
V
485.80120
7.169)2
2sin1(.2)( =−=+−=
πα
πα
RVI m
rmso A
72010.485.8 22)( === RIP rmsoL W
א٢٦١ א א א
אאא א
- ٤١ -
FEאאα = 45oW
1.46)45cos1.(2
7.169)(
=+= oavgoV π
V
09.8290sin1.
180.451.
207.169 0
)( =+−=ππ
πI rmso A
55.65410.09.8 2 ==∴PL W
FEאאα = 90oW 27)90cos1.(
27.169
)(=+= o
avgoV πV
62180sin1.
180.901.
207.169 0
)( =+−=ππ
πI rmso A
36010.62 ==∴PL W
FEאא:α = 135o 91.7)135cos1.(
27.169
)(=+= o
avgoV π V
56.22270sin1.
180.1351.
207.169 0
)( =+−=ππ
πI rmso A
4.6510.56.2 2 ==∴PL W
FEאאα = 180oW 0)180cos1.(
27.169
)(=+= o
avgoV π V
02360sin1.
180.1801.
207.169 0
)( =+−=ππ
πI rmso A
0=∴PL W
אאאאאאאא'α'אאW
α 0 45o 90o 135o 180o Vo(avg) V 54 46.1 27 7.91 0 PL W 720 654.6 360 65.4 0
א٢٦١ א א א
אאא א
- ٤٢ -
٣ J٢W אאאאא120
VKאאא10 Ωאאא‘α’60o،W J אאאאא'PL'K J אאא'PF'K
אW J אאא'Im'W
97.1610
2120===
RVI m
m A
J אאW RIP rmsoL
2)(=
)2
2sin1(.2)( π
απα+−= II m
rmsoQ
5792120sin
180.601.(10.
497.16)
22sin1.(.
4
22
=+−=+−=∴π
πππ
απαRmI
PL W
J א' PF'אאF٣ J١٢EW
)2
2sin1.(21
πα
πα+−=PFQ
634.)2120sin
180.601.(
21
=+−=∴π
ππ
PF Lag.
٣ J٣W
אאאאא150 V60 Hz10 ΩKאאא'α'30o،W
J אאא'Im'K J אאא'Vo(avg)'K J אאא'Io(avg)'K J אאא'Io(rms)'K J אאא'PL'K
א٢٦١ א א א
אאא א
- ٤٣ -
J אא'γ'K J א'fo'K J אא'PF'K
אW J אאא'Vm'
21221502 ===VV sm V
J אאא‘Im’
2.2110212
===R
VI mm A
J אאא‘Vo(avg)’
63)30cos1.(2212)cos1.(
20
)( =+=+=π
απ
VV mavgo V
J אאא‘Io(avg)’
3.61063)(
)( ===R
VI avgoavgo A
J אאא‘Io(rms)'
45.102
60sin180
.301.2
2.21)2
2sin1(.2)( =+−=+−=
ππ
ππα
πα o
mrmso
IIQ A
J אאא'PL' WRIP rmsoL 109210.45.10 22
)( === J אא'γ''R'
oooo 15030180180 =−=−= αγ אFאEאאאא
F٣ J٣KEאא'fo'אאW 60== ff so
Hz
J אא'PF'
)2
2sin1.(21
πα
πα+−=PFQ
7.0)2
60sin180
.301.(21
=+−=∴π
ππ
PF Lag.
א٢٦١ א א א
אאא א
- ٤٤ -
٣ J٣אאאאאא Single-Phase Half-Wave Controlled Rectifiers with an Inductive Load 'R-L'
אF٣ J٤Eאאאא
‘R-L’אF٣ J٥Eאא'vs'א'vo'א'io'אאאא'vT'K
אF٣ J٤WEאאאא'R-L'K
٣ J٣ J١אאW אאF٣ J٥EW
אאא'Vs'FEא’α’אאא
אאאאאωt = αאא'α'אא⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛= −
RωLtanΦ 1א
אאאאאא'β'אאא(Extinction angle)K
אאאא180oאאאאאא
אאאאאאאאאאאאאאאא
א٢٦١ א א א
אאא א
- ٤٥ -
אא'β'א180oאאאאאאβωπ ≤≤ tKאאאא'vT'אאאα < ωt <β א
F٣ J٥Eאאאא'R'אאK
אF٣ J٥WEאאאאF٢ J٤E
א٢٦١ א א א
אאא א
- ٤٦ -
٣ J٣ J٢אאאW אאאאאאאא
F٣ J٤EW
)cos.(cos2)(
βαπ
−=VV mavgo
F٣ J١٣E
אאאאW
)cos.(cos2
)()( βα
π−==
RRVVI mavgo
avgo F٣ J١٤E
אא' β'אאW φβα
φααβ tan)
().sin()sin(
−
−=− e W
αאא Φאאאא⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛=Φ −
RLω1tanK
אא' β'אF٣ J٦Eאא'α'אא'Φ'Kβ Φ א
αאא'γ'β(β = γ + α)KאF٣ J٦EאאאΦ = 0oאא'R' אΦ = 90o
אאא(L)K
٣ J٣ J٣W אאW
• אא'α'WאאאאאאאאאאאאK
• אא'β'WאאאאאאאאאאK
• אא'γ'WאאאאאאK
א٢٦١ א א א
אאא א
- ٤٧ -
אF٣ J٦Eאא'α'א'β'אא'Φ'
٣ J٤ אאאאאאאאא Single-Phase Half-Wave Controlled Rectifiers with an Inductive Load and a Free-Wheeling Diode
אאאאאאאאאאאא
אאאאאאא(Free-wheeling diode)K
אF٣ J٧Eאאאא‘R-L’אאאאאאאאא
אאאאאאאאאאאא(Short-circuit)אאאאאאא
אאF٣ J٧KE
α
א٢٦١ א א א
אאא א
- ٤٨ -
אF٣ J٧Eא 'R-L'אאK
٣ J٤ J١אאW אאאF٣ J٧Eאאא
F٣ J٨EKאאאאאאא
אא'α'אאאאאF٣ J٨KEאאא
0א < ωt < αאאאא'α'אאאאωt = αא
אאאאאאאא'β'Kאאα < ωt < β
α <ωt < π،βωπ ≤≤ tאאאα < ωt < πאאאאאאאאאאא'vs'אא'R-L'
א'vo'א'vs'vo = vsאאאאא
אאKאF٣ J٨Eאאωt = πאאאאאאFאאאE
אאאβωπ ≤≤ tאאאאאאאאאאא
א٢٦١ א א א
אאא א
- ٤٩ -
אאאאאאאאאאאאאאאאאא
אאאK
אF٣ J٨WEאאאאF٣ J٧E
٣ J٤ J٢אאאW אאאאאאW
א'vo'אאאKאאאא
אאאאאאאאאK
א٢٦١ א א א
אאא א
- ٥٠ -
אאאאאאF٣ J١E،F٣ J٣EW
)cos1.(2)(
απ
+=VV mavgo
)cos1.(2)( απ
+=R
VI mavgo
٣ J٤W אאאאא 150 V
60 HzאאKאא'R'א10 Ωאא'ωL'10 ΩKאאא30oאא،
אK
אW אאאאאW
)cos1.(2)( απ
+=VV mavgo
)cos1.(2)( απ
+=R
VI mavgo
אא
63)30cos1.(2
2150)(
=+= oavgoV π
V
3.61063
)( ==I avgo A
٣ J٥אאאאאSingle Phase Full-Wave Controlled Rectifiers
٣ J٥Z١אאResistive Load אF٣ J٩Eאאאאא،א
אא‘Vs‘ ’R‘.אאאאF٣ J٩KE
א٢٦١ א א א
אאא א
- ٥١ -
אF٣ J٩WEאאאאאא 'R'K
٢ J٥ J١ J١אאאאאW אאאאא’T1, T2‘
אאא’T3,T4‘אאאאאאאאאאא
אאאאאאKאT1T4אא0 ≤ ωt ≤ π
אT2T3אπ ≤ ωt ≤ 2πאאאא’Pulse Transformer‘
אאא’Opto-Coupler‘K
٣ J٥ J١ J٢ אאW אאאF٣ J٩Eאאא
F٣ J١٠KEאT1אT4א’α‘אאאא’0 ≤ ωt ≤ π‘אא
אאT1,T4אאאא
אאאאאאאאvsאT1אא’R‘אT4א’Vo‘אא
אא’R‘אFאאEאאK
א٢٦١ א א א
אאא א
- ٥٢ -
אאאאאאאT2,T3אאאאא+ παאאא
אאאאאא T2אא’R‘ אT3 אאאT4,T1אT2,T3 180o
אאאאאאאאאT1אT4 א
T2אT3 אא’vAK‘אאאאא’is‘
אאא’io‘אאא
אאKאπאאאאK
אF٣ J١٠WEאאאאאאא
'R'K
א٢٦١ א א א
אאא א
- ٥٣ -
٣ J٥ J١ J٣אאאW F٣אאאאא J٩Eאא
אאאאאאאאאF٣ J٢EאאאאאW
)cos1.()( απ
+=VV mavgo
F٣ J١٥E
אאאאאW
)cos1.()()( α
π+==
RRVVI mavgo
avgo F٣ J١٦E אF٣ J١٦EW
)cos1.()( απ
+= II mavgo F٣ J١٧E
W Vmאאאאא
Vsאאאאא ImאאאאIm אאW
RRVVI sm
m
2== F٣ J١٨E
٣ J٥ J١ J٤אאאW אאאאאאאא
F٣ J٩EW
)2
2sin1(.2)( π
απα+−=VV m
rmso F٣ J١٩E
אאאאאאW
)2
2sin1(.2)( π
απα+−= II m
rmso F٣ J٢٠E
א٢٦١ א א א
אאא א
- ٥٤ -
٣ J٥W אאאא
150אV60 Hzאא’R‘10 Ω Kאאא30o،W
J אאא‘Vo(avg)’K J אאא‘Io(avg)’K J אא’Im‘K J אאא'Io(rms)'K J אאא'PL'K J א'fo'K J אא'PF'K
אW J אאאאW
)cos1.()( απ
+=VV mavgo
126)30cos1.(2150)(
=+=∴ oavgoV π
V
J אאאW
6.1210
126)()( ===
RVI avgo
avgo A
J אאאW
2.2110
2150===
RVI m
m A
J אאאW
77.14260sin
180.301.
22.21)
22sin1(.
2)( =+−=+−=π
πππ
απα o
mrmso
II A
J אאאW WRIP rmsoL 218210.77.14 22
)( ===
J אאאא 120)60.(22 ===∴ ff o
Hz
א٢٦١ א א א
אאא א
- ٥٥ -
J אאאאא ’Io(rms)‘ אאא’Is‘
VI
IVI
s
orms
ormss
orms RRPF ==
2
98.0150
)10.(77.14==∴PF Lag.
٣ J٥ J١ J٥אא’R-L‘ אF٣ J١١Eאאאאאא
א(R-L) K
אF٣ J١١WEאאאאא 'R-
L'K
٣ J٥ J١ J٦ אאW אאאT1,T4
אאאא ωt = αאאT2,T3אאאאא ωt = α + πאF٢ J١٢Eאאאאאא
Kאאαא
א٢٦١ א א א
אאא א
- ٥٦ -
T1,T4אאאאאא ’vs‘ ωt = πאאאאאT4אאאT1 א
אא אאאאאRאאאvo
אvsאאאאאא אא’β‘אT1, T4
אאא’vo‘אאβωπ ≤≤ t אאאאאא’L‘אא
אKאF٣ J١٢EאT2, T3אאωt = π + αאאא
אאאאאא ’Vs‘אT2אאאT3אאא
אאωt = π + βאאאאאא’ωL‘אא
אאאאאאאאאאאאאא
F٣ J١٢E،F٣ J١٣EאאאאKאF٣ J١٢Eאא
180oאאא’is‘360oאF٣ J١٣Eאא
’β‘π + αאאאאאאאאא
K
א٢٦١ א א א
אאא א
- ٥٧ -
אF٣ J١٢WEאאאאאאא
'R-L'K
אF٣ J١٣WEאאאאאאא
אK
א٢٦١ א א א
אאא א
- ٥٨ -
٣ J٥ J١ J٧אאאW אאאאאאאא
F٣ J١١EאאאFאאאEW
)cos.(cos)(
βαπ
−=VV mavgo
F٣ J٢١E אאאאאאאא
F٣ J١١EאאאאFאאאEאאW
απ
cos.2)( VV mavgo= F٣ J٢٢E
אאאI avgo )(Vo(avg)/R אאאאאאאא
F٣ J١١EאאאFאאאEW
)cos.(cos)( βαπ
−=R
VI mavgo F٣ J٢٣E
אאאאאאאאF٣ J١١EאאאFאאאEW
απ
cos.2)( VI mavgo R= F٣ J٢٤E
אF٣ J٢٢Eאאאא0 א 90oאא
(rectifier)אא 90o 180oאאאא(inverter)א
אאאאאאאאאאאאא(2-Quadrant)אא
אאאאאאאאאאאאאK
א٢٦١ א א א
אאא א
- ٥٩ -
٣ J٥ J١ J٨אאאVAKW
אT1FEאT2FEאאאT2
אאאT1אאאאאאאvsאT1אT2
אאאאאW
VVV TsT 12 += F٣ J٢٥E אאT1א
אאT2אאvssT vv =2אT1K
٣ J٦W
אאאא230אV60 Hzאאא
א ’ωL >> R‘א.0.5 Ω אאאא200א VK
אW אאאא ωL >> Rא
F٣ J٢٢EW α
πcos.2
)( VV mavgo=
απ
cos).2230.(2200 =∴ o15966.0cos =∴=∴ αα
٣ J٧W אאאא א
120V 60 HzאאאאωL >> R’‘א.10 Ω אאא30o،W
א٢٦١ א א א
אאא א
- ٦٠ -
J אאא’Vo(avg)’K J אאא'Io(avg)’K J אאא’Im‘K J אאא'Io(rms)'K J אאא’IoTh‘K J אאא'PL'K J אא’PF‘K
אW J אאאאא’Vm‘
17021202 ===VV sm V
J אאאFאE 9430cos.170.2cos.2
)(=== o
mavgo VV πα
π V
J אאא
6.91094)(
)( ===R
VI avgoavgo A
J אאאאאאW 4.9)( == II avgom A
J אאאאאאW AII avgormso 4.9)()( ==
J ’180o‘אאאאא
7.424.9
21
)( === II avgooTh A
J אאא WRIP rmsoL 3.88310.4.9 22
)( ===
J אאאאאאאאא Io(rms) = Is (rms)W
.78.012094)( lag
VRI
PFs
rmso ===
א٢٦١ א א א
אאא א
- ٦١ -
٣ J٥ J٢אאאאW
אאאאאF٣ J١١EאאאאאאFאEא
אאאKאאאאאאאאאאאאאאאא
אF٣ J١٤EאאאאאK
אF٣ J١٤WEאאאאא
אאK
٣ J٥ J٢ J١ אא אאאF٣ J١٤Eאאא
F٣ J١٥Eאאא’ωL >> R‘אאאאW
אאT1,T4אאאא ωt = αאאאאאאא ’vs
אT1 אאאT4אאאאωt = π אא(α ≤ ωt ≤ π)אאאא
Kאאאאאאאωt = πאאאא
אאאאאאאא
א٢٦١ א א א
אאא א
- ٦٢ -
אא(π ≤ ωt ≤ π +α)אאאא אאאאאאאאאאאא
אאאא’is‘אאאאאאאא’ωt=π +α‘
אאT2 ,T3אאאאאאאאT2אאאT3א
אאא’vo = -
vs‘אאאωt = 2πאאאאאωt = 2 π + α אאאאאאאא
אאאאאאאאאא
אאT1,T4KאF٣ J١٥Eאאאא
אאאאאאאאאF٣ J١٥Eאאאאא
אאאisK
אF٣ J١٥WEאאאאאאא
אאאK
א٢٦١ א א א
אאא א
- ٦٣ -
٣ J٥ J٢ J٢אאאW אF٣ J١٠E،F٣ J١٥E
אאאאאאאאאFF٣ J١٥EW
)cos1.()( απ
+=VV mavgo
F٣ J٢٦E אאא
)cos1.()()( α
π+==
RRVVI mavgo
avgo F٣ J٢٧E
٣ J٥ J٢ J٣אאאאא אאאאF٣ J١٥Eא
אאאאאאא2π
אאאאאאαאאאאאW
)cos1.(. 2)()( απα
πα
+==R
VII mavgoavgD F٣ J٢٨E
٣ J٨W אאאא א
120V 60 Hzאאאא’ωL >> R‘א10 ΩאאKאאא
30o،W J אאא'Vo(avg)'K J אאא'Io(avg)' J אאא’Im‘K J אאא'Io(rms)'K J אאאאאא’ID(avg)‘K J אאא’IoTh‘K
א٢٦١ א א א
אאא א
- ٦٤ -
J אאא'PL'K J אא’PF‘K
אW J אאאאא’Vm‘
17021202 ===VV sm V
J אאאFאE
101)30cos1.(170)cos1.( 0)(
=+=+=π
απ
VV mavgo
V
J אא
1.1010101)(
)( ===R
VI avgoavgo A
J אאאאא
1.10)( == II avgom A
J אאאאא 1.10)()( == avgormso II A
J אאאאא 683.1)
18030(1.10.)()( ===
παII avgoavgD A
J(π-α)2πאא
21.4)1.10.(360150.
2)(
)( ==−
= II avgooTh παπ A
J אאא 102010.)1.10( 22
)( === RIP rmsoL W
J אאW
)()( 1201020
rmssrmsss
L
IIVPPF == (I)
Is(rms)אאאאW
AII avgormss 22.9180150
1.10)()( ==−
=π
απ (II)
א٢٦١ א א א
אאא א
- ٦٥ -
(II)א(I)W 92.0
)22.9.(1200201
==PF Lag.
אאאאאאאאאאאאאאא
אאאK
٣ J٦אאאאאאא'R-L' Single-Phase Full-Wave Half-Controlled Rectifiers with an Inductive Load
אאאאא
אאאאאאאאאאאא
אאאאאאאאאאאאאא
אאאאאאאאאאאא
אאאאאאא(1-Quadrant)אF٣ J١٦Eאאאאא
אF٣ J١٦EאאאF٣ J١٠EאT3, T4אD3, D4F٣ J١٦KE
٣ J٦ J١אאאאא אאאאאF٣ J١٧E
אאא’ωL >> R‘אאאאW
א٢٦١ א א א
אאא א
- ٦٦ -
F٣ J١٦WEאאאאא 'R-L'K
אאT1אαאאאאאאאאאאאא
א’vs‘אT1אאאאD4אאאאωt
= πאאאאאα ≤ ωt≤ πא’io‘אאא’is‘אא
אאאאאאאωt = πאא
אא’io‘אאאאאאאא’T1‘אאאאD3אאאאאωt = π + αאאאאא
אאאאאאאאאאאאF٣ J١٤KEא
אאωt = π + αאאאאאאאאאאא’vs‘אT2אאאאD3
א אאאωt = 2πאאאא
א٢٦١ א א א
אאא א
- ٦٧ -
אπ + α ≤ ωt≤ 2πאאאאאאאאא
אאאאא2π ≤ ωt≤ 2π + α אאאאאאאאT2אא
אאD4אאאאאT2אאD4אאאאאאF٣ J١٤KE
אאאאאאאאF٣ J١٤Eאא
K
אF٣ J١٧WEאאאאאא
אK
א٢٦١ א א א
אאא א
- ٦٨ -
٣ J٦ J٢אאא אאאאF٣ J١٦E
אאאF٣ J١٤EאאאאF٣ J٢٦E،F٣ J٢٧EאאF٣ J١٤EW
)cos1.()( απ
+=VV mavgo
F٣ J٢٩E אאא
)cos1.()( απ
+=R
VI mavgo F٣ J٣٠E
٣ J٩W אא’vo‘אאאאאא
F٣ J١٦Eאאא120V60 Hzאאאא ’ωL >>
R‘א10 ΩאאW FE α = 0K FE α = 45oK FE α = 90oK FE α = 135oK
אW אאאאא
אאאאאאאאאαK
FE אאאאאT1אאD4אאאα = 0
אאאאאאאאT2אאD3א
א٢٦١ א א א
אאא א
- ٦٩ -
אאF٣ J١٨FEEאא’vs‘א’vo‘K
FE אאאאT1אאD4אאאאω = 45oא ω = πאאאא0 ≤ ωt≤ 45o
אאאT1א’vo‘אאπ ≤ ωt≤ 225o
אאT2אאT2אאD3אאא
אF٣ J١٨FEEאא’vs‘א’vo‘K
FE אFEFEאאW
אא0 ≤ ωt ≤ 90° אאאא90אo ≤ ωt≤ 180oאאא
אT1אאD4אאאא180o ≤ ωt≤ 270o
אאאא270אo ≤ ωt≤ 360oF٣ J١٨FEEאא’vs‘א’vo‘K
FE אFEFEFEאא
אF٣ J١٨Eאא’vs‘א’vo‘K
א٢٦١ א א א
אאא א
- ٧٠ -
FE
FE
FE
אF٣ J١٨WEאאאאאאאK
א٢٦١ א א א
אאא א
- ٧١ -
٣ J٤אאאאThree phase controlled rectifiers
٣ J٤ J١
אאאאאאאאאאאאאאאא
אאאאאאאאאאKאאאאאאאאאאא
אאאאאאאאאאאאאא
אאאאאאK
אאאאאאאאאאאאאW
• אאK
• אאאאאK
• אאK
אאאאאאאאאאאאאאאK
אאאאאאאאאאאאאאא
אKאאאאאאאאאאאא
W
• אאאאאK
א٢٦١ א א א
אאא א
- ٧٢ -
• אאאאאאK
٣ J٤ J٢אאא Three - phase half – wave controlled rectifier connected with a resistive load (R )
F٣ J١٩EאאאאאR
אאאאאאאאאFאEא
אאKאvoאioאאאאאאo30<α
אאoo 12030 ≤≤ αאאאאK
אF٣ J١٩WEאאאאאK
٣ J٤ J٢ J١אאאא
אאאאאאאאF٣ J١٩Eאאא
אאα شعال واقعة في المدي ن قيمة زاوية اإلوتكوo30<α.
א٢٦١ א א א
אאא א
- ٧٣ -
אאWאאאאאאאאאאFE120°א
אאTh1FאאאT1אאt1 ωאEאTh2אT2אאאאאא
אTh2אωt = 120o + ωt1Th3אωt =
240o + ωt1אאאאאאאא Th1א
אאot 120+≤≤ αωαF٣ J٢٠EאאאTh2אאoo t 240120 +≤≤+ αωα
אTh3oo t 360240 +≤≤+ αωαאאαאאאא°= 30tωאאא(ωt = 0) AאFEאTh1αאTh2א120oאTh1אTh3אא120o
אTh2FEאאאאא120oאאאאאאKF٣ J٢٠E
אvoאאא(iA, iB iC) אioאTh1אαאא
אא FאEא120oאאא360oK
אF٣ J٢١ETh1אα = 0אאאא°= 30tωא°30אא
°− 30tωאאאאאאאא°≤≤° 15030 tωאA(vAN)
אאאאאTh1אאאאאאRאvANאא
Th2Th3אאKאTh2אא°≤≤° 270150 tωאאωt = 150o
א٢٦١ א א א
אאא א
- ٧٤ -
אאאא120oאאאB(vBN)אאאTh2
אאאאאRאvBNאאTh1Th3
אKאTh3אא°≤≤° 390270 tωאאωt
= 270oאאאC(vCN)אאאTh3אאאאאא
אRאvCNאאTh1Th2אאא360oאאKאא
Th1אאωt = 390oK
אF٣ J٢٠WEאאאאאא
א٢٦١ א א א
אאא א
- ٧٥ -
אאo30<αK
אF٣ J٢١WEאאאאא
א= 0αK
אF٣ J٢٠Eאvoאioאאא30° (α < 30°) אTh1Fאא
vA E א Th2 FאאvB Eא 120o Th3FאאvC E 120o
אTh2אvoאiovo ،io F٣ J٢٠EF٣ J٢١Eאאא
אאα < 30° אאאא α =0°. אאאVo(avg)אאא)(avgoI
W
ααπ
cos827.0cos2
33)( mmavgo VVV == F٣ J٣١E
א٢٦١ א א א
אאא א
- ٧٦ -
ααπ
cos827.0cos2
33)()( R
VV
RRV
I mm
avgoavgo === F٣ J٣٢E
VmאאאאאK ITh(avg)אאאא
אVTh(m)אאאfrF٣ J٢٠WE
3)(
)(avgo
avgTh
II =F٣ J٣٣E
)()( 3 mLmmTh VVV ==F٣ J٣٤E ff r 3=F٣ J٣٥E
)(mLV א(line voltage)fאK
٣ J١٠W אאאא208 V
(VL)60 Hzא10 ΩKאאא'α'20o،W
Jאאא'Im'K Jאאא'Vo(avg)'K Jאאא'Io(avg)'K Jאאא'ITh (m)'K J אאא'ITh (avg)'K Jא'vTh (m)'K J א'fr'K
אW
VVV
VVV
phasem
Lphase
170120*22
1203
2083
===
===
א٢٦١ א א א
אאא א
- ٧٧ -
JAR
VI m
m 1710
170===
JVVV omavgo 13220cos*170*827.0cos827.0)( === α
JAR
VI avgo
avgo 2.1310132)(
)( === JAII mmTh 17)( == JA
II avgo
avgTh 4.43
2.133
)()( ===
JVVVVV LmLmmTh 294220823 )()( ===== JHzff r 18060*33 ===
٣ J٤ J٢ J٢אאאא
אאאאאאאF٣ J١٩Eאא
אאאα אאאא°≤≤° 15030 α. F٣ J٢٢ E א א א אא א א
F٣ J٢٢ Eאא WאTh1אαא°≤≤° 15030 αא
א א א VAN א אRא א א ot 150' =ω אאאאVo
אא°≤≤° 15030 αאVo א א א א א א א
°+≤≤° 150180 αωt)120150( ' oo t +≤≤ αω א א Th1א אאTh1Th2Th3 אא
Th2 א א ot 150+= αω)120'( ot += αω א Th2א Th2 Th3 א א אTh2
א אRאVBN אא א
א٢٦١ א א א
אאא א
- ٧٨ -
)270120( ' oo t ≤≤+ ωαאאoo t 240270 ' +≤≤ αωאאאTh1Th2Th3 אא
א א Th3 א א ot 270+= αω)240'( ot += αωאTh3אTh2Th1 אא
אTh3אאRאVCNאא270240(א( ' oo t ≤≤+ ωαאאoo t 360390 ' +≤≤ αωאאאTh1Th2Th3 אא
אאTh1K
אF٣ J٢٢WEאאאאאא
אאא°≤≤° 15030 αK
א٢٦١ א א א
אאא א
- ٧٩ -
io،Vo א א αא אאVo(avg)א א א)(avgoIא
)15030( °≤≤° αW ( )[ ] ( )[ ]°++=°++= 30cos1477.030cos1
23
)( ααπ mavgo VVmVF٣ J٣٦E
( )[ ]°++== 30cos1477.0)(
)( αR
VR
VI mavgo
avgoF٣ J٣٧E
אאאαא°≤≤° 180150 αא)0( )( =avgoVK
٣ J١١W
אאאא208 V (VL)60 Hzא10 ΩKאאא'α'100o،W
Jאאא'Im'K Jאאא'Vo(avg)'K Jאאא'Io(avg)'K Jאאא'ITh (m)'K J אאא'ITh (avg)'K Jא'vTh (m)'K J א'fr'K
אW אאאTh1א100oאא
אvANאאאא)( )(loadmVאאאאW
א٢٦١ א א א
אאא א
- ٨٠ -
VVV
VVV
VVV
ooosourcemloadm
phasesourcem
Lphase
130)10030sin(170)30(sin
170120*22
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2083
)()(
)(
=+=+=
===
===
α
)(sourcemVאא)(loadmIאאאK JA
RV
I loadmloadm 13
10130)(
)( ===
J( )[ ]V
VVo
sourcemavgo
29)]10030(sin1[*)170*477.0(
30cos1477.00
)()(
=++=
°++= α
JAR
VI avgo
avgo 9.21029)(
)( === JAII loadmmTh 13)()( == JA
II avgo
avgTh 97.039.2
3)(
)( === JVVVVV LmLmmTh 294220823 )()( ===== JHzff r 18060*33 ===
٣ J٤ J٣אאאאאא
Three - phase full– wave bridge - controlled rectifier connected with a resistive load (R )
אאאאאאאאאאאאאאKF٣ J٢٣Eאאאאא
אאRאאאאאאFאאEאאאKאאTh1Th3Th5
אאאאאאאאאאאTh2Th4Th6א
אאאאאאאאKאאאא
FEאאאא60o360oK
אאFאאEאאFא
א٢٦١ א א א
אאא א
- ٨١ -
אEאאא(vL)אאאאאאאאTh3 Th2
אאאvBCKאאאא)(avgoVאא)(avgoIאאαK
אF٣ J٢٣WEאאאאאאאK
אאאאאאא
אאאאאאFאEאאא60oא
אאאאKאאאאאא
אאאאאK F٣ J٢٣Eאאא1
אאא2אאα אאא )٢٤-٣ (אא α אאא VCN,VAN א )א) ٢٤-٣אא
אא =0° α אאא F٣ J٢٤E
א٢٦١ א א א
אאא א
- ٨٢ -
Wאאאאא0°120°אאא Th1אאאא
אא VAN אאא1Aאאא120° 240° אTh3
אא1Bאא240° 360°אTh5אא1Cאא
אאv1NאאVANVBNVCNK אאאא2אTh4אא
אא°180300°אTh42אAאא300° حتى420° أو(60o) אTh6א
2אB אא60o180oאTh2אא2Cאאא(v2N) 2
א VANVBN VCNK א(v12) voNN vv 21 −KאF٣ J١EאאאK
א א1 א2 אv12
0o60o A B AB
60o120o A C AC
120o180o B C BC
180o240o B A BA
240o300o C A CA
300o360o C B CB
360o420o A B AB
F٣ J١E
א٢٦١ א א א
אאא א
- ٨٣ -
אF٣ J٢٤WEאאאאאא
= 0oαK אF٣ J٢٤Eאאאא
אאאאאFאEאfrא
אfKאאאאאאאא120o
240oKאאאאאאABCאאTh6Th5 Th4 Th3 Th2 Th1
אאאK אF٣ J١Eאא
אאTh1(vTh1 = vA1)אא0o120o01 =AVאTh1 אאא120o240o
א٢٦١ א א א
אאא א
- ٨٤ -
vA1 = vABא1Bאא240o360ovA1 = vACא1CKאF٣ J٢Eא
אאK
א vTh1vTh3vTh5 vTh4 vTh6 vTh2
0o60o
0
BA
CA
AB
0
CB
60o120o
0
BA
CA
AC
BC
0
120o180o
AB
0
CB
AC
BC
0
180o240o
AB
0
CB
0
BA
CA
240o300o
AC
BC
0
0
BA
CA
300o360o
Ac
BC
0
AB
0
CB
אF٣ J٢E א F٣ J٢٥ E א אvTh1 אא א
אאאאאא(VL(m))אאאαאא(α =0o)F٣ J٢٥Eא
א א0o120o א אא אא א א א K אF٣ J٢٦ E
אאiAiBiCאאF٣ J٢٥EW
א٢٦١ א א א
אאא א
- ٨٥ -
⎪⎩
⎪⎨
⎧
−=−=−=
25
63
41
iiiiiiiii
C
B
A
F٣ J٣٨E
א٢٦١ א א א
אאא א
- ٨٦ -
א F٣ J٢٥ WE א א vTh1אא א א אאאאא = 0oαK
א F٣ J٢٦ WEא א א א א א א א
= 0oαK
אאאאאאאאאאאאאאא
oo 600 ≤≤α א א א א oo 12060 ≤≤αK א א א
אאאoo 600 ≤≤αW
ααπ
cos654.1cos33)( mmavgo VVV == F٣ J٣٩E
ααπ
cos654.1cos33)()( R
VV
RRV
I mm
avgoavgo === F٣ J٤٠E
Vmאאא(Vphase (m))K אאא
אאאoo 12060 ≤≤αW
א٢٦١ א א א
אאא א
- ٨٧ -
)]30cos(1[654.1)]30cos(1[33)(
om
omavgo VVV ++=++= αα
π F٣ J٣٩E
)]30cos(1[654.1)()(
omavgoavgo R
VR
VI ++== αF٣ J٤٠E
٣ J١٢W אאאאאא
208א V (VL)60 Hzא10 ΩKאאא'α'20o،W
Jאאא'Im'K Jאאא'Vo(avg)'K Jאאא'Io(avg)'K Jאאא'ITh (m)'K J אאא'ITh (avg)'K Jא'vTh (m)'K J א'fr'K
אW אאאאאo20=α
אאoo 600 ≤≤α
VVV
VVV
VVV
phasem
Lphase
LmL
170120*22
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===
===
===
J AR
VI mL
m 419.2910
15.294)( === JVVV o
mavgo 26420cos*170*654.1cos654.1)( === α
JAR
VI avgo
avgo 4.2610264)(
)( === JAII mmTh 419.29)( == J A
II avgo
avgTh 8.83
4.263
)()( ===
א٢٦١ א א א
אאא א
- ٨٨ -
J VVVVV LmLmmTh 15.294220823 )()( ===== J Hzff r 36060*66 ===
٣ J١٣W i1i4אא(vSCR1) vTh1אאvoאא
אiAאאאאאאאאאW
Jאא'α'30oK Jאא'α'60o'K Jאא'α'90oK אW
Jאאאאאאא120o
אאאFאEאאאאFאEא60oאאאi1i4א
iAאאאא30oאF٣ J٣٨EאiA)( 41 ii −KאאאF٣ J٢٧EאאW
• אא09030 ≤≤ to ωאiAאTh1Th6אאvABiA = i1K
• אא015090 ≤≤ to ωאiAאTh1Th6אאvACiA = i1K
• אא0270210 ≤≤ to ωאiAאTh3Th4אאvBCiA = - i4K
• אא0330270 ≤≤ to ωאiAאTh5Th4אאvCAiA = - i4K
JאFEאאאאK
א٢٦١ א א א
אאא א
- ٨٩ -
F٣ J٢٨Eאאא60oK JF٣ J٢٩Eאאא90oK
אF٣ J٢٧WEאאאאאא
א٢٦١ א א א
אאא א
- ٩٠ -
= 30oαK
אF٣ J٢٨WEאאאאאא
א٢٦١ א א א
אאא א
- ٩١ -
= 60oαK
אF٣ J٢٩WEאאאאאא
א٢٦١ א א א
אאא א
- ٩٢ -
= 90oαK
W ٣ J١ אאא'vs'א'vo'א'io'
אאא'vAK': J אאאאא'R'
J אאאאאאאאK
٣ J٢ אאאא'Vo(avg)'אא'α'
אאאאאאאאא220VK
٣ Jא ٣אFאE'io'אאאאא
אאאאKW J אא 'α' J אא'γ' J אא'β'K
٣ J٤ אאאאאאאא؟א
אאאאאא؟אאאא K؟
א٢٦١ א א א
אאא א
- ٩٣ -
٣ J٥ אא'L'אאאאא 'io'Kאא؟
٣ J٦ אאאאאא
א(ωL>>R): J אאK
J אאK
٣ J٧ אא'vo'א'io'א'is'אאא:
J א'60°'K J א'60°'K
٣ J٨ אאאאאא220V60Hz50 ΩKאא'60°':
J אאא J אאא J אאא J אאK
٣ J٩ אאאאא
אKאא220V60Hz50 ΩKאאא'60°'K
J אאא J אאא J אאא J אאא
א٢٦١ א א א
אאא א
- ٩٤ -
J אאאאFאE J אאאאאK
٣ J١٠ אאאאאאאא220V60HzKא
אא20 Ωאא'60°'KW J אא J J אאא
٣ J١١אאאאאא؟
٣ J١٢אאאאאאאאאא
؟אא
٣ J١٣אאאאאW Jאאאא208 V
(VL)60 Hzא10 Ωא'α' 30oK
Jאאא 208 V(VL)60 Hzא10 Ωא
'α'60oK
٣ J١٤אאאא208
V (VL)60 Hzא10 ΩKא אא'α'30o،W
Jאאא'Im'K Jאאא'Vo(avg)'K
א٢٦١ א א א
אאא א
- ٩٥ -
Jאאא'Io(avg)'K Jאאא'ITh (m)'K J אאא'ITh (avg)'K Jא'vTh (m)'K
J א'fr'K
٣ J١٥אא 208א V (VL)60 Hzא10 ΩKא
אא'α'60o،W Jאאא'Im'K Jאאא'Vo(avg)'K Jאאא'Io(avg)'K Jאאא'ITh (m)'K J אאא'ITh (avg)'K Jא'vTh (m)'K J א'fr'K
אאאאDDCC
אא
א
א
DC
٤
אאא ٢٦١ א א
אאDC א
- ٩٦ -
אאW אאאאאאאW
• א • אאא • אאאאא • אאאאK
W
אאאאאאאאאאאאאאאא
אאאאאאאאאאאא
אאאאאאאאאKאאאאא
אאאאאאאאאאאאא(duty cycle)
אאאאאאKאאW
J step-down (buck) choppersאאאאאאאK
J א step-up (boost) chopperאאאאK
אאא ٢٦١ א א
אאDC א
- ٩٧ -
٤ J١אאאA Basic DC ChopperW אF٤ J١Eאאאא
אSאא’Vs‘RKאא’Thyristor‘אא’Power
Transistor‘'MOSFET'אאאא'Insulated Gate Bipolar
Transistor'אK אאאא’switches‘
'ideal'אאאאW J אאאא
א’turn-on‘K J אאאאא
’turn-off‘K J אאאאאK
אאאאא’power loss‘א
אאאא’Input dc power‘אא’output dc
power‘W
IVIV ooss= F٤ J١E
W : VsאאK : Voאאא?אK?
IsWאאאאK IoWאאאK
אאא ٢٦١ א א
אאDC א
- ٩٨ -
אF٤ J١WERK
٤ J٢אDuty CycleW אאאאאאא
’TOFF‘א’TON‘אאאאאאאאאF٤ J٢Eא
אKא’D‘אאא’TON‘אאא’T‘אאאW
TD T
TTT ON
OFFON
ON =+
= F٤ J٢E
W DWאאאאTK :TאאאK
:TONאאFאאEK :TOFFאאFאאEK
אF٤ J٢WEאאאK
VPULSE
TON 0 T T+TON
t
TOFF
אאא ٢٦١ א א
אאDC א
- ٩٩ -
אF٤ J٢Eאאאאא(0 ≤ D ≤ 1)
אאאאאאאאאאא
אאKאאאאא’Base current‘אאא١א
אאאאאאאאאאא
אאאאאאאאאא(Auxiliary Circuit)FEאאא’Commutation
circuit‘Kאאאאאאאאאאאאא
אאאאאאאאאאK
٤ J٣אאאאR The Principle of Operation of a Basic DC Chopper Connected with a Resistive Load:
אא’vo‘אאאF٤ J١E
אאא’Vs‘(0 ≤ vo ≤ Vs)אאאא’S‘אאא
אKא’vo‘אא'S'אא'OFF'א
א’vo‘אא’Vs‘אא'S'אא'ON'אאאF٤ J٣E
א’vo‘K
אאא ٢٦١ א א
אאDC א
- ١٠٠ -
אF٤ J٣WE’vo‘אאK
٤ J٣ J١אאאאW
אאאא’Vo‘W
VTVTTTV s
ONs
OFFON
ONo T
.. =+
= F٤ J٣E
אF٤ J٢EאF٤ J٣Eאאאאא
VV so
D= F٤ J٤E
אF٤ J٤Eאאאא’Vo‘א’D‘אF٤ J٤EאאVoא
א’Vs‘0 ≤ V0 ≤ VsK אאאאא’Io‘אאאאF٤ J٣E
אאא’Io‘אאאאאאאאW
VVI so
o RD
R.== F٤ J٥E
אאא ٢٦١ א א
אאDC א
- ١٠١ -
אF٤ J٤WEאאאא’Vo‘א’D‘K
٤ J٣ J٢אאאאW
אאאא’Vo(rms)‘אא’Io(rms)‘W
DVV srmso =)( F٤ J٦E
DIDRV
I Ps
rmso ==)( F٤ J٧E
WאIPאאאRVsK
٤ J٣ J٣אאW אאאאאאא
אאא’Pi‘א’POrms‘KאאאאאאאW
RIR
VR
VDPP orms
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אt2 ≤ t ≤ TאS2 S3 אאאאאאאאאאS2, S3אאא
'Vs' א א א א Vo = - Vsא'Imin'אאt=T t=0
א'Imax'אא t=3⋅T/2 t=T/2אIminאאאאאאא
אK
אא ٢٦١ א א
א א
- ١٣٧ -
אF٥ J٩WEאאאאאאאאאאאאאK
אא ٢٦١ א א
א א
- ١٣٨ -
אאאאW אאאא
א א א א א א אF٥ J٢KE
אאאW
אאאאאאW
⎪⎪⎩
⎪⎪⎨
⎧
≤≤++−
≤≤−+=
−−
−
TtTeR
VI
RV
TteR
VI
RV
iTtSS
tSS
O
2)(
20)(
/)(max
/min
2 τ
τ
F٥ J٤E
W τ WאאאL/RK
IminWאאאK ImaxWאאאK
א א א א א א א
W
II maxmin −= F٥ J٥E אאאאאW
⎥⎦
⎤⎢⎣
⎡
+−
=−=−
−
τ
τ
2/
2/
minmax 11
T
Ts
ee
RVII F٥ J٦E
٥ J٣W
אאאF٥ J٨E'R'א10 ΩאL = 25 mH'Vs'100 VKא
א60א Hz،אאK
אא ٢٦١ א א
א א
- ١٣٩ -
אW אאאאאאW
0167.06011===
f o
T s
0025.010025.0
===RLτ s
67.60025.0*2
0167.02
==∴τ
T
אאאאאאF٤ J٥EW
31.911.
10100
67.6
67.6
minmax =⎥⎦
⎤⎢⎣
⎡+−
=−=−
−
eeII A
אאאאF٤ J٤EW
( )
( )601
120131.1910
1010031.9
10100
1201031.1910
1010031.9
10100
0025.0/)00835.0(0025.0/)2
0167.0(
0025.0/0025.0/
≤≤+−=⎟⎠⎞
⎜⎝⎛ ++−=
≤≤−=⎟⎠⎞
⎜⎝⎛ −−+=
−−−−
−−
teeti
teeti
tt
o
tto
٥ J٤אאInverter Voltage Control Techniques אאאאא
אאאאאW ١K אאאK ٢K אאאK ٣K אאאK
אאאאאא
אאאאאאאאאא
אאאאאאאאא
אא ٢٦١ א א
א א
- ١٤٠ -
אאאאאאK
אאאאאאאאאא’PWM‘אאא
אאאאאאאא
אאK
٥ J٤ J١אPulse-Width Modulation PWM אאאאאאא
אW ١K אSingle Pulse-Width ModulationK ٢K אMultiple Pulse-Width ModulationK ٣K אSinusoidal Pulse-Width ModulationK
٥ J٤ J١ J١א אאאאא
KאF٥ J١٠Eאאאא S2 S1אאאא
אאF٥ J٦EאArAcKאאאאאFאאEאArAcאδא
אא180oArAcא’Modulation Index‘אאW
AA
c
rM = F٥ J٦E
אאא’Vo‘אW
אא ٢٦١ א א
א א
- ١٤١ -
πδVV so
= F٥ J٧E W
MWאK VsWאאאK ArWאאאK AcWאאאK δ :א.
אF٥ J١٠WEאאאאS2, S1
אא
٥ J٤ J١ J٢א אאאאאא
אאאאfoאאא
אאאאאאאאfcKאF٥ J١١Eאאאאאא
אאאאאW
אא ٢٦١ א א
א א
- ١٤٢ -
ff
mmff
o
cf
fcP === ,22 0
F٥ J٨E
W PWאאK fcWאאאK foWאאאK
mfWאK אא’M‘M
١אVsאπ/Pאאאאאא
W
πδPVV so = F٥ J٩E
אF٥ J١١WEאאאאאאא
٥ J٤ J١ J٣א אאאא
אאאאאאKאאאאאאא
אא ٢٦١ א א
א א
- ١٤٣ -
אאאKאF٥ J١٢EאS2, S1אאfofc
אאאאאאאאאאא’M‘אאא
א’Vo‘אF٥ J١٢EאאאKאאאאW
∑=
=P
m
mso VV
1 πδ
W PWאאK
: δmאאmK VsWאאאK
אF٥ J١٢WEא S2 S1אא
אK
אא ٢٦١ א א
א א
- ١٤٤ -
٥ J٥אCurrent Source Inverter CSI אא
אאאאאאKאאא
אאאאאאאאאK
٥ J٥ J١אאאSingle Phase Current Source Bridge Inverter אF٥ J١٣Eאאאאא
אאאאאאWא S1 S4 אא0 ≤ t ≤ T/2
אאאאאאאאאאאאאאאאאאא
Lא S1 S4 אFEא S1 S4 אא
אאT/2אא S2 S3 אאאאאאא S2 S3 אא
אאאאאI אא 0 ≤ t ≤ T/2 -Iא אT/2 ≤ t ≤ T
א אTא אאא TאאKאF٥ J١٤E
אאK
אא ٢٦١ א א
א א
- ١٤٥ -
אF٥ J١٣WEאאאאא
אF٥ J١٤WEאא
אא ٢٦١ א א
א א
- ١٤٦ -
W
٥ J؟ ١א ٥ Jא ٢אא؟א ٥ J٣ א؟אאא ٥ J؟ ٤א ٥ J؟ ٥אאאאא ٥ J؟ ٦אאא ٥ J؟ ٧אאאאא ٥ J؟ ٨אאאאאא ٥ J٩ א؟אאאא ٥ J١٠ ؟אאאא
אא؟٥ J١١ ؟אאאאא ٥ J١٢ א220V
20ΩKW 'Vo'אאא -أ 'V1'אאאאא -ب Kאאא -ج
٥ J١٣ אאאFא٥ J١٢EאK ٥ J١٤ אאאF٥ J٨E'R'
10א ΩאL = 50 mH'Vs'110 VKא א60א Hz،א אK
אאאאDDCCAACC
אא
א
DC
A
C
٦
אא ٢٦١ א א
אאDCAC א
- ١٤٧ -
אאW אאאאאאW
• אאאאאאאא
• אאאא • אאאאא
א • אאאא
א W
אאאאאאאאאאאאאאאאאאאK
אאאאאאא
Kאאאאאאאאא אאאאאא
אאאאאאאאאאאאאאKאאאאאאאאאאא
אאאאאאאאVa
אאאאאאאאאאאא
אאאאאאאאאאאאאאאאאאאαK
אאאאאאאאאאאאאאאK
אא ٢٦١ א א
אאDCAC א
- ١٤٨ -
٦ J١אאאאאאאאא Speed Control of a DC Motor Using single-Phase Controlled Rectifiers
אF٦ J١Eאאאא
אאאאאאKF٦ J٢EאVaאאאאiaאLaא
אאאאאאאαH πZ βאאאאW
)(cos22
)( απ
α VV sa= F٦ J١E
אאF٢ J٢٢Eאאאאאאαא= 0αα = 180oא
אVa(α)אאא90°אאאאא)(α>90°אא
אאאאα = 90oאאKאאאא
אאK
אF٦ J١WEאאאאאאא
א
אא ٢٦١ א א
אאDCAC א
- ١٤٩ -
אF٦ J٢WEאאא
אאאאאאW
Va = Ea +Ia Ra F٦ J٢E
Ea = K Φ ω = Kb ω F٦ J٣E
Ta = K Φ Ia = KT Ia F٦ J٤E
אאאאΦאאאאEaאωאאאאא
NW
602 Nπ
ω = F٦ J٥E
אא ٢٦١ א א
אאDCAC א
- ١٥٠ -
אא Kb KTאאPאאΦאZאאאaW
aPZKK Tb π
φ2
== F٦ J٦E אא ωאTaאאVa(α)
אF٦ J٢EF٦ J٣EF٦ J٤EאאW
TKKR
KV
aTb
a
b
a −=)(α
ω F٦ J٧E
אא ωאTaאאVa(α)אF٥ J٢EF٥ J٣EF٥ J٤Eא
אW
TKKR
KV
aTb
a
b
a −=)(α
ω F٦ J٧E
אאאא אF٦ J١EאF٦ J٧EאW
TKKR
KV
aTb
a
b
s −= )(cos22
αωπ
F٦ J٨E
א(N.m) Taאאאω(Rad/Sec)אאא
אאאאאאאאאאאאאאאoω
W
)(cos22
απ
ωb
S
KV
= F٦ J٩E
אF٦ J٣Eאאoωאאאα=0 α = 180oאא α > 90°
אKאF٦ J٤EאאωאTaאאאF٦ J٨KE
אא ٢٦١ א א
אאDCAC א
- ١٥١ -
אF٦ J٤EאאאאαKאאאאאאאאאא
אאאאאאאאFאאאEאאFאאאEF٦ J٥KE
אF٦ J٣WEאאωoאאאאα
אF٦ J٤WEאאωאא
FEאא FEאאא
אF٦ J٥WEאאאאאאא
אא ٢٦١ א א
אאDCAC א
- ١٥٢ -
F٦ J١WE 1200 rpm 10 HP 230 Vא
אאאאאF٦ J١KEאאIa= 38 A א Ra = 0.3 ΩאVs=260 VKאאKb =
KT = 1.74אאאאα
=30oW J אאא J אאא J אK אW
J אאאF٦ J٤EW
mNTIKT
a
aTa
.121.6638*74.1 ==∴
=Q
J אאאאאF٦ J٨EW
TKKR
KV
aTb
a
b
s −= )(cos22
αωπ
sec/11055.656.116
121.6674.1
3.0)(cos74.1
260222
rad=−=
−=∴ απ
ω
אאאF٦ J٥EW
602 Nπ
ω =Q
rpmN 10512
110*602
60===∴
ππω
J אאאW
IVIV
ss
aaPF =
אאאאאאאW
82.202)30(cos260*22
)(cos22
=== osa
VV πα
πV
אא ٢٦١ א א
אאDCAC א
- ١٥٣ -
78.0260
82.202===∴
VV
s
aPF
٦ J٢אאאאאא Speed Control of A DC Motor Using DC Choppers
אאאאאא
F٦ J٦Eאאאאאאאאאא
אKאאאאF٦ J٢EאF٦ J٩EאF٦ J١EאאאW
VV sa D= F٦ J٩E
DאK אאK
אF٦ J٦WEאאאאאא
אא ٢٦١ א א
אאDCAC א
- ١٥٤ -
F٦ J٢WE Vs = 150 VKא
אאW Ra = 0.5 Ω, La = 10 mH, Kb = 0.05 V/rpm
אא(TON)1.6 msאאN = 2000 rpmא40 AK
Wא
אאאF٦ J٢EF٦ J٣EW IRKV aaba N +=
1202010040*5.02000*05.0 =+=+=V a V
אאאF٦ J١٠EW
8.0150120
===VV
s
aD
אW
TTON
ON fT
D ==Q
50010*6.18.0
3 ===∴−T ON
Df Hz
אא ٢٦١ א א
אאDCAC א
- ١٥٥ -
W ٦ J١ אאאאאאאא
אא ٦ J٢ אאאאאאא
א ٦ J٣ אאאאאאא
٦ J٤ 1000 rpm,10 kW, 240 Vא
אאאאאF٦ J١KEאאIa= 51.43 A א Ra = 0.45 ΩאVs=240 VK
אאKb = KT = 2אאאאα =20oW
J אאא J אאא J אK
٦ J٥ Vs = 220
VKאאאW Ra = 0.3 Ω, La = 15 mH, Kb = 0.04 V/rpm
אא(TON)1 msאאN = 2000 rpmא25 AK
٢٦١ א א א
א
- ١٥٦ -
א ٣-٣ α=55°, γ=160°, β=215° ٨-٣ Vo=148.6 V, Io=3.95 A, Po=778.8 W, PF=0.9 lag ٩-٣ Vo=148.6 V, Io=2.972 A, Io(rms)=2.972 A, Po=441.6 W, ISCR(avg)=0.99 A,
IFWD(avg)=0.99 A ١٠-٣ ITh(avg)=2.47 A, ITh(max)=7.43 A, VTh(max)=311 V, Po=1104 W ١٤-٣ Im = 17A, Vo(avg) = 121.75 V, Io(avg) = 12.175 A, ITh(m) = 17A,
ITh(avg) = 4.06 A, VL(m) = 294 V, fr = 180Hz
١٥- ٣ Im = 29.41 A, Vo(avg) = 140.45 V, Io(avg) = 14.045 A, ITh(m) = 29.41A, ITh(avg) = 4.06 A, VL(m) = 294 V, fr = 360Hz
٨ -٤ 44 V, 2.2 A, 69.6 V, 5.5 A, 242 W ٩-٤ D=0.5, Is(avg)=10 A, Is(rms)=14.14 A ١٠-٤ on=0.68 ms, Toff=0.32 ms ١١-٤ 44 V, 5.5 A, 69.6 V, 5.5 A, 2.2 A, 3.3 A, 6.16 A, 4.84, 2.4 mH ١٢-٥ 10 V, 99 V, 605 W ١٣-٥ 20 V, 198 V, 2420 W ٤-٦ 102.86 N.m, 860 rpm, 0.85 ٥-٦ 400 Hz
א٢٦١ א א א
א
אא (1) Ashfaq Ahmed : “Power Electronics for Technology”, Prentice-Hall,
1999. (2) M. H. Rashid: “Power Electronics: Circuits, Devices, and
Applications”, Second Edition, Prentice-Hall, 1993. (3) David A. Bradley: “Power Electronics”, Second Edition, Nelson
Thornes, 1995. (4) Ned Mohan, Tore M. Undeland, and William P. Robbins: “Power
Electronics: Converters, Applications, and Design”, Second Edition, John Wiley & Sons, 1995.
٢٦١ א א א
א
א
K K K K K K K K K K K K K K K K K K K K K K K K K K K K
אאWא K K K K K K K K K K K K K K K K K K١ אא K K K K K K K K K K K K K K K K K K K K K K K K K K١ K K K K K K K K K K K K K K K K K K K K K K K K K K K١ ١ J١א K K K K K K K K K K K K K K K K K K K K K K K١ ١ J١ J١ א K K K K K K K K K K K K K K K K K K K٢
١ J١ J٢אאא ٢
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١ J٢ J١אאאאאא K K K K K K K٧
١ J٣ א K K K K K K K K K K K K K K K K K K K K K K K K ٨
١ J٤א K K K K K K K K K K K K K K K K K K K K K K K K١٠
١ J٥אאא K K K K K K K K K K K K K K K K K K K K١١
١ J٥ J١אאא ١٢
١ J٥ J١ J١אאאאאא K K K K K K١٣
١ J٥ J٢אאאאFאE K K K K K K١٥
١ J٥ J٢ J١ אאא K K K K K K K K K K K K K١٧
١ J٥ J٣אאאאאא ١٩
١ J٥ J٣ J١אאאאאאאא K K K٢٠
١ J٥ J٣ J٢אאאאאאאאא K٢١
K K K K K K K K K K K K K K K K K K K K K K K K K K K٢٢
٢٦١ א א א
א
אאWאאאא K K K K K K K K K K K K K K K٢٣
אא K K K K K K K K K K K K K K K K K K K K K K K K K K٢٣ K K K K K K K K K K K K K K K K K K K K K K K K K K K٢٣ ٢ J١אאאא K K K K K K K K K K٢٣ ٢ J٢ אאאא K K K K K K K K K K K٢٥
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٢ J٥ J٢ אא K K K K K K K K K K K K K K K K K K٢٨
٢ J٥ J٣אאא K K K K K K K K K K K K K K K K٢٨
٢ J٥ J٤אא K K K K K K K K K K K K K K K K K K K K٢٨
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٢ J٦ J١אאא K K K K K K K K K K K K K K K K٢٩
٢ J٦ J٢אאא K K K K K K K K K K K K K K K K٢٩
٢ J٦ J٣ אא K K K K K K K K K K K K K K K K K٣٠
٢ J٧א ٣١
٢ J٧ J١א K K K K K K K K K K K K K K K K٣١
٢ J٧ J٢אאא K K K K K K K K K K K K٣٢
K K K K K K K K K K K K K K K K K K K K K K K K K K K٣٤
אאWאאא K K K K K K K K K K K K K K K K K K K K٣٥ אא K K K K K K K K K K K K K K K K K K K K K K K K K K٣٥ K K K K K K K K K K K K K K K K K K K K K K K K K K K٣٥ ٣ J١אאאFאאאE K K K K K K٣٥ ٣ J٢אאאאאא K K K K K K K٣٦
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٢٦١ א א א
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אא K K K K K K K K K K K K K K K K K K K K K K K K K ١٢٢ K K K K K K K K K K K K K K K K K K K K K K K K K K ١٢٢
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٥ J٣ J١אאא ١٢٦ ٥ J٣ J١ J١אא K K K K K K K K K K K K K K K K K ١٢٧ ٥ J٣ J١ J٢אא K K K K K K K K K K K K K K K K K ١٢٨
٥ J٣ J٢אאא ١٣١ ٥ J٣ J٢ J١אאR K K K K K K K K K K K K K K K K ١٣١ ٥ J٣ J٢ J٢אא'R-L' K K K K K K K K K K K K K K K ١٣٥ ٥ J٤אא K K K K K K K K K K K K K K ١٣٩
٥ J٤ J١א ١٤٠ ٥ J٤ J١ J١א K K K K K K K K K K K K K K ١٤٠ ٥ J٤ J١ J٢א K K K K K K K K K K K K K ١٤١ ٥ J٤ J١ J٣א K K K K K K K K K K K K K K ١٤٢ ٥ J٥א K K K K K K K K K K K K K K K K K K K ١٤٤
٥ J٥ J١אאא ١٤٤ K K K K K K K K K K K K K K K K K K K K K K K ١٤٦
אאWאאDCAC K K K K K K K K K K K K ١٤٧
אא K K K K K K K K K K K K K K K K K K K K K K K K K ١٤٧ K K K K K K K K K K K K K K K K K K K K K K K K K K ١٤٧ ٦ J١אאאאאאא אאאא K K K K K K K K K K K K K K K K K K K K K K ١٤٨ ٦ J٢אאאאאא K K K ١١٤
K K K K K K K K K K K K K K K K K K K K K K K ١٥٣
א K K K K K K K K K K K K K K K K K K K K K K K K K K K ١٥٦ אא K K K K K K K K K K K K K K K K K K K K K K K K K K K ١٥٧
