tste19 power electronics · half-wave rectifier output voltage ... • in the ideal three-phase...
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TSTE19 Power ElectronicsLecture 3
Tomas JonssonICS/ISY
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Outline• Rectifiers
– Current commutation
• Rectifiers, cont.
– Three phase
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Effect of Ls on current commutation• Current commutation =
current path changed fromone diode to another
– Commutation notinstantaneous when Lsnonzero
– Magnetic energy change
• Use simplified example
– Output represented byconstant dc current source
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vs>0
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Effect of Ls on current commutation• Current commutation =
current path changed fromone diode to another
– Commutation notinstantaneous when Lsnonzero
– Magnetic energy change
• Use simplified example
– Output represented byconstant dc current source
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vs<0
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Source inductance effects, cont• Waveform if L=0
• Prior to ωt = 0, vs is negative, current flow through D2
– vd = 0, is = 0
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Current commutation• During commutation (ωt > 0)
– vs positive, D1 turns on
– iD1 = is
– iD2 = Id – is
– iD1 +iD2 = Id
– D2 stops conductingwhen iD2 = 0
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0 5 10 15 20 25 300
2
4
6
8
10
12
wt [deg]
[A]
iD1
iD2
After commutation completedValid for 0 < is < Id
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Commutation current
• Commutationcurrent– Temporary
currentcontributionrelated toenergy transfer
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Current commutation waveforms• Large Ls used
to clearly showeffect
• Time forcommutationdepend onLs size andcurrent changein Ls
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Current commutation time• is through inductor starts at zero, end at Id when ωt=u
• Integrate both sides, left is area Au (voltage * angle)
• Commutation angle can be calculated
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= 2 sinω = = ω ω 0 < ω <
2 sinω ω = ω
= ∫ 2 sinω ω = 2 1 − cos = ω ∫ = ω
cos = 1 −ω
2
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Half-wave rectifier output voltage• Vdo = Ideal average voltage of half-wave rectified voltage
(effect of the commutation inductance Ls neglected)
• = ∫ 2 sin = −cos =
• ≈ 0.45
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0 30 60 90 120 150 180 210 240 270 300 330 360-1.5
-1
-0.5
0
0.5
1
1.5vd
vsVd
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Output voltage incl commutation voltage drop
• Vd = Vd0 - DVd = Vd0 – = 0.45Vs -
• Commutation voltage drop appears as a resistance to the dc-side current. Rcomm =
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Commutation conclusions• Conduction:
– Magnetic energy isstored related to theinductance of theconduction path
• Commutation– Transfer of current
between two paths:– ÞStored magnetic
energy needs to betransfered!
– Output voltagereduction proportionalto Id and Ls
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Exercise 5-5Consider the basic commutation circuit of Fig. 5-11a with Id = 10 A.
a) With Vs=120 V at 60 Hz and Ls = 0, calculate Vd and theaverage power Pd
b) With Vs=120 V at 60 Hz and Ls = 5 mH, calculate u, Vd , and Pd
c) With data as i b) calculate u, Vd , and Pd with Id = 20 A
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Current commutation in full-bridge• Same principle for area Au due to Ls
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Rectifier during current commutation• vs negative before t = 0
– D3 and D4 conducting
– is = -Id
• vs positive
– D1 and D2 startsconducting(Short circuit paththrough D3 and D4)
• iu are commutationcurrents
• vd = 0 during commutation
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Valid for -Id < is < Id
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Current commutation angle• is change is double that of previous example (from -Id to Id)
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cos = 1 −2ω
2
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Full-bridge rectifier output voltage• Vdo = average voltage of full wave rectified voltage
(effect of the commutation inductance Ls neglected)
– = ∫ 2 sin = −cos =
– ≈ 0.9
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0 30 60 90 120 150 180 210 240 270 300 330 360-1.5
-1
-0.5
0
0.5
1
1.5vd
vs
Vd
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In the single-phase rectifier circuit shown in Fig. 5-14a, Vs = 120 Vat 60 Hz, Ls = 1 mH, and Id = 10 A.
1. Calculate u, Vd, and Pd
2. What is the percentage voltage drop in Vd due to Ls?
Exercise 5-8
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3-phase full-bridge rectifier, general view
• Less ripple on output
• Handles higher power
• No current in neutral wire
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3-phase full bridge rectifiers, L = 0• One diode in each group is conducting at any time
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6-pulse Graetzrectifier bridge
To load
From load
+
-0
D1
ua - ub
ua
ub
uc
D6
D3 D5
D4 D2
Diode rectifier
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6-pulse Graetzrectifier bridge
To load
From load
0
+
-
ua
ub
uc
D1
D6
D3 D5
D4 D2
ua - uc
Diode rectifier
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6-pulse Graetzrectifier bridge
To load
From load
0+
-
ua
ub
uc
D1
D6
D3 D5
D4 D2
ub - uc
Diode rectifier
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6-pulse Graetzrectifier bridge
To load
From load
0
-
+
ua
ub
uc
D1
D6
D3 D5
D4 D2
ub - ua
Diode rectifier
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6-pulse Graetzrectifier bridge
To load
From load
0
-
+
ua
ub
uc
D1
D6
D3 D5
D4 D2
uc - ua
Diode rectifier
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6-pulse Graetzrectifier bridge
To load
From load
0-
+
ua
ub
uc
D1
D6
D3 D5
D4 D2
uc - ub
Diode rectifier
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3-phase full bridge rectifier waveforms• Every diode conducts 1/3
of the cycle
• Output waveformcontains 6 segments
• Instantaneouscurrent commutationdue to L = 0
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= −
= 2
=1π 3⁄ 2
⁄
⁄
cosω ω
= 1.35
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Principles of AC/DC conversion, 6-pulse bridgeId
1 3 5
Ud
4 6 2
Ua
Ub
Uc
Ia
Ib
a
c
b
Ic
Ua Ub Uc
16
12
32
34
54
56
Uac Ubc
tw
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Exercise 3-100• In the ideal three-phase rectifier circuit, construct the wave
forms of diode D1 and D2 voltages and currents.
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Input line current3ph rectifier• No 3rd harmonic
• Compare with single phasePF = 0.9
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: =23
: =1π 6 = 0.78
= cosϕ = 1.0
= =cosϕ
= cosϕ =3π = 0.955
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§ Fourier analysis gives additional harmonic components§ Remember calculation uses RMS of Is, Is1 and Id
=2π 2 = 0.9 = 0 ℎ
= ℎ ℎ
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Single phase rectifier, input current
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Source inductance effects, DC current load
• Source L not 0
• Only one current commutation at a time
– 6 commutations during oneline-frequency cycle
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Transfer of current from valve 1 to valve 3
1
I
d a b
d
I I1 3
3
U
Ua
b
Xc
cX
t
tu
I
I
1
3
U = 0.5 ( U +U )
2015-11-09TSTE19/Tomas Jonsson
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Current commutation• Current commutation
phase c -> phase a (D5 -> D1)
• Au indicates the currentcommutation voltage drop
• Au only half of areabetween va and vcbecause of twoinductances
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+ =
= ω ∫ = ∫ ω =
=∫ ( ) ω = ( )
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Effect of commutation inductance
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= ω ∫ = ω =
=∫ ω =∫ ( ) ω = ( )
D =ω
3=
3ω
= - D = 1.35 − ω
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A 3-ph rectifier feeding a constant current load has the following data:VLL = 400 V at 50 Hz, Ls = 7 mH.
The maximum ac-side rms current Is = 10 A.
Exercise 3-101
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Calculate
a) Max dc-side current
b) Average dc-side voltageat max current
c) Max active power
d) Diode average current
e) Diode rms current
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Exercise 3-102Using results from exercise 3-101, calculate
• Diode conduction losses (pD1=∫ uD1 iD1)using the diode BYW29E withV0=0.79V, Rs = 0.013 ohm (Tj=25C)
• Use the diode on-state model belowwhere iD can be expressed with itsaverage and rms current as calculatedabove
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Inrush current• LC-circuit fed by voltage step
– Worst case when input voltage at maximum when applied
– Peek voltage twice the input voltage step
• DC circuit needs to support twice the peak input voltage!
• Alternative: limit current, using resistor. Short resistor afterstart using thyristor
2015-11-09 38TSTE19/Tomas Jonsson
= 2 2 (singlephase)= 2 2 (threephase)
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www.liu.se
TSTE19/Tomas Jonsson