ie - lunds tekniska högskola 09/20090902 lecture2b selfcomm1.pdfie hvdc i dc,i l dci v dci line,i t...
Post on 16-Jul-2020
2 Views
Preview:
TRANSCRIPT
IE
1. Converters
IE
Diode rectifier with capacitive DC link
Figure 1.1: A single-phase diode rectifierwith a capacitive DC link.
��
Llineiline
eLN
��
Cdcvdc
D1
D2
D3
D4
0 5 10 15 20−400
−200
0
200
400
t [ms]
v dc [
V] e
LN
−eLN
Figure 1.2: Line-to-neutral voltage and DC side voltage for a single-phase diode rectifier with a capacitive DC link.
LNLNLN
TLNdc Eetdtedtte
TV
ππωω
πω
π
π
22ˆ2)()cos(2ˆ2)cos(ˆ
21 2
22==== ∫∫
−
0 5 10 15 20−100
−50
0
50
100
t [ms]
i line [
A]
0 300 600 900 1200 1500 1800 21000
5
10
15
20
f [Hz]
i line,
pk [
A]
Figure 1.3: Line current (left) and its frequency spectrum (right),for a single-phase diode rectifier with a capacitive DC link.
IE
Diode rectifier with inductive DC link
Figure 1.4: A single-phase diode rectifierwith an inductive DC link.
Figure 1.5: Line current for a single-phase diode rectifier with an inductive DC link.
Figure 1.5: Line current frequency spectrum for a single-phase diode rectifier with an inductive DC link.
��
Llineiline
eLN
D1
D2
D3
D4
��
vdc
idcLdc
0 0.005 0.01 0.015 0.02−8
−6
−4
−2
0
2
4
6
8
t [s]
i line [
A]
eLN
/50
0 300 600 900 1200 1500 1800 21000
2
4
6
8
10
f [Hz]
i line,
pk(f
) [A
]
IE
The three-phase diode rectifier with capacitive DC link (I)
Figure 1.6: A three-phase diode rectifierwith capacitive DC link.
Figure 1.7: DC side voltage for a three-phase diode rectifier with capacitive DC link.
� �
��
Llineiline
eLN
Cdcvdc
D1
D4
D3 D5
D6 D2
0 0.005 0.01 0.015 0.02−600
−400
−200
0
200
400
600
t [s]
v dc [
V]
eRS
eTR
eST
LLLL
TLLdc Etdtedtte
TV
πωω
πω
π
π
23)()cos(2ˆ6)cos(ˆ
61 6
66=== ∫∫
−
IE
The three-phase diode rectifier with capacitive DC link (II)
Figure 1.7: DC side voltage for a three-phase diode rectifier with capacitive DC link.
Figure 1.8: Line current frequency spectrum for a three-phase diode rectifier with capacitive DC link.
0 0.005 0.01 0.015 0.02−600
−400
−200
0
200
400
600
t [s]
v dc [
V]
eRS
eTR
eST
0 300 600 900 1200 1500 1800 21000
5
10
15
20
25
f [Hz]
i line
,pk(f
) [A
]
Figure 1.8: Line current (R-phase)for a three-phase diode rectifier with capacitive DC link.
0 0.005 0.01 0.015 0.02−100
−75
−50
−25
0
25
50
75
100
t [s]
i line [
A]
IE
Three-phase thyristor rectifier with inductive DC link
� �
��
Llineiline
eLN
vdc
T1
T4
T3 T5
T6 T2
idcLdc
Figure 1.9: Three-phase thyristor rectifier with an inductive DC link.
( )
)cos()cos(23
)cos(2ˆ6)cos(ˆ
61
0
6
66
ααπ
ωωπ
ωαπ
απ
dcLL
LL
TLLdc
VE
tdtedtteT
V
==
=== ∫∫+
+−
⎪⎩
⎪⎨⎧
=
=
)sin(3
)cos(3
1,
1,
α
α
lineLL
lineLL
IEQ
IEP
)cos(23 απ dcLLdcdc IEIVP ==
dclinedcLLlineLL IIIEIEPπ
απ
α 6)cos(23)cos(3 1,1, =⇔==
⎟⎠⎞
⎜⎝⎛=3
sin22,
ππ
kIk
I dckline
IE
HVDC
idc,i
Ldci
��
vdci
��
Lline,iiline,i
eLNiT1
T4
T3 T5
T6 T2
� �
��
Lliner,riline,r
eLNr
vdcr
T1
T4
T3 T5
T6 T2
idcr
Ldcr
��
vcable,r
��
vcable,i
Cable
Figure 1.10: Principal schematic of a HVDC power transmission system.
Figure 1.11: Line-to-line voltages, DC side voltage and control angles for the rectifier (left) and inverter (right) of an HVDC transmission system.
0 0.005 0.01 0.015 0.02−600
−400
−200
0
200
400
600
t [s]
v dc,r [
kV] e
RS,r
α
eTR,r
eST,r
0 0.005 0.01 0.015 0.02−600
−400
−200
0
200
400
600
t [s]
v dc,i [
kV]
eRS,i
α
eTR,i
eST,i
IE
HVDC Converter Currents
0 300 600 900 1200 1500 1800 21000
0.5
1
1.5
2
2.5
f [Hz]
i line,
r,pk
(f)
[kA
]
0 0.005 0.01 0.015 0.02−3
−2
−1
0
1
2
3
t [s]
i line
,r [
kA]
0 0.005 0.01 0.015 0.02−3
−2
−1
0
1
2
3
t [s]
i line,
i [kA
]
0 300 600 900 1200 1500 1800 21000
0.5
1
1.5
2
2.5
f [Hz]
i line
,i,pk
(f)
[kA
]
Figure 1.12: R-phase line current (top) and its spectrum (bottom) for the rectifier of an HVDC transmission system.
Figure 1.13: R-phase line current (top)and its spectrum (bottom) for theinverter of an HVDC transmissionsystem.
IE
Commutation Overlap
Figure 1.14: Commutation current (top) and voltage (bottom) for the rectifier.
9.15 9.17 9.19 9.21 9.23 9.25−1
0
1
2
3
t [ms]
i T,r [
kA]
iT1
µ
iT3
9.15 9.17 9.19 9.21 9.23 9.25350
400
450
500
550
600
650
t [ms]
v dc,r [
kV]
eST,r
µ
−eTR,r
dcdcrdcdclinedc
dclinedcdcdcdcr
IRVIXV
ILVVVV
−⋅=−⋅=
=−⋅=∆−⋅=
)cos(3)cos(
3)cos()cos(
00
00
απ
α
ωπ
αα
The line inductance determines the commutation time, and therefore results in a loss of average voltage
IE
Practical HVDC installations
Figure 1.15: Realistic schematic of an HVDC power station.
Ldc
��
vcable
��
vdc
T1
T4
T3 T5
T6 T2
Y Y
T1
T4
T3 T5
T6 T2
Y D
Ldc
CVAr
LfAC
CfAC
LfDC
CfDC
LfDC
CfDC
IE
The Buck Converter (Step-Down Converter)
Figure 1.16: Buck converter.
Figure 1.17: Ideal waveforms of the Buck converter.
S ”on”
swloaddc
LL
Lloaddc DTLVVi
dtdiLvVV ⋅
−=∆⇒==−
S ”off”
( ) swloadL
LLload TD
LVi
dtdiLvV −⋅−=∆⇒==− 1
IE
The Boost Converter (Step-Up Converter)
Figure 1.18: Boost converter.
Figure 1.17: Ideal waveforms of the Boost converter. ReplaceVdc and Vload of the Buckconverter with Vout and Vin
S ”on”
S ”off”
swin
L DTLV
i ⋅=∆inSinLL VvVvdtdiL ≈−== ⇒
outinoutDinLL VVVvVvdtdiL −≈−−== ⇒
( ) swoutinL TD
LVV
i −⋅−
=∆ 1
IE
The Buck-Boost Converter (Half-Bridge)
Figure 1.19: Buck-boost converter.
Figure 1.17: Ideal waveforms of the Buck-boost converter.
S ”on”
swloaddc
LL
Lloaddc DTLVVi
dtdiLvVV ⋅
−=∆⇒==−
S ”off”
( ) swloadL
LLload TD
LVi
dtdiLvV −⋅−=∆⇒==− 1
IE
Diode rectifier with Power Factor Corrector
��
Llineiline
eLN
��
Cdcvdc
D1
D2
D3
D4
Time
0s 2ms 4ms 6ms 8ms 10ms 12ms 14ms 16ms 18ms 20ms
I(L1)
0A
10A
20A
30A
SEL>>
V(V4:+)- V(V4:-)
0V
-325V
325V
Single-phase diode rectifier with power factor corrector (PFC).
Line-to-neutral voltage (top) and rectified line current (bottom)for a diode rectifier equipped with PFC.
IE
VSC Based HVDC
Figure 1.30 Basic VSC based HVDC power transmission interconnection.
� �
��
Ll1Rl1eLN1
Cdc1 Vdc1
��
�
�
Ll2 Rl2eLN2
Cdc2Vdc2
��
Vcable1
��
Vcable2
Cable
Figure 1.31 DC bus voltage controller for VSC based HVDC.PI+
Vdc,ref+
++
ICdc,ref+ -
Vdc
Iq,dc,ref
Vdc
eq
Iq,inv,ref
1
eqPinverter
Iq,ref�
�
Ll1
Cdc1 Vdc1D Y
��
Cf21
��
��
Cf31 Vcable1
Lf21
Lf31
Lf11
Cf11
Figure 1.32 Realistic VSC based HVDC light converter station.
IE
Effect of DSP Controller Delay
Figure 1.33 Inverter AC side power (black) and rectifier AC side power (grey).
Figure 1.34 Rectifier DC side voltage.
20 20.25 20.5 20.75 21 21.25 21.5 21.75 22−200
−150
−100
−50
0
50
100
150
200
t [ms]
p i, pr [
MW
]
0 0.01 0.02 0.03 0.04 0.05 0.06250
275
300
325
t [s]
v dc [
kV]
IE
Converter Currents for VSC Based HVDC
0 0.01 0.02 0.03 0.04 0.05 0.06−1500
−1000
−500
0
500
1000
1500
t [s]
i line
, ico
nv [
A]
0 0.01 0.02 0.03 0.04 0.05 0.06−1500
−1000
−500
0
500
1000
1500
t [s]
i line
, ico
nv [
A]
0 0.005 0.01 0.015 0.02−1500
−1000
−500
0
500
1000
1500
t [s]
i line
, ico
nv [
A]
1650 1750 1850 1950 2050 2150 22500
10
20
30
40
50
60
f [Hz]
i line
,pk(f
), i co
nv,p
k(f)
[A]
Figure 1.35 Line current (black) and converter current (grey) for the rectifier (top) and line current (black) and converter current (grey) for the inverter (bottom) during load power increase.
Figure 1.36 Line current (black) andconverter current (grey) for the inverter(top) and line current spectrum (black)and converter current spectrum (grey)for the inverter at frequencies close toswitching frequency (bottom).
IE
General SMPS
Figure 1.20: Principal schematic of a switch-mode power supply.
IE
The Laboratory Flyback Converter
Flyback converter with input filter, inrush current limitation, diode rectifier, dc link capacitors, power MOSFET, transformer, output filter and three snubber circuits. The controller circuits are not included in the circuit.
C
CC
DC
CDC
N1
N2
N2
GND
+15 V
-15 V
F
N T-
IE
The Flyback Converter
Figure 1.23: Principal schematic of a flyback converter. Only the devices needed to understand the operation are included.
IE
The switch-transformer
Figure 1.21: Principal transformer withco-ordinated reference directions marked.
( )
( )⎪⎪⎩
⎪⎪⎨
⎧
Φ⋅=Φ⋅=
Ψ=≈
Φ⋅=Φ⋅=
Ψ=≈
dtdNN
dtd
dtdev
dtdNN
dtd
dtdev
2222
222
1111
111
2
1
2
1
2
2
1
121 N
Nvv
Nv
Nv
=⇒=⇒Φ=Φ
1
2
2
12211 N
Niiiviv =⇒⋅=⋅
2
2
2
1
2
22
2
1
1
12
2
1
2
1
1
2
22 R
NN
iv
NN
ivR
NN
iv
ivR ⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛=⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛==′⇒⎟⎟
⎠
⎞⎜⎜⎝
⎛⋅==
Figure 1.22: The equivalent circuit of a transformer.Note that the winding resistances have been neglected.In the full equivalent circuit they show up in serieswith the leakage inductances, L1λ and L2λ. The coreloss equivalent resistance has also been omitted.This is located in parallel to the magnetizing inductance.
IE
The Flyback Converter
Figure 1.23: Principal schematic of a flyback converter. Only the devices needed to understand the operation are included.
IE
Flyback Converter - Operation
Figure 1.25: The flyback converter when the switch S is open. Since the transformer is demagnetized from the secondary, the magnetizing inductance is placed on the secondary.
Figure 1.24: The flyback converter when the switch S is closed. Since the transformer is magnetized from the primary in this case, the magnetizing inductance is placed on the primary.
( ) ( ) ( ) 000 ttttLVtiti
tiL
dtidLV
m
dcmm
mm
mmdc >−⋅
′+′=′⇒
∆′∆
⋅′≈′
⋅′=
( ) ( ) ( ) 111 ttttLVtiti
tLL
dtidLV
m
Cmm
mm
mmC >−⋅
′′−′′=′′⇒
∆′′∆
⋅′′≈′′
⋅′′=−
IE
Power Semiconductor Voltage Stress
CdcD VVNNV +⋅=1
2,maxS ”on”:
S ”off”: ( )CONDDCS VVNNVV +⋅+= )(2
1,max
Figure 1.23: Principal schematic of a flyback converter. Only the devices needed to understand the operation are included.
IE
Ideal Waveforms
Figure 1.26: Waveforms for ideal operation of aflyback converter.
The energy stored in the transformerCore is conserved (during switchings)
maxmax ,1
2,
2
2
1 , mmmm iNNiL
NNL ′′⋅=′′′⋅⎟⎟
⎠
⎞⎜⎜⎝
⎛=′
2,
2,, 2
121
maxmaxmax mmmmm iLiLW ′′⋅′′⋅=′⋅′⋅=
( )pswm
Cmm
pm
dcmm
tTLVii
tLVii
−⋅′′
−′′=′′
⋅′
+′=′
maxmin
minmax
,,
,,
and
Cdc
C
sw
p
VNNV
VTt
⋅+=
2
1
The duty cycle is calculated from the current changes
IE
The Forward Converter
Figure 1.27: Principal schematic of a forward converter. Only the devices needed to understand the operation are included. Note that in this schematic a zener diode is connected across the primary, which is rarely used in practice.
IE
Forward Converter - Operation
( ) ( ) ( ) 000 ttttLVtiti
tiL
dtidLV
m
dcmm
mm
mmdc >−⋅
′+′=′⇒
∆′∆
⋅′≈′
⋅′=
loadmmm iNNii
NNiiii ⋅+=⋅+=′+=
1
22
1
221
( ) ( ) ( ) 111 ttttLVtiti
tiL
dtidLV
m
Zmm
mm
mmZ >−⋅
′−′=′⇒
∆′∆
⋅′≈′
⋅′=−
Figure 1.28: The forward converter with the simplified transformer equivalent included.
IE
Power Semiconductor Voltage Stress
S ”off”:
Figure 1.27: Principal schematic of a forward converter. Only the devices needed to understand the operation are included. Note that in this schematic a zener diode is connected across the primary, which is rarely used in practice.
ZdcS VVV +=max,
ZD VNNV ⋅=1
2,1max
IE
Ideal Waveforms
Figure 1.29: Waveforms for ideal operation of aforward converter.
The duty cycle is calculated from the fact that the energy stored in the transformer core is conserved (during switchings)
( ) pm
dcmm t
LVii ⋅′
=′⇒=′ max,00
( ) ( ) ( ) ( )pswm
Zpmswmswm tT
LVtiTiTi −⋅′
−′=′⇒=′ 0
Zdc
Z
sw
p
VVV
Tt
+≤
Note that when S is on:
loadmmm iNNii
NNiiii ⋅+=⋅+=′+=
1
22
1
221
top related