AC/DC/AC Converters: Two-Level and Multilevel VSIPage 1
Socrates – Erasmus Visit
AC/DC/AC Converters:Two-Level and Multilevel VSI
Josep PouAntoni Arias
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 2
Socrates – Erasmus Visit
Outline
1. Two-Level Inverter2. Multilevel Inverters
- Cascade H-Bridge Inverter- Flying-Capacitor Inverter- Diode-Clamped Inverter
3. Back-to-Back Connection
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 3
Socrates – Erasmus Visit
Outline
1. Two-Level Inverter2. Multilevel Inverters
- Cascade H-Bridge Inverter- Flying-Capacitor Inverter- Diode-Clamped Inverter
3. Back-to-Back Connection
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 4
Socrates – Erasmus Visit
1. Two-Level Three-Phase Inverter
Grid-connected inverter
2dcv
)0(dcv
C2
C2
as bs cs
as bs cs
+
−2dcv
)(a)(b
)(c
0av0bv0cv
cba eee ,,
)(n
L R
cba iii ,,
dci pi
pR
CiRpi
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 5
Socrates – Erasmus Visit
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
+++=
+++=
+++=
00
00
00
nccc
c
nbbb
b
naaa
a
veiRdtdiLv
veiRdtdiLv
veiRdtdiLv
Modeling the AC Side
( ) ( ) 0000 3 ncbacbacba
cba veeeiiiRdt
iiidLvvv +++++++++
=++
( )3
0000
cbacban
eeevvvv ++−++=
0=++ cba iii
0av0bv0cv
cba eee ,,
)(n
L R
cba iii ,,
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 6
Socrates – Erasmus Visit
( )
( )
( )⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−−−=
−−−=
−−−=
00
00
00
1
1
1
ncccc
nbbbb
naaaa
veiRvLdt
di
veiRvLdt
di
veiRvLdt
di
( )
( )
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
−−=
−−−==
−−−==
∫∫
∫∫
bac
nbbbbb
naaaaa
iii
dtveiRvL
dii
dtveiRvL
dii
00
00
1
1
Modeling the AC Side
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 7
Socrates – Erasmus Visit
Matlab-Simulink Model
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 8
Socrates – Erasmus Visit
Modeling the DC Side
⎪⎪⎩
⎪⎪⎨
⎧
=
=−−=
p
dcRp
dcpRpdcC
Rvi
dtdvCiiii
⎟⎟⎠
⎞⎜⎜⎝
⎛−−= p
p
dcdc
dc iRvi
Cdtdv 1
dcv
+
−
dci pi
pR
CiRpi
C
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 9
Socrates – Erasmus Visit
∫∫ ⎟⎟⎠
⎞⎜⎜⎝
⎛−−== dti
Rvi
Cdvv p
p
dcdcdcdc
1
Matlab-Simulink Model
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 10
Socrates – Erasmus Visit
Converter
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
++=
−=
−=
−=
ccbbaap
dccc
dcbb
dcaa
isisisi
vsv
vsv
vsv
)21(
)21(
)21(
0
0
0
2dcv
)0(dcv
C2
C2
as bs cs
as bs cs
+
−2dcv
)(a)(b
)(c
0av0bv0cv
ai
pi
bici
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 11
Socrates – Erasmus Visit
Matlab-Simulink Model
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 12
Socrates – Erasmus Visit
Modulation (Sinusoidal PWM)
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 13
Socrates – Erasmus Visit
Control
qvΔ
dvΔ
di
*DCV Voltage
Controller
Current Controller
Current Controller
0* =qI
qi
DCv
LE
*dI
Lω
Lω-
dv
qv
Voltage Oriented Control (VOC)
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 14
Socrates – Erasmus Visit
Simulation Program
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 15
Socrates – Erasmus Visit
Simulation Results
Main data: VLRMS=400V, f=50Hz, L=6mH, R=0.1Ω, C=2200μF, Vdc*=750 V, fs=5kHz.
Particular data: Rp=100Ω, Idc=0, Iq*=0
0 0.02 0.04 0.06 0.08 0.1 0.12-400
-200
0
200
400
600
800
Time (s)
vdc
ea eb ec
ia*10 ib*10 ic*10(V),
(A)
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 16
Socrates – Erasmus Visit
Simulation Results
Main data: VLRMS=400V, f=50Hz, L=6mH, R=0.1Ω, C=2200μF, Vdc*=750 V, fs=5kHz.
Particular data: Rp=10kΩ, Idc=10A, Iq*=0
0 0.02 0.04 0.06 0.08 0.1 0.12-400
-200
0
200
400
600
800
Time (s)
(V),
(A)
vdc
ea eb ec
ia*10 ib*10 ic*10
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 17
Socrates – Erasmus Visit
Simulation Results
Main data: VLRMS=400V, f=50Hz, L=6mH, R=0.1Ω, C=2200μF, Vdc*=750 V, fs=5kHz.
Particular data: Rp=10kΩ, Idc=0, Iq*=20A
0 0.02 0.04 0.06 0.08 0.1 0.12-400
-200
0
200
400
600
800
vdc
ea eb ecia*10 ib*10 ic*10
(V),
(A)
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 18
Socrates – Erasmus Visit
Outline
1. Two-Level Inverter2. Multilevel Inverters
- Cascade H-Bridge Inverter- Flying-Capacitor Inverter- Diode-Clamped Inverter
3. Back-to-Back Connection
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 19
Socrates – Erasmus Visit
• Multilevel inverters can provide more than two voltage levels at the outputs.
• Main advantages compared with the two-level inverter:- high quality of the output voltage spectra and - larger voltages that can be handled.
• Suitable for high-power applications.
• Main multilevel topologies:- (1) cascade H-bridge inverter,- (2) floating-capacitor inverter, and- (3) diode-clamped inverter.
2. Multilevel Inverters
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 20
Socrates – Erasmus Visit
(1) Cascade H-Bridge Inverters
0
VDC VDC VDC
VDC VDC VDCaC C C b c
C C C
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 21
Socrates – Erasmus Visit
sH0a sHa va0
off off 0
off on +VDC
on off -VDC
on on 0
sL0a
sH0a sHa
sLa
VDC aC
VDC
C VDC
C b c
0
sL0a
sH0a sHa
sLa
VDC aC
VDC
C VDC
C b c
0
0 V
sL0a
sH0a sHa
sLa
VDC aC
VDC
C VDC
C b c
0
+VDC
sL0a
sH0a sHa
sLa
VDC aC
VDC
C VDC
C b c
0
-VDC
sL0a
sH0a sHa
sLa
VDC aC
VDC
C VDC
C b c
0
0 V
0offoff
off on +VDC
on off -VDC
on on 0
Control functions: sH0a and sHa
Three-Level Basic Structure
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 22
Socrates – Erasmus Visit
0
VDC VDC VDC
VDC VDC VDCaC C C b c
C C C
n= 2h+1 n: number of output levels (per phase)h: number of cascaded H cells
Even Number of Levels
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 23
Socrates – Erasmus Visit
sH20a sH2a
sH10a sH1a
VDC
VDC aC
C
0
sH10a sH1a va0
off off 0off on +VDCon off -VDCon on 0off off +VDCoff on +2VDCon off 0on on +VDCoff off -VDCoff on 0on off -2VDCon on -VDCoff off 0off on -VDCon off +VDCon on 0
sH20a sH2a
off offoff offoff offoff offoff onoff onoff onoff onon offon offon offon offon onon onon onon on
Cascaded Five-Level Inverter
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 24
Socrates – Erasmus Visit
0 2 4 6 8 10 12 14 16 18 20
2 VDC
1.5 VDC
VDC
0.5 VDC
0
-0.5 VDC
-VDC
1.5 VDC
-2 VDC
Time (ms)
sH20a sH2a
sH10a sH1a
VDC
VDC aC
C
0
Modulation Techniques
Example: Sinusoidal PWM (SPWM) in a Five-Level Inverter
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 25
Socrates – Erasmus Visit
Main Features
- Modular topologies. Very interesting for practical implementation.
- Main drawback: isolated DC voltage sources are required.- Isolation is not necessary for applications such as active
filtering and reactive compensation. In those cases, capacitors are used to provide DC voltages. Their voltages have to be controlled using redundant states of the converter.
- As many unities as necessary can be connected in cascade. Therefore, any AC voltage level can be achieved.
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 26
Socrates – Erasmus Visit
(2) Flying-Capacitor (FC) Multilevel Inverter
0
C
a
VDC
b c
Cf vfa
Cf vfb
Cf vfc
Three-level Topology
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 27
Socrates – Erasmus Visit
Cf
VDC 2DCV
DCV
sH2
sL2
sH1
sL1
a
0
iaiCf1
C
Imbricate Cells
C
VDC Cf
aia
0
2DCV
DCV
sH2
sL2
sH1
sL1
- Each leg of the converter is made up from a set of cells (imbricate cells). The output voltage is synthesized by connecting a number of cells (capacitors) in series.
- SHi and SLi, with i = {1, 2}, must be in opposite states to avoid short-circuits.
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 28
Socrates – Erasmus Visit
0
C
a
VDC
Cf1Cf2
b
Cf1 Cf2
c
Cf1Cf2
FC Four-Level Topology
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 29
Socrates – Erasmus Visit
C Cf(n-2) Cf1
VDC
...
...
...
1−nVDC
12
−nVDC
DCVnn
12
−−
DCV
sH(n-1)
sL(n-1)
sH(n-2)
sL(n-2)
sH3
sL3
sH2
sL2
sH1
sL1
a
0
iaiCf1iCf 2
Cf 2
iCf(n-2)
Imbricate Cells in an n-level FC Inverter
• Voltages on the floating capacitors are different.
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 30
Socrates – Erasmus Visit
• FC multilevel topologies require a large number of capacitors, specially in high-order structures (n>3).
• Precharge of the flying capacitors is required.
• Voltages on the flying capacitors can be controlled. Each leg regulates the voltages on their capacitors independently of the others.
Main Features
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 31
Socrates – Erasmus Visit
(3) Diode-Clamped Inverters
ic
ib
ia
i1
0
1 (NP)
2
c
b
a
CvC1
vDC
vC2 C
Three-level diode-clamped inverter =
Neutral-Point-Clamped (NPC) Inverter
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 32
Socrates – Erasmus Visit
2
0
abc
VDC
vC2
1
C vC1
C vC2
0
1
2
c
b
aia
ib
ic
sc0
sc2
sc1
sb0
sb2
sb1
sa0
sa1
sa2
CvC1
VDC
C
Functional diagram
NPC Inverter
Two consecutive switches must be in on-state
2
0
abc
VDC
vC2
1
C vC1
C vC2
0
1
2
c
b
aia
ib
ic
sc0
sc2
sc1
sb0
sb2
sb1
sa0
sa1
sa2
CvC1
VDC
C
2
0
abc
VDC
vC2
1
C vC1
C vC2
0
1
2
c
b
aia
ib
ic
sc0
sc2
sc1
sb0
sb2
sb1
sa0
sa1
sa2
CvC1
VDC
C
2
0
abc
VDC
vC2
1
C vC1
C vC2
0
1
2
c
b
aia
ib
ic
sc0
sc2
sc1
sb0
sb2
sb1
sa0
sa1
sa2
CvC1
VDC
C
Operation principles
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 33
Socrates – Erasmus Visit
CvC2
vC1
VDC
C
2
1
0a b c
0
vC1
Time, t
A low-frequency oscillation may appear in the neutral-point (NP) voltage.
Neutral-Point Voltage Oscillations
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 34
Socrates – Erasmus Visit
-180 -150 -30 0 60 1500.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Mod
ulat
ion
Inde
x, m
Current Phase Angle, ϕ (Degrees)
-90 -60 30 90 120 180-120
Oscillation Area
NP Voltage Oscillations
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 35
Socrates – Erasmus Visit
Current Phase Angle (Degrees)
2NPnVΔ
Modulation Index m
2NPnVΔ
-150 -100 -50 0 50 100 1500
0.005
0.01
0.015
0.02
0.025
0.03
m=1
m=0.9
m=0.8
m=0.7
m=0.6
Current Phase Angle (Degrees)
CfIVV
RMS
NPNPn 22
Δ=
Δ
Normalized amplitude of the NP voltage ripple (ΔVNPn /2):ΔVNP /2 : amplitude of the NP voltage rippleIRMS: RMS output currentf: line frequencyC: value of the DC-link capacitors
Voltage Oscillation Amplitude
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 36
Socrates – Erasmus Visit
Four-Level Diode-Clamped Inverter
vC1
0
VDC
C
1
2
3
vC2 C
vC3 C
a b c
Four-level topology
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 37
Socrates – Erasmus Visit
Four-Level Multilevel Inverter
0 10 20 30 40 50 60-400
-200
0
200
400
600
800 vC1
vC2
vC3
ia ib ic
Time (ms)
vab / 3
0 10 20 30 40 50 60-400
-200
0
200
400
600
800
Time (ms)
vC1
vC2vC3
ia ib ic
vab / 3
0 10 20 30 40 50 60-400
-200
0
200
400
600
800
Time (ms)
vC1
vC2
vC3
ia ib ic
vab / 3
Example operating under unity power factor
m=0.4 m=0.5 m=0.6
J. Pou, R. Pindado, and D. Boroyevich, “Voltage-Balance Limits in Four-Level Diode-Clamped Converters With Passive Front Ends,” IEEE Trans. Ind. Electron., vol. 52, no. 1, pp. 190-196, Feb. 2005.
Voltage balance problems
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 38
Socrates – Erasmus Visit
Limits of Voltage Balance
ϕπ cos3
=m
Four-Level Converter
n-Level Converter (n→∞)
UnstableArea
-180 -150 -30 0 60 1500.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Mod
ulat
ion
Inde
x, m
Load Current Angle (Degrees)
-90 -60 30 90 120 180-120
M. Marchesoni and P. Tenca, “Theoretical and practical limits in multilevel MPC inverters with passive front ends,”in Proc. EPE’01, Graz, Austria, Aug. 2001.
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 39
Socrates – Erasmus Visit
Outline
1. Two-Level Inverter2. Multilevel Inverters
- Cascade H-Bridge Inverter- Flying-Capacitor Inverter- Diode-Clamped Inverter
3. Back-to-Back Connection
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 40
Socrates – Erasmus Visit
AC-DC-AC NPC-Based System
(NP)
CvC2
vC1C
rVd
st
a
b
c
Wind-Turbine NPC Converter Grid-Connected NPC Converter
vr
vs
vt
3*Lgiwt ig
Multipole Synchronous Wind Turbine
ElectricalGrid
Back-to-back-connected NPC converters. Example of application to MPSG wind turbines.
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 41
Socrates – Erasmus Visit
-180 -150 -30 0 60 1500.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Out
put M
odul
atio
n In
dex,
mo
Output Phase Current Angle, ϕo (Degrees)
-90 -60 30 90 120 180-120
Passive Front End
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
Conditions: constant output current (IRMSo=ct.), unity input power factor (ϕi=0o, 180o), and 100% efficiency (η=1).
-180 -150 -30 0 60 1500.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Out
put M
odul
atio
n In
dex,
mo
Output Phase Current Angle, ϕo (Degrees)
-90 -60 30 90 120 180-120
Passive Front End
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
-180 -150 -30 0 60 1500.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1
Out
put M
odul
atio
n In
dex,
mo
Output Phase Current Angle, ϕo (Degrees)
-90 -60 30 90 120 180-120
Passive Front End
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
mi=0.5mi=0.6mi=0.7mi=0.8mi=0.9
Voltage-balance Improvements
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 42
Socrates – Erasmus Visit
Matlab-Simulink Simulation Platform
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 43
Socrates – Erasmus Visit
0 0.05 0.1 0.15 0.2 0.25 0.3
Time, s
vr vs vt
0-400
-200
0
200
400
(V)
0 0.05 0.1 0.15 0.2 0.25 0.3
Time, s
Real Angle
0 0
2
4
6
8 Detected Angle
0 0.05 0.1 0.15 0.2 0.25 0.3-50 -25
0 25 50 75
100
Time, s
Vdc/10
ir is it
(V),(A)
(rad)
Two-phase voltage dip process with a fifth harmonic
Utility Voltages
Positive-Sequence Phase Angle
Utility Currents and DC-Link Voltage
Simulation Results
AC/DC/AC Converters: Two-Level and Multilevel VSIPage 44
Socrates – Erasmus Visit
Remarks
• Multilevel topologies can be applied to high-power wind-turbine systems. They are expected to be extensively used when the wind turbines rated power reaches about 10 MW.
• Among the multilevel topologies, the three-level NPC is the most produced used nowadays. An important drawback of this topology is the voltage oscillations that may appear in the NP under some operating conditions.
• The back-to-back connection of NPCs forms an AC/DC/AC system. In such a configuration the NP voltage oscillations become significantly attenuated.