modulation and control for cascaded multilevel converters marco liserre [email protected] modulation...

Marco Liserre [email protected]

Modulation and control for cascaded multilevel converters


Marco Liserre

[email protected]



A glance at the lecture content A glance at the lecture content

• Cascaded multilevel converters:

• hybrid solution

• applications

• PI-based control

• Multilevel modulations in case of time-varying dc voltages:

• generalized hybrid modulation

• generalized phase-shifting carrier modulation



A glance at the lecture content A glance at the lecture content • Cascaded multilevel converters:

• hybrid solution

• applications







active rectifier inverter

1 1 21

1( )

n

i ii

x e Rx P xL

2 1 21 i i i i

i

x P x xC

1 1 21

1( )

n

i ii

x e Rx P xL

H-bridge multilevel convertersH-bridge multilevel converters



H-bridge multilevel convertersH-bridge multilevel converters• Advantages

• high voltage and high power

• modularity and simple layout

• reduced number of components compared to other multilevel topologies

• phase voltage redundancy

• reduced stress for each component

• small filters

• Disadvantages

• voltage unbalance of the dc link capacitors



H-bridge multilevel convertersH-bridge multilevel converters• How does it work ?

L

T21

a

i

C1

io1

iC1

iL1

+

vc1

-

e

bC2

io2

iC2

iL2

+

vc2

-

T11 T31

T41

T12

T22 T42

T32

R

R1

R2

if VC1=VC2=Vo

Vao = Vo T11 and T41 ON

Vao = -Vo T21 and T31 ON

Vao = 0 T11 and T31 ON

or

T21 and T41 ON

The lower bridge produces the same voltage levels by turning on/off the corresponding switches



H-bridge multilevel convertersH-bridge multilevel converters• How does it work ?

L

T21

a

i

C1

io1

iC1

iL1

+

vc1

-

e

bC2

io2

iC2

iL2

+

vc2

-

T11 T31

T41

T12

T22 T42

T32

R

R1

R2

Vab T11 T31 T12 T32 S1 S2

1 +2 Vo 1 0 1 0 1 1 2 Vo 1 0 0 0 1 0 3 Vo 1 0 1 1 1 0 4 Vo 0 0 1 0 0 1 5 Vo 1 1 1 0 0 1 6 0 0 0 0 0 0 0 7 0 0 0 1 1 0 0 8 0 1 1 0 0 0 0 9 0 1 1 1 1 0 0 10 0 1 0 0 1 1 -1 11 0 0 1 1 0 -1 1 12 -Vo 0 0 0 1 0 -1 13 -Vo 1 1 0 1 0 -1 14 -Vo 0 1 0 0 -1 0 15 -Vo 0 1 1 1 -1 0 16 -2 Vo 0 1 0 1 -1 -1

Voltage Levels and Switching Configurations



Hybrid multilevel converterHybrid multilevel converter

Multilevel converters based on the use of hybrid cell of converters subjected to different dc voltage levels.

The basic idea is to use a converter switching at low frequency hence employing Gate-Turn Off thyristors or IGCTs (as a quasi-square wave modulation technique is used) and one switching at higher frequency.

the fact that the dc-link voltage levels are in an integer relation among them allow to have (for subtraction) more voltage levels.



Hybrid multilevel converterHybrid multilevel converter• The converter working at low switching frequency is the greatest

contributor to the fundamental component of the overall output voltage and generates a considerable and well known harmonic content (typical of quasi-square waveform), and the PWM converter is generating an opposite harmonic content and the required additional fundamental component to obtain the desired voltage.

• The principle is very similar to that one of active filters. The positive consequence is that the low frequency converter (that is the converter with the higher dc-link voltage level) can be designed as an high voltage converter while the other ones can be designed as low voltage converters.

REF M. D. Manjrekar, P. K. Steimer, and T. A. Lipo, ” Hybrid Multilevel Power Conversion System: A Competitive Solution for High-Power Applications,” IEEE Transactions On Industry Applications, Vol. 36, No. 3, May/June 2000.



reduced line current harmonic distortion reduced weight and encumbrance voltage regulation

Active rectifier in traction systems

ApplicationsApplications



reduced EMI Many dc-links by one source

no step-down transformer

ApplicationsApplications



ApplicationsApplications• Hybrid electric vehicles with different electric storages

REF L. M. Tolbert, F. Z. Peng, T. Cunnyngham and J. N. Chiasson, ”Charge balance control schemes for cascade multilevel converter in hybrid electric vehicles,” IEEE Trans. on Industrial Electronics, vol. 49, n. 5, October 2002. pp. 1058 - 1064.



ApplicationsApplications• Distributed generation multilevel converters: photovoltaic system

REF F.-S. Kang, S.-J. Park, S.-E. Cho, C.-U. Kim and T. Ise, ”Multilevel PWM inverters suitable for the use of stand-alone photovoltaic power systems,” IEEE Transactions on Energy Conversion, vol. 20, n. 4, December 2005. pp. 906-915.



ApplicationsApplications• In Unified Power Flow Controller , employing multilevel converters, the

regulation of the dc voltage levels can be used to meet different design requirements in terms of harmonic compensation and losses reduction

shunt DVR

Iload

Ic

E

IgLg

VDVR

REF T. Gopalarathnam, M. D. Manjrekar and P. K. Steimer, ”Investigations on a unified controller for a practical hybrid multilevel power converter,” in APEC 2002, vol. 2, March 2002, pp. 1024-1030.




• hybrid solution

• applications







PI control of cascaded multilevel convertersPI control of cascaded multilevel converters In order to fulfil the control requirements above mentioned different

schemes based on PI controllers can be considered.

In ideal conditions completely independent H-bridges

would be expected in order to manage

distinct power transfers and

different voltage levels on each structure.

L

T21

a

i

C1

io1

iC1

iL1

+

vc1

-

e

bC2

io2

iC2

iL2

+

vc2

-

T11 T31

T41

T12

T22 T42

T32

R

R1

R2

REF A. Dell’Aquila, M. Liserre, V.G: Monopoli, P. Rotondo, “Overview of PI-based solutions for the control of the dc-buses of a single-phase H-bridge multilevel active rectifier”, IEEE Transactions on Industry Applications, May/June 2008.



First control scheme of the multilevel rectifierFirst control scheme of the multilevel rectifierA. One voltage PI and one current P for each H-bridge

to control them independently

s

KK 1,iv

1,pv vc1

*

vc1

+_

i*

e

1,piK

e

S1

P1

P2

i

1/E

PW

M

_+ _

+1/Vd

s

KK 1,iv

1,pv vc2

*

vc2

+_i*

e

S2

i

1/E

_+ 1/Vd2,piK

e

_ +

errorerror

This results in ineffective control of the grid current leading the system to the instability.

Instability is caused by the attempt at independently controlling the same current through two controllers.



Second control scheme of the multilevel rectifierSecond control scheme of the multilevel rectifier

B. Two PI’s for the two dc-links and one P for the current

S2·i S2

s

KK 1,iv

1,pv vc1

*

vc1

+_i*

piK

e

vl S1+S2 P1

P2

i

PW

M

_+

s

KK 2,iv

2,pv vc2

*

vc2

+_

_ + +_1/Vd

S2

S1

e1/E

+

i

+

÷

errorerror

The idea is to control the dc current in order to charge or discharge the dc-link.

However the non-linear relation i02=S2·i can not be used to calculate the switching function S2 simply dividing by i. Thus the division leads to instability problems both at start-up and

when the two reference voltages for the dc-links are different.



ThirdThird control control schemescheme of the multilevel rectifier of the multilevel rectifier

C. One PI for the overall voltage, one PI for a dc-bus and a P for the current

S2

s

KK 1,iv

1,pv vc1

*+vc2* I*

max

vc1+vc2

+_i*

e

piK

e

vl S1+S2P1

P2

i

1/E

PW M

_+

s

KK 2,iv

2,pv vc2

* S2,max

vc2

+_

e1/E

_ + +_1/Vd

S2

S1

The sum of the vC1 and vC2 is controlled through the choice of the grid current amplitude i.

Then the grid current is controlled calculating the voltage generated by the multilevel converter on the ac side.

The control of the voltage vC2 is made through another controller that directly selects the switching function amplitude S2,max

This control scheme works with different reference voltages and loads



Simulation for reference and load steps: scheme 1Simulation for reference and load steps: scheme 1

start-up dc-bus 1 load step

ERROR !




start-up dc-bus 2 reference

step

ERROR ! ERROR !



Vc1+Vc2 voltage controller

Currentloop

sC2

SS max,2max,1

s

KK 1,iv

1,pv 1

1 sm T s Systemplant

Vc1*(s)+Vc2

*(s) I*max(s) Vc1(s)+Vc2(s)

+_

Imax(s)

Tuning procedure: voltage loopTuning procedure: voltage loop

Vc2 voltage controller

max

2

I

C s s

KK 2,iv

2,pv

System plant

Vc2*(s) S2,max(s) Vc2(s)

+_

The two voltage control loop have different plants and they are designed following the “optimum

symmetrical” criteria



Indipendent load transientsIndipendent load transients



Indipendent voltage stepsIndipendent voltage steps



Loads unbalance conditionLoads unbalance condition

dc-link 1 voltage

load step on the dc-link

load step on the other dc-link



Different dc voltages conditionDifferent dc voltages condition

dc-link 1 voltage

reference step on the dc-link

reference step on the other dc-link




• hybrid solution

• applications







Hybrid modulation techniquesHybrid modulation techniques These techniques have been developed in order to optimize the

harmonic content of the voltage generated by multilevel converters with different dc-voltage levels

The basic principle can be easily explained in case two bridges are adopted:

One converter switches at low frequency (semi-square waveform). It carries all the fundamental power but it produces also low frequency harmonics

The other converter switches at high frequency (PWM), it works as an active filter compensating the harmonics generated by the first bridge

REF M. D. Manjrekar, P. K. Steimer and T. A. Lipo, ”Hybrid multilevel power conversion system: a competitive solution for high-power applications,” IEEE Trans. on Industry Applications, vol. 36, n. 3, May-June 2000. pp. 834-841.

C. Rech, H. A. Grundling, H. L. Hey, H. Pinheiro and J. R. Pinheiro, ”A generalized design methodology for hybrid multilevel inverters,” in IECON 02, vol. 1, November 2002. pp. 834-839.



Hybrid modulation techniquesHybrid modulation techniques More voltage levels are obtained as subtraction of the different dc-link

voltages

Hence four of the multilevel states that, in case of equal dc-link voltages, generate zero voltage on the ac side, in case of hybrid modulation, and non-equal dc-link voltages, generate one voltage level more both positive and negative

Major drawbacks:

It is difficult to control the dc-link voltages in case of active rectifier application

The dc-link currents have an heavy harmonic content (that is compensated on the ac-side and not on the dc-side)



Carrier shifting cascaded PWM techniquesCarrier shifting cascaded PWM techniques

These techniques have been developed in order to obtain optimum harmonic cancellation

Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier multiple

These techniques allow different power transfers and different voltage levels for each bridge

However in case of different voltage levels for each bridge the harmonic cancellation is not perfect

1 1012

0

2122cos1cos2

14

cos)(

m n

N

iicn

dc

dc

mtntmnmMmJm

V

tMNVtv

( 1)i

i

N

, 1, 2,3...m kN k •carrier shifting




0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-1

0

1

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-100

0

100

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-100

0

100

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055 0.06

-200

0

200

h

0 10 20 30 40 50 600

0.5

1

h

A [

pu]

v ab [

V]

v cd [

V]

v ad [

V]

v ref,

Vtr

iv re

f, V

tri

t [s]

t [s]

t [s]

t [s]

t [s]



Carrier shifting and hybrid modulationCarrier shifting and hybrid modulation

Carrier Shifting and Hybrid modulation (CSM and HM) techniques performances rely on time-invariant dc-voltages

However many applications such as traction, distributed generation and active filter could take advantage by using time-variant dc-link voltages

In this case both the techniques are not adequate:

CSM fails in obtaining optimum harmonic cancellation while preserving fundamental voltage control

HM cannot preserve fundamental voltage control, even if optimal harmonic cancellation could be possible



Proposed generalized hybrid modulationProposed generalized hybrid modulation The proposed Generalized Hybrid Modulation (GHM) technique

considers non-integer relationships between dc-link voltages which can be time-dependent

Then, switching signals will depend on the instantaneous values of the dc-link voltages and can not be evaluated independently for each PWM converter, it means that independent power management is lost

in case two bridges are adopted: One converter switches at low frequency (semi-square waveform). It carries all the

fundamental power but it produces also low frequency harmonics

The other converter switches at high frequency (PWM), adjusting switching signals to compensate the effect of time-variant dc-link levels and the absence of an integer ratio among them. The final objective is to minimize the output voltage THD

REF M. Liserre, A. Pigazo,V. G. Monopoli, A. Dell’Aquila, V. M. Moreno, “A Generalised Hybrid Multilevel Modulation Technique Developed in Case of Non-Integer Ratio Among the dc-Link Voltages” ISIE 2005, Dubrovnik (Croatia), June 2005.



Proposed generalized hybrid modulationProposed generalized hybrid modulation

Low voltage converter

High voltage converter



Proposed generalized hybrid modulationProposed generalized hybrid modulation Example:

v*(k)>V1(k)

Variations in V1(k) and V2(k) must be at a lower frequency than fsw=1/TC

LV converter must be centered on TC for a minimum final THD and

hence:0

V2(k)

V1(k)

V1(k)+V2(k)

v*(k)

TC

t2(k)k k+1

)()(* 221 ktkVTkVTkv CC

)(

)()(*)()(

2

122 kV

kVkv

T

ktkD

C

1)(2 kDD1(k)



Proposed generalized hybrid modulationProposed generalized hybrid modulation Switching plane

4 regions more respect to the traditional hybrid modulation

The proposed modulation has 9 regions in order to obtain optimum harmonic content and exact fundamental voltage also in case of time-varying dc-link voltages



Proposed generalized hybrid modulationProposed generalized hybrid modulation The fundamental frequency harmonics compensate, as in the hybrid modulationtechnique, the higher voltage converter harmonics.



Comparison in terms of modulation signalsComparison in terms of modulation signals



Simulation results: conditions and parametersSimulation results: conditions and parameters

1

max( *( ))v kM

V

2

2

n

n

VWHC

n

Analyzed modulation techniques: CSM, HM, GHM

Linear region

Modulation index (M) has been chosen in [0.6, 1.4] (step = 0.1)

LV converter dc-voltage (V2) is varied in [0.51,0.99] (step = 0.05)

Equal switching losses => mf = 40 for HM and GHM mf = 20 for CSM

Evaluation parameters:- Amplitude of the output voltage fundamental frequency component- Weighted Harmonic Content (WHC)- Weighted Total Harmonic Distortion (WTHD)

1

WHCWHC

VWTHD



Simulation results: generalized hybrid modulation techniqueSimulation results: generalized hybrid modulation technique

overall output voltage waveform

High voltage converter output waveform

Low voltage converter output waveform

M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40



Simulation results: time-domain comparisonSimulation results: time-domain comparison

GHM

HM

CSMExpects equal DC voltages

LV converter uses only its DC voltage to establish duty cycles

M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mf

shifting=20



Simulation results: spectra comparisonSimulation results: spectra comparison

GHM

HM

CSM

M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mf

shifting=20

I1=0.96 V (p.u.) WHC=1.19 10-2

I1=1.2 V (p.u.) WHC=7.17 10-4

I1=1.2 V (p.u.) WHC=5.1 10-3



Simulation results: overall comparisonSimulation results: overall comparison

M in [0.6,1.4], V2/V1 in [0.51,0.99], mfhybrid =40, mf

shifting=20

Technique minimum average maximum

GHM 6.2 10-4 0.12 0.5

HM 10-2 23.6 61.3

CSM 10-3 0.14 0.5

% error in the output signal at the fundamental frequency

WHC

Technique minimum average maximum

GHM 3.9 10-4 8.7 10-4 1.6 10-3

HM 5.5 10-4 3.5 10-2 0.13

CSM 8.6 10-4 3.6 10-3 6.6 10-3

GHM - There is not a clear dependency on dc-link voltage values

CSM – WHC improves when arriving to equal DC voltages



Experimental resultsExperimental results

Carrier shifting technique. Time and frequency domains overall output voltage using

V1 = 100 V (V1 = 1.0 pu), V2 = 61 V (V2 = 0.61 pu) and M =

120 V (M = 1.2 pu)

Hybrid Modulation. Time and frequency domains overall output voltage using

V1 = 100 V (V1 = 1.0 pu), V2 = 61 V (V2 = 0.61 pu) and M =

120 V (M = 1.2 pu)

Generalised Hybrid Modulation. Time and frequency domains overall

output voltageusing V1 = 100 V (V1 = 1.0 pu), V2 = 61 V (V2 = 0.61 pu) and M = 120 V

(M = 1.2 pu)



Discussion on the drawbacks of hybrid techniquesDiscussion on the drawbacks of hybrid techniques

M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40

Both converters introduce low frequency current harmonics



Discussion on the drawbacks of hybrid techniquesDiscussion on the drawbacks of hybrid techniques

The major drawback is the fact that is very difficult to control directly the different converters to have full control on the voltage generated by each of them.

In other words it is only possible to decide the overall multilevel modulation signal and not the modulation signal of each converter independently

The direct consequence is that it is difficult to control the dc-link voltages separately in an active rectifier application unless the phase of the converter ac voltages is controlled




These techniques have been developed in order to obtain optimum harmonic cancellation

A suitable phase-shifting among the carrier signals relevant to n different bridges has to be introduced: (i-1)/n, (for i=1, 2, …, n)

Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier multiple

These techniques allow different power transfers and different voltage levels for each bridge

However in case of different voltage levels for each bridge the harmonic cancellation is not perfect

REF M. Liserre, V. G. Monopoli, A. Dell’Aquila, A. Pigazo, V. Moreno, “Multilevel Phase-Shifting Carrier PWM Technique in Case of Non-Equal DC-Link Voltages”, IECON 2006, Paris (France), November 2006.



Principles of the PSC-PWM techniquePrinciples of the PSC-PWM technique

2 converters: The weighted total harmonic distortion (WTHD) of the output signal can be reduced if the carriers of leg A and B are shifted

rad

N cascaded converters: Using symmetrical PWM, the carrier of leg A in each converter must be shifted rad.

The phasorial representation forthe carrier signals is:

12

iN

Inv 1

Inv 1

Inv 2

Inv 3

Inv 4N=4Inv 3

Inv 1

Inv 2

N=3

Inv 2

N=2



Principles of the PSC-PWM techniquePrinciples of the PSC-PWM technique

1 10120 2122cos1cos

2

14cos)(

m n

N

iicn

dcdc mtntmnmMmJ

m

VtMNVtv

The overall output voltage:

where: N is the number of cascaded converters, M is the amplitude modulation coefficient, is the pulsation of the modulating signal, is the pulsation of the carrier signal, is the Bessel function of order 2n-1 and is the relative phase of the carrier signal applied to the leg A of

each converter

0

c12 nJ

i

It can be reducedby applying

...3,2,1, kkNmN

ii

)1(



Proposed PSC-PWM techniqueProposed PSC-PWM technique

The overall output voltage with non-equal dc-link voltages:

1 1

01201

2122cos1cos2

14cos)(

m n

N

iic

dcin

N

i

dci mtntmVnmMmJ

mtVMtv

A reduced WTHD can be obtained if:

02sin

02cos

1

1N

ii

dci

N

ii

dci

mV

mV

02122cos1

0

N

iic

dci mtntmV

And, hence:

which depend on the considered m and can not be verified for all m and i



Proposed PSC-PWM techniqueProposed PSC-PWM technique

The mathematical expression of the WTHD is

1

22

2

V

n

V

WTHD n

n

the minimum WTHD will be reached for m=1:

02sin

02cos

1

1N

ii

dci

N

ii

dci

V

V

Reduced WTHD condition:

The dc-link voltage phasors generate a polygon in the complex plane whose center should match the system origin.

thi01

N

i

dciV

is a phasor with amplitudematching the converter dc-linkvoltage and phase

dciV

i



Original and proposed PSC-PWM. N=3Original and proposed PSC-PWM. N=3

The original PSC-PWM angles can be obtained as a particular solution Asymmetrical PWM angles can be obtained dividing the obtained results

by 2

original

Vdc1=3.2 pu, Vdc

2=1.4 pu and Vdc3=4.4 pu

Shifting angles =0º, 120º and 240º

modified

Shifting angles =0º, 36º and 191º



Comparison of PSC-PWM techniques (N=3)Comparison of PSC-PWM techniques (N=3)

0.7248%

0.5928%

original

modified

V1dc+V2

dc+V3dc= 360V

V1dc<V2

dc<V3dc

M=0.6V1

dc=60V…120VV2

dc=60V…120Vf0=50 Hzfc=1.6 kHz



Comparison of PSC-PWM techniques (N=3)Comparison of PSC-PWM techniques (N=3)

improvement

Evaluation errors ->worst behaviour (-13.6%)

Improvement region ->Up to 50.6%

Limit of the reducedWTHD condition

The reduced WTHD condition can not beverified. Improvementaround 20%

V1dc+V2

dc+V3dc= 360V

V1dc<V2

dc<V3dc

M=0.6



Comparison of PSC-PWM techniques (N=3)Comparison of PSC-PWM techniques (N=3)V1

dc=70VV2

dc=120VV3

dc=170Vf0=50 Hzfc=1.6 kHz

Low M. The original techniqueoperates better. In average, a 3%

At medium M values the proposedmethod improves the WTHD

At high M values the proposed method improves the WTHD around a 20%



ConclusionsConclusions

• It is possible to control independently the dc buses of a cascaded multilevel converter both with a linear controller (PI-based control) both with a non-linear controller (Passivity-based control)

• Multilevel modulators should be adapted in case of time-varying dc voltages:



• A well design controller and a well designed modulation technique are indispensable in order to do not loose the harmonic advantages of the multilevel converter and do not lead the system to instability

modulation and control for cascaded multilevel converters marco liserre [email protected] modulation...

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