emr and inversion-based control of a modular multilevel converter · 2012-10-10 · emr’12 madrid...

EMR’12

Madrid

June 2012

Joint Summer School EMR’12

“Energetic Macroscopic Representation”

« EMR and inversion-based control of a

Modular Multilevel Converter »

Philippe DELARUE

L2EP, University Lille1

[email protected]

EMR’12, Madrid, June 2012 2

« EMR and IBC of MMC »

P, Q ?

Pref, Qref

- Context -

Rated voltage: kV

Rated current: kA

Electrical Network :

400kVeff (690 kV max)

<<<

Baixas

Santa Llogaia

France-Spain HVDC link :

Rated power: 2*1000 MW

DC voltage: ±320 kV

Reactive Power : +/-600 MVAR

Converter Contractor : Siemens

DC cable length: 64 km

Commisioning date: 2014

We are here

Electric power transmission

MMC



E

arm

• No DC bus

• Modular conception

• Difficult to model (High number of IGBTs and diodes)

• Difficult to control (Risks of instabilities)

DC side

AC side

MMC was introduced by

Siemens in 2005

- Context -

leg

module



- Outline -

Context

1. Principle Principle

Arm functionality

2. Arm of a MMC Principle

Modeling and control structure

Balancing strategy

Equivalent model for an arm

3. EMR and IBC of MMC

Step 1: equations

Step 2: EMR

Step 3: Tuning paths

Step 4: IBC

4. Simulation results

Matlab/simulink implementation

Simulation results

Conclusion



1. Principle



iDC

P, Q

E/2

E/2

E/2 E/2

E/2 E/2

Ideally we expect that arm current will be composed of a

DC component (iDC/3) + an AC component (iAC/2)

½ iAC

½ iAC 1/3 iDC

1/3 iDC+ 1/2 iAC

1/3 iDC

E/2

1. Principle : Ideal steady state working

E

To obtain 3-phase sinusoidal AC currents

arm voltages must be composed of a DC

component + an AC component



1. Principle : Arm functionality

v

i

uc1

uc2

uc3

ucN C

C

C

C

n : active cell number

N : total cell number

Inactive cell

ucj=0

ucj uc

Active cell

ucj=uc

ucj uc

v vref



2. Arm of a MMC



v

i

u1

u2

u3

u4

v

i

uc1

uc2

uc3

ucN C

C

C

C

2. Arm of MMC : Modelisation and control structure

v vref

-> Constraint not yet realized: control of uctot

uc1 = uc2 = … = uctot/N

vref u1

u3

u2

u4

Balancing

strategy

-> a choice is required: objective + voltage balancing

uctot = uc1+uc2+uc3+ …. +ucN

or balancing + control of uctot

no = 1 objective: build of v

nc = 4 constraints: control of ucx

ntv= 4 choppers: 4 tuning variables

But ntv < no + nc



i

Capacitor voltage balancing strategy:

v is build with the capacitor voltages:

- the less charged if i>0

- the most charged if i<0

If balancing works well then :

uc1 = uc2 = uc3 = …. = ucN = uc = uctot/N

but uctot is not yet controlled….

v

i

uc1

uc2

uc3

ucN C

C

C

C

2. Arm of MMC : Balancing strategy


v vref

i



tottot

tot icNnidt

duc

N

CNnucv /./

v

i

uc1

uc2

uc3

ucN C

C

C

C

t 0

1

Eq. Average

model

m Eq. Ideal switches model

C/N

ictot

uctot v

i

n/N = m

active cells number

Total cells number

i ictot

v uctot

2. Arm of MMC : Equivalent model

If balancing works well then :


m



3. MMC



Independent state variables: 11 (5 currents + 6 voltages)

Independent tuning variables: 6

Objectives et constraints :

- P and Q control with PFC

- control of the voltages uc

ie

C/N

C/N

C/N

C/N

C/N

C/N

P, Q

E

3. MMC : Equivalent topology / control objectives



Equations (with eventual change of variables) must lead to a most decoupled state

representation.

Change of variables: 222

uldiff

ulv

ludiff

uuu

uue

iii

iu

C/N

C/N

il iv

uu

ul

ucu_tot

ur

ucl_tot

E/2

E/2

vno

L’,R’

L,R

au

al

luv iii Kirchhoff’s current law:

C/N

C/N

uu

ul

ucu_tot

ucl_tot

E/2

E/2 L’,R’

au

al

ur

vno

L,R

L’,R’

L’,R’

ev

3. MMC : Step 1 : equations and change of variables

½ iv

½ iv

idiff

idiff

iv



diff

diff

diff

vv

norv

iRdt

diLu

E

iR

Rdt

diLLvee

2

)2

'()2

'(Equations :

dt

du

N

Ciiuu

dt

du

N

Ciiuu

totcucuuutotcuuu

totclcllltotclll

aa

aa

C/N

C/N

idiff

uu

ul

ucu_tot

ucl_tot

E/2

E/2 L’,R’

au

al

iv

ur

vno

L,R

L’,R’

L’,R’

ev

d, q x2

x3

x6

3. MMC : Step 1 : equations and change of variables



23

Inverse dq

transformation

13

// coupling

3. MMC : Step 2 : EMR

32

dq transformation

[6x6]

icul

ucul

Equivalent

capacitors

dt

du

N

Ci

dt

du

N

Ci

totcucu

totclcl

6

x6

Equivalent

converters

iul

uul 6

cuuutotcuuu

cllltotclll

iiuu

iiuu

aa

aa

m

6 iv

ev

2

2

2

uldiff

ulv

ludiff

uuu

uue

iii

23

Change of

variables

3

idiff

E idiff

u’diff

2L’

diff

diff

diff iRdt

diLu

E

2

[3x3]

3 3 BUS

E

idc

DC side

1

L+L’/2

vr-dq

iv-dq edq

iv-dq

vv

norv iR

Rdt

diLLvee )

2'()

2'(

[2x2] (with dq transformation)

2 2

AC side

NET

vr

iv

3



idiff

BUS

E

idc

E

iv

NET

vr-dq

ev

idiff

u’diff

vr

iv-dq

iul icul

uul ucul 6

edq

iv-dq

iv

The tuning paths link the tuning variables to the variables to be controlled. These

paths must pass through all accumulation elements to be sure to control all state

variables which leads to avoid oscillation or instability problems.

3. MMC : Step 3 : Tuning paths

m

6 6

3

3 2

3 1

2 3

Objectives and constraints :

- P and Q control with PFC

- control of the voltages uc



idiff

BUS

E

idc

E

iv

NET

vr-dq

ev

idiff

u’diff

vr

iv-dq

iul icul

uul ucul 6

edq

iv-dq

iv

ucul

3. MMC : Step 4 : MCS

6 6

3

3 2

3 1

2 3

ucul_ref

P_ref

Q_ref

3

2

6



iu

C/N

C/N

il

uu

ul

ucu_tot

ucl_tot

L’,R’

au

al

½ iAC

½ iAC

idiff-DC idiff-AC

idiff

2

ˆˆ

2.

2

ACdiffvACph

DCdiff

T

cuieP

iE

dt

dW

2

ˆˆ

2.

2

ACdiffvACph

DCdiff

T

clieP

iE

dt

dW

ACdiffDCdiffdiff iii

idiff-DC <ucu>

<ucl> idiff-AC

idiff-DC <ucl>+<ucu>

idiff-AC <ucl> - <ucu>

3. MMC : Storage energy control

22

22

ACdiff

T

cl

ACdiff

T

cu

Pi

E

dt

dW

Pi

E

dt

dW

.

.idiff <ucu>

<ucl>



idiff

BUS

E

idc

E

iv

NET

vr-dq

ev

idiff

u’diff

vr

iv-dq

iul icul

uul ucul 6

edq

iv-dq

iv

ucul

P_ref

idiff-ref

P_ref ev E

X

3

Q_ref

Uc_ref

3. MMC : Step 4’ : final MCS

6 6

3

3 2

3 1

2 1

2

3 3

3



4. Simulation results : Matlab/simulink implementation

vr_

iv_

ur_

iv_.

va,vb,vc --> uac,uab

? ? ?

teta

SE

source DC

E

u'diff_

idiff_

idiff_.

self l

ur_

eu_

iv_

iv_.

self eq ll+l/2

SE

reseau tri1

sample based

uc_tot

m_

i_ul

uc_ul

ic_

les 6 hacheurs eq.

ic_ uc_tot

les 6 condos

iv_

ev_

iv_.

eu_

euac,eubc-->eva,evb,evc

i_ul_refidif f _ref

u'dif f _ref

ev _ref

uc_ul_ref

In1

Out2

Out3

Subsystem

ev_dq

teta

ev_

Park2iv_

teta

iv_dq

Park1

vr_

teta

vr_dq

Park

i_ul

m_

vr_

idc_

idiff_

iv_

E

idiff_

E_

idc

E --> E, E, E

idiff_

uc_ul

iv_

u'diff_

i_ul

ev_

Couplage

électrique2

uc_tot

uc_ul_ref

m_ref

uc_tot

ev _

idc_sur_3

iv _

iuv _ref

idif f _ref

idif f _

E_

u'dif f _

v r_dq

iv _dq

iv _dq_ref

ev _dq




C/N

C/N

iu

il

ucu

ucl

L’,R’

au

al

iv

iul

ucul

P, Pref

iv

iu

il

2 kA

1 kA

500 kV

1 GW

0

0

0

0



Conclusion



- MMC is a complex system difficult to model and to

control.

- With the help of ‘EMR philosophy’ we have obtained a

relatively simple model (for the control)

- By ‘mechanical’ inversion of this model we have

obtained a control structure with a number of controllers

equals to the number of state variables of the system (

that leads to avoid instability problems which occur when

the number of controlled variable < the number of state

variable) .

Conclusion



Conclusion









- Author -

Dr. Philippe DELARUE

University Lille 1, L2EP, France

Associate Professor since 1991

PhD in Electrical Engineering at University of Lille (1989)

Research topics: EMR, power electronics, multi-machine systems

emr and inversion-based control of a modular multilevel converter · 2012-10-10 · emr’12 madrid...

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