Modular Multilevel Converter (MMC)

Ghazal Falahi

Modular Multilevel Converter (MMC) structure

2

SM  2

SM  n

SM  (n+1)

SM  (n+2)

SM  1

SM  (2n)

DC  link

vavb

vc

u0

ipa

Udc/2

Udc/2

iaib

ic

Larm

LaLbLc

ipb ipc

uaub

uc

Rarm

D1

D2

S1

S2

ipa Vc

incinbina

Larm Larm

RarmRarm

Larm

Rarm

Larm Larm

RarmRarm

q Modular multilevel converter

1.  Series connection of sub-modules

Make the arm of the converter to build

the output voltage stepwise

2. Sub-modules are Half-bridge (HB) or

Full-bridge (FB) converters

3. Each sub-module has a capacitor

with average voltage of

Udc

N

arm

leg

4. With n sub-modules in arm of the

converter output voltage has n+1 levels

MMC sub-module operation

3

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

iarm>0

iarm<0

Sub-module inserted

Capacitor in discharge mode

Sub-module bypassed

Sub-module inserted

Capacitor in charge mode

Sub-module bypassed

4

vavbvc

u0

ia-­‐up

ia-­‐low

Udc/2

Udc/2

iaib

ic

Larm

LaLbLc

ib-­‐up ic-­‐up

ib-­‐low ic-­‐low

ua

ub

uc

Rar

m

Larm Larm

Larm Larm Larm

Rar

m

Rarm

Rarm Rarm Rarm

Innervoltage

Innervoltage

Innervoltage

Innervoltage

Innervoltage

Innervoltage

N ≥Udc

Usm

Modular Multilevel Converter operation

q MMC equivalent circuit

q  Number of sub-modules in MMC arm

Each arm of the converter is equivalent

To a controlled voltage source with

magnitude of and a series

inductor

Where nactive is number of inserted

sub-modules

nactive ×Udc

N

MMC advantages and disadvantages

1.  Low THD

2.  Low on devices and good voltage sharing for semiconductors

3.  Modular structure with identical modules which has redundancy and allows to substitute failed

modules

4.  Scalable and no DC link voltage limitation

5.  Simple mechanical construction

6.  No need for bulk filters on ac side

7.  Lower losses

5

dvdt

q  Advantages

q  Disadvantages

1.  Extra controller required for balancing of capacitor voltages

2.  Need for monitoring all capacitor voltages

3.  Circulating current consisting double fundamental frequency component and increases device

losses if not suppressed

MMC mathematical equations

6

icirc =ip + in2

varm = vSMi=0

n

∑ + Larmdiarmdt

+ Rarmiarm

uk −u0 = varm

uk − (vk +u0 ) = varm

Vk : Phase voltage K= a, b, c

uk (t) =Udc

2mk (t)

mk (t) =mcos(ω0t +ϕ )

q MMC mathematical model

q MMC grid connection dynamic

Arm voltage

Output voltage

Circulating current

Modulation

Output voltage

MMC operation and analysis

7

)cos(22

)(,_ tVmVtV dcdcrefkarm ω−=

)cos(23

)( ϕω −+= tIIti adcarm

Upper arm reference voltage

Arm current

Varm,ref

iarm

D2 conducts S2 conducts D1 conducts S1 conducts

0

q  Device operation in MMC sub-module

m = 1 φ = 0

iarm>0

S1 or D2

S1

D2

iarm<0

S2 or D1

D1

S2

Device operation principal in MMC sub-modules

8

The arm current flowing out of the sub-module is considered as positive (a) and the current flowing into sub-module is considered as negative

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

D1

D2

S1

S2

ipaVc

(a) iarm>0

(b) iarm<0

0, >dt

dV refarm

0, <dt

dV refarm

0, >dt

dV refarm

0, <dt

dV refarm

q  Logic of operation

1.  Direction of arm current determines which devices can operate 2.  The rate reference arm voltage change determines if a sub-

module is inserted or bypassed

State S1 S2 Vsm

1 ON OFF Vc

2 OFF ON 0

Semiconductor rating

9

I!"#!$(t) =I!"3 ± !!" 2

2 sin!(!")

!!_!"# =!!"!4 + !!"

!

9

Valve current:

Valve rms current:

q Device voltage

Device voltage rating is the average capacitor voltage rating of sub-modules

With a margin depending on maximum allowed ripple

Udc

N

q Device current Device current in MMC is found from the following equations

Modular Multilevel Converter Conventional Control [1]

10

1.  An individual capacitor voltage controller

2.  The averaging controller

3.  The system controller

4.  Modulation reference generation

PI PI

1/2

Vc*

Vcu

Ik-­‐low

Ik-­‐up

Icir*

Icir

VAu*

Total DC voltage controller

PIVc*

Vcju  

(j=1-­‐2n)

±

-1 :-Ik-up , Ik-low ≥ 0+1 :-Ik-up , Ik-low ≤ 0

VBju*

Individual DC voltage controller

Vmk(k=a,b,c)

PIi*dref

Vod

iod

PIi*qref

ω0Leq

ω0Leqioq

Voq

3dq/abc

System controller ![1] Hagiwara, Makoto, and Hirofumi Akagi. "Control and experiment of pulsewidth-modulated modular multilevel converters." Power electronics, IEEE Transactions on 24.7 (2009): 1737-1746.

VAu*

VBju* Vi/n E/(2n)

Vju*  (j=1-­‐n)

dAnegVAu*

VBju* Vi/n E/(2n)

Vju*  (j=n+1-­‐2n)

dAneg

Modulation reference generation

MMC modulation methods

11

[1] Wang, Jun, Rolando Burgos, and Dushan Boroyevich. "A survey on the modular multilevel converters—Modeling, modulation and controls." Energy Conversion Congress and Exposition (ECCE), 2013 IEEE. IEEE, 2013.

Multilevel Modulation

Fundamental switching frequency

High switching frequency

Space vector PWM

Sinusoidal PWM

Level shifted PWM

Phase shifted PWM

Space vector control SHE NLM

High switching frequency modulation

techniques ü  Suitable for small & large number of sub-modules

ü  Lower harmonics

× High losses

Fundamental switching frequency modulation

techniques ü  Suitable for large number of sub-modules

ü  Lower losses

Passive components design ( Arm inductor and Sub-module capacitor)

12

L ≥ Vdc2αmax

!! =1

(8!!!!!!!)( !!3!!! + !!")

!!" = !!3.!.!.!! . !.!!! 1− (!. !"#$2 )!

!!

Ps: three phase apparent power K: voltage modulation index Cosφ: power factor N: number of sub-modules, ω0 is the fundamental frequency, VC: mean value of sub-module voltages ε: sub-module voltage ripple

[1] Tu, Qingrui, et al. "Parameter design principle of the arm inductor in modular multilevel converter based HVDC." Power System Technology (POWERCON), 2010 International Conference on. IEEE, 2010. [2] Zygmanowski, Marcin, Boguslaw Grzesik, and Radoslaw Nalepa. "Capacitance and inductance selection of the modular multilevel converter." Power Electronics and Applications (EPE), 2013 15th European Conference on. IEEE, 2013.

1.  Limit the circulation current

2.  Limit the fault current rise rate

q  Criteria to select arm inductor [1]:

q  Sub-module capacitor selection [2]:

1.  Provide the output power for at least one cycle

If DC link is defective

2. Limit sub-module voltage ripple

Three phase line PWM voltages and phase currents in MMC with sub-modules in each arm

13

0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6

-1

-0.5

0

0.5

1

time (secs)

Phas

e cur

rent

s (pu

)

iaibic

0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6

-2

-1

0

1

2

time (secs)

Line

-Lin

e PW

M v

olta

ges

(pu)

VaLLVbLLVcLL

Simulation results of a grid connected MMC with 3 sub-modules in each arm in Matlab

Arm voltages and sub-module voltages of the simulated MMC

14

0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60.97

0.98

0.99

1

1.01

1.02

1.03

time (secs)

Sub-

mod

ules c

apac

itor v

oltag

es (p

u)

Vsm1Vsm2Vsm3Vsm4Vsm5Vsm6

0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60

0.5

1

1.5

2

2.5

3

time (secs)Phas

e 1 u

pper

and

lowe

r arm

volta

ges (

pu)

References

[1] Falahi, Ghazal. "Design, Modeling and Control of Modular Multilevel Converter based HVDC Systems." PhD Dissertation NCSU (2014). [2] Falahi, Ghazal, and Alex Q. Huang. "Design consideration of an MMC-HVDC system based on 4500V/4000A emitter turn-off (ETO) thyristor." Energy Conversion Congress and Exposition (ECCE), 2015 IEEE. IEEE, 2015. [3] Falahi, Ghazal, and Alex Huang. "Control of modular multilevel converter based HVDC systems during asymmetrical grid faults." Industrial Electronics Society, IECON 2014-40th Annual Conference of the IEEE. IEEE, 2014. [4] Falahi, Ghazal, Wensong Yu, and Alex Q. Huang. "THD minimization of modular multilevel converter with unequal DC values." Energy Conversion Congress and Exposition (ECCE), 2014 IEEE. IEEE, 2014. [5] Falahi, Ghazal, and Alex Huang. "Low voltage ride through control of modular multilevel converter based HVDC systems." Industrial Electronics Society, IECON 2014-40th Annual Conference of the IEEE. IEEE, 2014.

15