The document discusses the modular multilevel converter (MMC) structure and operation, highlighting its series connection of sub-modules for multi-level output voltage production. It outlines the advantages, such as low total harmonic distortion and scalability, as well as disadvantages, including the need for voltage balancing and monitoring. Additionally, it covers mathematical models and control strategies for MMC operation along with simulation results.

1. Modular Multilevel Converter
(MMC)
Ghazal Falahi

2. Modular Multilevel Converter (MMC) structure
2
SM
2
SM
n
SM
(n+1)
SM
(n+2)
SM
1
SM
(2n)
DC
link
va
vb
vc
u0
ipa
Udc/2
Udc/2
ia
ib
ic
Larm
La
Lb
Lc
ipb ipc
ua
ub
uc
Rarm
D1
D2
S1
S2
ipa Vc
incinbina
Larm Larm
Rarm
Rarm
Larm
Rarm
Larm Larm
Rarm
Rarm
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

3. MMC sub-module operation
3
D1
D2
S1
S2
ipa
Vc
D1
D2
S1
S2
ipa
Vc
D1
D2
S1
S2
ipa
Vc
D1
D2
S1
S2
ipa
Vc
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. 4
va
vb
vc
u0
ia-­‐up
ia-­‐low
Udc/2
Udc/2
ia
ib
ic
Larm
La
Lb
Lc
ib-­‐up ic-­‐up
ib-­‐low ic-­‐low
ua
ub
uc
Rar
m
Larm Larm
Larm Larm Larm
Rar
m
Rarm
Rarm Rarm Rarm
Inner
voltage
Inner
voltage
Inner
voltage
Inner
voltage
Inner
voltage
Inner
voltage
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

5. 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
dv
dt
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

6. MMC mathematical equations
6
icirc =
ip +in
2
varm = vSM
i=0
n
∑ + Larm
diarm
dt
+ Rarmiarm
uk − u0 = varm
uk − (vk + u0 ) = varm
Vk : Phase voltage
K= a, b, c
uk (t) =
Udc
2
mk (t)
mk (t) = mcos(ω0t +ϕ)
q MMC mathematical model
q MMC grid connection dynamic
Arm voltage
Output voltage
Circulating current
Modulation
Output voltage

7. MMC operation and analysis
7
)cos(
22
)(,_ t
V
m
V
tV dcdc
refkarm ω−=
)cos(
23
)( ϕω −+= t
II
ti adc
arm
Upper arm reference voltage
Arm current
Varm,ref
iarm
D2 conducts
S2 conductsD1 conductsS1 conducts
0
q Device operation in MMC sub-module
m = 1
φ = 0

8. 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
ipa
Vc
D1
D2
S1
S2
ipa
Vc
D1
D2
S1
S2
ipa
Vc
D1
D2
S1
S2
ipa
Vc
(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

9. 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

10. 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
PI
Vc*
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)
PI
i*dref
Vod
iod
PI
i*qref
ω0Leq
ω0Leq
ioq
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)
dAneg
VAu*
VBju* Vi/n E/(2n)
Vju*
(j=n+1-­‐2n)
dAneg
Modulation reference generation

11. 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 SHENLM
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

12. Passive components design ( Arm inductor
and Sub-module capacitor)
12
L ≥
Vdc
2αmax
!! =
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

13. 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)
Phasecurrents(pu)
ia
ib
ic
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-LinePWMvoltages(pu)
VaLL
VbLL
VcLL
Simulation results of a grid connected MMC with 3 sub-modules in each arm in Matlab

14. 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 0.6
0.97
0.98
0.99
1
1.01
1.02
1.03
time (secs)
Sub-modulescapacitorvoltages(pu)
Vsm1
Vsm2
Vsm3
Vsm4
Vsm5
Vsm6
0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6
0
0.5
1
1.5
2
2.5
3
time (secs)
Phase1upperandlowerarmvoltages(pu)

15. 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