Performance of the Modular Multilevel ConverterWith Redundant Submodules

Noman Ahmed, Lennart Angquist, Antonios Antonopoulos, Lennart Harnefors, Staffan Norrga, Hans-Peter Nee.Department of Electrical Energy Conversion

KTH Royal Institute of Technology, Stockholm, Sweden.

Abstract—The modular multilevel converter (MMC) is thestate-of-the-art voltage-source converter (VSC) topology used forvarious power-conversion applications. In the MMC, submodulefailures can occur due to various reasons. Therefore, additionalsubmodules called the redundant submodules are included in thearms of the MMC to fulfill the fault-safe operation requirement.The performance of the MMC with redundant submoduleshas not been widely covered in the published literature. Thispaper investigates the performance of the MMC with redundantsubmodules in the arms. Two different control strategies areused and compared for integrating redundant submodules. Theresponse of the MMC to a submodule failure for the twostrategies is also studied. Moreover, the operation of the MMCwith redundant submodules is validated experimentally using theconverter prototype in the laboratory.

Index Terms—High-voltage dc (HVDC) transmission, modularmultilevel converter (MMC), redundant submodules, voltage-source converter (VSC).

I. INTRODUCTION

THE modular multilevel converter (MMC), first presentedin [1], has arguably become the most promising converter

topology for various medium and high power-conversion ap-plications [2], such as high-voltage dc (HVDC) transmission[3], [4], variable-speed drives [5], electric railway supplies [6],propulsion system of electric ships [7], and grid connection ofenergy storage systems [8]. Compared with conventional two-and three-level voltage-source converters (VSCs), the MMCallows reduction of the switching frequency down towardsthe fundamental frequency, whereas the harmonic content ofthe output voltage is still kept low owing to a large numberof levels. Other benefits are high scalability due to modulardesign and no requirement for a common dc-link capacitor[9], [10].

The research on the operation and control of the MMCincludes various modulation techniques such as carrier-basedpulse-width modulation (PWM) [11], [12], selective harmonicelimination PWM (SHE-PWM) [13], and nearest level con-trol (NLC) modulation [14]. The balancing control of thesubmodule capacitor voltages within the arm is a key issue.Several alternative voltage-balancing methods were presentedin [15], [16]. Other important research aspects include controlof circulating current and capacitor voltage ripple [17], [18] Inorder to understand the steady-state and dynamic behavior ofthe MMC, several mathematical models have been developed[19]–[21]. Simulation models play a very important rolein investing the performance of the MMC for control andprotection purposes. Equivalent simulation models of MMCswere presented in [22]–[24].

In the MMC, submodule failures can occur due to variousreasons [4]. Fault-tolerant operation of the MMC requires thatin case of a submodule failure, the converter must continue itsoperation without disturbing its performance. To accomplishthis, additional submodules called redundant submodules, areintegrated in the arms of the MMC [10]. This results inan increase in number of submodules in the arm. When asubmodule fails, the faulty submodule is shorted out and theconverter continues its operation, without any interruption.Despite its importance, the performance of the MMC withredundant submodules and its response to submodule failureshas not been widely covered in the existing literature. To date,a few studies on the behavior of the MMC with redundantsubmodules have been published [25], [26]. Reference [27]proposes a method for non-interruptible energy transfer of theMMC, in case of a submodule failure.

This paper investigates the performance of the MMC whenredundant submodules are included in the arms. Two differentstrategies for integrating the redundant submodules in the armare implemented and compared. Unlike [25] and [26], whichdescribe most steady-state properties of the approach to useredundant submodules, the present work provides a detailedanalysis of the transients occurring due to submodule failure.A computationally efficient detailed equivalent model (DEM)model [24] of the MMC developed in PSCAD is used forthe investigation. The operation of the MMC with redundantsubmodules is also validated experimentally using a three-phase 10-kVA MMC prototype in the laboratory.

II. MMC MODELING

The circuit schematic of a three-phase MMC is outlinedin Fig. 1. It consists of six arms, each constituted by Ncascaded submodules. Each submodule, representing a con-trollable voltage source, consists of a half-bridge with a dcstorage capacitor. The number of submodules in the arm canbe adjusted based upon the submodule voltage and the dc-link voltage. The arm inductance L is needed to limit faultand parasitic currents [4]. The arm resistance R models theresistive losses in the arm.

A. DEM

The DEM proposed and validated in [24] is used to studythe performance of MMC with redundant submodules. TheDEM as shown in Fig. 2, is based on the equivalent branchmodel of an arm of the MMC implemented in PSCAD. Thesource voltage represents the sum of the capacitor voltages of

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Fig. 1. Equivalent circuit diagram of a three-phase half-bridge MMC.

Fig. 2. Equivalent branch model of an arm of the half-bridge MMC.

the inserted submodules in the arm during the simulation time-step. The submodule capacitor voltages are kept in a vectorwhich is updated depending on the branch current and theswitching vector signal. Describing the arm of the MMC inthis way allows its computationally efficient modeling for anynumber of submodules in the arm. The arm model is alsocapable of representing the blocked-mode of the half-bridge.

The internal control of the MMC is based on the open-loop approach using estimation of stored energy [28]. Theopen-loop control method provides fast dynamic performanceand is less complicated to implement than most other high-performance control methods proposed for the MMC [12]. Theopen-loop controller generates six insertion indices governingeach arm of the MMC. The insertion indices are utilized bythe modulator to produce switching signals for the submodulesusing PWM.

TABLE IMMC PARAMETERS

Parameter Value

Rated power 808 MVARated output voltage (L-L) 400 kVRated dc-link voltage (Vd) 640 kVSubmodule capacitance (C) 525 μH

Arm inductance (L) 95.5 mHArm resistance (R) 1 Ω

Carrier frequency (fcarr) 5 kHz

B. DEM Without Redunndant Submodules

To study the effect of redundant submodules on the perfor-mance of the MMC, a 21-level MMC with N = 20 submodulesper arm (without redundant submodules) is simulated as areference case. The voltage of each submodule capacitor isset to

vc =Vd

N, (1)

where Vd is the dc-link voltage. The average value of thesubmodule capacitor voltages should be maintained to thisvalue. In order to limit the submodule capacitor voltage, thecapacitance of the submodule capacitors is selected such thatit corresponds to a stored energy of 39.5 kJ per MVA of theconverter rating [4]. The arm capacitance is given by

Carm =C

N. (2)

Table I shows the parameters used in the DEM for thesimulated MMC.

C. DEM With Redundant submodules

To study the operation of the MMC with redundant submod-ules, two additional submodules are considered in each arm ofthe reference case MMC. The arm of the MMC thus comprisesa total number of submodules N+R = 22 (10% redundancy).At any instant, if F is the number of faulty submodules in thearm, the total number of active submodules in the arm canbe obtained as N+R-F, where F varies from zero to R. Theequivalent circuit of the MMC with redundant submodules isshown in Fig. 3.

The parameters used for the reference case are also adaptedto the MMC configuration with redundant submodules. How-ever, compared to (2) the arm capacitance is changed and cannow be obtained using

Carm =C

N +R− F. (3)

Hence, with redundant submodules in the arm, the armcapacitance decreases. It also varies with the number of faultysubmodules.

III. CONTROL STRATEGIES

A. Constant Total Capacitor Voltage Strategy (Strategy 1)

In this strategy the average total capacitor voltage (sum ofthe capacitor voltages of the healthy submodules) across the

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Fig. 3. Equivalent circuit diagram of athree-phase half-bridge MMC withredundant submodules.

arm is kept constant. In this study this value is selected to beequal to the dc-link voltage. Hence, the individual submodulecapacitor voltage is given by

vc =vΣc

N +R− F=

Vd

N +R − F. (4)

This indicates that the individual submodule capacitor volt-ages are lower compared to the reference case. However,submodule capacitor voltages increase with the number offaulty submodules in the arm as the total capacitor voltagein the arm remains constant. This control strategy produces aN+R-F+1-level arm voltage, which implies a higher numberof levels than the MMC configuration without redundantsubmodules. Moreover, the number of levels in the arm voltagealso varies with the number of faulty submodules. The averageenergy stored in each arm of the converter will be

Earm =1

2(N +R− F )C[

Vd

N +R− F]2. (5)

This energy is lower, compared to the energy stored in the armof the MMC without redundant submodules. However, thisenergy will increase with the number of faulty submodules.The insertion index narm for each arm is given by

narm =varmvΣc

, (6)

and provided to the modulator which calculates the number ofinserted submodules as the fraction of N+R-F that are instantlyavailable. The individuals among the N+R-F submodules, thatwill be inserted, are determined by the selection mechanism

based on the instantaneous value of the capacitor voltages anddirection of the arm current as discussed in [21].

Considering above, the operation of the MMC during eachtime-step for this strategy can be summarized as

• The total voltage of the healthy capacitors in each armremains unchanged.

• Actual number of healthy submodules N+R-F is detected.• The open-loop control system in each arm will be given

a reference for the total energy of the healthy capacitorswhich changes depending on the number because theresulting arm capacitance will change accordingly.

• The open-loop control for each arm calculates the desiredinsertion index.

• The modulator for each arm obtains the desired insertionindex as well as the information of the number of healthysubmodules.

• The modulator for each arm accordingly inserts narm

times N+R-F submodules using a suitable sorting algo-rithm.

B. Constant Submodule Capacitor Voltages Strategy (Strategy2)

In this strategy the individual submodule capacitor voltagesvc in the arm are kept constant [26] to the value given by(1). The average total capacitor voltage (sum of the capacitorvoltages of the healthy submodules) across the arm is thusgiven by

vΣc = (N +R− F )Vd

N. (7)

Clearly, the average total capacitor voltage is greater thanthe dc-link voltage . However, it decreases with the numberof faulty submodules in the arm. The average energy storedin each arm of the MMC in this case will be

Earm =1

2(N +R − F )C(

Vd

N)2. (8)

It is obvious that the stored energy in the arm is increased,compared to the reference case. Though, this energy decreaseswith the increase in number of faulty submodules in thearm. The generation of the insertion indices and the selectionmechanism of submodules in the arm work in the same manneras in the case of the constant total capacitor voltage scheme.Fig. 4 shows the insertion indices obtained using (6) for thetwo strategies. It can be observed from the figure that strategy2 generates a lower insertion index. Hence, among the N+R-Fsubmodules in the arm, the submodules are selected in such away to generate an N+1-level arm voltage. Thus, the numberof levels in the arm voltage remains constant irrespective of thenumber of redundant and faulty submodules in the arm. Also,all submodules in the arm are treated equally with referenceto the balancing control of the capacitor voltage.

The operation of the MMC during each simulation time-stepfor this strategy can be summarized as

• The reference voltage for each submodule remains un-changed.

• Actual number of healthy submodules N+R-F is detected.

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0.9 0.925 0.95 0.975 1−0.1

0.2

0.5

0.8

1.1

n arm

time (s)

Strategy 1 Strategy 2

Fig. 4. Comparison of insertion indices for the two strategies.

Fig. 5. Schematic diagram of the simulated test circuit in PSCAD.

• Depending on the number of healthy submodules in thearm, the total voltage of the healthy submodule capacitorschanges as vΣc = (N + R− F )vc.

• The open-loop control system in each arm will be givena reference for the total energy of the healthy capacitorswhich changes depending on the number because theresulting arm capacitance will change accordingly.

• The open-loop control for each arm calculates the desiredinsertion index.

• The modulator for each arm obtains the desired insertionindex as well as the information of the number of healthysubmodules.

• The modulator for each arm accordingly inserts narm

N+R-F times submodules using a suitable sorting algo-rithm.

IV. STUDY RESULTS

The two strategies discussed in the previous sections arecompared to the reference case using a test circuit where an808-MVA converter is fed from a stiff dc-link and providespower to the ac-network. The ac-network has a line-to-linevoltage of 400-kV rms, and is connected to the converterthrough a 900 MVA, 400/400 kV, transformer, with deltaconnection on the converter side. The test circuit is outlinedin Fig. 5.

A. MMC Without Redundant Submodules

The performance of the MMC having 20 submodules perarm (without redundant submodules) is shown in Fig. 6.The 21-level upper and lower arm voltages of the converterare shown in Fig. 6(a). The arm and circulating currents ofone phase-leg are shown in Fig. 6(b). As can be seen fromthe figure, the circulating current does not contain secondharmonic ripple. This also shows that the open-loop approachis successful in eliminating the second harmonic ripple fromthe circulating current. Fig. 6(c) shows the total capacitorvoltage of the upper and lower arms of the same phase-leg. Thetotal capacitor voltage ripple was found to be 7.8%. Fig. 6(d)shows the submodule capacitor voltages in the upper arm ofone phase-leg.

0

200

400

600

Vol

tage

(kV

)

(a)

v

arm,uv

arm,l

−0.5

0

0.5

1

Cur

rent

(kA

)

(b)

iu

il

idiff

600

620

640

660

680

Vol

tage

(kV

)

(c)

vΣcu

vΣcl

0.9 0.92 0.94 0.96 0.98 1

31

32

33

Vol

tage

(kV

)

time (s)

(d)

Fig. 6. Simulation results without redundant submodules in the arms. (a)Upper and lower arm voltages. (b) Arm and circulating currents. (c) Totalcapacitor voltages of upper and lower arms. (d) Submodule capacitor voltagesof upper arm

B. MMC with Redundant Submodules (Strategy 1)

The performance of the MMC with redundant submodules(N = 20, R = 2) using the constant total capacitor voltagestrategy is shown in Fig. 7. At t = 1 s, a submodule failureoccurs (F = 1) in the upper arm, reducing the number ofredundant submodules in that arm to 1. Before the submodulefailure, both the upper and lower arms have a 23-level armvoltage. As a result of the submodule failure, the upper armvoltage levels reduce to 22, whereas the lower arm voltagelevels remain intact as shown in Fig. 7(a). A short transient inthe upper and lower arm currents is observed at the submodulefailure instant. However, except this transient, the arm currentsremain balanced as shown in Fig. 7(b). Compared to thereference case the addition of the redundant submodules inthe arm causes a slight increase in the total capacitor voltageripple as shown in Fig. 7(c). The total capacitor voltage rippledecreases with the number of faulty submodules. However,the average total capacitor voltage of healthy submodules inthe arm remains constant. The average submodule capacitorvoltages in the arm with the faulty submodule increase by4.8% as illustrated in Fig. 7(d). However, for a typical MMCused for HVDC transmission having hundreds of submodulesper arm, the increase in submodule capacitor voltages will benegligible.

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0

200

400

600

Vol

tage

(kV

)

(a)

v

arm,uv

arm,l

−0.5

0

0.5

1

Cur

rent

(kA

)

(b)

iu

il

idiff

600

620

640

660

680

Vol

tage

(kV

)

(c)

vΣcu

vΣcl

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

28

29

30

31

32

Vol

tage

(kV

)

time (s)

(d)

Fig. 7. Simulation results for the constant total capacitor voltage strategy.(a) Upper and lower arm voltages. (b) Arm and circulating currents. (c) Totalcapacitor voltages of upper and lower arms. (d) Submodule capacitor voltagesof upper arm.

C. MMC with Redundant Submodules (Strategy 2)

The performance of the MMC with redundant submodules(N = 20, R = 2) using the constant submodule capacitor voltagestrategy is shown in Fig. 8. This strategy produces a 21-levelarm voltage. Also, in this case a submodule failure occurs inthe upper arm at t = 1 s. The submodule failure has no impacton the output levels of the arm voltage as shown in Fig. 8(a).Fig. 8(b) shows that no transient is experienced by the arm andcirculating currents. As shown in Fig. 8(c), the total capacitorvoltage of the arm decreases, when the submodule failureoccurs. The total capacitor voltage of the lower arm remainsunaffected. Fig. 8(d) shows that the submodule failure hasno effect on the submodule capacitor voltages. It can also beobserved from the figure that compared to the reference case,this strategy reduces the submodule capacitor voltage ripple.

V. EXPERIMENTAL VERIFICATION

The performance of the MMC with redundant submodulesis also validated experimentally using a three-phase, 10-kVAMMC prototype in the laboratory. The prototype has 5 sub-modules per arm including 1 redundant submodule (N = 4, R= 1). On the ac-side each phase of the prototype is connectedto an RL load. The parameters for the MMC prototype usedfor experimental verification are summarized in Table II. Sameparameters are now adapted for the simulation model as well.

0

200

400

600

Vol

tage

(kV

)

(a)

v

arm,uv

arm,l

−0.5

0

0.5

1

Cur

rent

(kA

)

(b)

iu

il

idiff

600

650

700

750

Vol

tage

(kV

)

(c)

vΣcu

vΣcl

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1

31

32

33

Vol

tage

(kV

)

time (s)

(d)

Fig. 8. Simulation results for constant submodule voltage strategy. (a) Upperand lower arm voltages. (b) Arm and circulating currents. (c) Total capacitorvoltages of upper and lower arms. (d) Submodule capacitor voltages of upperarm.

TABLE IIEXPERIMENTAL VALUES FOR MMC PROTOTYPE

Parameter Value

Rated power of the prototype 10 kVAPeak value of internal emf reference (es) 225 V

Input dc voltage (Vd) 500 VSubmodule capacitance (C) 3.3 nF

Arm inductance (L) 4.5 mHArm resistance (R) 1 Ω

Load resistance per phase 12 ΩLoad inductance per phase 10 mHCarrier frequency (fcarr) 1 kHz

Direct modulation control [12] is used to obtain the insertionindices for both the prototype and the simulation model. Thedirect modulation approach is simply based on PWM usingsinusoidal insertion indices. In this approach, the insertionindices do not compensate for the voltage variations in thesubmodule capacitors in the arm.

As shown in the previous section that constant total ca-pacitor voltage strategy involves more internal dynamicsthan constant submodule capacitor voltage strategy. Hence,a submodule failure condition for this strategy was testedexperimentally. The redundant submodule in the upper armof one phase-leg is permanently bypassed. In response to that,a 25% increase in the submodule capacitor voltages of theremaining submodules was observed, as shown in 9(a). It

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90

100

110

120

130

Vol

tage

(V

)

Experimental Results(a)

90

100

110

120

130

Simulation Results(b)

0.6 0.7 0.8 0.990

95

100

105

110

115

Vol

tage

(V

)

time (s)

(c)

0.6 0.7 0.8 0.990

95

100

105

110

115

time (s)

(d)

Fig. 9. Experimental and simulation results when a submodule in the upperarm is bypassed. (a,b) Submodule capacitor voltages in the upper arm. (c,d)Submodule capacitor voltages in the lower arm.

can be observed from 9(c) that except a short transient, thesubmodule capacitor voltages in the lower arm of the samephase-leg remain unaffected. Simulation results obtained forthe same control strategy show an almost identical behavioras illustrated in 9(b)and (d).

VI. CONCLUSION

This paper has investigated the performance of the modularmultilevel converter with redundant submodules in the arms.Two different control strategies are used to integrate the re-dundant submodules in the arms of the MMC. Pros and condsof both strategies were compared using the detailed equivalentmodel of the MMC. Hence, based on the requirement for aparticular application, the suitable strategy can be selected.

REFERENCES

[1] A. Lesnicar and R. Marquardt, “An innovative modular multilevelconverter topology suitable for a wide power range,” in Proc. IEEEPower Tech Conf., Bologna, Italy, Jun. 2003.

[2] S. Debnath, J. Qin, B. Bahrani, M. Saeedifard, and P. Barbosa, “Oper-ation, control, and applications of the modular multilevel converter: Areview,” IEEE Trans. Power Electron., vol. 30, no. 1, pp. 37–53, Jan.2015.

[3] S. Allebrod, R. Hamerski, and R. Marquardt, “New transformerless,scalable modular multilevel converters for HVDC-transmission,” inProc. IEEE Power Electron. Specialists Conf., 2008., Jun. 2008.

[4] B. Jacobson, P. Karlsson, G. Asplund, and T. Jonsson, “VSC-HVDCtransission with cascaded two-level converters,” in Cigre Session, Osaka,Japan, Nov. 2008.

[5] M. Hagiwara, K. Nishimura, and H. Akagi, “A medium-voltage motordrive with a modular multilevel PWM inverter,” IEEE Trans. PowerElectron., vol. 25, no. 7, pp. 1786–1799, Jul. 2010.

[6] M. Winkelnkemper, A. Korn, and P. Steimer, “A modular direct converterfor transformerless rail interties,” in Proc. IEEE International Symp. onInd. Electron., Jul. 2010.

[7] M. Spichartz, V. Staudt, and A. Steimel, “Modular multilevel converterfor propulsion system of electric ships,” in Proc. IEEE Electric ShipTechnologies Symp., Apr. 2013.

[8] A. Hillers and J. Biela, “Optimal design of the modular multilevelconverter for an energy storage system based on split batteries,” in Proc.15th Power Electron. and Appl. Conf. (EPE), Sep. 2013.

[9] N. Ahmed, S. Norrga, H.-P. Nee, A. Haider, D. Van Hertem,L. Zhang, and L. Harnefors, “HVDC supergrids with modular multilevelconverters—the power transmission backbone of the future,” in Proc. 9thInt. Multi-Conf. on Syst., Signals and Devices (SSD), Mar. 2012.

[10] B. Gemmell, J. Dorn, D. Retzmann, and D. Soerangr, “Prospects ofmultilevel VSC technologies for power transmission,” in Proc. IEEETransm. and Dist. Conf. and Expo., Apr. 2008.

[11] A. Hassanpoor, S. Norrga, H. Nee, and L. Angquist, “Evaluation ofdifferent carrier-based PWM methods for modular multilevel convertersfor HVDC application,” in Proc. 38th Annual Conf. IEEE Ind. Electron.Society (IECON), Oct. 2012.

[12] D. Siemaszko, A. Antonopoulos, K. Ilves, M. Vasiladiotis, L. Angquist,and H.-P. Nee, “Evaluation of control and modulation methods formodular multilevel converters,” in Proc. IEEE Power Electron. Conf.(IPEC), Jun. 2010.

[13] G. Konstantinou, M. Ciobotaru, and V. Agelidis, “Selective harmonicelimination pulse-width modulation of modular multilevel converters,”IET Power Electron., vol. 6, no. 1, Jan. 2013.

[14] Q. Tu and Z. Xu, “Impact of sampling frequency on harmonic distortionfor modular multilevel converter,” IEEE Trans. Power Del., vol. 26,no. 1, pp. 298–306, Jan. 2011.

[15] M. Hagiwara, R. Maeda, and H. Akagi, “Control and analysis of themodular multilevel cascade converter based on double-star chopper-cells (MMCC-DSCC),” IEEE Trans. Power Electron., vol. 26, no. 6,pp. 1649–1658, Jun. 2011.

[16] H. Akagi, “Classification, terminology, and application of the modularmultilevel cascade converter (MMCC),” IEEE Trans. Power Electron.,vol. 26, no. 11, pp. 3119–3130, Nov. 2011.

[17] Y. Li and F. Wang, “Arm inductance selection principle for modularmultilevel converters with circulating current suppressing control,” inProc. IEEE 28th App. Power Electron. Conf. and Expo. (APEC), Mar.2013.

[18] X. She and A. Huang, “Circulating current control of double-starchopper-cell modular multilevel converter for HVDC system,” in Proc.38th Annual Conf. IEEE Ind. Electron. Society (IECON), Oct. 2012.

[19] L. Harnefors, A. Antonopoulos, S. Norrga, L. Angquist, and H.-P. Nee,“Dynamic analysis of modular multilevel converters,” IEEE Trans. Ind.Electron., vol. 60, no. 7, pp. 2526–2537, Jul. 2013.

[20] Q. Song, W. Liu, X. Li, H. Rao, S. Xu, and L. Li, “A steady-stateanalysis method for a modular multilevel converter,” IEEE Trans. PowerElectron., vol. 28, no. 8, pp. 3702–3713, Aug. 2013.

[21] A. Antonopoulos, L. Angquist, and H.-P. Nee, “On dynamics and voltagecontrol of the modular multilevel converter,” in Proc. 13th EuropeanPower Electron. and Appl. Conf. (EPE), Sep. 2009.

[22] U. Gnanarathna, A. Gole, and R. Jayasinghe, “Efficient modeling ofmodular multilevel hvdc converters (MMC) on electromagnetic transientsimulation programs,” IEEE Trans. Power Del., vol. 26, no. 1, pp. 316–324, Jan. 2011.

[23] N. Ahmed, L. Angquist, S. Norrga, A. Antonopoulos, L. Harnefors,and H.-P. Nee, “A computationally efficient continuous model for themodular multilevel converter,” IEEE Journal of Emerging and SelectedTopics in Power Electron., vol. 2, no. 4, pp. 1139–1148, Dec. 2014.

[24] N. Ahmed, L. Angquist, S. Mehmood, A. Antonopoulos, L. Harnefors,S. Norrga, and H. Nee, “Efficient modeling of an MMC-based multiter-minal dc system employing hybrid HVDC breakers,” IEEE Trans. PowerDel., vol. PP, no. 99, pp. 1–1, 2015.

[25] G. Konstantinou, M. Ciobotaru, and V. Agelidis, “Effect of redundantsub-module utilization on modular multilevel converters,” in Proc. IEEEInternational Conf. on Ind. Tech. (ICIT), Mar. 2012.

[26] G. Konstantinou, J. Pou, S. Ceballos, and V. Agelidis, “Active redundantsubmodule configuration in modular multilevel converters,” IEEE Trans.Power Del., vol. 28, no. 4, pp. 2333–2341, Oct. 2013.

[27] G. T. Son, H.-J. Lee, T. S. Nam, Y.-H. Chung, U.-H. Lee, S.-T. Baek,K. Hur, and J.-W. Park, “Design and control of a modular multilevelHVDC converter with redundant power modules for noninterruptibleenergy transfer,” IEEE Trans. Power Del., vol. 27, no. 3, Jul. 2012.

[28] L. Angquist, A. Antonopoulos, D. Siemaszko, K. Ilves, M. Vasiladiotis,and H.-P. Nee, “Open-loop control of modular multilevel convertersusing estimation of stored energy,” IEEE Trans. Ind. Appl., vol. 47,no. 6, pp. 2516–2524, Nov. 2011.

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