Reduced Dynamic Model of a Modular MultilevelConverter in PowerFactory

C.E. Spallarossa, M.M.C. Merlin, Y. Pipelzadeh, T.C. GreenControl and Power Research Group

Imperial College London, London, UKEmail: claudia.spallarossa10@imperial.ac.uk

Abstract—Modular Multi-level Converters (MMC) haveemerged as the preferred technology for High Voltage DCtransmission installations. The inclusion of these converters,characterized by complex control schemes, in large AC gridsmay cause AC/DC interactions that need to be fully investigated.The evaluation to what extent the MMC dynamics interactwith the dynamics of a transmission network is of primaryimportance. It becomes critical for the grid operators, whichusually rely on more traditional VSC topologies (two-level), touse such models when studying AC/DC interactions. This paperpresents the development of a MMC reduced dynamic model(RDM) in PowerFactory that will facilitate the analysis of largeAC systems incorporating MMC based VSC HVDC links. TheMMC control scheme is designed following an alternative strategywhich considers the energy balancing and the storage capabilityof the converter. The system is arranged as a point-to-point link,its operations are validated against a detailed equivalent circuitbased model in PSCAD/EMTDC. A close match between theoriginal system and the benchmark confirms the validity of theMMC RDM proposed.

Index Terms—HVDC, MMC, reduced dynamic model, DIgSI-LENT PowerFactory, PSCAD/EMTDC.

I. INTRODUCTION

Over the last few decades Voltage Source Converters(VSCs) have become the most adopted conversion technologyfor High Voltage Direct Current (HVDC) installations [1]. Theconventional types of VSCs (two-level and three-level) arebeing replaced by a better performing and innovative topologyknown as the Modular Multilevel Converter (MMC) [2]. TheMMC consists of three phase units, which are composed by anupper and a lower arm. A variable number of cells, accordingto the converter voltage rating required, are connected in seriesto form each arm. Every cell comprises two pair of switchingcomponents (IGBT and diode), and a DC capacitor [3]. TheMMC voltage output is a staircase AC voltage signal obtainedcombining the voltage output of every cell. The low harmoniccontent of the MMC voltage output allows the elimination ofAC filters. Other advantageous features are the reduction ofpower losses due to lower switching frequency, easy scalabilityto higher voltages and increased reliability thanks to addingredundant cells [4].

Reduced dynamic models (RDMs) of power electronicssystems are often used to represent static switching convertersfor system level studies. Since the application of complexand accurate switching models entails a long computing timefor electro-magnetic transient type (EMT) simulations, RDMs

are becoming a significant alternative for large-signal time-domain transient studies. An RDM approximates the initialsystem by “averaging” the effect of fast switching within aprototypical switching interval [5]. An exhaustive overviewof the averaging techniques for power electronics convertersis proposed by [3], and more accurate procedures are furtherdiscussed in [4], [6], [7].

DIgSILENT PowerFactory is a well-known power systemanalysis software used by a large number of transmissionsystem operators. This tool deals with the planning andoperation of power networks. It caters for all standard powersystem analysis requirements, comprising the handling of largetransmission grids, HVDC technology and renewable energysource installations, such as wind power [8]. The capability ofPowerFactory to perform system-level studies is recognizedworld-wide, however the software displays a limited abilityin the design of power electronics. Due to the increasingnumber of HVDC projects based on modular multilevel VSCs,this constraint leads to complications in the analysis of suchsystems. Although the realization of two-level VSC is stillpossible, the development of an MMC is quite challengingbecause of the difficulty of dealing with the cells switchingcomponents and the high frequency converter dynamics. Thedevelopment of an MMC RDM in PowerFactory is thereforemotivated by the urgency of having an MMC block availablefor the analysis of mixed AC and DC systems along with thecomplexity of realizing a detailed converter model.

The contribution of this paper consists of the descriptionof the MMC RDM developed in PowerFactory. This allowsthe realization of complex AC/DC systems in such softwareplatform offering the possibility to carry out a large num-ber of system level studies. These include the analysis ofAC/DC interactions and the provision of frequency supportvia HVDC converters. A second contribution resides in theenergy balancing approach adopted to design the MMC RDMcontrol strategy. In order to validate the operations of theMMC RDM, arranged in a point-to-point link, an equivalentscheme is modelled in PSCAD/EMTDC. The comparison andbenchmark between the two systems is carried out in SectionIV through time-domain simulations in normal and abnormalconditions.

II. REDUCED DYNAMIC MODEL OF MMC INPOWERFACTORY

A full scale model of an MMC may require the repre-sentation of several thousand individual switching compo-nents. Reduced Dynamic Models of MMCs aim to accuratelycapture the dynamic performance of a full switching modelat significantly decreased computation cost. RDMs of powerelectronics designs are therefore the preferred representationof static switching converters in system level studies. Thissection describes the topology and the control system of theMMC RDM developed in PowerFactory. The RDM is the onlyviable approach considering the software limited abilities inthe power electronics modelling field.

A. Circuit Topology

A variety of reduced dynamic models for modular multi-level VSCs have already been proposed [3], [4], [6], [7], [9]–[11]. In the RDM based on switching functions, the switchingcomponents are modelled as controlled voltage and currentsources as illustrated in Figure 1. To ensure the correct powertransfer, the principle of power balance (Pac = Pdc + Ploss) isapplied on the current sources on the DC side [3].

Vj,up

Ce

Idc

I’dc

Iloss

Vj,low

AC SIDE DC SIDE

Fig. 1: Traditional MMC RDM topology [3].

Despite having the same electrical topology, the layout ofan MMC RDM designed in PowerFactory requires a fewdifferences with respect to the conventional representation.Unlike what has been established in the literature [3], [4], [9],the suggested MMC RDM topology displays only two three-phase controlled voltage sources blocks, two arm inductors anda phase inductor. The three phases for the upper or the lowerarms are compacted inside a single voltage source block, butstill controlled independently. A significant difference appearson the DC side, where a DC voltage source replaces the usualDC current source. The DC voltage source is controlled viathe inner control algorithms and supplies the rated DC voltage.The layout of a stand-alone MMC RDM is illustrated in Figure2 and its properties are listed in Table I.

TABLE I: Properties of MMC RDM.

Parameter ValuePrated [MW] 800Vac [kV] ± 320Vdc [kV] 320Frequency [Hz] 50Phase Inductor [mH] 40.7Arm Inductor [mH] 163

Vup

Vlow

VACXsource Lphase

La

rm,u

pL

arm

,low

Vsig j,up

Vsig j,low

VsigDC

Line DC,up

Line DC,low

AC SIDE

DC SIDE

CONVERTER

Fig. 2: MMC RDM structure in PowerFactory.

A significant simplification of the control architecture justi-fies the use of two controlled AC voltage source blocks insteadof six. A set of three command signals are sent to the upperand lower controlled voltage source blocks so that each phaseis regulated independently. An array of three signals is sent toeach of the two voltage sources. This allows the independentcontrol of every phase. In PowerFactory a dedicated block fora controlled voltage source does not exist, therefore the inputvoltage signals need to be defined by the control scheme. In thecase where six sources were used, still an array of three signalswould be sent to each source. However, this would contain anactual reference for phase a, and two null references for phaseb and c (and so on for each phase of the upper and lowerarm). The use of only two three-phase voltage source blockscontrolled via an array of three no null signals simplifies thecontrol scheme significantly.

Another main difference is the representation of the DCside of the converter as a Thevenin equivalent voltage source,replacing the usual DC current source. Since the software isnot able to perform the load flow calculation in grids whichdo not contain active elements (voltage sources), the DCside must be modelled using an alternative design. Initiallya controlled DC current source was implemented on the DCside. Despite the system was working properly in stand-aloneconfiguration (thanks to the presence of the other DC voltagesource on the DC side), PowerFactory could not performthe load flow calculation when the system was arranged aspoint-to-point link. The DC side remained deactivated and thesoftware was not able to recognize that portion of the grid. Thisis the reason why an alternative configuration, which includesactive elements (voltage sources) on the DC side, is proposed.

Finally an artificial connection between the AC and DCbusses is emulated via the control system, as PowerFactorydoes not permit to link together at the same bus bar AC andDC components.

B. Control Architecture

A simplified version of the control strategy for detailedMMC models was implemented in the RDM [12], [13]. Itcreates a set of reference signals for the voltage source blocksin order to control the currents within the converter [14]. Thecontrol algorithm is based on an energy balancing approach.

It considers the energy content of every converter arm toderive the reference signals that nullify the energy deviationbetween arms and that maintain the energy within each arm ata nominal value. As shown in Figure 3, the scheme consistsof various nested control loops: the measurement system,the energy controller, the current controller and the DC sidecontroller.

CONTROLLER

SYSTEM

M

SIDE

LER

LER

Fig. 3: Schematic diagram of the MMC RDM control system.

1) Measurement System: The voltage and current mea-surement blocks calculate the voltage and current flowingthrough each arm. Since the currents in PowerFactory arenormalised two-axis plus zero sequence form (known as ir, ii,i0), in the measurement stage these are denormalised using (1)and subject to the Clarke transform (2) to recover the phasecurrents ia, ib, ic. The rating of the measurement device isindicated by irated, the current nominal value by inom and iα,iβ , iγ are intermediate variables. An equivalent formulation isvalid for the voltage. iα(t)

iβ(t)

iγ(t)

=

ir

ii

i0

×(inom

irated

)(1)

ia(t)

ib(t)

ic(t)

=

1 0 1

− 12

√32 1

− 12 −

√32 1

×

iα(t)

iβ(t)

iγ(t)

(2)

2) Energy Controller: In normal conditions, the capacitorsof each sub-module of an arm are required to carry a portionof the arm current for each cycle. The total energy containedwithin each arm is subject to a cycle-by-cycle energy de-viation. During abnormal conditions, the energy level maybe disturbed, drifting away from the nominal set-point. Theenergy controller therefore regulates the energy content in thewhole converter as well as the distribution of energy betweenarms.

As shown in Figure 3, the energy controller of the RDMMMC consists of the power calculation block, the energy cal-culation block, the vertical, horizontal and average balancingblocks. In the power calculation block, since the measurementof individual cell voltages is not available, the instantaneous

power of each arm is elaborated from the product of the volt-age generated by the arm, and the current flowing through it,provided by the measurement stage. In the energy calculationblock, the energy deviation of each arm is then calculated byintegrating the instantaneous power of the arm and subtractingit to the nominal energy stored within the arm. The energystored in the upper and lower arms (Ej,up and Ej,low) for phasej = a, b, c is given by (3) and (4). The arm currents and voltagesare defined as iac j and uac j. The DC current and voltage aredefined as idc and udc.

Ej,up =

∫ [(−iac j,up(t) +

idc(t)

3)× (−uac j,up(t) +

udc(t)

2)

]dt

(3)

Ej,low =

∫ [(iac j,up(t) +

idc(t)

3)× (uac j,up(t) +

udc(t)

2)

]dt

(4)The complete energy management system is composed by

average, horizontal and vertical balancing techniques [15]. Itaims to maintain the energy content of the whole converter atthe nominal value, so that the energy is distributed homoge-neously among the arms, as shown in Figure 4.

The average energy balancing technique attempts to main-tain the overall energy stored within the converter at itsnominal value, so that the power from the AC side is equal tothe power going to the DC side. To achieve this, the overallbalancing current, Idc,balTot shown in Figure 5a, is added as anoffset to the DC current reference.

The horizontal energy management aims to balance thestored energy between each phase leg of the converter suchthat Ea = Eb = Ec, by running a DC horizontal balancingcurrent (IHbal,j). The effectiveness of the horizontal balancing isshown in Figure 5b, as the energies in each leg of the converterare identical.

The vertical energy management aims to maintain an evenbalance in the energy stored within the upper and lower armsof each phase, in order to have Ej,up = Ej,low. This is achievedby running a corrective alternating current (IVbal,j) throughthe converter. Figure 5c indicates the deviation between theenergy content of the upper and lower arms for each case.The deviation is close to zero for every phase meaning thatthe vertical balancing technique is working properly.

3) Current Controller: The current controller generates thecontrol voltage signals that are sent to the controllable voltagesources. It consists of the power management block, thecurrent controller block and the signal generator block. In thepower management block, the AC current references (Iac j,ref)are generated from the power set-point and using the AC gridphase angles measured with a Phase Lock Loop (PLL). In thecurrent controller block, the current references are defined acombination of the outputs of the energy balancing controller(IHbal,j and IVbal,j) and the power management block. Thereference current sets (Ij,up and Ij,low) are expressed in (5) and(6). The reference is then compared to the measured currentsof the upper and lower arms (ia, ib, ic) in order to derive the

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Fig. 4: Action of the energy balancing, energy in the arms.

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Fig. 5: Average, horizontal and vertical energy balancing. Red indicates phase a, green phase b, and blue phase c.

error signals (errj,up, errj,low). The errors are then fed into theAC signal generator that creates the voltage commands for thecontrolled AC sources, Vsig j,up and Vsig j,low [15], [16].

I j,up =Iac j,ref

2+ IVbal,j + IHbal,j (5)

I j,low = −Iac j,ref

2+ IVbal,j + IHbal,j (6)

4) DC Side Controller: In the DC controller, the DC signalgenerator block operates the controlled DC voltage source.Vset is a function of all the DC current components present inthe circuit. The actual direct current Idc, the reference directcurrent Idc,ref and the overall balancing current Idc,balTot arecombined and passed to a proportional controller to producethe DC voltage command for the controlled DC voltage source.

III. MODELLING OF MMC BASED VSC HVDC LINK

The converters are arranged in point-to-point schemes, andthe system response after the application of an AC side faultis observed. Furthermore, an equivalent point-to-point linkis realised in PSCAD/EMTDC and used as a benchmark tovalidate the performance of the MMC RDM developed inPowerFactory. The selection of PSCAD/EMTDC is motivatedby the fact that it is a power system oriented software and itprovides a detailed MMC VSC built-in block.

A. PowerFactory

The MMC-based HVDC link is arranged in a balancedmonopole configuration, as illustrated in Figure 6. The con-verters are rated at ±320 kV, 800 MW. The outer controlstrategy defines the rectifier end (CONV1) to work in P-Qcontrol mode (set point at 800 MW, 0 Mvar), whilst theinverter end (CONV2) is set to operate in Vdc-Q control mode,maintaining constant DC bus voltage and unity power factorat the point of common coupling (±320 kV, 0 Mvar). The ACgrids are represented as equivalent voltage sources. The DClines are modelled as underground cables and implementedusing a lumped parameter model. The lines properties arelisted in Table II.

CONV CONV

Fig. 6: HVDC point-to-point link.

B. PSCAD/EMTDC

A single-line diagram of the MMC station and the controlsassociated with it are illustrated in Figure 7. The PLL ensuresthat the d’ axis of a synchronously rotating reference framed’-q’ is aligned to Vac to permit decoupled control of activeand reactive power. The MMC stations considered here arerepresented using a Detailed Equivalent Circuit (DEC) based

TABLE II: DC Cable Parameters.

Parameter ValueVrated [kV] 320Irated [kA] 1Length [km] 100Resistance [mΩ/km] 11.3Capacitance [µF/km] 0.212Inductance [mH/km] 0.362

model. The internal controls include the lower level controls(capacitor energy balancing, circulating current suppression)and upper level controls (power controllers, decoupled currentcontrol) [17].

The MMC settings match those defined in Section III.A.Each MMC station includes 401-levels per phase. The MMC-based HVDC link includes two underground DC cables. The320 kV single-core cables are modelled according to thefrequency-dependent model explained in [18].

d’q’

d’q’

P, Q

abcv

d’q’

qdv

P* ,Vdc*, Q*, Vac*

q d

q

d

acV

θ

θ

Fig. 7: Single line diagram of a MMC. Rc and Lc are the aggregatedresistance and inductance of converter transformer and phase reactors[17].

IV. SIMULATIONS AND RESULTS

A representative set of time domain simulations are run inPowerFactory and PSCAD/EMTDC in order to validate theresponse of the point-to-point link equipped with the MMCRDM. In PowerFactory the simulations are run as ElectroMagnetic Transients (EMT) with a time step of 100 µs, forPSCAD/EMTDC the time step is 50 µs. The dynamic per-formance of the system is examined in normal and abnormalconditions, considering the application of a three-phase faultat T1.

The HVDC link is observed to work properly under normalconditions. At the initialization, the converters respond quicklyand the steady state is reached promptly.

A. Normal and Abnormal Operations in PowerFactory

A solid three-phase symmetrical fault is applied at T1 onCONV1 at t = 1 second and it is cleared after 200 ms, asillustrated in Figures 8a (i). Figures 8a (ii), (iii) and (iv) show

the dynamic response from the DC side considering Vdc, Idcand active power respectively. The cross-over and change ofdirection of the direct currents visible during the fault is causedby the energy stored in the arms.

Figure 8a (iv) shows the active power from the AC (green)and DC (blue) side: Pdc follows the profile of Pac. Thediscrepancy between the areas defined by the two powercurves, named En1 and En2, indicates the energy deviationof the arms. When the fault is applied, the cells are depletedand Pdc is minor than Pac (in En1). After the fault is cleared,the cells absorb energy and are recharged (in En2). The totalenergy deviation is displayed in Figure 9 for CONV1 (blue)and CONV2 (green). As expected, the energy deviation inCONV1 is subject to fluctuations, whilst the energy devia-tion of CONV2 remains undisturbed. The energy deviationdefines the storage requirement of the converter and links thebehaviour of the AC and DC side [19].

Figure 10 (i) and (ii) illustrates the voltages of the upper andlower arms within each phase of the converter. The expectedDC offset [20] is not visible as it has not been included directlyin the definition of the voltage commands for the controlledsource. It has been considered in the energy mechanism. Thewaveforms are of good quality, the signals go to zero duringthe disturbance and recover to the nominal value as soon asthe fault is cleared.

B. Comparison between PowerFactory and PSCAD/EMTDC

The equivalent point-to-point HVDC link developed inPSCAD/EMTDC and discussed in the previous section, isused as a benchmark. The same event, a solid three-phasesymmetrical fault is applied at T1 as shown in Figure 8b (i).The response of the system is shown in Figure 8b (ii), (iii), (iv)and compared to Figure 8a (ii), (iii), (iv). It is observed thatthe quantities are closely matched. The voltage, current andpower waveforms follow reasonably similar patterns. However,some differences are due to the way the fault transient isdefined (different fault impedance), to the time-step at whichthe simulations are run and to the level of detail the converteris modelled in the two cases.

The direct voltage presents the same profile in both cases(Figure 8a (ii) and Figure 8b (ii)). The voltage deviation issmaller in PowerFactory, where its variation is limited by therobustness of the DC signal generator block tuned to restrictthe voltage drop in case of AC side disturbances. In the MMCDEC, the voltage is regulated through the upper level controlscheme and its variation is larger. The direct currents shown inFigure 8a (iii) and Figure 8b (iii) display a similar behaviour.The smaller time-step and the more detailed model used inPSCAD/EMTDC allow to capture the converter dynamicsthoroughly, showing a more meticulous representation of thedirect voltage and direct current than the one offered byPowerFactory.

In Figure 8a (iv) and Figure 8b (iv) the power curvesnearly match. The same discrepancy between Pdc follows Pacis observed in both cases. The area contained between the

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Fig. 8: System dynamic response. (i) AC Voltage; (ii) DC Voltage; (iii) DC current; (iv) Active power from the AC and DC side.

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Fig. 10: CONV1 phase voltages for the upper (i) and lower (ii) arms.

power curves indicates the total energy deviation within theconverter during the fault.

V. CONCLUSION

The increasing number of MMC based VSC HVDC projectsleads to the necessity of analysing large AC networks whichcontains such installations. This motivates the need of de-veloping an MMC model for transmission system orientedplatforms, like PowerFactory. Due to the software limitedability in power electronics design, the only viable approach isa converter reduced dynamic model. The MMC RDM realisedin PowerFactory is presented in this paper. An alternativecontrol strategy based on an energy balancing approach isdesigned. The performance of the system, arranged in a point-to-point link, is validated against an equivalent scheme inPSCAD/EMTDC for an AC fault scenario. A close matchis observed between the original system and the benchmark.The availability of a MMC RDM block in PowerFactory is of

crucial importance as it will enable a wide range of studiesconcerning AC large grids and VSC MMC technologies.

ACKNOWLEDGMENT

The authors gratefully acknowledge the financial supportprovided by the Top & Tail Transformation programme(ESPRC grant EP/I031707/1) for Ms Spallarossa, the UKPower Electronics Centre (ESPRC grant EP/K035096/1) forDr Merlin and Hubnet (ESPRC grant EP/I013636/1) for DrPipelzadeh.

REFERENCES

[1] D. V. Hertem, M. Ghandhari, and M. Delimar, “Technical limitationstowards a supergrid a european prospective,” in Energy Conference andExhibition (EnergyCon), 2010 IEEE International, 2010, pp. 302–309.

[2] A. Beddard, M. Barnes, and R. Preece, “Comparison of detailed mod-eling techniques for mmc employed on vsc-hvdc schemes,” pp. 1–11,2014.

[3] H. Saad, J. Peralta, S. Dennetiere, J. Mahseredjian, J. Jatskevich, J. A.Martinez, A. Davoudi, M. Saeedifard, V. Sood, X. Wang, J. Cano, andA. Mehrizi-Sani, “Dynamic averaged and simplified models for mmc-based hvdc transmission systems,” Power Delivery, IEEE Transactionson, vol. 28, no. 3, pp. 1723–1730, 2013.

[4] J. Peralta, H. Saad, S. Dennetiere, J. Mahseredjian, and S. Nguefeu,“Detailed and averaged models for a 401-level mmchvdc system,” PowerDelivery, IEEE Transactions on, vol. 27, no. 3, pp. 1501–1508, 2012.

[5] S. Chiniforoosh, J. Jatskevich, A. Yazdani, V. Sood, V. Dinavahi, J. A.Martinez, and A. Ramirez, “Definitions and applications of dynamicaverage models for analysis of power systems,” Power Delivery, IEEETransactions on, vol. 25, no. 4, pp. 2655–2669, 2010.

[6] S. Rohner, J. Weber, and S. Bernet, “Continuous model of modular mul-tilevel converter with experimental verification,” in Energy ConversionCongress and Exposition (ECCE), 2011 IEEE, 2011, pp. 4021–4028.

[7] N. Ahmed, L. Angquist, S. Norrga, and H. P. Nee, “Validation ofthe continuous model of the modular multilevel converter with block-ing/deblocking capability,” in AC and DC Power Transmission (ACDC2012), 10th IET International Conference on, 2012, pp. 1–6.

[8] DIgSILENT PowerFactory, DIgSILENT PowerFactory 15, IntegratedPower System Analysis Software. User Manual., 1st ed. UnitedKingdom: PowerFactory, 2013.

[9] H. Saad, S. Dennetiere, J. Mahseredjian, P. Delarue, X. Guillaud,J. Peralta, and S. Nguefeu, “Modular multilevel converter models forelectromagnetic transients,” Power Delivery, IEEE Transactions on,vol. 29, no. 3, pp. 1481–1489, 2014.

[10] C. E. Sheridan, M. M. C. Merlin, and T. C. Green, “Reduced dynamicmodel of the alternate arm converter,” in Control and Modeling forPower Electronics (COMPEL), 2014 IEEE 15th Workshop on, 2014,pp. 1–6.

[11] Working Group B4.57, “Guide for the development of models for hvdcconverters in a hvdc grid,” Cigre, Tech. Rep. 604, Dec. 2014 2014.

[12] Z. Yan, H. Xue-hao, T. Guang-fu, and H. Zhi-yuan, “A study onmmc model and its current control strategies,” in Power Electronics forDistributed Generation Systems (PEDG), 2010 2nd IEEE InternationalSymposium on, 2010, pp. 259–264.

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

[14] M. M. C. Merlin, T. C. Green, P. D. Mitcheson, D. R. Trainer,R. Critchley, W. Crookes, and F. Hassan, “The alternate arm converter:A new hybrid multilevel converter with dc-fault blocking capability,”Power Delivery, IEEE Transactions on, vol. 29, no. 1, pp. 310–317,2014.

[15] P. Munch, D. Gorges, M. Izak, and S. Liu, “Integrated current control,energy control and energy balancing of modular multilevel converters,”in IECON 2010 - 36th Annual Conference on IEEE Industrial Electron-ics Society, 2010, pp. 150–155.

[16] E. Rakhshani, A. M. Cantarellas, D. Remon, P. Rodriguez, and I. Can-dela, “Modeling and control of multi modular converters using optimallqr controller with integral action,” in Energy Conversion Congress andExposition (ECCE), 2013 IEEE, 2013, pp. 3965–3970.

[17] U. N. Gnanarathna, A. M. Gole, and R. P. Jayasinghe, “Efficient mod-eling of modular multilevel hvdc converters (mmc) on electromagnetictransient simulation programs,” Power Delivery, IEEE Transactions on,vol. 26, no. 1, pp. 316–324, 2011.

[18] A. Morched, B. Gustavsen, and M. Tartibi, “A universal model foraccurate calculation of electromagnetic transients on overhead lines andunderground cables,” Power Delivery, IEEE Transactions on, vol. 14,no. 3, pp. 1032–1038, 1999.

[19] M. M. C. Merlin, T. C. Green, P. D. Mitcheson, F. J. Moreno, K. J.Dyke, and D. R. Trainer, “Cell capacitor sizing in modular multilevelconverters and hybrid topologies,” in Power Electronics and Applications(EPE’14-ECCE Europe), 2014 16th European Conference on, 2014, pp.1–10.

[20] F. Kammerer, M. Gommeringer, J. Kolb, and M. Braun, “Energybalancing of the modular multilevel matrix converter based on a newtransformed arm power analysis,” in Power Electronics and Applications(EPE’14-ECCE Europe), 2014 16th European Conference on, 2014, pp.1–10.