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Energy Difference Controllers for MMC without DCCurrent Perturbations

Kosei Shinoda, Julian Freytes, Abdelkrim Benchaib, Jing Dai, Hani Saad,Xavier Guillaud

To cite this version:Kosei Shinoda, Julian Freytes, Abdelkrim Benchaib, Jing Dai, Hani Saad, et al.. Energy DifferenceControllers for MMC without DC Current Perturbations. The 2nd International Conference on HVDC(HVDC2016), Sep 2016, Shanghai, China. �hal-01423721�

https://hal-centralesupelec.archives-ouvertes.fr/hal-01423721https://hal.archives-ouvertes.fr

Energy Difference Controllers for MMC withoutDC Current Perturbations

Kosei Shinoda∗, Julian Freytes†, Abdelkrim Benchaib∗, Jing Dai∗‡, Hani Saad§, Xavier Guillaud†∗ SuperGrid Institute SAS, 130 rue Léon Blum, 69611 Villeurbanne, France† Université Lille, Centrale Lille, Arts et Metiers, HEI EA 2697 - L2EP France

‡ Group of Electrical Engineering - Paris (GeePs), UMR CNRS 8507,CentraleSupélec, Univ. Paris-Sud, Université Paris-Saclay, Sorbonne Universités, UPMC Univ Paris 06, France

§ Réseau de Transport d’Électricité (RTE), La Défense, France

Abstract—The Modular Multilevel Converter (MMC) is amost promising converter technology for the High Voltage DCapplication. The complex topology of the MMC requires severaladditional controllers to balance the energy in the capacitorswhich are distributed all over the converter. Typically, there isa requirement of two controls; one is the regulation of the totalenergy in each leg, and the other is the distribution of the energybetween the upper and the lower arms. This paper presentscontrol strategies for the latter one being capable of distributingthe energy only by internal power flow, so that undesiredinterference with the associated grids can be completely avoided.The proposed controls are achieved by forcing the common modecurrents to be balanced while keeping the classic cascaded controlstructure as much as possible. The effectiveness and advantageof the proposed solutions are demonstrated by simulations.

Index Terms—High Voltage Direct Current (HVDC), ModularMultilevel Converter (MMC), Energy Difference.

I. INTRODUCTION

The Modular Multilevel Converter (MMC) is a new typeof converter which attracts large attention due to its severaladvantages compared to the conventional two-level VoltageSource Converter (VSC). MMC was first introduced in [1] andthe basic concepts and the operational principles are presentedin [2] [3].

The general topology of the MMC consists of a large num-ber of two-level converter modules, so-called sub-modules.This modular topology enables to output nearly ideal sinu-soidal voltage waveform, allowing prevention of harmonicinjection to the power system; hence, implementation oflarge filters are no longer needed. Furthermore, its scalablemodular topology allows to easily adjust the voltage rating,thus, it is suitable for High Voltage Direct Current (HVDC)Transmission Systems applications.

In general, the conventional VSCs type converters areattached with a large station capacitor at their DC side. Inthe MMC, however, the capacitors are distributed all overthe converter. This makes the balancing and control of thedistributed energies as an important aspect [4]. In literature,the requirements on the energy balancing are often dividedinto two [5] [6]:

1) Horizontal Balancing: The energy stored in each legmust be regulated to achieve equal energy in all threephase legs. This can be achieved by a simple control

which regulates the deference between the power inflowand outflows to/from the MMC in each phase.

2) Vertical Balancing: The difference between the energystored in the upper and the lower parts must be con-trolled to avoid having an excess energy in one of thearms. This is also refereed to as "Energy DifferenceControl" [7].

This paper discuss on the control strategies of EnergyDifference. The control schemes proposed in [2] and [8]use additional oscillatory components on the common modecurrents to regulate this energy difference. However, thisapproach can result in unwanted interferences with the DCpower which may lead to fluctuations of the DC grid voltage.[5] presented a novel control structure utilizing a periodiclinear quadratic regulator, and referred to balanced referencegeneration. Inspired by [5], this paper proposes differentcontrol structures, which enables to regulate energy differencewithout disturbing the DC grid. In this work, the cascadedcontrol structure such that energy controllers adjusting thereferences of inner current control is preserved. Thus, theproposed controllers are simpler and more intuitive.

This paper is structured as follows. Section 2 recalls theMMC topology and the fundamental variables as well as itscontrol hierarchy. In Section 3, the proposed energy differ-ence controllers are presented, and difference in structure ishighlighted. The functionality of the proposed controllers isvalidated by simulations carried out on EMTP-RV platform.

II. MODULAR MULTILEVEL CONVERTER

A. Arm Average Model (AAM)

The topology of the AAM is recalled in Fig. 1. There is oneleg for each phase a, b, c. Each phase leg can be divided intoupper and lower parts called arms. This model assumes thatthe voltages of all the sub-module capacitors in each arm aremaintained in a close range, thus allowing to replace them byan equivalent capacitor. Therefore, each arm includes an arminductance Larm, an arm resistance Rarm and an equivalentcapacitor Ctot in parallel with a chopper.

The voltages vuj (vlj ) and currents iuj (ilj ) of each arm j(j = a, b, c) are described by the following equations:

vuj = mujvCtotuj , vlj = mljvCtotlj (1)

https://www.researchgate.net/publication/265171742_Operation_Control_and_Applications_of_the_Modular_Multilevel_Converter_A_Review?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/261504233_Energetic_macroscopic_representation_and_inversion_based_control_of_a_modular_multilevel_converter?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/235886748_An_Energy-Based_Controller_for_HVDC_Modular_Multilevel_Converter_in_Decoupled_Double_Synchronous_Reference_Frame_for_Voltage_Oscillation_Reduction?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/4078034_An_Innovative_Modular_Multilevel_Converter_Topology_Suitable_for_a_Wide_Power_Range?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224207796_Integrated_current_control_energy_control_and_energy_balancing_of_Modular_Multilevel_Converters?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224207796_Integrated_current_control_energy_control_and_energy_balancing_of_Modular_Multilevel_Converters?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224207796_Integrated_current_control_energy_control_and_energy_balancing_of_Modular_Multilevel_Converters?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/270792593_MMC_Capacitor_Voltage_Decoupling_and_Balancing_Controls?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224600316_On_dynamics_and_voltage_control_of_the_Modular_Multilevel_Converter?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224600316_On_dynamics_and_voltage_control_of_the_Modular_Multilevel_Converter?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==

vgc vgb vga

Rf Lf

Rf Lf

Rf Lf igc

igb

iga

iua iub iuc

ila ilb ilc

vdc2

vdc2

idc

idc

Rarm

Larm

Rarm

Larm

Rarm

Larm

Larm

Rarm

Larm

Rarm

Larm

Rarm

vua

vla

iCtotua

CtotvCtotua

mua

iCtotub

CtotvCtotub

mub

iCtotuc

CtotvCtotuc

muc

iCtotla

CtotvCtotla

mla

iCtotlb

CtotvCtotlb

mlb

iCtotlc

CtotvCtotlc

mlc

Figure 1: MMC Arm average model

iCtotuj = muj iuj , iCtotlj = mlj ilj (2)

where vCtotuj (vCtotlj ) is the voltage across the upper (lower)arm equivalent capacitor, muj (mlj ) is the correspondinginstantaneous duty cycle and iCtotuj (iCtotlj ) is the currentthrough the upper (lower) arm capacitor. The voltage andcurrent of the equivalent capacitor are related through thecapacitor equation:

iCtotuj = CtotdvCtotuj

dt, iCtotlj = Ctot

dvCtotljdt

(3)

Applying Kirchhoff’s law, the following equations are de-rived for each phase j:

vdc2 − vuj − Larm

diujdt −Rarmiuj − Lf

digjdt −Rf igj − vgj = 0 (4)

−vdc2 + vlj + Larmdiljdt +Rarmilj − Lf

digjdt −Rf igj − vgj = 0 (5)

The addition of (4) and (5) yields:

vvj − vgj = Laceqdigjdt

+Raceqigj (6)

where:

igj = iuj − ilj , vvj =−vuj + vlj

2, (7)

Raceq =Rarm + 2Rf

2, Laceq =

Larm + 2Lf2

(8)

Equation (6) describes the AC side dynamics of the AAM.The subtraction of (4) and (5) gives:

vdc2− vdiffj

2= Larm

didiffjdt

+Rarmidiffj (9)

where the differential current idiff and voltage vdiff aredefined as:

idiffj =iuj + ilj

2, vdiffj =

vuj + vlj2

(10)

Equation (9) describes the DC side dynamics of the AAM.The DC current will be then expressed as:

idc = idiffa + idiffb + idiffc (11)

P ∗ac

Q∗ac

Controller

Coupling&

Linearization

Controllerig current

Controlleridiff current

v∗v,abc

v∗diff,abc

m∗u,abc

m∗l,abc

i∗gdq

i∗diff,abc

i∗gd

i∗gq

÷

÷

vgd

vgd

WΣ∗

abc Energy

(14)

(12)

(13)

igdq

idiff,abc

WΣabc

Figure 2: General Control Scheme of MMC

B. Current control and Energy control

For the 3-phase MMC, as well as a classical VSC, thecontrol of ig is achieved in rotating frame by applying Parktransformation. Phase Lock Loop (PLL) is implemented totrack the grid voltage angle. The implemented PI controller isdenoted as Cig . Applying Park transformation on (6), the igcontrol in dq frame is derived

v∗vd = vgd+(i∗gd− igd)Cig −

(Larm2

+ Lf

)ωigq (12a)

v∗vq = vgq+(i∗gq − igq )Cig +

(Larm2

+ Lf

)ωigd . (12b)

The differential current in each phase is regulated by anotherPI controller Cidiff . From (9), the idiff control for phase jis derived as:

v∗diffj =Vdc2− (i∗diffj − idiffj )Cidiff . (13)

The difference between the DC power inflow and theAC outflow causes variation of the energy stored inside theMMC. Since it is preferred that the AC power follows thereference value, it is reasonable to adjust the DC power toobtain the desired internal energy level. A PI controller CWΣis implemented to give appropriate i∗diffj to the differentialcurrent controllers. The control of WΣ is obtained as:

i∗diffj =1

Vdc

[{WΣ∗j −WΣj

}CWΣ +

Pac3

](14)

whereWΣi =

1

2Ctot

(v2Ctotui + v

2Ctotli

). (15)

Assembling the derived control laws, general control struc-ture is built as shown in Fig. 2.

The developed controller is implemented in a simulation ofan MMC station model. The pre-contingency operating poweris set at Pac = 1[p.u.] and Qac = 0[p.u.]. Then step referencechanges are created at t = 1[s] for the active power and 1.1[s]for the reactive power. Fig. 3 shows the transition of the activeand reactive powers. It is clearly seen that the both powersfollow the change of the reference correctly. Fig. 4 picturesthe capacitor voltage in each arm. Even though the capacitorvoltages were perfectly balanced beforehand, each time thedisturbance occurs, the voltages in the upper arms deviate fromthe lower ones. This is because the aforementioned energycontroller can only regulate the sum of the upper and lowerarms’ energy, but it does not take into account the distribution

Qac

Q∗ac

Pdc

Pac

P ∗ac

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0

0.2

0.4

0.6

0.8

1

Figure 3: Active power and DC power [pu] - No EnergyDifference control

vCtotlc

vCtotuc

vCtotlb

vCtotub

vCtotla

vCtotua

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0.9

1

1.1

1.2

Figure 4: Equivalent arm capacitor voltages [pu]

of the energy between the upper and lower arms. Withoutexplicit control, the energy in the upper and lower arms maytake various levels and endanger the secure operation of theMMC. Therefore, an additional controller which enables toexplicitly eliminate the deviation of the energy between thearms is needed.

III. ENERGY DIFFERENCE CONTROL

Theoretically, the power exchanged by the arm can beexpressed by the product of the applied voltage vulj andthe current flows through the arms iulj . Defining the energydifference by

W∆j =1

2Ctot

(v2Ctotuj − v2Ctotlj

), (16)

The evolution of the energy difference can be expressed byusing the variables defined in the previous section:

dW∆jdt

= iujvuj − iljvlj = igjvdiffj − 2idiffjvvj . (17)

In normal operation, igj and vvj are sinusoidal with an averageof zero, while idiffj and vdiffj are constant. In such condition,both terms in the right side of (17) are products of a constantvalue and a fundamental-frequency component. Thus, the timeaverage over the period is zero. This means that, as it is, theenergy difference is uncontrollable. One possible solution is toimpose fundamental-frequency components on the differentialcurrent (idiff = idiffac + idiffdc) [2]. This decompositionallows to generate a non-zero component over the period onthe right side of (17), which can be used to regulate the energy

difference. Further simplification is done by supposing thatvvj is fairly close to the AC grid voltage vgi since an MMCdoes not require large filters at its AC side. Introducing thedecomposition of differential current into (17), then the timeaverage of the evolution of the energy difference over oneperiod is expressed by:〈

dW∆jdt

〉=〈−2idiffacj vgj

〉. (18)

From (18), three control laws will be considered. One isthe classical control scheme [8]. The second one is developedbased on the classical scheme, but the reference generationmethods are improved to overcome the problem of the classicalscheme. The proposed control is further improved by applyingthe phase shifting technique proposed by [5]. Each scheme isdetailed in the followings.

A. Classical W∆ control

The value of the energy difference can vary for each phase.Therefore, it is reasonable to regulated them individually byimplementing one controller for each phase leg. Then theappropriate rms value of the AC components of the differentialcurrent I∗diffac can be derived by a PI controller denoted byCW∆ . The control law can be expressed as:

I*diffacj= − 1

2Vg

(W∆∗j −W∆j

)CW∆ . (19)

where Vg is the rms value of the AC grid voltage. Next, thefundamental-frequency differential current reference must begenerated in some way. The AC voltage angle (i.e. θ = ωt) ismonitored by the PLL and used to align the current referencewith the voltage in each arm. In the classical energy differ-ence control, the instantaneous differential current reference

i∗diffac =(i∗diffaca i

∗diffacb

i∗diffacc

)Tis generated by

i∗diffac = AI*diffac (20)

where

A =√2

cosωt 0 00 cos (ωt− 2π3 ) 00 0 cos

(ωt− 2π3

) (21)

and I∗diffac =(I∗diffaca I

∗diffacb

I∗diffacc

)T. The multiplica-

tion with the matrix A allows aligning the output of the con-troller with the AC grid voltage. Fig. 5 illustrates an exampleof the relation between the generated current references andthe AC grid voltages.

According to (19) and (20), the classic energy differencecontroller is developed as depicted in Fig. 6. The developedcontroller is tested in the same simulation set up as previoussection. The equivalent arm capacitor voltages are depicted inFig. 7. Unlike the previous case, the capacitor voltage is wellbalanced after a short time. However, unwanted oscillationson the DC power are observed in Fig. 8. In this controlstructure, the energy difference is individually regulated perleg. Since there is no coupling between the phases, the balance

https://www.researchgate.net/publication/261504233_Energetic_macroscopic_representation_and_inversion_based_control_of_a_modular_multilevel_converter?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224207796_Integrated_current_control_energy_control_and_energy_balancing_of_Modular_Multilevel_Converters?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==https://www.researchgate.net/publication/224600316_On_dynamics_and_voltage_control_of_the_Modular_Multilevel_Converter?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==

Figure 5: Vectorial representation of differential currents inClassical Control

Figure 6: Classical W∆ controller

of them are not guaranteed. As a consequence, unbalancedreference i∗diffac may possibly be generated by the controller,and it results in inducing oscillations on the DC power. Suchoscillations may cause fluctuations on the DC voltage andjeopardize the stability of the entire system, especially in smallMTDC grids. Therefore, this must be avoided.

B. W∆ Control with Balanced idiffac

The classical W∆ controller presented in Section III-Amay generate unbalanced three-phase current references sincethe W∆ of each phase is regulated individually. In otherwords, the current sum i∗

′diffaca

+ i∗′diffacb

+ i∗′diffacc

maybe non-zero, which would change the current exchangedwith the DC grid. Thus, a new transform is needed so thatthe new current reference vector, denoted by i∗

′

diffac , with

i∗′

diffac =(i∗

′diffaca

i∗′diffacb

i∗′diffacc

)Twill have no impact on

the external current, i.e. i∗′diffaca

+ i∗′diffacb

+ i∗′diffacc

= 0.

vCtotlc

vCtotuc

vCtotlb

vCtotub

vCtotla

vCtotua

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0.9

1

1.1

1.2

Figure 7: Equivalent arm capacitor voltages [pu] - ClassicalW∆ control

pdc

pac

pref

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0.2

0.4

0.6

0.8

1

1.2

Figure 8: Active power and DC power [pu] - Classical W∆

control

The general principle is that to balance the current reference,for each component of i∗diffac , two new current references areintroduced, one for each of the other two phases. Formally, let

i∗′

diffac = Ki∗diffac =

kaa kab kackba kbb kbckca kcb kcc

i∗diffac (22)where coefficient kmn quantifies the contribution of the orig-inal reference i∗diffacn to the new reference i

∗′diffacm

.This transform should satisfy the following 3 requirements,

where we only consider phase a for simplicity:1) It should not modify the contribution of the original ref-

erence to the corresponding phase in the new reference.This yields:

kaa = 1

2) The new reference should be balanced. This yields:

kaa + kba + kca = 0

3) The absolute values of the two new references in phasesb and c should be identical. This yields

|kba| = |kca|The above 3 requirements allow one to obtain:

K =

1 −12 − 12

− 12 1 − 12− 12 − 12 1

(23)where we used the symmetry between the three phases.

Fig. 9 shows the compensation of the original currentreference i∗diffaca for phase a. The colored vectors are definedas i∗

′diffacaa

= kaai∗diffaca

, i∗′diffacba

= kbai∗diffaca

, andi∗

′diffacca

= kcai∗diffaca

. With matrix K given in (23), we seethat i∗diffaca is well balanced by i

∗′diffacba

and i∗′diffacca

. Thecontrol structure is shown in Fig. 10.

C. Modified W∆ Control with Balanced idiffacIn the W∆ Control with Balanced idiffac , the balancing of

the current reference in each phase is achieved by introducinga new current into each of the other two phases. Recallthat in Fig. 9, to balance i∗diffaca in phase a, i

∗′diffacba

and

Figure 9: Vectorial representation of differential currents inW∆ Control with Balanced idiffac

Figure 10: W∆ Controller with Balanced idiffac

i∗′diffacca

are introduced respectively in phases b and c, eachwith an amplitude of 12 i

∗diffaca

. With this choice, i∗′diffacba

andi∗

′diffacca

are both phase shifted by 180 degrees with i∗diffaca(and thus vga ), which makes it possible to use a constantmatrix K to calculate the new reference vector i∗

′

diffac fromthe original one i∗diffac .

Obviously, the choice of i∗′diffacba

and i∗′diffacca

is notunique. As long as their sum is equal to −i∗diffaca , the newcurrent reference vector is already balanced, although thecontributions by phase b and c are no longer bound to be equal.Furthermore, if the constraint on the phase shift of i∗

′diffacba

and i∗′diffacca

with respect to i∗diffaca is relaxed, i.e. i∗′diffacba

and i∗′diffacca

are allowed to have other directions than i∗diffaca ,then more freedom is permitted in their choice, as long as theirvector sum equal to −i∗diffaca to guarantee current balance inthe three phases. However, in that case, it is no longer possibleto use a constant matrix to calculate i∗

′

diffac from i∗diffac as in

(22). Instead, a time-varying matrix, denoted by M , is neededto calculate i∗

′

diffac from I∗diffac , i.e.

i∗′

diffac =MI*diffac (24)

An example of choosing M is given in [5]. Its objective isto remove power exchanges imposed by the newly introducedcurrent used for balancing, and its general principle is to shiftthe current vectors by 90 degrees from the correspondingvoltage angle. Taking phase a as example, let

i∗′diffacaa

(t) = laa√2I∗diffaca cos (ωt+ φa) (25)

i∗′diffacba

(t) = lba√2I∗diffaca cos

(ωt+ φb − 2π3

)(26)

i∗′diffacca

(t) = lca√2I∗diffaca cos

(ωt+ φc +

2π3

)(27)

Figure 11: Vectorial representation of differential currents inModified W∆ Control with Balanced idiffac

where φm is the phase shift between i∗′diffacma

and the voltagein phase m, and laa, lba and lca are positive1 constantcoefficients.

To determine the value of lma and φm, the followingrequirements are used.

1) The contribution of the original reference to the cor-responding phase in the new reference should not bemodified. This yields:

laa = 1, φa = 0.

2) The new reference should be balanced. This yields:

laa cos (ωt+ φa) + lba cos(ωt+ φb − 2π3

)+lca cos

(ωt+ φc +

2π3

)= 0

3) The instantaneous active powers due to i∗′diffacba

andi∗

′diffacca

in phases b and c are zero. This yields:

lbaVgI∗diffaca

cosφb = lcaVgI∗diffaca

cosφc = 0

4) The absolute values of the two new references in phasesb and c should be identical. This yields

lba = lca

The above four requirements allow one to obtain

laa = 1, lba = lca =1√3, φa = 0 φb = −

π

2, φc =

π

2.

(28)By symmetry between the three phases, M can be obtainedas

M =√2

cosωt1√3cos(ωt+ π2

)1√3cos(ωt− π2

)1√3cos(ωt− 7π6

)cos(ωt− 2π3

)1√3cos(ωt− π6

)1√3cos(ωt+ 7π6

)1√3cos(ωt+ π6

)cos(ωt+ 2π3

)(29)

Fig. 11 illustrates the generated current reference by thecoupling matrix M with phase a as example. The vectorsi∗

′diffacba

and i∗′diffacca

satisfy the above four requirements.According to (24) with M given in (29), the control

structure is developed as illustrated in Fig. 12.

1This can always be achieved by properly choosing φm.

https://www.researchgate.net/publication/224207796_Integrated_current_control_energy_control_and_energy_balancing_of_Modular_Multilevel_Converters?el=1_x_8&enrichId=rgreq-bb04c1fce50d48f7f4542b7659979e68-XXX&enrichSource=Y292ZXJQYWdlOzMwODE5OTk0NDtBUzo0MjU3MDIzNTM4MzgwODBAMTQ3ODUwNjc1ODE3Mw==

Figure 12: Modified W∆ Controller with Balanced idiffac

Qac,2

Qac,1

Q∗ac

Pdc,2

Pdc,1

Pac,2

Pac,1

P ∗ac

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0

0.2

0.4

0.6

0.8

1

Figure 13: AC active and reactive power and DC powercomparisons [pu] — 1: Modified Balanced W∆, 2: BalancedW∆

D. Simulation results

The two developed control structures are applied to thesimulation of an MMC model. The same events as SectionII are tested with the Modified Balanced W∆ Control (Case1)and Balanced idiffac (Case2). Fig. 13 shows the responses tothe step change of the active and reactive power references.Unlike the case with the classic control (Fig. 8), no oscillationis observed on the DC power for both cases as expected.Fig. 14 shows the dynamics of the energy difference duringthe events. As it is observed, the energy difference is correctlyregulated and converged to the reference value of zero aftera short time. The Case2 takes slightly longer time due to theinteractions from the other phases, which exert a modificationfrom the expected active power exchange. In Fig. 15, thedifferential currents are depicted. For both cases, fundamental-frequency components are observed. Nonetheless, they haveno impact on the DC power. This proves the effectiveness ofthe proposed control structures which enable to regulate theenergy difference without having any interaction with DC sideand allows to treat them internally.

IV. CONCLUSION

In this paper, control strategies of energy difference ofthe MMC have been analyzed. While maintaining the cas-caded control structure, two structures of energy differencecontrollers have been presented. The proposed controllersallow regulating the energy difference by generating balanceddifferential current references. Simulation results have shownthe effectiveness of the proposed controllers which enable toregulate the energy difference without having any interactionwith the DC and AC grid. This implies that the regulation ofthe energy difference is treated as internal dynamics and can

Wdiff,c,2

Wdiff,b,2

Wdiff,a,2

Wdiff,c,1

Wdiff,b,1

Wdiff,a,1

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

−0.1

−0.05

0

0.05

0.1

0.15

Figure 14: W∆ comparison (filtered) [pu] — 1: ModifiedBalanced W∆, 2: Balanced W∆

idiffc,2

idiffb,2

idiffa,2

idiffc,1

idiffb,1

idiffa,1

Time [s]1 1.05 1.1 1.15 1.2 1.25 1.3

0

0.1

0.2

0.3

0.4

Figure 15: idiff comparison [pu] — 1: Modified BalancedW∆, 2: Balanced W∆

be dissociated from the global system in large-scale dynamicsstudies.

REFERENCES[1] A. Lesnicar and R. Marquardt, “An innovative modular multilevel

converter topology suitable for a wide power range,” in Power TechConference Proceedings, 2003 IEEE Bologna, vol. 3, pp. 6 pp. Vol.3–, June 2003.

[2] A. Antonopoulos, L. Angquist, and H.-P. Nee, “On dynamics and voltagecontrol of the modular multilevel converter,” 2009 13th Eur. Conf. PowerElectron. Appl., 2009.

[3] S. Debnath, J. Qin, B. Bahrani, M. Saeedifard, and P. Barbosa, “Oper-ation, control, and applications of the modular multilevel converter: Areview,” IEEE Transactions on Power Electronics, vol. 30, pp. 37–53,Jan 2015.

[4] H. Saad, X. Guillaud, J. Mahseredjian, S. Dennetière, and S. Nguefeu,“Mmc capacitor voltage decoupling and balancing controls,” in PowerEnergy Society General Meeting, 2015 IEEE, pp. 1–1, July 2015.

[5] 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 ElectronicsSociety, pp. 150–155, Nov 2010.

[6] S. Wenig, F. Rojas, K. SchÃűnleber, M. Suriyah, and T. Leibfried,“Simulation framework for dc grid control and acdc interaction studiesbased on modular multilevel converters,” IEEE Transactions on PowerDelivery, vol. 31, pp. 780–788, April 2016.

[7] G. Bergna, E. Berne, P. Egrot, P. Lefranc, A. Arzande, J.-C. Vannier,and M. Molinas, “An energy-based controller for hvdc modular mul-tilevel converter in decoupled double synchronous reference frame forvoltage oscillation reduction,” Industrial Electronics, IEEE Transactionson, vol. 60, pp. 2360–2371, June 2013.

[8] P. Delarue, F. Gruson, and X. Guillaud, “Energetic macroscopic repre-sentation and inversion based control of a modular multilevel converter,”in Power Electronics and Applications (EPE), 2013 15th EuropeanConference on, pp. 1–10, Sept 2013.

The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate.The author has requested enhancement of the downloaded file. All in-text references underlined in blue are linked to publications on ResearchGate.

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