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Improving Small-Signal Stability of an MMC WithCCSC by Control of the Internally Stored Energy

Julian Freytes, Gilbert Bergna, Suul Jon Are, Salvatore d’Arco, FrançoisGruson, Frederic Colas, Hani Saad, Xavier Guillaud

To cite this version:Julian Freytes, Gilbert Bergna, Suul Jon Are, Salvatore d’Arco, François Gruson, et al.. ImprovingSmall-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy. IEEETransactions on Power Delivery, Institute of Electrical and Electronics Engineers, 2018, 33 (1), pp.429-439. 10.1109/TPWRD.2017.2725579. hal-01760346

1

Improving Small-Signal Stability of an MMC withCCSC by Control of the Internally Stored Energy

Julian Freytes, Student Member, IEEE, Gilbert Bergna, Jon Are Suul, Member, IEEE, Salvatore D’Arco,François Gruson, Frédéric Colas, Hani Saad, Member, IEEE and Xavier Guillaud, Member, IEEE

Abstract—The DC-side dynamics of Modular Multilevel Con-verters (MMCs) can be prone to poorly damped oscillations orstability problems when the second harmonic components of thearm currents are mitigated by a Circulating Current SuppressionController (CCSC). This paper demonstrates that the source ofthese oscillations is the uncontrolled interaction of the DC-sidecurrent and the internally stored energy of the MMC, as resultingfrom the CCSC. Stable operation and improved performanceof the MMC control system can be ensured by introducingclosed loop control of the energy and the DC-side current.The presented analysis relies on a detailed state-space modelof the MMC which is formulated to obtain constant variables insteady state. The resulting state-space equations can be linearizedto achieve a Linear Time Invariant (LTI) model, allowing foreigenvalue analysis of the small-signal dynamics of the MMC.Participation factor analysis is utilized to identify the sourceof the poorly damped DC-side oscillations, and indicates thesuitability of introducing control of the internal capacitor voltageor the corresponding stored energy. An MMC connected to a DCpower source with an equivalent capacitance, and operated withDC voltage droop in the active power flow control, is used as anexample for the presented analysis. The developed small-signalmodels and the improvement in small-signal dynamics achievedby introducing control of the internally stored energy are verifiedby time-domain simulations in comparison to an EMT simulationmodel of an MMC with 400 sub-modules per arm.

Index Terms—HVDC Transmission, Modular Multilevel Con-verter, State-Space Modeling, Small-Signal Stability Analysis

I. INTRODUCTION

The Modular Multilevel Converter (MMC) is currently themost promising topology for High Voltage DC transmissionsystems (HVDC) [1]. Several advantages of the MMC com-pared to other topologies may be enumerated, such as lowerlosses, modularity, scalability and low harmonic content in theoutput AC voltage [1], [2]. Nevertheless, the internal dynamicsof the MMC topology makes the modeling, control and stabilitystudies of this converter highly challenging [3].

Without control of the internal dynamics, a three-phase MMCwill experience large second harmonic currents circulatingbetween the different phases, and potential resonances betweenthe internal equivalent capacitance and the filter inductor [4].Thus, a Circulating Current Suppression Controller (CCSC) iscommonly applied for eliminating the double frequency circulat-ing currents [5]. However, recent studies have demonstrated thatpoorly damped oscillations or even instability associated withthe DC-side current can occur for MMCs with conventionalCCSC-based control [6]–[9].

Due to the multiple frequency components naturally appear-ing in the internal circulating currents and the arm capacitorvoltages of an MMC [10], traditional power-system-oriented ap-proaches for state-space modeling, linearization and eigenvalue

analysis cannot be directly applied. Thus, in [8], the stabilityof an MMC was studied by application of time-periodic systemtheory (Poincaré multipliers), to demonstrate how the doublefrequency dq current control loops of the CCSC can makethe system unstable. Similar conclusions were obtained in [6],[7], [11], by eigenvalue analysis within a modeling frameworkbased on dynamic phasors and harmonic superposition, forseparately representing the different frequency componentsof the internal MMC variables. However, recent modelingefforts have lead to the development of state-space models thatavoid the approximation of harmonic superposition. Indeed,the MMC model from [12] is first expressed in a form thatseparates the variables into groups with only one steady-stateoscillation frequency, before the variables are transformed intotheir associated Synchronously Rotating Reference Frames(SRRFs). The resulting model can be linearized for applicationof traditional eigenvalue analysis, as demonstrated in [9] whereonly the Classical CCSC strategy was considered.

This paper extends the MMC model from [12] by includinga simplified representation of the DC bus voltage dynamics in aMulti-Terminal DC grid (MTDC), represented by an equivalentcapacitance and a power source. A DC voltage droop control,as expected for HVDC operation in MTDC grids [13], [14], isalso included in the model.

Furthermore, the adapted state-space model is linearized,and the impact of the equivalent DC-side capacitance andthe droop gain on the poorly damped oscillation modes thatoccur with the Classical CCSC are investigated by eigenvalueanalysis. Participation factor analysis is applied to identify thesource of these oscillations, which is shown to be mainly theinteraction between the uncontrolled DC-side current and thevoltage or the energy of the internal capacitance of the MMC.This indicates that the stability and control system performancecan be improved by introducing closed loop control of theDC-side current and the total stored energy within the MMC.By introducing such Energy-based control, with a structuresimplified from [14], the stability problems are avoided andgood performance of the control system can be ensured forthe full range of expected operating conditions. The obtainedimprovement in the small-signal stability is demonstrated bytime-domain simulations as well as by eigenvalue analysis.

II. AVERAGED MMC MODELS FOR MATHEMATICALANALYSIS

In this section, the Arm Averaged Model (AAM) from[15], [16] is first presented to describe the basic mathematicalrelations of an MMC. Then, a time-invariant model that can

2

be linearized for small-signal eigenvalue analysis is developedaccording to the approach presented in [12].

A. Continuous time-periodic Arm Averaged Model

The Arm Averaged Model (AAM) of the MMC is recalledin Fig. 1. The model presents for each phase j (j = a, b, c), aleg consisting of an upper and a lower arm. Each arm includesan inductance Larm, an equivalent resistance Rarm and anaggregated capacitance Carm [15].

vGc vGb vGa

Rf Lf

Rf Lf

Rf Lf i∆c

i∆b

i∆a

iUa iUb iUc

iLa iLb iLc

idc

idc

vUma

vLma

iUma

Carm

vUCa

mUa mU

b

mLa

vdc

Cdc

DC Bus

il

il =Plvdc

AC source

Rarm

Larm

Rarm

Larm

Rarm

Larm

Larm

Rarm

Larm

Rarm

Larm

Rarm

iUmb

Carm

vUCb

iUmc

Carm

vUCc

mUc

iLmc

Carm

vLCc

mLc

iLmb

Carm

vLCb

mLb

iLma

Carm

vLCa

Figure 1. Schematic of the reference configuration with MMC connected toa DC bus capacitor

A simplified model is assumed for the DC bus dynamicsconsisting of an equivalent capacitor Cdc which emulates thecapacitance of the DC cables and other converter stationsconnected to the grid. Also, in parallel with Cdc there is acontrolled current source il whose output power is Pl as anequivalent model of the power exchanged in the HVDC system.

The modulated voltages vUmj and vLmj , as well as the currentsiUmj and iLmj of each arm j are described as follows:

vUmj = mUj v

UCj , vLmj = mL

j vLCj (1)

iUmj = mUj i

Uj , iLmj = mL

j iLj (2)

where mUj (mL

j ) is the corresponding insertion index, and vUCj

(vLCj) is the voltage across the upper (lower) equivalent armcapacitance Carm. The voltage and current of the equivalentcapacitor are related by the following equation:

Carm

dvUCj

dt= iUmj , Carm

dvLCj

dt= iLmj . (3)

For deriving the current dynamics of the AAM, the modula-tion indexes m∆

j and mΣj as well as modulated voltages v∆mj

and vΣmj are introduced [16]:

m∆j

def= mUj −mL

j , mΣj

def= mUj +mL

j (4)

v∆mjdef= (−vUmj + vLmj)/2, vΣmj

def= (vUmj + vLmj)/2 (5)

The MMC currents can be expressed as:

i∆jdef= iUj − iLj , iΣj

def= (iUj + iLj )/2 (6)

where i∆j corresponds to the AC grid current, and iΣj is thecommon-mode current flowing through the upper and lowerarm. The current iΣj is commonly referred as “circulatingcurrent” or “differential current” [16]. However, the moregeneral term “common-mode current” is preferred in this paper,since iΣj is calculated as a sum of two currents.

The AC grid current dynamics are expressed as:

Laceq

di∆jdt

= v∆mj − vGj −Raceqi

∆j (7)

where Raceq

def= (Rarm + 2Rf )/2 and Laceq

def= (Larm + 2Lf )/2.The common-mode arm currents dynamics are given by:

Larm

diΣjdt

=vdc2

− vΣmj −RarmiΣj (8)

Finally, the addition and difference of the terms in (3) yields,

2Carm

dvΣCj

dt= m∆

j

i∆j2

+mΣj i

Σj (9)

2Carm

dv∆Cj

dt= mΣ

j

i∆j2

+m∆j i

Σj (10)

where v∆Cjdef= (vUCj − vLCj)/2 and vΣCj

def= (vUCj + vLCj)/2. Withthe new definitions, the modulated voltages v∆mj and vΣmj canbe expressed as follows:

v∆mj = −1

2

(m∆

j vΣCj +mΣ

j v∆Cj

)(11)

vΣmj =1

2

(mΣ

j vΣCj +m∆

j v∆Cj

)(12)

In steady state, “∆” variables are sinusoidal at the fundamen-tal grid frequency ω, while “Σ” variables contain a sinusoidaloscillation at −2ω superimposed to a DC-component [12].Thus, the variables can be classified as summarized in Table I.

Table IMMC VARIABLES IN Σ-∆ REPRESENTATION

Variables oscillating at ω Variables oscillating at −2ω

i∆j , v∆mj , m∆j , v∆Cj iΣj , vΣmj , mΣ

j , vΣCj

In the following section, a non-linear time-invariant modelis obtained from the MMC model in “Σ-∆” representationgiven by (7)–(12).

B. Non-linear time-invariant model using voltage-based for-mulations in Σ-∆ representation

This section summarizes the time-invariant model of theMMC with voltage-based formulation as proposed in [12]. Toachieve a time-invariant model, it is necessary to refer theMMC variables to their corresponding SRRFs, following thefrequency classification shown in Table I. For generic variablesxΣ and x∆, time-invariant equivalents are obtained with thePark transformation defined in (13) as (bold variables meansmatrix or vectors):

ω ⇒ x∆dqz

def=[x∆d x∆

q x∆z

]>= Pω

[x∆a x∆

b x∆c

]>−2ω ⇒ xΣ

dqzdef=

[xΣd xΣ

q xΣz

]>= P−2ω

[xΣa xΣ

b xΣc

]>

3

Pnω = 23

cos(nωt) cos(nωt− 2π3 ) cos(nωt− 4π

3 )sin(nωt) sin(nωt− 2π

3 ) sin(nωt− 4π3 )

12

12

12

(13)

The formulation of the MMC variables such that this initialseparation of frequency components can be achieved constitutesthe basis for the used modelling approach, as illustrated inFig. 2.

+ω 3ω

v∆Cabc Pω

vΣCabc

P−2ω

v∆Cz

T3ω

⊥90

v∆⊥90Cz

vΣCdqz

v∆Cdq

v∆CZ

i∆abc Pω

iΣabc

P−2ω iΣdqz

i∆dq

mΣabc

P−2ω mΣdqz

m∆abc Pω m∆

z = 0m∆

dq

−2ω DC

MM

CIn

tern

alS

tate

Var

iab

les

Con

trol

vari

able

s

Figure 2. The used modelling approach based on three Park transformationsto achieve SSTI state variables

As shown in (7)–(12), the Σ and ∆ quantities are notfully decoupled. This results in time-periodic variables in theequations after applying the above transformations. For theΣ variables, time-periodic terms of 6ω are neglected withoutcompromising the accuracy of the model. Conversely, the zerosequences of the vectors in “∆” variables present time-periodicterms of 3ω which has to be taken into account. This componentwas modeled by means of an auxiliary virtual variable, 90°shifted from the real one, and by using a transformation T3ω

at +3ω to achieve a model with a defined equilibrium point.

3ω+ ⇒ x∆Z

def=

x∆Zd

x∆Zq

=

cos(3ω) sin(3ω)

sin(3ω) − cos(3ω)

︸ ︷︷ ︸

T3ω

x∆z

x∆90°z

Using the above definitions, the MMC dynamics in their

“Σ-∆” representation can be reformulated as a state-spacemodel where all states reach constant values in steady-sate[12]. The resulting system is recalled in the following.

1) AC grid currents: Applying the Park transformation atω to (7), the SRRF representation of the AC side currentdynamics i∆dq are given as:

Laceq

di∆dqdt

= −vGdq + v∆

mdq −Raceqi

∆dq − JωL

aceqi

∆dq (14)

where vGdq is the grid voltage at the point of interconnection and

Jω is the cross-coupling matrix at the fundamental frequency,as defined in (15),

Jωdef=

[0 ω−ω 0

]. (15)

The AC-side modulated voltage v∆mdq is defined in (16) as a

function of the modulation indexes m∆dq and mΣ

dqz ,

v∆mdq =

1

4V ∆

[m∆

dq

>,mΣ

dq

>,mΣ

z

]>. (16)

V ∆ is defined as the following 2× 5 voltage matrix, whereall elements are represented in their associated SRRFs:

V ∆ def=

−2vΣCz − vΣCd; vΣCq; −v∆Cd − v∆CZd;v∆Cq + v∆CZq

;−2v∆Cd

vΣCq; vΣCd − 2vΣCz; v∆Cq − v∆CZq; v∆Cd − v∆CZd

;−2v∆Cq

. (17)

2) Common-mode arm currents: Similarly, applying the Parktransformation at −2ω to (8), the dynamics of the common-mode arm currents in their time invariant representation iΣdqand iΣz are obtained, shown in (18a).

Larm

diΣdqdt

= −vΣmdq −RarmiΣdq − 2JωLarm iΣdq (18a)

LarmdiΣzdt

= −vΣmz −RarmiΣz +vdc2

(18b)

with vdc representing the voltage at the MMC DC terminals.The modulated voltages driving the currents iΣdq and iΣz arevΣmdq and vΣmz . These voltages are defined in (19), as a function

of the modulation indexes:

vΣmdqz =

1

4V Σ

[m∆

dq

>,mΣ

dq

>,mΣ

z

]>. (19)

V Σ corresponds to the following 3× 5 voltage matrix:

V Σ def=

v∆Cd + v∆CZd

−v∆Cq + v∆CZq2vΣCz 0 2vΣCd

−v∆Cq − v∆CZq−v∆Cd + v∆CZd

0 2vΣCz 2vΣCq

v∆Cd v∆Cq vΣCd vΣCq 2vΣCz

. (20)

3) Arm capacitor voltages sum: Applying the Park trans-formation at −2ω to (9), the time invariant dynamics of thevoltage sum vector vΣ

Cdqz can be expressed by (21).

Carm

dvΣCdqz

dt= iΣmdqz −

[−2Jω 02×1

01×2 0

]CarmvΣ

Cdqz

(21)

with iΣmdqz representing the modulated current as defined in(22), as a function of the modulation indexes,

iΣmdqz =1

8IΣ[m∆

dq

>,mΣ

dq

>,mΣ

z

]>. (22)

IΣ is the following 3× 5 time invariant current matrix:

IΣ def=

i∆d −i∆q 4iΣz 0 4iΣd

−i∆q −i∆d 0 4iΣz 4iΣq

i∆d i∆q 2iΣd 2iΣq 4iΣz

. (23)

4) Arm capacitor voltages difference: Finally, the steady-state time invariant dynamics of the voltage difference vectorsv∆Cdq and v∆CZ are now recalled. Results are obtained by

applying the Park transformation at ω and 3ω to (10). For thesake of compactness, the voltage difference vector is defined

as v∆CdqZ

def=[v∆Cd, v

∆Cq, v

∆CZd

, v∆CZq

]>.

Carm

dv∆CdqZ

dt= i∆mdqZ −

[Jω 02×2

02×2 3Jω

]Carmv∆

CdqZ

(24)with i∆mdqZ representing the modulated current as defined in(25), as a function of the modulation indexes,

i∆mdqZ =1

16I∆[m∆

dq

>,mΣ

dq

>,mΣ

z

]>. (25)

4

I∆ is the following 4× 5 time-invariant current matrix:

I∆ def=

2iΣd + 4iΣz −2iΣq i∆d −i∆q 2i∆d−2iΣq −2iΣd + 4iΣz −i∆q −i∆d 2i∆q2iΣd 2iΣq i∆d i∆q 0−2iΣq 2iΣd i∆q −i∆d 0

. (26)

5) DC bus dynamics: The DC bus dynamics are modelledby (27), where Cdc is the cable model terminal capacitanceand Pl represents the power injection as seen from the MMCstation.

Cdcdvdcdt

=Pl

vdc− 3iΣz (27)

An overview of the model structure corresponding to theMMC and DC bus equations is shown in Fig. 3.

Grid currentsvGdq

vdc

iΣdqz

Eq. (14)

Eq. (18)

CalculationsCalculations

Eq. (16)

Calculations

v∆mdq

vΣmdqz

Eq. (19)

Eq. (24)

v∆CdqZ

Calculations

Eq. (21)

vΣCdqz

mΣdqz

m∆dq

Common-modecurrentsiΣdqz

i∆dq

DC busvdc

vdciΣz

÷Pl il Eq. (27)

InputsStatesAlgebraic equationsDifferential equations

v∆CdqZ

vΣCdqz

i∆dq

vΣCdqz

v∆CdqZ

vΣCdqz

v∆CdqZ

vΣmdqz

v∆mdq

Figure 3. MMC and DC bus equations resume

III. MMC MODEL WITH CLASSICAL CCSC AND DCVOLTAGE DROOP

This section presents the control scheme for an MMC asshown in Fig. 4. For the AC-side, the MMC control strategyis based on a classical scheme with two cascaded loops. Theouter loop controls the active power Pac following a Pac—vdcdroop characteristic with gain kd [14], and reactive power Qac.

ωLaceq

ωLaceq

vGd

vGq

i∆∗d

i∆∗q

i∆d

i∆q

+

−

−+

v∆∗md

v∆∗mq

++

+

−+

+PIi∆

PIi∆

m∆dq

mΣdqz

Grid currents control

vGd

iΣd

+

−

−+

vΣ∗md

vΣ∗mq

CCSC

iΣq

iΣ∗d = 0

iΣ∗q = 0

vdc2

2ωLarm

2ωLarm

−

−

−+

÷

+

−

v∗dc

vdc÷

vGd

DC voltage droop control

−1kd

+P ∗ac0

Q∗ac

P ∗ac

vdc

23

23

vΣ∗mz

(28)Equation

PIiΣ

PIiΣ

+

−Kp

1Tis

Ref.

Meas.+

Out

Generic PI structure

ξ: State of the integral part

ξ

Figure 4. MMC droop-controlled with Classical CCSC

The inner loops control the AC currents in dq frame. Thevariables v∆∗

md and v∆∗mq are the output of the controllers

regulating the grid side current i∆dq to the desired reference i∆∗dq

by implementing standard current controllers with decouplingfeed-forward terms. This controller is tuned to have a responsetime τ∆i of 10 ms with a damping coefficient ζ∆i of 0.7.

Furthermore, vΣ∗md and vΣ∗

mq are the outputs of the CCSC [5],forcing the circulating currents iΣdq to zero. The gains of thecontrollers are calculated to achieve a response time τΣi of 5ms and ζΣi of 0.7. The output DC current of the converter isleft uncontrolled with this strategy, and it is naturally adjustedto balance the AC and DC power flow.

The MMC insertion indexes are calculated directly from theoutput of the control loops for the ac-side and CCSC as shownin (28).

mΣd = 2

vΣ∗md

vdc, mΣ

q = 2vΣ∗mq

vdc, mΣ

z =2vΣ∗mz

vdc(28a)

m∆d = −2

v∆∗md

vdc, m∆

q = −2v∆∗mq

vdc(28b)

where, for this controller, mΣz is equal to 1 and vdc is the

measured DC voltage. Instead of vdc, a fixed value (i.e. thenominal voltage) can be used, but this choice can reduce thestability region of the MMC [9]. Calculation of the insertionindexes in this way will be referred to as the “Un-CompensatedModulation” (UCM) [17], since there is no compensation forthe impact of the oscillations in the equivalent arm capacitorvoltages on the modulated output voltages.

IV. SMALL SIGNAL STABILITY ANALYSIS OF AN MMCWITH CLASSICAL CCSC

A. Model linearization and time domain validation

The non-linear time-invariant model presented in Section IIwith the control from Section III are connected as shown inFig. 5.

MMC + DC bus

Figure 3

Classical CCSC

Figure 4

strategy

mΣdqz m∆

dq

i∆dqiΣdq vdcvGdq

vGdq

PliΣ∗dq =0

v∗dcP ∗ac0

Q∗ac

Figure 5. Non-linear time-invariant model of MMC, DC bus and ClassicalCCSC

This interconnected model is represented by a subset ofordinary differential equation f as expressed in (29), where xrepresents the states of the system as in (30) and u the inputsas in (31).

x(t) = f (x(t),u(t)) (29)

x = [ξi∆dqξiΣdq︸ ︷︷ ︸

Controllers

i∆dq iΣdqz vΣCdqz v∆

CdqZ︸ ︷︷ ︸MMC

vdc︸︷︷︸DC bus

]> (30)

u = [v∗dc P∗ac0 Q∗

ac iΣ∗d iΣ∗

q︸ ︷︷ ︸Controllers

vGd vGq︸ ︷︷ ︸AC grid

]> (31)

The non-linear model from (29) can be linearized arounda steady-state operating point by means of the Jacobianlinearization method, resulting in a Linear Time-Invariant (LTI)representation as expressed in (32) [18]. It is recalled that eachelement Aij and Bij of the matrices A and B are related tothe equations f as shown in (33).

∆x(t) = A(x0,u0)∆x(t) +B(x0,u0)∆u(t) (32)

Aij =∂fi(x,u)

∂xj

∣∣∣∣(x0;u0)

; Bij =∂fi(x,u)

∂uj

∣∣∣∣(x0;u0)

(33)

5

The equilibrium point, defined by (x0,u0), is calculatedfrom the direct resolution of the system equations from (29) bysetting x(t) equal to zero. The obtained LTI model is used forevaluating small-signal dynamics and stability by eigenvalueanalysis.

To validate the developed small-signal model of the MMCwith Classical CCSC, results from a time-domain simulationof two different models will be shown and discussed in thefollowing:

1) EMT: The system from Fig. 1 implemented in EMTP-RVwith 400 submodules. The MMC is modeled with the so-called “Model # 2: Equivalent Circuit-Based Model” from[15]. It is worth noticing that the modulation indexes aretransformed from “Σ-∆” and dq frame to “Upper-Lower”and abc frame.

2) LTI: This model represents the linearized time-invariantmodel of the interconnected system from Fig. 5, im-plemented in Matlab/Simulink. The operating pointcorresponds to the nominal ratings.

The main system parameters are listed in Table II.

Table IIPARAMETERS FOR THE TIME DOMAIN SIMULATION

U1n 320 kV Rf 0.521 Ω τ∆i 10 msPn 1 GW Lf 58.7 mH ζ∆i 0.7fn 50 Hz Rarm 1.024 Ω τΣi 5 ms

Carm 32.55µ F Larm 48 mH ζΣi 0.7Cdc 195.3µ F vdcn 640 kV kd 0.1 pu

Starting with a DC power transfer of 1 pu (from DC to AC),a step is applied on Pl of −0.1 pu at 0.05 s. The reactivepower is controlled to zero during the event. Simulation resultsare gathered in Fig. 6.

The dynamic response of the DC power Pdc is shown inFig. 6(a) (i.e. measured power in the reference model and thecalculated power for the linearized model as Pdc = 3iΣz vdc).The results of the common-mode currents are shown in Fig. 6(b)(only dq components). The EMT model presents oscillationsat 6ω in steady state. These oscillations were neglected duringthe development of the time-invariant model [12]. As seenin the comparisons from Fig. 6(b), the model captures theaverage dynamics with reasonable accuracy even if the 6th

harmonic components are ignored (notice the scale). For allother variables, there are negligible differences between thedifferent models.

The step applied on Pl produces power imbalance in theDC bus, and the MMC reacts with the droop controller andits internal energy to achieve the new equilibrium point. TheDC voltage results are shown in Fig. 6(c). Due to the DCvoltage droop control (proportional controller with gain kd), asteady-state error is obtained after the transient. The internalenergy of the MMC participates in the dynamics of the DCvoltage regulation by discharging its internal capacitors intothe DC bus during the transients, as seen in the voltage vΣCz

from Fig. 6(d). The behavior of vΣCz is similar to the DC busvoltage as expected from the discussion in [14].

Pdc - LTIPdc - EMTPl

Pdc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.85

0.9

0.95

1

1.05

(a) Pdc[pu]

iΣq - LTI

iΣd - LTI

iΣq - EMT

iΣd - EMT

iΣ dq×10

−3[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

−4

−2

0

2

4

6

(b) iΣdq[pu]

vdc - LTIvdc - EMT

v dc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.98

0.985

0.99

0.995

1

(c) vdc[pu]

vΣCz - LTI

vΣCz - EMT

vΣ Cz[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.98

0.985

0.99

0.995

1

(d) vΣCz[pu]

Figure 6. Time domain validation Classical CCSC – Step applied on Pl of0.1 pu – EMT : EMTP-RV simulation with detailed converter, LTI: Lineartime-invariant state-space model in Simulink

B. Stability analysis

Since the linearized model from Fig. 5 has been validated,it can be used for small signal stability analysis. The impactof three main parameters influencing the DC voltage dynamicsare evaluated: the DC capacitance, the droop gain kd [14] andthe response time of the current loops.

1) Influence of the DC capacitance: In MTDC systems, thevalue of the equivalent DC capacitance depends on the numberof MMC stations connected to the grid as well as the cablelenghts [14]. This value may vary because some converterscould be disconnected or the grid topology reconfigured. Forthis reason, the MMC should be able to operate under differentsituations that can result from changes of the DC grid topologyand parameters. For evaluating the impact of the DC sidecapacitance on the small-signal stability, a parametric sweepis performed. The electrostatic constant Hdc is defined as,

Hdc =1

2Cdc

v2dcnPn

. (34)

6

The value of Hdc is varied from 40 ms down to 5 ms.This last value represents a small capacitance of the DC bus(24, 4µF << (6 × Carm)), which could represent the DCcapacitance of a short cable. The first results consider a powerdirection from DC to AC side of 1 GW (1 pu) of power transfer.Results are shown in Fig. 7(a). In this case, for the selectedvalues the system remains stable.

It is known that the converters dynamics depend on theoperating point [19]. The same parametric sweep as theprevious example is performed with the opposite power transferdirection (i.e. from AC to DC side). The results are shownin Fig. 7(b), demonstrating that the system becomes unstablewhen the equivalent DC capacitor decreases.

Real

Imaginary

−250 −200 −150 −100 −50 0

−1000

0

1000

λ1,2

Hdc[s ]

0.01

0.02

0.03

0.04

0.005

(a) Pdc0 = 1 pu – Power flow: DC ⇒ AC

Real

Imaginary

−250 −200 −150 −100 −50 0

−1000

0

1000

λ1,2

Hdc[s ]

0.01

0.02

0.03

0.04

0.005

(b) Pdc0 = −1 pu – Power flow: DC ⇐ AC

Figure 7. Parametric sweep of DC capacitor Hdc — DC Operating pointvdc0 = 1 pu — kd = 0.1 pu — Classical CCSC

2) Influence of the droop parameter: In this case, the droopparameter kd is varied from 0.2 pu down to 0.05 pu. Theconsidered power direction is from AC to DC since it is theworst case from the previous section. Results are shown inFig. 8. When lower values of droop are used, the eigenvaluesλ1,2 shift to the right-hand plane (RHP) resulting in unstablebehavior.

kd[pu ]

Real

Imaginary

−250 −200 −150 −100 −50 00.05

0.1

0.15

0.2

−1000

0

1000

λ1,2

Figure 8. Parametric sweep of Droop parameter kd — DC Operating pointvdc0 = 1 pu, Pdc0 = −1 pu — Classical CCSC

3) Influence of current controllers: For evaluating the impactof the current controllers on the stability, the response timesof the grid current control loops are varied as well as thecirculating current control loops (CCSC). Results are shown inFig. 9(a) for the variation of τ∆i and Fig. 9(b) for τΣi . When

faster controllers are used (lower values of response times),the eigenvalues λ1,2 shift to the RHP.

τ∆ i[ms ]

Real

Imaginary

−250 −200 −150 −100 −50 02345678910

−1000

0

1000

λ1,2

(a) Parametric sweep of response time of current control loop τ∆i

τΣ i[ms ]

Real

Imaginary

−250 −200 −150 −100 −50 01.5

2

3

4

5

−1000

0

1000

λ1,2

(b) Parametric sweep of response time of circulating current control loop(CCSC) τΣi

Figure 9. Parametric sweep of response time of current controllers — DCOperating point vdc0 = 1 pu, Pdc0 = −1 pu

C. Identification of unstable eigenvalues

As observed in the previous results (Figs. 7, 8 and 9),the system may become unstable due to the same pair ofeigenvalues for all cases (λ1,2). For understanding the originof these eigenvalues, participation factor analysis is performedfor the case from the previous sub-section and the resultsare shown in Fig. 10, where the considered parameters andoperating point are given in Table II.

ParticipationRatioλ

1,2

0

0.1

0.2

0.3

0.4

vdcv∆CZq

v∆CZd

v∆Cqv∆

CdvΣCzvΣ

CqvΣCdiΣziΣqiΣdi∆qi∆dξiΣqξiΣd

ξi∆qξi∆d

Controllers

Circulating Current

DC CurrentMMC Capacitors DC Voltage

Figure 10. Results from participation factor analysis - Eigenvalues λ1,2 —τ∆i = 10 ms; τΣi = 5 ms; kd = 0.1 pu; Hdc = 40 ms

Results from Fig. 10 indicate that the states with the highestparticipation in the critical mode are iΣz (i.e. the DC current),vΣCz (the state of the MMC which represents the internallystored energy) and vdc (DC voltage). It shows also thatthe internal circulating currents iΣdq do not have significantinfluence on these eigenvalues and neither do the integral partof the controllers (with the chosen bandwidths).

The impact of the proportional gains of the controllers areevaluated by calculating the participation factors for each pointfrom Figs. 9 and the results are shown in Fig. 11. In Fig. 11(a),a similar pattern is observed for the participation factors asin Fig. 10. For fast response times of the CCSC, the dq

7

components of vΣC participate more on the studied eigenvalues,but the system is unstable as shown in Fig. 9(b). Nevertheless,for realistic values of response times, the most important statesare iΣz , vΣCz and vdc, which corresponds to the results in Fig. 10.

Part.Ratioλ

1,2

τ∆i [ms]

2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

vdcv∆Cqv∆

CdvΣCzvΣ

CqvΣCdiΣz

(a) Results from participation factor analysis - Eigenvalues λ1,2

vdcv∆Cqv∆

CdvΣCzvΣ

CqvΣCdiΣz

Part.Ratioλ

1,2

τΣi [ms]

1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

(b) Results from participation factor analysis - Eigenvalues λ1,2

Figure 11. Participation factors for different response times — Dashed linescorrespond to the states that are not listed in the legend — DC Operatingpoint vdc0 = 1 pu, Pdc0 = −1 pu

V. SMALL SIGNAL STABILITY IMPROVEMENT OF AN MMCWITH ENERGY BASED CONTROLLER

Since the instabilities identified in the studied cases are duemainly to the uncontrolled output current iΣz , the natural furtherstep is the explicit control of this current for improving thebehavior of the system.

A. Energy-based controller

The considered control strategy from previous section controltwo out of three common-mode currents iΣ. The uncontrolledzero-sequence component of iΣ may cause interactions with theDC bus and the internal capacitor voltages, and can potentiallymake the system unstable. To improve the stability of thestudied system, it is proposed to add a DC current control loop(or what is the same, a controller for iΣz ).

In the Classical CCSC strategy from last section, the energyis naturally following the DC bus voltage. The DC current isadjusting itself to achieve an implicit balance of energy andbetween AC and DC power in steady state. When controllingthe DC current, this natural balance is lost so the DC currenthas to be determined explicitly to regulate the internally storedenergy and balance the AC and DC power flow.

1) Inner control loop — Z-sequence Σ current: The designof the controller for iΣz is based on the second equation of(18a), and a simple PI can be deduced as shown in Fig. 12.For tuning purposes, vΣmz is supposed to be equal to vΣ∗

mz .

vdc2

PIiΣ

iΣz

iΣ∗z +

−vΣ∗mz−

+

Z-seq. Σ Current Controller

1Larms+Rarm

iΣz

vdc2

+

−vΣmz

Equation (18b)

÷mΣ

z Eq.

vdc2

(19)

Figure 12. Block diagram of the iΣz current control

2) Outer control loop — Energy controller: For generatingthe current reference iΣ∗

z an outer loop is needed. The proposedstrategy is based on the explicit control of the the total storedenergy WΣ

z on the MMC capacitors Carm given by the powerbalance between AC and DC sides [16]. For designing thiscontroller, a model with the explicit relation between the DCcurrent idc and the total stored energy WΣ

z is needed. AssumingP ∗ac ≈ Pac, a simplified expression of the sum energy dynamics

can be defined as [16]:

dWΣz

dt≈ Pdc − Pac ≈ vdc 3iΣz︸︷︷︸

idc

−P ∗ac (35)

The deduced controller structure is shown in Fig. 14. For tuningpurposes, the inner iΣz current controller is considered as aunity gain.

P ∗ac

PIWΣ

WΣz

WΣ∗z +

−P ∗dc

+

Total Energy Controller

1s

WΣz

P ∗ac

−+

Equation (35)

vdc

×idc

3iΣz PdciΣ∗

z

vdc

÷ 13

i∗dc iΣzCtrl.loop

Figure 13. Controller design for WΣz

Finally, the complete control structure is shown in Fig. 14,where the response time for the total energy τΣW is set to 50 ms(i.e. 10 times slower than the inner Σ current loop). The energyreference WΣ∗

z is set to 1 pu in this paper, for maintaininga constant level of stored energy (corresponding to the ratedcapacitor voltages). As explained in [20], the energy WΣ

z is

vdc2

vdc

÷ 13

+

−

WΣ∗z

Wz +P ∗acP ∗ac iΣz

iΣ∗z +

−i∗dc

vΣ∗mz−

+

P ∗dc

Z-seq. Σ Current ControllerTotal Energy Controller

CCSC

Grid currents controlDC voltage droop controli∆∗dq v∆∗

mdq

iΣ∗dq = 0 vΣ∗

mdqm∆

dq

mΣdqz

vdc

PIiΣPIWΣ

Eq.(28)

Figure 14. Complete Energy based control - Current and Energy controllers

calculated from the dqz components as in (36).

WΣz ≈Carm

((vΣCd

)22

+

(vΣCq

)22

+(vΣCz

)2)+ ... (36)

...+ Carm

∑k=d,q,Zd,Zq

(v∆Ck

)22

B. Model linearization and time domain validationIn a similar way as in Section IV, the system comprising the

non-linear model from Fig. 3 and the controller from Fig. 14 are

8

connected as shown in Fig. 15. The state variables of the newcontrollers ξiΣz and ξWΣ

z, which correspond to the integral part

of the PI controllers, are concatenated to the system states x.Also, the energy reference WΣ∗

z is now included in the inputsvector u. The new interconnected model can be linearizedaround any operating point for stability analysis.

vΣCdqz

v∆CdqZ

Energy based

Figure 14

controller

Equation (36)WΣ

z WΣz calculation

MMC + DC bus

Figure 3

mΣdqz m∆

dq

i∆dqiΣdq vdcvGdq

iΣ∗dq =0

v∗dcP ∗ac0

Q∗ac

vGdq

PlWΣ∗z

Figure 15. Non-linear time-invariant model of MMC, DC bus and Energybased controller

To validate the developed small-signal model of the MMCwith Energy based control, results from time domain simula-tions are shown in Fig. 16. The event and parameters are thesame as for Section IV, but it can be observed that the transientbehavior of the DC power and voltage are well controlledcontrary to the oscillatory behavior from the Classical CCSCstrategy (Fig. 6).

Pdc - LTIPdc - EMTPl

Pdc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.85

0.9

0.95

1

1.05

(a) Pdc[pu]

vdc - LTIvdc - EMT

v dc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.98

0.985

0.99

0.995

1

(b) vdc[pu]

Figure 16. Time domain validation Energy based controller – Step applied onPl of 0.1 pu – EMT : EMTP-RV simulation with detailed converter, LTI:Linear time-invariant state-space model in Simulink

C. Stability analysis with Energy-based controller

As shown in Section IV-B, when the Classical CCSC fromFig. 4 was considered, some instabilities were observed withlow values of droop gain kd or low equivalent capacitanceon the DC side (i.e. low values of Hdc). For demonstratingthe stability improvement with the Energy-based controllerfrom Fig. 14, the same parametric sweep is performed as forFig. 7 and Fig. 8. The results are gathered in Fig. 17. Forboth situations, it is only shown the case where the powerflow is from the DC side to the AC side since it was the casewhere the instabilities occurred in Section IV-B. However, with

Hdc[s ]

Real

Imaginary

−250 −200 −150 −100 −50 0

0.01

0.02

0.03

0.04

−1000

0

1000

0.005

(a) Influence of DC capacitor Hdc — kd = 0.1 pu

kd[pu ]

Real

Imaginary

−250 −200 −150 −100 −50 00.05

0.1

0.15

0.2

−1000

0

1000

(b) Influence of droop gain kd — Hdc = 40 ms

Figure 17. Parametric sweeps for Energy-based control — vdc0 = 1 pu,Pdc0 = −1 pu, kd = 0.1 pu — Power flow: DC ⇐ AC

this controller, the system presents similar behavior from bothpower directions.

For the case of the variation of Hdc in Fig. 17(a), as wellfor the variation of kd in Fig. 17(b) it can be clearly observedthat stability is guaranteed for the studied cases.

VI. STABILITY COMPARISON

A. DC Capacitance

For comparing the stability improvement, the eigenvaluesfrom Fig. 7(b) and Fig. 17(a) with an electrostatic constantHdc of 14.2 ms are shown in Fig. 18. The value of Hdc ischosen for highlighting the stability limits for the ClassicalCCSC. The unstable poles have a value of 2.81± j781, whichcorresponds to a frequency of 124 Hz approximately.

Energy basedClassical CCSC

Imaginary

Real−250 −200 −150 −100 −50 0

−1000

0

1000

Figure 18. Eigenvalues comparison Energy-based and Classical CCSC control— DC Operating point vdc0 = 1 pu, Pdc0 = −1 pu, Power flow: DC ⇐ AC— kd = 0.1 pu

The stability improvements with the Energy-based controllerare highlighted by a time domain simulation. The operatingpoint is the same as for Fig. 18, and results are shown inFig. 19. Since, for this set of parameters, the configuration ofthe MMC with Classical CCSC is unstable, the simulation isstarted with an extra capacitor connected in parallel with Cdc

for stabilizing the system, which is disconnected at t = 0 s.The frequency of the oscillations corresponds to the frequencyof the unstable eigenvalues from Fig. 18.

9

Pdc - Energy basedPdc - Classical CCSCPl

Pdc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

−1

−0.9

−0.8

(a) Pdc[pu]

vdc - Energy basedvdc - Classical CCSC

v dc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25

0.995

1

1.005

1.01

1.015

(b) vdc[pu]

Figure 19. Time domain comparison in EMTP-RV with detailed converterswith Classical CCSC and Energy based strategies — Step applied on Pl of0.1 pu — Hdc = 14.2 ms

B. Active power reversal

In this section, an active power reversal from 1 pu to −1pu is considered. Fixing a DC capacitance with Hdc equal to10ms, and a droop parameter kd equal to 0.1 pu, a parametricsweep for both control strategies is performed and the resultsare gathered in Fig. 20. For the Classical CCSC in Fig. 20(a)the system is unstable for DC power values lower than −0.15pu approximately, whereas in Fig. 20(b), i.e. the case withEnergy based controller, the system remains stable for all thepower range.

[pu ]

Real

Imaginary

250 200 150 100 50 0

1000

0

1000

Pdc

− − − − −

−

λ1,2

−1

−0.5

0

0.5

1

(a) Classical CCSC

Pdc[pu]

Real

Imaginary

−250 −200 −150 −100 −50 0−1

−0.5.

0

0.5

1

−1000

0

1000

(b) Energy-based control

Figure 20. Parametric sweep of DC power reversal with Classical CCSC andEnergy based strategies — Hdc = 10 ms — kd = 0.1 pu

Results from Fig. 20 are validated in time domain simulationsas shown in Fig. 21. The AC power reference P ∗

ac0 (see Fig. 4)is also ramped during the transient with the same rate for takinginto account the voltage deviation. This represents the casewhere the power reversal signal is coordinated by a dedicated

MTDC master controller. The time domain results highlight thebenefits of the Energy based control approach for improvingthe stability of the system.

Pdc - Energy basedPdc - Classical CCSCPl

Pdc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

−1

−0.5

0

0.5

1

(a) Pdc[pu]

vdc - Energy basedvdc - Classical CCSC

v dc[pu ]

Time [s]0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0.99

0.995

1

1.005

1.01

(b) vdc[pu]

Figure 21. Time domain comparison in EMTP-RV with detailed converterswith Classical CCSC and Energy based strategies — Hdc = 10 ms —kd = 0.1 pu

VII. CONCLUSIONS

This paper has identified the source of the poorly dampedand even possible unstable oscillations that can appear forMMCs relying on a CCSC without control of the internallystored energy. It has been demonstrated by participation factoranalysis that the source of these potential stability problems isthat the classical CCSC leaves the DC-side current uncontrolled,which leads to potential interaction with the DC bus voltageand the internally stored energy of the the MMC. To avoidthese interactions, a control loop for regulating the energystored in the MMC is introduced. The output of this controlloop is the reference for controlling the DC-side current, whichis corresponding to the zero-sequence component resultingfrom the dq- transformation used for the implementation of theclassical CCSC. The stability improvement due to the additionalcontrol loops is clearly demonstrated by small-signal eigenvalueanalysis based on linearization of the presented state-spacemodel, which is accurately representing the internal dynamicsof the MMC. The applied state-space modeling approach andthe improved dynamic response obtained with the added energy-and DC-side current controllers is validated by time-domainsimulations in comparison to a detailed EMT model of anMMC with 400 sub-modules per arm. Further developmentsshould consider the dynamic analysis of a more advancedmanagement of the energy in the MMC, i.e. where the energysum and difference are explicitly controlled.

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[2] A. Antonopoulos, L. Angquist, and H. P. Nee, “On dynamics and voltagecontrol of the modular multilevel converter,” in Power Electronics andApplications, 2009. EPE ’09. 13th European Conference on, pp. 1–10,Sept 2009.

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

[4] K. Ilves, A. Antonopoulos, S. Norrga, and H.-P. Nee, “Steady-stateanalysis of interaction between harmonic components of arm and linequantities of modular multilevel converters,” IEEE Transactions on PowerElectronics, vol. 27, pp. 57–68, January 2012.

[5] Q. Tu, Z. Xu, and J. Zhang, “Circulating current suppressing controller inmodular multilevel converter,” in IECON 2010 - 36th Annual Conferenceon IEEE Industrial Electronics Society, pp. 3198–3202, Nov 2010.

[6] A. Jamshidifar and D. Jovcic, “Small signal dynamic dq model ofmodular multilevel converter for system studies,” Power Delivery, IEEETransactions on, vol. 31, pp. 191–199, February 2016.

[7] T. Li, A. Gole, and C. Zhao, “Stability of a modular multilevel converterbased hvdc system considering dc side connection,” IET ConferenceProceedings, pp. 21 (6 .)–21 (6 .)(1), January 2016.

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[9] J. Freytes, G. Bergna, J. Suul, S. D’Arco, H. Saad, and X. Guillaud,“Small-signal model analysis of droop-controlled modular multilevelconverters with circulating current suppressing controller,” in 13th IETInternational Conference on AC and DC Power Transmission (ACDC2017), pp. 16–24, February 2017.

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[18] X.-F. Wang, Y. Song, and M. Irving, Modern power systems analysis.Springer Science & Business Media, 2010.

[19] J. Freytes, S. Akkari, J. Dai, F. Gruson, P. Rault, and X. Guillaud, “Small-signal state-space modeling of an hvdc link with modular multilevelconverters,” in 2016 IEEE 17th Workshop on Control and Modeling forPower Electronics (COMPEL), pp. 1–8, June 2016.

[20] J. Freytes, G. Bergna, J. A. Suul, S. D’Arco, H. Saad, and X. Guillaud,“State-space modelling with steady-state time invariant representationof energy based controllers for modular multilevel converters,” in IEEEPES PowerTech 2017, Manchester UK, June 2017.

Julian Freytes (S’15) received the Electrical Engineering degree from theUniversidad Nacional del Sur (UNS), Bahía Blanca, Argentina in 2013.He received the M.Sc. degree in Electrical Engineering for SustainableDevelopment from Université des Sciences et Technologies de Lille, Francein 2014. Since 2015, he is pursuing his Ph.D on interoperability analysis of

Modular Multilevel Converters connected to Multi-Terminal DC grids in EcoleCentrale de Lille, France. His main research interests include the modelingand control of power electronics for HVDC systems.

Gilbert Bergna received his electrical power engineering degree from the“Simón Bolívar University”, in Caracas, Venezuela, in 2008; his “ResearchMaster” from SUPÉLEC (École Supérieure d’Électricité), in Paris, France,in 2010; and a joint PhD degree between SUPÉLEC and the NorwegianUniversity of Science and Technology (NTNU) in 2015. In march 2014 hejoined SINTEF Energy Research as a research scientist, and since august 2016started a post-doctoral fellowship at NTNU working on control and modellingof power electronic systems.

Jon Are Suul (M’11) received the M.Sc. degree in Energy and EnvironmentalEngineering and the PhD degree in Electric Power Engineering from theNorwegian University of Science and Technology (NTNU), Trondheim,Norway, in 2006 and 2012, respectively. From 2006 to 2007, he was withSINTEF Energy Research, until starting his PhD studies. From 2012 heresumed a position as a Research Scientist at SINTEF Energy Research, firstin part-time while also working as a postdoctoral researcher at the Departmentof Electric Power Engineering of NTNU until 2016. His research interestsare mainly related to modelling, analysis and control of power electronicconverters in power systems and for renewable energy applications.

Salvatore D’Arco received the M.Sc. and Ph.D. degrees in electricalengineering from the University of Naples “Federico II”, Naples, Italy, in2002 and 2005, respectively. From 2006 to 2007, he was a postdoctoralresearcher at the University of South Carolina, Columbia, SC, USA. In 2008,he joined ASML, Veldhoven, the Netherlands, as a Power Electronics Designer,where he worked until 2010. From 2010 to 2012, he was a postdoctoralresearcher in the Department of Electric Power Engineering at the NorwegianUniversity of Science and Technology (NTNU), Trondheim, Norway. In 2012,he joined SINTEF Energy Research where he currently works as a ResearchScientist. His main research activities are related to control and analysis ofpower-electronic conversion systems for power system applications, includingreal-time simulation and rapid prototyping of converter control systems.

François Gruson received the Ph.D. degree in electrical engineering fromthe Ecole Centrale de Lille, Lille, in 2010. Since 2011, he has been workingas Associate Professor at Arts and Metiers ParisTech in the Laboratoired’Electrotechnique et d’Electronique de Puissance of Lille (L2EP), Lille,France. His research interests include power electronic converter and powerquality for distribution and transmission grid application and especially forHVDC transmission grid.

Frédéric Colas was born in Lille, France, on October 17, 1980. He receivedhis Ph.D. degree in control systems from Ecole Centrale de Lille, Lille, in 2007.He is a member of the Laboratory of Electrical Engineering (L2EP), Lille, anda Research Engineer at Arts et Metiers Paristech. His research interests includethe integration of dispersed generation systems in electrical grids, advancedcontrol techniques for power systems, and hardware-in-the-loop simulation.

Hani Saad (S’07) received his B.Sc. and Ph.D. degrees in electrical engineeringfrom the École Polytechnique de Montréal in 2007 and 2015, respectively. From2008 to 2010 he worked at Techimp Spa. and in the Laboratory of MaterialsEngineering and High Voltages (LIMAT) of the University of Bologna onresearch and development activities. In 2014, he joined the French TSO RTE(Réseau de Transport d’Electricité), where he is currently involved in HVDCprojects and EMT studies.

Xavier Guillaud (M’04) has been professor in L2EP - Lille since 2002. First,he worked on the modeling and control of power electronic systems. Then,he studied the integration of distributed generation and especially renewableenergy in power systems. Nowadays, he is studying the high voltage powerelectronic converters in transmission system. He is leading the developmentof an experimental facility composed of actual power electronic convertersinteracting with virtual grids modelled in real-time simulator. He is involvedon several projects about power electronic on the grid within European projectsand different projects with French companies. He is member of the TechnicalProgram Committee of Power System Computation Conference (PSCC) andassociated editor of Sustainable Energy, Grids and Networks (SEGAN).