Ejlal Shahriari
email: ejlal.shahriari@kuleuven.be

Member, IEEE François Gruson
email: francois.gruson@ensam.eu

Pierre Vermeersch
email: pierre.vermeersch@centralelille.fr

Philippe Delarue
email: philippe.delarue@univ-lille.fr

Member, IEEE Frederic Colas
email: frederic.colas@ensam.eu

Member, IEEE N Xavier Guillaud
email: xavier.guillaud@centralelille.fr

E Shahriari

A Novel DC Fault Ride Through Control Methodology for Hybrid Modular Multilevel Converters in HVDC Systems

Keywords: DC fault ride through capability, energy-based control, HVDC, Modular Multilevel Converter (MMC), Multiterminal dc (MTDC), Non-energy-based control

Modular Multilevel Converter (MMC) is an established technology for HVDC or Multi-Terminal DC (MTDC) systems, due to its advantages over classical Voltage Source Converters (VSCs) such as two or three level VSCs. To achieve a full control of all state variables, it is essential to implement energy-based method in which a cascade control loop is employed to regulate all state variables including ac and differential currents, and stored energy within MMC arms. In addition to normal operation control, dc Fault Ride Through (DC-FRT) capability of the MMC is a crucial and challenging control issue especially for overhead line HVDC system where non-permanent dc fault occurrence is statistically more probable. Furthermore, the main problematic technical obstacle to develop HVDC/MTDC grids is the lack of mature dc fault protection. Since conventional control in normal operation cannot be employed in case of dc fault, an efficient control strategy is indispensable. The principal objectives of the novel control methodology are to (i) obtain DC-FRT capability, (ii) decay short circuit current to zero, (iii) secure the MMC through leg and arm energy balancing, (iv) support ac grid as a Static Synchronous Compensator (STATCOM) and (v) resume normal operation after dc fault clearance. The simulation results verify the validity of proposed control strategy to fulfill the abovementioned objectives in dc fault operation of the hybrid MMC.

INTRODUCTION

OWADAYS, HVDC is a favorable method for longdistance and large-scale power transmission systems, which provides a reliable solution for interconnection between asynchronous grids and renewable energy integration. Moreover, it is essential to consider the development of multiterminal dc (MTDC) grids as the future trend of power system, which brings several advantages like the possibility of connecting islands to grids, a broader access to power markets, and an increase in the reliability and security of electricity supply [START_REF] Dantas | Progressive Fault Isolation and Grid Restoration Strategy for MTDC Networks[END_REF]. For example, the implementation of MTDC grid in the North Sea can help the reserve exchange between the UK and Northern European countries, access to a broader power market with more financial advantages, and increase in the offshore wind farms integration [START_REF] Haileselassie | Power system security in a meshed north sea HVDC grid[END_REF]. However, the main problematic technical challenge to develop MTDC grids is the lack of the mature dc fault protection.

As a promising voltage source converter (VSC) topology, Modular Multilevel Converter (MMC), presented in Fig. 1, has been the technology chosen for HVDC transmission system. The main advantages of MMC over two or three level VSCs are: lower switching losses due to lower both modulation frequency and peak transient voltage on Isolated-Gate Bipolar Transistors (IGBTs) [START_REF] Saad | Modular Multilevel Converter Models for Electromagnetic Transients[END_REF], lower total harmonic distortion, thus greatly improving the power quality [START_REF] Gnanarathna | Efficient modeling of modular multilevel hvdc converters (mmc) on electromagnetic transient simulation programs[END_REF]; and modularity and scalability of power and voltage. Despite the mentioned advantages of MMC, more complex control strategy, in comparison with two or three level VSCs, is required due to a large number of submodules (SM). Control strategies proposed for MMC in the literature can be classified as non-energy-based and energy-based methods. In nonenergy-based method, mainly with Circulating Current Suppression Control (CCSC), dc component of differential current is not under control; therefore, large over currents and oscillations might occur during transient [START_REF] Samimi | MMC Stored Energy Participation to the DC Bus Voltage Control in an HVDC Link[END_REF]. Moreover, CCSC method can cause instability problems [START_REF] Freytes | Improving Small-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy[END_REF]. On the contrary, energy-based control proposes a favorable solution for normal operation of the MMC. However, the proposed control strategies in normal operation are not directly applicable for dc fault incidence.

In order to obtain dc fault protection of HVDC systems, several papers propose the combination of Half Bridge (HB)-MMC with DC-Circuit Breakers (DC-CBs) [START_REF] Li | An Auxiliary DC Circuit Breaker Utilizing an Augmented MMC[END_REF], [START_REF] Xiang | A Transient Voltage-Based DC Fault Line Protection Scheme for MMC-Based DC Grid Embedding DC Breakers[END_REF]. The major drawbacks in this protection scheme can be highlighted:  In case dc fault travelling wave time from the fault point to converter station is lower than total interruption time of DC-CB, a high overcurrent can impose two undesirable impacts [START_REF] Kontos | Impact of HVDC Transmission System Topology on Multiterminal DC Network Faults[END_REF]: I. Blocking mode operation of HB-MMC (turning off all IGBTs and operating as diode bridge rectifier) which means losing the controllability of MMC. II. High level of overcurrent can damage or reduce the lifetime of semiconductors.

 DC-CBs are immature and high cost technologies without DC-FRT capability.

In addition, embedded protection devices in the output of converter submodules [START_REF] Ding | New technologies of voltage source converter (VSC) for HVDC transmission system based on VSC[END_REF] and [START_REF] Li | Protection of nonpermanent faults on DC overhead lines in MMC-based HVDC systems[END_REF] or in the ac side of the converter [START_REF] Elserougi | A new protection scheme for HVDC converters against DC-side faults with current suppression capability[END_REF] are employed to prevent damage in MMC. Nevertheless, these approaches do not provide DC-FRT capability for MMC-HVDC system, and the lack of converter controllability in dc fault operation is common drawback. Thus, suitable submodule topology and an effective control strategy are required for dc fault operation of MMC [START_REF] Du | Modular Multilevel Converters, Analysis, Control, and Applications[END_REF]. To achieve DC-FRT capability of MMC, it is essential to utilize topologies that have the possibility to operate in negative voltage mode such as Full Bridge (FB)-MMC. In [START_REF] Jovcic | Full bridge MMC converter controller for HVDC operation in normal and DC fault conditions[END_REF], a dc modulation index is proposed for FB-MMC to control the dc fault current and the CCSC is employed to suppress 2 nd order harmonic currents. Also, the CCSC method is utilized in the proposed control for dc fault operation of FB-MMC in [START_REF] Li | DC Fault Protection of Diode Rectifier Unit Based HVDC System Connecting Offshore Wind Farms[END_REF]. Since in this approach all state variables are not controlled efficiently, large dc fault short circuit current oscillations may occur during dc fault transients. An adaptive autoreclosing concept for FB-MMC HVDC is developed in pole-to-ground dc fault [START_REF] Stumpe | Adaptive Single-Pole Auto-Reclosing Concept with advanced DC Fault Current Control for Full-Bridge MMC VSC Systems[END_REF]. This concept enables the detection of the final arc extinction and fast normal operation resumption. In [START_REF] Jovcic | Low Energy Protection System for DC Grids Based on Full Bridge MMC Converters[END_REF] protection and control methods for MTDC system using the FB-MMC controllability in dc fault operation is developed. The control/protection method shows low energy dissipation in DC-CB in case of dc fault operation of FB-MMC and proposes a low-cost mechanical DC-CB for dc-grid protection. Using DC-FRT capability of FB-MMC, a comprehensive energy-based control approach is proposed in [START_REF] Cui | A comprehensive dc short-circuit fault ride through strategy of hybrid modular multilevel converters (MMCs) for overhead line transmission[END_REF]. However, the efficiency of control method depends on grounding impedance in the ac side of the converter. In this paper, to reduce MMC losses and obtain DC-FRT capability a hybrid HB-and FB-SM topology is utilized, as shown in Fig. 1.

The main contribution of this paper is to propose a novel energy-based control methodology in order to achieve DC-FRT capability of the hybrid MMC. This approach ensures during dc fault leg and arm energy balancing controls are obtained properly. In this method, employing STATCOM operation of the hybrid MMC, ac grid voltage is supported effectively through reactive power compensation. In addition, the control method curbs the transients at the transition time between STATCOM and converter operation of the hybrid MMC. The study achieves leg energy balancing in which the suppression of zero sequence current in the control loop can be highlighted using the novel control methodology. In addition, in arm energy balancing, the sum of circulating currents in the converter feeds dc side short circuit and causes transient dc current oscillations that are effectively removed. Furthermore, the proposed control method reduces transient overvoltage on equivalent arm capacitors efficiently. Finally, resuming the normal state operation of the hybrid MMC after dc fault incidence complete the final stage of the study using the novel control methodology.

I. MMC MODELING AND INNER LEVEL CONTROL

A. Average Arm Model

The MMC modelling in this paper is based on Average Arm Model (AAM), which leads to the replacement of the stacks of submodules with an equivalent arm model consists of an average chopper connected to an equivalent capacitor [START_REF] Samimi | Synthesis of different types of energy based controllers for modular multilevel converter integrated in an hvdc link[END_REF], as shown in Fig. 2. This model assumes that capacitor voltages are well balanced by the control operation (i.e. vc1= vc2=…= vcN), and this assumption allows considering an equivalent capacitor (Ceq_i=C/N) for each arm with a voltage uculi=vc1+ vc2+…+ vcN.

Where N is the number of submodules that can reach hundreds in number in HVDC applications. Based on modelling method above, 6 modulation indexes (mui, mli) as duty cycle for equivalent chopper are defined.

Next, based on average arm model, the equations below can be expressed for each equivalent arm of the MMC:

(1) where is the upper or lower arm modulated voltage is the equivalent upper or lower arm capacitor voltage is the upper or lower arm modulation index is the equivalent upper or lower arm capacitor current is the upper or lower arm current is the equivalent arm capacitance of phase i

ui li mui mli mli mui diff i diff i v i i i u u u u i V e       (2)
Where is differential current consisted of a dc component and harmonic components, is internal voltage which is driving , and is internal ac voltage of the MMC. Finally, decoupling ac and dc side of the MMC leads to:

(

where and are ac grid voltage and current of phase i, and are ac filter resistance and inductance; and and are arm resistance and inductance respectively. In addition, is dc side voltage.

B. Inner Level Control

Based on ( 3) and ( 4), Inner level control of the MMC includes ac current and differential current control loops. To propose ac grid current control, it is imperative to express (3) in dq0 frame. Thus, the ac grid currents can be formulated as: [START_REF] Samimi | MMC Stored Energy Participation to the DC Bus Voltage Control in an HVDC Link[END_REF] Where , , and are d/q component of ac grid voltage and current. Also, is d/q components of internal ac voltage. Using inversion-based method of abovementioned modeling equations, the block diagram of the inner level control of the MMC can be illustrated in Fig. 3.

II. ENERGY-BASED CONTROL (OUTER LEVEL CONTROL)

A. Conventional energy-based control Uncontrolled state variables (equivalent arm voltages) can jeopardize the system security through having undesired values which lead to unstable modes in particular operating conditions. To achieve the full control of the MMC inner dynamics and the stored energy in the system, energy-based control is a solution in which the number of controllers is equal to the number of independent state variables of the system. Hence, energy-based control includes a cascade control loop composed of power and energy controls in the outer level and ac grid and differential current controls in the inner level control.

Considering the differential currents contain both dc and ac circulating current components ( ) leads to proposing total and differential energy stored in each leg of the MMC, as shown in [START_REF] Saad | MMC Capacitor Voltage Decoupling and Balancing Controls[END_REF]:

(6) 2 2 _ ( ) 1 ( ) 2 2 cui cli eq i cui cli T gi diff ac i d W W dW d C u u dt dt dt v i              (7)
where and are stored energy in upper and lower arm of phase i in the MMC respectively. If a balanced three phase system is assumed, average per phase active power and per phase dc power can be expressed as following:

3 ac ac i dc i dc diff dc i P P P V i        (8)
In addition, the formulation of the whole ac power in dq0 frame is given by: ( 9) Assuming ( 6)-( 9), energy-based control block diagram can be illustrated as in Fig. 4. In this block diagram, is the RMS value of ac grid voltage ( ).

It is important to notice that the total and differential energy in each phase of the MMC are modelled effectively. Therefore, it can be evidently claimed that leg and arm energy balancing controls are fulfilled as it is studied in [START_REF] Samimi | Synthesis of different types of energy based controllers for modular multilevel converter integrated in an hvdc link[END_REF]- [START_REF] Sanchez | Analysis of MMC energy-based control structures for VSCHVDC links[END_REF]. The outputs of leg and arm energy balancing control are employed as differential current references in the inner level control. In addition, grid current references are the output of ac power controllers.

Assuming the pole-to-pole dc fault at the MMC dc terminal as the worst-case scenario, dc voltage collapses to zero [START_REF] Cui | A comprehensive dc short-circuit fault ride through strategy of hybrid modular multilevel converters (MMCs) for overhead line transmission[END_REF]. In such a severe dc fault, conventional energy-based control strategy is not valid as it can be noticed in [START_REF] Freytes | Improving Small-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy[END_REF]. Therefore, control of stored energy in the hybrid MMC should change from dc-power-based to ac-power-based control during dc fault operation.

diff i i diff i V diff i i v i e ( ) ( ) 2 2 gi arm arm vi gi g gi g di R L e v R i L dt      2 diff i dc diff i arm diff i arm di V V R i L dt    gi v gi i g R g L arm R arm L dc V gd vd
gd eq gd eq eq gq gq vq gq eq gq eq eq gd di

e v R i L L i dt di e v R i L L i dt                  2 arm eq g R R R   2 arm eq g L L L   / gd q v / gd q i / vd q e _ diff i diff dc i diff ac i i i i   2 2 _ ( ) 1 ( ) 2 cui cli eq i cui cli T dc diff dc i ac i d W W dW d C u u dt dt dt V i P              cui W cli W . ac gd gd P v i  gi V gi v

B. Total energy control of MMC based on ac power

The energy-based control of the MMC can be achieved through using ac or dc power. As a result, the role of the grid current and differential current in control loops is exchanged based on using ac or dc power. In previous section, leg and arm capacitor energy balancing illustrate comprehensive control of all MMC state variables based on dc power in a cascade control loop. On the other hand, converter total stored energy control can be proposed based on ac power. In this method, the converter total stored energy is formulated as the sum of 3 phase (leg) stored energy: [START_REF] Ding | New technologies of voltage source converter (VSC) for HVDC transmission system based on VSC[END_REF] The block diagram of the three phase stored energy control in the MMC can be depicted as following: In this method, only the converter total energy control is obtained, and there is neither leg nor arm energy balancing. Unlike dc power based energy control, the total energy control output is ac grid current reference (in this case on the 'd' axis). AC power based energy control solves the problem of dc side voltage in dc fault incidence. However, the lack of arm and leg energy capacitor balancing reveals the necessity to modify this control strategy, which is detailed in the novel control methodology proposed in the next section.

III. PROPOSED CONTROL OF MMC WITH DC-FRT CAPABILITY

DC-short-circuit in HVDC systems is possibly caused by the destruction of insulation because of aging or physical damage. Overhead line HVDC systems also may expose to dc fault occurrence originated from lightening, pollution, and extreme weather conditions [START_REF] Teodorescu | Design, control, and application of modular multilevel converters for HVDC transmission Systems[END_REF].

As shown in Fig. 6, to reduce MMC losses and obtain DC-FRT capability a hybrid arm composed of HB-and FB-SMs is used. To ensure dc fault short circuit current decays to zero, the sum of capacitor voltages of FB-SMs in the short circuit loop must be more than line-to-line ac voltage in steady state. Abovementioned reasons lead to considering half of SMs as FB ones. After dc fault occurrence, modulation indices change to enable the hybrid MMC to operate in both positive and negative voltage levels. During the fault, FB-SMs generate positive and negative output voltages whereas HB-SMs are bypassed, which means the output voltage of each HB-SM is zero. It is supposed low level switching controls manage to accomplish the aforementioned assumption; therefore, AAM depicted in Fig. 2 is considered sufficient for the dc fault study. Considering the characteristic of dc fault clarifies that dc fault current does not have zero crossing, unlike ac fault, and this makes arc distinguishing a practically challenging issue.

              
Developing suitable control strategy under dc fault occurrence is the main challenging issue of VSC-HVDC transmission system since under aforementioned operation losing the control of MMC is probable. Full-bridge MMC is the most well-known topology with dc fault ride through capacity both in the literature and industrial applications. Fault detection techniques have a key role in dc fault study of HVDC systems. However, implementing dc fault detection is not considered in this paper. Therefore, for simplicity, based on dc current measurement and its defined threshold value, the dc fault is detected to change the control strategy to dc fault operation. The crucial objectives of the proposed control strategy for operation of MMC after dc fault detection can be expressed as following:

1. To decay short circuit current to zero 2. To propose DC-FRT operation of the FB-MMC 3. To ensure the security of the MMC-HVDC system through control of all state variables: I. To propose leg and arm energy balancing control II. To reduce overvoltage on arm capacitors 4. To operate the MMC as a STATCOM to compensate reactive power (reactive current injection) and ac voltage support during DC fault. 5. To resume MMC operation to its normal control state after dc fault clearance. In the worst case scenario of dc fault studied in this paper Vdc with an extreme dv/dt plummets to zero. Hence, based on (6) conventional energy-based control is not applicable anymore. On the other hand, in the converter total energy control there is neither leg nor arm energy balancing control. Therefore, a holistic control strategy is required to ensure all defined objectives in dc fault operation of the hybrid MMC. First, the threshold value for dc fault detection in this paper is equal to 1.5 pu (2343.8 A). After detecting dc fault, an energy-based control strategy based on controlling of transiently unbalanced power in ac grid without imposing zero sequence current to triangle connection of transformer is proposed to obtain arm and leg energy balancing, as triangle connection of transformer is illustrated in Fig. 7. To accomplish the mentioned objectives, the proposed control strategy is discussed in details in two following sections.

A. Arm energy balancing control

As soon as dc fault is detected, the controller sets the ac power reference to zero [START_REF] Leterme | Modeling of MMCs With Controlled DC-Side Fault-Blocking Capability for DC Protection Studies[END_REF]. This implies that the dc components of differential current references decay to zero. Unlike the control strategy in normal operation, only the ac components of differential current references are generated for the inner level control as long as they sum to zero; thus, to avoid feeding the dc short circuit. Re-arranging (7) using inversionbased model gives:

* _ _ 1 ( )( ) 2 W W i diffac i p i ref i meas K I K W W V s                 (11)
where W p K  and W i K  are proportional and integral gains of the PI controller for arm energy balancing respectively. The classical approach proposed in [START_REF] Samimi | Synthesis of different types of energy based controllers for modular multilevel converter integrated in an hvdc link[END_REF], generating three-phase ac circulating current references requires the multiplication of matrix  by RMS value of differential circulating currents as:

2 3 2 3 cos( ) 0 0 2 0 cos( ) 0 0 0 cos( ) t t t                    (12) (13)
Conventional energy-based control strategy has managed to suppress internal ac circulating currents. However, due to independent control of energy difference in each phase, the sum of ac circulating current is not zero. It means that the shortcircuit is fed by the sum of the ac circulating currents. Thus, as depicted in Fig. 8 In order to ensure the three-phase ac circulating currents sum to zero, different types of coupling matrix are proposed for the normal operation of MMC-HVDC in the literature [START_REF] Munch | Integrated current control, energy control and energy balancing of modular multilevel converters[END_REF]- [START_REF] Zhang | On Comprehensive Description and Analysis of MMC Control Design: Simulation and Experimental Study[END_REF]. More details of the coupling matrix M1 employed in this paper can be found in [START_REF] Shinoda | Energy Difference Controllers for MMC without DC Current Perturbations[END_REF]- [START_REF] Zhang | On Comprehensive Description and Analysis of MMC Control Design: Simulation and Experimental Study[END_REF]:

(14) * * 1 diff aci diff ac i i M I  ( 15
)
Considering phase a in [START_REF] Jovcic | Full bridge MMC converter controller for HVDC operation in normal and DC fault conditions[END_REF], in case of unbalanced ac circulating currents, half amplitude of aforementioned current in phase a with 180 degree shift phase is applied to phase b and phase c. Due to a high degree of symmetry, this method can be extended for two other phases. Finally, developing [START_REF] Li | DC Fault Protection of Diode Rectifier Unit Based HVDC System Connecting Offshore Wind Farms[END_REF] shows ac circulating components of differential currents sum to zero, as depicted in Fig. 8(b).

* * _ _ diffac i ref diffac i ref i I   2
t M t t                                   (b) (a)

B. Leg energy balancing control

Proposing leg or phase energy balancing for MMC under dc fault operation requires the novel control methodology. As mentioned in Section III.B, in case of dc fault, the stored energy is controlled based on the ac side power because of voltage collapse on the dc side. In dc fault incidence, the stored energy in the MMC deviates differently in each phase due to numerous elements. Re-balancing the energy inside each leg may generate unbalanced three phase ac grid currents with a zero sequence component. However, due to the delta arrangement of the transformer as seen in Fig. 7, this zero sequence current is not tolerated and the removal of this component is inevitable. Therefore, zero sequence current ( Z i  ), which is an active component as a consequence of 3 unbalanced active power references, depicted in Fig. 9, can be suppressed considering following steps:

1. Generating the opposing zero sequence current ( )

Z i   as a
reactive component based on ( 16), as seen in Fig. 10 (a):

( ) 0 Z Z i i      (16)
3. The opposing current for each phase can be created by two other phases, and this is obtained only by injecting reactive currents in order to ensure they do not affect active power references and more importantly leg energy balancing remains intact. More details of this approach are clarified as following: For example, considering phase a, in order to generate opposing current for this phase transient reactive currents in the other two phases are applied. To generate reactive currents in phase b and c, it is necessary to shift these two axes by 90 degree. As seen in Fig. 11 The variables defined in Fig. 11 can be formulated as:

i I t i I t i I t                        (18)
The similar approach can be developed to apply the opposing currents for phase b ( gb i ) and phase c ( gc i ). Therefore, the sum of these opposing currents for each phase is ( )

Z i   which
suppresses zero sequence component of ac grid currents. Hence, the idea of using a coupling matrix M2 for leg energy balancing is developed as following:

1 1 2 2 3 3 7 2 1 1 2 6 3 6 3 3 7 2 1 1 6 6 3 3 3 cos( ) cos( ) cos( ) 2 cos( ) cos( ) cos( ) cos( ) cos( ) cos( )
M                                       (19)
* * _ 2 gi ref gi i M I  (20)
where , t

    
 is initial phase angle, and * gi I is the RMS value of ac grid current references of phase i calculated as:

* _ _ _ 1 ( )( ) W W i gi dc i p i ref i meas gi K I P K W W V s                         (21) where W
I I                                      (22)
Finally, as illustrated in Fig. 9, the outputs of leg energy balancing, * d w i  and * q w i  , are applied to the inner level control.

As soon as energy is balanced within each phase of the MMC, these transient currents converge to zero. Moreover, the input of the reactive power control reference * q i consists of two components: 1) reactive current component * q s i  that ensures the STATCOM operation of the MMC to support the ac grid during dc fault, and 2) a transient component * q w i  from leg energy balancing controller. In addition to arm and leg energy balancing, the other advantages of this novel control methodology under dc fault operation are eliminating dc short circuit current oscillations properly and reducing overvoltage on capacitors effectively.

IV. SIMULATION RESULTS

In order to verify the validity of the proposed control strategy under dc fault operation, the simulation results for pole-to-pole dc fault are proposed and discussed in details. The simulation results include three different stages in dc fault study: normal operation from t=0.4 s to 0.5 s, dc fault operation from t=0.5 s to 0.9 s, and after dc fault clearance from t=0.9 s to 1.2 s. The normal operation initializes with Pac_ref=1 GW and Qac_ref=0 MVAR and continues up to t=0.5 s. Then, a dc fault is considered as a pole-to-pole dc fault at t=0.5 s, this fault is taken into account as a sudden step-down of dc-side voltage to zero. As soon as dc current reaches the threshold value (1.5 pu or 2343.8 A), the control strategy is changed to the proposed control method in this paper. In this DC-FRT control in addition to leg and arm energy balancing control, using Qac_ref=300 MVAR the hybrid MMC supports the AC grid voltage through STATCOM operation. Finally, to resume normal operation of the HVDC system ac power is applied with a rising slope from t=0.9 s to 0.95 s in order to reduce transient oscillations.

There are two major drawbacks in using the proposed control classical approach to generate ac circulating current references through using (13): 1) ac circulating current references are not balance as seen in Fig. 12(a). 2) These unbalanced ac circulating current references impose undesirable oscillations on dc current during short circuit fault as shown in Fig. 12(b). Using coupling matrix M1 in [START_REF] Li | DC Fault Protection of Diode Rectifier Unit Based HVDC System Connecting Offshore Wind Farms[END_REF] eliminates those drawbacks through suppressing zero sequence component of ac circulating currents. Fig. 12(c) shows the effectiveness of this method to balance ac circulating currents. Since ac circulating currents are employed to achieve arm energy balancing, as soon as stored energies in upper and lower arm in each phase reach their references after dc fault, ac circulating currents decay to zero. After dc fault clearance at t=0.9 s ac power with a rising slope supply the system and this reduces peak transient of ac circulating currents at t=0.924 s in comparison with t=0.516 s. Finally, after achieving arm energy balancing these circulating currents decay to zero. In addition, Fig. 12(d One of the advantages of the proposed control strategy is low overvoltage on equivalent voltage of each arm of the MMC due to effective control strategy, as shown in Fig. 13(a)-(b). These figures also show that in case of dc fault at t=0.5 s, voltages of each arm after experiencing abrupt deviation from each other due to power unbalance, obtain their balancing quantity with correct mean value around Vdc. Moreover, after dc fault clearance at t=0.9 s, the MMC arm voltages reach their normal operation values with initially transient oscillations. Although Fig. 13(c)-(d) show that total stored energy in converter and leg or per phase energy deviate from their references transiently both at dc fault incident time, t= 0.5 s, and dc fault clearance at t=0.9 s, total and per phase energy of the hybrid MMC are completely under the control after transient oscillations.

As it is illustrated in Fig. 14(a), reactive current injection through STATCOM operation of the hybrid MMC ensures ac grid voltage support. These ac grid currents contain transient harmonics which is the consequence of transient current injection for leg energy balancing. Upper and lower arm currents are also illustrate transient oscillations after fault occurrence. However, Fig. 14 (b)-(c) show that arm currents control properly during normal operation, dc fault incidence and power supply resumption. Finally, simulation results for modulation index in Fig. 14(d)-(e) propose that in the pole-topole dc fault, which is the worst case scenario in dc fault studies, hybrid topology of MMC submodules consists of HB-and FB-SMs is applicable since modulation index is not lower than -0.5, and this reduces the extra losses imposed by FB-MMC.

V. CONCLUSION

Energy-based control method has been considered as a reliable solution in the literature to obtain the full control of MMC. On the one hand, in the pole-to-pole dc fault incidence, 0.516 0.924 the conventional control of MMC based on dc power is not applicable anymore. On the other hand, control of MMC based on ac power only proposes total stored energy control; thus, it is evident that through using such control methods, MMC arm and leg capacitor energy balancing is not attainable. Therefore, a novel control methodology using ac power control to achieve leg and arm energy balancing is proposed. In this method, after dc fault detection through defined threshold value for dc current, the dc component of differential current references are regulated to zero in arm energy balancing control loop. Meanwhile, three unbalanced ac power references in the output of leg energy-balancing controllers are utilized to generate grid current references. Then the suppression of zero sequence current is attained using a coupling matrix. Finally, proposed control method has the capability of dc short circuit fault elimination, arm and leg energy balancing, low transient overvoltage within each arm caused by dc fault incidence, reactive current injection through STATCOM operation of the hybrid MMC to support ac grid voltage, and normal operation resumption after dc fault clearance.

Fig. 1 .

 1 Fig. 1. A simplified schematic of the hybrid MMC.

Fig. 2 .

 2 Fig. 2. Average Arm Model (AAM) of the MMC.

Fig. 3 .

 3 Fig. 3. The block diagram of the inner level control.

Fig. 4 .

 4 Fig. 4. Block diagram of energy-based control (outer level control).

Fig. 5 .

 5 Fig. 5. The block diagram of the converter total energy control based on AC power.

Fig. 6 .

 6 Fig. 6. The hybrid MMC under dc fault operation.

Fig. 7 .

 7 Fig.7. Schematic diagram of VSC-based HVDC system.

  (a), generating ac circulating current references based on (13) leads to on dc short circuit current.

Fig. 8 .

 8 Fig. 8.Vectorial diagram of (a) conventional and (b) coupled generation of circulating current references.

Fig. 9 .

 9 Fig. 9. Block diagram of proposed control strategy for DC-FRT of the MMC.

Fig. 10 .

 10 Fig.10. (a) Opposing zero sequence current and (b) decomposing opposing zero sequence current for each phase.

2 .

 2 To obtain ( ) Z i   , it is possible to generate an opposing current for each phase, which means ( ) Z i   is decomposed for 3 phases. So, the opposing current for each phase ( gi i ) is defined based on (17) as depicted in Fig.10 (

Fig. 11 .

 11 Fig.11. Vectorial diagram of generating opposing current for phase a.

  ) illustrates the elimination of transient oscillations on dc current during short circuit fault.

Fig. 12 .

 12 Fig. 12. Simulation results of dc fault operation of the hybrid MMC (set 1).

Fig. 13 .

 13 Fig. 13. Simulation results of dc fault operation of the hybrid MMC (set 2).

Fig. 14 .

 14 Fig. 14. Simulation results of dc fault operation of the hybrid MMC (set 3).

  TABLE I indicates the parameters of the case study.

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 renewable energy in power systems. Nowadays, he is studying the high voltage power electronic converters in transmission system. He is leading the development of an experimental facility composed of actual power electronic converters interacting with virtual grids modelled in real-time simulator. He is involved on several projects about power electronic on the grid within European projects and different projects with French companies. He is member of the Technical Program Committee of Power System Computation Conference (PSCC) and associated editor of Sustainable Energy, Grids and Networks (SEGAN).