Antoine Cizeron
email: antoine.cizeron@geeps.centralesupelec.fr

Member, IEEE Javier Ojeda

Senior Member, IEEE Eric Monmasson

Olivier B Éthoux

Control of a Segmented Three-Phase Synchronous Motor with Highly Coupled Sub-Windings

Keywords: AC motor drives, segmented motor drives, highly coupled segmentation

This article addresses the control issue of a structure enabling the segmentation of three-phase electric drives. The proposed segmentation process offers an additional degree of freedom in terms of voltage rating for power electronics but results in a three-phase system with highly coupled sub-windings. Thus, for such a segmented motor, the true challenge lies in controlling the machine global electromagnetic torque while balancing the power among the different inverters. To tackle this issue, the dq standard synchronous frame is extended to common and differential modes. This approach enables to design a suitable control structure based on an analytical model and physical considerations. The developed model is calibrated with realistic numerical values obtained from a finite element analysis. Finally, an experimental setup allows developing a proof of concept which shows the interest of the proposed control method compared to a standard multiple dq-frame method. The key finding is that the above-mentioned control objective of the segmented synchronous motor can be achieved without additional inductors and despite the severe constraint imposed by such highly coupled segmentation.

I. INTRODUCTION

T HE current trend in transport electrification is to supply the electric motor drives with a DC bus voltage of several hundred Volt. It induces electrical risks to persons and requires complex insulation monitoring [START_REF] Zoeller | Inverterfed drive stator insulation monitoring based on reflection phenomena stimulated by voltage step excitation[END_REF]. Lowering the electric drives voltages down to 48V standard drastically mitigates electrical hazards, which is of particular benefit to transportation applications. It also significantly reduces the insulation system stress [START_REF] Ghassemi | Accelerated insulation aging due to fast, repetitive voltages: A review identifying challenges and future research needs[END_REF] and enables using silicon MOSFETs or wide band-gap technologies, both having low switching and conduction losses [START_REF] Wang | Integrated Modular Motor Drive Design With GaN Power FETs[END_REF], [START_REF] Maislinger | Design of a 100 kHz wide bandgap inverter for motor applications with active damped sine wave filter[END_REF]. For a given three-phase motor and a given current rating, it is possible to reduce the voltage rating by using several independently supplied winding sets [START_REF] Alosa | Modular Multi-Three-Phase Electric Drives for Enhanced Reliability and Current Ripple Minimization[END_REF]. These structures, often referred to as segmented drives, are also relevant approaches in ensuring continuity of service and enhancing drive energy efficiency since each phase is made of several sub-windings [START_REF] Sala | Power-Sharing Control in Bearingless Multi-Sector and Multi-Three-Phase Permanent Magnet Machines[END_REF]. Improvements in connector technology [START_REF] Rubey | Lifetime estimation of a novel high current low resistance single phase plug-in connector for the ISCAD application[END_REF], [START_REF] Mohamed | Design of an Integrated DC-Link Structure for Reconfigurable Integrated Modular Motor Drives[END_REF] as well as the attractive benefit of integrating power converters close to the motor end windings [START_REF] Wang | Integrated Modular Motor Drive Design With GaN Power FETs[END_REF], [START_REF] Abebe | Integrated motor drives: State of the art and future trends[END_REF], [START_REF] Verkroost | Simultaneous DC-Link and Stator Current Ripple Reduction with Interleaved Carriers in Multiphase Controlled Integrated Modular Motor Drives[END_REF] highly mitigate the drawback of modular structures, namely the increased number of terminals. On the basis of these considerations, a recent patent [START_REF] Hoang | Electric machine supplied at low voltage and associated multicellular power train[END_REF] suggests the innovative Highly Coupled Segmentation (HCS) of motor drive structures. It opens up the possibility of dramatically lowering the drive voltage rating. However, it also induces high magnetic coupling between each winding sets [START_REF] Cizeron | Prediction of PWMinduced current ripple in subdivided stator windings using admittance analysis[END_REF] and may challenge the related torque and flux control structure. The key point of this article is to demonstrate that this issue can be addressed by an appropriate controller.

Among the numerous ways to obtain multiple three-phase winding sets, two categories can be distinguished [START_REF] Raherimihaja | Integration of Battery Charging Process for EVs into Segmented Three-Phase Motor Drive with V2G-Mode Capability[END_REF] and are compared in Table I. The first category concerns the multiphase motor having k × 3 phases (MK3P) which can be split in k three-phase winding sets with different phase angles [START_REF] Rubino | Modular Vector Control of Multi-Three-Phase Permanent Magnet Synchronous Motors[END_REF]- [START_REF] Sala | Impact of Star Connection Layouts on the Control of Multiphase Induction Motor Drives under Open-Phase Fault[END_REF]. Most of the MK3P drives require an individual design of a specific multiphase motor and a multiphase control frame. The main expected benefit is a reduced torque ripple [START_REF] Verkroost | Simultaneous DC-Link and Stator Current Ripple Reduction with Interleaved Carriers in Multiphase Controlled Integrated Modular Motor Drives[END_REF], [START_REF] Rubino | A Novel Matrix Transformation for Decoupled Control of Modular Multiphase PMSM Drives[END_REF]. However, the open-circuit fault of a winding set influences the torque harmonics and requires a dedicated faulttolerant structure [START_REF] Sala | Impact of Star Connection Layouts on the Control of Multiphase Induction Motor Drives under Open-Phase Fault[END_REF]. The second category corresponds to the segmented drives, which are obtained through the reconfiguration of the windings of an existing three-phase stator in several independant winding sets [START_REF] Wang | Integrated Modular Motor Drive Design With GaN Power FETs[END_REF], [START_REF] Lin | An innovative multiphase PWM control strategy for a PMSM with segmented stator windings[END_REF]- [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF]. The aim of the segmentation approach is to enable an effective drive resilience, an efficient drive power sharing and a reduced power supply voltage. In this context, the only requested constraint is to keep the torque ripples similar to the one produced by the initial three phase motor (without segmentation of its stator windings) driven by its conventional inverter. This category is declined into two segmentation processes in Table I.

Multi-Sector Segmentation (MSS) layout is the standard approach in segmenting the windings of a three-phase motor. Each elementary three-phase winding set is housed in a distinct stator sector [START_REF] Sala | Power-Sharing Control in Bearingless Multi-Sector and Multi-Three-Phase Permanent Magnet Machines[END_REF], [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF], [START_REF] Wu | Robust Predictive Torque Control of Nx3-Phase PMSM for High-Power Traction Application[END_REF]- [START_REF] Zhang | Thermal Model Approach to Multisector Three-Phase Electrical Machines[END_REF]. As any other segmentation process, the MSS approach induces no change in the motor Matrix with MDQF, Scalar with the proposed CDM method low harmonic torque ripple distribution [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF] while enabling the parallelization of low voltage DC sources [START_REF] Wang | Integrated Modular Motor Drive Design With GaN Power FETs[END_REF]. However, an additional radial force control is required in the MSS structure in order to take advantage of its power sharing capability [START_REF] Sala | Power-Sharing Control in Bearingless Multi-Sector and Multi-Three-Phase Permanent Magnet Machines[END_REF] or to implement a fault-tolerant scheme [START_REF] Sala | Post-Fault Operation of Bearingless Multisector SPM Machines by Space Vector Control[END_REF]. Moreover, the MSS approach is limited by the number of poles per phase N p . Consequently, it cannot adapt all electrical machine to a low voltage standard specification.

A recent international patent suggests an alternative segmentation option enabling to extend the drive modularity level up to the theoretical limit of the winding turn [START_REF] Hoang | Electric machine supplied at low voltage and associated multicellular power train[END_REF]. As such, this innovative architecture, referred to as the HCS, allows a full degree of freedom in the sizing of current and voltage ratings [START_REF] Ben Ahmed | Electric Traction Chain with Segmented Power Supply[END_REF], [START_REF] Zhang | Design and Performance Analysis of Segmented Three-Phase IPMSM for EVs Integrated Battery Charger[END_REF]. It also facilitates the integration of the power converters close to the motor windings, thus limiting electromagnetic compatibility issues and boosting inverters heat power transfer. Since the number of turns per phase N t is usually higher than the number of poles per phase N p , the HCS is significantly more flexible than the MSS and enables using low voltage power supply for almost any electric drive. To enlighten their differences in terms of magnetic configuration and control strategy, the MSS and HCS layouts are both implemented on an existing three-phase Hybrid Excitation Flux Switching Machine (HEFSM). The choice of the hybrid motor topology is only due to laboratory availability. The HCS approach can easily be adapted to any kind of synchronous motor since it has already been used to achieve an on-board 3phase charger in an electrical vehicle [START_REF] Raherimihaja | Integration of Battery Charging Process for EVs into Segmented Three-Phase Motor Drive with V2G-Mode Capability[END_REF], [START_REF] Zhang | Design and Performance Analysis of Segmented Three-Phase IPMSM for EVs Integrated Battery Charger[END_REF] and to mitigate the Pulse Width Modulation (PWM) noise [START_REF] Zhang | Vibration reduction for dualbranch three-phase permanent magnet synchronous motor with carrier phase-shift technique[END_REF].

Concerning the control of a segmented motor, the Multiple dq-Frame (MDQF) method independently treats each elementary winding set. It can easily be used to control the MSS structure since its magnetic couplings are low between different sectors [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF]. However, contrary to the MSS structure, the HCS structure presents large mutual inductances between each winding set. They are namely in the order of their self inductances [START_REF] Zhang | Design and Performance Analysis of Segmented Three-Phase IPMSM for EVs Integrated Battery Charger[END_REF], which is specific regarding the other segmented drives [START_REF] Lin | An innovative multiphase PWM control strategy for a PMSM with segmented stator windings[END_REF]- [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF] and mars the effectiveness of the feed forward compensation, even in a healthy mode (Table I). As a matter of fact, the traditional MDQF control structure requires to combine the HCS structure with additional external coupled inductors [START_REF] Zhang | Vibration reduction for dualbranch three-phase permanent magnet synchronous motor with carrier phase-shift technique[END_REF]. Then, for reasons of cost, performance and space, the present article focuses on the feasibility of controlling the HCS structure without any additional coupled inductors and proposes an adapted Common and Differential Mode (CDM) control scheme, based on physical considerations, and easy to design and tune.

The main contributions of the paper are: 1) an in-depth analysis of the magnetic specificity of the proposed HCS structure. 2) a comparison between MSS and HCS structures based on inductance measurements. 3) the analysis, design and tuning of a dq-based CDM controller applied to a segmented three-phase synchronous motor with HCS structure. 4) an experimental validation as a proof of concept of the proposed CDM controller and its comparison with the MDQF control, both implemented on the HCS structure. 5) an experimental demonstration of the promising capability of the CDM controller in terms of power-sharing between inverters, even in case of faulty operation. The rest of this paper is organized as follows. Section II introduces the HCS configuration in comparison with the well-known MSS approach. Using Finite Element Analysis (FEA), it assesses the coupling value of the 3-phase motor sub-windings for both HCS and MSS approaches. It hence permits to highlight the need to set up a specific control law based on a dedicaded transform applied in the rotating dqframe. In section III, the dq-based suggested components are investigated in details and then the suggested control architecture is described. Section IV reports the experimental results obtained using a laboratory setup based on a 1 kW HCS drive. Finally, section V provides conclusions and perspectives.

II. COMPARISON OF MS AND HC APPROACHES

A. Three-phase motor segmentation

Based on an already existing conventional three-phase electric drive (Fig. 1), segmenting the initial windings in multiple electrically independent winding sets provides an attractive mean to lower the electric drive rated voltage. An elementary winding set is made of three sub-windings belonging to different phases and is powered by its dedicated inverter. The elementary winding set and its associated inverter constitute an elementary drive. The number of elementary drives is called the scaling factor, defined as N sc . In this context, the electric motor is driven by several independent inverters as illustrated in Fig. 2 for the specific case of N sc = 3. The segmented power supply has to produce in the air-gap the same global magnetomotive force (mmf) than the original power supply (Fig. 1). Thereby, based on Ampere law, each elementary drive conducts the initial motor rated current while the Faraday law shows that their rated voltage is N sc times smaller than in the initial drive.

In this paper, the control issue of the studied HCS approach is compared with the one of the standard MSS method. Fig. 3a and 3b show the spatial stator layouts of the MSS and the HCS structures, respectively. Obviously the innovative HCS layout is more flexible than the MSS segmentation one and could lead to an ultimate voltage reduction when each turn has its own inverter. As the electrical phase shift between sub-windings of a single phase is zero for both cases, the N sc electric angles of each structure is set to an identical control value. An ordinary PWM technique is implemented [START_REF] Chung | Unified voltage modulation technique for real-time three-phase power conversion[END_REF]. Moreover, a common PWM carrier is used for the N sc elementary drives [START_REF] Cizeron | Prediction of PWMinduced current ripple in subdivided stator windings using admittance analysis[END_REF]. The key control difference between the two approaches lies in the coupling factor between sub-windings of the same phase, represented by double dotted lines in Fig. 2. It is low in the MSS structure [START_REF] Jiang | Four-Module Three-Phase PMSM Drive for Suppressing Vibration and Common-Mode Current[END_REF] and high in the HCS structure [START_REF] Cizeron | Prediction of PWMinduced current ripple in subdivided stator windings using admittance analysis[END_REF].

B. Machine modelling in the rotating dq-frame

To design the control of the different elementary winding sets, a low frequency model has to be defined. It is hence based on the phenomena involved at the fundamental frequency. Magnetic saturation, saliency and iron losses are not taken into account. The considered segmentation process of N sc = 3 elementary drives (Fig. 3) results in a total of 3N sc = 9 subwindings in both configurations. Each sub-winding has its own voltage equation based on Faraday's law. The related 3N sc equations lead to the following dynamical model

V -V N = [R] • I + [L] • dI dt + E (1)
where [R] is a diagonal matrix containing the resistive terms of each sub-winding. As the number of turns, and consequently the conductor length, is the same for each elementary subwinding, it is assumed that this term presents insignificant discrepancies between all the sub-windings. Thus, the resistance term is considered as a scalar R in the different frame.

V are the voltages applied at the middle point of the inverter legs while V N are the voltages of the related neutral points. I is the sub-winding current vector and E is the back-emf term.

The structure of the inductance matrix [L] could be simplified by using a proper ordering. Within the matrix expression, the sub-windings are ordered by their elementary drive number (Fig. 2) and then by their phase one. Hence, the vector X in the natural frame includes the following 3N sc components

X = x a1 x a2 x a3 x b1 x b2 x b3 x c1 x c2 x c3 T . (2)
Based on this ordering method, the resulting inductance matrix [L] is arranged as a conventional three-phase structure. Equation (3) shows the equivalent three-phase inductance matrix for the considered segmented winding layouts (Fig. 3)

[L] =   [L a ] [M ab ] [M ac ] [M ba ] [L b ] [M bc ] [M ca ] [M ba ] [L c ]   (3)
where [L a ] is a (N sc × N sc ) matrix containing the selfinductances of each sub-winding of phase a and the mutual inductances representing the magnetic coupling among them.

It is assumed that all phases are symmetric, so the selfinductance matrices are equal to [L s ] and the mutual inductance matrices are equal to [M s ]. In this way, the inductance matrix becomes

[L] =   [L s ] [M s ] [M s ] [M s ] [L s ] [M s ] [M s ] [M s ] [L s ]   . (4)
The dq transformation is applied to each of the N sc electrically independent three-phase elementary drives. X becomes the vector X dq in the standard dq-frame whose length is 2N sc

X dq = x d1 x d2 x d3 x q1 x q2 x q3 T = X d X q . (5)
Similarly, in the multiple dq-frame, the inductance matrix is simplified under non-saliency hypothesis as the following (2N sc × 2N sc ) matrix

[L dq ] = [L dq ] [0] [0] [L dq ] , (6)
where [L dq ] is a symmetric (N sc × N sc ) matrix containing the self inductances L dq,i of the three-phase elementary drive indexed i and the mutual inductances M dq,ij between the elementary drives i and j

[L dq ] = [L d ] = [L q ] =   L dq,1 M dq,12 M dq,13 M dq,21 L dq,2 M dq,23 M dq,31 M dq,32 L dq,3   . ( 7
)
These terms have to be assessed in the MSS and HCS layouts in order to show the limit of the MDQF control method applied to the proposed HCS structure.

C. Control comparison of the MSS and HCS structures

In order to compare the two segmentation processes described in Fig. 3, an already existing three-phase HEFSM has been rewound with N sc = 3 coils per phase per sector. Each coil has dedicated terminals enabling the implementation of either the MSS or HCS configurations (Fig. 3). Both structures are powered similarly by N sc independent inverters (Fig. 2).

As the hybrid excitation of the motor is not exploited in this article, the excitation current remains constant at its rated value for all experiments. Moreover, the saliency of this motor is under 5 %. Hence, it is considered as a simple non-salient three-phase permanent magnet synchronous motor.

Inductance measurements are performed on each subwinding of each phase for both configurations. As an example, [L a ] and [M ab ] are shown in Fig. 4 and 5 for the MSS and HCS segmentation approaches, respectively. The inductance values corresponding to different sectors present discrepancies even though their conductors are arranged in a similar way (Fig. 4a). This is caused by disparities in the magnetic circuit. The rotor and the stator may have a small concentricity defect, technically inducing small discrepancies in the airgap thickness from one sector to another. As far as the HCS windings are concerned, such discrepancies have no impact on their inductance values since they have a symmetrical configuration around the motor.

The coupling factor between i and j sub-windings is defined as

k ij = M ij / L i L j . (8)
Obviously, the MSS structure has low negative mutual inductance values between the sub-windings belonging to different sectors. As shown in Fig. 4a, the resulting coupling factor between two coils of the same phase is lower than 10 %.

Conversely, the HCS structure shows high positive mutual inductances between sub-windings of the same phase, namely with a coupling factor higher than 90 % (Fig. 5a). Note that, within one elementary drive, the coupling factor of subwindings (e.g. a 1 and b 1 ) is close to 25 % for both the MSS and the HCS structures (Fig. 4b and5b).

Based on the previous inductance measurements, the resulting [L dq ] matrix is computed and depicted in Fig. 6a and6b for the MSS and HCS structures, respectively. Regarding the MSS approach, the mutual inductances values in the multiple dq-frame are negligible compared with the self inductances ones (Fig. 6a). Conversely, for the HCS approach, the mutual inductances values of the [L dq ] matrix are in the same order of magnitude than the self inductances ones (Fig. 6b). Obviously, these properties impact the control structure. Fig. 7 illustrates the general control scheme of the segmented HEFSM and clarifies the chosen notations. As the current is accurately measured to be efficiently tracked, equation [START_REF] Abebe | Integrated motor drives: State of the art and future trends[END_REF] shows that the control law should integrate feedforward terms to improve the controller dynamic performance:

V dq = R I dq + [L dq ]
d dt

I d I q + E dq +Ω e [L dq ] -I q I d . (9)
The last term is particularly useful since it permits to fully decouple the d and q axes. However, this compensation term is only effective if the non-diagonal terms (i.e. the mutual inductances) are precisely known. As a matter of fact, the poor MSS layout coupling makes possible to choose the standard MDQF control architecture (Fig. 8) where the Decoupling block refers to this feedforward term. However, the HCS layout strong positive coupling makes the MDQF control law ineffective regarding the decoupling purpose. Consequently, the suggested approach consists in finding a new frame enabling a good decoupling of the related components. Besides, the adopted transform should not rely on the machine parameters knowledge. Based on these key ideas, the Common and Differential Modes (CDM) control law is proposed and its scheme is given in Fig. 9. The following section gives an indepth description of the CDM control architecture guidelines and assesses its relevancy based on additional FEA.

III. DQ-BASED CDM CONTROL ARCHITECTURE

A. Additional dq-based transform

As for any 3-phase motor, the standard synchronous dqframe remains the right option to impose the desired torque and magnetic flux references. However, the HCS structure is characterized by high magnetic coupling between the elementary winding sets. Consequently determining relevant dq-based variables is a key issue to comprehensively control the HCS structure. In the perfect scenario, the latter would 1) have a direct link with the torque/flux as well as the internal power transmission variables. 2) ensure a proper decoupling permitting to switch a 2N sc MIMO system into 2N sc SISO systems.

The key idea is to exhibit the main physical dynamics of the segmented machine, namely the rapid modes linked to the leakage inductances and the slow mode related to the self and mutual inductances. Additionally, to maintain a proper decoupling between torque and flux variables, the suggested additional transform, named [T Σδ ] treats independently the d and q axes. It can then be written as

[T Σδ ] = [T d ] [0] [0] [T q ] = [T ] [0] [0] [T ] (10)
where [T ] is the (N sc × N sc ) matrix applied equally to the d and q axes and defined as

[T ] =   1 1 1 1 -1 0 0 1 -1   . (11)
Transformation ( 10) is applied to X dq (5), thus leading to X Σδ , the 2N sc -component vector in the suggested Σδ-frame.

It is structured as follows:

X Σδ = [T Σδ ] • X dq = x dΣ X dδ x qΣ X qδ T . ( 12
)
The first component x dΣ is named common mode variable of the d-axis. The remaining two components, x dδ12 and x dδ23 , included in X dδ , are the differential mode variables of the daxis and reflect the difference between two elementary drives. Similar reasoning applies on the q-axis.

A FEA assessment justifies the relevancy of this choice. Indeed, the basis for this approval is typically that the HCS sub-windings are located around the same stator tooth and hence embrace almost the same flux lines. The FEA study is carried out using Ansys Maxwell 2D software and it is applied on the HCS winding configuration (Fig. 3b). First, the test sets a non-zero common mode current for the N sc = 3 subwindings of phase a, setting the 2 differential mode currents to zero. Fig. 10a shows the resulting magnetic field lines. They cross radially the rotor-stator air-gap and hence impact the interaction of magnetic flux between both mechanical parts and leads to an electromagnetic torque. Moreover, as by design, the air-gap thickness is very small, the common mode inductance value is large. It results that the common mode is low. Second, the two other numerical experiments enforce a non-zero differential mode current. Fig. 10b and 10c exhibits the corresponding magnetic field lines which obviously remain located in the stator. They solely cross the stator slots, thicker than the air-gap. As a result, the differential mode inductance value is much lower than the common mode one. It proves that the dynamics of the common and differential modes are highly different and should be accounted for separately. Besides, based on the FEA, it is also clear that the differential currents have no impact on either the air-gap magnetic flux or the machine torque. They mainly modify the power sharing between elementary drives.

B. Impact on the inductance matrix

The common and differential modes transformation [T ] is applied to the inductance matrix obtained in [START_REF] Rubey | Lifetime estimation of a novel high current low resistance single phase plug-in connector for the ISCAD application[END_REF]. It derives:

[L Σδ ] = [T ] • [L dq ] • [T ] -1 = L Σ L Σδ L δΣ [L δ ] . (13)
The inductance matrix in the dq-based Σδ frame is computed either using the FEA or the previous inductance measurements performed on the HCS prototype (Fig. 11). Although the 2D assumption slightly overestimates the various coupling impacts, both results are clearly consistent. They confirm the previous FEA assessment based on physical considerations. They lead to the conclusion that:

1) The differential modes has no impact on the air-gap magnetic flux and the electromagnetic torque (dΣ and qΣ modes, respectively). Accordingly the [L Σδ ] inductance matrix could be simplified as:

[L Σδ ] = L Σ [0] L δΣ [L δ ] . (14)
2) The common mode dynamic is imposed by the L Σ value which is very large in comparison with the other terms of the related matrix. 3) Each differential mode has small inductances compared to L Σ (hundred times smaller), leading to a relative high dynamic with regard to the common mode one. 4) The common mode slightly impacts the differential ones.

Moreover, since the former dynamics is very slow in comparison to the latter one, the differential mode controller easily reject this perturbation.

C. HCS dedicated controller

Combining ( 9), ( 12) and ( 14), the common mode components are governed by

   v dΣ = R • i dΣ + L Σ • di dΣ dt + e dΣ -Ω e • L Σ • i qΣ v qΣ = R • i qΣ + L Σ • diqΣ dt + e qΣ +Ω e • L Σ • i dΣ (15)
Fig. 10: Flux lines without excitation around three subwindings of phase a in the HCS structure (Fig. 3b) for the common and differential components defined by [START_REF] Hoang | Electric machine supplied at low voltage and associated multicellular power train[END_REF]. where e dΣ and e qΣ represent the back emf due to permanent magnets and excitation coils along the Σ-axis.

To achieve an effective transient decoupling of dΣ and qΣ components, it is crucial to combine the feedback action with a specific feedforward term. Fig. 9 shows this additional term as a Decoupling block permitting to compensate the last terms of [START_REF] Golovanov | 4-MW Class High-Power-Density Generator for Future Hybrid-Electric Aircraft[END_REF]. Apart from measuring the rotor speed and the subwinding currents, the compensation term only requires the knowledge of L Σ value. Moreover, the two differential modes are independently controlled (Fig. 9). Indeed, the measured inductance matrix is practically diagonal (Fig. 11b) while the common component current evolves slowly and is hence easily rejected by the feedback term.

Furthermore, the 2D FEA model also enables to compute the back-emf which is then compared to the no-load voltages measured on the prototype in its HCS configuration (Fig. 3b). ig. 13: Open-loop transfer function Nichols plot for the MDQF and CDM tuning parameters described in Table III.

These estimated variables are actually consistent with the real voltages measured in the HCS structure (Fig. 12). Moreover, Table II shows that the two differential mode components of E δ are thousand times lower than the common mode one. Hence, feeding each elementary drive with an equal current set point yields to a similar electromagnetic torque contribution. For comparative purposes, the PI parameters of the standard MDQF technique (Fig. 8) and the proposed CDM method (Fig. 9) have been tuned based on the same specifications. The PI regulators settings should provide 10 dB-60 • gainphase margins while maximizing the open-loop gain crossover frequency f x . Assuming that for both cases, the plant is sufficiently well decoupled by the aforementioned feedforward compensation terms [START_REF] Abebe | Integrated motor drives: State of the art and future trends[END_REF], the relation between the duty cycle α and the related current i is given by a first order system (r, l) associated with a pure delay. The latter includes both the computational delay of the microcontroller equal to one sampling period and the stochastic delay induced by the digital PWM. Denoting T s = 50µs the control sampling time, the global delay to be considered is therefore equal to 1.5 × T s . Consequently, the SISO system transfer function to be regulated is as follows:

H(s) = I(s) α(s) = V DC • e -1.5•Ts•s r + l • s (16)
with V DC = 48V the DC-link voltage of the segmented power supply, r the winding resistance and l the considered inductance. This latter could be either L Σ or L δ . In the proposed CDM controller, each of the common (Σ) and differential (δ) components benefit from a specific PI parameter setting whereas in the MDQF controller, the PI parameter setting acts on both components without distinction. In all cases, the open- loop transfer function in Σ or δ component can be written as: However, the MDQF method imposes, because of the intrinsic structure of such controller (Fig. 8), that the PI parameter setting is unique and therefore, affects both the common (Σ) and differential (δ) components. It is then necessary to choose the best trade-off which maximizes the bandwidth of the Σ component with a phase margin of at least 60 • and at the same time do not degrade too much the stability on the δ axis (phase margin> 60 • and gain margin> 10 dB). Thus, this unique parameter set induces a lower bandwidth for the Σ component (f x,Σ = 50 Hz) compared to what was obtained with the CDM method, resulting in a larger settling time. The δ component cross-frequency is also low in order to ensure the 10 dB gain margin (f x,δ = 75 Hz). Fig. 13 (M DQF, Σ and M DQF, δ) shows the related open-loop frequency responses and the adopted PI parameters are given in Table III.

H OL (s) = K p • 1 + 1 T i • s • H(s) (17

IV. EXPERIMENTAL RESULTS

To validate the proposed controller, an experimental setup has been implemented (Fig. 14). The synchronous motor described in section II is configured in the HCS structure and driven by N sc = 3 basic 3-phase inverters. The latter, located on the same Printed Circuit Board (PCB) are powered by a common 48 V DC source and their switching frequency is set at F s = 20 kHz. The aforementioned control laws are implemented in a dSpace MicroLabBox and the sampling frequency is synchronized with the switching one. In addition, a DC motor imposes a controlled load torque.

The purpose of the following experiments is to highlight the relevancy of the proposed CDM control compared to the standard MDQF method initially developed to drive MSS motor structures. It also aims at demonstrating the capability to drive the HCS motor structure at any speed and to enforce any power distribution reference even in case of faulty operation.

A. Control Methods Comparison for the HCS Structure

The first test consists in enforcing torque setpoint steps from its rated value to 0, and vice-versa between 0 ms and

Fig. 1 :Fig. 2 :Fig. 3 :

 123 Fig. 1: Conventional drive of a three phase motor.

Fig. 4 :

 4 Fig. 4: Inductance values of the prototype with the MSS layout (a) [L s ] and (b) [M s ] inductance sub-matrices (µH).

Fig. 5 :

 5 Fig. 5: Inductance values of the prototype with the HCS layout (a) [L s ] and (b) [M s ] inductance sub-matrices (µH).

Fig. 6 :

 6 Fig. 6: Comparison of [L dq ] in (a) the MSS and (b) the HCS layouts (µH). Results are equivalent following d and q axes.

Fig. 7 :

 7 Fig. 7: General control structure of the HEFSM with N sc = 3 elementary drives.

Fig. 8 :

 8 Fig. 8: Current controller implementing the MDQF method with the same PI regulator on each component.

Fig. 9 :

 9 Fig. 9: Current controller implementing the proposed CDM method with specific PI regulator for Σ and δ components.

Fig. 11 :

 11 Fig. 11: Comparison of [L Σδ ] (µH) obtained through a) FEA and b) the inductance measurements of the HCS approach shown in Fig. 6b. Results are equivalent following d and q axes.

Fig. 12 :

 12 Fig. 12: Comparison of back electromotive force measurements and FEA results. ( Ê = 12.5 V , f e = 200 Hz).

Fig. 14 :

 14 Fig. 14: View of the triple three-phase inverter (left) and the HEFSM motor with HCS layout (right).

  ) where K p and T i are the proportional gain and the integral time constant of the PI. Based on the [L Σδ ] values listed in Fig. 11b, the CDM parameter sets of the Σ and δ are adjusted as shown in Table III. It results in the same Σ and δ openloop frequency response as depicted in Fig. 13 (CDM, Σ and CDM, δ). The resulting gain crossover frequency is f x,Σδ = 1 kHz.

TABLE I :

 I Comparison of electric machines based on multiple three-phase winding sets.

	Objectives	Subdivision types	MK3P	MSS	Segmentation processes	HCS
	Power-sharing capability	✓ [14]	✓ [6]			✓ [11]
	Degraded mode operation (open-circuit fault of a subdivision)	✗ (Requires harmonic control [17])	✗ (Requires radial force control [22])		✓
	Torque harmonics reduction	✓ [23]	✗			✗
	Maximum segmentation level	Number of three-phase winding sets	Number of poles per phase	Number of turns per phase [11]
	Interleaved PWM implementation	✓ [10]	✓ [21]		✗ (Requires external coupler [24])
	Feed forward compensation	Matrix with MDQF [14]	Scalar with MDQF [21]

TABLE II :

 II HCS back-emf Σδ components (f e = 200Hz)

		Experimental	FEA
	e qΣ	37.5 V	37.5 V
	e qδ12	35 mV	23 mV
	e qδ23	15 mV	10 mV

TABLE III :

 III PI Controllers tuning (10 dB gain margin and 60 • phase margin criteria)

		r (Ω)	l (µH) τ =	l r	(ms)	Kp (10 -3 ) T i (ms)
	MDQF,Σ MDQF,δ	0.2 0.2	760 10	3.8 0.05	2.1	1.24
	CDM,Σ	0.2	760		3.8	100	4.0
	CDM,δ	0.2	10	0.05	1.4	0.05
				+60°F
		-10dB

40 ms. Meanwhile, the rotor speed is maintained constant by controlling the load torque. Both differential references are set to zero: I * dδ = 0 and I * qδ = 0. Then, a step response occurs on the qδ12 component between 80 ms and 120 ms in order to validate the differential mode controller design. The test has been implemented in simulation (Fig. 15) using MATLAB/Simulink software. Worth to be mentioned here, the control feedforward terms used in this simulation are ideal since they perfectly match their actual counterparts (Fig. 6b and ( 9)).

First, the simulation results fully validate the predictions based on the open-loop frequency response. The standard MDQF method shows poor performances (Fig. 15a). The q-axis common mode current component (i qΣ ) exhibits a significant overshoot and a long settling time (≈ 20 ms) which is consistent with its low computed open-loop cross frequency (≈ 50 Hz). This overshoot may lead to exceed the acceptable current limit in one of the elementary drives. Similarly, the δ-axis settling time also proves to be large, which is in line with its reduced bandwidth (Fig. 13). Conversely the suggested CDM control structure exhibits good and similar performances regarding either i qΣ or i qδ12 (Fig. 15b). It also highly mitigates the overshoot on the qΣ-axis. Each component features the same 1 ms settling time, which is fully consistent with the computed 1 kHz open-loop cross frequency (Fig. 13).

Second, the same test is then experimentally done. An antiwindup method is implemented on the duty-cycle values and, as it is on the actual system, only approximated parameters are used in the feedforward action (Fig. 16). As can be seen, the experimental waveforms are in close agreement with the simulation results (Fig. 15). In all measurements, Fig. 17 the residual ripples on i qΣ are due to the non-sinusoidal waveforms of back-emf (Fig. 12). Apart from that, a few other differences and similarities are worth to be mentioned. Regarding the standard MDQF technique, the measured d-axis common mode current component (i dΣ ) is deeply impacted by the i qΣ transient (Fig. 16a), which negatively induces a magnetic field transient in the air-gap. Indeed, in practice, the feed forward compensation terms (9) imperfectly compensates the coupling terms, since these terms are based on measurements of mutual inductances that are of course affected by uncertainties. Conversely, CDM approach presents very small discrepancies between simulation and experimental results. Even though the q-axis dynamics is slowed by the brief duty-cycle value saturation during transient, it is more than ten times faster than the the results obtained with the MDQF method. Moreover, using the CDM method, the daxis common mode component is not impacted by the q-axis Σ component transient since it remains equal to zero (Fig. 16b). This proves that the dq axes decoupling remains efficient even though affected by measurement uncertainties. Indeed, the additional Σδ transform used in the CDM control method permits to base the feedforward compensation term on a single measurement, namely L Σ . This latter measurement is truly quite easy to perform correctly.

Finally, the proposed CDM method is well adapted to drive a HCS structure. Since this method also improves the differential component control, it opens up the possibility to consider for future works the power-sharing between the different elementary drives.

B. Faulty Operation

A second test is performed to illustrate the promising abilities of the HCS structure controlled with both the standard MDQF method (Fig. 17) and the proposed CDM method (Fig. 18). For both control methods, one of the three inverters is suddenly turned off at 0 ms while keeping i * qΣ constant to Using the MDQF method, the common component (Σ) is deeply affected by the open-winding fault and the differential component step response interferes with the common component behavior (Fig. 17). This is mainly due to the poor dynamical performances of the MDQF control, described in Fig. 13. Conversely, using the CDM method, the torque control remains effective even when only two out of three elementary drives are operating (Fig. 18a). Additionally, the power-sharing between the two remaining elementary drives is still operational since the differential component control can still be realized in such degraded mode (Fig. 18b).

V. CONCLUSIONS AND PERSPECTIVES

The novel stator winding segmentation process studied in this article enables to supply an electric machine with a reduced DC-link voltage without changing its operational range or increasing the rated current of the feeding inverters.

With its multiple degrees of freedom and high magnetic couplings, this attractive topology offers important control challenges which the present study addresses. The scope of the current contribution is limited to designing a proof of concept based on an existing three-phase machine configured as a segmented three-phase motor facing high positive magnetic coupling between each elementary drives. The developed approach consists in extending the standard dq transform with a common and differential modes transform. A comprehensive dynamical model is developed using analytical equations and FEA method. It shows that the extended transformation is suitable to easily track the control objectives, i.e. the global machine operating point (the torque and air-gap magnetic field) while ensuring a balanced power distribution between all the elementary drives. An experimental setup has been developed. The experiments show that the aforementioned model is reliable, enabling to tune properly the control parameters. The stability enhancement provided by the proposed CDM control method compared to the standard MDQF technique has been shown. Moreover, the CDM control architecture can enforce balanced power distribution between elementary drives whatever the electric machine operating point and even under open-fault condition. As a consequence, the elementary drive power allocation ability seems to be an interesting opportunity for future research lines.


Lucile Lescot

Mathilde Lefort

Soizic Leguy

Emmanuelle Le Page

Sandra Vukusic

Anne Kerbrat

Christine Lebrun-Frenay

Jérôme De Sèze

David-Axel Laplaud

Md ; Lefort

PhD; Leguy Soizic

Md ; Le Page Emmanuelle

Vukusic Sandra

PhD ; Edan Gilles

PhD ; Lebrun-Frenay Christine

PhD ; De

Sèze Jérome

PhD ; Laplaud

David Axel

PhD Wiertlewski Sandrine

Md ; Leray Emmanuelle

Michel Laure
email: laure.michel@chu-rennes.fr

Dr Laure Michel

Disease modifying therapies and disease activity during pregnancy and postpartum in a contemporary cohort of relapsing Multiple Sclerosis patients

Keywords: multiple sclerosis, post-partum, relapses, Disease Modifying Therapies

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Multiple Sclerosis (MS) predominantly affects young women, and especially those of childbearing age [START_REF] Leray | Epidemiology of multiple sclerosis[END_REF][START_REF] Thompson | Multiple sclerosis[END_REF]. During pregnancy and postpartum, a typical pattern of clinical activity evolution was reported in 1998 with a continuous decrease of the annualized relapse rate (ARR) during pregnancy, then an increase during the first 3 months of postpartum before returning to the pre-pregnancy rate [START_REF] Confavreux | Rate of pregnancy-related relapse in multiple sclerosis. Pregnancy in Multiple Sclerosis Group[END_REF]. Several other studies confirmed these data (4-6) Nevertheless, they were conducted in MS women either untreated or treated by first-line disease-modifying therapies (DMT) before conception. This does not accurately reflect current clinical practice. Indeed, in more recent studies, between 61% and 92% of Relapsing-Remitting MS (RRMS) patients were on first-or second-line DMT in the year before conception [START_REF] Correia | Pregnancy in Multiple Sclerosis: A Portuguese cohort study[END_REF][START_REF] Bsteh | Pregnancy and multiple sclerosis in the DMT era: A cohort study in Western Austria[END_REF][START_REF] Alroughani | Relapse occurrence in women with multiple sclerosis during pregnancy in the new treatment era[END_REF][START_REF] Nguyen | Incidence of pregnancy and disease-modifying therapy exposure trends in women with multiple sclerosis: A contemporary cohort study[END_REF]. Although there are no controlled data, it is currently admitted to discontinue most of DMTs before conception or at pregnancy onset to minimize risk of fetal harm [START_REF] Vukusic | Pregnancy with multiple sclerosis[END_REF]. However, discontinuation can lead to disease reactivation, in particular after second-line DMTs withdrawal in pregnant women [START_REF] Sepúlveda | Rebound of multiple sclerosis activity after fingolimod withdrawal due to planning pregnancy: Analysis of predisposing factors[END_REF][START_REF] Novi | Dramatic rebounds of MS during pregnancy following fingolimod withdrawal[END_REF][START_REF] Martinelli | Recurrent disease-activity rebound in a patient with multiple sclerosis after natalizumab discontinuations for pregnancy planning[END_REF][START_REF] De Giglio | Natalizumab discontinuation and disease restart in pregnancy: a case series[END_REF][START_REF] Verhaeghe | Pseudotumoral rebound of multiple sclerosis in a pregnant patient after stopping natalizumab[END_REF][START_REF] Sempere | Rebound of disease activity during pregnancy after withdrawal of fingolimod[END_REF][START_REF] Portaccio | Pregnancy decision-making in women with multiple sclerosis treated with natalizumab: II: Maternal risks[END_REF].

Therapeutic management for pregnancy planification and during pregnancy still represents a challenge regarding timing of DMT stop, risk of disease reactivation and potential fetal toxicity.

More data are needed to better understand the impact of DMT use before conception on disease activity during pregnancy and postpartum.

The objectives of our study were, in a large contemporary cohort, [START_REF] Leray | Epidemiology of multiple sclerosis[END_REF] to describe the course of the clinical disease activity during pregnancy planification, pregnancy and postpartum periods depending on treatment status and type before pregnancy; [START_REF] Thompson | Multiple sclerosis[END_REF] to compare the time from conception to first relapse, first disability progression and first MRI activity, depending on treatment status and type before pregnancy; and (3) to identify factors associated with disease activity during the period from conception to 3 months postpartum.

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METHODS

The OFSEP cohort and participating centers

OFSEP is a French multimodal nationwide MS registry supplemented by neurologists from MS centres and regional networks [START_REF] Vukusic | Observatoire Français de la Sclérose en Plaques (OFSEP): A unique multimodal nationwide MS registry in France[END_REF]. Data are collected retrospectively at the first visit and then prospectively during follow-up on a standardized clinical form in the European Database for MS (EDMUS) software [START_REF] Confavreux | EDMUS, a European database for multiple sclerosis[END_REF]. For this study, we used data from five OFSEP centers.

Standard protocol approvals, registrations, and patient consents

All patients included in the OFSEP cohort signed an informed consent to allow the registration of their medical data in the database and its use after anonymization for research. For the present study, approval of the Comité de Protection des Personnes has been obtained on 16 th April 2019 (registration number SI: 19.03.05.63609). All patients received an information letter and a nonconsent form that they could return in case of refusal to participate. Data extraction from EDMUS database was performed in January 2020.

Study cohort

Inclusion

Treatment status

A patient was considered as "treated" if she fulfilled one of the following cases:

(1) treated at least 6 months with the same first-or second-line DMT continuously over a period of 18 months before conception;

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(2) treated with mitoxantrone for a minimum of 3 cures over a period of 18 months before conception;

(3) treated with alemtuzumab for a minimum of one cycle over a period of 18 months before conception.

These definitions were applied to DMT started before conception and which could be continued during pregnancy.

Interferon, glatiramer acetate, teriflunomide and dimethyl fumarate were classified as first-line DMT, while natalizumab and fingolimod were classified as second-line DMT and mitoxantrone and alemtuzumab as third-line DMT. Patients were classified according to the last DMT received before conception.

Patients not fulfilling this definition were considered as "untreated" before conception.

The washout period was defined as the period from DMT stop to conception and did not exceed one year.

Data collection and protocol

Following variables were collected using EDMUS database (from 18 months before conception to 12 months after delivery): age and MS duration at conception, clinical activity (number of relapses, EDSS), radiological activity (new T2-lesions and gadolinium enhancing lesions on MRI) and DMTs exposure.

Missing or incomplete data were collected directly using MS patients' files in each centre by two neurologists (SL, LL). Information about Assisted Reproductive Techniques (ART), delivery, breastfeeding, vitamin D supplementation and smoking habits were collected through an auto-questionnaire or medical file when available.

Outcomes

The following outcomes were considered and compared between groups according to DMT exposure before conception:

ACCEPTED MANUSCRIPT / CLEAN COPY [START_REF] Leray | Epidemiology of multiple sclerosis[END_REF] The ARR over several periods of interest.

(2) The time from conception to first relapse, first disability progression and first MRI activity up to 12 months of postpartum.

Disability progression was defined as follows: an increase of 1.5 point on EDSS if baseline EDSS was 0, of 1 point if it was 1 and 5.5 or of 0.5 if the baseline EDSS was 5.5.

MRI activity was defined as either a gadolinium enhancing lesion or a new T2-lesion over the period of interest. Cerebral and medullar MRI were grouped together.

(3) Risk factors of disease activity during the period from conception to 3 months postpartum were assessed among: age at MS onset and at conception, MS duration at conception, status of treatment during pregnancy (ongoing vs stopped), relapse occurrence over one year before conception, EDSS at conception, MRI activity over one year before conception, use of ART, smoking and vitamin D exposure before conception.

Statistical analysis

Demographic characteristics and MS disease activity parameters at conception were described overall and by treatment groups. Treated and untreated patients were compared on baseline characteristics using Student's t-tests for continuous variables or Fisher's exact tests for categorical variables. For comparison of measures over two periods, paired-tests were used.

Treatment exposure before conception and washout duration were described. Patients with ongoing treatment at conception were described by treatment exposure and the time of stop was reported. For each group, ARR were computed, every 3 months, from the 12 months preceding pregnancy to 12 months postpartum. Trends of ARR were compared using linear regression.

For comparison of mean ARR, by group, at each trimester, one-way analysis of variance (ANOVA) was used. Time before reaching each outcome of interest was studied using Kaplan-Meier estimates. Restricted mean survival time (RMST) were computed to describe each outcome of interest in each group. Factors associated with MS activity over the 12 months from ACCEPTED MANUSCRIPT / CLEAN COPY conception to 3 months postpartum were studied using a logistic regression analysis. The level of significance was 5%, except for the variable selection process with univariate logistic regression models where the level of significance was 20%. Statistical analysis was performed using R 4.0.3 software.

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RESULTS

Characteristics of the cohort at conception

Among the 350 patients fulfilling inclusion criteria [START_REF] Leguy | COrticosteroids during the Post-Partum in relapsing Multiple Sclerosis patients[END_REF], 11 were treated by an off-label treatment (azathioprine, mycophenolate mofetil, methotrexate, rituximab and cyclophosphamide) before pregnancy and were excluded of the analysis. Characteristics at conception for the 339 patients are presented in Table 1. Overall, 217 women (64.0%) were treated in the 18 months period before conception, most of them (147 (67.7%)) by a first-line DMT.

Untreated women were older at MS onset and at conception with a lower EDSS at conception compared to treated ones. They presented a more active disease with 46.7% of them who had at least one relapse in the 12 months before conception, versus 35.0% in the treated group.

Second/third-line treated patients were younger at MS onset and presented a higher EDSS at conception compared to first-line treated patients.

Proportion of smokers as well as proportion of vitamin D supplementation before conception were comparable between the groups. The proportion of children conceived through ART were similar between the groups.

Treatment status before conception and during pregnancy

Table 2 reports the last DMT received in the 18 months before conception in the whole cohort and in the treated group.

Over the 147 first-line treated patients, 42.8% stopped their treatment at a median time of 3.8 months (IQR: 1.9-7.1) before conception. In the second-line DMT group, 21 (41.1%) patients stopped natalizumab before pregnancy with a median time of wash out duration of 3.6 months (IQR: 1.1-5.6) and 12 (75.0%) stopped fingolimod before pregnancy with a median time of wash out duration of 3.1 months (IQR: 1.2-3.9).

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Among treated patients, 57.2% continued their DMT for a median duration of 4.9 weeks (IQR: 2.7 -12.3) during the pregnancy. Most of them were on interferon (48%), glatiramer acetate (24%) or natalizumab (24%). Among patients who continued DMT during pregnancy, 78% stopped it during the first trimester of pregnancy.

ARR before conception, during pregnancy and over 12 months after delivery

For untreated and first-line treated patients, we observed a similar evolution of the mean ARR with a decrease during pregnancy and a moderate increase in the 3 months postpartum period (Figure 1). During pregnancy, 15.6% of untreated patients and 14.3% of first-line treated patients presented at least one relapse and they were respectively 12.3% and 10.9% during the 3 months of postpartum (Table S2).

The course of clinical disease activity was different for patients treated by second/third-line DMT before conception (Figure 1). During pregnancy, mean ARR increased from 0.60 on the year before conception to 0.91 and 0.84 during the second and third trimester respectively, with 47.1% of the patients facing at least one relapse during pregnancy. Mean ARR remained high during the first three months postpartum (ARR = 0.80) with 18.6% of the patients facing at least one relapse before returning to the pre-pregnancy rate (Table S3). During pregnancy, 49% of patients on natalizumab before pregnancy and 43.7% of patients on fingolimod before pregnancy had at least one relapse.

Mean ARR for the second/third-line group was significantly different compared to the untreated and first-line group for each trimester of pregnancy, and concerning the whole post conception period we observed a significant difference of the mean ARR between the first-line DMT group and second/third-line DMT group.

Time to first relapse from conception

The restricted mean time (RMST) before first relapse from conception to 12 months postpartum were 12.2 (95% Confidence Interval (CI): [10.3; 14]) months for second/third-line versus 16.5

ACCEPTED MANUSCRIPT / CLEAN COPY (95% CI: [15.4; 17.5]) and 16.8 (95% CI: [15.7; 17.9]) months for first-line and untreated, respectively. Comparisons of Kaplan-Meier estimates showed a significant difference (log-rank test p < 10 -4 ) (Figure 2A). Median time to the first relapse was 10 months after conception for patients treated with a second/third-line while the median was not reached for patients treated with a first-line or untreated. From conception to 3 months postpartum, the probability of being free from relapse was 77% (95% CI: [69%; 85%]) for untreated patients and 75% (95%CI:

[68%; 82%]) for first-line treated patients and only 47% (95%CI: [37%; 60%]) for patients treated with second/third-line treatment before conception.

Time to first disability progression from conception

From conception to 12 months postpartum, the RMST before first disability progression in the three groups were 19.9 (95% CI: [19.1; 20.7]) months for second/third-line versus 20.6 (95% CI: [20.3; 20.9]) and 20.9 (95% CI: [20.7; 21.0]) months for first-line and untreated, respectively. Comparisons of Kaplan-Meier estimates showed a significant difference (log-rank test p = 0.020) (Figure 2B). From conception to 3 months postpartum, the probability of being free from disability progression was 99% (95%CI: [98%; 100%]) for untreated patients, 96% (95%CI: [93%; 99%]) for first-line treated patients and 91% (95%CI: [85%; 98%]) for patients treated with second/third-line treatment.

For untreated patients, mean EDSS didn't change significantly from pre-pregnancy compared to the end of the first postpartum year (1.08 vs 1.05, p = 0.950). For treated patients, however, the mean pre-pregnancy EDSS and at the end of post-partum year were statistically different (1.50 vs 1.72, p = 0.021).

Time to first MRI activity from conception

This analysis was conducted on patients with available MRI over the outcome study period (N = 176, 50%). The RMST before first MRI activity from conception to 12 months postpartum, were 11.9 (95% CI: [10.4; 13.5]) months for second/third-line versus 14.1 (95% CI: [12.9;

ACCEPTED MANUSCRIPT / CLEAN COPY Comparisons of Kaplan-Meier estimates showed a significant difference (log-rank test p=0.002) (figure 2C). From conception to 3 months postpartum, the probability of being free from MRI activity was 77% (95%CI: [67%; 89%]) for untreated patients, 60% (95%CI: [50%; 72%]) for first-line treated patients and 38% (95%CI: [26%; 55%]) for patients treated with second/third-line treatment.

Factors associated with the risk of relapse during the period including pregnancy and the 3 months postpartum

In the multivariate analysis (Table 3), the risk of relapse during pregnancy and 3 months postpartum was significantly associated with occurrence of pre-conception relapses and exposition to second or third-line treatment before pregnancy. Then, focusing on the first-line treated patients (Table S4), we showed that to continue treatment during a part of pregnancy was significantly associated with lower risk of relapse in pregnancy and 3 months postpartum period (OR = 0.31 95%CI: [0.13; 0.72], p = 0.006). In contrast, for the second/third-line treated patients (Table S5), no significant association between the occurrence of relapse during pregnancy and 3 months postpartum period and the maintenance of treatment or not during a part of pregnancy (p = 0.817) was demonstrated.

Resumption of DMT after delivery

The majority of untreated patients before pregnancy remained without DMT after delivery (64%). Among first-line treated patients, 75% resumed or continued first-line DMT. In the second/third-line group, 81% resumed or continued the same DMT.

The RMST from delivery to DMT resumption over 12 months, were statistically different with 3.5 months (95%CI: [2.9; 4.0]) for treated patients and 9.4 months (95%CI: [8.6; 10.1]) for untreated patients (p < 10 -4 ). Among treated patients, the second/third-line patients resumed their DMT earlier than those treated with first-line (RMST: 2.3 months 95%CI: [1.6; 3.1] vs 3.8 ACCEPTED MANUSCRIPT / CLEAN COPY months 95% CI: [3.2; 4.5], p = 0.003). At one year after delivery, the probability of being treated was 88% (95%CI: [83%; 92%] for treated patients before conception and 36% (95%CI: [27%; 44%] for the untreated patients.

Breastfeeding

Breastfeeding was more frequent for untreated patients (66.7%) compared to first-line treated patients (45.1%) and second/third-line patients (28.1%) (p < 10 -4 ). Mean breastfeeding duration was 7.3 months (±10.5) for untreated patients, 4.2 months (±3.5) for first-line treated patients and 6.0 months (± 8.8) for second/third-line patients, and was not statistically different between the different groups (p = 0.147).

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DISCUSSION

Therapeutic management of pregnancy has been considerably challenged these last years. Timing of DMT stop, risk of disease reactivation during and after pregnancy and potential fetal toxicity are some of the practical issues that are not fully resolved. In this study, we aimed to describe the influence of DMT before pregnancy onset on disease activity during pregnancy and early postpartum in a large prospective national cohort.

We first observed that 13% of the patients presented a relapse in the 3 months postpartum period in the whole cohort with a mean ARR of 0.61. These data confirm the decreased risk of disease reactivation described these last years during the postpartum period. Indeed, ARR in the 3 months postpartum was estimated at 1.2 in PRIMS in 1998 [START_REF] Confavreux | Rate of pregnancy-related relapse in multiple sclerosis. Pregnancy in Multiple Sclerosis Group[END_REF] whereas it was estimated between 0.27 and 0.94 in more recent cohorts [START_REF] Bsteh | Pregnancy and multiple sclerosis in the DMT era: A cohort study in Western Austria[END_REF][START_REF] Nguyen | Incidence of pregnancy and disease-modifying therapy exposure trends in women with multiple sclerosis: A contemporary cohort study[END_REF][START_REF] Langer-Gould | Pregnancy-related relapses and breastfeeding in a contemporary multiple sclerosis cohort[END_REF][START_REF] Vukusic | Oral nomegestrol acetate and transdermal 17-beta-estradiol for preventing post-partum relapses in multiple sclerosis: The POPARTMUS study[END_REF]. In the same way, between 23% and 43% of the patients had a relapse on this postpartum period in the historical cohorts [START_REF] Confavreux | Rate of pregnancy-related relapse in multiple sclerosis. Pregnancy in Multiple Sclerosis Group[END_REF][START_REF] Roullet | Pregnancy and multiple sclerosis: a longitudinal study of 125 remittent patients[END_REF][START_REF] Nelson | Risk of multiple sclerosis exacerbation during pregnancy ACCEPTED MANUSCRIPT / CLEAN COPY and breast-feeding[END_REF] compared to 7% to 22 % in more recent studies [START_REF] Correia | Pregnancy in Multiple Sclerosis: A Portuguese cohort study[END_REF][START_REF] Langer-Gould | Pregnancy-related relapses and breastfeeding in a contemporary multiple sclerosis cohort[END_REF][START_REF] Hughes | Predictors and dynamics of postpartum relapses in women with multiple sclerosis[END_REF]. These current results are probably explained by a better control of the disease activity before pregnancy with an increasing proportion of treated patients and the availability of highly effective DMTs. Indeed, the mean ARR before pregnancy is lower in the recent studies [START_REF] Bsteh | Pregnancy and multiple sclerosis in the DMT era: A cohort study in Western Austria[END_REF][START_REF] Nguyen | Incidence of pregnancy and disease-modifying therapy exposure trends in women with multiple sclerosis: A contemporary cohort study[END_REF][START_REF] Langer-Gould | Pregnancy-related relapses and breastfeeding in a contemporary multiple sclerosis cohort[END_REF][START_REF] Vukusic | Oral nomegestrol acetate and transdermal 17-beta-estradiol for preventing post-partum relapses in multiple sclerosis: The POPARTMUS study[END_REF] (between 0.09 and 0.64) and in our study (0.48) than in PRIMS (0.7).

The second important observation we made in our cohort was on the risk of disease reactivation during pregnancy in MS patients treated by second-line DMT before pregnancy with 47 % of those patients that had at least one relapse during pregnancy. Importantly, in our cohort, the second/third-line group was composed of 73% (n=51) of patients treated with natalizumab and 23% (n=16) of patients treated with fingolimod before conception. It is now well known that patients who discontinue natalizumab, especially in a context of pregnancy, are at high risk of disease reactivation [START_REF] Portaccio | Pregnancy decision-making in women with multiple sclerosis treated with natalizumab: II: Maternal risks[END_REF][START_REF] Kleerekooper | Disease activity following pregnancy-related discontinuation of natalizumab in MS[END_REF][START_REF] Yeh | Natalizumab, Fingolimod, and Dimethyl Fumarate Use and Pregnancy-Related Relapse and Disability in Women With Multiple Sclerosis[END_REF]. In the situation of fingolimod discontinuation associated to pregnancy within the year, disease reactivation has also been described with increased ARR ACCEPTED MANUSCRIPT / CLEAN COPY during pregnancy (from 0.49 to 0.7) [START_REF] Alroughani | Relapse occurrence in women with multiple sclerosis during pregnancy in the new treatment era[END_REF][START_REF] Yeh | Natalizumab, Fingolimod, and Dimethyl Fumarate Use and Pregnancy-Related Relapse and Disability in Women With Multiple Sclerosis[END_REF][START_REF] Bianco | Disease Reactivation after Fingolimod Discontinuation in Pregnant Multiple Sclerosis Patients[END_REF]. Our results give insight to the attitude suggested to maintain natalizumab for at least one or two trimesters during pregnancy [START_REF] Hellwig | Multiple sclerosis and pregnancy: experience from ACCEPTED MANUSCRIPT / CLEAN COPY a nationwide database in Germany[END_REF][START_REF] Alroughani | Relapse occurrence in women with multiple sclerosis during pregnancy in the new treatment era[END_REF][START_REF] Nguyen | Incidence of pregnancy and disease-modifying therapy exposure trends in women with multiple sclerosis: A contemporary cohort study[END_REF][START_REF] Portaccio | Pregnancy decision-making in women with multiple sclerosis treated with natalizumab: II: Maternal risks[END_REF][START_REF] Demortiere | Maintenance of natalizumab during the first trimester of pregnancy in active multiple sclerosis[END_REF] but also to be careful with the use of fingolimod in patients with pregnancy desire.

Concerning the disease activity during post-partum, we didn't show significant differences comparing ARR of the groups. One explanation could be that patients in the second/third line DMT group resumed their DMT faster after delivery decreasing the risk of disease reactivation [START_REF] Bsteh | Pregnancy and multiple sclerosis in the DMT era: A cohort study in Western Austria[END_REF][START_REF] Portaccio | Postpartum relapses increase the risk of disability progression in multiple sclerosis: the role of disease modifying[END_REF].

The strength of our study is firstly the quality of our data. This study was based on five French centers dataset with a prospective follow-up. There were very few missing data concerning our clinical endpoints, thanks to the use of EDMUS database and a checking of medical records on sites. Moreover, questionnaires allowed us to collect additional information. Despite substantial missing data (only 50% of patients had undergone MRI during the period of interest in our study), this study included MRI data that are rarely described in similar studies. Data were collected over a substantial period of time: 24 months before conception, during pregnancy and 12 months after delivery. However, despite a population of 350 women, we did not have sufficient numbers of patients to evaluate the specific effects of each treatment during pregnancy and early postpartum. As such, we decided to group treatments by line status and pooled second-and third-lines in a same group. However, conclusions concerning the course of ARR before, during and after pregnancy were similar when third-line patients were excluded (N=3) (data not shown).

To conclude, this study provides reassuring data on the course of pregnancy and postpartum in a contemporary MS cohort with more than 85% of MS patients who were relapse-free during the 3 months postpartum period. However, a peculiar attention should be paid to women treated with natalizumab or fingolimod before conception who are at higher risk of disease reactivation after treatment stop, especially during pregnancy. The p-value was computed using a linear regression for testing trends. The number of patients currently treated in each trimester is reported for each group defined according to treatment before conception (as specifically defined in the methodology). The asterisk indicates significant difference between Annual Relapses Rates (ARR) by trimester.

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  criteria were: (a) RRMS patients according to McDonald criteria 2017 (21) nonopposed to participation to the study, (b) aged 15 to 49 at conception, (c) having at least one pregnancy with live birth after MS onset from January 1, 2007 to January 1, 2017, (d) having at least one neurological visit per year in the 24 months preceding the pregnancy and one neurological visit within 12 months after delivery. In case of several pregnancies per woman, only the last one fulfilling the criteria was analyzed.

15. 2 ]

 2 ) and 15.3 (95% CI:[13.6; 17.1]) months for first-line and untreated, respectively.

Figure 1 :

 1 Figure 1: Mean annual relapse rate 12 months before, during and after pregnancy by trimesters, according to last treatment status before pregnancy: first-line, second/third-line treated or untreated.

Figure 2 :

 2 Figure 2: Kaplan-Meier estimates of the time to first relapse (A) to first disability progression (B), to first MRI activity (C) from conception to one-year postpartum according to last treatment status before pregnancy: first-line treated, second/third line treated or untreated.

  overall and according to (1) treatment status before conception: treated and untreated and (2) last treatment line before conception for treated patients: first-line or second/third-line treated.

Table 1 : Demographic and clinical/MRI patients' characteristics before conception

 1

Table 1

 1 Click here to access/download;Table;Table 1_rv.docx

	4	<10 -4	24.1 ± 4.9	22.3 ± 5.1	0.016

‡ N(%); § ARR: Annual Relapse Rate; ⁋ computed on available data

Table 2 : Descriptive of the last treatment received in the 18 months period before conception

 2

	All	Treated
	N = 339	N = 217

† DMT : Disease Modifying Treatment

Table 2

 2 Click here to access/download;Table;Table 2_rv.docx

ACKNOWLEDGMENTS

This work has been done with data from the OFSEP (http://www.ofsep.org/fr/). The authors thank the technicians of participating centers for their help (Mr Leport from Rennes, Mrs Moyon from Nantes, Mrs Callier from Nice, Mrs Berthe from Strasbourg).

BIBLIOGRAPHY

Funding statement: This work has been done with data from the OFSEP (http://www.ofsep.org/fr/), which is supported by a grant provided by the French State and handled by the Agence Nationale de la Recherche within the framework of the Investments for the Future program under the reference ANR-10-COHO-002 OFSEP and by the Eugene Devic Foundation Against Multiple Sclerosis.

Disclosure: LM received honoraria as speaker from Biogen, Merck Serono, BMS Celgene, Sanofi Genzyme, Roche, and Novartis. SV reports consulting and lecture fees, travel grants and research support from Biogen, Celgène, Novartis, Merck, Roche, Sanofi Genzyme and Teva Pharm. DAL has received consulting and lecturing fees, travel grants and unconditional research support from Biogen, Genzyme, Novartis, Merck, Roche, Sanofi, Medday, Teva Pharma and BMS. SW received honoraria as speaker or consultant from Alexion, Biogen, Merck Serono, Roche, and Novartis. ELP received honoraria for lectures or consulting from Biogen Idec, Merck Serono, Novartis, Sanofi-Aventis, TEVA, Roche, Alexion. SL, ML, LL, AM, GE, AK, JDS, CLF, EL have no disclosure regarding this work.

Conflict of Interest/ Role of Funding Source

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