Single-carrier phase-disposition PWM techniques for multiple interleaved voltage-source converter legs

Interleaved converter legs are typically modulated with individual carriers per leg and phase-shifted PWM (PS-PWM) as it facilitates current balancing amongst the legs. Phase-disposition PWM (PD-PWM), despite the better harmonic performance, cannot be directly used due to the resulting current imbalance that may damage the converter. This paper addresses the current sharing issue and proposes a single-carrier PD-PWM technique for multiple leg two-level converters based on a hierarchy scheme derived from current sorting algorithms. An extension of the proposed algorithm through a switching state feedback loop, limiting the average switching frequency, is also developed. In both cases, the load current is shared amongst the legs and the high-quality of the output voltages and currents is maintained while the circulating currents amongst the converter legs are kept to a minimum. Simulation results demonstrate the method for multiple interleaved legs as well as its current sharing capabilities for high-power applications. Experimental results from a low-power laboratory prototype validate the operation of the proposed approach.Peer ReviewedPostprint (published version

A Transformerless PCB Based Medium-Voltage Multilevel Power Converter with A DC Capacitor Balancing Circuit and Algorithm

This dissertation presents a new method of constructing a transformerless, voltage-sourced, medium-voltage multilevel converter using existing discrete power semiconductor devices and printed circuit board technology. While the approach is general, it is particularly well-suited for medium-voltage converters and motor-drives in the 4.16 kV, 500 - 1000 kW range. A novel way of visualizing the power stage topology is developed which allows simplified mechanical layouts while managing the commutation paths. Using so many discrete devices typically drives cost and complexity of the gate-drive system including its control and isolation; a gate-drive circuit is presented to address this problem. As with most multilevel topologies, the dc-link voltages must be balanced during operation. This is accomplished using an auxiliary circuit made up of the same power stage and an associated control algorithm. Experimental results are presented for a 4.16 kV, 746 kW, five-level power converter prototype. This dissertation also analyzes a new capacitor voltage-balancing converter along with a novel capacitor voltage balancing control algorithm. Analysis of the inverter system provides a new description of capacitor voltage stability as a function of system operating conditions

Integrated motor drives: state of the art and future trends

With increased need for high power density, high efficiency and high temperature capabilities in Aerospace and Automotive applications, Integrated Motor Drives (IMD) offers a potential solution. However, close physical integration of the converter and the machine may also lead to an increase in components temperature. This requires careful mechanical, structural and thermal analysis; and design of the IMD system. This paper reviews existing IMD technologies and their thermal effects on the IMD system. The effects of the power electronics (PE) position on the IMD system and its respective thermal management concepts are also investigated. The challenges faced in designing and manufacturing of an IMD along with the mechanical and structural impacts of close physical integration is also discussed and potential solutions are provided. Potential converter topologies for an IMD like the Matrix converter, 2-level Bridge, 3-level NPC and Multiphase full bridge converters are also reviewed. Wide band gap devices like SiC and GaN and their packaging in power modules for IMDs are also discussed. Power modules components and packaging technologies are also presented

Design of module level converters in photovoltaic power systems

The application of distributed maximum power point tracking (DMPPT) technology in solar photovoltaic (PV) systems is a hot topic in industry and academia. In the PV industry, grid integrated power systems are mainstream. The main objective for PV system design is to increase energy conversion efficiency and decrease the levelized cost of electricity of PV generators. This thesis firstly presents an extensive review of state-of-the-art PV technologies. With focus on grid integrated PV systems research, various aspects covered include PV materials, conventional full power processing DMPPT architectures, main MPPT techniques, and traditional partial power processing DMPPT architectures. The main restrictions to applying traditional DMPPT architectures in large power systems are discussed. A parallel connected partial power processing DMPPT architecture is proposed aiming to overcome existing restrictions. With flexible ‘plug-and-play’ functionality, the proposed architecture can be readily expanded to supply a downstream inverter stage or dc network. By adopting smaller module integrated converters, the proposed approach provides a possible efficiency improvement and cost reduction. The requirements for possible converter candidates and control strategies are analysed. One representative circuit scheme is presented as an example to verify the feasibility of the design. An electromagnetic transient model is built for different power scale PV systems to verify the DMPPT feasibility of the evaluated architecture in a large-scale PV power system. Voltage boosting ability is widely needed for converters in DMPPT applications. Impedance source converters (ISCs) are the main converter types with step-up ability. However, these converters have a general problem of low order distortion when applied in dc-ac applications. To solve this problem, a generic plug-in repetitive control strategy for a four-switch three-phase ISC type inverter configuration is developed. Simulation and experimental results confirm that this control strategy is suitable for many ISC converters.The application of distributed maximum power point tracking (DMPPT) technology in solar photovoltaic (PV) systems is a hot topic in industry and academia. In the PV industry, grid integrated power systems are mainstream. The main objective for PV system design is to increase energy conversion efficiency and decrease the levelized cost of electricity of PV generators. This thesis firstly presents an extensive review of state-of-the-art PV technologies. With focus on grid integrated PV systems research, various aspects covered include PV materials, conventional full power processing DMPPT architectures, main MPPT techniques, and traditional partial power processing DMPPT architectures. The main restrictions to applying traditional DMPPT architectures in large power systems are discussed. A parallel connected partial power processing DMPPT architecture is proposed aiming to overcome existing restrictions. With flexible ‘plug-and-play’ functionality, the proposed architecture can be readily expanded to supply a downstream inverter stage or dc network. By adopting smaller module integrated converters, the proposed approach provides a possible efficiency improvement and cost reduction. The requirements for possible converter candidates and control strategies are analysed. One representative circuit scheme is presented as an example to verify the feasibility of the design. An electromagnetic transient model is built for different power scale PV systems to verify the DMPPT feasibility of the evaluated architecture in a large-scale PV power system. Voltage boosting ability is widely needed for converters in DMPPT applications. Impedance source converters (ISCs) are the main converter types with step-up ability. However, these converters have a general problem of low order distortion when applied in dc-ac applications. To solve this problem, a generic plug-in repetitive control strategy for a four-switch three-phase ISC type inverter configuration is developed. Simulation and experimental results confirm that this control strategy is suitable for many ISC converters

Digital Control of Power Converters and Drives for Hybrid Traction and Wireless Charging

In the last years environmental issues and constant increase of fuel and energy cost have been incentivizing the development of low emission and high efficiency systems, either in traction field or in distributed generation systems from renewable energy sources. In the automotive industry, alternative solutions to the standard internal combustion engine (ICE) adopted in the conventional vehicles have been developed, i.e. fuel cell electric vehicles (FCEVs), hybrid electric vehicles (HEVs), plug-in hybrid electric vehicles (PHEV) or pure electric vehicles (EVs), also referred as battery powered electric vehicles (BEV). Both academic and industry researchers all over the world are still facing several technical development areas concerning HEV components, system topologies, power converters and control strategies. Efficiency, lifetime, stability and volume issues have moved the attention on a number of bidirectional conversion solutions, both for the energy transfer to/from the storage element and to/from the electric machine side. Moreover, along with the fast growing interest in EVs and PHEVs, wireless charging, as a new way of charging batteries, has drawn the attention of researchers, car manufacturers, and customers recently. Compared to conductive power transfer (usually plug-in), wireless power transfer (WPT) is more convenient, weather proof, and electric shock protected. However, there is still more research work needs to be done to optimize efficiency, cost, increase misalignment tolerance, and reduce size of the WPT chargers. The proposed dissertation describes the work from 2012 to 2014, during the PhD course at the Electric Drives Laboratory of the University of Udine and during my six months visiting scholarship at the University of Michigan in Dearborn. The topics studied are related to power conversion and digital control of converters and drives suitable for hybrid/electric traction, generation from renewable energy sources and wireless charging applications. From the theoretical point of view, multilevel and multiphase DC/AC and DC/DC converters are discussed here, focusing on design issues, optimization (especially from the efficiency point-of-view) and advantages. Some novel modulation algorithms for the neutral-point clamped three-level inverter are presented here as well as a new multiphase proposal for a three-level buck converter. In addition, a new active torque damping technique in order to reduce torque oscillations in internal combustion engines is proposed here. Mainly, two practical implementations are considered in this dissertation, i.e. an original two-stage bi-directional converter for mild hybrid traction and a wireless charger for electric vehicles fast charge

Voltage-source-inverters with legs connected in parallel

The number of applications that require the use of power converters has been continually increasing in the last years on account of environmental and economical concerns. The power to be processed by these converters has been growing too. These applications include uninterruptible power supplies, motor drives, and distributed generation, such as solar photo-voltaic panels and wind turbines. The rated power of such converters can be raised by increasing the output currents. This can be chieved by connecting converter, converter legs or power devices in parallel. The connection of legs in parallel in a voltage ource inverter is made by means of inductors, hich can be either magnetically coupled or uncoupled. One of the issues that needs to be addressed is achieving an even contribution to the output current from all the legs. Current imbalances are due to circulating currents among the legs which must be avoided or controlled since they produce additional losses and stress to the power devices of the converter. An efficient technique to attain such a balance is presented in this thesis. The balancing technique achieves the objective regardless of the type of inductors used. In spite of the afore mentioned issues, the potential benefits of paralleling converter legs make their use a worthwhile option. Some of the additional benefits of paralleling are the improvement in the total harmonic distortion of the output current and voltage and the reduction of the output filters. Besides, inverters with legs connected in parallel are modular and because of that, their production and maintenance become less expensive. Moreover, they qualify for the implementation of fault-tolerant techniques thus offering the possibility to achieve systems with improved overall reliability. Interleaving of the carriers can be used to modulate the reference signals for each leg, which leads to a reduction in the output current ripple without resorting to increasing the switching frequency. A whole set of shifted carriers is required if interleaved pulse-width modulators are used. Implementing this by means of a digital signal processor (DSP) means that the higher the number of carriers, the higher the number of DSP timing resources required. Provided that the latter are usually limited, this could be a drawback when increasing the number of interleaved carriers. In this thesis the implementation of a pulse-width modulation (PWM) scheme where all modulators use the same carrier offering the same results as if a set of n interleaved carriers were used is presented. Since the proposed algorithm takes maximum benefit from the PWM units available in a DSP, a higher number of legs connected in parallel can be controlled without adding any external processing hardware. In multiphase voltage source inverters with n interleaved parallel-connected legs, the best single-phase output voltage is achieved when the carriers are evenly phase shifted. However, switching among nonadjacent levels can be observed at regular intervals in the line-to-line voltages, causing bad harmonic performance. This thesis includes a novel implementation of PWM that improves the quality of the line-to-line output voltages in interleaved multiphase voltage-source inverters. With the proposed method, switching in the line-to-line voltages happens exclusively between adjacent levels. The modulator utilizes two sets of n evenly phase-shifted carriers that are dynamically allocated. Because of its generality, the proposed implementation is valid for any number of phases and any number of legs in parallel. All the modulation and control algorithms proposed in this thesis have been firstly simulated on Matlab/Simulink models, and then experimentally corroborated on a low power laboratory prototype.El número de aplicaciones que requiere del uso de convertidores de potencia ha crecido de forma regular en los últimos años debido a cuestiones económicas y ambientales. Entre ellas se incluyen fuentes de alimentación ininterrumpibles, accionamientos de motores y sistemas de generación distribuida, como paneles fotovoltaicos o turbinas eólicas. La potencia nominal de dichos convertidores puede aumentarse incrementando las corrientes de salida. Esto puede lograrse mediante la conexión en paralelo de: semiconductores, ramas de convertidor o convertidores. La conexión en paralelo de las ramas de un inversor con fuente de tensión se efectúa mediante inductancias, que pueden estar magnéticamente acopladas o no. Una de las cuestiones que hay que lograr es una contribución equitativa a la corriente de salida por parte de todas las ramas. Los desequilibrios se deben a las corrientes que circulan entre las ramas y que deben evitarse, o controlarse, pues causan solicitaciones y pérdidas adicionales en los dispositivos de potencia del convertidor. En esta tesis se presenta una técnica eficiente para conseguir dicho equilibrio. Dicha técnica es efectiva independientemente del tipo de bobinas utilizado. A pesar de las cuestiones mencionadas, los beneficios de la conexión de ramas en paralelo las convierte en una opción a considerar. Entre sus beneficios adicionales se encuentran la mejora en la distorsión armónica total de las tensiones y corrientes de salida y la reducción de los filtros de salida. Además, los convertidores con ramas en paralelo son modulares y, de este modo, su producción y mantenimiento resulta más económico. Es más, son ideales para la implantación de técnicas tolerantes a fallos, lo que permite obtener sistemas con una mejor fiabilidad global. Para la modulación de las señales de cada rama pueden utilizarse técnicas de entrelazado de las portadoras, lo que conduce a un menor rizado en la corriente de salida sin tener que recurrir a mayores frecuencias de conmutación. Si se usan moduladores de anchura de pulso entrelazados, se necesita un conjunto de señales portadoras desplazadas. La implantación de esto mediante un procesador digital de señal (DSP) implica que a mayor número de portadoras, mayor será el número de recursos de temporización del DSP que se necesiten. Dado que estos últimos son normalmente limitados, esto podría ser un inconveniente cuando se quiera incrementar el número de portadoras entrelazadas. En esta tesis se presenta la implementación de un esquema de modulación de anchura de pulso (PWM) en el que todos los moduladores usan una misma portadora y que ofrece el mismo resultado que si se utilizara todo un conjunto de portadoras entrelazadas. Como el algoritmo propuesto saca el mejor provecho de las unidades de PWM disponibles en el DSP, se podría controlar un mayor número de ramas en paralelo sin necesidad de ninguna circuitería externa adicional. En inversores con fuente de corriente polifásicos con n ramas conectadas en paralelo, la mejor tensión de fase de salida se obtiene cuando las portadoras están desfasadas por igual. Sin embargo, se observan transiciones entre niveles de salida no adyacentes en las tensiones de línea a intervalos regulares, lo que ocasiona malas prestaciones armónicas. Esta tesis incluye una novedosa implementación de PWM que mejora la calidad de la tensión de línea en inversores con fuente de tensión. Con el método propuesto, las transiciones en las tensiones de línea se producen únicamente entre niveles de tensión adyacentes. El modulador utiliza dos conjuntos de n Portadoras regularmente desfasadas cuyo uso se va asignando de forma dinámica. Dada su formulación genérica, la implementación propuesta es válida para cualquier número de fases y cualquier número de rama

Dynamic Phasor Modeling of Type 3 Wind Farm including Multi-mass and LVRT Effects

The proportion of power attributable to wind generation has grown significantly in the last two decades. System impact studies such as load flow studies and short circuit studies, are important for planning before integration of any new wind generation into the existing power grid. Short circuit modelling is central in these planning studies to determine protective relay settings, protection coordination, and equipment ratings. Numerous factors, such as low voltage situations, power electronic switching, control actions, sub-synchronous oscillations, etc., influence the response of wind farms to short circuit conditions, and that makes short circuit modelling of wind farms an interesting, complex, and challenging task. Power electronics-based converters are very common in wind power plants, enabling the plant to operate at a wide range of wind speeds and provide reactive power support without disconnection from the grid during low voltage scenarios. This has led to the growth of Type 3 (with rotor side converter) and Type 4 (with stator side full converter) wind generators, in which power electronics-based converters and controls are an integral part. The power electronics in these generators are proprietary in nature, which makes it difficult to obtain the necessary information from the manufacturer to model them accurately in planning studies for conditions such as those found during faults or low voltage ride through (LVRT) periods. The use of power electronic controllers also has led to phenomena such as sub-synchronous control interactions in series compensated Type 3 wind farms, which are characterized by non-fundamental frequency oscillations. The above factors have led to the need to develop generic models for wind farms that can be used in studies by planners and protection engineers. The current practice for short circuit modelling of wind farms in the power industry is to utilize transient stability programs based on either simplified electromechanical fundamental frequency models or detailed electromagnetic time domain models. The fundamental frequency models are incapable of representing the majority of critical wind generator fault characteristics, such as during power electronic switching conditions and sub-synchronous interactions. The detailed time domain models, though accurate, demand high levels of computation and modelling expertise. A simple yet accurate modelling methodology for wind generators that does not require resorting to fundamental frequency based simplifications or time domain type simulations is the basis for this research work. This research work develops an average value model and a dynamic phasor model of a Type 3 DFIG wind farm. The average value model replaces the switches and associated phenomena by equivalent current and voltage sources. The dynamic phasor model is based on generalized averaging theory, where the system variables are represented as time varying Fourier coefficients known as dynamic phasors. The two types models provide a generic type model and achieve a middle ground between conventional electromechanical models and the cumbersome electromagnetic time domain models. The dynamic phasor model enables the user to consider each harmonic component individually; this selective view of the components of the system response is not achievable in conventional electromagnetic transient simulations. Only the appropriate dynamic phasors are selected for the required fault behaviour to be represented, providing greater computational efficiency than detailed time domain simulations. A detailed electromagnetic transient (EMT) simulation model is also developed in this thesis using a real-time digital simulator (RTDS). The results obtained with the average value model and the dynamic phasor model are validated with an accurate electromagnetic simulation model and some state-of-the-art industrial schemes: a voltage behind transient reactance model, an analytical expression model, and a voltage dependent current source model. The proposed RTDS models include the effect of change of flux during faulted conditions in the wind generator during abnormal system conditions instead of incorrectly assuming it is a constant. This was not investigated in previous studies carried out in the real-time simulations laboratory at the University of Saskatchewan or in various publications reported in the literature. The most commonly used LVRT topologies, such as rotor side crowbar circuit, DC-link protection scheme, and series dynamic braking resistance (SDBR) in rotor and stator circuits, are investigated in the short circuit studies. The RTDS model developed uses a multi-mass (three-mass) model of the mechanical drive train instead of a simple single-mass model to represent torsional dynamics. The single mass model considers the blade inertia, the turbine hub, and the generator as a single lumped mass and so cannot reproduce the torsional behaviour. The root cause of sub-synchronous frequencies in Type 3 wind generators is not well understood by system planners and protection engineers. Some literature reports it is self excitation while others report it is due to sub-synchronous control interactions. One publication in the stability literature reports on a small signal analysis study aimed at finding the root cause of the problem, and a similar type of analysis was performed in this thesis. A linearized model was developed, which includes the generator model, a three mass drive train, rotor side converter, and the grid side converter represented as a constant voltage source. The linear model analysis showed that the sub-synchronous oscillations are due to control interactions between the rotor side controller of the Type 3 wind power plant and the series capacitor in the transmission line. The rotor side controls were tuned to obtain a stable response at higher levels of compensation. A real-time simulation model of a 450 MW Type 3 wind farm consisting of 150 units transmitting power via 345 kV transmission line was developed on the RTDS. The dynamic phasor method is shown to be accurate for representing faults at the point of interconnection of the wind farm to the grid for balanced and unbalanced faults as well as for different sub- synchronous oscillation frequencies

Dynamic Averaged Models of VSC-Based HVDC Systems for Electromagnetic Transient Programs

RÉSUMÉ Les systèmes d’haute tension à courant continu (HTCC) basés sur technologies de convertisseur de source de tension (CST) offrent des prometteur opportunités dans une variété de domaines au sein de l'industrie des systèmes de puissance en raison de leurs avantages reconnus par rapport aux systèmes HTCC classiques basés à convertisseurs de commutation de ligne (CCL). La technologie CST-HTCC combine des convertisseurs de puissance, basé sur des IGBT (Insulated Gate Bipolar Transistor), avec des liens au courant continus pour transmettre la puissance dans l'ordre de milliers de mégawatts. En plus de contrôler le flux d'énergie entre deux réseaux à courant alternatif, les systèmes CST-HTCC peuvent fournir de réseaux faibles et même des réseaux passifs. Les systèmes CST-HTCC présentent une réponse dynamique plus rapide grâce à la méthode de modulation de largeur d'impulsions (MLI) en comparaison avec l'opération de commutation de fréquence fondamentale des systèmes HTCC traditionnels. Représentation détaillée des systèmes CST-HTCC dans les programmes d’Électromagnétique Transitoire (EMT) comprend la modélisation des valves IGBT et doit normalement utiliser de pas d'intégration petit pour représenter avec précision les événements de commutation rapides. Les simulations et les calculs informatiques introduits par les modèles détaillés compliquent l'étude des événements en régime permanent et transitoire mettant en évidence la nécessité de développer des modèles plus efficaces qui assurent un comportement similaire de la réponse dynamique. L'objectif de cette thèse est de développer des modèles moyennés qui reproduit avec précision le comportement statique et dynamique, en plus les transitoires des systèmes CST-HTCC dans des programmes de type EMT. Ces modèles simplifiés représentent la valeur moyenne des réponses des dispositifs de commutation, convertisseurs, et des contrôles à l'aide de techniques de valeur moyenne, de sources contrôlées et des fonctions de commutation. Cette thèse contribue également à l'élaboration de modèles CST détaillés utilisés pour valider les modèles moyenne proposés. Les modèles détaillés développés comprennent convertisseur avec topologies à deux et à trois niveaux et la plus récente topologie du convertisseur modulaire multiniveaux (CMM). Comparaison des différentes topologies de convertisseur approprié pour VSC-HVDC transmission, y compris leurs avantages et leurs limitations, sont également discutés.----------ABSTRACT High Voltage Direct Current (HVDC) systems based on Voltage-sourced Converter (VSC) technologies present a bright opportunity in a variety of fields within the power system industry due to their recognized advantages in comparison to conventional line-commutated converter (LCC) based HVDC systems. VSC-HVDC technology combines power converters, based on IGBTs (Insulated Gate Bipolar Transistors), with dc links to transmit power in the order of thousands of megawatts. In addition to controlling power flow between two ac networks, VSC-HVDC systems can supply weak and even passive networks. VSC-HVDC systems present a faster dynamic response thanks to its Pulse-width Modulation (PWM) control in comparison with the fundamental switching frequency operation of traditional HVDC systems. Detailed representation of VSC-HVDC systems in Electro Magnetic Transient (EMT) programs includes the modeling of IGBT valves and must normally use small integration time-steps to accurately represent fast switching events. Computational burden introduced by such a detailed models complicates the study of steady-state and transient events highlighting the need to develop more efficient models that provide similar behavior and dynamic response. The objective of this thesis is to develop, test and validate averaged models to accurately replicate the steady-state, dynamic and transient behavior of VSC-based HVDC systems in EMT-type programs. These simplified models represent the average response of switching devices and converters by using averaging techniques involving controlled sources and switching functions. The work also contributes to the development of detailed VSC models used to validate the proposed average models. The detailed models developed include two- and three-level converter topologies and the most recent Modular Multilevel Converter (MMC) topology. Comparison of different converter topologies suitable to VSC-HVDC transmission, including their advantages and limitations, are also discussed. A control system is implemented based on vector control which permits independent control both active and reactive power (and/or voltage) at each VSC terminal. Available modulation techniques are presented and compared in terms of performance and power quality

Advanced Modeling and Research in Hybrid Microgrid Control and Optimization

This book presents the latest solutions in fuel cell (FC) and renewable energy implementation in mobile and stationary applications. The implementation of advanced energy management and optimization strategies are detailed for fuel cell and renewable microgrids, and for the multi-FC stack architecture of FC/electric vehicles to enhance the reliability of these systems and to reduce the costs related to energy production and maintenance. Cyber-security methods based on blockchain technology to increase the resilience of FC renewable hybrid microgrids are also presented. Therefore, this book is for all readers interested in these challenging directions of research

Etude et modélisation de stratégies de régulation linéaires découplantes appliquées à un convertisseur multicellulaire parallèle

Les structures de conversion multi-niveaux parallèles permettent de faire transiter de fortscourants tout en gardant une bonne puissance massique ; celles-ci sont réalisées en parallélisantdes cellules de commutation. Cette parallélisation permet de réduire le courant dans chaquecellule et ainsi de revenir dans des gammes plus standard de composants de puissance. Laparallélisation, en utilisant une commande adaptée, améliore les formes d’onde en sortie duconvertisseur. Ce manuscrit se focalisera sur une structure de conversion multiniveaux parallèlespécifique constituée de bras de hacheur dévolteur en parallèles couplés magnétiquement. Eneffet du fait de la commande entrelacée mise en place, l’ondulation du courant de sortie se voitréduite mais en contrepartie l’utilisation d’inductances séparées sur chaque bras entraine uneaugmentation de l’ondulation des courants de bras, directement liée au nombre de cellules decommutation, en fonction de l’ondulation du courant de sortie. Afin de palier à ce problème cesinductances sont remplacées par un (ou plusieurs) coupleur(s) magnétique(s) qui permet(tent) deréduire l’ondulation de courant dans chaque bras. Cependant dans le but de garantir la nonsaturation ainsi qu’une bonne intégration des coupleurs il est nécessaire de s’assurer del’équilibrage des courants de chaque bras malgré une différence entre les paramètres. Ainsi cemanuscrit s’est axé vers la détermination de différentes méthodes de modélisation découplant lesystème permettant le maintien de l’égale répartition des courants en utilisant des différences derapports cycliques. Ces méthodes de modélisation ont été généralisées afin de réaliser unalgorithme permettant de générer des lois de commande quel que soit le nombre de cellules enparallèle. Dans une dernière partie ces lois de commande ont été testées sur un prototype en lesimplémentant sur FPGA afin de procéder à une vérification expérimental