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  • 1.
    Ahmed, Noman
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion. ABB Corporate Research.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Performance of the modular multilevel converter with redundant submodules2015In: IECON 2015 - 41st Annual Conference of the IEEE Industrial Electronics Society, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 3922-3927, article id 7392712Conference paper (Refereed)
    Abstract [en]

    The modular multilevel converter (MMC) is the state-of-the-art voltage-source converter (VSC) topology used for various power-conversion applications. In the MMC, submodule failures can occur due to various reasons. Therefore, additional submodules called the redundant submodules are included in the arms of the MMC to fulfill the fault-safe operation requirement. The performance of the MMC with redundant submodules has not been widely covered in the published literature. This paper investigates the performance of the MMC with redundant submodules in the arms. Two different control strategies are used and compared for integrating redundant submodules. The response of the MMC to a submodule failure for the two strategies is also studied. Moreover, the operation of the MMC with redundant submodules is validated experimentally using the converter prototype in the laboratory.

  • 2.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Control, Modulation and Implementation of Modular Multilevel Converters2011Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis deals with the analysis and control of the modular multilevel converter (M2C). The M2C is a promising converter technology for various high-voltage high-power applications. The reason to this is that low-distortion output quantities can be achieved with low average switching frequencies per switch and without output filters. With the M2C the output voltage has such a low harmonic content that high-power motors can be operated without any derating. However, the apparent large number of devices, requires more complex converter control techniques than a two-level counterpart. The internal control of an M2C must be designed so that the submodule capacitor voltages are equalized and stable independent of the loading conditions. An active submodule selection mechanism, included in the modulator, has been shown able to provide voltage sharing inside the converter arm. Apart from the individual capacitor voltage sharing, a strategy has to be designed to ensure that the total amount of energy stored inside the converter will always be controlled. Based on an analytical description of the converter, both feedback and open-loop control methods are suggested, simulated and experimentally evaluated, which will ensure stable operation in the whole operation range. The potential interaction of the internal controllers with an external motor current controller is also investigated. Both simulation and experimental results show that any interaction will not result in any problems neither for the converter nor for the motor control itself. A hardware implementation of a down-scaled 10 kVA three-phase laboratory prototype converter is performed, in order to evaluate the modeling and the controllers developed. The controller implementation is described in detail, as it exhibits remarkably fast response, and can be expanded up to an arbitrary number of levels. Therefore it can be used even by a full-scale converter implementation in the MW range.

  • 3.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    On the Internal Dynamics and AC-Motor Drive Application of Modular Multilevel Converters2014Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis is an effort to investigate the operation and the performanceof modular multilevel converters (M2Cs). Proven to be the most promisingtopology in high-voltage high-power applications, it is necessary to put aneffort in understanding the physical laws that govern the internal dynamicsof such converters, in order to design appropriate control methods. AlthoughM2Cs belong to the well-studied family of voltage-source converters (VSCs),and claim a modular structure, their control is significantly more complicatedcompared to two- or three-level VSCs, due to the fact that a much highernumber of switches and capacitors are needed in such a topology. This thesishighlights the important parameters that should be considered when designingthe control for an M2C, through analyzing its internal dynamics, and alsosuggests ways to control such converters ensuring stable operation withoutcompromising the performance of the converter.Special focus is given on ac motor-drive applications as they are very demandingand challenging for the converter performance. Interactions betweenthe internal dynamics and the dynamics of the driven motor are experimentallyinvestigated. The problem of operating the converter when connectedto a motor standing still is visited, even under the condition that a greatamount of torque and current are requested, in order to provide an idea forthe converter requirements under such conditions. Finally, an optimization ofthe converter operation is suggested in order to avoid overrating the convertercomponents in certain operation areas that this is possible.All analytical investigations presented in this thesis are confirmed by experimentalresults on a laboratory prototype converter, which was developedfor the purposes of this project. Experimental verification proves the validityof the theoretical investigations, as well as the correct performance of thecontrol methods developed during this project on a real, physical converter,hoping that the results of this thesis will be useful for large-scale implementations,in the mega- or even giga-watt power range.

  • 4.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    On Interaction between Internal Converter Dynamics and Current Control of High-Performance High-Power AC Motor Drives with Modular Multilevel Converters2010In: Proc. IEEE Energy Conversion Congress and Exposition (ECCE), 2010, p. 4293-4298Conference paper (Refereed)
    Abstract [en]

    The modular multilevel converter (M2C) is a promising converter technology for various high-voltage highpower applications. The reason to this is that low-distortion output quantities can be achieved with low average switching frequencies per switch and without output filters. With the M2C the output voltage has such a low harmonic content that highpower motors can be operated without any derating. However, the apparent large number of devices, requires more complex converter control techniques than a two-level counterpart. Even though there have been several ways suggested to control the converter itself, it is still a challenge to investigate the interaction of these controllers with an external motor current controller. It is shown in the paper that the anticipated interaction will not result in any problems neither for the converter nor for the motor control itself.

  • 5.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Mörée, Gustav
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Soulard, Juliette
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Experimental evaluation of the impact of harmonics on induction motors fed by modular multilevel converters2014In: Proceedings - 2014 International Conference on Electrical Machines, ICEM 2014, 2014, p. 768-775Conference paper (Refereed)
    Abstract [en]

    Inverter-based electrical-machine drives suffer from significantly higher losses compared to sinusoidal-supply-based alternatives, fed directly from the grid. Using multilevel inverters it becomes possible to partially mitigate the effects of the switched supply waveform, while keeping the advantages of variable-speed operation. This paper aims to evaluate the increase of the losses occurring in an induction motor (IM) fed by a modular multilevel converter (M2C), when compared to grid-connected operation, in order to evaluate the impact of the inverter-generated harmonics in the machine. It is confirmed that the losses created in the motor due to the harmonic content of the inverter-generated waveforms are very low, and almost equivalent to a purely sinusoidal supply. The investigation includes an analysis of the harmonic content from experimental waveforms obtained by an 11-kW IM laboratory setup, and it is further supported by measurements of the temperature rise in the IM-stator windings. It is concluded that the M2C could create the conditions even for high-power motors to be operated without any derating.

  • 6.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Siemaszko, Daniel
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Vasiladiotis, Michail
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Evaluation of Control and Modulation Methods forModular Multilevel Converters2010In: Proc. Int. Power Electronics Conf. (IPEC), 2010, p. 746-753Conference paper (Refereed)
    Abstract [en]

    The modular multilevel converter is a promising converter technology for various high-voltage high-power applications. Despite the apparent simplicity of the circuit, the inherent dynamics of the converter and the balancing of the sub-module capacitor voltages impose high requirements on the control system, which can be implemented in quite different ways. To illustrate this, and to provide a guidance for future research on the subject, this paper presents an evaluation of four different control and modulation methods. The investigation is based on experiments on a down-scaled 10 kVA converter having 10 submodules per phase leg. The main items to be investigated are dynamics within the sub-modules, arm voltages and circulating currents. It is found that the suggested open-loop control method provides the fastest arm-voltage response and that the balancing approach based on a sorting algorithm is substantially faster and less complicated to implement than the method using a dedicated voltage controller for each sub-module.

     

     

  • 7.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion. ABB, Sweden.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Global Asymptotic Stability of Modular Multilevel Converters2014In: IEEE transactions on industrial electronics (1982. Print), ISSN 0278-0046, E-ISSN 1557-9948, Vol. 61, no 2, p. 603-612Article in journal (Refereed)
    Abstract [en]

    Modular multilevel converters require that the controller is designed so that the submodule capacitor voltages are equalized and stable, independent of the loading conditions. Assuming that the individual capacitor-voltage sharing is managed effectively, an open-loop strategy has been designed to ensure that the total amount of energy stored inside the converter always will be controlled. This strategy, using the steady-state solutions of the dynamic equations for controlling the total stored energy in each converter arm, has proven to be effective. The intention of this paper is to explain in a rigorous way the mechanism behind the suggested strategy and to prove that, when this open-loop strategy is used, the system becomes globally asymptotically stable. Experimental verification on a three-phase 10-kVA prototype is presented.

  • 8.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Stability Analysis of Modular Multilevel Converters With Open-Loop Control2013In: 39th Annual Conference of the IEEE Industrial Electronics Society, IECON 2013, IEEE , 2013, p. 6316-6321Conference paper (Refereed)
    Abstract [en]

    Modular multilevel converters (M2Cs) require that the controller is designed so that the submodule capacitor voltages are equalized and stable, independent of the loading conditions. Provided that the individual capacitor voltage sharing is managed effectively, an open-loop strategy can been designed to ensure that the total amount of energy stored inside the converter always will be controlled. This strategy, using the steady-state solutions of the dynamic equations for controlling the total stored energy in each converter arm, has proven to be effective. The intention of this paper is to explain in a rigorous way the mechanism behind the suggested strategy, and to prove that, when this open-loop strategy is used, the system becomes globally asymptotically stable.

  • 9.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Optimal selection of the average capacitor voltage for modular multilevel converters2013In: 2013 IEEE Energy Conversion Congress and Exposition, ECCE 2013, IEEE , 2013, p. 3368-3374Conference paper (Refereed)
    Abstract [en]

    Variable-speed drives have reduced voltage requirements when operating below the base speed. In a modular-multilevel-converter-based (M2C-based) motor drive it is then possible to operate with reduced voltage in the submodule capacitors, than at the base speed. In this sense, a greater capacitor-voltage ripple can be accommodated, without exceeding the maximum peak-capacitor voltage. This paper presents an analytical investigation for the optimal selection of the average capacitor voltage for M2Cs, when the motor is operating with rated torque, below the base speed. This method does not require any power exchange between the converter arms, so it keeps the conduction losses at the minimum level. Additionally, the method decreases the switching losses, due to the decreased capacitor-voltage level. The overall ratings of the converter remain the same as in the base-speed operation. It is shown that this method can be applied at a speed range between the base speed and down to approximately one third of it, i.e, an operating range that covers the requirements for typical pump- and fan-type applications. The results obtained from the analytical investigation are experimentally verified on a down-scaled laboratory prototype M2C.

  • 10.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Optimal Selection of the Average Capacitor Voltage for Variable-Speed Drives With Modular Multilevel Converters2015In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 30, no 1, p. 227-234Article in journal (Refereed)
    Abstract [en]

    Variable-speed drives have reduced voltage requirementswhen operating below the base speed. In a modularmultilevel-converter-based (M2C-based) motor drive it is thenpossible to operate with reduced voltage in the submodulecapacitors, than at the base speed. In this sense, a greatercapacitor-voltage ripple can be accommodated, without exceedingthe maximum peak-capacitor voltage. This paper presents ananalytical investigation for the optimal selection of the averagecapacitor voltage for M2Cs, when the motor is operating withrated torque, below the base speed. This method does not requireany power exchange between the converter arms, so it keepsthe conduction losses at the minimum level. Additionally, themethod decreases the switching losses, due to the decreasedcapacitor-voltage level. The overall ratings of the converterremain the same as in the base-speed operation. It is shownthat this method can be applied at a speed range betweenthe base speed and down to approximately one third of it,i.e, an operating range that covers the requirements for typicalpump- and fan-type applications. The results obtained from theanalytical investigation are experimentally verified on a downscaledlaboratory prototype M2C.

  • 11.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    On Dynamics and Voltage Control of the Modular Multilevel Converter2009In: 2009 13th European Conference on Power Electronics and Applications, EPE '09, IEEE , 2009, p. 3353-3362Conference paper (Refereed)
    Abstract [en]

    This paper discusses the impact of modulation on stability issues of the Modular Multilevel Converter (M2C). The main idea is to describe the operation of this converter system mathematically, and suggest a control method that offers stable operation in the whole operation range. A possible approach is to assume a continuous model, where all the modules in each arm are represented by variable voltage sources. and as a result, all pulse width modulation effects are disregarded. After simulating this model and testing different control methods, useful conclusions on the operation of the M2C have been extracted. The control methods are then implemented on a model with discrete half-bridge modules, in order to compare the results and to validate continuous model approach. When assuring that this model functions as expected, the goal of this paper is to conclude into a self-stabilizing voltage controller. A controller is proposed, which eliminates circulating currents between the phase legs and balances the arm voltages regardless of the imposed alteranting current.

  • 12.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Modular multilevel converter AC motor drives with constant torque from zero to nominal speed2014In: IEEE transactions on industry applications, ISSN 0093-9994, E-ISSN 1939-9367, Vol. 50, no 3, p. 1982-1993Article in journal (Refereed)
    Abstract [en]

    Modular multilevel converters are shown to have a great potential in the area of medium-voltage drives. Low-distortion output quantities combined with low average switching frequencies for the semiconductor devices create an ideal combination for very high-efficiency drives. However, the large number of devices and capacitors that have to conduct the fundamental-frequency current require more complex converter control techniques than its two-level counterpart. Special care needs to be taken for starting and operation at low speeds, where the low-frequency current may cause significant unbalance between the submodule capacitor voltages and disturb the output waveforms. In this paper, principles for converter operation with high torque in the whole speed range are investigated. Experimental results from a down-scaled 12-kVA prototype converter running a loaded motor at various speeds between standstill and the rated speed are also provided.

  • 13.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Modular multilevel converter ac motor drives with constant torque form zero to nominal speed2012In: 2012 IEEE Energy Conversion Congress and Exposition, ECCE 2012, IEEE , 2012, p. 739-746Conference paper (Refereed)
    Abstract [en]

    Modular multilevel converters (M2Cs) are shown to have a great potential in the area of medium-voltage drives. Low-distortion output quantities, combined with low average switching frequencies for the semiconductor devices create the ideal combination for very high-efficiency drives, both from an electric motor and an inverter point of view. With M2Cs the output voltage has such a low harmonic content that high-power motors can be operated without any derating. However, the large number of devices and the existence of capacitors that have to conduct the fundamental frequency current, requires more complex converter control techniques than its two-level counterpart. Special care needs to be taken under starting and operation with low frequency, where the low-frequency current may cause significant unbalance between the submodule capacitor voltages, disturb the output waveforms, and eventually cause the converter to trip. In this paper, principles for converter operation with high torque in the whole speed range, from standstill to rated speed will be investigated. The converter-control method utilizes estimation of the capacitor voltage variation, based on equations describing steady-state conditions. Experimental results from a down-scaled 12 kVA prototype converter running a loaded motor from zero up to the rated speed are provided in the paper.

  • 14.
    Antonopoulos, Antonios
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Siemaszko, Daniel
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Vasiladiotis, Michail
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics.
    Inner Control of Modular Multilevel Converters - An Approach using Open-loop Estimation of Stored Energy2010In: Proc. Int. Power Electronics Conf. (IPEC), 2010, p. 1579-1585Conference paper (Refereed)
  • 15. Gregoire, Luc-Andre
    et al.
    Blanchette, Handy Fortin
    Li, Wei
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Al-Haddad, Kamal
    Modular Multilevel Converters Overvoltage Diagnosis and Remedial Strategy During Blocking Sequences2015In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 30, no 5, p. 2777-2785Article in journal (Refereed)
    Abstract [en]

    In this paper, the authors first highlight an existing overvoltage phenomenon that is inherent to the modular multilevel converter (MMC) topology. The latter occurs during the blocking sequences of semiconductor devices if the converter needs to be stopped due to circulating current, loss of control, or unexpected faults. An analysis based on time-domain expressions describing each operating sequence during normal and faulty blocking conditions is used to demonstrate the origin of this overvoltage. Thereafter, system behaviour is obtained when devices gating signals are withheld as well as the exact overvoltage cause. Real-time simulation, with submicrosecond time steps, and experimental results validate the overvoltage phenomena and the proposed remedial strategy to avoid uncontrolled faulty conditions.

  • 16.
    Harnefors, Lennart
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion. ABB, Sweden.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Global asymptotic stability of current-controlled modular multilevel converters2015In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 30, no 1, p. 249-258, article id 6883248Article in journal (Refereed)
    Abstract [en]

    In this paper, previously developed stability results for open-loop sum-capacitor-voltage control of modular multilevel converters are extended. To give improved damping, circulating-current feedback is included in the control law. With the output-current control loop and a first-order measurement lag taken into account, global asymptotic stability is proven. Careful consideration of the on-line sum-capacitor-voltage reference computation is given, since this is the most critical part of the control system.

  • 17. Harnefors, Lennart
    et al.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Global asymptotic stability of modular multilevel converters with measurement lag and circulating-current control2013In: Power Electronics and Applications (EPE), 2013, IEEE , 2013, p. 1-10Conference paper (Refereed)
    Abstract [en]

    In this paper, previously developed stability results for open-loop sum-capacitor-voltage control of modular multilevel converters are extended. To obtain improved damping, circulating-current feedback is included in the control law. A first-order measurement lag is added to this feedback. With these additions, global asymptotic stability is proven. Careful consideration of the online control-law computation is given, since this is the most critical part of the control system. Experimental results verify the theory.

  • 18.
    Harnefors, Lennart
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Dynamic Analysis of Modular Multilevel Converters2013In: IEEE transactions on industrial electronics (1982. Print), ISSN 0278-0046, E-ISSN 1557-9948, Vol. 60, no 7, p. 2526-2537Article in journal (Refereed)
    Abstract [en]

    Theory for the dynamics of modular multilevel converters is developed in this paper. It is shown that the sum capacitor voltage in each arm often can be considered instead of the individual capacitor voltages, thereby significantly reducing the complexity of the system model. Two selections of the so-called insertion indices, which both compensate for the sum-capacitor-voltage ripples, are considered. The dynamic systems which respectively result from these selections are analyzed. An effective dc-bus model, which takes into account the contribution from the submodule capacitors, is obtained. Finally, explicit formulas for the stationary sum-capacitor-voltage ripples are derived.

  • 19.
    Harnefors, Lennart
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Dynamic modeling of modular multilevel converters2011In: Proceedings of the 2011-14th European Conference on Power Electronics and Applications (EPE 2011) / [ed] EPE Association, 2011Conference paper (Refereed)
    Abstract [en]

    Theory for the dynamics of modular multilevel converters is developed in this paper. It is shown that the sum capacitor voltage in each arm often can be considered instead of the individual capacitor voltages, thereby significantly reducing the complexity of the system model. A selection of the so-called insertion indices, which compensates for the sum-capacitor-voltage ripples, is considered. The system which results for this selection is analyzed, and is shown to be asymptotically stable. Finally, explicit formulas for the steady-state sum-capacitor-voltage ripples are derived.

  • 20.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Hans-Peter, Nee
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Circulating current control in modular multilevel converters with fundamental switching frequency2012In: Conference Proceedings - 2012 IEEE 7th International Power Electronics and Motion Control Conference - ECCE Asia, IPEMC 2012, IEEE , 2012, p. 249-256Conference paper (Refereed)
    Abstract [en]

    The modular multilevel converter is a suitable topology for high-voltage applications as it combines very low switching frequency and excellent harmonic performance. In fact, it has been shown that the modular multilevel converter can even be operated at the fundamental switching frequency. If the circulating current is not controlled, a second-order harmonic component will appear. This component increases the resistive losses and the capacitor voltage ripple. Different control methods have been developed for eliminating this component in the circulating current. These are, however, based on continuous representations of the system and no control method suitable for fundamental switching frequency have yet been proposed. This paper presents a control method that combines a fundamental switching frequency scheme with an active control of the circulating current. The controller is verified experimentally on a 10-kVA laboratory prototype with five submodules per arm. The experimental validation is performed in both inverter and rectifier modes.

  • 21.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Capacitor Voltage Ripple Shaping in Modular Multilevel Converters Allowing for Operating Region Extension2011In: IECON 2011: 37TH ANNUAL CONFERENCE ON IEEE INDUSTRIAL ELECTRONICS SOCIETY, New York: IEEE , 2011, p. 4403-4408Conference paper (Refereed)
    Abstract [en]

    The second-order harmonic in the circulating current of a modular multilevel converter (M2C) influences the capacitor voltage ripple. If no measures are taken to control it, it is not possible to operate the converter with unity modulation index. An open-loop method that precalculates the instantaneous values of the circulating current and the capacitor voltages is used, in order to control the circulating current. A desired second-order harmonic is intentionally induced in the circulating current in order to make the peak of the capacitor voltage coincide with the maximum requested voltage, aiming either to extend the limits of the instantaneous available voltage or avoid unnecessarily high capacitor voltages. A method for numerical estimation of the appropriate amplitude and phase of the induced second-order harmonic is described. The method is experimentally evaluated on a three-phase down-scaled laboratory prototype. From the experiments it was found that significantly improved operating conditions could be obtained.

  • 22.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES).
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES).
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES). ABB, Sweden.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES).
    A new modulation method for the modular multilevel converter allowing fundamental switching frequency2011In: IEEE 8th International Conference on Power Electronics and ECCE Asia (ICPE & ECCE), 2011: 'Green World with Power Electronics' / [ed] IEEE, IEEE , 2011, p. 991-998Conference paper (Refereed)
    Abstract [en]

    This paper presents a new modulation method for the modular multilevel converter. The proposed method is based on a fixed pulse pattern where harmonic elimination methods can be applied. Modulation methods with harmonic elimination based on calculated pulse patterns have been presented for other multilevel topologies. However, similar modulation schemes have not yet been presented for the modular multilevel topology. In the proposed modulation method, the pulse pattern is chosen in such a way that the stored energy in each submodule remains stable. It is shown that this can be done at the fundamental switching frequency without measuring the capacitor voltages or using any other form of feedback control. Such a modulation scheme has not been presented before. The theoretical results are verified by both simulations and experimental results. The simulation results show successful operation at the fundamental switching frequency with a larger number of submodules. When a smaller number of submodules are used, harmonic elimination methods may be applied. This is verified experimentally on a converter with eight submodules per phase leg. The experimental results verify that stable operation can be maintained at the fundamental switching frequency while successfully eliminating the fifth harmonic in the ac-side voltage.

  • 23.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    A New Modulation Method for the Modular Multilevel Converter Allowing Fundamental Switching Frequency2012In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 27, no 8, p. 3482-3494Article in journal (Refereed)
    Abstract [en]

    This paper presents a new modulation method for the modular multilevel converter. The proposed method is based on a fixed pulse pattern where harmonic elimination methods can be applied. In the proposed modulation method, the pulse pattern is chosen in such a way that the stored energy in each submodule remains stable. It is shown that this can be done at the fundamental switching frequency without measuring the capacitor voltages or using any other form of feedback control. Such a modulation scheme has not been presented before. The theoretical results are verified by both simulations and experimental results. The simulation results show successful operation at the fundamental switching frequency with a larger number of submodules. When a smaller number of submodules are used, harmonic elimination methods may be applied. This is verified experimentally on a converter with eight submodules per phase leg. The experimental results verify that stable operation can be maintained at the fundamental switching frequency while successfully eliminating the fifth harmonic in the ac-side voltage.

  • 24.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Steady-State Analysis of Interaction Between Harmonic Components of Arm and Line Quantities of Modular Multilevel Converters2012In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 27, no 1, p. 57-68Article in journal (Refereed)
    Abstract [en]

    The fundamental frequency component in the arm currents of a modular multilevel converter is a necessity for the operation of the converter, as is the connection and bypassing of the submodules. Inevitably, this will cause alternating components in the capacitor voltages. This paper investigates how the arm currents and capacitor voltages interact when the submodules are connected and bypassed in a sinusoidal manner. Equations that describe the circulating current that is caused by the variations in the total inserted voltage are derived. Resonant frequencies are identified and the resonant behaviour is verified by experimental results. It is also found that the effective values of the arm resistance and submodule capacitances can be extracted from the measurements by least square fitting of the analytical expressions to the measured values. Finally, the analytical expression for the arm currents is verified by experimental results.

  • 25.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Machines and Power Electronics (closed 20110930).
    Controlling the ac-side voltage waveform in a modular multilevel converter with low energy-storage capability2011In: Proceedings of the 2011-14th European Conference on Power Electronics and Applications (EPE 2011) / [ed] EPE Association, 2011, p. 1-8Conference paper (Refereed)
    Abstract [en]

    During nominal operation of a modular multilevel converter the stored energy in the submodule capacitors will vary with time. If the energy storage capability of the capacitors is relatively small compared to the energy variations, this will give large variations in the capacitor voltages. These voltage variations will distort the ac-side voltage waveform and induce harmonic components in the current that is circulating between the dc terminals. The adverse effects on the ac-side voltage can be compensated for by identifying the factors that cause the distortion. It is shown that the compensation can be done by means of feed forward control while maintaining stable operating conditions and thus eliminating the need of additional stabilizing controllers. It is also shown that the voltage controller can be combined with a circulating current controller that removes the harmonics in the current that is circulating between the dc terminals. The functionality of the proposed controller is verified by both simulations and experimental results from a 10 kVA laboratory prototype. The simulations illustrate how the proposed controller successfully removes the distortion from the ac-side voltage waveform. The experimental results demonstrate stable operation during a step transient when the output power is increased by 125%.

  • 26.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Taffner, Franz
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    A submodule implementation for parallel connection of capacitors in modular multilevel converters2013In: Power Electronics and Applications (EPE), 2013 15th European Conference on, 2013Conference paper (Refereed)
    Abstract [en]

    The modular multilevel converter is a suitable converter topology for high-voltage high-power applications and consists of series-connected submodules. Typically, these submodules are half-bridges with dc capacitors. A voltage ripple in the submodule capacitors is inevitable due to the current flowing in the arms. The converter should therefore be controlled in such a way that the capacitor voltages are kept balanced and close to their nominal values over time. This paper presents a new submodule circuit which alleviates the balancing of the capacitor voltages. The proposed submodule circuit consists of two capacitors and eight switches, forming a three-level submodule. Ideally, the voltage and current rating of the switches can be chosen such that the combined power rating of the semiconductors is the same as for equivalent half-bridge submodules. The proposed submodule circuit provides the possibility of connecting the two capacitors in parallel when the intermediate voltage level is used. This will reduce the capacitor voltage ripple, especially at low switching frequencies and thus allow for a reduction of the size, weight, and cost of the submodule capacitors. The proposed submodule circuit is validated by both simulation results and experiments on a laboratory prototype. It is found that the parallel connection of the submodule capacitors will, in fact, significantly improve the balancing of the capacitor voltages.

  • 27.
    Ilves, Kalle
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Taffner, Franz
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Harnefors, Lennart
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    A Submodule Implementation for Parallel Connection of Capacitors in Modular Multilevel Converters2015In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 30, no 7, p. 3518-3527Article in journal (Refereed)
    Abstract [en]

    In modular multilevel converters there is a trade-off between the switching frequency and the voltage ripple in the submodule capacitors. The reason for this is that it becomes increasingly difficult to balance the capacitor voltages when the switching frequency is reduced. This paper presents a new submodule circuit which improves the balancing of the capacitor voltages at low switching frequencies. The proposed submodule circuit consists of two capacitors and eight switches, forming a three-level submodule. Ideally, the voltage and current ratings of the switches can be chosen such that the combined power rating of the semiconductors is the same as for the equivalent solution with conventional half-bridge submodules. The proposed submodule circuit provides the possibility of connecting the two capacitors in parallel when the intermediate voltage level is used. This will reduce the capacitor voltage ripple, especially at low switching frequencies and thus allow for a reduction of the size, weight, and cost of the submodule capacitors. The proposed submodule circuit is validated by both simulations and experimental results. It is found that the parallel connection of the submodule capacitors will, in fact, significantly improve the balancing of the capacitor voltages.

  • 28.
    Nee, Hans-Peter
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Rabkowski, Jacek
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Peftitsis, Dimosthenis
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Tolstoy, Georg
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Colmenares, Juan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Sadik, Diane
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Bakowski, Mietek
    Acreo Swedish ICT AB, Sweden.
    Lim, Jang-Kwon
    Acreo AB, Kista.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Zdanowski, Mariusz
    Warsaw University of Technology.
    High-Efficiency Power Conversion Using Silicon Carbide Power Electronics2013In: Proc. of International Conference on silicon carbide and related materials (ICSCRM) 2013, Miyazaki, Japan, Sept. 29–Oct. 4, 2013, Trans Tech Publications Inc., 2013, p. 1083-1088Conference paper (Refereed)
    Abstract [en]

    The message of this paper is that the silicon carbide power transistors of today are good enough to design converters with efficiencies and switching speeds beyond comparison with corresponding technology in silicon. This is the time to act. Only in the highest power range the devices are missing. Another important step towards high powers is to find new solutions for multi-chip circuit designs that are adapted to the high possible switching speeds of unipolar silicon carbide power transistors.

  • 29.
    Norrga, Staffan
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    The polyphase cascaded-cell DC/DC converter2013In: Energy Conversion Congress and Exposition (ECCE), 2013 IEEE, IEEE , 2013, p. 4082-4088Conference paper (Refereed)
    Abstract [en]

    This paper describes a new type of unisolated dc/dc converter employing cascaded converter cells, and its operation is analyzed. The topology and the operation of the converter have similarities with the modular multilevel converter for polyphase ac/dc conversion, but the ac voltages and currents are in this case only employed for redistributing power within the converter. It is shown how the nominal modulation indices for ac and dc voltage influence the semiconductor expenditure for the converter. A methodology for optimizing the design of the converter with regard to the required silicon area is devised. It is found that at voltage conversion ratios close to unity it is preferable to use a combination of full-bridge cells and half-bridge cells. Under such circumstances the proposed converter can offer lower semiconductor expenditure than a conventional buck converter.

  • 30.
    Peftitsis, Dimosthenis
    et al.
    KTH, School of Electrical Engineering (EES).
    Tolstoy, Georg
    KTH, School of Electrical Engineering (EES).
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES).
    Rabkowski, Jacek
    KTH, School of Electrical Engineering (EES).
    Lim, Jang-Kwon
    Acreo, Kista.
    Bakowski, Mietek
    Acreo, Kista.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES).
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES).
    High-power modular multilevel converters with SiC JFETs2010In: 2010 IEEE Energy Conversion Congress and Exposition (ECCE) / [ed] IEEE, IEEE , 2010, p. 2148-2155Conference paper (Refereed)
    Abstract [en]

    This paper studies the possibility of building a Modular Multilevel Converter (M2C) using Silicon Carbide (SiC) switches. The main focus is on a theoretical investigation of the conduction losses of such a converter and a comparison to a corresponding converter with silicon insulated gate bipolar transistors. Both SiC BJTs and JFETs are considered and compared in order to choose the most suitable technology. One of the sub-modules of a down-scaled 10 kVA prototype M2C is replaced with a sub-module with SiC JFETs without anti-parallel diodes. It is shown that diode-less operation is possible with the JFETs conducting in the negative direction, leaving the possibility to use the body diode during the switching transients. Experimental waveforms for the SiC sub-module verify the feasibility during normal steady-state operation. The loss estimation shows that a 300 MW M2C for high-voltage direct current transmission would potentially have an efficiency of approximately 99,8 % if equipped with future 3.3 kV 1.2 kA SiC JFETs.

  • 31.
    Peftitsis, Dimosthenis
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Tolstoy, Georg
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Rabkowski, Jacek
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Lim, Jang-Kwon
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Bakowski, Mietek
    Acreo AB.
    Ängquist, Lennart
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    High-Power Modular Multilevel Converters With SiC JFETs2012In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 27, no 1, p. 28-36Article in journal (Refereed)
    Abstract [en]

    This paper studies the possibility of building a modular multilevel converter (M2C) using silicon carbide (SiC) switches. The main focus is on a theoretical investigation of the conduction losses of such a converter and a comparison to a corresponding converter with silicon-insulated gate bipolar transistors. Both SiC BJTs and JFETs are considered and compared in order to choose the most suitable technology. One of the submodules of a down-scaled 3 kVA prototype M2C is replaced with a submodule with SiC JFETs without antiparallel diodes. It is shown that the diode-less operation is possible with the JFETs conducting in the negative direction, leaving the possibility to use the body diode during the switching transients. Experimental waveforms for the SiC submodule verify the feasibility during normal steady-state operation. The loss estimation shows that a 300 MW M2C for high-voltage direct current transmission would potentially have an efficiency of approximately 99.8% if equipped with future 3.3 kV 1.2 kA SiC JFETs.

  • 32.
    Ängquist, Lennart
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Norrga, Staffan
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Arm-current-based control of modular multilevel converters2013In: 2013 15th European Conference on Power Electronics and Applications, EPE 2013, IEEE , 2013, p. 6631999-Conference paper (Refereed)
    Abstract [en]

    Inner control of a Modular Multilevel Converter (M2C) based on direct tolerance-band modulation of the arm currents has been studied. This approach is attractive because it allows low switching frequency, directly provides the desired arm-current waveform and enables fast protective actions at the same time as the complexity of the over-all control system is reduced. Issues related to common-mode voltage are discussed and supporting PSCAD simulations are presented together with some results from experiments with a reduced-power prototype converter.

  • 33.
    Ängquist, Lennart
    et al.
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Antonopoulos, Antonios
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Siemaszko, Daniel
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Ilves, Kalle
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Vasiladiotis, Michail
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Nee, Hans-Peter
    KTH, School of Electrical Engineering (EES), Electrical Energy Conversion.
    Open-Loop Control of Modular Multilevel Converters Using Estimation of Stored Energy2011In: IEEE transactions on industry applications, ISSN 0093-9994, E-ISSN 1939-9367, Vol. 47, no 6, p. 2516-2524Article in journal (Refereed)
    Abstract [en]

    The internal control of a modular multilevel converter aims to equalize and stabilize the submodule capacitor voltages independent of the loading conditions. It has been shown that a submodule selection mechanism, included in the modulator, can provide voltage sharing inside the converter arm. Several procedures for controlling the total stored energy in each converter arm exist. A new approach is described in this paper. It is based on estimation of the stored energy in the arms by combining the converter electromotive force reference, the measured alternating output current, and the known direct voltage. No feedback controllers are used. Experimental verification on a three-phase 10 kVA prototype is presented along with the description of the new procedure.

1 - 33 of 33
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