Search

The stability of a power electronics system can be assessed by means of the impedance-based stability criterion. Impedance modeling is a useful tool to analyze the effect of different circuit parameters and control schemes on the behavior of a converter. Modeling the input impedance of a power electronics converter is often successful when having full knowledge of the converter topology, the circuit parameters, and the parameters and implementation of the control system. However, due to the proprietary nature of voltage source converter-based high voltage direct current systems, their exact control structure is often concealed. This complicates the calculation of the impedance of a modular multilevel converter, known for its complex internal dynamics. This paper proposes a method to estimate the impedance of a modular multilevel converter with partially black-boxed converter control. A discussion on partitioning the control system into open and closed parts is made, and the results are verified with simulations in time and frequency domains., QC 20230118

Future multivendor, and multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today's existing point-to-point HVDC links, control and harmonic interaction issues and instabilities related to the control and protection system of the converters have been reported. The converter control software is usually black-boxed and issues are therefore solved in close cooperation with the HVDC vendor. This paper discusses a possible paradigm shift in HVDC technology: an open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as well as future control-related problems, both in point-to-point links as well as in multiterminal, and multivendor HVDC grids., The Summary, Section 1, 2, 4, 4.4, 4.5, 5, and 6 are in major parts copied from [1].[1] I. Jahn, L. Bessegato, J. Björk, F. Hohn, S. Norrga, N. Svensson, K. Sharifabadi, and O. Despouys, “A Proposal for Open-Source HVDC Control,” in Proc. IEEE ISGT, Bucharest, 29 Sept.-2 Oct. 2019.QC 20201028

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model., QC 20201202

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., Not a duplicate with DiVA 1302284QC 20200217

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model., QC 20201202

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model., QC 20201202

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model., QC 20201202

The dc-side admittance of a modular multilevel converter can be used in assessing the stability of the dc system by means of impedance-based stability criteria. An accurate mathematical representation of the small-signal admittance can be given using harmonic linearization. To this end, the effect of the internal dynamics of the converter, e.g., the circulating current, the converter control scheme, and the controller parameters on the admittance of the converter should be analyzed. In this paper, a linear analytical model for the dc-side admittance of the converter is derived based on a combination of harmonic linearization and frequency-domain representation which incorporates different control schemes. Moreover, an admittance model is given for the closed-loop voltage control mode of the converter, where the ideal insertion indices are applied. To this end, the impact of an arm-balancing controller and its parameters on the dc-side admittance of the converter is investigated. Finally, experiments are carried out on a down-scaled prototype to validate the accuracy of the analytical model., QC 20201202

Future multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today’s existing point-to-point HVDC links, harmonic interaction issues and instabilities related to the controland protection system of the converters have been reported. The converter control software is usually black-boxed and problems are therefore solved in close cooperation with the HVDC vendor. This paper aims to provide a starting point for a discussion onan open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as wellas future control-related problems, both in point-to-point links as well as in multiterminal and multivendor HVDC grids., QC 20190917

Future meshed high-voltage direct current grids require modular multilevel converters with extended functionality. One of the most interesting new submodule topologies is the semi-full-bridge because it enables efficient handling of DC-side short circuits while having reduced power losses compared to an implementation with full-bridge submodules. However, the semi-full-bridge submodule requires the parallel connection of capacitors during normal operation which can cause a high redistribution current in case the voltages of the two submodule capacitors are not equal. The maximum voltage difference and resulting redistribution current have been studied analytically, by means of simulations and in a full-scale standalone submodule laboratory setup. The most critical parameter is the capacitance mismatch between the two capacitors. The experimental results from the full-scale prototype show that the redistribution current peaks at 500A if the voltage difference is 10V before paralleling and increases to 2500A if the difference is 40V. However, neglecting very unlikely cases, the maximum voltage difference predicted by simulations is not higher than 20-30V for the considered case. Among other measures, a balancing controller is proposed which reduces the voltage difference safely if a certain maximum value is surpassed. The operating principle of the controller is described in detail and verified experimentally on a down-scaled submodule within a modular multilevel converter prototype. It can be concluded that excessively high redistribution currents can be prevented. Consequently, they are no obstacle for using the semi-full-bridge submodule in future HVDC converters., QC 20190107

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., QC 20190404

The stability of a modular multilevel converter connected to an ac grid can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. The converter control parameters have a strong impact on the admittance and they can be adjusted for achieving system stability. This paper focuses on the admittance-shaping effect produced by different current-control schemes, either designed on a per-phase basis or in the $dq$ frame using space vectors. A linear analytical model of the converter ac-side admittance is developed, including the different current-control schemes and the phase-locked loop. Different solutions for computing the insertion indices are also analyzed, showing that for a closed-loop scheme a compact expression of the admittance is obtained. The impact of the control parameters on the admittance is discussed and verified experimentally, giving guidelines for designing the system in terms of stability. Moreover, recommendations on whether a simplified admittance expression could be used instead of the detailed model are given. The findings from the admittance-shaping analysis are used to recreate a grid-converter system whose stability is determined by the control parameters. The developed admittance model is then used in this experimental case study, showing that the stability of the interconnected system can be assessed using the Nyquist stability criterion., QC 20181113

Modular multilevel converters (MMCs) have recently become the state-of-the-art solution for various grid-connected applications, such as high-voltage direct current (HVDC) systems and flexible alternating current transmission systems (FACTS). Modularity, scalability, low power losses, and low harmonic distortion are the outstanding properties that make MMCs a key technology for a sustainable future. The main objective of this thesis is the modeling of grid-connected MMCs for stability analysis. The stability of the interconnected system, formed by the converter and the ac grid, can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. Therefore, a method for the calculation of the ac-side admittance of MMCs is developed. This method overcomes the nonlinearities of the converter dynamics and it can be easily adapted to different applications. Moreover, the effects of different control schemes on the MMC ac-side admittance are studied, showing how the converter admittance can be reshaped. This is a useful tool for system design, because it shows how control parameters can be selected to avoid undesired grid-converter interactions. This thesis also studies ac/ac MMCs for railway power supplies, which are used in countries with a low-frequency railway grid, such as Germany (16.7 Hz) and Sweden (16 2/3 Hz). A hierarchical control scheme for these converters is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. For computing the insertion indices, an open-loop scheme with sum capacitor voltage estimation is applied to the ac/ac MMC. Lyapunov stability theory is used to prove the asymptotic stability of the converter operated with the proposed control method. This specific open, Modulära multinivåomvandlare (MMC) har under senare år utvecklats till den mest relevanta lösningen för olika tillämpningar där kraftelektroniska omriktare är anslutna till växelströmsnät, såsom system för högspänd likströmsöverföring (HVDC) och flexibla system för överföring av växelström (FACTS). Den modulära uppbyggnaden, skalbarhet, låga förluster och låga övertoner är egenskaperna som gör MMC omriktare till en central komponent för framtida hållbara elenergisystem. Huvudsyftet med denna avhandling är modellering av nätanslutna omvandlare av typ MMC för stabilitetsanalys. Stabiliteten för systemet omvandlare och nät, kan bedömas genom att analysera omvandlarens växelströmssidiga admittans i förhållande till nätimpedansen. En metod har därför utvecklats för att beräkna den modulära multinivåomvandlarens admittans. Metoden tar hänsyn till olinjäriteter i omvandlarens dynamik och kan enkelt anpassas till olika tillämpningar. Därutöver studeras effekterna av hur olika reglersystem påverkar omvandlarens admittans och hur omvandlarens admittans kan omformas. Denna möjlighet är användbar vid utformning av en systemlösning, eftersom reglerparametrarna kan väljas för att undvika oönskade störningar mellan nät och omriktare. I avhandlingen undersöks även modulära ac/ac-omvandlare för järnvägsbanmatning. Dessa används i länder med lågfrekvensbanmatning så som Tysk-land med 16,7 Hz och Sverige med 16 2/3 Hz. Ett hierarkiskt reglersystem har utvecklats och utvärderats med avseende på järnvägstillämpningens specifika krav och dess driftsförhållanden. Admittansmodeller har utvecklats, för dessa modulära ac/ac-omvandlare, som visar hur det föreslagna hierarkiska reglersystemet påverkar omvandlarens admittans på både trefas- och enfassidan. För att beräkna ac/ac-omvandlarens inkopplingsförhållande appliceras en öppen styrning som estimerar summan av submodulernas kondensatorspänningar. Lyapunovs stabilitetsteori har använts för att bevisa den asymptotiska stabiliteten hos om, QC 20190405

Future multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today’s existing point-to-point HVDC links, harmonic interaction issues and instabilities related to the controland protection system of the converters have been reported. The converter control software is usually black-boxed and problems are therefore solved in close cooperation with the HVDC vendor. This paper aims to provide a starting point for a discussion onan open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as wellas future control-related problems, both in point-to-point links as well as in multiterminal and multivendor HVDC grids., QC 20190917

Future meshed high-voltage direct current grids require modular multilevel converters with extended functionality. One of the most interesting new submodule topologies is the semi-full-bridge because it enables efficient handling of DC-side short circuits while having reduced power losses compared to an implementation with full-bridge submodules. However, the semi-full-bridge submodule requires the parallel connection of capacitors during normal operation which can cause a high redistribution current in case the voltages of the two submodule capacitors are not equal. The maximum voltage difference and resulting redistribution current have been studied analytically, by means of simulations and in a full-scale standalone submodule laboratory setup. The most critical parameter is the capacitance mismatch between the two capacitors. The experimental results from the full-scale prototype show that the redistribution current peaks at 500A if the voltage difference is 10V before paralleling and increases to 2500A if the difference is 40V. However, neglecting very unlikely cases, the maximum voltage difference predicted by simulations is not higher than 20-30V for the considered case. Among other measures, a balancing controller is proposed which reduces the voltage difference safely if a certain maximum value is surpassed. The operating principle of the controller is described in detail and verified experimentally on a down-scaled submodule within a modular multilevel converter prototype. It can be concluded that excessively high redistribution currents can be prevented. Consequently, they are no obstacle for using the semi-full-bridge submodule in future HVDC converters., QC 20190107

Future meshed high-voltage direct current grids require modular multilevel converters with extended functionality. One of the most interesting new submodule topologies is the semi-full-bridge because it enables efficient handling of DC-side short circuits while having reduced power losses compared to an implementation with full-bridge submodules. However, the semi-full-bridge submodule requires the parallel connection of capacitors during normal operation which can cause a high redistribution current in case the voltages of the two submodule capacitors are not equal. The maximum voltage difference and resulting redistribution current have been studied analytically, by means of simulations and in a full-scale standalone submodule laboratory setup. The most critical parameter is the capacitance mismatch between the two capacitors. The experimental results from the full-scale prototype show that the redistribution current peaks at 500A if the voltage difference is 10V before paralleling and increases to 2500A if the difference is 40V. However, neglecting very unlikely cases, the maximum voltage difference predicted by simulations is not higher than 20-30V for the considered case. Among other measures, a balancing controller is proposed which reduces the voltage difference safely if a certain maximum value is surpassed. The operating principle of the controller is described in detail and verified experimentally on a down-scaled submodule within a modular multilevel converter prototype. It can be concluded that excessively high redistribution currents can be prevented. Consequently, they are no obstacle for using the semi-full-bridge submodule in future HVDC converters., QC 20190107

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., QC 20190404

Modular multilevel converters (MMCs) have recently become the state-of-the-art solution for various grid-connected applications, such as high-voltage direct current (HVDC) systems and flexible alternating current transmission systems (FACTS). Modularity, scalability, low power losses, and low harmonic distortion are the outstanding properties that make MMCs a key technology for a sustainable future. The main objective of this thesis is the modeling of grid-connected MMCs for stability analysis. The stability of the interconnected system, formed by the converter and the ac grid, can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. Therefore, a method for the calculation of the ac-side admittance of MMCs is developed. This method overcomes the nonlinearities of the converter dynamics and it can be easily adapted to different applications. Moreover, the effects of different control schemes on the MMC ac-side admittance are studied, showing how the converter admittance can be reshaped. This is a useful tool for system design, because it shows how control parameters can be selected to avoid undesired grid-converter interactions. This thesis also studies ac/ac MMCs for railway power supplies, which are used in countries with a low-frequency railway grid, such as Germany (16.7 Hz) and Sweden (16 2/3 Hz). A hierarchical control scheme for these converters is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. For computing the insertion indices, an open-loop scheme with sum capacitor voltage estimation is applied to the ac/ac MMC. Lyapunov stability theory is used to prove the asymptotic stability of the converter operated with the proposed control method. This specific open, Modulära multinivåomvandlare (MMC) har under senare år utvecklats till den mest relevanta lösningen för olika tillämpningar där kraftelektroniska omriktare är anslutna till växelströmsnät, såsom system för högspänd likströmsöverföring (HVDC) och flexibla system för överföring av växelström (FACTS). Den modulära uppbyggnaden, skalbarhet, låga förluster och låga övertoner är egenskaperna som gör MMC omriktare till en central komponent för framtida hållbara elenergisystem. Huvudsyftet med denna avhandling är modellering av nätanslutna omvandlare av typ MMC för stabilitetsanalys. Stabiliteten för systemet omvandlare och nät, kan bedömas genom att analysera omvandlarens växelströmssidiga admittans i förhållande till nätimpedansen. En metod har därför utvecklats för att beräkna den modulära multinivåomvandlarens admittans. Metoden tar hänsyn till olinjäriteter i omvandlarens dynamik och kan enkelt anpassas till olika tillämpningar. Därutöver studeras effekterna av hur olika reglersystem påverkar omvandlarens admittans och hur omvandlarens admittans kan omformas. Denna möjlighet är användbar vid utformning av en systemlösning, eftersom reglerparametrarna kan väljas för att undvika oönskade störningar mellan nät och omriktare. I avhandlingen undersöks även modulära ac/ac-omvandlare för järnvägsbanmatning. Dessa används i länder med lågfrekvensbanmatning så som Tysk-land med 16,7 Hz och Sverige med 16 2/3 Hz. Ett hierarkiskt reglersystem har utvecklats och utvärderats med avseende på järnvägstillämpningens specifika krav och dess driftsförhållanden. Admittansmodeller har utvecklats, för dessa modulära ac/ac-omvandlare, som visar hur det föreslagna hierarkiska reglersystemet påverkar omvandlarens admittans på både trefas- och enfassidan. För att beräkna ac/ac-omvandlarens inkopplingsförhållande appliceras en öppen styrning som estimerar summan av submodulernas kondensatorspänningar. Lyapunovs stabilitetsteori har använts för att bevisa den asymptotiska stabiliteten hos om, QC 20190405

The stability of a modular multilevel converter connected to an ac grid can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. The converter control parameters have a strong impact on the admittance and they can be adjusted for achieving system stability. This paper focuses on the admittance-shaping effect produced by different current-control schemes, either designed on a per-phase basis or in the $dq$ frame using space vectors. A linear analytical model of the converter ac-side admittance is developed, including the different current-control schemes and the phase-locked loop. Different solutions for computing the insertion indices are also analyzed, showing that for a closed-loop scheme a compact expression of the admittance is obtained. The impact of the control parameters on the admittance is discussed and verified experimentally, giving guidelines for designing the system in terms of stability. Moreover, recommendations on whether a simplified admittance expression could be used instead of the detailed model are given. The findings from the admittance-shaping analysis are used to recreate a grid-converter system whose stability is determined by the control parameters. The developed admittance model is then used in this experimental case study, showing that the stability of the interconnected system can be assessed using the Nyquist stability criterion., QC 20181113

The stability of a modular multilevel converter connected to an ac grid can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. The converter control parameters have a strong impact on the admittance and they can be adjusted for achieving system stability. This paper focuses on the admittance-shaping effect produced by different current-control schemes, either designed on a per-phase basis or in the $dq$ frame using space vectors. A linear analytical model of the converter ac-side admittance is developed, including the different current-control schemes and the phase-locked loop. Different solutions for computing the insertion indices are also analyzed, showing that for a closed-loop scheme a compact expression of the admittance is obtained. The impact of the control parameters on the admittance is discussed and verified experimentally, giving guidelines for designing the system in terms of stability. Moreover, recommendations on whether a simplified admittance expression could be used instead of the detailed model are given. The findings from the admittance-shaping analysis are used to recreate a grid-converter system whose stability is determined by the control parameters. The developed admittance model is then used in this experimental case study, showing that the stability of the interconnected system can be assessed using the Nyquist stability criterion., QC 20181113

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., QC 20190404

The stability of a modular multilevel converter connected to an ac grid can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. The converter control parameters have a strong impact on the admittance and they can be adjusted for achieving system stability. This paper focuses on the admittance-shaping effect produced by different current-control schemes, either designed on a per-phase basis or in the $dq$ frame using space vectors. A linear analytical model of the converter ac-side admittance is developed, including the different current-control schemes and the phase-locked loop. Different solutions for computing the insertion indices are also analyzed, showing that for a closed-loop scheme a compact expression of the admittance is obtained. The impact of the control parameters on the admittance is discussed and verified experimentally, giving guidelines for designing the system in terms of stability. Moreover, recommendations on whether a simplified admittance expression could be used instead of the detailed model are given. The findings from the admittance-shaping analysis are used to recreate a grid-converter system whose stability is determined by the control parameters. The developed admittance model is then used in this experimental case study, showing that the stability of the interconnected system can be assessed using the Nyquist stability criterion., QC 20181113

Future multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today’s existing point-to-point HVDC links, harmonic interaction issues and instabilities related to the controland protection system of the converters have been reported. The converter control software is usually black-boxed and problems are therefore solved in close cooperation with the HVDC vendor. This paper aims to provide a starting point for a discussion onan open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as wellas future control-related problems, both in point-to-point links as well as in multiterminal and multivendor HVDC grids., QC 20190917

Future meshed high-voltage direct current grids require modular multilevel converters with extended functionality. One of the most interesting new submodule topologies is the semi-full-bridge because it enables efficient handling of DC-side short circuits while having reduced power losses compared to an implementation with full-bridge submodules. However, the semi-full-bridge submodule requires the parallel connection of capacitors during normal operation which can cause a high redistribution current in case the voltages of the two submodule capacitors are not equal. The maximum voltage difference and resulting redistribution current have been studied analytically, by means of simulations and in a full-scale standalone submodule laboratory setup. The most critical parameter is the capacitance mismatch between the two capacitors. The experimental results from the full-scale prototype show that the redistribution current peaks at 500A if the voltage difference is 10V before paralleling and increases to 2500A if the difference is 40V. However, neglecting very unlikely cases, the maximum voltage difference predicted by simulations is not higher than 20-30V for the considered case. Among other measures, a balancing controller is proposed which reduces the voltage difference safely if a certain maximum value is surpassed. The operating principle of the controller is described in detail and verified experimentally on a down-scaled submodule within a modular multilevel converter prototype. It can be concluded that excessively high redistribution currents can be prevented. Consequently, they are no obstacle for using the semi-full-bridge submodule in future HVDC converters., QC 20190107

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., QC 20190404

Modular multilevel converters (MMCs) have recently become the state-of-the-art solution for various grid-connected applications, such as high-voltage direct current (HVDC) systems and flexible alternating current transmission systems (FACTS). Modularity, scalability, low power losses, and low harmonic distortion are the outstanding properties that make MMCs a key technology for a sustainable future. The main objective of this thesis is the modeling of grid-connected MMCs for stability analysis. The stability of the interconnected system, formed by the converter and the ac grid, can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. Therefore, a method for the calculation of the ac-side admittance of MMCs is developed. This method overcomes the nonlinearities of the converter dynamics and it can be easily adapted to different applications. Moreover, the effects of different control schemes on the MMC ac-side admittance are studied, showing how the converter admittance can be reshaped. This is a useful tool for system design, because it shows how control parameters can be selected to avoid undesired grid-converter interactions. This thesis also studies ac/ac MMCs for railway power supplies, which are used in countries with a low-frequency railway grid, such as Germany (16.7 Hz) and Sweden (16 2/3 Hz). A hierarchical control scheme for these converters is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. For computing the insertion indices, an open-loop scheme with sum capacitor voltage estimation is applied to the ac/ac MMC. Lyapunov stability theory is used to prove the asymptotic stability of the converter operated with the proposed control method. This specific open, Modulära multinivåomvandlare (MMC) har under senare år utvecklats till den mest relevanta lösningen för olika tillämpningar där kraftelektroniska omriktare är anslutna till växelströmsnät, såsom system för högspänd likströmsöverföring (HVDC) och flexibla system för överföring av växelström (FACTS). Den modulära uppbyggnaden, skalbarhet, låga förluster och låga övertoner är egenskaperna som gör MMC omriktare till en central komponent för framtida hållbara elenergisystem. Huvudsyftet med denna avhandling är modellering av nätanslutna omvandlare av typ MMC för stabilitetsanalys. Stabiliteten för systemet omvandlare och nät, kan bedömas genom att analysera omvandlarens växelströmssidiga admittans i förhållande till nätimpedansen. En metod har därför utvecklats för att beräkna den modulära multinivåomvandlarens admittans. Metoden tar hänsyn till olinjäriteter i omvandlarens dynamik och kan enkelt anpassas till olika tillämpningar. Därutöver studeras effekterna av hur olika reglersystem påverkar omvandlarens admittans och hur omvandlarens admittans kan omformas. Denna möjlighet är användbar vid utformning av en systemlösning, eftersom reglerparametrarna kan väljas för att undvika oönskade störningar mellan nät och omriktare. I avhandlingen undersöks även modulära ac/ac-omvandlare för järnvägsbanmatning. Dessa används i länder med lågfrekvensbanmatning så som Tysk-land med 16,7 Hz och Sverige med 16 2/3 Hz. Ett hierarkiskt reglersystem har utvecklats och utvärderats med avseende på järnvägstillämpningens specifika krav och dess driftsförhållanden. Admittansmodeller har utvecklats, för dessa modulära ac/ac-omvandlare, som visar hur det föreslagna hierarkiska reglersystemet påverkar omvandlarens admittans på både trefas- och enfassidan. För att beräkna ac/ac-omvandlarens inkopplingsförhållande appliceras en öppen styrning som estimerar summan av submodulernas kondensatorspänningar. Lyapunovs stabilitetsteori har använts för att bevisa den asymptotiska stabiliteten hos om, QC 20190405

The stability of a modular multilevel converter connected to an ac grid can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. The converter control parameters have a strong impact on the admittance and they can be adjusted for achieving system stability. This paper focuses on the admittance-shaping effect produced by different current-control schemes, either designed on a per-phase basis or in the $dq$ frame using space vectors. A linear analytical model of the converter ac-side admittance is developed, including the different current-control schemes and the phase-locked loop. Different solutions for computing the insertion indices are also analyzed, showing that for a closed-loop scheme a compact expression of the admittance is obtained. The impact of the control parameters on the admittance is discussed and verified experimentally, giving guidelines for designing the system in terms of stability. Moreover, recommendations on whether a simplified admittance expression could be used instead of the detailed model are given. The findings from the admittance-shaping analysis are used to recreate a grid-converter system whose stability is determined by the control parameters. The developed admittance model is then used in this experimental case study, showing that the stability of the interconnected system can be assessed using the Nyquist stability criterion., QC 20181113

Modular multilevel converters (MMCs) have recently become the state-of-the-art solution for various grid-connected applications, such as high-voltage direct current (HVDC) systems and flexible alternating current transmission systems (FACTS). Modularity, scalability, low power losses, and low harmonic distortion are the outstanding properties that make MMCs a key technology for a sustainable future. The main objective of this thesis is the modeling of grid-connected MMCs for stability analysis. The stability of the interconnected system, formed by the converter and the ac grid, can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. Therefore, a method for the calculation of the ac-side admittance of MMCs is developed. This method overcomes the nonlinearities of the converter dynamics and it can be easily adapted to different applications. Moreover, the effects of different control schemes on the MMC ac-side admittance are studied, showing how the converter admittance can be reshaped. This is a useful tool for system design, because it shows how control parameters can be selected to avoid undesired grid-converter interactions. This thesis also studies ac/ac MMCs for railway power supplies, which are used in countries with a low-frequency railway grid, such as Germany (16.7 Hz) and Sweden (16 2/3 Hz). A hierarchical control scheme for these converters is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. For computing the insertion indices, an open-loop scheme with sum capacitor voltage estimation is applied to the ac/ac MMC. Lyapunov stability theory is used to prove the asymptotic stability of the converter operated with the proposed control method. This specific open, Modulära multinivåomvandlare (MMC) har under senare år utvecklats till den mest relevanta lösningen för olika tillämpningar där kraftelektroniska omriktare är anslutna till växelströmsnät, såsom system för högspänd likströmsöverföring (HVDC) och flexibla system för överföring av växelström (FACTS). Den modulära uppbyggnaden, skalbarhet, låga förluster och låga övertoner är egenskaperna som gör MMC omriktare till en central komponent för framtida hållbara elenergisystem. Huvudsyftet med denna avhandling är modellering av nätanslutna omvandlare av typ MMC för stabilitetsanalys. Stabiliteten för systemet omvandlare och nät, kan bedömas genom att analysera omvandlarens växelströmssidiga admittans i förhållande till nätimpedansen. En metod har därför utvecklats för att beräkna den modulära multinivåomvandlarens admittans. Metoden tar hänsyn till olinjäriteter i omvandlarens dynamik och kan enkelt anpassas till olika tillämpningar. Därutöver studeras effekterna av hur olika reglersystem påverkar omvandlarens admittans och hur omvandlarens admittans kan omformas. Denna möjlighet är användbar vid utformning av en systemlösning, eftersom reglerparametrarna kan väljas för att undvika oönskade störningar mellan nät och omriktare. I avhandlingen undersöks även modulära ac/ac-omvandlare för järnvägsbanmatning. Dessa används i länder med lågfrekvensbanmatning så som Tysk-land med 16,7 Hz och Sverige med 16 2/3 Hz. Ett hierarkiskt reglersystem har utvecklats och utvärderats med avseende på järnvägstillämpningens specifika krav och dess driftsförhållanden. Admittansmodeller har utvecklats, för dessa modulära ac/ac-omvandlare, som visar hur det föreslagna hierarkiska reglersystemet påverkar omvandlarens admittans på både trefas- och enfassidan. För att beräkna ac/ac-omvandlarens inkopplingsförhållande appliceras en öppen styrning som estimerar summan av submodulernas kondensatorspänningar. Lyapunovs stabilitetsteori har använts för att bevisa den asymptotiska stabiliteten hos om, QC 20190405

Modular multilevel converters (MMCs) have recently become the state-of-the-art solution for various grid-connected applications, such as high-voltage direct current (HVDC) systems and flexible alternating current transmission systems (FACTS). Modularity, scalability, low power losses, and low harmonic distortion are the outstanding properties that make MMCs a key technology for a sustainable future. The main objective of this thesis is the modeling of grid-connected MMCs for stability analysis. The stability of the interconnected system, formed by the converter and the ac grid, can be assessed by analyzing the converter ac-side admittance in relation to the grid impedance. Therefore, a method for the calculation of the ac-side admittance of MMCs is developed. This method overcomes the nonlinearities of the converter dynamics and it can be easily adapted to different applications. Moreover, the effects of different control schemes on the MMC ac-side admittance are studied, showing how the converter admittance can be reshaped. This is a useful tool for system design, because it shows how control parameters can be selected to avoid undesired grid-converter interactions. This thesis also studies ac/ac MMCs for railway power supplies, which are used in countries with a low-frequency railway grid, such as Germany (16.7 Hz) and Sweden (16 2/3 Hz). A hierarchical control scheme for these converters is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. For computing the insertion indices, an open-loop scheme with sum capacitor voltage estimation is applied to the ac/ac MMC. Lyapunov stability theory is used to prove the asymptotic stability of the converter operated with the proposed control method. This specific open, Modulära multinivåomvandlare (MMC) har under senare år utvecklats till den mest relevanta lösningen för olika tillämpningar där kraftelektroniska omriktare är anslutna till växelströmsnät, såsom system för högspänd likströmsöverföring (HVDC) och flexibla system för överföring av växelström (FACTS). Den modulära uppbyggnaden, skalbarhet, låga förluster och låga övertoner är egenskaperna som gör MMC omriktare till en central komponent för framtida hållbara elenergisystem. Huvudsyftet med denna avhandling är modellering av nätanslutna omvandlare av typ MMC för stabilitetsanalys. Stabiliteten för systemet omvandlare och nät, kan bedömas genom att analysera omvandlarens växelströmssidiga admittans i förhållande till nätimpedansen. En metod har därför utvecklats för att beräkna den modulära multinivåomvandlarens admittans. Metoden tar hänsyn till olinjäriteter i omvandlarens dynamik och kan enkelt anpassas till olika tillämpningar. Därutöver studeras effekterna av hur olika reglersystem påverkar omvandlarens admittans och hur omvandlarens admittans kan omformas. Denna möjlighet är användbar vid utformning av en systemlösning, eftersom reglerparametrarna kan väljas för att undvika oönskade störningar mellan nät och omriktare. I avhandlingen undersöks även modulära ac/ac-omvandlare för järnvägsbanmatning. Dessa används i länder med lågfrekvensbanmatning så som Tysk-land med 16,7 Hz och Sverige med 16 2/3 Hz. Ett hierarkiskt reglersystem har utvecklats och utvärderats med avseende på järnvägstillämpningens specifika krav och dess driftsförhållanden. Admittansmodeller har utvecklats, för dessa modulära ac/ac-omvandlare, som visar hur det föreslagna hierarkiska reglersystemet påverkar omvandlarens admittans på både trefas- och enfassidan. För att beräkna ac/ac-omvandlarens inkopplingsförhållande appliceras en öppen styrning som estimerar summan av submodulernas kondensatorspänningar. Lyapunovs stabilitetsteori har använts för att bevisa den asymptotiska stabiliteten hos om, QC 20190405

Future multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today’s existing point-to-point HVDC links, harmonic interaction issues and instabilities related to the controland protection system of the converters have been reported. The converter control software is usually black-boxed and problems are therefore solved in close cooperation with the HVDC vendor. This paper aims to provide a starting point for a discussion onan open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as wellas future control-related problems, both in point-to-point links as well as in multiterminal and multivendor HVDC grids., QC 20190917

Future meshed high-voltage direct current grids require modular multilevel converters with extended functionality. One of the most interesting new submodule topologies is the semi-full-bridge because it enables efficient handling of DC-side short circuits while having reduced power losses compared to an implementation with full-bridge submodules. However, the semi-full-bridge submodule requires the parallel connection of capacitors during normal operation which can cause a high redistribution current in case the voltages of the two submodule capacitors are not equal. The maximum voltage difference and resulting redistribution current have been studied analytically, by means of simulations and in a full-scale standalone submodule laboratory setup. The most critical parameter is the capacitance mismatch between the two capacitors. The experimental results from the full-scale prototype show that the redistribution current peaks at 500A if the voltage difference is 10V before paralleling and increases to 2500A if the difference is 40V. However, neglecting very unlikely cases, the maximum voltage difference predicted by simulations is not higher than 20-30V for the considered case. Among other measures, a balancing controller is proposed which reduces the voltage difference safely if a certain maximum value is surpassed. The operating principle of the controller is described in detail and verified experimentally on a down-scaled submodule within a modular multilevel converter prototype. It can be concluded that excessively high redistribution currents can be prevented. Consequently, they are no obstacle for using the semi-full-bridge submodule in future HVDC converters., QC 20190107

Modular multilevel converters (MMCs) can be configured to perform ac/ac conversion, which makes them suitable as railway power supplies. In this paper, a hierarchical control scheme for ac/ac MMCs for railway power supplies is devised and evaluated, considering the requirements and the operating conditions specific to this application. Furthermore, admittance models of the ac/ac MMC are developed, showing how the suggested hierarchical control scheme affects the three-phase and the single-phase side admittances of the converter. These models allow for analyzing the stability of the interconnected system using the impedance-based stability criterion and the passivity-based stability assessment. Finally, the findings presented in this paper are validated experimentally, using a down-scaled MMC., QC 20190404

Future multiterminal high-voltage direct-current (HVDC) grids are considered an enabling technology to efficiently integrate large amounts of renewable energy into the existing grid. However, already in today’s existing point-to-point HVDC links, harmonic interaction issues and instabilities related to the controland protection system of the converters have been reported. The converter control software is usually black-boxed and problems are therefore solved in close cooperation with the HVDC vendor. This paper aims to provide a starting point for a discussion onan open-source HVDC control system. In particular, it covers the control design including technical and non-technical aspects. The open-source approach can be useful to solve current as wellas future control-related problems, both in point-to-point links as well as in multiterminal and multivendor HVDC grids., QC 20190917

As modular multilevel converters gradually become the preferred topology for many high-voltage andhigh-power applications, they are widely studied among researchers, who need experimental results tovalidate their studies. This paper discusses the design of a down-scaled modular multilevel converterprototype for research purposes, equipped with 30 full-bridge submodules and 10 kW rating. The designof this prototype is aimed at safety, flexibility, orderliness, and compactness. The challenges posed by theimplementation of the converter prototype are examined, discussing the design of the prototype structure,the communication scheme, the full-bridge submodules, and the control hierarchy. The control systemis based on Xilinx Zynq system-on-chip, which integrates programmable logic and processing system,allowing for extensive computational capability as well as simple reconfiguration. Experimental resultsshowing the prototype in operation at nominal ratings are presented along with the devised graphical userinterface., QC 20181128

Connecting a modular multilevel converter to anac grid may cause stability issues, which can be assessed byanalyzing the converter ac-side admittance in relation to the gridimpedance. This paper presents a method for calculating theac-side admittance of modular multilevel converters, analyzingthe main frequency components of the converter variables individually.Starting from a time-averaged model of the converter,the proposed method performs a linearization in the frequencydomain, which overcomes the inherent nonlinearities of theconverter internal dynamics and the phase-locked loop usedin the control. The ac-side admittance obtained analytically isfirstly validated by simulations against a nonlinear time-averagedmodel of the modular multilevel converter. The tradeoff posedby complexity of the method and the accuracy of the result isdiscussed and the magnitude of the individual frequency componentsis shown. Finally, experiments on a down-scaled prototypeare performed to validate this study and the simplification onwhich it is based., QC 20181113

Connecting a modular multilevel converter to anac grid may cause stability issues, which can be assessed byanalyzing the converter ac-side admittance in relation to the gridimpedance. This paper presents a method for calculating theac-side admittance of modular multilevel converters, analyzingthe main frequency components of the converter variables individually.Starting from a time-averaged model of the converter,the proposed method performs a linearization in the frequencydomain, which overcomes the inherent nonlinearities of theconverter internal dynamics and the phase-locked loop usedin the control. The ac-side admittance obtained analytically isfirstly validated by simulations against a nonlinear time-averagedmodel of the modular multilevel converter. The tradeoff posedby complexity of the method and the accuracy of the result isdiscussed and the magnitude of the individual frequency componentsis shown. Finally, experiments on a down-scaled prototypeare performed to validate this study and the simplification onwhich it is based., QC 20181113

Connecting a modular multilevel converter to anac grid may cause stability issues, which can be assessed byanalyzing the converter ac-side admittance in relation to the gridimpedance. This paper presents a method for calculating theac-side admittance of modular multilevel converters, analyzingthe main frequency components of the converter variables individually.Starting from a time-averaged model of the converter,the proposed method performs a linearization in the frequencydomain, which overcomes the inherent nonlinearities of theconverter internal dynamics and the phase-locked loop usedin the control. The ac-side admittance obtained analytically isfirstly validated by simulations against a nonlinear time-averagedmodel of the modular multilevel converter. The tradeoff posedby complexity of the method and the accuracy of the result isdiscussed and the magnitude of the individual frequency componentsis shown. Finally, experiments on a down-scaled prototypeare performed to validate this study and the simplification onwhich it is based., QC 20181113

Connecting a modular multilevel converter to anac grid may cause stability issues, which can be assessed byanalyzing the converter ac-side admittance in relation to the gridimpedance. This paper presents a method for calculating theac-side admittance of modular multilevel converters, analyzingthe main frequency components of the converter variables individually.Starting from a time-averaged model of the converter,the proposed method performs a linearization in the frequencydomain, which overcomes the inherent nonlinearities of theconverter internal dynamics and the phase-locked loop usedin the control. The ac-side admittance obtained analytically isfirstly validated by simulations against a nonlinear time-averagedmodel of the modular multilevel converter. The tradeoff posedby complexity of the method and the accuracy of the result isdiscussed and the magnitude of the individual frequency componentsis shown. Finally, experiments on a down-scaled prototypeare performed to validate this study and the simplification onwhich it is based., QC 20181113

Connecting a modular multilevel converter to anac grid may cause stability issues, which can be assessed byanalyzing the converter ac-side admittance in relation to the gridimpedance. This paper presents a method for calculating theac-side admittance of modular multilevel converters, analyzingthe main frequency components of the converter variables individually.Starting from a time-averaged model of the converter,the proposed method performs a linearization in the frequencydomain, which overcomes the inherent nonlinearities of theconverter internal dynamics and the phase-locked loop usedin the control. The ac-side admittance obtained analytically isfirstly validated by simulations against a nonlinear time-averagedmodel of the modular multilevel converter. The tradeoff posedby complexity of the method and the accuracy of the result isdiscussed and the magnitude of the individual frequency componentsis shown. Finally, experiments on a down-scaled prototypeare performed to validate this study and the simplification onwhich it is based., QC 20181113

Power electronic converters may interact with the grid, thereby influencing dynamic behavior and resonances. Impedance and passivity based stability criteria are two useful methods that allow for studying the grid-converter system as a feedback system, whose behavior is determined by the ratio of grid and converter impedances. In this paper, the ac-side admittance of the modular multilevel converter is calculated using harmonic linearization and considering five specific frequency components of the converter variables. The proposed model features remarkable accuracy, verified through simulations, and insight into the influence of converter and control parameters on the admittance frequency characteristics, which is useful for understanding grid-converter interaction and designing the system., QC 20180220

This paper applies a control method based on current control and sum-capacitor-voltage estimation to the direct ac/ac modular multilevel converter. As capacitor voltages are estimated, their measurements are not needed in the high-level control, which simplifies the communication between the main controller and the submodules of the converter. The stability of the internal dynamics of the converter, using the aforementioned control method, is studied using Lyapunov stability theory, proving that the system is globally asymptotically stable. The behavior of the converter is simulated focusing on three-phase 50 Hz to single-phase 16 (2)/(3) Hz conversion, which is typical for railway power supply systems of some European countries. Simulation results are in agreement with the expected behavior of the converter, both in steady-state and dynamic situations., QC 20161209

In this paper, a control method based on capacitor voltage estimation is applied to the modular multilevel matrix converter topology. By using such control method, capacitor voltage measurement is not needed in the high-level control. A state-space model of the converter and the control method is developed. Lyapunov stability theory is used to prove global asymptotic stability of the internal dynamics of the converter. Simulation results showing the behavior of the converter in steady-state and dynamic situations are presented., QC 20161207

The energy variations in each arm of the modular multilevel converter comprises two components. The first component relates to the difference between the instantaneous input and output power of each phase-leg, and the second component relates to the energy which is moved back and forth between the two arms of the phase-leg. The latter component can be reduced or even eliminated if the peak-to-peak amplitude of the alternating voltage is greater than the pole-to-pole voltage of the dc link. This will, however, require submodules which can insert negative voltages. Therefore, a semi-full-bridge submodule which uses less semiconductors than the conventional full-bridge is proposed. Simulation results shows that by using the negative voltage-levels the capacitor voltage ripple can be reduced by up to 59%. Experimental results also shows that a 7-level voltage waveform can be generated using only one semi-full-bridge submodule with two capacitors per arm., QC 20160226

The tapped-inductor buck (TI-buck) converter has shown to be a suitable solution for auxiliary power supply for modular multilevel converter submodules. Such application features a large step-down voltage conversion, made at relatively low output power. This converter operates in discontinuous conduction mode with zero voltage switching of the high-voltage valve. This paper treats the dynamic behaviour of the aforementioned converter. First, an average output current model of the converter is developed and a small signal model is obtained. Then, a closed-loop output voltage control, which uses the switching frequency as control variable, is designed and implemented using a microcontroller. Measurements on a down-scaled prototype shows that the control system provides a well-controlled average output voltage, which is stable under significant load variation. Finally, a solution for implementing the start-up of the converter is presented and tested., QC 20150521

This paper presents a simplified qualitative comparison of previously presented cascaded multilevel converter topologies for ac-ac conversion with particular emphasis on motor drive applications. Performance criteria such as the pulsation of the stored energy in the cell capacitors and the total required semiconductor rating are derived by analytical methods. The main conclusion is that the back-to-back connected modular multilevel converter operates best at synchronous speed, whereas the modular matrix converter and Hexverter are better suited for low-frequency output. However, by injecting circulating currents in the phase arms the operating region can be extended for all of the studied topologies., QC 20141010

QS 2014