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.

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.

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.

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.

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.

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. 

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.

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.

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-loop scheme is also adapted to a modular multilevel matrix converter, which performs three-to-three phase direct conversion.

Finally, this thesis presents the design of a down-scaled MMC prototype for experimental verification, rated at 10 kW with 30 full-bridge submodules. The hardware and the software are designed to be easily reconfigurable, which makes the converter suitable for different research projects focused on MMCs. Experiments on this down-scaled MMC are used to support and validate the key results presented throughout the thesis.

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 omvandlaren. Den föreslagna öppna styrningen kan också anpassas till en modulär multinivåomvandlare för direkt trefas till trefas omformning.

För att kunna verifiera resultaten experimentellt har en nedskalad prototyp utvecklats. Prototypens märkeffekt är 10 kW och den är uppbyggd av 30 submoduler med helbryggor. Hårdvaran och mjukvaran är utformade så att omvandlaren på ett enkelt sätt kan konfigureras för olika tillämpningar vilket gör den lämplig för olika forskningsprojekt som inkluderar modulära multinivåomriktare. Experiment på den nedskalade MMC:n har genomförts för att validera de resultat och slutsatser som presenteras i avhandlingen.

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.