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Modeling of Modular Multilevel Converters for Stability Analysis
KTH, School of Electrical Engineering and Computer Science (EECS), Electric Power and Energy Systems. (Power Electronics)
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Abstract [sv]

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.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019.
Keywords [en]
Modular multilevel converters (MMCs), stability, admittance, frequency-domain analysis, linearization techniques, current control, voltage control, ac/ac converters, railway engineering.
Keywords [sv]
Modulära multinivåomvandlare (MMC), stabilitet, admittans, frekvensanalys, linjäriseringsmetoder, strömreglering, spänningsreglering, ac/ac omvandlare, järnvägsteknik.
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-248132ISBN: 978-91-7873-144-2 (print)OAI: oai:DiVA.org:kth-248132DiVA, id: diva2:1302318
Public defence
2019-04-26, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20190405

Available from: 2019-04-05 Created: 2019-04-04 Last updated: 2019-04-05Bibliographically approved
List of papers
1. A Method for the Calculation of the AC-Side Admittance of a Modular Multilevel Converter
Open this publication in new window or tab >>A Method for the Calculation of the AC-Side Admittance of a Modular Multilevel Converter
2018 (English)In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Modular multilevel converters, admittance, linearization techniques, frequency-domain analysis, stability.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-238815 (URN)10.1109/TPEL.2018.2862254 (DOI)000464911900018 ()2-s2.0-85050974319 (Scopus ID)
Note

QC 20181113

Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2019-05-14Bibliographically approved
2. Effects of Control on the AC-Side Admittance of a Modular Multilevel Converter
Open this publication in new window or tab >>Effects of Control on the AC-Side Admittance of a Modular Multilevel Converter
2019 (English)In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107, Vol. 34, no 8, p. 7206-7220, article id 8514034Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE Press, 2019
Keywords
Modular multilevel converters, admittance, current control, stability, frequency-domain analysis, linearization techniques.
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-238818 (URN)10.1109/TPEL.2018.2878600 (DOI)000469912200014 ()2-s2.0-85055681354 (Scopus ID)
Note

QC 20181113

Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2019-06-26Bibliographically approved
3. Control and Admittance Modeling of an AC/AC Modular Multilevel Converter for Railway Supplies
Open this publication in new window or tab >>Control and Admittance Modeling of an AC/AC Modular Multilevel Converter for Railway Supplies
Show others...
2019 (English)In: IEEE transactions on power electronics, ISSN 0885-8993, E-ISSN 1941-0107Article in journal (Refereed) In press
Abstract [en]

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. 

Keywords
Modular multilevel converters, ac/ac converters, current control, voltage control, admittance, frequency-domain analysis, linearization techniques, stability, railway engineering.
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-248130 (URN)
Note

QC 20190404

Available from: 2019-04-04 Created: 2019-04-04 Last updated: 2019-08-19Bibliographically approved
4. Control of Modular Multilevel Matrix Converters Based on Capacitor Voltage Estimation
Open this publication in new window or tab >>Control of Modular Multilevel Matrix Converters Based on Capacitor Voltage Estimation
2016 (English)In: IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia), 2016, IEEE, 2016, p. 3447-3452, article id 7512848Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE, 2016
Keywords
Asymptotic stability, Control theory, Matrix converters, Motion control, Power converters, Power electronics, State space methods, Capacitor voltages, Control methods, Global asymptotic stability, High level control, Internal dynamics, Lyapunov stability theory, Multilevel matrix converter, State - space models
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-197596 (URN)10.1109/IPEMC.2016.7512848 (DOI)000390949703101 ()2-s2.0-84983261009 (Scopus ID)978-1-5090-1210-7 (ISBN)
Conference
8th IEEE International Power Electronics and Motion Control Conference, IPEMC-ECCE Asia 2016, Hefei, China, 22 May 2016 through 26 May 2016
Note

QC 20161207

Available from: 2016-12-05 Created: 2016-12-05 Last updated: 2019-04-04Bibliographically approved
5. Control of Direct AC/AC Modular Multilevel Converters Using Capacitor Voltage Estimation
Open this publication in new window or tab >>Control of Direct AC/AC Modular Multilevel Converters Using Capacitor Voltage Estimation
Show others...
2016 (English)In: 2016 18TH EUROPEAN CONFERENCE ON POWER ELECTRONICS AND APPLICATIONS (EPE'16 ECCE EUROPE), IEEE, 2016Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE, 2016
Series
European Conference on Power Electronics and Applications, ISSN 2325-0313
Keywords
AC-AC converters, multilevel systems, current control, Lyapunov methods
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-197010 (URN)10.1109/EPE.2016.7695319 (DOI)000386637300068 ()2-s2.0-84996836164 (Scopus ID)
Conference
18th European Conference on Power Electronics and Applications (EPE), SEP 05-09, 2016, GERMANY
Note

QC 20161209

Available from: 2016-12-09 Created: 2016-11-28 Last updated: 2019-04-04Bibliographically approved
6. Ac-side admittance calculation for modular multilevel converters
Open this publication in new window or tab >>Ac-side admittance calculation for modular multilevel converters
2017 (English)In: 2017 IEEE 3rd International Future Energy Electronics Conference and ECCE Asia, IFEEC - ECCE Asia 2017, Institute of Electrical and Electronics Engineers (IEEE), 2017, p. 308-312Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2017
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223036 (URN)10.1109/IFEEC.2017.7992056 (DOI)000426696300055 ()2-s2.0-85034016542 (Scopus ID)9781509051571 (ISBN)
Conference
3rd IEEE International Future Energy Electronics Conference and ECCE Asia, IFEEC - ECCE Asia 2017, Kaohsiung, Taiwan, 3 June 2017 through 7 June 2017
Note

QC 20180220

Available from: 2018-02-20 Created: 2018-02-20 Last updated: 2019-04-04Bibliographically approved
7. Design of a Modular Multilevel Converter Prototype for Research Purposes
Open this publication in new window or tab >>Design of a Modular Multilevel Converter Prototype for Research Purposes
2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

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.

Keywords
Multilevel converters, Test bench, Field Programmable Gate Array (FPGA), Measurement
National Category
Other Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-238816 (URN)000450299300187 ()2-s2.0-85057055682 (Scopus ID)9789075815290 (ISBN)
Conference
EPE'18 ECCE Europe
Note

QC 20181128

Available from: 2018-11-12 Created: 2018-11-12 Last updated: 2019-04-04Bibliographically approved

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  • harvard1
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