Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation
(2021) TFRT(1134).- Abstract
- This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.
First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for... (More) - This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.
First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory.
Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.
Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.
Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters.
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Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9b80740c-9026-4868-a707-490aed1595e7
- author
- Jouini, Taouba LU
- supervisor
-
- Anders Rantzer LU
- Emma Tegling LU
- opponent
-
- Associate Professor Ioannis Lestas, University of Cambridge, UK
- organization
- publishing date
- 2021-12-15
- type
- Thesis
- publication status
- published
- subject
- keywords
- networked systems, coupled oscillator synchronization, inverse optimal (robust) control, power systems, inverter control
- volume
- TFRT
- issue
- 1134
- pages
- 199 pages
- publisher
- Department of Automatic Control, Lund University
- defense location
- Lecture hall A, building KC4, Naturvetarvägen 18, Lund. Zoom: https://lu-se.zoom.us/j/68961843437
- defense date
- 2022-01-28 13:15:00
- ISSN
- 0280–5316
- 0280–5316
- ISBN
- 978-91-8039-089-7
- 978-91-8039-090-3
- project
- Scalable Control of Interconnected Systems
- language
- English
- LU publication?
- yes
- additional info
- In reference to IEEE copyrighted material which is used with permission in this thesis, the IEEE does not endorse any of Lund University's products or services. Internal or personal use of this material is permitted. If interested in reprinting/republishing IEEE copyrighted material for advertising or promotional purposes or for creating new collective works for resale or redistribution, please go to http://www.ieee.org/publications_standards/publications/rights/rights_link.html to learn how to obtain a License from RightsLink. If applicable, University Microfilms and/or ProQuest Library, or the Archives of Canada may supply single copies of the dissertation.
- id
- 9b80740c-9026-4868-a707-490aed1595e7
- date added to LUP
- 2021-12-20 11:47:55
- date last changed
- 2022-04-07 09:25:01
@phdthesis{9b80740c-9026-4868-a707-490aed1595e7,
abstract = {{This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.<br/><br/>First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. <br/><br/>Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.<br/><br/>Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.<br/>Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters.<br/>}},
author = {{Jouini, Taouba}},
isbn = {{978-91-8039-089-7}},
issn = {{0280–5316}},
keywords = {{networked systems; coupled oscillator synchronization; inverse optimal (robust) control; power systems; inverter control}},
language = {{eng}},
month = {{12}},
number = {{1134}},
publisher = {{Department of Automatic Control, Lund University}},
school = {{Lund University}},
title = {{Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation}},
url = {{https://lup.lub.lu.se/search/files/111178508/printed_version.pdf}},
volume = {{TFRT}},
year = {{2021}},
}