Robust & Optimal Control of Mass-Spring Networks : with Power System Applications
(2026)- Abstract
- Electric power systems are undergoing significant transformations as more sectors in society are electrified and new electric power generation from solar and wind is added to the grid. The growing share of renewable generation is expected to influence the dynamic behaviour of power systems, creating a need to develop new control strategies for power systems. This thesis investigates robust and optimal control with a focus on performance, robustness and disturbance attenuation. The systems under consideration are damped mass-spring systems that can capture key aspects of AC frequency dynamics in power systems.
The type of control investigated is the so-called H2 and H∞ optimal control. These are... (More) - Electric power systems are undergoing significant transformations as more sectors in society are electrified and new electric power generation from solar and wind is added to the grid. The growing share of renewable generation is expected to influence the dynamic behaviour of power systems, creating a need to develop new control strategies for power systems. This thesis investigates robust and optimal control with a focus on performance, robustness and disturbance attenuation. The systems under consideration are damped mass-spring systems that can capture key aspects of AC frequency dynamics in power systems.
The type of control investigated is the so-called H2 and H∞ optimal control. These are two common frameworks for deriving optimal controllers with respect to different objectives. The H2 optimal control framework seeks to minimise the energy throughput from external stochastic disturbances to the system's performance outputs. The H∞ optimal control framework seeks instead to minimise the effect of the worst-case disturbance on the performance outputs.
Papers I to III in this thesis focus on finding analytical results for the smallest possible gain from disturbances in the two norms, and deriving analytical expressions for the controllers that achieve these. The main contributions are the analytical nature of the controllers and the expressions of the gains. This stands in contrast to the conventional methods for solving the H2 and H∞ optimal control problems, which usually involve numerical methods and require recalculating the controllers numerically for each new problem configuration. Thanks to the analytical expressions for both the controllers and the gains, this thesis provides transparency into what affects the system the most, how the controller can be implemented, and how they relate to existing controllers.
Papers III and IV investigate a robustness margin that is closely related to H∞ control. These papers present analytical expressions for the robustness margin and the controllers that achieve it. The robustness expressions are also highly transparent in showcasing exactly what in the processes affects robustness the most and gives clear guidance in how to implement controllers with good robustness properties.
In all the papers, the theoretical results are applied to power system models that closely resemble damped mass-spring networks, demonstrating the strong applicability of the theory to power system control, particularly AC frequency control. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/b0644a67-ddda-49e5-bd58-ea0b0c446a6b
- author
- Lindberg, Johan LU
- supervisor
-
- Richard Pates LU
- Anders Rantzer LU
- opponent
-
- Prof. Ilic, Marija D., Massachusetts Institute of Technology, USA.
- organization
- publishing date
- 2026
- type
- Thesis
- publication status
- published
- subject
- pages
- 164 pages
- publisher
- MediaTryck Lund
- defense location
- Lecture Hall M:A, building M, Ole Römers väg 1F, Faculty of Engineering LTH, Lund University, Lund. The dissertation will be live streamed, but part of the premises is to be excluded from the live stream.
- defense date
- 2026-06-05 09:15:00
- ISBN
- 978-91-90202-11-1
- 978-91-90202-10-4
- project
- Scalable control for Electrical Power Systems
- language
- English
- LU publication?
- yes
- id
- b0644a67-ddda-49e5-bd58-ea0b0c446a6b
- date added to LUP
- 2026-05-08 11:55:18
- date last changed
- 2026-05-11 09:36:24
@phdthesis{b0644a67-ddda-49e5-bd58-ea0b0c446a6b,
abstract = {{Electric power systems are undergoing significant transformations as more sectors in society are electrified and new electric power generation from solar and wind is added to the grid. The growing share of renewable generation is expected to influence the dynamic behaviour of power systems, creating a need to develop new control strategies for power systems. This thesis investigates robust and optimal control with a focus on performance, robustness and disturbance attenuation. The systems under consideration are damped mass-spring systems that can capture key aspects of AC frequency dynamics in power systems. <br/><br/>The type of control investigated is the so-called <i>H<sub>2</sub></i> and <i>H</i><sub>∞</sub> optimal control. These are two common frameworks for deriving optimal controllers with respect to different objectives. The <i>H<sub>2</sub></i> optimal control framework seeks to minimise the energy throughput from external stochastic disturbances to the system's performance outputs. The <i>H</i><sub>∞</sub> optimal control framework seeks instead to minimise the effect of the worst-case disturbance on the performance outputs. <br/><br/>Papers I to III in this thesis focus on finding analytical results for the smallest possible gain from disturbances in the two norms, and deriving analytical expressions for the controllers that achieve these. The main contributions are the analytical nature of the controllers and the expressions of the gains. This stands in contrast to the conventional methods for solving the <i>H<sub>2 </sub></i>and <i>H</i><sub>∞</sub><i> </i>optimal control problems, which usually involve numerical methods and require recalculating the controllers numerically for each new problem configuration. Thanks to the analytical expressions for both the controllers and the gains, this thesis provides transparency into what affects the system the most, how the controller can be implemented, and how they relate to existing controllers. <br/><br/>Papers III and IV investigate a robustness margin that is closely related to <i>H</i><sub>∞</sub> control. These papers present analytical expressions for the robustness margin and the controllers that achieve it. The robustness expressions are also highly transparent in showcasing exactly what in the processes affects robustness the most and gives clear guidance in how to implement controllers with good robustness properties.<br/><br/>In all the papers, the theoretical results are applied to power system models that closely resemble damped mass-spring networks, demonstrating the strong applicability of the theory to power system control, particularly AC frequency control.}},
author = {{Lindberg, Johan}},
isbn = {{978-91-90202-11-1}},
language = {{eng}},
publisher = {{MediaTryck Lund}},
school = {{Lund University}},
title = {{Robust & Optimal Control of Mass-Spring Networks : with Power System Applications}},
url = {{https://lup.lub.lu.se/search/files/249583686/Johan_Lindberg_Thesis.pdf}},
year = {{2026}},
}