Description du sujet de thèse

Control of Subharmonics in Nonlinear Systems: Application to Power Grids

The rise of renewable energy, particularly solar and wind power, is driving a profound transformation of modern power grids. The transition towards a cleaner energy mix increasingly relies on inverter-based resources (IBRs), which are progressively replacing traditional synchronous generators. However, this shift introduces new challenges in grid stability and regulation, particularly the emergence of subharmonic oscillations. These complex oscillations, which occur at frequencies lower than the fundamental network frequency, are not always detected by conventional harmonic analysis used in the design phase. They can lead to equipment performance degradation, significant economic losses, and, in some cases, compromise grid security.

The objective of this PhD thesis is to investigate the origins of subharmonics in power grids by developing a rigorous approach based on nonlinear dynamical systems theory and nonlinear control. Several research questions will be explored:

What are the fundamental mechanisms responsible for the emergence of subharmonic oscillations in IBRs?

Why do current IBR models fail to accurately capture these phenomena?

What control strategies can be developed to mitigate or suppress these undesirable oscillations?

The results of this thesis will contribute to a deeper understanding of dynamic interactions in modern power grids and provide concrete tools to improve grid compliance and the integration of IBRs into existing infrastructures.

This PhD project is part of a joint research initiative between CNRS and Imperial College London. The selected PhD candidate will closely collaborate with researchers from both institutions and will complete a three-month research stay at Imperial College London.

Desired Profile: We are looking for a candidate with a strong background in control theory and applied mathematics (nonlinear analysis, systems theory). A basic knowledge of electrical engineering will also be an asset to better understand the context of power grids and inverters.

References:
[1] Y. Cheng et al (2023). Real-world subsynchronous oscillation events in power grids with high penetrations of inverter-based resources. IEEE Transactions on Power Systems, 38(1): 316–330.
[2] Hayashi, C. (2014). Nonlinear oscillations in physical systems (Vol. 432). Princeton University Press.
[3] Fyrillas, M. M., & Szeri, A. J. (1998). Control of ultra-and subharmonic resonances. Journal of Nonlinear Science, 8: 131-159.
[4] Astolfi, D., Praly, L., & Marconi, L. (2022). Nonlinear Robust Periodic Output Regulation of Minimum Phase Systems. Mathematics of Control, Signals, and Systems, 34: 129-184.
[5] Bin, M., Astolfi, D., & Marconi, L. (2023). About Robustness of Control Systems Embedding an Internal Model. IEEE Transactions on Automatic Control, 68(3): 1306 - 1320.

Contexte de travail

The PhD candidate will be hosted at LAGEPP (Laboratoire d'Automatique, de Génie des Procédés et de Pharmacie Industrielle), a CNRS research unit located in Villeurbanne and affiliated with University Claude Bernard Lyon 1. The laboratory has recognized expertise in the modeling, analysis, and control of nonlinear systems, with applications in various fields ranging from industrial processes to energy systems.

The PhD research will take place within the DYCOP team (Dynamique, Commande et Observation des Procédés), which specializes in the control and observation of complex dynamical systems. The DYCOP group includes researchers with strong expertise in control theory, system identification, and observer design.

The thesis will be supervised by Daniele Astolfi (CNRS, LAGEPP), an expert in nonlinear control and regulation. The project is conducted in collaboration with Giordano Scarciotti (Imperial College London), a renowned expert in nonlinear systems theory and model reduction. Regular exchanges with the research group at Imperial College are planned throughout the PhD.

Contraintes et risques

This PhD thesis will be mainly theoretical, with no experimental implementation or industrial platform testing. However, the proposed control strategies will need to be validated on representative models of modern power grids.

The PhD candidate should consider international mobility as part of the collaboration with Imperial College London. This includes a three-month research stay in London and frequent exchanges between the two institutions. Adaptability to an international research environment and strong autonomy will be essential for the success of this project.