Self-Synchronization in Power Networks with Periodic Dynamics

• Applicant: Professor Dr.-Ing. Johannes Schiffer
• Subject Area: Electrical Energy Systems, Power Management, Power Electronics, Electrical Machines and Drives ; Automation, Mechatronics, Control Systems, Intelligent Technical Systems, Robotics
• Term: from 2020 to 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 446182476

• Final Report Year: 2025

Final Report Abstract

Positioning renewable energy as the primary source for electricity generation is a key strategy for tackling climate change. However, the reliable operation of electrical networks governed by renewable generators presents challenges due to the complex dynamics of the grid elements. This issue requires rigorous analyses of stability and robustness, as well as the implementation of advanced control techniques for networks of renewable generators. The main problem in analyzing the stability and robustness of power systems lies in the presence of state periodic functions in their state-space models, leading to multiple equilibria. In this context, the applicants have proposed an innovative approach for the stability and robustness analyses of systems with state periodic dynamics by introducing the concept of Leonov functions. This approach leverages the periodic nature of the system and relaxes the standard conditions of the Lyapunov function method for such systems. The practical importance of this method has been shown through the study of the boundedness of solutions and Input-to-State Stability (ISS) properties of microgrids. The Leonov function method has been successfully extended to the control synthesis of state periodic systems by introducing the concepts of Control Leonov Functions (CLeFs) for ensuring the boundedness of solutions of the closed-loop system, and ISS-CLeFs for endowing the closed-loop system with ISS properties. From the practical perspective, important results comprise: the derivation of sufficient conditions for designing the parameters of two-parallel synchronverters with a resistive-capacitive load based on a mathematical model in the Port-Hamiltonian form of a microgrid; the development of a controller that ensures the ISS property for a microgrid of two-parallel synchronverters with a resistive load; and the demonstration of almost global attractivity of solutions for networks of heterogeneous Kuramoto oscillators. As tangible results, six papers were published in peer-reviewed international conferences. Furthermore, two papers have been published in internationally renowned peer-reviewed journals, while two others are currently under review.

Publications

• On Relaxed Conditions of Integral ISS for Multistable Periodic Systems. 2022 IEEE 61st Conference on Decision and Control (CDC), 7072-7077. IEEE.
  Mendoza-Avila, Jesus; Efimov, Denis; Mercado-Uribe, Angel & Schiffer, Johannes
  
• A Control Leonov Function Guaranteeing Global ISS of Two Coupled Synchronverters. 2023 62nd IEEE Conference on Decision and Control (CDC), 4580-4585. IEEE.
  Mercado–Uribe, Angel; Mendoza-Ávila, Jesús; Efimov, Denis & Schiffer, Johannes
  
• A Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators. IFAC-PapersOnLine, 56(2), 9505-9510.
  Mercado-Uribe, Angel; Mendoza-Ávila, Jesús; Efimov, Denis & Schiffer, Johannes
  
• Design of Controls for Boundedness of Trajectories of Multistable State Periodic Systems. 2023 62nd IEEE Conference on Decision and Control (CDC), 6647–6652.
  Mendoza-Avila, Jesus; Efimov, Denis; Mercado-Uribe, Ángel & Schiffer, Johannes
  
• Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems. IFAC-PapersOnLine, 56(2), 4472-4477.
  Mendoza-Avila, Jesus; Mercado-Uribe, Angel; Efimov, Denis & Schiffer, Johannes
  
• Strong and Weak Leonov Functions for Global Boundedness of State Periodic Systems. IEEE Transactions on Automatic Control, 68(12), 7958-7965.
  Schiffer, Johannes & Efimov, Denis
  
• Sufficient Conditions for Global Boundedness of Solutions for Two Coupled Synchronverters. 2024 IEEE 63rd Conference on Decision and Control (CDC), 2785-2790. IEEE.
  Mercado-Uribe, Angel; Mendoza-Ávila, Jesús; Efimov, Denis & Schiffer, Johannes
  
• Conditions for global synchronization in networks of heterogeneous Kuramoto oscillators. Automatica, 175, 112180.
  Mercado-Uribe, Angel; Mendoza-Avila, Jesus; Efimov, Denis & Schiffer, Johannes