Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus

Conditions for existence and global attractivity of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. First, necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Then, sufficient conditions for local asymptotic stability and almost global attractivity of one of these equilibria are given. The analysis is carried out by employing a new Lyapunov–like function to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus. The efficiency of the derived sufficient conditions is illustrated via extensive numerical experiments based on two benchmark examples taken from the literature

On boundedness of solutions of periodic systems: a multivariable cell structure approach

A wide range of practical systems exhibits dynamics, which are periodic with respect to several state variables and which possess multiple invariant solutions. Yet, when analyzing stability of such systems, many classical techniques often fall short in that they only permit to establish local stability properties. Motivated by this, we present a new sufficient criterion for global stability of such a class of nonlinear systems. The proposed approach is characterized by two main properties. First, it develops the conventional cell structure framework to the case of multiple periodic states. Second, it extends the standard Lyapunov theory by relaxing the usual definiteness requirements of the employed Lyapunov functions to sign-indefinite functions. The stability robustness with respect to exogenous perturbations is analyzed. The efficacy of the proposed approach is illustrated via the global stability analysis of a nonlinear system

On boundedness of solutions of state periodic systems: a multivariable cell structure approach

International audienceMany dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability (ISS), i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system

Algorithms for Efficient, Resilient, and Economic Operation of Pre-Emptively Reinforced Reconfigurable Distribution Substations

Stochasticity of demand profiles at electricity distribution substations is increasing due to the proliferation of low carbon technologies; in particular mobile, bi-directional, or intermittent loads such as electric vehicles and heat pumps. The decarbonisation of heat and transport will cause a long-term increase in overall connected load, making substation reinforcement necessary, whilst planning of upgrade locations and capacities remains challenging. This project will investigate pre-emptive substation reinforcement with algorithmic topology control, to utilise the additional installed substation capacity only when required. Distribution Substation Dynamic Reconfiguration (DSDR) proposes the installation of additional transformers in parallel with the existing transformer in each substation, removing the need to scrap and replace these. Telematics-controlled switches are installed on the high- and low-voltage side of each transformer in the substation, with local agent algorithms deployed to control in real-time when each parallel transformer is brought into or taken out of service. Substation reconfiguration is thus controlled to optimise for maximum operating efficiency. The threshold algorithm most recently trialled in medium voltage parallel transformer substations is implemented as a baseline, and a novel model-based reconfiguration algorithm is proposed, implemented, and evaluated in software and hardware. This work led to a 1.34% improvement in algorithm performance on substation efficiency, over a yearly demand profile including residential and new electric vehicle load for the year 2050, equivalent to a potential saving of 2.68 TWh annually if deployed UK-wide. This approach unlocks several opportunities to operate existing substations in the smart, flexible, resilient, and efficient manner that will be required to reach the net zero target by 2050