ABSTRACT:

Accurate and robust estimation of system parameters from complex nonlinear mappings is central to a wide range of data-driven inference problems, from dynamic monitoring to adaptive control. In many modern systems, however, conventional parameter estimation laws can become ill-conditioned or singular in certain regions of the parameter space, leading to unreliable or undefined estimates. This issue is particularly acute in renewable-dominated electrical power systems, where the Short Circuit Ratio (SCR) – a key indicator of grid strength and stability – must be monitored continuously. As synchronous generators are retired and inverter-based resources proliferate, the dynamic behaviour of the grid becomes increasingly nonlinear, and the mappings that relate operating data to strength indicators exhibit singularities that pose practical barriers to classical inversion methods.

This project develops a novel safe dynamic mapping inversion framework that enables reliable estimation even in the presence of singularities that disrupt conventional adaptation laws. By integrating concepts from geometric data science with adaptive estimation and selective learning, the proposed approach systematically characterizes and manages unsafe sets in the parameter search space where standard inversion laws become ill-posed. Crucially, when these singular regions act as algorithmic barriers that partition the estimator’s reachable trajectories, the framework constructs structured coordinate transformations and higher-dimensional immersions that allow the estimation process to traverse these regions while maintaining numerical stability and interpretability.

In the primary application domain of SCR monitoring, this allows continuous, robust estimation of grid strength indicators directly from standard operational data, i.e. without intrusive system perturbations, even as the system approaches weak-grid operating regimes. By enabling singularity-free estimation in complex, dynamically evolving environments, the proposed research advances both the theoretical foundations of adaptive inversion and its practical utility in sustainability-critical infrastructure monitoring. The results are expected to provide new tools for dependable grid health assessment, supporting renewable integration and stable operation in evolving power systems.