Fault Diagnostics and Tolerance Analysis of a Microgrid System Using Hamilton-Jacobi-Isaacs Equation and Game Theoretic Estimations in Sliding Mode Observers

This paper focuses on robustness and sensitivity analysis for sensor fault diagnosis of a voltage source converter based microgrid model. It uses robust control parameters such as minimum sensitivity parameter (H-), maximum robustness parameter (H∞), and compromised both (H-/H∞), being incorporated in the sliding mode observer theory using the game theoretic saddle point estimation achieved through convex optimization of constrained LMIs. The approach used works in a way that the mentioned robust control parameters are embedded in Hamilton-Jacobi-Isaacs-Equation (HJIE) and are also used to determine the inequality version of HJIE, which is, in terms of the Lyapunov function, faults/disturbances and augmented state/output estimation error as its variables. The stability analysis is also presented by negative definiteness of the same inequality version of HJIE, and additionally, it also gives linear matrix inequalities (LMIs), which are optimized using iterative convex optimization algorithms to give optimal sliding mode observer gains enhanced with robustness to maximal preset values of disturbances and sensitivity to minimal preset values of faults. The enhanced sliding mode observer is used to estimate states, faults, and disturbances using sliding mode observer theory. The optimality of sliding mode observer gains for sensitivity of the observer to minimal faults and robustness to maximal disturbance is a game theoretic saddle point estimation achieved through convex optimization of LMIs. The paper includes results for state estimation errors, faults' estimation/reconstruction, fault estimation errors, and fault-tolerant-control performance for current and potential transformer faults. The considered faults and disturbances in current and potential transformers are sinusoidal nature composite of magnitude/phase/harmonics at the same time.