Sub-Riemannian Approach to Design Nonlinear Optimal Controller for Multimachine Power System
Abstract
Sub-Riemannian geometry (SRG) is one of the innovative areas of modern optimal control theory. In this work the idea of Riemannian’s has been implemented to design nonlinear Static Compensator (STATCOM) for the application of transient stability mitigation in power systems. The efficacy of this newly proposed nonlinear controller has been tested for mitigation of power system stability problem in a Western System Coordinating Council (WSCC) type 9-bus multi-machine power system. The concept of minimizing geodesic of the sub-Riemannian geometry is employed to determine the optimal control law for STATCOM. To test for nonlinear controllability and the stability of the study systems the method of Lie brackets and Lyapunov stability theory has been used respectively. The robustness of the designed controller has been investigated by applying different loads and typical contingency to the study systems. The proposed work exhibits that the nonlinear controller based on the Sub-Riemannian geometry not only efficacious in normal operating conditions but also works substantially well in 3-phase-to-earth fault circumstances and with progressive increasing load. Advantage of SRG based controller design over other approaches is that the concept of Hamiltonian geodesic can be easily framed to get nonlinear control law despite the lack of applicability of Pontryagin Maximum Principle and other methods.