Sub-Riemannian Geometric Approach to Design Nonlinear Optimal STATCOM Controller for Power Systems

Abstract

Sub-Riemannian geometry (SRG) is one of the important and innovative areas of modern optimal control theory. This work implements the idea of Riemannian’s to design nonlinear Static Compensator (STATCOM) for the mitigation of power system stability problem. The concept of minimizing geodesic of the sub-Riemannian geometry is employed to determine the optimal control law for a STATCOM. To test the nonlinear controllability of the study systems the method of iterative Lie brackets has been used. The robustness of the designed controller has been investigated by applying typical contingency to the study system. It has been revealed that the Sub-Riemannian geometry based nonlinear controller is effective in 3-phase-toearth fault circumstances. Advantage of SRG based controller design over other approaches is that the concept of geodesic can be easily framed to get nonlinear control law despite the lack of applicability of Ponttyagin’s Maximum Principle and other methods. Moreover, the complexity of solving the state and co-state equations required in the Hamilton-Jacobi-Bellman (HJB) approach can be avoided in SRG method.