Back Stepping Optimal Scheme with Fractional Order Control for Power System Model

In power system networks, system perturbations may cause severe instability in synchronous generator (SG) states. The SG dynamics rely on unknown and uncertain parameters like, transient time constants that are varying under power system operation. Therefore, to achieve the reference trajectory in the fixed final time, an adequate control strategy is essential for the SG state stabilization in the power system under uncertainties. In this paper, a fractional order optimal control is proposed along with backstepping for fixed final time state stabilization of SG states by estimating unknown parameters through an adaptive law. First power system dynamics are partially linearized, then for each state error backstepping method is employed to achieve robust performance. In the final step of backstepping algorithm, a fractional order optimal control scheme is applied by designing the respective cost functions. The fractional-order term is integrated with the optimal control to achieve a fast transient response. The efficacy of the proposed control technique is validated using single machine infinite bus power system model as well as two area four machine power system model.