Evolutionary Fractional-Order Extended Kalman Filter of Cyber-Physical Power Systems

State estimation of cyber-physical power systems (CPPSs) is of great significance for power system optimization, control, and security analysis. Additionally, fractional differential calculus is based on differentiation and integration of arbitrary fractional order, which can more accurately describe the physical phenomenon model than the traditional integer calculus. Thus, this article proposes a novel fractional-order extended Kalman filter (FOEKF) based on the evolutionary algorithm and deep ensemble learning techniques for the state estimation problem of CPPSs from the fractional-order theory perspective. First, the power system is modeled as a fractional version to describe the physical phenomenon better according to the fractional differential calculus theory. Then, considering the difficulties in determining fractional orders in the fractional-order power system, a deep ensemble learning-based approach is used to design the fitness function and a genetic algorithm is developed to determine these parameters by optimizing the designed objective function. Furthermore, to solve the difficulties in estimating for fractional-order power system by integral extended Kalman filter (EKF), the evolutionary FOEKF (EFOEKF) is presented as the estimator for the designed fractional-order power system. Finally, to improve the performance of EFOEKF under bad datum scenarios caused by cyber-attacks or sudden loads, an enhanced EFOEKF method is developed by using an adapted exponential weighting function. The numerical simulation results show that the proposed EFOEKF is better than EKF and FOEKF on four different IEEE bus systems in terms of the mean absolute error.