Optimized Fractional Order Conditional Integrator

In this paper, an optimized fractional order conditional integrator (OFOCI) is proposed. The key feature of this OFOCI is that, the fractional order alpha and the parameter k for the "hold" value in the course of integration can be tuned following the analytical optimality design specifications, to achieve the optimized performance not achievable using integer order conditional integrators. The proposed optimality specifications are given to satisfy the desired phase delay, and minimize the preferred magnitude ratio, which can be calculated from the high order harmonic magnitudes divided by the magnitude of the fundamental wave. The numerical solution of calculating the optimized parameters alpha and k of the OFOCI is introduced. The phase delays and magnitude ratios of four designed OFOCIs are compared with the integer order conditional integrators. Simulation results with the FFT spectra are also presented to validate the theoretical analysis.