Fractional order controller PIλ designed via heuristic optimization algorithm Lévy-Flight Firefly for connection of renewable energy sources to the grid

The connection of renewable energy sources to the grid, in a way that characterizes distributed generation, enables the optimization of local available natural resources. These sources should be managed in order to produce a distortion-free AC terminal voltage, and to inject in the grid the power that is not consumed by the local load. In the system here analyzed for connection of renewable energy sources to the grid, the AC terminal voltage is controlled via a proportional resonant controller. For most loads this solution is satisfactory, however, for a parallel RLC load with the resonant frequency equal the fundamental frequency of the grid, the system has characteristics of instability with an unacceptable amount of harmonic distortion at the Voltage Source Inverter (VSI) terminals. Due to the limited bandwidth of classical PI controller, and the undesired behavior of the proportional resonant controller for RLC load, this paper proposes the use of a fractional order PI^λ controller instead of a proportional resonant controller at the fundamental frequency. For design of the fractional order controller we employed a heuristic optimization algorithm to obtain a stable response with attenuation around 0 dB at the fundamental frequency and total harmonic distortion smaller than 5%.