Hedge-Algebra-Based Phase-Locked Loop for Distorted Utility Conditions

This paper presents the first application of the hedge-algebra theory in the field of grid synchronization. For this purpose, an optimized hedge-algebra controller (HAC) is developed and incorporated within the three-phase phase-locked loop (PLL) with moving average filters (MAFs) inside its feedback loop. Optimized fuzziness parameters and linguistic rule base of the HAC are obtained by a genetic algorithm using the integral of absolute error as the performance index during optimization. Calculated optimal parameter values of the HAC depend on the most frequently occurring disturbance in the electric grid. Two different PLL structures are proposed, depending on the types of disturbances occurring in the electric grid. The first structure is the conventional synchronous reference frame PLL with the nonadaptive MAF (i.e., MAF without order adjustment), but with the PI/PID controller in the phase loop replaced by the developed HAC. Such PLL structure is suitable for all analyzed disturbance types, expect for step-changes in the grid frequency. The second PLL structure introduces the adaptive MAF (i.e., MAF with order adjustment) and a new feedback signal in the output stage of the controller to achieve zero steady-state error in the case of step-changes in the grid frequency. The disturbance rejection capability of the two developed PLLs with the HAC (HAC-PLLs) is tested separately and compared experimentally with the PID- and fuzzy-controller-based PLLs.