Frequency-based relays, commonly used for islanding detection of synchronous distributed generation (SDG), may either have large non-detection zones (NDZs) or wrongly operate for non-islanding disturbances unless they are efficiently adjusted. Trial and error simulation-based methods, employing application region (AR) and/or power imbalance AR (PIAR), are presented in the literature to adjust these relays for quick islanding detection without false trips. However, the associated settings are not optimal and finding them is time-consuming. In this study, an approach utilising particle swarm optimisation algorithm is proposed to adjust a rate of change of frequency (ROCOF) relay, one of the most effective relays in SDG islanding detection. The proposed approach needs a set of analytical formulas for determining the ROCOF relay performance curve and NDZ as well as AR and PIAR. These formulas are developed to be employed in the relay adjustment. By applying the developed analytical formulas to the optimisation-based approach, the ROCOF relay is adjusted fast and systematically. It is shown that while the performance of the relay adjusted by the proposed approach is close to the one with setting obtained by corresponding trial and error-based method, the latter is much more time-consuming than the former.
