Zonotope-based method for optimal allocation of wind capacity in microgrids considering generation uncertainty

The increasing wind capacity integration brings new challenges to power system planning and operation, due to the intermittency and uncertainty of its power generation. This study determines the optimal allocation of wind capacity in microgrids, with considerations of the impact of generation uncertainty on both static and dynamic performance of the system, for reducing the possible violations of operation limits caused by wind power fluctuations. The system performance under uncertainty is evaluated using a zonotope-based set-theoretic method. The uncertain variations of wind power are modelled by a zonotope, then the uncertainty sets of static and dynamic state variables, which capture all possible values of the system states, are further calculated by set operations and are embedded in the optimisation model as constraints for system performance. The proposed method is applied to a 33-bus microgrid; the results prove the validity of the method and show that the system can be guaranteed to operate within acceptable security regions in all possible situations when subjected to certain level of uncertainty.