Adaptive robust optimal reactive power dispatch in unbalanced distribution networks with high penetration of distributed generation

Due to the increasing penetration of the uncertain single-phase distributed generations (DGs), the current distribution networks are becoming more uncertain, unbalanced, and complicated than ever before, which brings great challenges for distribution network operators. This study proposes an adaptive robust optimal reactive power dispatch approach for the unbalanced distribution networks (U-DNs) considering uncertainty caused by DGs. Leveraging the reactive power compensation from inverters of DGs, the purpose of the proposed method is to minimise power losses and maintain the voltage within regulatory limits. The feasible region of DGs is estimated and considered as a new constraint, aiming to guarantee the reliable operation of U-DNs. The optimal reactive power dispatch problem is then formulated as an adaptive robust optimisation problem based on semidefinite programming. The adaptive function, which derives the relationship between reactive power and active power outputs of DGs, is utilised to make the method more flexible and less conservative. The cutting plane algorithm is introduced to solve the proposed adaptive robust reactive power dispatch model efficiently. Moreover, case studies are separately conducted on the modified IEEE 13-bus and 123-bus test systems to demonstrate the effectiveness of the proposed method.