An analytical and probabilistic method to determine wind distributed generators penetration for distribution networks based on time-dependent loads

This paper proposes an analytical approach for optimal allocation of wind DG units in radial distribution networks. Using this analytical approach, size and location of wind DG units are determined at different optimal power factors of a wind DG (OPFws), while different types of time-dependent load models and probabilistic wind DG generation are considered. The proposed approach is based on the partial derivative of a multi-objective index (IMO) including four impact indices of real power loss (ILP), reactive power loss (ILQ), voltage profile (IVD) and voltage stability (IVS). IVS methods based on analytical expression are usually assumed separately (not in an IMO), to find only the optimum location. In this study, the IVS is defined for a new application as an index in the IMO so as to determine both optimal size and location of the wind DG units. Also, the impact of the wind DG penetration on system voltage stability is evaluated. The 33 and 69 bus systems are examined to show the validity of the proposed approach. From the results, the load models have a significant effect on the wind DG penetration in the network, and the match rate between wind DG output and demand curves for each load model is different.