Stochastic Modeling and Planning of Wind-Based Distributed Generators in Distribution System

The increasing strain on the Earth resulting from pollution, climate change, and finite resources has established the development of renewable energy sourcing methods, such as wind, solar and geothermal energy. By reorganizing the power system structures, and the growth in customer demand, the development of Distributed Generation (DG) play a vital role in the power system planning. Furthermore, because of the inexhaustibility and cleanliness of the renewable DG units, they are inevitably the key to a sustainable energy supply infrastructure. Nevertheless, the random nature associated with the renewable DG units produces specific challenges that have to be addressed to accelerate the expansion of the renewable DG units in the distribution system. Firstly, a new method for the determination of the wind speed distribution based on hourly wind speed data is proposed. Thus, instead of using only the well-known unimodal distributions such as Weibull and Rayleigh, a combination of probability density functions (PDFs) is taken into account, considering four sets of parameters in which each set represents a distribution. Furthermore, this model enhances the likelihood of the estimated wind speed probabilities. The maximum likelihood estimation (MLE) method for finite mixture models through the expectation-maximization (EM) algorithm is used to estimate the optimal parameters of the mixture distribution. Then two types of error measurements assessed the performance of each unimodal and multimodal distribution. As a result, the mixture of Gamma (MoG) distribution returned the most accurate results. Secondly, the results of wind speed modeling will be used in the siting and sizing wind-based DG units. The methodology addresses a probabilistic generation load model that combines all possible operating conditions of the wind-based DG units and load levels with their probabilities. The objective of siting and sizing formulation is to minimize the annual energy losses of the system as well as keeping the system constraints such as voltage limits at different buses (slack and load buses) of the system, feeder capacity, discrete size of the DG units, maximum investment on each bus, and maximum penetration limit of DG units in an acceptable limit