Probabilistic Approaches for the Steady-State Analysis of Distribution Systems with Wind Farms

This chapter deals with probabilistic approaches for the steady-state analysis (probabilistic load flow) of distribution systems with wind farms. The probabilistic analysis is performed taking into account the randomness of both the distribution system loads and the wind energy production. Several approaches are presented to obtain the probability functions of state and dependent variables (e.g., voltage amplitudes and line flows). These approaches are mainly concentrated on wind farm probabilistic models, using one of the classical probabilistic techniques (e.g., Monte Carlo simulation, convolution process, and special distribution functions) to perform the probabilistic load flow. Numerical applications on a 17-bus balanced test distribution system and on an IEEE 34-bus unbalanced test distribution system are presented and discussed, considering the various wind farm models.