A probabilistic approach for optimal capacitor planning in distribution systems with wind generators

This thesis proposes a probabilistic approach based on the Cumulant method for optimal capacitor planning in distribution systems with high penetration of wind generators. To account for the problem uncertainties, the probabilistic behaviour of load forecasts and wind generators are modeled using Probability Density Functions. Once the probabilistic framework is defined, an optimization problem can be formulated to minimize the total costs of the capacitors and of the annual energy losses. The optimization problem is then solved by using the Logarithm Barrier Interior Point Method, which provides a linear relationship between the cumulants of load and wind variables and the cumulants of the system parameters and solution cost. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the traditional Monte Carlo Simulation method. The proposed method is tested on a 7-bus and on a 33-bus systems, and the results are reported and discussed.