Mathematical Methods for Probabilistic Estimation of Power Shortage in Concentrated Electric Power Systems

As an integral part of assessing the reliability of electric power systems, the calculation of probabilistic indices for power deficit between load and generation are needed considering the stochastic nature of generation and load. Therefore, the mathematical basis and estimation procedure for different analytical and approximate probabilistic techniques such as convolution method, equivalent method, cumulants combined with Gram-Charlier expansion and cumulant combined with Von Mises functions required to define the probability distribution of generation system is introduced in this paper. Also presented are numerical results for the expected value, standard deviation, and probability of the power shortage, which are calculated under a condition of system load loss and compared with the numerical method, i.e., Monte Carlo simulation, in two generation cases (identical - diverse generation unit sizes). Since the convolution of the probability series of generating power method provides the most accurate solution, it is taken as a benchmark method. The results show that with a large number of heterogeneous generator groups for practical application, the von Mises method is recommended as a more accurate method on average and equivalent method as a fairly accurate, but mathematically more simple.