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This paper analyzes the behavior of Hong's point estimate method to account for uncertainties in probabilistic energy management systems to optimize the operation of a microgrid (MG). These uncertainties may arise from different sources, such as the market prices, load demands, and electric power generation of wind farms and photovoltaic systems. Point estimate methods constitute a remarkable tool to handle stochastic power system problems because good results can be achieved using the same routines as those corresponding to deterministic problems, while keeping the computational burden low. The problem is formulated as a nonlinear constraint optimization problem to minimize the total operating cost. Weibull, beta, and normal distributions are used to model the uncertain input variables in this study. Moreover, the firefly algorithm is applied to achieve optimal operational planning with regard to cost minimization. The efficiency of Hong's point estimate method is validated on a typical MG. Results for the case study are presented and compared against those obtained from the Monte Carlo simulation. Specifically, this paper shows that the use of the 2m + 1 scheme provides the best performance when a high number of random variables, both continuous and discrete, are considered.

Optimal operation management of microgrids using the point estimate method and firefly algorithm while considering uncertainty