Statistical analysis of optimal energy and security controls under different sources of uncertainties

The management of uncertainties is a challenging task for reliable and secure operation of power systems. The uncertainties come from multiple sources, including the forecast errors of wind power and load, the forced outage of generating units, loss of transmission equipments, etc. This paper classifies different uncertainties based on their binary and continuous attributes. The main idea is to investigate the effect of each source of uncertainties on the cost of energy and security controls. For this purpose, a specific optimization method is developed which takes into account a forecasted scenario and a stochastic scenario. This optimization problem is solved for a fixed forecasted scenario and a varying stochastic scenario. The stochastic scenarios are constructed using a Monte Carlo Simulation that considers various sources of uncertainties. The main advantage of the proposed optimization is that the number of incorporated stochastic scenarios does not increase the size of the optimization problem. The models of different uncertainties, particularly wind power forecast errors, are discussed in depth. This optimization allows obtaining the statistical moments and constructing the probability distributions. The proposed optimization approach is then applied to the IEEE RTS 24-bus system. The probability distributions and statistical moments of objective functions and control variables are assessed for three cases, namely: (i) with only binary uncertainties, (ii) with only continuous uncertainties and (iii) with both of them.