Probability theory-based economic dispatch model for insular power systems

The main problem in integration of renewable power sources to the electricity grid is the uncertainty introduced by the power forecasting process in the optimal scheduling problem, which can considerably increase the generation cost. This problem has been widely analyzed using scenario generation/reduction methodologies. However, the consideration of a reduced number of scenarios can limit the capabilities of these methodologies. As an alternative, in this manuscript the dynamic economic dispatch problem has been solved by estimating the probability density function of energy surplus, the energy not supplied and the power production considering the forecasting error and system reliability. The incorporation of the system reliability and the forecasting error as probability distribution functions can avoid the use of scenario generation and reduction processes, which are time consuming tasks. The proposed model was illustrated by analyzing a typical insular power system under different conditions of load and uncertainty, concluding that the hardware failure can introduce a relevant increment in the generation costs, due to their relationship with the value of lost load. Moreover, the scalability of the proposed model was studied by analyzing several power systems between 10 and 150 units, which have been solved in an acceptable computational time.