Combining analytical models and Monte-Carlo techniques in probabilistic power system analysis

The authors describe a general framework for combining analytical models and Monte Carlo simulation. The basic idea is to use a simpler analytical model as an approximation to a more detailed model in a Monte Carlo simulation scheme. The simulation then deals with the residual, i.e. the difference between the result of the detailed model and the approximation. The component of probabilistic indices which can be explained by the analytical model is factored out of the Monte Carlo sampling scheme, which then handles only the unexplained residuals. The proposed scheme is flexible and easy to implement, as no modification of existing analytical models is required. The approach is illustrated in case studies with utility-derived systems in several application areas: composite reliability evaluation, multi-area production costing, chronological production costing with ramping constraints, and operation of a multireservoir hydroelectric system