In minimization problems with uncertain parameters, cost savings can be achieved by solving stochastic programming (SP) formulations instead of using expected parameter values in a deterministic formulation. To obtain such savings, it is crucial to employ high quality probabilistic scenarios for the uncertain parameters. A convincing way to assess the quality of a scenario generation method is to simulate employing the resulting scenarios when solving the SP problem while measuring the costs incurred when the solution is implemented and observed parameter values occur. Simulation studies to assess the quality in this way are computationally very demanding. This research is aimed at developing faster methods to assess the quality via statistical metrics. Relibility, which is defined as the statistical consistency between scenarios and observation, is a prerequisite for quality. The dissertation is presented in a three-paper format.

The stochastic unit commitment problem in electric power system operation is an application of SP that motivated this study. In power systems with high penetration of wind generation, probabilistic scenarios for the available wind energy are generated for use in stochastic formulations of day-ahead thermal unit commitment problems. To minimize the expected cost of dispatching the committed units, the wind energy scenarios should accurately represent the stochastic process for available wind energy. In the first paper, aiming to assess the reliability of probabilistic scenarios for wind energy time series, we employ some existing forecast verification approaches and introduce a mass transportation distance rank histogram to assess the reliability of unequally likely scenarios. In the second paper, we examine the relationship between the statistical reliability assessment metrics and the cost results of solving SUC using the assessed scenario generation method. Based on this relationship, we understand the importance of scenario reliability to ensure scenario quality for the SUC problem. In the third paper, we extend this work to make it more robust and general enough to be applied to any two-stage SP problem that is repeatedly solved and for which observational data exist for some historical period. Focusing on scenario quality, we develop two novel approaches: expected value based and perfect information based scenario generation assessment. With the proposed approaches, we can assess the quality of scenario sets without having to repeatedly solve the related SP problem. Instead of comparing scenarios to observations directly, these approaches take into consideration the impact of each scenario on the solution to the SP problem.