To handle significant variability in loads, renewable energy generation, as well as various contingencies, two-stage robust optimization method has been adopted to construct unit commitment models and to ensure reliable solutions. In this paper, we further explore and extend the modeling capacity of two-stage robust optimization and present two new robust unit commitment variants, the \emph{expanded robust unit commitment} and \emph{the risk constrained robust unit commitment} models. We derive some structural properties, show the connection to the scenario based stochastic unit commitment model, and present a customized column-and-constraint generation method. Numerical experiments on those models are performed using a practical data set, which illustrate their modeling strength, economic outcomes and the algorithm performance in solving those models.