A Risk-Averse Optimization Model for Unit Commitment Problems

In this paper, we consider the unit commitment problem of a power system with high penetration of renewable energy. The optimal day-ahead scheduling of the system is formulated as a risk-averse stochastic optimization model in which the load balance of the system is satisfied with a high prescribed probability level. In order to handle the ambiguous joint probability distribution of the renewable generation, the feasible set of the optimization problem is approximated by an quantile-based uncertainty set. Results highlight the importance of large sample size in providing reliable solutions to the SCUC problems. The method is flexible in allowing a range of risk into the problem from higher-risk to robust solutions. The results of these comparisons show that the higher cost of robust methods may not be necessary or efficient. Numerical results on a test network show that the approach provides significant scalability for the stochastic problem, allowing the use of very large sample sets to represent uncertainty in a comprehensive way. This provides significant promise for scaling to larger networks because the separation between the stochastic and the mixed-integer problem avoids multiplicative scaling of the dimension that is prevalent in traditional two-stage stochastic programming methods.