A New Hybrid Uncertainty Set for the Multi-Period Prot Unit Commitment Problem

Unit commitment (UC) is one of the most important problems in electric power system
operations. It seeks an economic policy to operate a system of generating units over a
multi-period nite horizon. This policy determines the hourly power output of each unit,
implying which units to commit (operate) in order to meet the demand subject to equip-
ment and physical constraints. We consider the prot UC (PUC) problem of a generator
operating in a deregulated market wishing to maximize its prot under uncertain demand
and renewable energy. Given the uncertain parameters this problem is modeled as a mixed
integer and linear problem (MILP). We employ the Robust Optimization (RO) method-
ology to solve the PUC model. The RO is a distribution-free methodology designed for
uncertain problems. It provides a feasible solution for any realization within a bounded
uncertainty set, with corresponding worst-case value. The resulting robust counterpart
(RC) is a mixed integer bilinear program with linear constraints, which is generally NP-
hard. We suggest a new hybrid uncertainty set and solve the associated RC problem in
specic cases to optimality having essentially the same size as the deterministic problem.
Also, we propose an approximate algorithm for an intractable RC. Our simulation results
show that the performance of the RO methodology is better than a popular method.