A Stochastic Optimization Formulation of Unit Commitment With Reliability Constraints

This paper proposes a new formulation for a stochastic unit commitment (UC) problem that incorporates two major and common sources of uncertainty in short-term generation scheduling, namely, unavailability of generators and load uncertainty. The objective is to minimize operating cost and expected loss of load cost subject to reliability constraints in terms of loss of load probability. The problem is first formulated as a two-stage recourse model in stochastic programming framework where generator unavailability is expressed by a discrete set of outage scenarios and system demand is set to be a nominal value in power balance equations. Then, load uncertainty is represented as a continuous random variable in loss of load probability constraint, which is approximated by a mixed-integer piecewise linear function and integrated to the second stage problem. As a result, the UC problem has a much smaller dimension as compared to the original two-stage recourse model. The proposed formulation can be solved in a timely manner even though the formulation requires some extra binary decision variables. Although loss of load probability constraint is approximated in the optimization problem, simulation results show that the optimal solutions yield desired reliability performance. Several case studies are conducted to examine the impact of reliability requirements and system uncertainties on UC decisions.