Temporal Decomposition for Improved Unit Commitment in Power System Production Cost Modeling

Long-term planning in power systems requires simulations of unit commitment (UC) for long time periods up to 20 years. Such simulations are conducted with production cost models (PCMs), which involve solving large-scale mixed-integer programming (MIP) problems with a large number of variables and constraints, because of the long planning horizon. We have developed new optimization modeling and solution techniques based on a decomposition scheme to reduce the solution time and improve the accuracy in PCMs. We propose a temporal decomposition that solves the UC problem by systematically decoupling the long-horizon MIP problem into several subhorizon models. The decomposition is obtained by the Lagrangian relaxation of the time-coupling constraints such as ramping constraints and minimum uptime/downtime constraints. The key challenge is to solve several sub-MIP problems while effectively searching for dual variables to accelerate the convergence of the algorithm. We implement the temporal decomposition in an open-source parallel decomposition framework, which can solve the multiple subproblems in parallel on high-performance computing clusters. We also implement the branch-and-bound method on top of the decomposition in order to find a primal optimal solution. Numerical results of the decomposition method are reported for the IEEE 118-bus and PEGASE 1354-bus test systems with up to an 168-hour time horizon.