A two-stage model for planning energy investment under uncertainty

Abstract

We consider risk-averse stochastic programming models for the Generation Expansion Planning problem for energy systems with here-and-now investment decisions and generation variables of recourse. The resulting problem is coupled both along scenarios and along power plants. We develop a new decomposition technique to solve the energy optimization problem, resulting from the combination of two existing procedures, one to deal with stochastic programming problems through decomposition for different realizations of the stochastic process representing the uncertain data, and the second one is a method aim to find solutions to nonsmooth optimization problems. More precisely, we combine the Progressive Hedging algorithm to deal with scenario separability, obtaining a separate subproblem for each scenario, and an inexact proximal bundle method to handle separability for different power plants in each subproblem. By suitably combining these approaches, if the evaluation errors of the proximal bundle method vanish asymptotically, then bundle method converges to an approximate solution to each scenario subproblem. Thus, under mild convexity assumptions, the Progressive Hedging algorithm generates a sequence that converges to a solution to the original problem. The methodology is satisfactorily assessed on a test instance of the Generation Expansion Planning problem, whose reduced size allows us to compare the results with those obtained when solving the problem directly, and without decomposition.