Partially Adaptive Stochastic Optimization for Electric Power Generation Expansion Planning

Abstract

Electric Power Generation Expansion Planning (GEP) is the problem of determining an optimal construction and generation plan of both new and existing electric power plants to meet future electricity demand. We consider a stochastic optimization approach for this capacity expansion problem under demand and fuel price uncertainty. In a two-stage stochastic optimization model for GEP, the capacity expansion plan for the entire planning horizon is decided prior to the uncertainty realized and hence allows no adaptivity to uncertainty evolution over time. In comparison, a multi-stage stochastic optimization model allows full adaptivity to the uncertainty evolution, but is extremely difficult to solve. To reconcile the trade-off between adaptivity and tractability, we propose a partially adaptive stochastic mixed integer optimization model in which the capacity expansion plan is fully adaptive to the uncertainty evolution up to a certain period and follows the two-stage approach thereafter. Any solution to the partially adaptive model is feasible to the multi-stage model, and we provide analytical bounds on the quality of such a solution. We propose an efficient algorithm that solves a sequence of partially adaptive models, to recursively construct an approximate solution to the multi-stage problem. We identify sufficient conditions under which this algorithm recovers an optimal solution to the multi-stage problem. Finally, we conduct extensive test of our algorithm on a realistic GEP problem. Experiments show that, within a reasonable computation time limit, the proposed algorithm produces a significantly better solution than solving the multi-stage model directly.

In Memoriam: Shabbir Ahmed (1969–2019)

“…With an eye toward realworld implementation, the developed algorithm was fully automated and produced multiple candidate solutions, allowing practitioners to choose a treatment plan based on their own subject-matter expertise. Next, the work of Zou et al (2018) extends Shabbir's work in power-generation optimization. The problem they consider is to solve location-allocation problems in the context of electric power plants, but without knowing future power demands or fuel prices.…”

“…A multistage model in which adaptive decisions can be made over time in response to evolving data provides the desired flexibility for decision makers but is extraordinarily difficult to solve. Zou et al (2018) develop a compromise between these approaches: a partially adaptive SIP that essentially curtails the point past which adaptive decisions can be made.…”

Adaptive Two-stage Stochastic Programming with an Application to Capacity Expansion Planning

“…Following the studies Singh et al (2009), Zou et al (2018), we represent the generation capacity expansion planning problem as a stochastic program. We reformulate this problem as an adaptive two-stage program, where the capacity acquisition decisions can be revised once within the planning horizon.…”

“…Another two-stage approximation to multi-stage models is presented in Bodur and Luedtke (2018) using Linear Decision Rules by limiting the decisions to be affine functions of the uncertain parameters. As an alternative intermediate approach, Zou et al (2018) proposes solving a generation capacity expansion planning problem by first considering a multi-stage stochastic program until a predefined stage, and then representing it as a two-stage program. They also develop a rolling horizon heuristic as discussed in Ahmed (2016) to approximate the multi-stage model.…”

Importance Sampling based Exploration in Q Learning

“…One class of algorithms builds on the stochastic programming paradigm and extends two-stage decomposition schemes such as Benders Decomposition [54] or Progressive Hedging [38]. However, these methods depend on the existence of dual variables in the subsequent stage or on efficient and stable quadratic programming solvers and can be difficult to extend to problems with non-convex constraints, although some recent work has been done to address this [59,60,27].…”