(273c) Stochastic Programming Framework for Electric Power Infrastructure Planning

Energy systems planning models can be used to study the impact of new technology developments, resource cost trends, and policy shifts on the projected generation mix to meet future demand. Such systems are highly stochastic due to the uncertainty in future fuel prices, load demand and renewable generation. However, because of the computational expense of integrating detailed operating decisions in the hourly (or sub-hourly) level with investment decisions over a few decades, and having a fairly good representation of the grid, most of the available planning tools are deterministic.

In this paper, we address the long-term planning of electric power infrastructures under uncertainty. We propose a multi-stage stochastic integer programming (MSIP) formulation that includes investment decisions on a yearly basis and operating decisions on an hourly basis. This model optimizes the generation expansion required to meet the projected electricity demand over the next few decades while considering detailed operational constraints (i.e., unit commitment), the variability and intermittency of renewable generation sources, and the power flow between regions. We consider scenarios of low, medium and high load demand in each stage.

The major challenge lies in the tractability of the model, as its deterministic version already has 1,000,000+ constraints and 400,000+ integer variables [1]. To be able to solve such a large-scale model, we decompose the problem using Stochastic Dual Dynamic Integer Programming (SDDiP) [2]. SDDiP is a stage-based decomposition that solves each node of the scenario tree separately. The algorithm solves the problem in a forward and backward fashion, in which the Forward Pass provides a feasible solution and upper bound to the expected value, and the Backward Pass projects the problem onto the subspace of the stage variables using Benders-like cuts. Additionally, to reduce solution time, we incorporate scenario sampling to the algorithm, solving the Forward and Backward Passes for a randomly selected subset of scenarios [2], and solve nodes within the same stage in parallel.

The proposed formulation and algorithm are applied to a case study in the region managed by the Electric Reliability Council of Texas (ERCOT), and we show that an initially intractable model can be solved in a reasonable amount of time.

[1] Lara, C. L., Mallapragada, D., Papageorgiou, D., Venkatesh, D., & Grossmann, I.E. (2017) “Electric Power Infrastructure Planning: Mixed-Integer Programming Model and Nested Decomposition Algorithm”, Submitted for publication.

[2] Zou, J., Ahmed, S. & Sun, X.A., (2018). “Stochastic dual dynamic integer programming”, Mathematical Programming. pp. 1-42., https://doi.org/10.1007/s10107-018-1249-5