Learning-assisted Stochastic Capacity Expansion Planning: A Bayesian Optimization Approach

TL;DR

This work tackles large-scale two-stage stochastic capacity expansion planning under weather-driven uncertainty by combining time series aggregation with Bayesian optimization to tune representative-period hyperparameters. By solving surrogate CEPs instantiated on carefully weighted representative days and evaluating performance on validation scenarios, the method identifies low-cost investment and operation strategies for a joint power–gas system. The authors demonstrate that the BO-assisted approach yields robust plans with up to 3.8% cost savings over conventional aggregation baselines and reveals how hyperparameters influence asset mix, storage deployment, and decommissioning decisions. The framework offers a scalable, deployment-ready procedure for planning under uncertainty with practical implications for decarbonization and cross-energy-vector coordination.

Abstract

Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable energy (VRE) supply and energy demand becomes crucially important. However, the resulting stochastic optimization models are often less computationally tractable than their deterministic counterparts. Here, we propose a learning-assisted approximate solution method to tractably solve two-stage stochastic CEPs. Our method identifies low-cost planning decisions by constructing and solving a sequence of tractable temporally aggregated surrogate problems. We adopt a Bayesian optimization approach to searching the space of time series aggregation hyperparameters and compute approximate solutions that minimize costs on a validation set of supply-demand projections. Importantly, we evaluate solved planning outcomes on a held-out set of test projections. We apply our approach to generation and transmission expansion planning for a joint power-gas system spanning New England. We show that our approach yields an estimated cost savings of up to 3.8% in comparison to benchmark time series aggregation approaches.

Figures (8)

• Figure 1: Effect of varying the number of representative days on the CEP objective evaluated over 14 out-of-sample supply-demand projections using a single projection solution for a joint power-gas CEP (Sec. \ref{['sec:experiments']}).
• Figure 2: Conceptual difference between offline learning-assisted heuristic approaches in training and deployment (a) and our proposed BO-assisted approach (b). Here, $\theta$ denotes the heuristic hyperparameters, $x$ denotes the decision variables of the optimization task, and ML denotes the machine learning module (i.e., BO in our approach). Dashed lines indicate the flow of decision costs to ML model estimation.
• Figure 3: Supply-demand projections KhorramfarEtal-NE2024 (top) and constraints (bottom) for an illustrative stochastic capacity expansion problem with two projections and three periods (i.e., days).
• Figure 4: Pearson correlations between supply-demand parameter groups for our computational study (Sec. \ref{['sec:experiments']}). Each row/column of pixels corresponds to one hour of the day (averaged over system nodes) except for NG, where pixels correspond to daily nodal loads. For each pair of parameter groups, pixel $(i,j)$ shows the correlation of parameter $i$ in the first group with parameter $j$ in the second group.
• Figure 5: Surrogate problems are instantiated as "single-scenario" CEPs with a representative day set constructed using days sourced from different supply-demand projections. Different choices of RPC hyperparameters instantiate different surrogate problems. Setting $(k,\lambda) = (2,1)$, the resulting surrogate problem (top right) captures typical solar availability and nominal energy demand patterns. Setting $(k,\lambda) = (3,0)$, the resulting surrogate problem (bottom right) captures a wider range of load profiles but fails to capture days with high solar availability.