Data-driven capacity planning of highway multi-energy systems under photovoltaic uncertainty using CVAE-enhanced distributionally robust optimization

Capacity planning in highway multi-energy systems faces significant challenges due to the high uncertainty of renewable energy generation and the limited availability of historical data during the planning stage. This paper proposes an integrated framework that combines photovoltaic (PV) scenario generation using a Conditional Variational Autoencoder (CVAE) with a Wasserstein-type distributionally robust optimization (DRO) model for capacity planning under renewable generation uncertainty. The CVAE generates representative PV scenarios by learning statistical characteristics and latent temporal patterns from limited datasets, thereby improving scenario representation in data-constrained highway energy systems. Based on the generated scenarios, a two-stage DRO model is formulated to jointly optimize investment and operational decisions, while explicitly accounting for probability distribution uncertainty through a norm-constrained probability ambiguity set. This approach enhances the robustness of capacity planning without relying on a single assumed probability distribution. A case study of a highway demonstrates that the proposed framework significantly improves renewable energy utilization, substantially reduces PV curtailment, and maintains stable system operation. Comparative analyses with stochastic optimization and traditional robust optimization further show that, although the DRO-based solution does not always achieve the minimum expected cost, it provides a more practical and reliable capacity planning strategy by balancing economic efficiency and robustness under uncertainty. The proposed framework therefore provides a practical decision-support tool for planning resilient highway energy infrastructures under increasing renewable penetration.