Data-Driven Distributionally Robust Optimization for Long-Term Contract vs. Spot Allocation Decisions: Application to Electricity Markets

TL;DR

The paper develops a data-driven DRO framework with Wasserstein ambiguity to jointly optimize long-term contract commitments and spot allocations in electricity markets, addressing distributional uncertainty beyond traditional risk-neutral models. It compares risk-neutral, CVaR-based risk-averse, and Wasserstein DRO formulations within an elasticity-aware price-taking setting, applying them to PJM market case studies. The results show that CVaR and DRO can yield comparable aggregate risk–reward tradeoffs, while NODE- and market-specific allocations differ due to the DRO penalty structure and price covariance, highlighting practical implications for risk management and contract design. The work advances robust decision-making in energy portfolio optimization and suggests avenues for incorporating transmission constraints, market power, and broader process-system contexts into DRO-augmented planning tools.

Abstract

There are numerous industrial settings in which a decision maker must decide whether to enter into long-term contracts to guarantee price (and hence cash flow) stability or to participate in more volatile spot markets. In this paper, we investigate a data-driven distributionally robust optimization (DRO) approach aimed at balancing this tradeoff. Unlike traditional risk-neutral stochastic optimization models that assume the underlying probability distribution generating the data is known, DRO models assume the distribution belongs to a family of possible distributions, thus providing a degree of immunization against unseen and potential worst-case outcomes. We compare and contrast the performance of a risk-neutral model, conditional value-at-risk formulation, and a Wasserstein distributionally robust model to demonstrate the potential benefits of a DRO approach for an ``elasticity-aware'' price-taking decision maker.

Figures (8)

• Figure 1: The power portfolio optimization problem in relation to other prominent electricity planning and scheduling problems.
• Figure 2: Illustration of key ingredients in the power portfolio optimization problem.
• Figure 3: Numerical example and explanation of the "reward-to-risk" metric $\rho_{\gamma}(\mathbf{y}^{\textrm{Spot}})$ used to compare results. Here $\gamma=0.90$ and $\mathbf{y}^{\textrm{Spot}}$ is a given non-zero spot allocation vector.
• Figure 4: Histogram of historical real-time hourly location marginal prices (LMP) at PJM node 48612 from 1 Jan 2021 through 1 May 2022.
• Figure 5: Profit vs risk tradeoff curves for Case Study 1. $\Delta$Profit and $\Delta$Risk are {the expected profit increase} and {the absolute value of the $\mathbb{CVAR}_{\gamma}$ decrease}, respectively, relative to the risk-free allocation of committing all supply to long-term contracts. The $(\alpha,\epsilon)$ values shown next to a subset of points refer to the $\mathbb{CVAR}_{\alpha}$ confidence level and the Wasserstein radius $\epsilon$ that induce the spot allocation on the horizontal axis. Two $\gamma$ values (0.95 and 0.90) are used in the $\Delta$Risk calculation, while $\alpha$ values from 0 to 1 are tested to generate the four curves.