Risk-constrained stochastic scheduling of multi-market energy storage systems

TL;DR

This paper tackles the challenge of scheduling energy storage under electricity price uncertainty by formulating a risk-constrained two-stage stochastic optimization framework using Conditional Value-at-Risk (CVaR). The method separates here-and-now design decisions from wait-and-see operational decisions and leverages a sample average approximation over price scenarios, enforcing an explicit tail-risk bound $\epsilon$. It validates the approach on two archetypal storage systems: an Integrated Hydrogen System (IHS) and a Battery Energy Storage System (BESS), each interacting with day-ahead and intraday markets. Key findings show that increasing risk aversion can drive larger installed capacities or more cautious dispatch, reducing tail losses at the expense of higher expected costs or lower profits, while still delivering substantial tail-risk reductions and enabling practical deployment through open-loop and rolling-horizon strategies. The results highlight the framework’s potential to help operators hedge tail risk in energy storage scheduling, with implications for capital planning, live trading, and integration of renewables, along with directions for computational improvements and extended market participation.

Abstract

Energy storage can promote the integration of renewables by operating with charge and discharge policies that balance an intermittent power supply. This study investigates the scheduling of energy storage assets under energy price uncertainty, with a focus on electricity markets. A two-stage stochastic risk-constrained approach is employed, whereby electricity price trajectories or specific power markets are observed, allowing for recourse in the schedule. Conditional value-at-risk is used to quantify tail risk in the optimization problems; this allows for the explicit specification of a probabilistic risk limit. The proposed approach is tested in an integrated hydrogen system (IHS) and a battery energy storage system (BESS). In the joint design and operation context for the IHS, the risk constraint results in larger installed unit capacities, increasing capital cost but enabling more energy inventory to buffer price uncertainty. As shown in both case studies, there is an operational trade-off between risk and expected reward; this is reflected in higher expected costs (or lower expected profits) with increasing levels of risk aversion. Despite the decrease in expected reward, both systems exhibit substantial benefits of increasing risk aversion. This work provides a general method to address uncertainties in energy storage scheduling, allowing operators to input their level of risk tolerance on asset decisions.

Figures (11)

• Figure 1: Tree diagram for two-stage stochastic program.
• Figure 2: Schematic of the integrated hydrogen system.
• Figure 3: Schematic of the battery energy storage system.
• Figure 4: Two-stage stochastic price structure - first-stage (initial trajectory) deterministic, second-stage (latter trajectory) uncertain.
• Figure 5: Scaling of computational effort with discretization quality for IHS.