[Paper Review] Operational Valuation for Energy Storage under Multi-stage Price Uncertainties

Bolun Xu, Audun Botterud+1 more|arXiv (Cornell University)|Oct 21, 2019

Smart Grid Energy Management19 references4 citations

TL;DR

This paper proposes an analytical, computationally efficient method to value energy storage under multi-stage electricity price uncertainties by directly using price distribution functions rather than scenario sampling. It achieves near-instantaneous computation (up to 100,000× faster than SDDP) while accurately capturing tail events like price spikes and negative prices, enabling real-time valuation for storage operators.

ABSTRACT

This paper presents an analytical method for calculating the operational value of an energy storage device under multi-stage price uncertainties. Our solution calculates the storage value function from price distribution functions directly instead of sampling discrete scenarios, offering improved modeling accuracy over tail distribution events such as price spikes and negative prices. The analytical algorithm offers very high computational efficiency in solving multi-stage stochastic programming for energy storage and can easily be implemented within any software and hardware platform, while numerical simulation results show the proposed method is up to 100,000 times faster than a benchmark stochastic-dual dynamic programming solver even in small test cases. Case studies are included to demonstrate the impact of price variability on the valuation results, and a battery charging example using historical prices for New York City.

Motivation & Objective

• To develop a high-speed, accurate method for valuing energy storage under multi-stage price uncertainties, especially extreme events like price spikes and negative prices.
• To overcome the limitations of scenario-based stochastic programming methods that struggle with tail distribution modeling and suffer from high computational complexity.
• To enable real-time, on-device valuation of energy storage by minimizing computational overhead and hardware requirements.
• To demonstrate the method’s superiority over benchmark solvers like SDDP in speed and accuracy using real-world New York City price data.
• To support energy storage participants in making optimal operational decisions under imperfect price forecasts using instantaneous value computation.

Proposed method

• The method formulates energy storage arbitrage as a stochastic optimal control problem with nonanticipatory policies, maximizing expected profit under known price distributions.
• It computes the storage value function analytically from the cumulative distribution function of future prices and the value function from the next period, avoiding scenario discretization.
• The solution uses a backward recursion that operates in linear time and constant space, enabling near-instantaneous computation over hundreds of forecast periods.
• The approach models price uncertainty via stage-wise independent probability distributions (e.g., normal distributions with varying standard deviations), directly incorporating tail behavior.
• It integrates real-time and day-ahead price forecasts with historical bias distributions to model uncertainty, using the New York ISO dataset for validation.
• The algorithm is implemented using only basic arithmetic and logical operations, making it deployable on low-resource hardware and software platforms.

Experimental results

Research questions

• RQ1 How can energy storage value be computed efficiently and accurately under multi-stage price uncertainties, particularly for rare but impactful events like price spikes and negative prices?
• RQ2 What is the computational advantage of using analytical distribution-based valuation over scenario-based stochastic programming methods like SDDP?
• RQ3 How does price volatility, modeled through varying standard deviations in price forecasts, affect the operational value of energy storage?
• RQ4 Can the proposed method outperform heuristic benchmarks like day-ahead price-only valuation in real-world applications with actual price data?
• RQ5 To what extent can the method be used for real-time decision-making in distributed energy storage systems with minimal computational overhead?

Key findings

• The proposed method is up to 100,000 times faster than the benchmark stochastic dual dynamic programming (SDDP) solver, even in small test cases, due to its linear time and constant space complexity.
• The method achieves higher modeling accuracy for tail events such as price spikes and negative prices by directly using distribution functions instead of sampled scenarios.
• Storage value spans a wider range as price uncertainty increases—e.g., with standard deviations of 10, 30, and 50, the marginal value range widens significantly, reflecting higher arbitrage potential.
• In a real-world case study using New York City prices, the distribution-based valuation yielded $4 in profit for charging a 100kW/200kWh battery from 10% to 90% SoC, outperforming the day-ahead price heuristic ($2) but underperforming the perfect information real-time benchmark ($8).
• The method enables instantaneous valuation computation, making it suitable for real-time deployment on low-cost hardware, unlike SDDP which becomes infeasible at high time resolutions (e.g., 5-minute markets).
• The framework successfully captures inter-temporal price variability and uncertainty, demonstrating robustness across different storage states of charge and forecast horizons.