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Operational Valuation for Energy Storage under Multi-stage Price Uncertainties

Bolun Xu, Audun Botterud, Magnus Korpas

TL;DR

This paper presents an analytical method for calculating the operational value of an energy storage device under multi-stage price uncertainties that calculates the storage value function from price distribution functions directly instead of sampling discrete scenarios, offering proved modeling accuracy over tail distribution events such as price spikes and negative prices.

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.

Operational Valuation for Energy Storage under Multi-stage Price Uncertainties

TL;DR

This paper presents an analytical method for calculating the operational value of an energy storage device under multi-stage price uncertainties that calculates the storage value function from price distribution functions directly instead of sampling discrete scenarios, offering proved modeling accuracy over tail distribution events such as price spikes and negative prices.

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.

Paper Structure

This paper contains 17 sections, 3 theorems, 30 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Formulation
  3. Formulation
  4. Value Function and Stochastic Dynamic Programming
  5. Main Results
  6. Dual Decomposition
  7. Quantifying SoC Value Distribution
  8. Value Function for Risk-Neutral Policies
  9. Algorithmic Implementation
  10. Extension to General Objectives
  11. Empirical Analysis
  12. Computation Performance
  13. Impact of Price Standard Deviations
  14. Storage Charging Case Study
  15. Conclusion
  16. ...and 2 more sections

Key Result

Proposition 2

(Dual decomposition)

Figures (3)

  • Figure 1: Comparison between the proposed method and the benchmark SDDP solver over 24 look-ahead stages.
  • Figure 2: Example of energy storage value vs. different price distributions, assuming normal distribution with standard deviations $\sigma$ of 10, 30, and 50.
  • Figure 3: Charging a 100kW/200kWh battery from 10% to 90% SoC using real-time prices and different price forecasts.

Theorems & Definitions (8)

  • Remark 1
  • Proposition 2
  • Remark 3
  • Theorem 4
  • Proposition 5
  • Remark 6
  • Remark 7
  • proof