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Robust and learning-augmented algorithms for degradation-aware battery optimization

Jack Umenberger, Anna Osguthorpe Rasmussen

TL;DR

This paper proposes an algorithm, based on online mirror descent, that is no-regret in the stochastic i.i.d. setting and attains finite asymptotic competitive ratio in the adversarial setting (robustness) while still retaining robustness properties when the advice is poor.

Abstract

This paper studies the problem of maximizing revenue from a grid-scale battery energy storage system, accounting for uncertain future electricity prices and the effect of degradation on battery lifetime. We formulate this task as an online resource allocation problem. We propose an algorithm, based on online mirror descent, that is no-regret in the stochastic i.i.d. setting and attains finite asymptotic competitive ratio in the adversarial setting (robustness). When untrusted advice about the opportunity cost of degradation is available, we propose a learning-augmented algorithm that performs well when the advice is accurate (consistency) while still retaining robustness properties when the advice is poor.

Robust and learning-augmented algorithms for degradation-aware battery optimization

TL;DR

This paper proposes an algorithm, based on online mirror descent, that is no-regret in the stochastic i.i.d. setting and attains finite asymptotic competitive ratio in the adversarial setting (robustness) while still retaining robustness properties when the advice is poor.

Abstract

This paper studies the problem of maximizing revenue from a grid-scale battery energy storage system, accounting for uncertain future electricity prices and the effect of degradation on battery lifetime. We formulate this task as an online resource allocation problem. We propose an algorithm, based on online mirror descent, that is no-regret in the stochastic i.i.d. setting and attains finite asymptotic competitive ratio in the adversarial setting (robustness). When untrusted advice about the opportunity cost of degradation is available, we propose a learning-augmented algorithm that performs well when the advice is accurate (consistency) while still retaining robustness properties when the advice is poor.
Paper Structure (54 sections, 12 theorems, 96 equations, 1 figure, 2 algorithms)

This paper contains 54 sections, 12 theorems, 96 equations, 1 figure, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Preliminaries
  5. Online resource allocation problem
  6. Application to BESS optimization
  7. Time horizon
  8. Limitations of the model
  9. Offline solution and dual problem
  10. Measures of performance
  11. Related work
  12. Degradation-aware BESS optimization
  13. Online resource allocation
  14. Learning-augmented algorithms
  15. Robust algorithm
  16. ...and 39 more sections

Key Result

Theorem 1

When requests $\gamma_t$ are drawn i.i.d. from an unknown distribution, alg:robust with stepsize $\eta$ achieves: where $C_1 = \bar{f}\bar{b}/\rho$, $C_2 = (5\mu_{\max}^2\bar{f}(1+\bar{b}/\underline{b}))/(2\underline{b})$ and $C_3 = (\rho + \bar{b})^2/2$.

Figures (1)

  • Figure 1: Illustration of \ref{['ex:stochastic_case']}, showing (top to bottom) cumulative reward, cumulative degradation, and opportunity cost estimates. The optimal total reward and multiplier are $\text{\scriptsizeOPT}\approx 173.90$ and $\mu^\star \approx 0.87$, respectively. The rolling average estimate in \ref{['eq:ratio_of_averages']} systematically underestimates $\mu^\star$, leading to early resource depletion and lower cumulative reward ($140.19$). The rolling average estimate in \ref{['eq:rolling']} allows our \ref{['alg:robust']} to approach $\mu^\star$ more quickly than pure mirror descent, resulting in higher total reward ($171.08$ vs $166.10$).

Theorems & Definitions (22)

  • Definition 1
  • Definition 2
  • Remark 1
  • Theorem 1: Regret bound
  • Corollary 1
  • proof
  • Theorem 1: Asymptotic competitive ratio
  • Corollary 2
  • proof
  • Example 1
  • ...and 12 more