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Aging-Aware Battery Control via Convex Optimization

Obidike Nnorom, Giray Ogut, Stephen Boyd, Philip Levis

TL;DR

This work addresses aging-aware battery control by balancing short-term objectives (e.g., energy arbitrage and load smoothing) with long-term lifetime. It combines a semi-empirical aging model with a convex approximation of the aging rate and implements model predictive control (MPC) to optimally manage the trade-off under forecasts. The main contributions are (i) a convex aging-rate approximation suitable for real-time MPC, (ii) quantitative characterization of the performance-longevity trade-off in both arbitrage and smoothing settings, and (iii) an open-source implementation and data. The results demonstrate that aggressive cycling boosts short-term gains but shortens battery life, while conservative operation preserves life at the cost of reduced short-term performance, highlighting the practical value of aging-aware optimization for battery management.

Abstract

We consider the task of controlling a battery while balancing two competing objectives that evolve over different time scales. The short-term objective, such as arbitrage or load smoothing, improves with more battery cycling, while the long-term objective is to maximize battery lifetime, which discourages cycling. Using a semi-empirical aging model, we formulate this problem as a convex optimization problem. We use model predictive control (MPC) with a convex approximation of aging dynamics to optimally manage the trade-off between performance and degradation. Through simulations, we quantify this trade-off in both economic and smoothing applications.

Aging-Aware Battery Control via Convex Optimization

TL;DR

This work addresses aging-aware battery control by balancing short-term objectives (e.g., energy arbitrage and load smoothing) with long-term lifetime. It combines a semi-empirical aging model with a convex approximation of the aging rate and implements model predictive control (MPC) to optimally manage the trade-off under forecasts. The main contributions are (i) a convex aging-rate approximation suitable for real-time MPC, (ii) quantitative characterization of the performance-longevity trade-off in both arbitrage and smoothing settings, and (iii) an open-source implementation and data. The results demonstrate that aggressive cycling boosts short-term gains but shortens battery life, while conservative operation preserves life at the cost of reduced short-term performance, highlighting the practical value of aging-aware optimization for battery management.

Abstract

We consider the task of controlling a battery while balancing two competing objectives that evolve over different time scales. The short-term objective, such as arbitrage or load smoothing, improves with more battery cycling, while the long-term objective is to maximize battery lifetime, which discourages cycling. Using a semi-empirical aging model, we formulate this problem as a convex optimization problem. We use model predictive control (MPC) with a convex approximation of aging dynamics to optimally manage the trade-off between performance and degradation. Through simulations, we quantify this trade-off in both economic and smoothing applications.
Paper Structure (32 sections, 11 equations, 11 figures, 1 table)

This paper contains 32 sections, 11 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Setting and tasks
  3. Short term objectives.
  4. Long term objective.
  5. Related work
  6. Battery aging models.
  7. Optimization in batteries.
  8. Model predictive control (MPC).
  9. Energy arbitrage.
  10. Renewable generation and load smoothing.
  11. Outline
  12. Cell aging model
  13. Cell charge and current
  14. Short and long term quantities.
  15. Cell aging
  16. ...and 17 more sections

Figures (11)

  • Figure 1: Charging profiles. Top. 2 cycles per day. Bottom. 4 cycles per day.
  • Figure 2: Actual and approximate aging. Top. 2 cycles per day. Bottom. 4 cycles per day.
  • Figure 3: ERCOT hourly local marginal prices for day-ahead market in 2012. The dashed lines show the mean and the maximum.
  • Figure 4: Two different weeks of price data. Top. January 2012. Bottom. June 2012.
  • Figure 5: Average hourly revenue versus battery lifetime.
  • ...and 6 more figures