# Non-ideal Linear Operation Model for a Li-ion Battery

## TL;DR

This paper introduces a detailed, non-ideal linear model for Li-ion batteries that accurately captures their performance and operational limits, improving upon traditional ideal models in power system optimization.

## Contribution

It proposes a novel linear reformulation of a complex battery model that accounts for non-linear efficiencies and power limits without binary variables, enhancing accuracy and computational efficiency.

## Key findings

- The model provides a more accurate representation of battery performance.
- Simulation shows about 12% energy mismatch with ideal models.
- The approach outperforms existing non-convex and mixed-integer models.

## Abstract

Currently, the characterization of electric energy storage units used for power system operation and planning models relies on two major assumptions: charge and discharge efficiencies, and power limits are constant and independent of the electric energy storage state of charge. This approach can misestimate the available storage flexibility. This work proposes a detailed model for the characterization of steady-state operation of Li-ion batteries in optimization problems. The model characterizes the battery performance, including non-linear charge and discharge power limits and efficiencies, as a function of the state of charge and requested power. We then derive a linear reformulation of the model without introducing binary variables, which achieves high computational efficiency, while providing high approximation accuracy. The proposed model characterizes more accurately the performance and technical operational limits associated with Li-ion batteries than those present in classical ideal models. The developed battery model has been compared with three modelling approaches: the complete non-convex formulation; an ideal model typically used in the power system community; and a mixed integer linear reformulation approach. The models have been tested on a network-constrained economic dispatch for a 24-bus system. Based on the simulations, we observed approximately 12% of energy mismatches between schedules that use an ideal model and those that use the model proposed in this study.