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

TL;DR

The work addresses the misestimation of Li-ion battery flexibility in power-system optimization caused by constant-efficiency and constant-power-limit assumptions. It develops a detailed nonlinear electrochemical model based on an equivalent-circuit representation and then derives a convex, linear reformulation using sampling-based convex envelopes to enable binary-free optimization. The approach yields SOC-dependent power limits and efficiencies, and is validated against NLP, ideal, and MILP benchmarks in a 24-bus economic dispatch study, showing notable improvements over ideal models and comparable performance to NLP with lower computational burden. This framework enhances the realism and scalability of storage integration in planning and operation, and provides a practical tool for reliability-aware energy storage scheduling.

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.

Figures (7)

• Figure 1: Steady-state battery equivalent circuit
• Figure 2: Maximum current normalized to the battery capacity, as a function of the SOC. Shadow areas indicate feasible operation.
• Figure 3: Discharging and charging efficiencies vs. the SOC and discharging and charging power
• Figure 4: Operating region of Li-ion battery in variable space of (a) $[p^\text{dis}, SOC, p^\text{out}]^{\top}$, and (b) $[p^\text{cha}, SOC, p^\text{in}]^{\top}$. The curve indicates non-linear dependence, black dots denote sampled points, and the lines between the sampled points define the convex envelope of the sampled points.
• Figure 5: Scheduling of the battery charge and discharge processes for (a)-(b) Case NLP, and (c)-(d) Case LP--Ideal. The dotted line denotes the maximum power as a function of the $SOC$ based on Model \ref{['mod:NLPModel']}. The red areas indicate infeasible operation.