Mixed-Integer Linear Programming Model to Assess Lithium-Ion Battery Degradation Cost

• Main Authors: Coelho, R.F (Author), Dias, D.P (Author), Glória, L.L (Author), Gruner, V.F (Author), Kramer, R.A.S (Author), Ludwig, M.A (Author), Martins, M.A.I (Author), Oliveira, A.C (Author), Oliveira, D.B.S (Author), Schmitz, L. (Author), Silva, A.C (Author)
• Format: Article
• Language: English
• Published: MDPI 2022
• Subjects: battery energy storage system; Battery energy storage systems; Battery management systems; Battery storage; Charging (batteries); Controllers; Cost functions; Cost models; degradation cost model; Degradation cost model; Digital storage; Electric load dispatching; Energy resources; Integer Linear Programming; Integer programming; Integrated control; Ions; Lithium-ion batteries; lithium-ion battery; Microgrid; microgrid power dispatch; Microgrid power dispatch; Microgrids; Mixed integer linear; mixed-integer linear programming; Mixed-integer linear programming; Power dispatch; States of charges
• Online Access: View Fulltext in Publisher

 This work proposes a mixed-integer linear programming model for the operational cost function of lithium-ion batteries that should be applied in a microgrid centralized controller. Such a controller aims to supply loads while optimizing the leveled cost of energy, and for that, the cost function of the battery must compete with the cost functions of other energy resources, such as distribution network, dispatchable generators, and renewable sources. In this paper, in order to consider the battery lifetime degradation, the proposed operational cost model is based on the variation in its state of health (SOH). This variation is determined by experimental data that relate the number of charge and discharge cycles to some of the most important factors that degrade the lifespan of lithium-ion batteries, resulting in a simple empirical model that depends on the battery dispatch power and the current state of charge (SOC). As proof-of-concept, hardware-in-the-loop (HIL) simulations of a real microgrid are performed considering a centralized controller with the proposed battery degradation cost function model. The obtained results demonstrate that the proposed cost model properly maintains the charging/discharging rates and the SOC at adequate levels, avoiding accelerating the battery degradation with use. For the different scenarios analyzed, the battery is only dispatched to avoid excess demand charges and to absorb extra power produced by the non-dispatchable resources, while the daily average SOC ranges from 48.86% to 65.87% and the final SOC converges to a value close to 50%, regardless of the initial SOC considered. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.