Definition of multi-objective operation optimization of vanadium redox flow and lithium-ion batteries considering levelized cost of energy, fast charging, and energy efficiency based on current density

The life cycle of Vanadium Redox Flow Batteries (VRFBs) is about 13,000-15,000 cycles, and the life of the battery is about 20 years, while for Lithium-ion (Li-ion) batteries, the life cycle is between 300 and 500 cycles and battery life is about five years; therefore, the VRFBs are longer duration. The computation of the Levelized Cost of Energy (LCOE) for these battery types; i.e. the VRFBs and Li-ion batteries and comparing the LCOE for these batteries, and minimization of the LCOE can be helpful for larger market for these batteries in future, with lower cost, and optimized operation, which is the goal of this research study. It can be also very useful to find out differences between VRFB and Li-ion batteries in terms of cost related indexes, fast charging capabilities, and energy efficient operation. The LCOE ($/kWh) is a financial cost related index, which is used and redefined to find out the battery costs per kWh. This index is normally not related on battery internal parameters. In this research study, the Capital Expenditure (CAPEX) of the batteries are defined related to the current density for VRFB, and related to the positive electrode surface capacity of the Li-ion battery. These relative definitions leads to finding the relation of the LCOE of the batteries and the current density of the batteries, as the CAPEX and positive electrode surface capacity are related to the LCOE of the batteries. The technological advances of these batteries in near future will lead to the higher current density batteries using the new and better battery materials, which based on the result of the proposed methods in this research study will result in the lower CAPEX, and LCOE for the batteries. Then, as will be shown in the results section of this paper, these batteries will be less costly to be used in different applications in future with the optimized operation, e.g., small or large-scale ESS, electric vehicles' batteries, etc. This paper also proposes a new framework for multi-objective optimization for simultaneously minimize the charging duration (for fast charging) of the batteries, and minimization of the LCOE, and the energy loss (for higher energy efficiency) of the VRFBs and Li-ion batteries in charging mode. This optimization framework, can lead to improvement in the performance of the batteries. The results of the proposed multi-objective optimization is demonstrated for different weighing factors, and the results are compared. The results of the multi-objective optimization of the batteries are useful for optimized operation of the battery and future studies that facilitates more use of these batteries for different applications in the future and the option to choose which kind of battery is less costly, more energy efficient, and charges faster.