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• Design of an optimization framework for battery economic-conscious charging. • Costs of both electrical energy waste and battery ageing are directly considered. • Contradictory objectives along with immeasurable states and constraints are optimized. • Charging strategies towards time, energy and economic managements are obtained. • Effects of three sensitive elements are comparatively studied via Pareto frontier. Technical challenges facing the development of battery economic charging for energy management arise from various contradictory objectives, immeasurable internal states, and hard constraints. Available solutions often resort to optimizing economic charging from the perspective of power grid, while few focus on the benefits of electric vehicle (EV) owners. This paper proposes a constrained multi-objective optimization framework to achieve economy-conscious battery charging management. Specifically, a coupled electrothermal-aging model is first applied to capture the nonlinear electrical, thermal, and aging dynamics of a lithium-ion battery with different timescales. Then an economic indicator considering the total charging cost caused by both the battery aging and electrical energy loss is formulated, based on a battery resale cost model and the Beijing peak-valley time-of-use (TOU) price. In addition, two crucial but contradictory objectives including the charging time and battery average temperature are also taken into account, along with hard constraints on the battery State of Charge (SOC), charging current, terminal voltage, and temperature. The complicated multi-objective charging problem is solved by using NSGA-II to optimize the multistage constant-current (MCC) profile. Sensitivities of the cut-off voltage, convection resistance, and ambient temperature are comparatively analysed via Pareto frontier. Numerical results of two extreme cases and several balanced charging cases demonstrate that feasible, economy-conscious battery charging management for various user demands can be achieved through suitable equilibrations among charging speed and thermal variations during charging. [ABSTRACT FROM AUTHOR]