Maintaining the balance between electricity production and consumption is an essential task in the operations of modern power grids. In recent years, battery energy storage system (BESS) has been gaining more and more attention owning to its decreasing capital cost, high flexibility and short response time. However, there exist several technical challenges in developing accurate models and effective algorithms for the operations of BESS. One major challenge is that in order to precisely describe the changing dynamics of battery status, usually highly non-linear functions and integer variables must be used in the model, leading to optimization models with nonlinear and non-convex objective function/constraints that are difficult to handle. To address the above challenges, in this paper we first explore the physical law in the battery charging and discharging process to develop a new model which naturally addresses both the charging and discharging processes through a single current decision variable. Then we propose to approximate the dependency relationship between the open circuit voltage (OCV) and the state of charge (SOC) by some linear functions. This leads to a new non-convex quadratic programming model with linear and bilinear constraints (BLCQP) for the identification of the optimal operational strategy for the BESS. To cope with the bilinear constraints in the BLCQP, we introduce a novel transformation technique to transfer the original BLCQP into another equivalent exponential optimization problem with linear constraints (LCEO). A new sequential linear and quadratic programming approach (SLQP) for the LCEO is developed and its convergence is established. Preliminary experiments are conducted to demonstrate the efficacy of the new model and the efficiency of the new algorithm.