Grid-scale battery energy storage systems (BESSs) are promising to solve multiple problems for future power systems. Due to the limited lifespan and high cost of BESS, there is a cost-benefit trade-off between battery effort and operational performance. Thus, we develop a battery degradation model to accurately represent the battery degradation and related cost during battery operation and cycling. A linearization method is proposed to transform the developed battery degradation model into the mixed integer linear programming (MILP) optimization problems. The battery degradation model is incorporated with a hybrid deterministic/stochastic look-ahead rolling optimization model of wind-BESS bidding and operation in the real-time electricity market. Simulation results show that the developed battery degradation model is able to effectively help to extend the battery cycle life and make more profits for windBESS. Moreover, the proposed rolling look-ahead operational optimization strategy can utilize the updated wind power forecast, thereby also increase the wind-BESS profit.