In this paper‎, ‎a formulation is developed for sizing of a Hybrid Energy Storage System (HESS) in different applications‎. ‎Here‎, ‎the HESS is a combination of Lithium battery and Ultra-Capacitor (UC)‎, ‎which is useful for many high energy and high power applications such as Hybrid Electric Vehicles (HEVs) and renewable energy‎. ‎The sizing formulas are based on initial cost and 10-years battery replacement cost which is arranged as an optimization problem‎. ‎For battery replacement cost‎, ‎the Lithium battery capacity depletion formulas are studied for a LiFePO4 battery‎. ‎As a case study‎, ‎application of HESS in a Series Hybrid Electric Bus (SHEB) is considered‎. ‎The results show by the addition of UC‎, ‎the Lithium battery life is improved significantly‎. ‎Furthermore‎, ‎the optimum sizing of the HESS is dependent to the SHEB driving cycle‎. ‎Therefore‎, ‎considering the power profile of the HESS in its sizing process may reduce HESS cost‎. ‎This effect is studied in three different cycles of the SHEB‎. ‎In addition‎, ‎the formulation is applied to cycle-based optimization of the Power Distribution Control Strategy (PDCS) of the HESS by dynamic programming‎. ‎The results show the optimum PDCS has better LiFePO4 battery life in comparison with the conventional PDCS‎.