In this paper, a multi-stage planning-operation co-optimization model of an active distribution network (ADN) integrated with energy storage systems (ESSs) is proposed, in which the lifetime of batteries is also considered. By adopting piecewise linearized battery lifetime model and approximate power balance constraints based on Kirchhoff's Current Law and Kirchhoff's Voltage Law, the problem is reconstructed as a mixed integer linear programming model. This model considers the bi-directional power flows in the ADN, multi-stage planning logical constraints, and the replacement/addition of feeders/ESS. In addition, the cost of construction, operation, power trading, ESS lifetime loss, and lost load are included in the objective function. Moreover, Benders decomposition is utilized to improve the convergence speed of the model, which becomes difficult to solve due to the complex battery lifetime evaluation. Case studies based on a fictitious 18-node ADN demonstrate the effectiveness of the proposed method, which produces economic planning result considering the battery lifetime for an ADN with ESS.