Series elastic actuator (SEA) has been widely used in rehabilitation robotics, where human-robot interaction is required. Due to its intrinsic compliance, SEA can improve the usage of power for its motor, which leads to a compact and lightweight SEA design. The aim of this paper is to reduce the energy consumption and the power requirements of the motor of the SEA by optimizing the stiffness of its spring. This study is inspired by the biomechanics of a human ankle joint, which stores elastic energy during the first phases of the walking process and releases the stored energy in the next gait phases to propel the human body forward. Power analysis and optimization procedure are conducted on complete SEA models with different complexity, including inertia, damping and stiffness, and with open loop and closed loop control strategies. Simulation results demonstrate that a reduction of 56.6% of the peak motor power can be achieved with the optimized spring stiffness.