An extended-power pinch analysis (EPoPA) is proposed as a means of extending the power pinch analysis (PoPA) for optimal design of renewable energy systems with battery and hydrogen storage (RES-BH). The EPoPA concept is based on the storage of wasted electricity that cannot be stored by the battery bank designed by PoPA. This energy is stored in the form of hydrogen and is discharged in the form of electricity when the external electricity source is needed. EPoPA graphical and numerical tools are introduced to determine the minimum required external electricity source, wasted electricity sources, and appropriate hydrogen storage system capacity of the RES-BH system during first and normal operation years. Furthermore, the integration of the RES-BH system with a diesel generator as a high reliable system is investigated in view point of economic. The optimal sizes of diesel generator and hydrogen storage system components, such as electrolyzer, fuel cell and hydrogen tank are obtained with the minimization of the total annual cost (TAC) of the system. The implementation results of the EPoPA tools on three possible case studies indicate that EPoPA, unlike other process integration methodologies such as PoPA, is able to optimally design RES-BH systems.