Storage technology in Hybrid Power System (HPS) is urgently required to adapt with the mismatch between the renewable energy (RE) production and the time distribution of load demands. Different storage systems incur different types and amount of losses depending on the power conditioning as well as storage system efficiencies. This work focuses on the design of HPS with pumped hydro storage systems using Power Pinch Analysis (PoPA). The previously developed modified Storage Cascade Table (SCT) for HPS with battery storage is adapted to calculate losses associated with the pumped hydro storage system. The demonstration of the method on an Illustrative Case Study shows that the application of pumped hydro storage in HPS yield lower total losses in the system. The maximum power demand target is reduced while the targeted maximum storage capacity is increased compared to when battery storage is applied.