The application of Process Integration using the Pinch Analysis technique has been recently extended to the design of hybrid power systems to determine the maximum power recovery and the battery storage capacity. The graphical and the numerical Power Pinch Analysis (PoPA) tools provide designers with visualisation tools that are systematic and simple to implement for the optimisation of power systems. However, the power losses incurred in the systems, have so far, not been considered in detail in the previous works. This paper extends the PoPA method by considering the power losses that occur during the power system's conversion, transfer and storage. The effects of the losses on the minimum outsourced electricity targets and the storage capacity are evaluated. The Storage Cascade Table (SCT) of PoPA has been further developed to include the effect of energy losses in the system's design. Application of the developed method on a case study yields the more realistic power targets for off-grid hybrid power systems
