This paper develops mathematical models for dynamic simulation and predicting of the future performance of a solar-PV hybrid battery and hydrogen energy storage system that is capable of satisfying residential electrical loads in the example at Port Harcourt in Nigeria. The models from experimentally determined works were taken from various published sources in order to develop a detailed, validated and generalised model for the proposed integrated system that is hitherto lacking. Thus, the hybrid energy storage system is implemented using ideal electronic switches that ensure solar-PV power is directly utilised for battery charging, and any excess generated PV power can be converted into hydrogen fuel for domestic applications including fuel cell power generation systems. The results indicate that conversion efficiency of the solar-PV module is about 34% at this location, and battery power can satisfy low power loads for relatively longer operating period compared to fuel cell power that can satisfy higher power loads but for a shorter operating time. Apparently, the fuel cell dynamic response was limited due to reactants flow conditions near the electrodes which increase internal resistances. The inverter output waveform however, can be maintained at the standard magnitude and frequency that is required by the load.