This paper investigates the modelling and multi-objective optimization (using Non-dominated Sorting Genetic Algorithm (NSGA-II)) of a photovoltaic-battery-hydrogen hybrid renewable energy system (HRES) for a net zero energy building (NZEB) that is a five-bedroom duplex detached residential house located in the heart of Lagos, Nigeria. Three battery technologies: lithium iron phosphate (LFP) battery, retired electric vehicle battery (REVB) and Ortsfest - stationary PanZerplatte - tubular plate Verschlossen - closed lead acid (OPzV) battery, were investigated for their economic viability. An in-house simplified degradation model was used to evaluate the capacity loss (as this can have significant impact on cost calculations if not done) of the batteries with cycling and calendar aging. This addresses the lack of implementation of battery degradation modelling by many authors optimizing for HRES due to inapplicability of the models in literature for different battery chemistries. Also, this work evaluated battery-fuel cell hybrid configurations on the three objectives: annualized cost of system (ACS), loss of power supply probability (LPSP) and potential energy waste probability (PEWP) and the results were contrasted with the battery only configurations to identify scenarios where hybrid energy storage system might be more economical. The results showed that LFP and REVB are the best battery options. LFP and REVB battery only configurations are better for LPSP constraints >1 % whereas for LPSP of 1 % and below LFP-hydrogen and REVB-hydrogen are more economical.