Following the societal electrification trend, airports face an inevitable transition of increased electric demand, driven by electric vehicles (EVs) and the potential rise of electric aviation (EA). For aviation, short-haul flights are first in line for fuel exchange to electrified transportation. This work studies the airport of Visby, Sweden and the effect on the electrical power system from EA and EV charging. It uses the measured airport load demand from one year’s operation and simulated EA and EV charging profiles. Solar photovoltaic (PV) and electrical battery energy storage systems (BESS) are modelled to analyse the potential techno-economical gains. The BESS charge and discharge control are modelled in four ways, including a novel multi-objective (MO) dispatch to combine self-consumption (SC) enhancement and peak power shaving. Each model scenario is compared for peak power shaving ability, SC rate and pay-back-period (PBP). The BESS controls are also evaluated for annual degradation and associated cost. The results show that the novel MO dispatch performs well for peak shaving and SC, effectively reducing the BESS’s idle periods. The MO dispatch also results in the battery controls’ lowest PBP (6.9 years) using the nominal economic parameters. Furthermore, a sensitivity analysis for the PBP shows that the peak power tariff significantly influences the PBP for BESS investment.