Abstract Generally, off-grid fossil fuel generators provide energy supply to remote regions. The integration of photovoltaic (PV) plants to battery energy storage (BES) systems potentially increases reliability, the system autonomy and lifetime, reducing the generator working hours and the system environmental impact. PV–BES–Diesel generator hybrid energy systems (HESs) offer technical, economic and environmental benefits compared to traditional off-grid systems. This paper proposes a bi-objective design model for off-grid PV–BES–Diesel generator HESs. The aim is to identify the PV plant rated power, the BES system capacity and the technical configuration able to jointly reduce the levelised cost of the electricity ( LCOE ) and the carbon footprint of energy ( CFOE ) . Furthermore, the comparison of the LCOE and CFOE values of the HES against a traditional diesel generator allows determining the economic and environmental advantages coming from the described system. Despite the proposed model is general and suitable for any installation site and HES configuration, this paper exemplifies its application designing a HES to be installed in a remote village in Yakutsk, Russia. The model takes into account the hourly energy demand, the irradiation and temperature profiles of the installation location calculating the hourly PV plant yield, the battery charge–discharge processes and the required generator energy. Results highlight the technical, economic and environmental feasibility of the system for a context with a medium irradiation level, i.e. ∼1400 kW h/(m2 year), and relatively low fuel cost, i.e. 0.7 €/l. For the best economic scenario LCOE and CFOE reductions are of about 8% and 28%, respectively. Finally, the most effective trade-off between economic and environmental performances leads to a CFOE decrease of about 48% and a slight decrease of the economic performances (−2%).