Common types of ESSs for renewable energy sources include electrochemical energy storage (batteries, fuel cells for hydrogen storage, and flow batteries), mechanical energy storage (including pumped hydroelectric energy storage (PHES), gravity energy storage . Common types of ESSs for renewable energy sources include electrochemical energy storage (batteries, fuel cells for hydrogen storage, and flow batteries), mechanical energy storage (including pumped hydroelectric energy storage (PHES), gravity energy storage . This paper focuses on the latest studies and applications of Photovoltaic (PV) systems and Energy Storage Systems (ESS) in buildings from perspectives of system configurations, mathematic models, and optimization of design and operation. Mathematical models, which can accurately calculate PV yield. Battery Storage Dominance with Rapid Cost Decline: Lithium-ion batteries have become the dominant energy storage technology, with costs falling over 85% since 2010 to $115/kWh in 2024. The technology choice depends essentially on system requirements, cost, and performance characteristics. Common types of ESSs for renewable energy sources include.