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This paper investigates an optimal sizing strategy for an islanded building microgrid. The microgrid composites a rooftop Photovoltaic (PV) system, a Battery Energy Storage System (BESS), an ice-Thermal Energy Storage System (ice-TESS), and loads. The loads are divided into two sets based on their ability to participate in demand response: i) Plugged Loads (PL) such as lights, and ii) Cooling Loads (CL) such as air-conditioners. The microgrid is islanded and loads must be supplied with local generation resources. Therefore, the BESS is deployed to offset the PV output's variability, and the absence of PV power supply at night time. However, relying only on the BESS incurs high stress and shortens the BESS's lifetime. Hence, we propose an optimal sizing strategy of the microgrid constituents, where the BESS coordinates with the ice-TESS to maintain the balance between generation and load in the microgrid …