Intermittency of renewable resources brings new challenges for the optimal investment planning of industrial power systems. Reliability, availability, and power quality constraints force to strictly ensure the system's power balance during the operation. The risk of power quality degradation is increased with the integration of large-scale photovoltaic plants that face power variation due to cloud passage. If fossil generators cannot quickly compensate for the solar power drops, a fast-responding storage system must take over to guarantee electrical stability. Therefore, the sizing of industrial microgrid must integrate this storage system and consider cloud passage which modifies the techno-economic optimization paradigm. In this paper, sub-minute solar variability is anticipated thanks to robust scenarios and integrated within the optimization formulation. A linear power quality constraint is formulated to evaluate the storage needs for cloud passage resiliency. A case study is detailed and reports that short-term variability impacts the optimal solution due to additional storage costs.