This paper presents an optimal design procedure for internally insulated, carbon steel, molten salt thermal storage tanks for parabolic trough solar power plants. The exact size of the vessel and insulation layers and the shape of the roof are optimized by minimizing the total investment cost of the storage system under three technical constraints: remaining within the maximum allowable values of both temperature and stress in the steel structure, and avoiding excessive cooling and consequent solidification of the molten salt during long periods of no solar input. The thermal, mechanical and economic aspects have been integrated into an iterative step-by-step optimization procedure, which is shown to be effective through application to the case study of a $600MWh$ thermal storage system. The optimal design turns out to be an internally insulated, carbon steel storage tank characterized by a maximum allowable height of $11m$ and a diameter of $22.4m$. The total investment cost is about 20% lower than that of a corresponding AISI 321H stainless steel storage tank without internal protection or insulation.

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