Concentrating Solar Power (CSP) dish systems use a parabolic dish to concentrate sunlight, providing heat for a thermodynamic cycle to generate shaft power and ultimately, electricity. Currently, leading contenders use a Stirling cycle engine with a heat absorber surface at about 800°C. The concentrated light passes through an aperture, which controls the thermal losses of the receiver system. Similar systems may use the concentrated light to heat a thermochemical process. The concentrator system, typically steel and glass, provides a source of fuel over the service life of the system, but this source of fuel manifests as a capital cost up front. Therefore, it is imperative that the cost of the reflector assembly is minimized. However, dish systems typically concentrate light to a peak of as much as 13,000 suns, with an average geometric concentration ratio of over 3000 suns. Several recent dish-Stirling systems have incorporated reflector facets with a normally-distributed surface slope error (local distributed waviness) of 0.8 mrad RMS (1-sigma error). As systems move toward commercialization, the cost of these highly accurate facets must be assessed. However, when considering lower-cost options, any decrease in the performance of the facets must be considered in the evaluation of such facets. In this paper, I investigate the impact of randomly-distributed slope errors on the performance, and therefore the value, of a typical dish-Stirling system. There are many potential sources of error in a concentrating system. When considering facet options, the surface waviness, characterized as a normally-distributed slope error, has the greatest impact on the aperture size and therefore the thermal losses. I develop an optical model and a thermal model for the performance of a baseline system. I then analyze the impact on system performance for a range of mirror quality, and evaluate the impact of such performance changes on the economic value of the system. This approach can be used to guide the evaluation of low-cost facets that differ in performance and cost. The methodology and results are applicable to other point- and line-focus thermal systems including dish-Brayton, dish-Thermochemical, tower systems, and troughs.

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