Sensitivities in Fitting a Parabolic Trough Facet

The collector accuracy requirements for parabolic trough systems are a function of the concentrator and receiver geometry. As the current trend is to use larger trough designs the need for higher accuracy is generally more important. Concentrating solar power (CSP) companies developing and deploying collectors need to meet stringent optical performance requirements and thus require accurate surface characterization instruments to validate that performance. All reflective characterization processes are sensitive to the instrument resolution, experimental setup, data fitting process, and analysis. Small changes in any of these factors can impact the estimated optical performance. It is desirable to have total local surface measurement uncertainties less than 0.5 milliradians (mrad) for a parabolic trough reflector and many instruments are capable of achieving this. Most surface characterization instruments perform a fitting process on measured data that yields a best fit description of the collector surface using some sort of polynomial. Because of this relationship it is desirable to have a robust fitting process. The type and order of the fitted polynomial and fitting process are the two major contributors to describing a facet’s surface based on the measured data. The order of the polynomial can increase or decrease the accuracy of surface description relative to the true surface. This is a function of the existing aberrations in the facet and the surface naturally described by the polynomial. An accurate description of a surface is typically obtained by performing a least squares fit on measured surface data relative to the polynomial. The best analytical description of the surface is achieved when residual errors relative to the polynomial are minimized. The difference between measured data and the best fit description is completed using an iterative process. However, not all surface imperfections on a single reflector can be accurately described with a polynomial as an exact mathematical description of the surface can never be truly achieved. Local positional errors exist in isolated areas of a facet cannot always be fit accurately. The sensitivity in the best fit description of the surface and the surface resulting from the fitting process using higher order polynomials will be discussed in this paper. The change in calculated facet location and surface slope are compared to determine the sensitivity of the process. The results are then used to calculate the intercept factor using ray tracing and estimate the sensitivity in this calculated performance metric.