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Technical Briefs

# A Solar Trough Concentrator for Pill-Box Flux Distribution Over a CPV Panel

[+] Author and Article Information

Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland

A. Steinfeld1

Department of Mechanical and Process Engineering, ETH Zurich, Zurich 8092, Switzerland; and Solar Technology Laboratory, Paul Scherrer Institute, Villigen 5232, Switzerlandaldo.steinfeld@ethz.ch

The mean concentration ratio $C$ over a targeted area $A$ at the focal plane, normalized with respect to the incident direct normal irradiation $I$, is defined as $C=Qsolar/(I⋅A)$, where $Qsolar$ is the solar power intercepted by the target. $C$ is often expressed in units of “suns” when normalized to $I=1 kW/m2$.

1

Corresponding author.

J. Sol. Energy Eng 132(1), 014501 (Jan 11, 2010) (4 pages) doi:10.1115/1.4000597 History: Received June 29, 2009; Revised October 22, 2009; Published January 11, 2010; Online January 11, 2010

## Abstract

An integral methodology is formulated to analytically derive the exact profile of a solar trough concentrator that delivers a uniform radiative flux distribution over a flat rectangular target area at the focal plane. The Monte Carlo ray-tracing technique is applied to verify the analytical solution and investigate the effect of sun shape and mirror surface imperfections on the radiation uniformity and spillage. This design is pertinent to concentrating photovoltaics at moderate mean solar flux concentration ratios of up to 50 suns.

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## Figures

Figure 3

Reflector profiles for: (a) focal lengths f in the range of 3–7 m and (b) solar concentration ratios C in the range of 3–50 suns. The remaining parameters are set to the baseline values of Table 1.

Figure 4

Distribution of the solar concentration ratios at the focal plane of the solar trough concentrator for the ideal case of parallel incident radiation and no surface errors (indicated by “ideal”), and for real cases of sunrays (sunshape with CSR=5%) and surface error mode (Bivariate Chi Squared distribution) σ=0 mrad, 2 mrad, 4 mrad, and 6 mrad

Figure 5

Variation in the intercept factor γ as a function of uniformity U for the real cases of sunrays (sunshape with CSR=5%). The parameter is the surface error mode (Bivariate Chi Squared distribution), σ=0 mrad, 2 mrad, 4 mrad, and 6 mrad.

Figure 6

C-distributions on the target area after shifting the two reflector wings to their optimum relative position, for the real cases of sunrays (sunshape with CSR=5%) and for: (a) U=0.05, (b) U=0.15, and (c) U=0.3. The parameter is the surface error mode (Bivariate Chi Squared distribution), σ=0 mrad, 2 mrad, 4 mrad, and 6 mrad. The thick lines denote the C-distribution intercepted by the target area, while the thin lines denote the truncated regions to fulfill the prescribed U.

Figure 2

(a) Exact right-wing profile of the solar trough reflector for the geometrical parameters listed in Table 1; (b) distance between the exact (Fig. 2) and approximated profiles using second- and fifth-order polynomial functions

Figure 1

Right wing of the solar trough concentrator (y-axis of symmetry), comprising the reflector R and the right-half of target area T at focal distance f

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