Concentrating Solar Thermal Power with point focus Fresnel lens and reflector.

A bifacial thermal absorber is used. 50% of the light falls on the front of the absorber. The rest is reflected to the back of the absorber with a mirror.  The input aperture is 1m2, the radius of the absorber is 10mm, the average concentration level is 3087 with an optical geometric efficiency of 97% (excluding reflection/transmission/tip losses).  

If only the front surface is used, then the optical efficiency drops to 87.3% for an average concentration level of 3080 (run fresnelx w1000 g2500 l10000 s1000 c870:9.5 r0). About 6% (after subtracting the reflective loss due to the mirror) more energy can be extracted by using both surfaces.

The heat from an array of these absorbers will be stored in graphite pebbles. The heat from the storage system will be used to produce mechanical work (Rankine, Ericsson, Stirling, Scroll, Brayton and rotary engines). Mechanical compressor can use this mechanical energy for cooling or heating purpose. The mechanical energy can be converted directly to AC electricity with a 3-phase induction motor (thus avoiding the cost of using an inverter).

The 1000mm square fresnel lens is available as part number BHPA1000-2 from http://www.bhlens.com/fresnel_lens.aspx 

The higher the difference in temperature between the heat source and the heat sink, the greater the theoretical efficiency. Convection and conduction losses are insignificant at high concentration ratio. Since practical selective coatings only work up to 800K, they are irrelevant for high temperature concentrators.

Tstagnation  Maximum achievable temperature = (IC/σ)0.25
oC
Direct beam solar irradiation [W/m2] = 887 W/m2
Solar concentration ratio 
σ Stefan-Boltzmann = 5.67x10-8 W/(m2 K4)
Tc Temperature of hot reservoir (K)  oC
Ta Temperature of cold reservoir (K)  oC
Carnot Efficiency 1 - Ta/Tc %
Ts Sun's photosphere temperature = 5778K
Black body limit (1-Tc4/Ts4)(1-Ta/Tc) %

Simulation

run 'fresnelx w1000 g2500 l1000 s100 r51 c50:10 c97:10' first to calculate concentration levels

fresnelx w1000 g2500 l1000 s100 r51 13531 2677 v.2
 887.65W/m2 refractive index at 589.2nm(1.492) m(20), eff(99.990%) SunHalfAngle(0.26657o)
Total input energy 888 Watts
Acrylic Fresnel Lens Width 1000mm x 0.150mm, Area 1.00m2, Focal Length 1000mm (f/1.000), 2500 grooves
Slice  Radius   Power    Tot   Tot  QEff        Ix      Ax     Area    UV  Blue Green   Red   NIR    IR
                                                                       390   492   622   760  1110  4000
           mm       W      W     %     %                        cm2     %     %     %     %     %     %
   0  564.190  887.65    888 100.0  50.8      1.0      1.0 10000.00   5.6  13.0  19.6  18.2  27.5  16.0
Cell 1 Concentration Level 3531.000x, distance from lens 983.171mm, 0.9832f, nominal radius 9.495mm
   1    0.200   17.57     18   2.0  65.9 157450.4 157450.4     0.00   8.3   7.5   0.0  17.4  66.8   0.0
   2    0.400   18.06     36   4.0  66.3  53956.7  79839.5     0.00   8.0   7.3   0.0  17.2  67.4   0.0
   3    0.600   18.19     54   6.1  66.7  32606.3  53599.7     0.01   8.0   7.4   0.0  17.4  67.2   0.0
   4    0.800   18.40     72   8.1  67.2  23570.4  40462.2     0.01   7.9   7.4   0.0  18.0  66.7   0.0
   5    1.000   18.05     90  10.2  67.5  17975.6  32367.2     0.01   8.0   7.7   0.0  21.2  63.0   0.0
   6    1.200   17.42    108  12.1  67.8  14196.1  26814.5     0.01   8.3   8.2   0.0  28.7  54.8   0.0
   7    1.400   16.76    124  14.0  67.2  11556.3  22766.6     0.02   8.7   8.8   0.0  35.1  47.4   0.0
   8    1.600   17.24    142  16.0  68.7  10303.5  19845.6     0.02   8.4   8.9   0.0  32.3  50.4   0.0
   9    1.800   18.46    160  18.0  71.3   9735.0  17723.7     0.02   7.9   8.7   0.0  28.3  55.1   0.0
  10    2.000   19.25    179  20.2  73.5   9084.4  16082.3     0.02   7.5   8.7   0.0  25.7  58.0   0.0
  11    2.200   20.04    199  22.5  75.7   8553.4  14775.6     0.03   7.2   8.9   0.0  24.0  59.8   0.0
  12    2.400   19.04    218  24.6  66.4   7419.0  13600.5     0.03   7.6  10.0   0.1  25.2  51.6   5.4
  13    2.600   19.39    238  26.8  51.5   6952.8  12617.1     0.03   7.5  10.5   0.7  23.2  34.6  23.5
  14    2.800   21.27    259  29.2  37.2   7061.3  11851.8     0.03   6.8  10.3   1.1  19.5  21.4  41.0
  15    3.000   20.76    280  31.5  31.6   6417.7  11151.4     0.04   6.9  11.4   1.5  18.6  14.8  46.7
  16    3.200   16.95    297  33.4  36.8   4903.3  10394.8     0.04   8.4  15.3   2.4  21.5  16.0  36.5
  17    3.400   21.78    319  35.9  27.9   5916.1   9883.4     0.04   6.5  13.1   2.3  16.1  11.2  50.8
  18    3.600   19.18    338  38.1  30.7   4912.1   9346.4     0.04   7.3  16.6   3.1  17.1  11.5  44.4
  19    3.800   15.78    354  39.8  36.6   3823.7   8780.4     0.05   8.8  22.8   4.2  19.3  12.7  32.2
  20    4.000   14.76    368  41.5  38.7   3392.3   8255.0     0.05   9.3  28.1   5.1  18.8  12.3  26.4
  21    4.200   14.49    383  43.1  39.9   3169.4   7782.2     0.05   9.3  34.3   5.7  17.5  11.4  21.8
  22    4.400   15.21    398  44.8  40.2   3170.9   7372.6     0.05   8.8  42.0   6.0  15.0   9.9  18.4
  23    4.600   20.87    419  47.2  41.7   4157.8   7099.1     0.06   5.7  53.2   8.2  11.7   8.2  12.9
  24    4.800   28.99    448  50.5  47.4   5530.1   6971.0     0.06   1.6  31.5  23.2  16.0  14.7  13.0
  25    5.000   25.46    473  53.3  48.0   4657.4   6789.7     0.06   1.7  24.8  25.6  17.4  16.3  14.2
  26    5.200   23.66    497  56.0  48.4   4159.1   6591.2     0.06   1.8  21.7  27.0  17.8  17.0  14.6
  27    5.400   22.24    519  58.5  48.6   3761.5   6385.5     0.07   1.9  19.2  28.3  17.9  17.7  15.0
  28    5.600   21.18    540  60.9  48.8   3451.9   6179.7     0.07   2.0  17.7  29.4  17.4  18.2  15.3
  29    5.800   20.27    561  63.2  49.0   3188.4   5976.9     0.07   2.0  16.0  30.6  17.3  18.6  15.5
  30    6.000   19.41    580  65.4  49.1   2948.7   5778.4     0.07   2.1  14.8  32.0  16.4  19.0  15.7
  31    6.200   18.71    599  67.5  49.1   2749.6   5586.2     0.08   2.1  13.7  33.8  15.4  19.1  15.9
  32    6.400   18.10    617  69.5  49.1   2575.6   5400.9     0.08   2.2  12.8  36.0  13.7  19.2  16.1
  33    6.600   17.31    634  71.4  49.1   2388.0   5221.1     0.08   2.2  11.1  36.6  14.2  19.4  16.4
  34    6.800   16.85    651  73.3  49.0   2254.8   5049.2     0.08   2.3  10.8  36.7  14.3  19.4  16.5
  35    7.000   16.21    667  75.2  49.0   2105.8   4883.4     0.09   2.3   9.5  37.1  14.8  19.5  16.8
  36    7.200   15.75    683  76.9  48.9   1989.2   4724.8     0.09   2.3   8.9  37.3  15.0  19.4  17.0
  37    7.400   15.21    698  78.7  48.8   1868.4   4572.5     0.09   2.4   7.8  37.7  15.4  19.5  17.3
  38    7.600   14.76    713  80.3  48.6   1764.5   4426.7     0.09   2.4   7.1  37.8  15.7  19.5  17.5
  39    7.800   14.29    727  81.9  48.5   1664.3   4286.8     0.10   2.5   6.2  38.2  16.0  19.5  17.8
  40    8.000   13.90    741  83.5  48.4   1577.0   4153.0     0.10   2.5   5.4  38.4  16.3  19.5  18.0
  41    8.200   13.48    755  85.0  48.6   1492.0   4024.8     0.10   2.5   4.5  38.6  16.6  19.8  18.1
  42    8.400   13.17    768  86.5  48.7   1422.1   3902.3     0.10   2.5   3.7  38.7  16.8  20.1  18.1
  43    8.600   12.81    781  87.9  48.9   1350.6   3785.0     0.11   2.5   2.9  38.9  17.0  20.5  18.1
  44    8.800   12.49    793  89.4  49.2   1287.5   3672.8     0.11   2.5   2.3  39.2  17.3  20.8  17.9
  45    9.000   12.14    805  90.7  49.5   1223.2   3565.2     0.11   2.5   1.6  39.4  17.6  21.3  17.7
  46    9.200   11.80    817  92.1  49.8   1162.0   3461.8     0.11   2.5   0.8  39.7  17.9  21.7  17.4
  47    9.400   11.47    829  93.3  50.1   1106.1   3362.6     0.12   2.5   0.1  39.9  18.2  22.1  17.1
  48    9.600   11.15    840  94.6  50.5   1052.0   3267.4     0.12   2.5   0.0  39.6  18.5  22.6  16.8
  49    9.800   10.84    851  95.8  50.8   1001.7   3175.8     0.12   2.5   0.0  39.1  18.8  23.1  16.5
  50   10.000   10.55    861  97.0  51.2    955.5   3087.9     0.12   2.5   0.0  38.7  19.1  23.4  16.2
Cell 2 Concentration Level 677.000x, distance from lens 1038.433mm, 1.0384f, nominal radius 21.684mm

run 'fresnelx w1000 g2500 l1000 s100 r51 13531 28570.214' to calculate the radius and placement of the mirror. 8570.214 = (1000 / (1000 - (1038.433 + 983.171) / 2)) ^ 2 

Tracking Error

Visualisation of tracking error from 0 to 0.5 degree in step of 0.01 degree. The absorber is a double ended cone with a radius of 10mm and end to end height of 10mm. The heat transfer liquid will enter from the front center and exit at the back center. The image at the top right corner is the reflection of the back of the cone. The average concentration level over the entire absorber is 1380 = 1e6 * 0.97 / (2 * pi * 10 * sqrt(10^2 + 5^2))

Cost Calculations

Direct Beam Solar irradiation W/m2
Input Aperture

m2

Lens Thickness mm
Optical Transmission/Reflective Efficiency %
Optical Geometric Efficiency %
Heat engine Efficiency %
Generator Efficiency %
Daily Sunshine Hours Hours Storage Period Hours
Equipment Lifetime Years
Interest rate %
Acrylic G UVT Resin Cost

$/litre

$ $/kW
Tracking structure Cost $/m2 $ $/kW
Cost of heat engine $/kWe $ $/kW
Cost of generator $/kWe $ $/kW
Cost of inverter (not required) $/kWe $ $/kW
Storage Cost $/kWht $ $/kW
Balance of system $/kWe $ $/kW
Total cost $/m2 $ $/kW
Investment $/kWh/year GWh/year kWh/year
Levelized $/kWh $/hectare/year
Electrical Output kWe Module Efficiency % Thermal Output kWt
Barrel of oil equivalent (574kWhe/Barrel) $/Barrel tonnes of CO2
Coal Equivalent (2767kWhe/tonne) tonnes $/tonne tonnes of CO2
Gas Equivalent (5572kWhe/1000m3) 1000m3 $/1000m3 tonnes of CO2

Links

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Last updated: 20 February 2011