Abstract

Area utilization efficiency (AUE) is formulated for a sloping heliostat system facing any direction. The effects of slope shading, incidence factor, sun shading, and tower blocking by the mirrors are all taken into account. Our results show that annually averaged AUEs calculated for heliostat systems (1) increase with tower height at low slope angles but less rapidly at high slopes, (2) increase monotonically with slope angle and saturate at large slopes for systems facing due south, (3) reach a maximum at a certain slope for systems facing other directions than due south, and (4) drop sharply at slopes greater than a certain value for systems facing due east or west due to slope shading effect. The results are useful for solar energy collection on nonflat terrains.

© 1983 Optical Society of America

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References

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  1. G. Francia, Sol. Energy 12, 51 (1968).
    [CrossRef]
  2. F. Trombe, A. Le Phat Vinh, Sol. Energy 18, 57 (1973).
    [CrossRef]
  3. L. L. Vant-Hull, A. F. Hilderbrandt, Sol. Energy 18, 31 (1976).
    [CrossRef]
  4. J. L. Abatut, A. Achaibou, Sol. Energy 21, 453 (1978).
    [CrossRef]
  5. T. Tanaka, Sol. Energy 25, 97 (1980).
    [CrossRef]
  6. J. T. Holmes, in Proceedings, Facility Operators and Experiments Workshop, 3–4 May 1979, Albuquerque, N.M., p. 31.
  7. M. R. Riaz, Eng. Power 98, 375 (1976).
    [CrossRef]
  8. L. Y. Wei, Appl. Opt. 19, 3196 (1980).
    [CrossRef] [PubMed]
  9. F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978).
  10. L. Y. Wei, Sol. Energy 26, 559 (1981).
    [CrossRef]

1981 (1)

L. Y. Wei, Sol. Energy 26, 559 (1981).
[CrossRef]

1980 (2)

1978 (1)

J. L. Abatut, A. Achaibou, Sol. Energy 21, 453 (1978).
[CrossRef]

1976 (2)

L. L. Vant-Hull, A. F. Hilderbrandt, Sol. Energy 18, 31 (1976).
[CrossRef]

M. R. Riaz, Eng. Power 98, 375 (1976).
[CrossRef]

1973 (1)

F. Trombe, A. Le Phat Vinh, Sol. Energy 18, 57 (1973).
[CrossRef]

1968 (1)

G. Francia, Sol. Energy 12, 51 (1968).
[CrossRef]

Abatut, J. L.

J. L. Abatut, A. Achaibou, Sol. Energy 21, 453 (1978).
[CrossRef]

Achaibou, A.

J. L. Abatut, A. Achaibou, Sol. Energy 21, 453 (1978).
[CrossRef]

Francia, G.

G. Francia, Sol. Energy 12, 51 (1968).
[CrossRef]

Hilderbrandt, A. F.

L. L. Vant-Hull, A. F. Hilderbrandt, Sol. Energy 18, 31 (1976).
[CrossRef]

Holmes, J. T.

J. T. Holmes, in Proceedings, Facility Operators and Experiments Workshop, 3–4 May 1979, Albuquerque, N.M., p. 31.

Kreider, J. F.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978).

Kreith, F.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978).

Le Phat Vinh, A.

F. Trombe, A. Le Phat Vinh, Sol. Energy 18, 57 (1973).
[CrossRef]

Riaz, M. R.

M. R. Riaz, Eng. Power 98, 375 (1976).
[CrossRef]

Tanaka, T.

T. Tanaka, Sol. Energy 25, 97 (1980).
[CrossRef]

Trombe, F.

F. Trombe, A. Le Phat Vinh, Sol. Energy 18, 57 (1973).
[CrossRef]

Vant-Hull, L. L.

L. L. Vant-Hull, A. F. Hilderbrandt, Sol. Energy 18, 31 (1976).
[CrossRef]

Wei, L. Y.

Appl. Opt. (1)

Eng. Power (1)

M. R. Riaz, Eng. Power 98, 375 (1976).
[CrossRef]

Sol. Energy (6)

L. Y. Wei, Sol. Energy 26, 559 (1981).
[CrossRef]

G. Francia, Sol. Energy 12, 51 (1968).
[CrossRef]

F. Trombe, A. Le Phat Vinh, Sol. Energy 18, 57 (1973).
[CrossRef]

L. L. Vant-Hull, A. F. Hilderbrandt, Sol. Energy 18, 31 (1976).
[CrossRef]

J. L. Abatut, A. Achaibou, Sol. Energy 21, 453 (1978).
[CrossRef]

T. Tanaka, Sol. Energy 25, 97 (1980).
[CrossRef]

Other (2)

J. T. Holmes, in Proceedings, Facility Operators and Experiments Workshop, 3–4 May 1979, Albuquerque, N.M., p. 31.

F. Kreith, J. F. Kreider, Principles of Solar Engineering (McGraw-Hill, New York, 1978).

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Figures (7)

Fig. 1
Fig. 1

Relative position of a mirror on a slope to the sun and to the tower top.

Fig. 2
Fig. 2

Solar altitude angles vs hour along the south direction on summer solstice (SS), equinox (EQ), and winter solstice (WS).

Fig. 3
Fig. 3

Solar altitude angles vs hour along the east (in the morning) or along the west (in the afternoon) on SS, EQ, and WS.

Fig. 4
Fig. 4

Configuration of a trapezoidal heliostat array.

Fig. 5
Fig. 5

Annually averaged 〈ηan vs slope angle of a sloping heliostat system facing due south.

Fig. 6
Fig. 6

Annually averaged 〈ηan vs slope angle of a sloping heliostat system facing due north.

Fig. 7
Fig. 7

Annually averaged 〈ηan vs slope angle of a sloping heliostat system facing due east (or west).

Equations (16)

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η = C U = C A k / N A = ( C / N ) k = 1 N cos θ k ,
U = ( 1 / N ) ( j = 1 N 1 cos θ i j + N 2 cos θ s + k = 1 N 3 cos θ t k ) ,
α p = tan 1 s 3 / s p ,
η = U u ( α p β ) ,
s 1 = sin θ s sin β s , s 2 = sin θ s cos β s , s 3 = cos θ s ,
cos θ s = sin L sin δ + cos L cos δ cos t ,
sin β s = cos δ sin t / sin θ s .
s p = s 1 cos γ + s 2 sin γ .
H m n = H ± γ n sin β ,
cos θ i = 0.707 ( 1 + cos 2 θ i ) 1 / 2 = 0.707 ( 1 + s ˆ · t ˆ m n ) 1 / 2 ,
s ˆ = i ˆ s 1 + j ˆ s 2 + k ˆ s 3 ,
t ˆ m n = ( i ˆ x m n j ˆ y m n + k ˆ H m n ) a m n ,
a m n = ( x m n 2 + y m n 2 + H m n 2 ) 1 / 2 .
η a n = 1 4 ( η ¯ s s + η ¯ w s + 2 η ¯ E Q ) .
cos θ t k = H m n / ( x k 2 + y k 2 + H m n 2 ) 1 / 2 ,
k cos θ k j

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