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        !       !       !       !           !       !
                        !

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                                                        !
Tracking Control System of the Two Axes
         Passive Solar Tracker
                        !
                        !
                        !
            !   !   !               !
                    !       !   !       !       !
!
        !   !   !   !           !       !   !   !
(95   7   )




!


                                                                          



         K W W S    E O R J O L E Q F X H G X W Z  S O R J
(high concentrated photovoltaic,

HCPV)                         HCPV



                  0.5°




               Labview       Labview

                                           0.2°

                                    0.1°          (collimating

tube)

                             0.5°

        HCPV




                         I
The purpose of this research is to develop a passive sun-tracking control system

for high concentrated photovoltaics (HCPV), which uses two axes tracking

mechanisms. HCPV uses III-V solar cell which has higher efficiency and can only

absorb the direct solar irradiation. In order to reducing the error of incident angle,

which causing degradation of insolation absorption of the solar cell, the precision of

tracker is set to be smaller than 0.5°.

     The passive tracking adopted in this study is utilizing the horizontal coordinates

of astronomy, which depends on the latitude, longitude and time zone of the tracker’s

location to calculate the altitude and azimuth of the solar. The stepping motor, which

drive the tracking mechanisms, is chosen to provide adequate rotating torque for

mechanism and rpm for coping with rapid motion of the solar trajectories (particularly

in the noon).

     This control system is programming with Labview software. When the solar

altitude and solar azimuth move at angle of 0.2°, the controller drives the stepping

motor to actuate the tracker. A collimating tube with an accuracy of 0.1° is used to

measure the error of tracking angle, and recorded the light spot in the collimating tube

with a digital camera to analyzing the error distribution. At the outdoor test,

experiment results show that the average angle error is less than 0.5° and which prove

the feasibility of the passive sun-tracking system can be used in HCPV.



Key word: HCPV, two axes passive solar tracker, sun-tracking control system




                                           II
III
....................................................................................................................I

       .................................................................................................................. II

........................................................................................................................ III

........................................................................................................................ IV

   ..................................................................................................................... VI

   ..................................................................................................................... IX

       .................................................................................................................. X

                        ................................................................................................. 1

1-1                 ..................................................................................................... 1

1-2                              ........................................................................................ 3

1-3                  .................................................................................................... 4

                           .............................................................................................. 5

2-1                          ............................................................................................ 5

      2-1-1                         ..................................................................................... 5

      2-1-2                        ...................................................................................... 5

      2-1-3                         ..................................................................................... 6

      2-1-4                                    .......................................................................... 6

2-2                                                     ................................................................. 7

      2-2-1                         ..................................................................................... 7

      2-2-2                         ..................................................................................... 8

      2-2-3                     ......................................................................................... 8

      2-2-4                                    .......................................................................... 9

2-3                                                          ............................................................ 10

                                                        IV
2-4                                            ....................................................................... 10

                              ........................................................................................ 12

3-1                             ...................................................................................... 12

3-2                         .......................................................................................... 12

3-3                 .................................................................................................. 14

3-4                         .......................................................................................... 15

                                                 ..................................................................... 17

4-1                         .......................................................................................... 17

4-2                         .......................................................................................... 18

      4-2-1                            ............................................................................... 18

      4-2-2                            ............................................................................... 19

      4-2-3                               ............................................................................ 20

      4-2-4                            ............................................................................... 21

4-3                         .......................................................................................... 22

      4-3-1                    ....................................................................................... 23

      4-3-2                    ....................................................................................... 23

           ........................................................................................................... 25

5-1         .......................................................................................................... 25

5-2                         .......................................................................................... 25

      ................................................................................................................. 27

A                                     ................................................................................ 30

B                                 .................................................................................... 38




                                                       V
1-1                                             ...................................................................... 41

1-2                 Fresnel lens                 ..................................................................... 41

1-3            Fresnel               CPV                    550                      ................................. 42

1-4                                       (a)                              [3] (b)                                   42

1-5                                    MicroDish                              HCPV               .................... 43

1-6 PV-fibre               HCPV                  (a)                 (b)                            ................. 43

1-7                                   (a)               Tetra-Track                                          (b)

 Zomeworks                               (thermal-liquid)                      (c)          Lorentz

                ..................................................................................................... 44

1-8                                                     .............................................................. 44

1-9                                                               ................................................... 45

1-10                                                                                    40°

                                          .......................................................................... 46

1-11                                                                                    32°

                              ...................................................................................... 46

1-12                                              .................................................................... 47

2-1                ................................................................................................. 48

2-2                ................................................................................................. 48

2-3                               .................................................................................. 49

2-4                  (a)                             (b)                                        ..................... 49

2-5                                             ...................................................................... 50

2-6                                       (a)               (b)        .............................................. 51

2-7                                                                                                 (a)            (b)

                                                       VI
......................................................................................................... 52

3-1                              .................................................................................. 53

3-2                          ...................................................................................... 53

3-3                                (a) PM               (b)VR             (c)                 ...................... 54

3-4                          ...................................................................................... 54

3-5            0.2°                         (a)               (b)            ....................................... 55

3-6            0.2°                         (a)               (b)            ....................................... 56

3-7                       ......................................................................................... 57

3-8                                          (a) RK564AA-T30                    (b) RK564AA-T10 ....... 57

3-9                                                           ....................................................... 58

3-10                                           .................................................................... 58

4-1               ................................................................................................. 59

4-2                          ...................................................................................... 60

4-3                              .................................................................................. 60

4-4 MathScript                                       ................................................................ 61

4-5                              (a)                   0.2° (b)                       0.2°........................ 61

4-6                          ...................................................................................... 62

4-7                                      .......................................................................... 62

4-8        Sequence                    ............................................................................. 63

4-9        Sequence                    ............................................................................. 63

4-10         Sequence                   ........................................................................... 64

4-11                           (a)                      (b)                  ........................................ 65

4-12         Sequence                   ........................................................................... 65

4-13             Sequence                   ....................................................................... 66

4-14             Sequence                   ....................................................................... 66

4-15                                           (a)                     (b)                     ..................... 67
                                                     VII
4-16   Sequence                ....................................................................... 67

4-17                 (a)                 (b)           ................................................ 68

4-18                 ................................................................................ 68

4-19       ........................................................................................... 69

4-20                                                ................................................. 69

4-21                                                                                    0.6°

                    0.4°........................................................................... 70

4-22                  2008          6       10           (a)            (b)              ............. 71

4-23                     (a)                     (b)                         (c)                ..... 72




                                     VIII
1.1        .................................................................... 40

3.1                                   ......................................... 40

4.1   .......................................................................... 40




                IX
a        (altitude)

ET         (equation of time)

H

Gs

Gw

lst

llocal

LST

n

tsolar




α        (right ascension)

β        (latitude)

γ          (azimuth)

φ

                 obliquity of the ecliptic, ε = 23°26’20.512”
ε

λ        (longitude)

δ        (declination)

θz




                                    X
1-1

                           CO2




                                                          (solar cell)

(photovoltaic, PV)

                            1-1

                        15% ~ 20%                                          III-V

                     (multi-junction, MJ)                           Spectrolab         2007

                                                  40.7%



                                                    (solar concentrator)

                                   (concentrated photovoltaic, CPV)

                                  CPV




                                            CPV                                      Fresnel

lens                                             (Fresnel lens)

       1-2                                            [1]            (concentration ratio, C)

                         (apearature area)                        (cell area)            1-3


                                             1
Araki       [2]                           (dome-shaped)                  CPV

                                 550       CPV            1970

                                                              CPV                           CPV

                 300         1000                                                  HCPV (high

concentrated photovoltaic)

                                 (parabolic dish)[3]                        (parabolic trough)[4]

       1-4 (a)         1-4 (b)

                                            HCPV                    Kusek       [5]

                                                          1-5

       Anton           [6]

                                                                                       1-6 (a)



(Cassegrain)                           1-6 (b)



                                                        1-7

                                                  [7-9]




                                                                    1-100 mm2



        Cowle            [10]

         HCPV                                     1-8                                 1°

                 90%                                                           0.5°

0.5°




                                                   2
1-2




                                                                 (open-loop)




(closed-loop)

                 20-30% [11, 12] Huang      Sun [13]




                                          [14, 15] Bako [16]

                                1-9                     40°



                46 %     1-10                    [17]

                                                                     Abdallah

Nijmeh [18]       PLC

                                          (pyranometer)              32°



      41%         1-11

                         [19]

                                                              1-12




                                      3
1-1 [20]

                          44%

                       (N-S)

                 15%

                         34%    37%


1-3

                           HCPV




                 4
2-1




  (ecliptic coordinates)                 (equatorial coordinates)

  (horizon coordinates)


2-1-1

         (ecliptic)

                             (       2-1)

                                 (vernal equinox)           (autumnal equinox)

                           (obliquity of the ecliptic, ε)                         (ε

= 23°26’20.512”)

                                                                       (latitude, β)

         (longitude, λ)



(0° ~ 90°)                           (0° ~ -90°)                                 0°



  (0 °~ 360°)


2-1-2



                                        5
(declination, δ)        (right

ascension, α) (         2-1)



                                                          ±23.45°




(hour angle)                               24

                      15°(360°/24 = 15°)


2-1-3




                                                (altitude, a)

(elevation)                                                                0° ~

                  (azimuth, γ)
90°

(-180°)                                                    ±180°          2-2



  [21]




2-1-4



                                                                     (±0.064°)

          (2-3)
                                            6
2-2




Cucuno         [22]

                                                           Goswami

        [23]




2-2-1

                                         mean solar time

                      360 56’       24


                                7
(true solar time)                                                                     (equation

of time, ET)

15                                                                 2-3



                                                   365.2422

                                          365

                                                            [24]

                            LST = tsolar − ET − (−lst + llocal ) ⋅ 4min/ deg                           (2-1)

     LST                       lst                                                llocal

ET

                                                                                                       (2-2)
                                                        B = 360( n − 81) / 364 deg
 ET = 9.87 sin 2 B − 7.53cos B − 1.5sin B


2-2-2

                                         2-1-2                                                  2-1



23.45                                                    ±23.45°             2-4 (a)

         [24]                                                                                    2-5

                                           δ     ±23.45 o                                         [23, 24]



                                 δ = 23.45o sin[360(284 + n) / 365]o                                   (2-3)

     n          1       1                         n=1              1     1


2-2-3

                                     24                                                    15

                    0                H                  [23]

                                                    8
H = 15o [t solar − 12]                                     (2-4)

             tsolar = 12 H×4 min/deg                   tsolar                              24




                                                             (Hsr)               (Hss)



                              H ss or H sr = ± cos −1[ − tan ϕ ⋅ tan δ ]                        (2-5)

     φ


2-2-4

                           2-4 (b)

         P                                                       (S         )   (P     )

θz                                                    [23]

                            θ z = cos −1[sin ϕ sin δ + cos ϕ cos δ cos H ]                      (2-6)

                    a

                            a = sin −1[sin ϕ sin δ + cos ϕ cos δ cos H ]                        (2-7)

                   γ

                                                      [22, 23]

                        cos γ = (sin a sin ϕ − sin δ ) / cos a cos ϕ                            (2-8)

                                   sin γ = cos δ sin H / cos a                                  (2-9)

                                      ±180°



                                                      0° ~ 180° Cucuno          [22]            (2-8)

                                     (2-8) (2-9)         cosγ        sinγ

                                                  9
2-3

                                            6   22

                     90°



                                 12    22

        40°




                                            121.15°      24.49°

                                                              2-6 (a)



              ±62°               0°~43°

                            2-6 (b)

±120°

                      89°




2-4




                            (precession)



                                                      25868
                                 10
(nutation)

                                                           (ephemeris)

         [25]                        A                                   2000

        6000




                2005   2008   2011                                              2-7




                              0.2°                                              (

0.5°)




                                         11
3-1

                                                                        [27]

                                                              60×60 cm2
                                 1.5 m

  HCPV                 180 kg




                            3-1 [27]



      1:6.25                                                     1:60

                                       0°~90°                        ±120°     HCPV

               30 kg                                      3-2 [27]


3-2




                              [28]                   (permanent magnet, PM)

(variable reluctance, VR)                   (hybrid)



      PM                               3-3(a)        PM

                                                12
PM

                                 PM

                      (alnico)                         45   90                (ferrite)

                                        7.5°     15°



       3-3(b)        VR                        PM



                                                 VR



               15°



                                                                 3-3 (c)



                                 1.8°~3.6°



       3-4                                                                 (pulses per

second, pps)

                                                             (start-stop region)



                                   10 pps




                                 (slew region)




                                          13
B


3-3



                          3-5 (a)   3-6 (a)



                B                                                [29]




                                                     2             3-6

                          RK564AA-T30            1:30                             0.024°

                     4 N•m                                       3-8 (a)



           3-5 (b)    3-6 (b)



                          B                                                          2

         3-7                                                 RK564AA-T10            1:10

                          0.072°                         3 N•m

                                              1:60

1:6.25                                                                  3-8 (b)



         3-1          B
                                         14
3-4



                                                              pulse

generator




              3-9



                    Adventech   ADAM-3952               DIN   50-

SCSI

                                                   (CW/CCW)



       3-10



                                            Adventech

PCI-1240U




                                 15
16
4-1

                                               National Instrument

  Labview          8          Labview



                                                                     Labview

        I/O



Labview

                                4-1



                                        [27]



                       0.2°

                                                    0.5°              0.2°

                              0.3°

      0.2°



             1-9         1-10




                                          17
4-2



                                                                   (sub

VI)




4-2-1




                   Labview

                                                  Labview

         Labview



4-2

              Get Date/Time String




        Format Date/Time String                 %H    %M     %S

             Decimal String To Number

                                        Get Date/Time In Seconds

Seconds To Date/Time
                                     18
UnBundle                day of year

                                              4-3




4-2-2

   Labview                                               M file     MathScript

MATLAB



                                      MathScript

                                                    4-4



             (shift register)



                                3-4     3-5

                                       0.2°

                                                                                     0.067°

                                                                    0.2°             Case

                 true   false                       Case

  true   false                                    0.2°       true          4-5 (a)



           0.2°         false           4-5 (b)




                                 millisecond multiple                                   (ms)

                                                                  0.2°


                                               19
4-6


4-2-3

                                           Labview

                                                  PCI-1240U



                                                                    4-7

                                                      End position

                                                      Az    Alt

                    Driving speed                           (pps)

         6000 pps                                           Movement mode

                           (relative)               (absolute)




           1000                            200

  800                                          1200                       error

out




                                    P1240DevOpen                    P1240Mot

Reset                                   Labview

                                          ID           0

      Sequence

Sequence            4-8

                                    X                  Y

                                                           268435455 ~
                             20
-268435455                                                 2147483648 ~ -2147483647

       Sequence                          4-9

                              P1240MotWrReg

                                                    For

                                                    P1240MotSavePara

                          Sequence                          4-10



P1240MotPtp

                                          Case                            true   false

4-11 (a)              false                                           4-11 (b)

                                     P1240MotStop
true

               Sequence                                   4-12

P1240MotDevClose




4-2-4

           4-2-2



                      Sequence

   Sequence                           4-13

                                                  0.2°

                                        4-14

                                         0.2°



               Case                  Sequence

0.2°                                                     0.2°      Case          true
                                             21
4-15 (a)                                                                    0.2°

Case                                      4-15 (b)



4-2-1



       Sequence

                                   4-16                         Case

                                                                                true

        4-17 (a)                                                        false

4-17 (b)



                                              4-18

Labview            Run



                                                     6000 pps          8000 pps




4-3



           0.5°          (collimating tube)

                                                                 (light spot)

                                                     4-19

                            4 mm



                                       0.02° 0.1° 0.2° 0.3° 0.4° 0.6° 0.8°

                                 4-1
                                        22
4-3-1



                                                   4-20




    4-21




4-3-2




              2008   6   10

                                                                       4-22

        (a)                                               12:30      12:50

                              0.5°    (b)

                                                             11:35     11:45

                                            0.6°




                                     23
4-23           (a)

              0.2°      (b)

                              0.4°    (c)

       (c)                    0.31°

                 0.5°




         24
5-1

              HCPV

Labview




      0.31°



                     [27]




                                 HCPV




5-2




1.




                            25
2.




3.                                            (position

     sensitive device, PSD) [31]        PSD




                                   26
1.   C. Sierra, A. J. Va´ Zquez, “high solar energy concentration with a fresnel lens,”

     J. Mterials Science 40, pp. 1339-1343, 2005.

2.   K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A.

     Akisawa, N. J. Ekins-Daukes, H. S. Lee, M. Yamaguchi “Development of

     concentrator modules with dome-shaped Fresnel lenses and triple-junction

     concentrator cells,” Prog. Photovolt: Res. Appl. 13, pp. 513-527, 2005.

3.        SES              http://stirlingenergy.com/

4.                                NREL http://www.nrel.org

5.   S. Kusek, J. Karni, M. Caraway, M. Lynn, “Description and performance of the

     microdish concentrating photovoltaic system,” 4th International Conference on

     Solar Concentrators for the Generation of Electricity or Hydrogen, pp.229-232,

     2007.

6.   I. Anton, D. Silva, G. Sala, A.W. Bett, G. Siefer, I. Luque-Heredia, T. Trebst,

     “The PV-FIBRE concentrator: a system for indoor operation of 1000X MJ solar

     cells,” Prog. Photovolt: Res. Appl. 15, pp. 431-447, 2006.

7.           Tetra-Track          http://www.dobontech.com

8.        Zomeworks             http://www.zomeworks.com

9.        Lorentz          http://www.lorentz.de

10. S. Cowley, S. Horne, S. Jensen, R. MacDonald, “Acceptance angle requirements

     for point focus CPV systems,” 4th Inter. Conf. on Solar Concentrators for the

     Generation of Electricity or Hydrogen, 2007

11. .E. Lorenzo, M. P’ erez, A. Ezpeleta, J. Acedo, “Design of tracking photovoltaic

     systems with a single vertical axis,” Prog. Photovolt: Res. Appl. 10, pp.553-543,

                                            27
2002.

12. V. Poulek, M. Libra, “New solar tracker,” Solar Energy energy Materials

      materials and Solar Cell 51, pp.113-120, 1998.

13. B. J. Huang, F. S. Sun, “Feasibility study of one axis three positions tracking

      solar PV with low concentration ratio reflector,” Energy Conversion and

      Management 48, pp. 1273-1280, 2007.

14.

                  2003      .

15. F. M. Al-naima, N. A. Yaghobian, “Design and construction of a solar tracking

      system,” Solar  Wind Technology 7, pp. 611-617, 1990.

16. G. Bakos, “Design and construction of a two-axis sun tracking system for

      parabolic trough collector (PTC) efficiency improvement,” Renewable Energy

      31, pp. 2411-2421, 2006.

17. P. Roth, A. Georgiev, H. Boudinov, “Design and construction of a system for

      sun-tracking,” Renewable energy 29, pp. 393–402, 2004.

18. S. Abdallah, S. Nijmeh, “Two axes sun tracking system with PLC control,”

      Energy Conversion and Management 45, pp. 1931–1939, 2004.

19. F.R. Rubio, M.G. Ortega, F. Gordillo, M. Lo’ pez-Martı’ nez, “Application of new

      control strategy for sun tracking,” Energy Conversion and Management 48, pp.

      2174–2184, 2007.

20. S. Abdallah, “The effect of using sun tracking systems on the voltage–current

      characteristics and power generation of flat plate photovoltaics,” Energy

      Conversion and Management 45, pp. 1671-1679, 2004.

21.

      http://zh.wikipedia.org/w/index.php?title=%E9%A6%96%E9%A1%B5variant

      =zh-tw
                                          28
22. M. Cucuno, D. Kaliakatsos, V. Marinelli, “General calculation methods for sorlar

      trajectories,” Renewable Energy 11, pp. 223-234, 1997.

23. D. Yogi Goswami, F. Kreith, Jan F. Kreider, Principle of Solar Engineering,

      Taylor  Francis, 2nd Ed., 1999.

24.                                                  “

                         ”               25                    , pp. 2148-2153, 2004.

25. I. Reda, A. Andreas, “Solar position algorithm for solar radiation applications,”

      NREL/TP-560-34302, January 2008.

26.                                http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html

27.

          2008

28.                                                              1994

29.              http://www.orientalmotor.com.tw/

30.              http://www.advantech.tw/

31. A. Luque and V. Andreev, Concentrator Photovoltaics, Chapter 11,

      Springer-Verlag Berlin Heidelberg 2007.




                                            29
A


A-1

                            Reda     Andreas [25]




                                                                                     0.0003°

                                            2000                6000


A-2

                                                 (Julian day)

                         JD                      4713    1      1                           12




                                                 (                  )



            JD=365.25× Y + 4716) + 30.6001×(M + 1) + D + B              1524.5             (A1)

      Y                  2000 2003           M                                   1

                         M3                M        Y              Y=Y 1 M=M +12

  D          decimal time                                                    2        12    30

             30   (UT)      D=2.521180556

  B                      JD2299160                                                   (Julian

          calendar)      B=0         JD2299160

          (Gregorian calendar)     B=2   A + A/4          A = Y/100

                                            30
(Julian Ephemeris Day, JDE)

                                                        ∆T
                                      JDE = JD +                                     (A2)
                                                      86400
               (Julian century, JC)                  (Julian Ephemeris Century, JCE)

                                             JD − 2451545
                                                                                               (A3)
                                      JC =
                                                36525
                                                  JDE − 2451545
                                                                                               (A4)
                                      JCE =
                                                     36525
               (Julian Ephemeris Millennium, JME)

                                                  JCE
                                                                                               (A5)
                                      JME =
                                                   10
          ∆T             (Terrestrial Time, TT)

                                                                                   NASA [26]

               ∆T                                              ∆T

          1986        2005

                                ∆T = c0 + c1t           c2t2 + c3t3 + c4t4 + c5t5              (A6)

                        c0=64.86, c1=0.3345, c2=0.060374, c3=0.0017275,

c4=0.000651814, c5=0.00002373599 t = y – 2000 y =                             +(       – 0.5)/12

          2005        2050

                                      ∆T = c0 + c1t + c2t2                                     (A7)

                        c0=62.92, c1=0.32217, c2=0.005589 t               y             (A6)



                                                                         ∆T

NASA           [26]                                     1999              3000


A-3

                                                                [25]

       (Earth periodic terms)                                       L0
                                             31
L0i = Ai × cos( Bi + Ci × JME )                   (A8)


                                                L0 = ∑ L0 i
                                                         n


                                                                                                  (A9)
                                                        i =0



      Ai Bi Ci                 A-1        L0        i               n     L0

      L1    L2   L3       L4     L5                      (A7)      (A8)

                          L(          )

                  L0 + L1 × JME + L2 × JME 2 + L3 × JME 3 + L4 × JME 4 + L5 × JME 5
             L=
                                                108
                                                                                                 (A10)



                                                               L(in radians) × 180
                                           L(in degree) =
                                                                       π                         (A11)
      L                        0°~360°                              B                R

      (A8) ~ (A11)


A-4

           A-3                                           L                 B

                      β               Θ:

                                               Θ = L + 180                                       (A12)

                                               0° ~ 360°

                                               β = −B                                            (A13)


A-5

                                                                                 (A14) ~ (A18)



                                                 (elongation)


                                                        32
JCE 3
      X 0 = 297.85036 + 445267.11148 × JCE − 0.0019142 × JCE 2 +
                                                                                            189474     (A14)
                                 (anomaly)

                                                               JCE 3
      X 1 = 357.52772 + 35999.05034 × JCE − 0.0001603 × JCE −                          2

                                                              300000                                   (A15)


                                                                                             JCE 3
      X 2 = 134.96298 + 477198.867398 × JCE + 0.0086972 × JCE 2 +
                                                                                             56250     (A16)
                            (argument of latitude)
                                                                                             JCE 3
      X 3 = 93.27191 + 483202.017538 × JCE − 0.0036825 × JCE 2 +
                                                                                            327270     (A17)
                                 (longitude of the ascending node)
                                                                                            JCE 3
      X 4 = 125.04452 − 1934.136261× JCE + 0.0020708 × JCE 2 +
                                                                                           450000      (A18)
                                                                               ∆ψi   ∆εi
        A-2                            (A19)       (A20)


                          ∆ψ i = (ai + bi × JCE ) × sin(∑ X j × Yi , j )
                                                                      4


                                                                                                       (A19)
                                                                     j=0




                          ∆ε i = (ci + di × JCE ) × cos(∑ X j × Yi , j )
                                                                      4


                                                                                                       (A20)
                                                                     j =0



     a i, bi, ci, di             a, b, c, d    i                          Xj           (A14) ~ (A18)

X0 ~ X4 Yi,j           Y0 ~ Y4         i                                                       [25]



                                  ∆ψ                    ∆ε

                                                   ∑ ∆ψ
                                                     n

                                                                 i
                                        ∆ψ =       i =0

                                               36000000                                                (A21)

                                                   ∑ ∆ε
                                                    n

                                                             i
                                        ∆ε =       i =0

                                               36000000                                                (A22)




                                                          33
A-6

             (A13)

                                             0°

   A-5

                                                      A-2

         λ                    (              )

                                       λ = Θ + ∆ψ + ∆τ                        (A23)
               20.4898
      ∆τ = −
                                            ∆ψ
                3600R


A-7



               (ε = 23°26’ 20.512” )

                                                      ∆ε)
                                        (                           (mean obliptic

of the ecliptic, ε0)

                       ε0
ε 0 = 84381.448 − 4680.93U − 1.55U 2 + 1999.25U 3 − 51.38U 4 − 249.67U 5
                                                                              (A24)
      − 39.05U 6 + 7.12U 7 + 27.87U 8 + 5.79U 9 + 2.45U 10
      U=JME/10

                       ε
                                             ε0
                                       ε=        + ∆ε
                                            3600                              (A25)

A-8




                                                 34
(mean sidereal time in Greenwich, ν0)

              ν 0 = 280.46061837 + 360.98564736629 × ( JD − 2451545) +
                                                 JC 3
                   0.000387933 × JC 2 −
                                              38710000                               (A26)


                                          α              δ
A-9



                                         α           δ                (observer local angle,

H)
                                     sin λ cos ε − tan β sin ε
                           tan α =
                                               cos λ                                 (A27)
                           sin δ = sin β cos ε + cos β sin ε sin λ                   (A28)

          α                     0° ~ 360°

                                H = ν + llocal − α                                   (A29)

      ν           llocal


A-10

          (A27)~(A29)



                                                         (parallax)




                                                    8.794
                                              ξ=
                                                   3600 × R                          (A30)
                      u

                                       tan u = 0.99664719 × tan ϕ                    (A31)


                                              35
φ

                    x
                                                  E
                                 x = cos u +           × cos ϕ
                                               6378140                                    (A32)
   E

                    y
                                                               E
                          y = 0.99664719 × sin u +                  × sin ϕ
                                                            6378140                       (A33)

A-11

                                                ∆α
                                                         − x sin ξ sin H
                                      tan( ∆ α ) =
                                                      cos δ − x sin ξ cos H               (A34)
               δ’
                                                    (sin δ − y sin ξ ) cos(∆α )
                                      tan δ '=
                                                      cos δ − x sin ξ cos H               (A35)
               H’

                                            H ' H − ∆α
                                               =                                          (A36)

               ξ, x, y                               A-10


A-12

       (A35) (A36)                                                                (2-7)

                         a0
                                   P    283            1.02
                          ∆a =       ×       ×
                                 1010 273 + T 60 tan( a + 10.3 )
                                                          a0 + 5.11
                                                       0
                                                                                          (A37)
   P                                 T

       (2-7)     (A37)                                         a'

                                            a ' a0 + ∆a
                                               =                                          (A38)

                                               36
(A35) ~ (A38)

(2-8) (2-9)

     γ’




                    37
B


B-1

        3-4   3-5                                            0.2°



      3-2




                            0.00033°/s                                0.06°/s

                              rpm




                  0.00033°/s×π/180°[rads]×60/2π[rpm] = 0.00055 rpm              (B1)



                      0.06°/s×π/180°[rads]×60/2π[rpm] = 0.01 rpm                (B2)

      (B1) (B2)

                                           (Gs)                     (Gw)




                      0.00055 rpm×6.25       Gs ×60    Gw      0.21 rpm         (B3)



                      0.01 rpm×6.25      Gs ×60   Gw        3.75 rpm            (B3)




                                      38
B-2




  100 kg                                                            50%

                                 80%




                            5.72°

                        100 kg × sin(5.72°) = 9.965 kg                    (B4)

                                       0.35 m

       T

                    T = 9.965 kg × 0.35 m × 9.81 m/s2 = 34.22 N.m         (B5)



                2                                T0

                    T0 = 34.22 N.m / (60×6.25×0.8×0.5)×2 = 0.43 N.m       (B6)



                         0.2 m

                                            T1

      T1 = (100 kg×0.2 m×9.81 m/s2) / (60×6.25×0.8×0.5)×2 = 1.31 N.m      (B7)




                                       39
1-1




3-1
             (rpm)
                                                                      (N•m)     (rpm)

      0.00055                     :   RK564AA-T30             1.31            0.21
                                      (        1:30
                     1:60
                              :           )
                     1:6.25
      0.01                        :   RK564AA-T10             0.43            3.75
                                      (        1:10
                     1:60
                              :           )
                     1:6.25



4-1


                                               H
        2            2            0                400            0             0         0
  2.69812            2      0.69812                400    0.0017453    0.10004894       0.1
  3.39556            2      1.39556                400    0.0034889    0.19999983       0.2
  4.09335            2      2.09335                400   0.00523338    0.29999965       0.3
  4.79116            2      2.79116                400    0.0069779    0.40000051       0.4
  6.18682            2      4.18682                400   0.01046705    0.60000006       0.6
   7.5825            2       5.5825                400   0.01395625    0.79998787       0.8
  8.97894            2      6.97894                400   0.01744735    1.00006509         1

                                          40
1-1                  [3]




1-2   Fresnel lens   [1]




                           41
1-3   Fresnel   CPV         550         [2]




         (a)                      (b)

1-4              (a)              [3] (b)     [4]




                       42
1-5                   MicroDish            HCPV     [5]




                                                            (a)




                                              (b)
1-6 PV-fibre   HCPV       (a)        (b)              [6]




                                43
(a)             (b)                         (c)

1-7               (a)         Tetra-Track                    [7] (b)

Zomeworks         (thermal-liquid)     [8] (c)     Lorentz




1-8         500                             [10]




                           44
1-9        [16]




      45
1-10                40°

                   [16]




1-11                32°

       [18]




              46
1-12   [19]




          47
2-1      [21]




2-2             (   )    (   )   (

) [21]




                    48
2-3




      (a)         (b)

2-4   (a)   (b)         [23]




            49
2-5




      50
(a)




            (b)

2-6   (a)         (b)




            51
(a)




      (b)

2-7         (a)   (b)


      52
3-1   [27]




3-2




             53
(a)                        (b)           (c)

3-3           [28] (a) PM        (b)VR   (c)




3-4         [28]




                            54
(a)




         (b)

3-5   0.2°     (a)   (b)




         55
(a)




         (b)

3-6   0.2°     (a)   (b)




         56
3-7         [29]




      (a)                                (b)



3-8                (a) RK564AA-T30   (b) RK564AA-T10 [29]




                      57
3-9




3-10




       58
4-1




      59
4-2




4-3




      60
4-4 MathScript




                 (a)                  (b)

4-5                (a)    0.2° (b)   0.2°




                         61
4-6




4-7




      62
4-8   Sequence




4-9   Sequence




                 63
4-10   Sequence




                  64
(a)            (b)

4-11                (a)    (b)




4-12   Sequence




                          65
4-13   Sequence




4-14   Sequence



                  66
(a)                      (b)

4-15              (a)        (b)




4-16   Sequence




                        67
(a)                (b)

4-17         (a)    (b)




4-18




                   68
4-19




4-20


       69
4-21               0.6°

       0.4°




              70
(a)




              (b)

4-22   2008   6        10   (a)   (b)




                  71
(a)




             (b)




             (c)

4-23   (a)         (b)   (c)




             72

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FW:

  • 1. ! ! ! ! ! ! ! ! ! ! ! ! ! Tracking Control System of the Two Axes Passive Solar Tracker ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
  • 2. (95 7 ) ! K W W S E O R J O L E Q F X H G X W Z S O R J
  • 3. (high concentrated photovoltaic, HCPV) HCPV 0.5° Labview Labview 0.2° 0.1° (collimating tube) 0.5° HCPV I
  • 4. The purpose of this research is to develop a passive sun-tracking control system for high concentrated photovoltaics (HCPV), which uses two axes tracking mechanisms. HCPV uses III-V solar cell which has higher efficiency and can only absorb the direct solar irradiation. In order to reducing the error of incident angle, which causing degradation of insolation absorption of the solar cell, the precision of tracker is set to be smaller than 0.5°. The passive tracking adopted in this study is utilizing the horizontal coordinates of astronomy, which depends on the latitude, longitude and time zone of the tracker’s location to calculate the altitude and azimuth of the solar. The stepping motor, which drive the tracking mechanisms, is chosen to provide adequate rotating torque for mechanism and rpm for coping with rapid motion of the solar trajectories (particularly in the noon). This control system is programming with Labview software. When the solar altitude and solar azimuth move at angle of 0.2°, the controller drives the stepping motor to actuate the tracker. A collimating tube with an accuracy of 0.1° is used to measure the error of tracking angle, and recorded the light spot in the collimating tube with a digital camera to analyzing the error distribution. At the outdoor test, experiment results show that the average angle error is less than 0.5° and which prove the feasibility of the passive sun-tracking system can be used in HCPV. Key word: HCPV, two axes passive solar tracker, sun-tracking control system II
  • 5. III
  • 6. ....................................................................................................................I .................................................................................................................. II ........................................................................................................................ III ........................................................................................................................ IV ..................................................................................................................... VI ..................................................................................................................... IX .................................................................................................................. X ................................................................................................. 1 1-1 ..................................................................................................... 1 1-2 ........................................................................................ 3 1-3 .................................................................................................... 4 .............................................................................................. 5 2-1 ............................................................................................ 5 2-1-1 ..................................................................................... 5 2-1-2 ...................................................................................... 5 2-1-3 ..................................................................................... 6 2-1-4 .......................................................................... 6 2-2 ................................................................. 7 2-2-1 ..................................................................................... 7 2-2-2 ..................................................................................... 8 2-2-3 ......................................................................................... 8 2-2-4 .......................................................................... 9 2-3 ............................................................ 10 IV
  • 7. 2-4 ....................................................................... 10 ........................................................................................ 12 3-1 ...................................................................................... 12 3-2 .......................................................................................... 12 3-3 .................................................................................................. 14 3-4 .......................................................................................... 15 ..................................................................... 17 4-1 .......................................................................................... 17 4-2 .......................................................................................... 18 4-2-1 ............................................................................... 18 4-2-2 ............................................................................... 19 4-2-3 ............................................................................ 20 4-2-4 ............................................................................... 21 4-3 .......................................................................................... 22 4-3-1 ....................................................................................... 23 4-3-2 ....................................................................................... 23 ........................................................................................................... 25 5-1 .......................................................................................................... 25 5-2 .......................................................................................... 25 ................................................................................................................. 27 A ................................................................................ 30 B .................................................................................... 38 V
  • 8. 1-1 ...................................................................... 41 1-2 Fresnel lens ..................................................................... 41 1-3 Fresnel CPV 550 ................................. 42 1-4 (a) [3] (b) 42 1-5 MicroDish HCPV .................... 43 1-6 PV-fibre HCPV (a) (b) ................. 43 1-7 (a) Tetra-Track (b) Zomeworks (thermal-liquid) (c) Lorentz ..................................................................................................... 44 1-8 .............................................................. 44 1-9 ................................................... 45 1-10 40° .......................................................................... 46 1-11 32° ...................................................................................... 46 1-12 .................................................................... 47 2-1 ................................................................................................. 48 2-2 ................................................................................................. 48 2-3 .................................................................................. 49 2-4 (a) (b) ..................... 49 2-5 ...................................................................... 50 2-6 (a) (b) .............................................. 51 2-7 (a) (b) VI
  • 9. ......................................................................................................... 52 3-1 .................................................................................. 53 3-2 ...................................................................................... 53 3-3 (a) PM (b)VR (c) ...................... 54 3-4 ...................................................................................... 54 3-5 0.2° (a) (b) ....................................... 55 3-6 0.2° (a) (b) ....................................... 56 3-7 ......................................................................................... 57 3-8 (a) RK564AA-T30 (b) RK564AA-T10 ....... 57 3-9 ....................................................... 58 3-10 .................................................................... 58 4-1 ................................................................................................. 59 4-2 ...................................................................................... 60 4-3 .................................................................................. 60 4-4 MathScript ................................................................ 61 4-5 (a) 0.2° (b) 0.2°........................ 61 4-6 ...................................................................................... 62 4-7 .......................................................................... 62 4-8 Sequence ............................................................................. 63 4-9 Sequence ............................................................................. 63 4-10 Sequence ........................................................................... 64 4-11 (a) (b) ........................................ 65 4-12 Sequence ........................................................................... 65 4-13 Sequence ....................................................................... 66 4-14 Sequence ....................................................................... 66 4-15 (a) (b) ..................... 67 VII
  • 10. 4-16 Sequence ....................................................................... 67 4-17 (a) (b) ................................................ 68 4-18 ................................................................................ 68 4-19 ........................................................................................... 69 4-20 ................................................. 69 4-21 0.6° 0.4°........................................................................... 70 4-22 2008 6 10 (a) (b) ............. 71 4-23 (a) (b) (c) ..... 72 VIII
  • 11. 1.1 .................................................................... 40 3.1 ......................................... 40 4.1 .......................................................................... 40 IX
  • 12. a (altitude) ET (equation of time) H Gs Gw lst llocal LST n tsolar α (right ascension) β (latitude) γ (azimuth) φ obliquity of the ecliptic, ε = 23°26’20.512” ε λ (longitude) δ (declination) θz X
  • 13. 1-1 CO2 (solar cell) (photovoltaic, PV) 1-1 15% ~ 20% III-V (multi-junction, MJ) Spectrolab 2007 40.7% (solar concentrator) (concentrated photovoltaic, CPV) CPV CPV Fresnel lens (Fresnel lens) 1-2 [1] (concentration ratio, C) (apearature area) (cell area) 1-3 1
  • 14. Araki [2] (dome-shaped) CPV 550 CPV 1970 CPV CPV 300 1000 HCPV (high concentrated photovoltaic) (parabolic dish)[3] (parabolic trough)[4] 1-4 (a) 1-4 (b) HCPV Kusek [5] 1-5 Anton [6] 1-6 (a) (Cassegrain) 1-6 (b) 1-7 [7-9] 1-100 mm2 Cowle [10] HCPV 1-8 1° 90% 0.5° 0.5° 2
  • 15. 1-2 (open-loop) (closed-loop) 20-30% [11, 12] Huang Sun [13] [14, 15] Bako [16] 1-9 40° 46 % 1-10 [17] Abdallah Nijmeh [18] PLC (pyranometer) 32° 41% 1-11 [19] 1-12 3
  • 16. 1-1 [20] 44% (N-S) 15% 34% 37% 1-3 HCPV 4
  • 17. 2-1 (ecliptic coordinates) (equatorial coordinates) (horizon coordinates) 2-1-1 (ecliptic) ( 2-1) (vernal equinox) (autumnal equinox) (obliquity of the ecliptic, ε) (ε = 23°26’20.512”) (latitude, β) (longitude, λ) (0° ~ 90°) (0° ~ -90°) 0° (0 °~ 360°) 2-1-2 5
  • 18. (declination, δ) (right ascension, α) ( 2-1) ±23.45° (hour angle) 24 15°(360°/24 = 15°) 2-1-3 (altitude, a) (elevation) 0° ~ (azimuth, γ) 90° (-180°) ±180° 2-2 [21] 2-1-4 (±0.064°) (2-3) 6
  • 19. 2-2 Cucuno [22] Goswami [23] 2-2-1 mean solar time 360 56’ 24 7
  • 20. (true solar time) (equation of time, ET) 15 2-3 365.2422 365 [24] LST = tsolar − ET − (−lst + llocal ) ⋅ 4min/ deg (2-1) LST lst llocal ET (2-2) B = 360( n − 81) / 364 deg ET = 9.87 sin 2 B − 7.53cos B − 1.5sin B 2-2-2 2-1-2 2-1 23.45 ±23.45° 2-4 (a) [24] 2-5 δ ±23.45 o [23, 24] δ = 23.45o sin[360(284 + n) / 365]o (2-3) n 1 1 n=1 1 1 2-2-3 24 15 0 H [23] 8
  • 21. H = 15o [t solar − 12] (2-4) tsolar = 12 H×4 min/deg tsolar 24 (Hsr) (Hss) H ss or H sr = ± cos −1[ − tan ϕ ⋅ tan δ ] (2-5) φ 2-2-4 2-4 (b) P (S ) (P ) θz [23] θ z = cos −1[sin ϕ sin δ + cos ϕ cos δ cos H ] (2-6) a a = sin −1[sin ϕ sin δ + cos ϕ cos δ cos H ] (2-7) γ [22, 23] cos γ = (sin a sin ϕ − sin δ ) / cos a cos ϕ (2-8) sin γ = cos δ sin H / cos a (2-9) ±180° 0° ~ 180° Cucuno [22] (2-8) (2-8) (2-9) cosγ sinγ 9
  • 22. 2-3 6 22 90° 12 22 40° 121.15° 24.49° 2-6 (a) ±62° 0°~43° 2-6 (b) ±120° 89° 2-4 (precession) 25868 10
  • 23. (nutation) (ephemeris) [25] A 2000 6000 2005 2008 2011 2-7 0.2° ( 0.5°) 11
  • 24. 3-1 [27] 60×60 cm2 1.5 m HCPV 180 kg 3-1 [27] 1:6.25 1:60 0°~90° ±120° HCPV 30 kg 3-2 [27] 3-2 [28] (permanent magnet, PM) (variable reluctance, VR) (hybrid) PM 3-3(a) PM 12
  • 25. PM PM (alnico) 45 90 (ferrite) 7.5° 15° 3-3(b) VR PM VR 15° 3-3 (c) 1.8°~3.6° 3-4 (pulses per second, pps) (start-stop region) 10 pps (slew region) 13
  • 26. B 3-3 3-5 (a) 3-6 (a) B [29] 2 3-6 RK564AA-T30 1:30 0.024° 4 N•m 3-8 (a) 3-5 (b) 3-6 (b) B 2 3-7 RK564AA-T10 1:10 0.072° 3 N•m 1:60 1:6.25 3-8 (b) 3-1 B 14
  • 27. 3-4 pulse generator 3-9 Adventech ADAM-3952 DIN 50- SCSI (CW/CCW) 3-10 Adventech PCI-1240U 15
  • 28. 16
  • 29. 4-1 National Instrument Labview 8 Labview Labview I/O Labview 4-1 [27] 0.2° 0.5° 0.2° 0.3° 0.2° 1-9 1-10 17
  • 30. 4-2 (sub VI) 4-2-1 Labview Labview Labview 4-2 Get Date/Time String Format Date/Time String %H %M %S Decimal String To Number Get Date/Time In Seconds Seconds To Date/Time 18
  • 31. UnBundle day of year 4-3 4-2-2 Labview M file MathScript MATLAB MathScript 4-4 (shift register) 3-4 3-5 0.2° 0.067° 0.2° Case true false Case true false 0.2° true 4-5 (a) 0.2° false 4-5 (b) millisecond multiple (ms) 0.2° 19
  • 32. 4-6 4-2-3 Labview PCI-1240U 4-7 End position Az Alt Driving speed (pps) 6000 pps Movement mode (relative) (absolute) 1000 200 800 1200 error out P1240DevOpen P1240Mot Reset Labview ID 0 Sequence Sequence 4-8 X Y 268435455 ~ 20
  • 33. -268435455 2147483648 ~ -2147483647 Sequence 4-9 P1240MotWrReg For P1240MotSavePara Sequence 4-10 P1240MotPtp Case true false 4-11 (a) false 4-11 (b) P1240MotStop true Sequence 4-12 P1240MotDevClose 4-2-4 4-2-2 Sequence Sequence 4-13 0.2° 4-14 0.2° Case Sequence 0.2° 0.2° Case true 21
  • 34. 4-15 (a) 0.2° Case 4-15 (b) 4-2-1 Sequence 4-16 Case true 4-17 (a) false 4-17 (b) 4-18 Labview Run 6000 pps 8000 pps 4-3 0.5° (collimating tube) (light spot) 4-19 4 mm 0.02° 0.1° 0.2° 0.3° 0.4° 0.6° 0.8° 4-1 22
  • 35. 4-3-1 4-20 4-21 4-3-2 2008 6 10 4-22 (a) 12:30 12:50 0.5° (b) 11:35 11:45 0.6° 23
  • 36. 4-23 (a) 0.2° (b) 0.4° (c) (c) 0.31° 0.5° 24
  • 37. 5-1 HCPV Labview 0.31° [27] HCPV 5-2 1. 25
  • 38. 2. 3. (position sensitive device, PSD) [31] PSD 26
  • 39. 1. C. Sierra, A. J. Va´ Zquez, “high solar energy concentration with a fresnel lens,” J. Mterials Science 40, pp. 1339-1343, 2005. 2. K. Araki, H. Uozumi, T. Egami, M. Hiramatsu, Y. Miyazaki, Y. Kemmoku, A. Akisawa, N. J. Ekins-Daukes, H. S. Lee, M. Yamaguchi “Development of concentrator modules with dome-shaped Fresnel lenses and triple-junction concentrator cells,” Prog. Photovolt: Res. Appl. 13, pp. 513-527, 2005. 3. SES http://stirlingenergy.com/ 4. NREL http://www.nrel.org 5. S. Kusek, J. Karni, M. Caraway, M. Lynn, “Description and performance of the microdish concentrating photovoltaic system,” 4th International Conference on Solar Concentrators for the Generation of Electricity or Hydrogen, pp.229-232, 2007. 6. I. Anton, D. Silva, G. Sala, A.W. Bett, G. Siefer, I. Luque-Heredia, T. Trebst, “The PV-FIBRE concentrator: a system for indoor operation of 1000X MJ solar cells,” Prog. Photovolt: Res. Appl. 15, pp. 431-447, 2006. 7. Tetra-Track http://www.dobontech.com 8. Zomeworks http://www.zomeworks.com 9. Lorentz http://www.lorentz.de 10. S. Cowley, S. Horne, S. Jensen, R. MacDonald, “Acceptance angle requirements for point focus CPV systems,” 4th Inter. Conf. on Solar Concentrators for the Generation of Electricity or Hydrogen, 2007 11. .E. Lorenzo, M. P’ erez, A. Ezpeleta, J. Acedo, “Design of tracking photovoltaic systems with a single vertical axis,” Prog. Photovolt: Res. Appl. 10, pp.553-543, 27
  • 40. 2002. 12. V. Poulek, M. Libra, “New solar tracker,” Solar Energy energy Materials materials and Solar Cell 51, pp.113-120, 1998. 13. B. J. Huang, F. S. Sun, “Feasibility study of one axis three positions tracking solar PV with low concentration ratio reflector,” Energy Conversion and Management 48, pp. 1273-1280, 2007. 14. 2003 . 15. F. M. Al-naima, N. A. Yaghobian, “Design and construction of a solar tracking system,” Solar Wind Technology 7, pp. 611-617, 1990. 16. G. Bakos, “Design and construction of a two-axis sun tracking system for parabolic trough collector (PTC) efficiency improvement,” Renewable Energy 31, pp. 2411-2421, 2006. 17. P. Roth, A. Georgiev, H. Boudinov, “Design and construction of a system for sun-tracking,” Renewable energy 29, pp. 393–402, 2004. 18. S. Abdallah, S. Nijmeh, “Two axes sun tracking system with PLC control,” Energy Conversion and Management 45, pp. 1931–1939, 2004. 19. F.R. Rubio, M.G. Ortega, F. Gordillo, M. Lo’ pez-Martı’ nez, “Application of new control strategy for sun tracking,” Energy Conversion and Management 48, pp. 2174–2184, 2007. 20. S. Abdallah, “The effect of using sun tracking systems on the voltage–current characteristics and power generation of flat plate photovoltaics,” Energy Conversion and Management 45, pp. 1671-1679, 2004. 21. http://zh.wikipedia.org/w/index.php?title=%E9%A6%96%E9%A1%B5variant =zh-tw 28
  • 41. 22. M. Cucuno, D. Kaliakatsos, V. Marinelli, “General calculation methods for sorlar trajectories,” Renewable Energy 11, pp. 223-234, 1997. 23. D. Yogi Goswami, F. Kreith, Jan F. Kreider, Principle of Solar Engineering, Taylor Francis, 2nd Ed., 1999. 24. “ ” 25 , pp. 2148-2153, 2004. 25. I. Reda, A. Andreas, “Solar position algorithm for solar radiation applications,” NREL/TP-560-34302, January 2008. 26. http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html 27. 2008 28. 1994 29. http://www.orientalmotor.com.tw/ 30. http://www.advantech.tw/ 31. A. Luque and V. Andreev, Concentrator Photovoltaics, Chapter 11, Springer-Verlag Berlin Heidelberg 2007. 29
  • 42. A A-1 Reda Andreas [25] 0.0003° 2000 6000 A-2 (Julian day) JD 4713 1 1 12 ( ) JD=365.25× Y + 4716) + 30.6001×(M + 1) + D + B 1524.5 (A1) Y 2000 2003 M 1 M3 M Y Y=Y 1 M=M +12 D decimal time 2 12 30 30 (UT) D=2.521180556 B JD2299160 (Julian calendar) B=0 JD2299160 (Gregorian calendar) B=2 A + A/4 A = Y/100 30
  • 43. (Julian Ephemeris Day, JDE) ∆T JDE = JD + (A2) 86400 (Julian century, JC) (Julian Ephemeris Century, JCE) JD − 2451545 (A3) JC = 36525 JDE − 2451545 (A4) JCE = 36525 (Julian Ephemeris Millennium, JME) JCE (A5) JME = 10 ∆T (Terrestrial Time, TT) NASA [26] ∆T ∆T 1986 2005 ∆T = c0 + c1t c2t2 + c3t3 + c4t4 + c5t5 (A6) c0=64.86, c1=0.3345, c2=0.060374, c3=0.0017275, c4=0.000651814, c5=0.00002373599 t = y – 2000 y = +( – 0.5)/12 2005 2050 ∆T = c0 + c1t + c2t2 (A7) c0=62.92, c1=0.32217, c2=0.005589 t y (A6) ∆T NASA [26] 1999 3000 A-3 [25] (Earth periodic terms) L0 31
  • 44. L0i = Ai × cos( Bi + Ci × JME ) (A8) L0 = ∑ L0 i n (A9) i =0 Ai Bi Ci A-1 L0 i n L0 L1 L2 L3 L4 L5 (A7) (A8) L( ) L0 + L1 × JME + L2 × JME 2 + L3 × JME 3 + L4 × JME 4 + L5 × JME 5 L= 108 (A10) L(in radians) × 180 L(in degree) = π (A11) L 0°~360° B R (A8) ~ (A11) A-4 A-3 L B β Θ: Θ = L + 180 (A12) 0° ~ 360° β = −B (A13) A-5 (A14) ~ (A18) (elongation) 32
  • 45. JCE 3 X 0 = 297.85036 + 445267.11148 × JCE − 0.0019142 × JCE 2 + 189474 (A14) (anomaly) JCE 3 X 1 = 357.52772 + 35999.05034 × JCE − 0.0001603 × JCE − 2 300000 (A15) JCE 3 X 2 = 134.96298 + 477198.867398 × JCE + 0.0086972 × JCE 2 + 56250 (A16) (argument of latitude) JCE 3 X 3 = 93.27191 + 483202.017538 × JCE − 0.0036825 × JCE 2 + 327270 (A17) (longitude of the ascending node) JCE 3 X 4 = 125.04452 − 1934.136261× JCE + 0.0020708 × JCE 2 + 450000 (A18) ∆ψi ∆εi A-2 (A19) (A20) ∆ψ i = (ai + bi × JCE ) × sin(∑ X j × Yi , j ) 4 (A19) j=0 ∆ε i = (ci + di × JCE ) × cos(∑ X j × Yi , j ) 4 (A20) j =0 a i, bi, ci, di a, b, c, d i Xj (A14) ~ (A18) X0 ~ X4 Yi,j Y0 ~ Y4 i [25] ∆ψ ∆ε ∑ ∆ψ n i ∆ψ = i =0 36000000 (A21) ∑ ∆ε n i ∆ε = i =0 36000000 (A22) 33
  • 46. A-6 (A13) 0° A-5 A-2 λ ( ) λ = Θ + ∆ψ + ∆τ (A23) 20.4898 ∆τ = − ∆ψ 3600R A-7 (ε = 23°26’ 20.512” ) ∆ε) ( (mean obliptic of the ecliptic, ε0) ε0 ε 0 = 84381.448 − 4680.93U − 1.55U 2 + 1999.25U 3 − 51.38U 4 − 249.67U 5 (A24) − 39.05U 6 + 7.12U 7 + 27.87U 8 + 5.79U 9 + 2.45U 10 U=JME/10 ε ε0 ε= + ∆ε 3600 (A25) A-8 34
  • 47. (mean sidereal time in Greenwich, ν0) ν 0 = 280.46061837 + 360.98564736629 × ( JD − 2451545) + JC 3 0.000387933 × JC 2 − 38710000 (A26) α δ A-9 α δ (observer local angle, H) sin λ cos ε − tan β sin ε tan α = cos λ (A27) sin δ = sin β cos ε + cos β sin ε sin λ (A28) α 0° ~ 360° H = ν + llocal − α (A29) ν llocal A-10 (A27)~(A29) (parallax) 8.794 ξ= 3600 × R (A30) u tan u = 0.99664719 × tan ϕ (A31) 35
  • 48. φ x E x = cos u + × cos ϕ 6378140 (A32) E y E y = 0.99664719 × sin u + × sin ϕ 6378140 (A33) A-11 ∆α − x sin ξ sin H tan( ∆ α ) = cos δ − x sin ξ cos H (A34) δ’ (sin δ − y sin ξ ) cos(∆α ) tan δ '= cos δ − x sin ξ cos H (A35) H’ H ' H − ∆α = (A36) ξ, x, y A-10 A-12 (A35) (A36) (2-7) a0 P 283 1.02 ∆a = × × 1010 273 + T 60 tan( a + 10.3 ) a0 + 5.11 0 (A37) P T (2-7) (A37) a' a ' a0 + ∆a = (A38) 36
  • 49. (A35) ~ (A38) (2-8) (2-9) γ’ 37
  • 50. B B-1 3-4 3-5 0.2° 3-2 0.00033°/s 0.06°/s rpm 0.00033°/s×π/180°[rads]×60/2π[rpm] = 0.00055 rpm (B1) 0.06°/s×π/180°[rads]×60/2π[rpm] = 0.01 rpm (B2) (B1) (B2) (Gs) (Gw) 0.00055 rpm×6.25 Gs ×60 Gw 0.21 rpm (B3) 0.01 rpm×6.25 Gs ×60 Gw 3.75 rpm (B3) 38
  • 51. B-2 100 kg 50% 80% 5.72° 100 kg × sin(5.72°) = 9.965 kg (B4) 0.35 m T T = 9.965 kg × 0.35 m × 9.81 m/s2 = 34.22 N.m (B5) 2 T0 T0 = 34.22 N.m / (60×6.25×0.8×0.5)×2 = 0.43 N.m (B6) 0.2 m T1 T1 = (100 kg×0.2 m×9.81 m/s2) / (60×6.25×0.8×0.5)×2 = 1.31 N.m (B7) 39
  • 52. 1-1 3-1 (rpm) (N•m) (rpm) 0.00055 : RK564AA-T30 1.31 0.21 ( 1:30 1:60 : ) 1:6.25 0.01 : RK564AA-T10 0.43 3.75 ( 1:10 1:60 : ) 1:6.25 4-1 H 2 2 0 400 0 0 0 2.69812 2 0.69812 400 0.0017453 0.10004894 0.1 3.39556 2 1.39556 400 0.0034889 0.19999983 0.2 4.09335 2 2.09335 400 0.00523338 0.29999965 0.3 4.79116 2 2.79116 400 0.0069779 0.40000051 0.4 6.18682 2 4.18682 400 0.01046705 0.60000006 0.6 7.5825 2 5.5825 400 0.01395625 0.79998787 0.8 8.97894 2 6.97894 400 0.01744735 1.00006509 1 40
  • 53. 1-1 [3] 1-2 Fresnel lens [1] 41
  • 54. 1-3 Fresnel CPV 550 [2] (a) (b) 1-4 (a) [3] (b) [4] 42
  • 55. 1-5 MicroDish HCPV [5] (a) (b) 1-6 PV-fibre HCPV (a) (b) [6] 43
  • 56. (a) (b) (c) 1-7 (a) Tetra-Track [7] (b) Zomeworks (thermal-liquid) [8] (c) Lorentz 1-8 500 [10] 44
  • 57. 1-9 [16] 45
  • 58. 1-10 40° [16] 1-11 32° [18] 46
  • 59. 1-12 [19] 47
  • 60. 2-1 [21] 2-2 ( ) ( ) ( ) [21] 48
  • 61. 2-3 (a) (b) 2-4 (a) (b) [23] 49
  • 62. 2-5 50
  • 63. (a) (b) 2-6 (a) (b) 51
  • 64. (a) (b) 2-7 (a) (b) 52
  • 65. 3-1 [27] 3-2 53
  • 66. (a) (b) (c) 3-3 [28] (a) PM (b)VR (c) 3-4 [28] 54
  • 67. (a) (b) 3-5 0.2° (a) (b) 55
  • 68. (a) (b) 3-6 0.2° (a) (b) 56
  • 69. 3-7 [29] (a) (b) 3-8 (a) RK564AA-T30 (b) RK564AA-T10 [29] 57
  • 70. 3-9 3-10 58
  • 71. 4-1 59
  • 72. 4-2 4-3 60
  • 73. 4-4 MathScript (a) (b) 4-5 (a) 0.2° (b) 0.2° 61
  • 74. 4-6 4-7 62
  • 75. 4-8 Sequence 4-9 Sequence 63
  • 76. 4-10 Sequence 64
  • 77. (a) (b) 4-11 (a) (b) 4-12 Sequence 65
  • 78. 4-13 Sequence 4-14 Sequence 66
  • 79. (a) (b) 4-15 (a) (b) 4-16 Sequence 67
  • 80. (a) (b) 4-17 (a) (b) 4-18 68
  • 81. 4-19 4-20 69
  • 82. 4-21 0.6° 0.4° 70
  • 83. (a) (b) 4-22 2008 6 10 (a) (b) 71
  • 84. (a) (b) (c) 4-23 (a) (b) (c) 72