Global, Diffuse and Direct Pyranometer - Of the Clux

Global, Diffuse and Direct Pyranometer
by
Eirik Albrigtsen
Bachelor Thesis in
Energy and Power Engineering
Grimstad, June 6, 2006

Table of Contents
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 The Sun 3
1.1 Position of the Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Julian Calendar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.2 True Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.3 Ecliptic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1.4 Equatorial Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.5 Observer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.6 Useful Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.1.7 Sunrise and Sunset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Solar Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Irradiance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Insolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Solar Irradiance Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.4 Ground Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.5 Atmospheric Extinction and Air Mass . . . . . . . . . . . . . . . . . . . . . . 10
1.2.6 Simple Estimation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2.7 Diffuse and Direct Components . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.1 Parallel Port . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Stepper Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.3 Tracker at an Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Development 16
2.1 Stepper Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.1 ULN2003A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.2 Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.3 Possible Complications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4 Two Bit Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Solar Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Silicon Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.2 Voltage Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.3 Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.4 NI-DAQ mx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 LabVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Sol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 DAQ Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.3 Corrective Spider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1

2.3.4 Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.5 Read Reset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.6 Write Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.7 Control Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Physical Realization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.1 Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.3 Constructional Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2

List of Figures
1 Diffuse radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Direct radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1 Annual mean insolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Solar irradiance spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Spectral response curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Annual mean insolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.5 Irradiance components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6 Parallel port . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7 Six wire steppers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.8 Half-step sequence and directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 ULN2003A - overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 ULN2003A - each driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Circuit diagram - stepper control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Two bit full-step sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Two bit circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6 PV cell equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 PV cell IV curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.8 Voltage Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.9 Circuit diagram - voltage amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.10 LabVIEW Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.11 sol.vi - Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.12 sol.vi - UI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.13 daq-tasks.vi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.14 corrector.vi - Code and UI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.15 step.vi - UI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.16 step.vi - Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.17 read-reset.vi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.18 write-step.vi - Code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.19 write-step.vi - UI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.20 DAQ false case structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.21 main.vi - UI and code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.22 Stepper circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.23 Solar circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.24 Lego construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.25 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3

Abstract
The instrument used to measure the various components of radiation is called a pyranometer. The
common, commercial pyranometer design uses a thermopile, setting up a voltage proportional to
the radiation based on temperature readings. This necessitates temperature compensation, as well
as a good budget. Commercial pyranometers with good functionality are very expensive and fragile.
The aim of this work is to construct a prototype for a cheap pyranometer of similar qualities as
their commercial counterparts. Using photovoltaic silicon cells, instead of thermocouples, we will
measure the global irradiance as well as its direct and diffuse components to great accuracy. The
latter requires a tracking system to either block out surrounding ’reflections’, or block out the Sun
itself.
We start out by laying down the theory for a cheap two-axis tracking system with focus on the
astronomical calculations that is needed for the tracker. Additional calculations that will improve
the functionality of the pyranometer will also have some focus.
The concepts of solar irradiance, atmospheric attenuation, air mass, spectral- and cosine responses
will be covered to show the reliability and significance of our results. As a precursor the
chosen solutions, the theory of stepper motors, and how the parallel port works, will be explained
briefly. Finally, we explain the workings of the chosen electrical circuitry and the flow of the
LabVIEW code written for our pyranometer.
This document was written for people who possess certain familiarity with mathematics and
electronics. As for programming in LabVIEW; the ability to understand and manipulate basic code
is paramount if this solution is to be replicated successfully. On the other hand, the code itself is
not hard to understand with for people with some experience.

Introduction
Pyranometer, from Greek: pyr; fire, ano; sky
A pyranometer is the main instrument used to measure the global solar irradiance (radiation). It
measures the sun’s energy from all directions (2π steradian) in the hemisphere in the plane above
the instrument. A proper pyranometer use a flat plate covered with thermopiles that absorbs
sunlight and produces a voltage proportional to the temperature. However, a less expensive and
less fragile instrument can be built from a simple circuit and a silicon photovoltaic cell.
The problem with these cells, however, is that they do not measure the whole spectrum, meaning
it will have to rely on parts of the spectrum and amplify the measured value to correlate with a
professional pyranometer. It is therefore advisable to gain access to professional pyranometer
readings to calibrate a photovoltaic pyranometer. Section 1.2 will look at this more closely.
The typical use of a pyranometer is for measurement of the global horizontal solar irradiance. For
this purpose, it is placed in a horizontal orientation and sufficiently high above the surroundings
so that it has a clear, hemispheric view of the entire sky with no shading or reflecting trees or
buildings within this field of view.
The global horizontal irradiance can be split up into two components, the direct irradiance (the
beam from the sun), and the diffuse irradiance. The latter is composed of photons scattered by the
atmosphere, and/or reflected by various surfaces if the pyranometer is located above ground level.
For ground level the diffuse component is usually around 5 → 26% [10].
Mathematically, the global horizontal irradiance I g is equal to
I g = I b cos z + I d (1)
Where I b is the beam irradiance, and I d is the diffuse. The beam irradiance measured on a horizontal
pyranometer is smaller than that of a pyrheliometer – which is pointed at the sun, and shielded from
everything else – by a factor of cos z, where z is the angle of incidence. A pyranometer stationed on
ground level for the purpose of measuring the beam irradiance, must first measure the global and
diffuse components, usually done by two separate instruments, and divide the difference by cos z.
Another solution is to simply make both a pyrheliometer and a global pyranometer, and from that,
calculate the diffuse. This, intuitively, seems like a much better solution as a diffuse sun shading
tracker is likely to result in either too much shading – because of the detachment of cell and tracker
– or periodical measurement of reflected beam irradiance from ground level if the cell is placed on
the tracker.
.
Figure 1: Normal way to measure the diffuse radiation [10]
1

A simple photovoltaic pyrheliometer can be constructed simply by placing the cell on top of
the tracker, and encasing it in some sort of tube with the proper dimensions. The global irradiance
can in turn, be measured by a free, horizontally placed cell.
.
Figure 2: Thermopile design pyrheliometer, measuring the direct radiation [10]
However, to be able to track the sun with a pyrheliometer, we need two angles, the angle of
incidence z, and the position of the sun along the horizon called the azimuth angle.
2

Chapter 1
The Sun
This chapter covers the theoretical part of the project. It starts out with the equations needed to
locate the sun using spherical geometry, and utilizes this foundation to cover additional elements
for functionality in the development. We will look at some topics on solar irradiance and what we
can expect to achieve in future measurements. Finally, the theory of stepper motors and how to
the parallel port works, will be explained briefly, as a precursor to the applications in chapter two.
1.1 Position of the Sun
The following equations follow a basic astronomical scheme to calculate the position of celestial
bodies in the sky. We have tried to indicate what each formula actually means, albeit quite briefly.
The section also goes a little beyond what’s strictly necessary to simply control a tracker, but it’ll
prove a nice addition to a pyranometer interface as you’ll see later. The first five sections are here
derived from Dr. Louis Strous’ equations and algorithms on his web page [13] (where the explanations
goes a bit further) and has proven to be very accurate.
Five factors must be considered in order to locate the sun in the sky relative to the observer:
1. Time 1.1.1
2. Speed of orbit (not constant) 1.1.2
3. Position on the ecliptic 1.1.3
4. The axial tilt (skewed rotation axis) 1.1.4
5. Position of the observer 1.1.5
1.1.1 Julian Calendar
Before we jump into these calculations, it is convenient to express the date and time in a more
mathematically compatible decimal scheme to simplify them. The astronomical standard is the
Julian Day Number J, a system effectively smacking year, month, day, hour, and minutes (and
additional subdivisions if such precision is necessary) into a single real number. This can be read
as the number of whole days elapsed since January 1. 4713 B.C. midnight UTC.
For algorithmic simplicity, we have modified Strous’ equations [14] a little to compensate for
current time, the local time zone and daylight savings time.
Definition 1.1.1 Suppose it is day number d of month number m of year y in the Gregorian
calendar (negative years and with a year 0). With the local hour h in 24 hour format, compensated
3

y the local Greenwich time zone tz and daylight savings time dst (active = 1, inactive = 0),
current minute i, second sc, the Julian day number J can then be calculated:
1. If m is less than 3, then replace m by m + 12 and y by y − 1.
2. Calculate: k = d +
h − tz − dst
24
3. The Julian Day Number J is equal to
J = ⌊
+ i
1440 + sc
86400 − 1522.5
1461 · (y + 4716) 153 · (m + 1)
⌋ + ⌊ ⌋ − ⌊ y
4
5 100 ⌋ + ⌊ y
400 ⌋ + k (1.1)
Where ⌊x⌋ means the floor of x, the closest whole number less than or equal to x. As an
interesting example, (J − ⌊J⌋) · 100% is a percentage measure of how long into the day we are
(12:00 UTC is the zero point).
1.1.2 True Anomaly
Because we observe the sun from a body rotating around it, we see our motion along the ecliptic
(plane of the Earth’s orbit) reflected in the apparent motion of the sun.
Definition 1.1.2 The mean anomaly M is the position of the earth relative to its perihelion (point
in the orbit that is closest to the sun) if the orbit were a circle. It is given by:
M = 357.5291 ◦ + 0.98560028 ◦ (J − J 2000 ) (1.2)
where J 2000 = 2451545, the latest Julian epoch (January 1. 2000 A.D.).
However, since our orbit is an elliptic one, the speed of the Earth varies and the mean anomaly is
in turn inaccurate, though only with about ±2 ◦ .
Definition 1.1.3 The true anomaly ν is the true position of the earth relative to its perihelion,
measured in degrees. The difference between the true anomaly and the mean anomaly is called the
Equation of Center, C.
1.1.3 Ecliptic
ν = M + C (1.3)
C = 1.9148 sin (M) + 0.0200 sin (2M) + 0.0003 sin (3M)
Since the perihelion is not a very expedient point of origin, the ecliptical longitude λ has been
defined as our position along the ecliptic relative to the vernal equinox. The vernal equinox occurs
when the sun, the Earth and the first point of Aries all fall on an intersecting line.
Definition 1.1.4 With the distance from the perihelion to the vernal equinox being 102.9372 ◦ , the
ecliptical longitude, λ, is equal to λ = ν + 102.9372 ◦
Conversely, if you’re looking at the sun from the Earth, you’d look exactly in the opposite direction
than if you’d look at the planet from the sun, so these angles are 180 ◦ apart.
λ sun = ν + 102.9372 ◦ + 180 ◦ (1.4)
Interestingly, λ sun (being referred to the equinox) determines the beginning of (astronomical) spring
when λ sun =0 ◦ . In fact, every whole 90 ◦ multiple of λ sun marks the beginning of a new season.
The ecliptical latitude β sun is the perpendicular distance to the sun, and negligible in most
calculations.
4

1.1.4 Equatorial Coordinates
Since the axis of rotation is not perpendicular, but rather tilted 23.45 ◦ to the side, it causes the
Earth to waltz around the sun like a predictably unstable humming top. The equatorial system
incorporates this tilt in the equations, by packing the Earth inside a large, imaginary sphere (known
as the celestial sphere) whose axis of rotation is perpendicular (i.e. points at the same North as
that of the sun).
Definition 1.1.5 The declination δ of the Earth, in the equatorial coordinate system, is the angle
between the celestial equator and the true equator in the direction of the sun. It is given simply by
δ sun = arcsin (sin(λ sun ) · sin(23.45 ◦ )) (1.5)
Definition 1.1.6 The right ascension α is the equatorial equivalent of longitude, measuring how
many hours (15 ◦ per hour) since the Earth passed the vernal equinox. Expressed modulo 360.
( sin λsun · cos (23.45 ◦ )
)
α sun = arctan
(1.6)
cos λ sun
It’s important to remember that all numerical calculations involving arctan must either have a
double input function to determine which quadrant we’re located in, or include if tests to determine
this manually. Otherwise you can expect them to flip over at the equinoxes, or whenever they cross
180 or 0. This is why sin λ
cos λ
is not reduced to tan λ.
1.1.5 Observer
The last variables needed to calculate the position of the sun are your geographical location; latitude
φ north, and longitude I w west.
Definition 1.1.7 The rotation angle of the Earth θ, measuring the sidereal time of the celestial
meridian, is given by
θ = 280.1600 ◦ + 360.9856235 ◦ (J − J 2000 ) − I w (1.7)
Definition 1.1.8 The hour angle H measures how long it’s been – in sidereal time – since the
celestial body passed through the celestial meridian.
H = θ − α (1.8)
Definition 1.1.9 The angular distance from the horizon and up to the sun, the sun’s height in the
sky, is called the altitude h. Similarly, the position along the horizon, measured from south to west,
is called the azimuth A. 1 h = arcsin (sin φ sin δ + cos φ cos δ cos H) (1.9)
(
)
sin H
A = arctan
cos H sin φ − tan δ cos φ
(1.10)
Definition 1.1.10 The zenith angle z is the angular distance from the the sun to zenith, i.e. the
complement of the altitude.
z = 90 ◦ − h (1.11)
Note that there are simplified, but less accurate, formulas for the hour angle 1.8, and declination
1.5 that lets you bypass some of the equations used here for other less elaborate ones. Check out
Power of the Sun [11] for more detail into this. Verily, neither approach drains much power from a
CPU, but the extra precision given by Strous’ equations [14] might be superfluous for the tracking
part. It does, however, add nice accuracy for the pyranometer interface.
1 These relationships work simply because all the angles are referred to the vernal equinox.
5

1.1.6 Useful Limits
The hour angle at sunset H ss , and at sunrise H sr can found [11][14] by setting h = h 0 = −0.83 into
equation 1.9
( sin (−0.83 ◦ )
) − sin φ sin δ
H ss = arccos
cos φ cos δ
(1.12)
The solution for H sr is here simply −H ss .
The reason for not setting h = 0 is to compensate for two problems. First, half of the sun is
still technically visible along the horizon when h = 0. Second, the atmosphere, tends to bend light
downwards, making the sun seem higher in the sky than it really is. The error, when using h = 0
to find the time for sunset, is up to ten minutes.
An interesting property here, and this only applies to the latitudes above ±66.55 ◦ ;
1. if tan δ · tan φ ≥ 1 the sun won’t set that day
2. if tan δ · tan φ ≤ −1 the sun won’t rise that day
The hours of daylight ω s is quickly calculable with H ss mod 360 [11]
ω s = 2H ss
15
(1.13)
It is of interest to note here that although the hours of daylight vary from month to month
except at the equator (where tan φ = 0), there are always 4, 380 hours of daylight in a year [11]
(non leap year) at any location on the earth.
H ss may also be substituted into equation 1.10 to get the azimuth at sunset.
Another limit that may be obtained is the maximum and minimum noontime solar altitude
angle by substituting H = 0 in equation 1.9
h max = 90 ◦ − |φ − δ| (1.14)
To find the extreme values at your location, simply substitute δ for δ min = −23.45 to get the
noontime altitude at winter solstice, and by δ max = 23.45 to get the highest altitude at summer
solstice.
Note that noon is used here as astronomical noon when H = 0, the time when the sun is at the
highest point. This tends to deviate a bit from the twelve o’clock noon.
6

1.1.7 Sunrise and Sunset
Having found the hour angle for sunrise and sunset quite easily, we would like to use this to calculate
backwards and find the time of it. This is a rather complicated process, since simply turning the
local sidereal time around to find the Julian date won’t work as too much information is lost in the
trigonometry and modular arithmetic.
The way out is a guessing algorithm, derived from Strous’ more universal one [14].
1. n ∗ = [J] − (0.324 + H target + I w ) · 360 −1
where [J] is the current Julian day roundest to the nearest integer
2. J ∗ = (0.324 + H target + I w ) · 360 −1 + [n]
where [n] is n ∗ rounded to the nearest integer
3. J target = J ∗ + 0.0053 sin M + 0.0069 sin (2λ sun )
4. (Optional) To improve accuracy, calculate the hour angle for J target and take
J target = J target + (H target − H improved ) · 360 −1
This can be repeated until J target no longer changes. However, the estimate will change by
about 3 minutes as λ sun and M changes throughout the day, so no need to overdo it (unless
you recalculate M and λ sun as well).
To, for instance, obtain the Julian date at sunset, it’s sufficient to simply substitute H target with
H ss . A quick manipulation of the Julian day number yields the real target hour T h, i.e. the hour
value with a decimal value to indicate where in the hour it happens.
T h = (J target − ⌊J target ⌋ + 0.5) · 24 + tz + dst mod 24 (1.15)
Here tz is the local timezone, and dst the daylight savings variable. Further manipulation to get
the date is useless to us since the day in question is always today!
7

1.2 Solar Radiation
1.2.1 Irradiance
The rate at which solar energy reaches a unit area at the Earth is called the solar irradiance or
solar radiation. The intensity of the radiation leaving the sun is relatively constant. Therefore, the
intensity of solar radiation at a distance of 1 AU (average Earth-Sun distance) is called the solar
constant I sc and has a currently accepted of 1367W/m 2 value [10]. This value is measured at a
plane perpendicular to the sun’s rays on the top of the atmosphere. This value varies with 6.8%,
as the distance to to the sun varies with 3.4% [15] (5.1 million km).
The part of this that passes through the atmosphere and hits the ground, is called the global
solar irradiance. This is composed of the diffuse component; light scattered by the atmosphere,
and the direct component; light coming directly from the sun in a beam.
1.2.2 Insolation
Earth receives a total amount of radiation determined by its cross section πr 2 , but as the planet
rotates this energy is distributed across the entire surface area 4πr 2 . Hence, the average incoming
solar radiation, known as the solar insolation, is 1/4th the solar constant or 342 W/m.
As shown in figure 1.1, the insolation diminishes the further away one gets from the equator, as
the intensity varies with the cosine of the angle of incidence, or in our case, the zenith angle 1.11.
The annual insolation mean for the south of Norway is a meager 45W/m 2 , but on a clear summer’s
day, the daily solar insolation can reach 354W/m 2 [3].
.
Figure 1.1: Annual mean insolation at top of the atmosphere [2]
1.2.3 Solar Irradiance Spectrum
The extraterrestrial solar irradiance spectrum is the wavelength range of the sun’s rays as seen
outside the atmosphere. It’s distributed relatively smooth, see the blue line in figure 1.2, with the
8

most frequent wavelength being around 500nm (which, when isolated, is percieved as green).
It is interesting to note that about 45 percent of the sun’s energy comes to us at wavelengths
in the visible spectrum, (nominally between 0.3 and 0.7 micrometers). Also, note that only a little
more than 1 percent of the sun’s energy at shorter wavelengths (UV and X-solar radiation) and the
rest (54 percent) is in the infrared (IR) region [10]. The spectrum of the sun’s radiation changes
as it passes through the earth’s atmosphere, as indicated by the orange line.
1.2.4 Ground Spectrum
As solar radiation passes through the earth ’s atmosphere, it is absorbed (the reason for some
atmospheric heating), reflected (the reason astronauts can see the earth from outer space), scattered
(the reason one can read this book in the shade under a tree), and transmitted directly (the reason
there are shadows). At the surface of the earth, the sun has a lower intensity, a different color, and
a different shape from that observed above the atmosphere. The magnitude of these effects can be
seen in figures 1.4 and 1.2.
The solar radiation spectrum extends roughly from 300 to 2800 nm (as shown in figure 1.2) at
the surface.
Figure 1.2: Solar irradiance spectrum at top of the atmosphere and the direct irradiance at sea
level. The difference between the two amount to atmospheric attenuation and scattering. [8]
It follows that a pyranometer should cover that spectrum with a spectral sensitivity that is as
flat as possible. With a photovoltaic pyranometer, however, this is simply not possible. A solar cell
responds differently to the actualy spectrum than what a professional pyranometer does – on the
other hand it does get away with the temperature compensation. In general, a solar cell can only
utilize a part of the spectrum so the producers concentrate on hitting the biggest chunk. Figure
1.3 shows how this works.
9

Figure 1.3: Example of a distorted wavelength scale plot. The relative spectral response of a silicon
photovoltaic cell is shown, indicating that it can utilize 58 percent of the sun’s energy. [10]
.
1.2.5 Atmospheric Extinction and Air Mass
The solar spectrum on Earth is not constant, and dependends on a variaety of factors, such as the
temporal condition of the atmosphere, level of ozone or other atmospheric gasses, but most of all,
the apparent size of the atmosphere. As the sun gets closer to the horizon, the sun’s rays has to
travel through more and more atmosphere to reach your location. The air mass is the ratio of the
distance a sunray has to travel through the earths atmosphere, to the distance it would travel if
the sun were directly overhead. In other words, air mass = 1 if the Sun is in zenith, and air mass
= 2 is at z around 60 ◦ . The secant of the zenith angle 1.11 is common approximation for angles
less than 60 ◦ .
More accurately, the air mass, as a function of the zenith angle z can be calculated as follows
[10]
1
Air mass =
cos z + 0.50572(96.07955 − z) −1.6364 (1.16)
In this equation, the air mass at sunset (z = 90 ◦ ) is about 37 which explains why there’s so little
radiation around that time. Note that this can only provide an intuitive estimation of what we
can expect at best. The atmospheric attenuation is a nonlinear process [9], and unique for each
10

.
Figure 1.4: Annual mean insolation at the surface (from HadCM3’s climate model [2])
wavelenght as indicated by figure 1.2. This will most likely prove to be a problem for proportional
measurements when the air mass gets big; the spectral response of the solar cell is constant, while
everything except the red part of the spectrum is torn away – incidentally the part we have most
problems with measuring.
1.2.6 Simple Estimation Model
A very simple half-sine model – which is very close to what a clear day graph will look like – for the
theoretical maximum irradiance as a function of time of sunrise and sunset can be easily calculated
[10].
(
)
T h − T h sunrise
I = I noon · sin π
(1.17)
T h sunset − T h sunrise
T h sunrise and T h sunset is here the target hour 1.15 obtained by reverse-engineering the hour angle
at sunrise and sunset 1.12. It follows that T h, the current target hour should follow the same
relative unit of measurement. Setting T h to h + i/60 should be sufficient – h being the current
hour, and i the current minute.
This model still suffer from the same flaws as the more advanced models; it needs the noontime
irradiance I noon , as well as optimal weather conditions to work. However, since our pyranometer
needs to be calibrated after this anyway, we might as well go out on a limb and interpolate a daily
maximum from a few days worth of measurement from Landvik weather station [1], a station close
to our location.
Setting I noon = 1000W/m 2 seems to be a constantly reinforcing bet for the summer [10][17][1],
and in the pyranometer interface code it will be left to this value to yield reasonable maximum
approximations during the season.
Technically, one could easily extend the usability of this by creating a similar half-sine model
for I noon based on an interpolation of monthly readings from the weatherstation, but there aren’t
enough data readily available for this at the moment.
11

1.2.7 Diffuse and Direct Components
If the global irradiance is all that hits a horizonal surface, then this can be broken down into
two components; what comes directly from the sun, and what seems to come from all around (the
diffuse). If we measure what comes directly from the sun with a horizontal solar cell, then the global
.
Figure 1.5: The two components of the global irradiance [10]
irradiance I g is the sum of the direct I b,h and the diffuse I d . However, if we measure the direct
component with a cell tilted towards the sun, then this (I d ) might at times seem bigger than the
global horizontal. This is because the cell absorbs a bigger part of the sunlight (the cosine effect).
In other words, to calculate the diffuse (horizontal) component from the direct (tilted towards the
sun) and global (horizontal) irradiance, we need to turn equation 1 around.
12

1.3 Tracking
An accurate azimuth and altitude angle from section 1 are paramount for tracking the sun. The
principle is simply to mount one motor onto the other, let one follow the azimuth, and the other
control the altitude, and thus it’s able to cover any point within 2π steradian, i.e. its hemispheric
view. NI LabVIEW 8.0 will stand for the tracker control and the required programming is to be
found in in section 2.3.
1.3.1 Parallel Port
A two-axis tracker needs two motors, and in our case those two are six-wire stepper motors 1.3.2,
necessitating a total of eight out ports to run properly. A basic reset system – to help the program
position the motors – will also be incorporated, with the reset signals for each motor being read
through two random status ports.
There are eight data out ports are accessible from
the data register (base address), while another four out
ports, some inverted, are accessible from the control
register (base address+2). A total of five in ports can
be read through the status register (base address+1) 2 .
To actually access the port from LabVIEW is not more
difficult than to place a prepared subroutine on your
diagram.
The base address should be obtainable (in Windows)
from the System Information program. It’s the
first I/O port address under Components → Ports →
Parallel, but it’s almost always at the default value of
0x378.
A high output signal should be interpreted electronically
as setting the port to 5V , while a sending a low
signal is equivalent to grounding it.
The plan is to utilize the eight data bits to control
the stepper motors through the appropriate electrical
circuitry.
Figure 1.6: Parallel port, face of a female
connector. [6]
1.3.2 Stepper Motors
To track the Sun, we need motors capable of incremental
adjustments. A stepper motor, almost identical to
the kind found in an old 5.25” floppy drive, is capable of this.
The six-wires from the steppers we have available are: two pairs of connectors for the motor
coils, a total of four wires, and two wires in addition connected to each center of the coil. Fivewire
motors often follow the exact same scheme, with the exception that their center tap is wound
together, which is perfectly fine for this project. Four wire steppers are bipolar steppers, and have
no center tap. These typically require more advanced drive circuitry that is not covered here.
To control a stepper, you’ll need to be able to send currents from the center-taps and through
one of the coils. Doing so will put up a magnetic field perpendicular to the current, i.e. in the
opposite direction of the resultant direction of the current through the coil. By choosing which way
to send the current on each coil, the motor can start to spin given the correct sequence of fields.
2 LabVIEW, at least version 7 or newer, includes the Parallel Port Read and Write Loop.vi that can be of great
help for testing functionality.
13

(a) The coil endings connected to switches
(b) Motor does one step when switch 3 and 4 are closed
Figure 1.7: Six wire steppers
For simplicity, we define the vectorial field from coil 1 B coil1 is to be called A + if its sum points
upwards, and conversely A − if it’s pointing downwards. From coil 2, similarly, B coil2 is B + to the
right, and B − to the left. See figure 1.8.
Using all eight directions to drive it around is not strictly necessary, only four adjacent ones are
needed, but this obviously limits the precision by a factor of two. It’s, however, what is referred to
as full-step mode, and the step angle (degree rotation per step) listed at the motors usually refer
to this when it actually can operate with double accuracy.
(a) Directions for half-step mode
(b) Sequence for half-step mode
Figure 1.8: Half-step sequence and directions
In half-step mode, the most accurate motor used does 400 steps per revolution, or 0.9 ◦ per
step. Figure 1.8(b) describes how a full gear rotation in half-step mode is possible by setting the
switches in the shown sequence. The switches are here closed if the value is 1 and open if 0.
To identify the correct wires for coil 1 and 2, simply measure the resistance over all the wires.
If you get an infinite resistance, then the wires are from two different coils. If you get resistance x
14

over wire A and B, and 2x over A and C, then B must be the center tap of coil A → C. Identifying
which coil is which, or the ’polarity’ is unnecessary because of the symmetry in the motor. If the
motor seems to be stuttering at the same place, simply reverse the polarity on one coil (if nothing
else is wrong). If the motor is going in the wrong direction, switch coil 1 with coil 2, or use a
reversed stepping sequence.
1.3.3 Tracker at an Angle
One of the primary specifications requested for this tracker was that it could be placed at an angle,
i.e. tilting the pyranometers horizontal plane. This has a series of implications.
1. The altitude used to control the motor tracker altitude will vary with the azimuth.
2. The incidence angle on the cell measuring the global irradiance will vary with the azimuth.
3. If the global pyranometer is tilted, it will measure parts of reflected beam irradiance and
exclude the diffuse component coming from behind it.
The first two can be compensated for, but the third cannot. Thus, under ideal circumstances, the
global pyranometer should remain horizontal. Following, at any rate, is a few mathematical tricks
to compensate for the two.
If a two-axis tracker is tilted β degrees, the new altitude, relative to the tilted plane is given by
h new = h + β cos A (1.18)
Where A is the azimuth angle. However, this is only holds if the plane tilts downwards towards
the south (azimuth zero). To find the new altitude with the tilted plane pointing γ degrees away
from azimuth zero, measured clockwise from south, the final relationship becomes
h new = h + β cos (A − γ) (1.19)
Similar solution for the incidence angle on the pyranometer (the apparent zenith angle of the
pyranometer)
z new = z + β cos (A − γ) (1.20)
As opposed to the pyrheliometer with the tracker, a change in the apparent zenith angle changes
the value of what we measure.
1. Actual measurement from G = D ∗ + B cos z new
2. Wanted measurement from G = D + B cos z
The diffuse component is irreconcilably distorted, but the change in direct irradiance can be compensated
as follows
G true = G measured − B(cos z − cos z new ) (1.21)
15

Chapter 2
Development
In this chapter we will take a look at the development part of the project. This will include the
electrical interaction between LabVIEW and the stepper motors, as well as the circuitry needed
for the solar cells. The basic flow of the code will be explained briefly at the end. The pros and
cons of the chosen implementation, will be discussed throughout the chapter, and at the end, our
prototype will introduce itself and flaunt its abilities.
2.1 Stepper Circuit
2.1.1 ULN2003A
For a practical realization of the switches in section 1.3.2, we have used the IC ULN2003A - Seven
Darlington Arrays (data sheet attached).
It would, of course, be expedient to have eight inputs for a chip,
since we need the outputs from eight data bits, and indeed, ULN2805A
[12] does provide such a scheme. Unfortunately, it was not what was
available at the time.
The ULN2XXX series has an open collector output, meaning that
the output gets grounded through transistor when corresponding input
line goes to high state. The corollary to this is that the previous switch
pattern 1.8(b) is exactly what needs to be written to the parallel port.
Figure 2.1: ULN2003A -
overview [7]
Figure 2.2: ULN2003A - Each driver (COM is pin 9). [7]
16

2.1.2 Circuit
The following figure shows our solution for the stepper control. The multitudes of resistors are
pull-ups to help avoid floating logic gates. Pin 18 through 25 are ground returns for all the parallel
port registers, and are here connected to the common ground from our power supply, which is an
old PC PSU. As suggested in the datasheet [7], the common line is here connected to the supply
line that feeds the motors for a cheap over-voltage protection.
Figure 2.3: Circuit layout, two axis motor control. Drawn on the left is the female connector input
from the parallel port. All resistors are 10 k.Ω
2.1.3 Possible Complications
Current over-voltage protection is widely considered dangerous. Given we only run the motors at 5
volts, and it has proven to work well in test runs, it is still a risky decision if it’s to stay permanent.
The problem is as follows. When we cut the connection to ground by setting a low input to the
respective ULN driver input, the motor coil will resist the change (V L = L di
dt
) and send a spike back
through the transistor to ground. With the ground connected to the parallel port in addition to
the power supply, this is a dangerous solution, and has in certain situations been known to break
entire motherboards [5].
The common way to solve this is to either put clamping diodes between each motor coil and
ground [5], or a zener diode (a few volts above the running voltage) between the common port on
the ULN and the power supply [6].
17

2.1.4 Two Bit Drive
F ields B1 B2
A + B + 1 1
A − B + 0 1
A − B − 0 0
A + B − 1 0
Figure 2.4: The two bit
full-step sequence
An alternative design – which in hindsight is more than good enough
given the external gears used 2.4 – features one motor in full-step mode.
Full-step mode is only half as accurate, but can be driven by only two
bit signals, while half-step requires all four. This is because in full step
mode, while utilizing only the diagonal 1.8(a) resultant fields, the field
from each coil is either positive or negative as opposed to half-step mode
where it sometimes turned off completely. The circuit can then be driven
like this
Figure 2.5: Two bit full-step drive [4]
2.2 Solar Circuit
As suggested earlier, our pyranometer is basically just comprised of two solar cells and a voltage amplifier.
To understand what necessitated these amplifiers, one must first look at the characteristics
of a PV cell.
2.2.1 Silicon Cell
Figure 2.6: PV cell equivalent circuit
[16]
A PV cell can be modeled as a current source with a diode
and resistance in parallel, in addition to a series resistance. In
this model, only the photo current I pv from the current source
itself is proportional to the sunlight hitting it. The voltage
V measured over the terminals equals (I pv − I d − I p )R s from
KCL, and here both the diode current I d and the current
through the shunt resistance I p will obliterate any idea of a
proportional measurement as I pv changes. The solution to
this debacle is to (almost) short the terminals, causing the
voltage to drop so close to zero it will eliminate I d and I p .
V sc = (I pv )R s (2.1)
If you want the cell to drop to about 100mV for full sunlight, then calculate the resistance required
for such a drop, 0.1/I sc,max = R, and connect it to the terminals. Our cell produces about 0.04A
in full sunlight, which indicates a resistance of no larger than 2.5Ω. A resistance of 0.8Ω which we
have used, will thus cause a bigger voltage drop, and will help us cope with additional resistances
in the long wires (measured to about 0.4Ω sum for the direct measuring cell), and other internal
resistances.
18

Figure 2.7: IV curve for a photovoltaic cell. The diagonal lines indicate the output at different
resistances at the terminals, and here R 1 < R 2 < R 3 . Only V R1 is proportional to the sunlight.
2.2.2 Voltage Amplifier
Figure 2.8: A simple voltage amplifier
With the amplification factor being R 1 /R G − 1.
2.2.3 Circuit
To measure such a small voltage, it’s necessary to amplify it
electrically first, lest our proportional measurement is brutalized
by noise or internal resistances of the voltmeter. A basic
amplification like the one below, works as follows.
1. The voltage at the operational amplifier’s plus gate is V sc ,
so it must be the same at the other.
2. The current from the minus gate through the potentiometer
is I = V sc /R G
3. But the current can’t come from the operational amplifier
itself, so it must come from V out and pass through R 1
V out = I(R G + R 1 ) = V sc /R G (R G + R 1 )
V out = V sc (1 + R 1
R G
) (2.2)
With R G as a 10kΩ potentiometer, and R 1 = 1MΩ, the amplification factor AF can be tuned from
100 and up, but with precise adjustments limited to factors less than 1000.
Practically, the amplifier causes a certain offset which I’ve not been able to eliminate. When
the cell is completely covered, and with the AF set to about 800, the offset is exactly one volt.
This should make it easy to take care of once signals are being interpreted by code.
19

Figure 2.9: Voltage amplifiers for V sc .
We have the used IC LM234AN - low power quad operational amplifiers (data sheet attached)
to amplify the two signals. With the supply set to 5V , the maximum output is 3.5V . Supply and
ground are taken from the NI-DAQ mx, which we will also use to transport the amplified voltages
to LabVIEW.
2.2.4 NI-DAQ mx
The NI USB-6008 is a multifunction data acquisition device for LabVIEW. It’s available at National
Instruments for 1200, − NOK. The data sheet is attached, although the accompanying instructions
are pretty much self-explanatory.
It will measure the global irradiance voltage on AI1, the direct irradiance voltage on AI2, and
deliver supply and ground from AO0 and AO1.
2.3 LabVIEW
Figure 2.10: LabVIEW Hierarchy
For a simplified and structured code, big chunks have been isolated and saved as substructures
(sub-vi’s). The main control panel, which you can see is on the top, will be saved for the end to
20

give a clearer view of how everything connects.
The hierarchy is a little simplified, there’s twenty or more sub-vi’s below DAQ measure (as
indicated by the blue DAQ Assist block), but they’re auto generated and don’t really contribute
to the big picture.
2.3.1 Sol
sol.vi contains possibly the biggest chunks in terms of pure code. The massive math formula node,
containing most of the equations presented in this document, is actually many times larger than
what is shown on the image, with the code itself presented on the next page. The multitude of
unused variables on the top is just a product of LabVIEW’s requirements.
Figure 2.11: sol.vi - Code. Looks simple, but the math inside the formula node goes beyond what
is shown
Figure 2.12: sol.vi - UI. Calculating the position of the sun and a bunch of interesting statistics
21

What is transferred to the control panel is the option to change your location and timezone –
definitely recommended if you don’t live here. The optional time and date is just there for toying
around, and to check if things really work. Outputs are the cluster of information as well as the
azimuth and altitude.
Program 1 sol.vi - Math Node Contents
if(m

5. Sunset and sunrise hour (multiplied by 3600 to help LabVIEW convert it in the UI), and the
half-sine global irradiance model.
2.3.2 DAQ Tasks
A .vi for reading the two amplified voltage signals, and keeping the supply voltage connected. The
new DAQ Assist blocks used are a vast simplification from earlier versions.
(a) Code
(b) UI
Figure 2.13: daq-tasks.vi
2.3.3 Corrective Spider
The corrective spider corrects the altitude and global irradiance as functions of the inclination angle
and position of inclination (see section 1.3.3 - Tracker at an angle). Additionally, it makes use of the
math node to remove the offset from the amplification circuit, and multiply the measured voltage
with the amplification constant [W/V m 2 ].
Figure 2.14: corrector.vi - Code and UI
23

Program 2 corrector.vi - Math Node Contents
k=pi/180;
hn=h+b*cos((A-g)*k);
z=(90-h)+b*cos((A-g)*k);
G=(Gv-1.01)*AF; //offset 1.01V
B=(Bv-1.01)*AF;
D=G-B*sin(h*k);
T=G-B*(sin(h*k)-cos(z*k));
An=mod(A+90,360); //A internally referred to east (reset pos)
if(hn location (else step down)
Figure 2.15: step.vi - UI.
Figure 2.16: step.vi - Code
2.3.5 Read Reset
read-reset.vi polls the two in-ports on the parallel port for changes. These control the reset functions
for the two axes. If the switch was just pushed (step number low) then the vi ignores subsequent
pushes to avoid stagnation.
24

(a) Code
(b) UI
Figure 2.17: read-reset.vi
2.3.6 Write Step
This is the part of the program that exports the step signal (position of the switches) to the circuit
board. It takes the newly modified step number from step.vi and picks out the appropriate signal
based on the step number modulo 8. A reversed motor array is there to avoid physically switching
cables if you mistook the polarity or which way external gears went.
Figure 2.18: write-step.vi - Code.
25

Figure 2.19: write-step.vi - UI.
2.3.7 Control Panel
The figure on the next page is pretty dense, but that’s mostly because all the earlier outputs –
except a couple that’s been deliberately neglected – come together in the control panel. The basic
flow is that two shift registers starts stepping down from 2000 (or 500 depending on the motor) until
the respective reset switches are physically in, at which point the pyrheliometer points towards the
east at horizon level. This means that the tracker needs to be placed in such a way that tracker
points to the east when it hits the switch. After the position has been reset, the shift register is
set to 0, and the tracker starts its intended sequence in the direction of the sun.
The two integers going to the step.vi is the respective motor’s required steps for a complete
rotation, and if they are connected to external gears, this needs to be figured out manually. The
best way is just to play around with the code, set the shift register to a massive value, and subtract
the stop value after a few rotations. The mean number of steps per single rotation should suffice.
The DAQ switch removes the necessity to have the DAQ mx plugged in
when just testing the code. It gives an example reading of 1.8V from the
global amplifier and a 1.5V from the direct amplifier. Obviously, the diffuse
reading is rarely reasonable with this setting as we’ve fed it a contradiction
(global > (tilted) direct at low altitudes).
To see the stepping sequence without connecting the stepper circuit,
Figure 2.20: DAQ
false case structure
you must do this from write-step.vi. This is because the switches works
perhaps the opposite way of what you might expect, pressed in, they split
the respective in-port from connection to ground, and when the parallel port
isn’t plugged in, they’re always on.
26

Figure 2.21: main.vi - UI and code
27

2.4 Physical Realization
2.4.1 Circuits
The circuits as realized from the sketches in section 2.1 and 2.2.
Figure 2.22: Stepper circuit
Figure 2.23: Solar circuit shown in the vicinity of the global cell
2.4.2 Construction
As shown in figure 2.24, our pyrheliometer is a simple Lego construction. In some areas, this
construction excels with its simplicity, in others, not quite so. Prime example of the pros is the
gears; they’ve increased the accuracy of otherwise inaccurate steppers two and threefold. The
peculiar placement of the switches is a product of a failed experiment; getting it all to run on 5V .
Turns out it’s not enough momentum even with a long arm and a perpendicular force (R × F ), so
it’s all being run on 12V even though it’s more than we strictly need.
Obviously, this is just a prototype, it’s not designed for prolonged usage as it, for instance,
is not waterproof. There are, however, two key implications with certain design aspects of this
construction that we feel would be of interest.
28

Figure 2.24: Lego construction with two integrated stepper motors
2.4.3 Constructional Implications
Placing reset buttons limit the total area the tracker can cover, necessitating more bypass coding.
In our code they also represent the zero point, meaning that if you place the buttons elsewhere,
then the reset behavior must also be altered.
One thing to note here is that if the tracker is to be placed at an angle facing up towards sunset,
then the altitude relative to the tracker will become less than zero, an impossible value for this
construction.
Similarly, if the tracker is placed at an angle at any point of the day, the compensated altitude
may become greater than 90 ◦ at locations with smaller latitudes. The easiest way out of this is
simply to design the altitude for semicircular rotation, but if 0 → 90 ◦ is all you can spare, than the
angles may be simply flipped with the code below. If the switch is placed at azimuth zero, then
the code segment on the next page should elude inauspicious collisions.
Another problem with our construction is the acceptance angle of the pyrheliometer. A professional
pyrheliometer has a 5 ◦ acceptance angle [10], implicitly redefining the magnitude of the
direct component (the size of the solar disk is less than 0.6 ◦ ). Our construction pushed this angle
up a little bit to accommodate a rectangular cell – because if you shade one part, the voltage drops
dramatically. However, inherent in such an elliptic tube directed towards the sun, are focal points.
29

Program 3 Flipping algorithm for altitudes greater than 90 ◦ . A is the azimuth angle
if(h>90)
{h=180-h; A=mod(A+180,360);}
The rays are reflected of the inside of the tube resulting in an amplification of the true value.
To bypass this amplification, we suggest that the inside of the tube is coated with an absorbing
material (like black paint), or the voltage reading amplified with a different factor than that of the
global.
2.4.4 Calibration
To calibrate the amplification for the voltage, we have made a series of measurements. First we
measured the radiation at Friday, June 2, 2006, at noon to find the proper amplification factor. The
idea is that if this factor is well calibrated, the subsequent measurements should correlate with our
source [1]. Landvik weather station [1] tells us that their last two hours readings have been stable,
R G Offset Voltage Range Voltage Mean
Global 1.11kΩ 1.01V 1.82 → 1.88V 1.85V
Direct 1.23kΩ 1.01V 1.60 → 1.65V 1.63V
Figure 2.25: Measurement Results at H ∈ < −10 ◦ , 5 ◦ > (13:05 → 13:45 true noon), at June 1,
2006
and the 13:00 to 14:00 mean being 848W/m 2 . This indicates an amplification of 1000W/m 2 V . The
direct measurements also seem reasonable enough to use the same amplification.
Further measurements has shown that this correlates to ±100W/m 2 with Landvik. This has
only been tested with quick checks throughout the day, as my testing location does not have a
complete hemispheric view. This kills off diffuse radiation and utterly destroys sunrise and sunset
values. It’s, however, reasonable to assume these values are not very accurate since our cell reacts
very poorly to red light.
The offset of about 1V is very expedient for our cells as the maximum output we’ve experienced
is then 2V . Scaling wise, this reveals a problem in the choice of the potentiometers, they’re
unnecessarily big, and therefore difficult to accurately adjust. With a small calculator cell like the
one shown in figure 2.23, we would suggest to rather replace the 1MΩ resistor with one of 5MΩ
thus decreasing the difficulty of calibrating it.
2.5 Conclusion
It is perfectly feasible to construct an advanced pyranometer from cheap electric components.
Although our project is most favorable for companies already in possession of LabVIEW and the
DAQ-mx, it’s still a far cheaper solution than what most thermopile oriented pyranometers offer.
Also, if LabVIEW doesn’t suit your purpose, the code could easily be ported to another language.
As compared to a professional pyranometer, the scores correlate pretty well with our inauspicious
location in mind. The reading is definitely proportional to the sunlight, but the cell’s spectral
response will render our readings at the beginning and end of the day dubious at best. For best
results, we would recommend that it’s calibrated side by side with a professional pyranometer.
The ideas listed in this report are worth considering when one wishes to acquire a pyranometer.
If the global and diffuse component of the irradiance is not needed, the process of making it can
be reduced to simply building and calibrating the solar circuit 2.2 and the effort is almost void.
30

Bibliography
[1] Bioforsk, Landbruksmeteorologisk tjeneste,
http://lmt.bioforsk.no/lmt/index.phptype=&weatherstation=29 [01.06.2006].
[2] William M. Connolley, Hadley centre coupled model, version 3,
http://en.wikipedia.org/wiki/Image:Insolation.png [30.05.2006].
[3] Norwegian Research Council and the NVE, Nye fornybare energikilder, KanEnergi AS, 2001.
[4] Ian Harries, Stepper motor controller connection diagrams,
http://www.doc.ic.ac.uk/~ih/doc/stepper/control2/connect.html [28.05.2006].
[5] Jason Johnson, Working with stepper motors,
http://www.eio.com/jasstep.htm [1.06.2006].
[6] Douglas W. Jones, A worked stepping motor example,
http://www.netmotion.com/htm_files/advisory/advisor_example.htm [1.05.2006].
[7] Allegro MicroSystems, Uln2003a datasheet,
http://www.ortodoxism.ro/datasheets/allegromicrosystems/2001.pdf [30.05.2006].
[8] NASA, Solar irradiance spectrum,
http://en.wikipedia.org/wiki/Image:MODIS_ATM_solar_irradiance.jpg [30.05.2006].
[9] J. Palmer and A. C. Davenhall, The ccd photometric calibration cookbook, 2001,
http://www.starlink.rl.ac.uk/star/docs/sc6.htx/sc6.html#stardoccontents
[30.05.2006].
[10] William B. Stine and Michael Geyer, Power From The Sun chp. 2,
http://www.powerfromthesun.net/book.htm [30.05.2006].
[11] , Power From The Sun chp. 3,
http://www.powerfromthesun.net/book.htm [30.05.2006].
[12] STMicroelectronics, Uln2805a datasheet,
http://www.st.com/stonline/products/literature/ds/1536.pdf [30.05.2006].
[13] Dr. Louis Strous, Julian day number, 2006,
http://www.astro.uu.nl/~strous/AA/en/reken/juliaansedag.html#julianday
[30.05.2006].
[14] , Position of the sun, 2006,
http://www.astro.uu.nl/~strous/AA/en/reken/zonpositie.html [30.05.2006].
[15] Wikipedia, Milankovitch cycles,
http://en.wikipedia.org/wiki/Milankovitch_cycles [30.05.2006].
31

[16] , Solar cell,
http://en.wikipedia.org/wiki/Solar_cell [30.05.2006].
[17] , Solar insolation,
http://en.wikipedia.org/wiki/Insolation [30.05.2006].
32