This paper proposes an implementable sun tracking algorithm for portable systems powered by alternative energy sources. The proposed system uses a 2axis tilt sensor and a 3axis magnetic sensor to measure the orientation and posture of the system, according to a horizon coordinates system, and compensate for tilt effects. Then, through an astronomical calculation, using the present time and position information obtained from GPS sensors, the azimuth and altitude of the sun in that location is calculated and converted to portable sun tracking system coordinates and used to control the A and Caxes of the system.
I. INTRODUCTION
Photovoltaic systems are receiving a great deal of attention as an environmentally friendly alternative energy source. Aided by government demonstration projects, the applicable scope of photovoltaic systems tends to be expanding gradually from smallscale systems for homes and buildings to largescale systems for power generation networks.
Increasing the efficiency of photovoltaic systems requires a sun tracking algorithm which can ensure that the solar cells face normal to the sun. Along with maximum power point tracking (MPPT)
[1]

[4]
this improves the efficiency of thesolar cells and power conditioning system.
The efficiency of solar cells and power conditioning systems has been consistently improved by developments in technology. The efficiency of a photovoltaic system is determined largely by the angle of incidence of sunlight on the solar cells. The sunflower type sun tracking algorithm generally used for fixed installations relies on alignment with the horizontal system of coordinates. When the azimuth and altitude of the sun are calculated for a given point in time, the system tracks the sun, using a 2axis control method with a pan and tilt drive. Since the sun tracking algorithm is aligned with the horizontal coordinates, it can control the array simply. The pan drive adjusts the array to the corresponding azimuth and the tilt drive compensates for the altitude angle. This general sun tracking method is shown in
Table I
.
On the other hand, photovoltaic systems are expected to be applied for use in portable applications as well as existing fixed installations. To use photovoltaic systems as a power source for automobiles, ships, and portable devices, as well as portable battery chargers, the system must be lightweight and be able to produce as much electric power as possible for use as an energy source. However, in portable systems it is difficult to track the sun with a simple method like that used in fixed systems, because the current position changes continuously and the sun tracking algorithm is not lined up with the horizontal coordinates of the current location. In a fixed system algorithm, it is necessary to know the position and direction of motion of the sun and its tilt angle with respect to the horizontal plane.
This paper proposes a sun tracking algorithm for portable applications, which tracks the sun both by measurements and astronomical calculations. The sun tracking algorithm measures the tilt angle made with respect to the horizontal plane, its posture (direction and position), and the current time in real time with a tilt sensor, a geomagnetic sensor, and a GPS.
Fig. 1
shows a flow diagram of the algorithm for portable applications.
CLASSIFICATION OF SUN TRACKING METHODS
CLASSIFICATION OF SUN TRACKING METHODS
Portable sun tracking system flow chart.
II. STRUCTURE OF THE SUN TRACKING ALGORITHM
The sun tracker shown in
Fig. 2
consists of solar cells, a rotating mechanical part and the mounting. The mounting is installed with the tilt sensor, GPS sensor, and geomagnetic sensor. The tilt sensor and geomagnetic sensor are aligned in the direction shown in the figure. The rotating mechanical part provides 2axis control of the Aaxis (the rotating angle in the direction of the xaxis: α) and the Caxis (the rotating angle in the direction of the zaxis: γ). It tracks so that the surface of the solar cell always faces the sun. The solar cells and mounting are aligned in parallel from the home position and have the relation of α=γ =0 that is, the rotation angle of the A and Caxes.
Structure of the sun tracker.
Sun tracking system and horizontal coordinates.
Fig. 3
shows the coordinate system of the sun tracking algorithm and the horizontal coordinate system.
The xyz axes in the horizontal coordinate system refer to a coordinate system that shows the location of the sun based on the horizontal plane of the current position. In this paper, the y, x, and zaxes indicate the respective directions to the south, west and sky. The xyz axes in the coordinate system of the sun tracking algorithm show the correlation with the axes as a rotation of the coordinate system. Rotate the xyz axis about the Zaxis as much as γ when the xyz axis is aligned with the XYZ axis. When rotating as much as β about the Yaxis after rotating as much as α about the Xaxis, the relation that converts one point P in the xyz coordinate system into the xyz coordinates can be expressed as in Expression (1) and the transform matrix
can be expressed as in Expression (2). Here, the lower left subscript of T indicates that the coordinate system to be transformed, and the upper left subscript shows the coordinate system upon transformation
[5]
.
Here,
III. SENSOR SIGNAL PROCESSING
This section describes the sensor used in the sun tracking algorithm for portable applications and its signal processing method
 A. Tilt Sensor
When the sun tracking system is positioned at a certain point, it measures the extent that the mountings are tilted in terms of the horizontal plane of the point. As shown in
Fig. 4
, the outputs
θ_{x}
and
θ_{y}
of the tilt sensor installed in the mounting are aligned with the x and yaxes of the coordinate system of the sun tracking algorithm, and they show the angle between the zaxis of the horizontal coordinate system and the xaxis and yaxis of the coordinate system of the sun tracking algorithm. As shown in Expression (4), the tilt sensor outputs
θ_{x}
and
θ_{y}
can be expressed as the inner product from the unit vector
α_{z}
of the zaxis of the horizontal coordinate system and the unit vector
α_{x}
of the xaxis, respectively, as viewed from the XYZ axis of the horizontal coordinate system and the unit vector
α_{y}
of the y–axis. G in
Fig. 4
represents the gravitational direction.
Gravitational direction.
When defining the rotational sequence as Euler’s angles, where the xy plane of the coordinate system of the sun tracking algorithm being aligned on the XY plane of the horizontal coordinate system is tilted by the rotation of
β
_{0}
about the Yaxis after the rotation of
α
_{0}
a about the Xaxis of the horizontal coordinate system as in
Fig. 4
, the unit vector
α_{x}
of the xaxis and
α_{y}
of the yaxis could be expressed as in Expression (5).
Here, the upper subscript T represents the transposed matrix. Hence, by arranging Expressions (3)(5), Expression (6) is obtained.
Here,
θ_{x}
and
θ_{y}
hold values in the range of [0,π].
Finding the solution of Expression (7), the following is obtained:
Here,
α
_{0}
and
β
_{0}
hold values in the range of
The values
α
_{0}
and
β
_{0}
obtained from Expression (7) are used in correcting the tilt of the sun tracking algorithm. They are also used in correcting the output of the geomagnetic sensor for the tilt of the geomagnetic sensor installed on the mounting of the sun tracker.
 B. GPS Sensor
By receiving signals from a satellite system, the GPS provides the time, latitude, longitude, and speed in the NMEA (National Marine Electronics Association) format. If the current position (latitude/longitude) and time are known, the azimuth and altitude angle of the sun can be calculated through astronomic calculation. This paper used an astronomic calculation method that has an accuracy of 0.01° for 100 years from 1950 to 2050.
 C. Geomagnetic Sensor
While the latitude and longitude information of the current point can be obtained from the GPS sensor, it is not possible to get direction information. Hence, this paper tries to obtain the direction information—which way the sun is heading at the current point. The geomagnetic sensor measures the magnetic north of the earth. The angle between true north and the magnetic north is referred to as the declination angle. If the declination of the current location is known, the direction oftrue north can be found by correcting the declination angle from the magnetic north found by the geomagnetic sensor. The declination differs by region. In Korea, the magnetic north is in the range of 68° to the west from true north.
When the output of a geomagnetic sensor, aligned and installed on the coordinate system of the sun tracking algorithm, is converted into the horizontal coordinate system, Expression (8) is obtained.
Fig. 5
shows the output of the geomagnetic sensor viewed from the horizontal coordinate system. Since the elements
H_{X}
and
H_{Y}
need to be known to get the direction information, as shown in the figure, Expression (9) can be obtained by finding these elements and using Expression (8).
Magnetic sensor output.
Accordingly, the rotation angle
δ
_{0}
about magnetic north for the sun tracking algorithm becomes as Expression (10), and the rotation angle
γ
_{0}
about true north can be arranged as Expression (11), which corrected the declination angle from δ
_{0}
.
A 2axis geomagnetic sensor can be used instead of a 3axis geomagnetic sensor. In this case, the inclination angle is needed—the angle made by the terrestrial magnetism of the surface of the earth. In the case of Korea, the inclination angle has a distribution of 4855°.
When the sun tracking algorithm for portable applications is in a random position, from the sensor information above, it can be seen that the current posture is rotated by
γ
_{0}
about the Zaxis of the horizontal coordinate system and by
β
_{0}
about the Yaxis after rotating by
α
_{0}
about the Xaxis. Accordingly, the transform matrix that converts one point of the coordinate system of the sun tracking algorithm into the horizontal coordinate system is expressed as Expression (12) using Expression (2).
IV. SUN TRACKING CONTROL
If the altitude angle and calculated latitude of the sun are
θ
and
Φ
, respectively, the unit vector
^{XYZ}
S looking at the sun from the horizontal coordinate system, as shown in
Fig. 6
, can be expressed as Expression (13).
Position of Sun.
If both sides of Expression (13) are multiplied by the inverse transform matrix of Expression (12) , the unit vector
^{XYZ}
S, when viewing the sun from the coordinate system of the sun tracking algorithm, can be expressed as Expression (14).
Here, the inverse transformation matrix is identical to the transposed matrix of the transformation matrix
[5]
.
Now, in order for the solar cell of the sun tracking algorithm to face the solar cells toward the sun, the unit normal vector of the solar cell face, viewed from the coordinate system of the sun tracking algorithm, must be matched with Expression (14) when, having rotated the Aaxis as much as α, after rotating the Caxis as much as γ in the home position of the sun tracking algorithm. The unit normal vector
u_{z}
of the solar cell face in the home position is matched to the Zaxis of the coordinate system of the sun tracking algorithm. In other words:
Thus, Expression (17) is obtained.
Arranging Expression (17) using Expressions (3), (14), and (16), the results of Expressions (18)(20) are obtained.
Calculating Expressions (18)(20) produces the two values (
γ
_{1}
,
α
_{1}
), (
γ
_{2}
,
α
_{2}
) in Expression (21).
or
Sun position in sun tracking system coordinates.
Here:
Fig. 7
(a) shows the view of
^{XYZ}S
from the Zaxis of the coordinate system of the sun tracking algorithm.
S_{xy}
reflected on the xy plane makes an angle of η in Expression (22) with the Xaxis. To look at the sun by rotating the Zaxis, the solar cell face needs to be rotated about the zaxis so that the xaxis becomes perpendicular to
S_{xy}
. As shown in the figure, there are two methods (
γ
_{1}
,
γ
_{2}
).
Fig. 7
(b) and
7
(c) show the views from the Xaxis after rotating the Zaxis as much as
γ
_{1}
and
γ
_{2}
, respectively. When rotating the Xaxis as much as
α
_{1}
or
α
_{2}
for each of these, the solar cells face the sun. To select one of the solutions, the one that produces the smaller movement from the current position while considering the limitations in the mechanical structure corresponding to the control range of α and γ is chosen.
V. EXPERIMENTAL RESULTS AND REVIEW
For one location in Seoul (latitude: 126.9833°E, longitude: 37.5667°N),
Table II
shows the results for the seasonal time of sunset/culmination/sunrise and the change range of the azimuth angle and altitude angle in the year 2009 through astronomical calculations.
As shown in
Table II
, the azimuth angle of the sun change to bilateral symmetry around the south (azimuth angle of 180°) and the altitude angle of the sun reach their maximum with the southing of the sun. In the case of a fixed PV generation system, it is normal to install the unit around an azimuth angle of 180° and an altitude angle of 32° so that the daily average PV generation is at its maximum. A fixed 1axis control solar tracking algorithm controls the azimuth angle while fixing the altitude angle. However, a fixed 2axis control system maximizes the PV generation by controlling both the altitude and the azimuth. For a fixed installation, it is possible to track the sun accurately through a simple astronomical calculation, since the installation can be done by aligning it to the horizontal coordinate system of that point. However, for a portable type system, the PV generation can be kept to its maximum only after measuring the posture with the method suggested in this paper, since the posture of the sun tracking algorithm changes continuously.
PV generation is determined by the cosine of the angle made between the normal of the solar cell face and the sunlight. For example, for a fixed installation, the PV generation during southing at the summer solstice is no more than 72% from cos(75.9°E32°E)=0.72. On the other hand, when the sun tracking algorithm proposed in this paper is used, a PV generation of 100% can theoretically be maintained.
SUN POSITION FOR SEOUL IN 2009
SUN POSITION FOR SEOUL IN 2009
Table III
shows the calculated locations of the sun on a given date for the region suggested previously, using astronomical calculation.
Table IV
shows the calculations of
α
_{0}
,
β
_{0}
and
γ
_{0}
from the sensor output, according to the posture of the sun tracking algorithm for portable applications under the same conditions, and α and γ, the controlled outputs for the sun tracking. In Case1,
α
_{0}
=
β
_{0}
=
γ
_{0}
= 0 when the sun tracking system is aligned with the horizontal coordinate system. From this, it can be expected that the controlled output from
Table III
is either 38.39° or 141.11° for γ, and α should be ±59.09°. This result is identical to the calculation in
Table IV
. For Case2, the controlled output γ was either 67.08° or 112.92° and the respective results for α were ±78.60° when
α
_{0}
=35.26°,
β
_{0}
=30°, and
γ
_{0}
=54.74° since the sun tracking algorithm is not aligned with the horizontal coordinate system.
Fig. 8
shows a prototype of the sun tracking algorithm made in this study. This paper performed a shadow test to evaluate the sun tracking performance of the proposed system. The shadow test is a method that calculates the accuracy of sun tracking by installing a rod (10 cm) in the normal direction of the solar cell face and measuring the length of the shadow. In Case2, under the conditions of
Table IV
, the result of about 1.4 cm were obtained—the PV generation in this case is 99% from cos(atan(0.14))=0.99. If the cause of the error is analyzed, the largest part of the error occurs due to the geomagnetic sensor. Since the geomagnetic sensor measures magnetic north rather than true north, true north must be determined using the declination angle information of the region. In addition, since the geomagnetic sensor is heavily influenced by the surrounding environment, this might cause an error. Additionally, an alignment error from the sensor installation, or an error in the processing of the mechanical part could be the cause.
EXAMPLE OF ASTRONOMICAL CALCULATION
EXAMPLE OF ASTRONOMICAL CALCULATION
EXAMPLE OF SUN TRACKING RESULTS
EXAMPLE OF SUN TRACKING RESULTS
Picture of the prototype model.
VI. CONCLUSIONS
In the future, it is expected that photovoltaic systems will be applied in fields such as for leisure and large ships, as they move from the existing fixed types to portable types. To use a photovoltaic system as the power source of an automobile, ship and portable devices, as well as for portable battery chargers, the system must be lightweight and able to produce as much electric power as possible. In portable systems, it is difficult to track the sun with a simple method like the ones used in fixed systems, since the current position changes continuously and the sun tracking algorithm is not aligned with the horizontal coordinate system of the current location. It is necessary to know the position and direction of the sun tracking algorithm for the current movement, and also to understand the tilt angle with respect to the horizontal plane.
In this paper, a sun tracking algorithm is presented for portable applications that can improve photovoltaic efficiency by tracking the sun in an arbitrary position in relation to a portable PV generation system. A prototype was developed for testing. In the future, the practicality of this proposal will be demonstrated by implementing an actual system with 2axis control of the sun tracking system so that the solar cell face could look at the sun perpendicularly, based on the calculations of the azimuth angle and altitude angle of the sun from the horizontal coordinate system. This will be accomplished through astronomical calculations that measure the posture of the sun tracking system in terms of the horizontal coordinate system with a tilt and geomagnetic sensors, using the rotation of coordinate system, and by acquiring current position and time information from the GPS sensor.
Acknowledgements
This work was supported in part by MEST & DGIST(13BD01) and also the present research has been conducted by the Research Grant of Kwangwoon University in 2013.
BIO
JuYeop Choi received his B.S. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1983, his M.S. from the University of Texas at Arlington, Arlington, TX, USA, in 1990, and his Ph.D. from the Virginia Polytechnic Institute and State University, Blacksburg, VA, USA, in 1994. He worked as a Research Engineer at the Intelligent Control Research Center, Korea Institute of Science and Technology, Seoul, Korea, from 1995 to 2000. Since 2000, he has been a Professor in the Department of Electronic Engineering, Kwangwoon University, Seoul, Korea. His current research interests include photovoltaic system control, applications, and modeling.
Ick Choy received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1979, 1981, and 1990, respectively. He worked as a Senior Research Engineer at the Intelligent Control Research Center, Korea Institute of Science and Technology, Seoul, Korea, from 1982 to 2003. Since 2003, he has been a Professor in the School of Robotics, Kwangwoon University, Seoul, Korea.
SeungHo Song was born in Korea, in 1968. He received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1991, 1993, and 1999, respectively. In 1992, he joined the Pohang Iron and Steel Control Company (POSCON) as a Research Engineer and worked on the development of DC and AC machine drives for steel rolling mill applications until 1995. From 2000 to 2006, he was an Assistant Professor in the Division of Electronics and Information, Chonbuk National University, Jeonju, Korea. He was also a Visiting Professor in WEMPEC, University of WisconsinMadison, Madison, WI, USA, from 2004 to 2005. Since 2006, he has been a faculty member in the Department of Electrical Engineering, Kwangwoon University, Seoul, Korea, where he is currently a fulltime Professor. His current research interests include electric machine drives and renewable energy conversion.
Jinung An received his B.S. in Mechanical Engineering from Sungkyunkwan University, Seoul, Korea, in 1993, his M.S. in Mechanical Engineering from KAIST (Korea Advanced Institute of Science and Technology), Daejeon, Korea, in 1997, and his Ph.D. in Robotics from KAIST, in 2005. He worked as a Professor in the Department of Information Control Engineering, Kwangwoon University, Seoul, Korea, from 2005 to 2008. Since 2008, he has been a Principal Researcher of the Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu, Korea. His current research interests include natureinspired technology and energy harvesting systems.
DongHa Lee received his B.S., M.S., and Ph.D. in Electronic Engineering from Kyungpook National University, Daegu, Korea, in 1985, 2001, and 2005, respectively. From 1987 to 2005, he worked as a Principal Engineer of LG Electronics. Since 2005, he has been a Principal Researcher of the Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu, Korea. His current research interests include renewable energy applications.
JungWon Kim received his B.S., M.S., and Ph.D. in Electrical Engineering from Seoul National University, Seoul, Korea, in 1994, 1996, and 2001, respectively. He was a Senior Engineer with Fairchild Korea Semiconductor, Ltd. From 2007 to July 2013, he was a Vice President of Silicon Mitus, Inc. He currently is a Senior Researcher in the Engineering Research Institute, Seoul National University, Seoul, Korea. His current research interests include power factor corrections, converter parallel operation, modular converter systems, distributed power systems, and soft switching converters.
Kim M.
2001
“Study on the making and application of portable smallsized tracking solar battery module,” Final Report of Korea Energy Management Corporation
Baltas P.
,
Tortoreli M.
,
Russell P. E.
1986
“Evaluation of power output for the fixed and step tracking photovoltaic arrays,”
Solar Energy
37
(2)
147 
163
DOI : 10.1016/0038092X(86)900721
Mosher D. M.
,
Boese R. E.
,
Soukup R. J.
1977
“The advantage of sun tracking for planar silicon solar cells,”
Solar Energy
19
(1)
91 
97
DOI : 10.1016/0038092X(77)900937
Craig John J.
1986
Introduction to Robotics Mechanics and Control
2nd ed.
AddisonWesley Publishing Company, Inc.
Burnett Keith
Position of the Sun
http://www.stargazing.net/kepler/sun.html