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A Novel Optical Sensor of Light Source Directions

Chia-Yen Lee2, Po-Cheng Chou1, Wen-Jen Hwang2

1Department of Interior Design, Shu-Te University, Kaohisung County, Taiwan

2Department of Mechanical and Automation Engineering, Da-Yeh University, Chunghua, Taiwan

ABSTRACT

This paper presents a novel technique for the measurement systems of solar orientation based

on solar cells. A methodology for the calculation of the solar orientation is developed which uses

solar cells as solar sensors. The time and latitude angles of the sun are proposed to be a function of

the output voltages of sloped solar cells. The solar cells are located at different angles of elevation

and azimuth for the comparative output voltages between the back-to-back solar cells. A variation in

the time and latitude angles of the sun causes a change of the output voltages of the eastern-western

(E-W) and southern-northern (S-N) solar cells, which changes the relative measured voltages

between the solar cells, respectively. The current experimental data show that the optimized

assembly of solar cells and the detailed calibration of time and latitude angles of the sun yield a

high degree of sensitivity. The relationship between the measured relative voltages of solar cells is

fully explored and documented. The proposed study indicates not only simplified solar orientation

measurement systems but also convenient and accurate correlations of the comparative output solar

cell voltages and the sun angles. As such, the proposed measurement systems make a valuable

contribution to the development of tracking systems in solar energy technologies.

Keywords: Solar cell, Solar collector, Solar orientation

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1. Introduction

In the past decades, emerging solar energy systems have been popular in the renewable energy

technology. As a result of these systems, solar collectors has now been developed which is capable

of collecting incident solar radiation and converting it into electrical power, thermal energy …etc.

Importantly, the absorbed solar energy within the collectors can be increased through their

integration with solar tracking systems that compute the direction of the solar vector on location and

time [Blanco-Muriel et al., 2001]. Therefore, the effectiveness of the solar collectors can also be

increased if it is always aimed at the sun [Berenguel et al., 2004; Hj Mohd Yakup et al., 2001;

Algifri et al., 2001].

Solar orientation measurement is essential in such solar energy fields. Many previous studies

have addressed the application of solar collectors to the development of solar energy technologies

[Kowalski, 1997; Surman, 1996; Raasakka, 1997; Bari, 2000; Tesfamichael et al., 2000]. Automatic

regulation systems of solar collectors integrated with sun sensors were proposed to improve the

solar radiation absorption. A review of the related literature reveals many forms of sun sensors

[Berenguel et al., 2004; Popat Pradeep, 1998; Wen et al., 2002; Falbet et al., 2002], including

brightness sensors [Popat Pradeep, 1998], artificial vision techniques and CCD devices [Berenguel

et al., 2004]. Measured solar energy values could be used to compute the absorbed solar energy as

function of time of day [Wen et al., 2002]. Of particular interest is the two axis analog device,

which measures the sun’s location relative to its optical axis based on the relative signal obtained in

a quadrant silicon detector [Falbet et al., 2002]. In the four detector quadrants, relative radiant

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powers are applied to estimate the angle that the sun line makes with the sensor’s optical axis. This

device is attractive since it is capable of providing highly precise solar orientation measurement

despite its complicated structure. Therefore, the intention of this present study is to present a novel

solar orientation measurement system which incorporates four elevated solar cells fixed on a wedge,

and which includes a methodology to calculate the time and latitude angles of the sun.

Generic algorithms with climate data were used to find out the optimum installation angle of

the solar collector for different locations in Taiwan [Chen et al., 2001]. The best monthly and annual

installation angles were obtained by computer simulations. In spite sufficient installation

information for solar collectors were provided, the solar orientation measurement was not

instantaneous and connectable with a tracking system. The current study develops a methodology

for the solar orientation based on solar cells and geometry models of direct solar irradiation into

different sun sensor configurations, namely single cell, double cells and quadrantal cells. By

correlating the output voltage signals of two back-to-back solar cells (eastern and western / southern

and northern), the time angle and the latitude angle of the sun can be estimated, respectively. The

characteristics of the three types of sun sensors were investigated and the correlations were

calibrated in this study. Experimental results show high coincidence between the calibrated angles

and the sun angles.

2. Sensor Design and Methodology

In this study, solar cells are adopted as the sun sensors for different solar time and latitude

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angles. The sun sensors are connected with a personal computer to record and analyze data. In solar

cells, the photo-induced current, or called the generation current is proportional to the number of

photons that can be collected on the surface area of the solar cells. Since the objective of the solar

cells is to sense the change of solar incident ray and to convert it to the analyzer, the irradiation

absorbency differs at different incident angles by time in a day-time. As a result, the output voltage

of the solar cells varies at different solar time and latitude angle. In this study, the time angle θ is

defined as the angle between the incident ray and the horizontal plane and the latitude angle φ is the

angle between the incident ray and the eastern direction. Many studies presented the geometry of

solar irradiation into the solar devices [Blanco-Muriel et al., 2001; Hj Mohd Yakup et al., 2001;

Wen et al., 2002; Chen et al., 2001; Duffie et al., 1991; Lorenz, 1998]. The present study uses the

rectangular coordinate-system to model the geometrical relationships between the sun and the sun

sensors (Fig. 1). To simplify the problem, the plane which equipped with sun sensors is assumed to

be horizontal. The latitude plane is bounded by the latitude of the sun location as season changes.

As day-hours go, the time plane sweeps the hemisphere from the east to the west. The intersection

line of the two planes (the latitude and the time planes) is the trajectory of the incident ray from the

sun. The latitude and time angles of the instantaneous locations of the sun can be established by the

geometrical analysis.

In order to compare the performance of different designs of solar orientation measurement

systems based on solar cells, three types of measurement systems were developed in the study, i.e.

(a) single cell, (b) double cells and (c) quadrantal cells. Incandescent lamps (SC5848, HOMES,

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Taiwan) were used to simulate the sun in a dark room. The wavelength of the incandescent lamp is

400-780 nm, which resemble the wavelength of the solar light (400-800 nm). A solar cell was lain

on a horizontal plane and connected with a voltage meter to record the voltage changes as the

elevation angle of the light source changed in the single cell type of measurement system (Fig. 2).

In the double cell type of system, two sloped solar cells leaned against each other to measure the

comparative output voltages of the two cells at different solar orientation (Fig. 3). Two sets of

double cell type of sensors were integrated into a quadrantal types of measurement system (Fig. 4).

Not only the time plane can be defined by sensors E and W, but also the latitude plane can be found

by sensors S and N. The output voltages were measured by a voltage meter and operated in a

personal computer to define the time and latitude angles of the incident ray from the sun. The

detailed experimental results were described in section 3.

3. Experimental Results

A systematic investigation of the performance of the three types of solar orientation systems

was conducted. The characterization of the sun sensors was carried out in a dark room (L: W: H =

3.5 m: 3.5 m: 2.5 m) using a voltage meter (3136A, Escort, Taiwan), which was connected to the

solar cells in the dark room to record the signal response to changes of light source locations. The

distance between the light source and the sun sensors was kept constant at 140 cm because the

distance change between the sun and any area on earth can be ignored as compared with the actual

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distance. All the measured data was recorded and operated in a personal computer.

3.1 Single cell type of measurement system

The output voltage of the single solar cell increases with the increase of the elevation angle

from -45o to 90o (Fig. 2). The output voltage increases abruptly as the elevation angle of the light

source is more than -5o, and it increases almost linearly when the elevation angle is more than 0o

(Fig. 5). To find the relationship of the output voltage and the negative elevation angle, the output

voltage was measure from the elevation angle = 45o. As the power of the light source increases, the

output voltage increases. As the light source is 250 W of incandescent lamp, the linearity of the

measured curve is better than the other two. In spite the output voltage is linear both at the ranges of

-45o - -5o and 0o – 90o at 250 W, the measured signal may decrease when it is cloudy or partly

cloudy. To compensate the deviation due to the environmental effects, a two cell type of system was

developed.

3.2 Double cell type of measurement system

For the optimization of the slope angle of the double cell type of measurement system, two

sloped solar cells leaned against each other to measure the comparative output voltages of the two

cells at different sloped angles δ (Fig. 3). The solar orientation measurement system was

characterized with different solar elevation angles θ in the range of 0o to 90o at a constant distance

from the light source of 140 cm. A voltage ratio R of the two solar cells was calculated to normalize

the measurement results. In Figure6, the results showed that the ratio drops as the elevation angle,

which is the time angle in the actual case, increases and the ratio approaches 1 when the time angle

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is more than the same value of the sloped angle δ. As the time angle is less than δ value, the fitted

curve equations for the voltage ratio R of different sloped angles are expressed by:

R = -0.0059θ2 + 0.905 θ + 9.9888 for δ = 45o (1)

R = -0.0099θ2 + 0.055 θ + 8.9372 for δ = 30o

R = -0.0223θ2 – 0.0315 θ + 6.0736 for δ = 15o

As the time angle is more than δ value, the fitted curve equations for the voltage ratio R of different

sloped angles are linear and can be expressed by:

R = -0.0053θ + 1.4587 for δ = 45o (2)

R = -0.0027θ + 1.2385 for δ = 30o

R = -0.0010θ + 1.0922 for δ = 15o

where R is the voltage ratio of the two solar cells and θ is the time (elevation) angle (o). Eqs. (1) and

(2) are useful for the estimation of the solar time angle at low elevation angle (<δ) and high

elevation angle (>δ).

4. Conclusions

This study has successfully demonstrated a new solar orientation measurement system with

integrated solar cells. A new assembly method and a geometrical model have been developed for the

precise measurement of the time and latitude angles of the sun at day-time and four seasons. It has

been shown that the change of the output voltages of two back-to-back sun sensors caused by their

sloped installation angle gives rise to a measurable change in the voltage ratio between the two

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sensors. In addition to its precise solar orientation measurement and its simplified geometrical

model, the device also exhibits a high degree of integrable with other solar energy devices.

Acknowledgement

The authors would like to thank the financial support provided by the National Science Council in

Taiwan (NSC 93-2218-E-212-011).

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E

N

W

S

incident ray

time plane

latitude plane

A

B

O

θ

φ

E

N

W

S

incident ray

time plane

latitude plane

A

B

O

θ

φ

Figure 1 Geometry of the irradiation of direct sunlight to sun sensors.

personalcomputer

voltage meter

RS232 Cablesingnal lines

sun sensor

N

N : normal Vector

θ

E

personalcomputer

voltage meter

RS232 Cablesingnal lines

sun sensor

NN

N : normal VectorN : normal Vector

θ

E

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Figure 2 A schematic representation of single cell type of measurement systems.

Figure 3 A schematic representation of double cell type of measurement systems.

α2

α1N2 N1

δ personalcomputer

RS232 Cablesingnal lines

N : normal Vector

sun sensor 1sun sensor 2E

θ

voltage meter

α2

α1N2 N1

δ personalcomputer

RS232 Cablesingnal lines

N : normal Vector

sun sensor 1sun sensor 2E

θα2

α1N2N2 N1N1

δ personalcomputer

RS232 Cablesingnal lines

N : normal VectorN : normal Vector

sun sensor 1sun sensor 2EE

θ

voltage meter

E

N

sensor Ssensor E

sensor Wsensor N

θ

φ

personalcomputer

voltage meter

E

N

sensor Ssensor E

sensor Wsensor N

θ

φ

personalcomputer

voltage meter

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Figure 4 A schematic representation of quadrantal type of measurement systems.

Figure 5 Output voltages at different elevation angles for single cell type of measurement

systems.

0

5

10

15

-45 0 45 90

elevation angle (degree)

output voltage (V)

□ 250 W

◊ 100 W ∆ 40 W

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1

3

5

7

9

11

0 10 20 30 40 50 60 70 80 90

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

1

3

5

7

9

11

0 10 20 30 40 50 60 70 80 90

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

1

3

5

7

9

11

0 5 10 15 20 25 30 35 40 45

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

1

3

5

7

9

11

0 5 10 15 20 25 30 35 40 45

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

1

1.05

1.1

1.15

1.2

1.25

45 50 55 60 65 70 75 80 85 90

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

1

1.05

1.1

1.15

1.2

1.25

45 50 55 60 65 70 75 80 85 90

time angle (degree)

volta

ge ra

tio

□ 45o

? 30o

Δ 15o

(a) 0o – 90º

(b) 0o – 45º

(c) 45º-90º.

Figure 6 Output voltages at different time angles for double cell type of measurement systems. (a)

0o – 90º, (b) 0o – 45º and (c) 45º-90º.