EVALUATION OF SUN POSITION USING THE PHOTOVOLTAIC

GENERATION

An Application for Attitude Estimation in Box-Shape Satellites

Ronilson Rocha, Alexandre Jos´e Ferreira, Caio Pequeno Gouvˆeia and Talita Bueno Barbosa

School of Mines - Department of Engineering of Control and Automation

Federal University of Ouro Preto, Campus Morro do Cruzeiro, 35400-000, Ouro Preto, MG, Brazil

Keywords:

Artiﬁcial Satellites, Attitude Determination, Photovoltaic System.

Abstract:

It is necessary at least two or more independent known vectors for attitude determination of an artiﬁcial

satellite. One of these vectors can be the Earth Magnetic Field, which is used as reference in navigation for

centuries. Other reference can be the sun, which is easily distinguished of other astronomical objects in the

proximities of the Earth. While the Earth Magnetic Field can be measured by a small solid-state three-axis

magneto-resistive transducer, the own photovoltaic system of the artiﬁcial satellite can provide a evaluation of

the azimuthal position of the sun. This paper presents a way to estimate the sun position from the own satellite

power system. This information is used for attitude determination, allowing the integration of two important

subsystems of an artiﬁcial satellite.

1 INTRODUCTION

An artiﬁcial satellite is a component of a spatial sys-

tem, an ample set of elements in the space (other

satellites, spacecrafts, spatial stations, etc.) and in

the ground (tracking stations, antennas, control cen-

ters, etc.). For the realization of a spatial mission,

an artiﬁcial satellite transports several onboard equip-

ments, such as radars, antennas, telescopes, photo-

graphic cameras, equipments for scientiﬁc measures,

etc. The power supply for onboard equipments has

vital importance in an artiﬁcial satellite. Considering

characteristics such as modularity, cost, maintenance

and life, the photovoltaic generation is the more ade-

quate energy resource for spatial applications. Since

the light-generated power in photovoltaic arrays is

highly dependent of the intensity and direction of the

incident sunlight, it is considerably variable in a satel-

lite and must be conditioned and regulated by power

electronic converters to supply onboard equipments.

The onboard equipments of an artiﬁcial satellite

must be pointed to a speciﬁed aim to interact with

others elements of the spatial system. Thus, the de-

termination of the spatial position and orientation of

an artiﬁcial satellite, also known as attitude, is fun-

damental for its perfect operation. The attitude re-

lated to an inertial reference is mathematically rep-

resented by an operator that rotates a vector inside

of a coordinate system, which can be estimated us-

ing algorithms that require the observation of at least

two independent and known vectors (Shuster and Oh,

1981). Several known vectors can be used as refer-

ence for attitude determination. One of these vectors

is the Geomagnetic Field, a magnetic dipole aligned

along the Earth’s rotational axis which points toward

to magnetic north. Since the sun is easily recognized

by any object near of the Earth due to its relatively

small apparent radius with a high brightness in rela-

tion to other astronomical bodies, its azimuthal posi-

tion related to artiﬁcial satellite can be considered as

a possible reference vector for attitude determination.

This paper proposes the attitude estimation of an

artiﬁcial satellite using the own photovoltaic gener-

ation to evaluate the azimuthal position of the sun.

A mathematical algorithm estimates the satellite at-

titude using this vector, which is evaluated from

the power converter operation, and the Geomagnetic

Field, which is measured using a three-axis solid-state

magnetometer. Thus, two important subsystems of an

artiﬁcial satellite can be integrated, providing various

beneﬁts always welcome in spatial applications, such

as economy, redundancy, autonomy, etc.

177

Rocha R., Gouvêia C., Ferreira A. and Barbosa T. (2009).

EVALUATION OF SUN POSITION USING THE PHOTOVOLTAIC GENERATION - An Application for Attitude Estimation in Box-Shape Satellites.

In Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 177-182

DOI: 10.5220/0002192601770182

 SciTePress

Figure 1: Sequential Shunt Regulator.

2 POWER REGULATION

An artiﬁcial satellite generally uses a regulated volt-

age bus and some form of direct energy transfer for

power conditioning of the photovoltaic energy (Shum

and Ashley, 1996). Due to a low and relatively con-

stant heat dissipation, the Sequential Shunt Regulator

(SSR) is widely used in satellite applications (Gar-

rig´os et al., 2006). This power electronic converter

is shown in Fig. 1, where is considered a segmented

photovoltaic array in six modules. Each photovoltaic

module can be admitted as a current source, which

contributions are summed by an OR connection of

very fast diodes. The photovoltaic current I can ei-

ther ﬂow to the bus when the MOSFET switch is off,

supplying loads and batteries, or be deviated, short-

circuiting the photovoltaic module when the MOS-

FET switch is on. Since the current in the bus is

pulsed, a large capacitor ﬁlter is required to smooth

current pulses and to reduce the voltage ripple.

Since the variations in the capacitor charge re-

ﬂect the energy exchanges between photovoltaic ar-

rays and electrical loads, the bus voltage must be

controlled to assure the power balance, restricting

the voltage variations to operational limits of the

onboard equipments. The voltage controller modu-

lates the duty cycle of a PWM signal, which simul-

taneously drives all six MOSFET’s switches of the

SSR. The battery operates in stand-by, assuming the

Figure 2: Equivalent electrical circuit of a photovoltaic cell.

Figure 3: Deﬁnition of the sunlight incidence angle β.

load when the bus voltage decreases and the series

diode becomes directly polarized, which occurs dur-

ing eclipses, faults and eventual current peeks. A

MOSFET switch can connect the battery to the power

bus for its recharge when the satellite is illuminated

again.

3 SUN POSITION ACQUISITION

Usually, the azimuthal position of the sun is evalu-

ated using a sensor based in photovoltaic cells, cam-

eras or CCD sensors (Winetraub et al., 2005; Chen

et al., 2006). However, an interesting possibility for

artiﬁcial satellites is the use of its own photovoltaic

system for evaluation of the azimuthal position of the

sun (Sityar, 1992; Santoni and Bolotti, 2000; Visc-

ito and Cerise, 2007), since the light-generated power

is highly dependent of the intensity and direction of

the incident sunlight. A photovoltaic module consists

in series-parallel arrays of several photovoltaic cells,

which equivalent electrical circuit is shown in Fig. 2.

The series resistance R

depends on the p-n junction

depth, impurities and the contact resistance, while the

shunt resistance R

is inversely related with leakage

current to the ground. The light-generated electrical

current I

depends on the efﬁciency of photovoltaic

conversion and the incident solar radiation over the

photovoltaic cell. This current can be approximated

by the mathematical cosine model (Patel, 1999)

= I

β=0

cosβ. (1)

where the incidence angle β is deﬁned in the Fig.

3. Since the electrical output in the real photovoltaic

cells deviates signiﬁcantly from the proposed cosine

model for β > 50

, this approach can lead to inac-

curacies in the determination of the sun positioning

(Winetraub et al., 2005; Sityar, 1992; Patel, 1999).

For a better accuracy, it is recommended the use of

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

178

Figure 4: Incidence of the sunlight in a box shaped satellite.

other power-angle curves of the photovoltaic cell,

such as the Kelly cosine (Patel, 1999). Neglect-

ing the diode and shunt-leakage currents, which are

very small in real cells, the current I

can be evalu-

ated short-circuitingthe output of a photovoltaicarray

(Sityar, 1992).

An illuminated box shape satellite with all six

sides covered by photovoltaic modules is shown in

Fig. 4. Considering a coordinate system constituted

by the normal axes to the surfaces of this box satellite,

a geometric inspection reveals that the components of

a vector that points towards to sun are the own sum-

mations of light-generated currents of opposite side

photovoltaic modules. Thus, the unitary vector

s that

points towards to sun is given by

s =

− I

−x

φ=0

,θ=0

− I

−y



φ=90

,θ=0

− I

−z



θ=90

(2)

where I

, I

−x

, I

−y

, I

, and I

−z

are the

light-generated currents by the photovoltaicpanels re-

spectively located in the axes +x, −x, +y, −y, +z,

and −z.

The scheme for acquisition of azimuthal position

of the sun from the SSR operation is shown in Fig.

5. When the outputs of opposite photovoltaic mod-

ule are short-circuited by their respective shunt MOS-

FET’s of the power converter, a Hall current trans-

ducer measures the differential light-generated cur-

rent in the respective coordinate axis. This signal is

sampled in S/H circuit while the shunt MOSFET’s are

on. When the shunt MOSFET’s are off, the S/H cir-

cuit holds the differential current measurement, assur-

ing that this component of vector

s is always availed

for acquisition.

4 SIMULATION RESULTS

The acquisition of the vector sun position is veriﬁed

from a computational simulation of the SSR using the

SimPowerSystems of the MATLAB/SIMULINK. It is

Figure 5: Scheme for acquisition of azimuthal position of

the sun from the SSR and bus voltage regulation.

considered that a box shape satellite is rotating in the

space at

φ = 1.26rad/s and

θ = 6.28rad/s (see Fig. 4).

The surface of this satellite is covered by six photo-

voltaic arrays that generates 6×10W

at an irradiance

of 1000W/m

. The sunlight irradiance in the space

is considered 1367W/m

. The duty cycle D of the

SSR is modulated by a PWM of 5kHz, and a capac-

itor of 1500µF is connected to power bus aiming to

reduce the voltage ripples. Since the bus capacitance

behaves as a big integrator, a simple proportional con-

troller, which gain is adjusted to 300, is enough for a

null error in the regulation of the bus voltage. The

voltage reference is adjusted to 15V to supply a resis-

tive load of 90Ω and a 12V battery. A hysteresis con-

troller monitors the battery charge and commands the

MOSFET switch, connecting the battery to the power

bus when its voltage level is the minimum. Aiming

to preserve the useful life of the battery, it is discon-

nected from bus voltage when the maximum charge is

reached.

The real and acquired azimuthal sun position is

shown in the Fig. 6. The error in the acquired vec-

tor is small, basically caused by the sample operation.

The attitude motion (angular frequencies of the satel-

lite) can be evaluated from the Fast Fourier Transform

(FFT) of the acquired data. Although the photovoltaic

power supply is highly variable due to satellite rota-

tion, the proposed P controller is enough to assure a

null voltage error, providingan excellent regulation of

the bus voltage for the considered load, as shown in

the Fig. 7.

EVALUATION OF SUN POSITION USING THE PHOTOVOLTAIC GENERATION - An Application for Attitude

Estimation in Box-Shape Satellites

179

−1

−0.5

0.5

−1

−0.5

0.5

−1

−0.5

0.5

sun position coordinates

−1

−0.5

0.5

−1

−0.5

0.5

−1

−0.5

0.5

light−generated currents

−1

−0.5

0.5

−1

−0.5

0.5

−1

−0.5

0.5

∆

acquisition error

∆

Figure 6: Azimuthal position of the sun.

0 1 2 3 4 5 6 7 8 9 10

time(s)

voltage (V)

Figure 7: Regulated bus voltage in the Sequential Shunt

Regulator.

Figure 8: Magnetometer circuit.

5 MAGNETOMETER CIRCUIT

The measurement circuit for Geomagnetic Field is

shown in Fig. 8. The heart of this circuit is a

small solid-state three-axis magneto-resistive trans-

ducer Honeywell HMC2003,which output voltage

signals are proportional to the magnitudes of the three

ordinal components of the applied magnetic ﬁeld in

a range of the 0 to +5V, where +2.5V represents the

reference value for a null intensity of the magnetic

ﬁeld. In order to maximize the transducer resolution,

a strong SET/RESET pulse must be occasionally ap-

plied to transducer to eliminate the effect of the past

magnetic history and to avoid the degradation of the

output signal. The output voltage signals X, Y and

Z can be connected directly to an analog-to-digital

(A/D) converter.

6 ATTITUDE ESTIMATION

A common way to specify the attitude of a body is the

use of the Euler’s angles ψθφ, which represent three

consecutiverotations in a convenientsequence around

the axis of an inertial system. The combination of

these rotations results in the attitude matrix A, which

represents the orientation of an object in relation to

inertial coordinate system. Considering a stipulated

reference vector v

, its rotation to obtain an observed

vector w

by one of the n sensors of the satellite is

described as

= Av

, (3)

where an estimative of the attitude matrix A can be

obtained from the minimization of the cost function:

L(A) =

∑

i=1

− Av

)

(4)

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

180

with the non negative weights a

submitted to restric-

tion

∑

i=1

= 1 (Shuster and Oh, 1981). This opti-

mization problem can be conveniently simpliﬁed ex-

pressing it in terms of the quaternion

q, an alternative

attitude representation deﬁned as:

q =







sin(θ/2)n

cos(θ/2)



(5)

and related with an attitude matrix A by:

q) = (q

− QQ

)I+ 2QQ

+ 2q

Q (6)

In terms of quaternions, the solution of this op-

timization problem is given by an algorithm known

as Q-method, which consists of a simple generalized

problem of eigenvalues and eigenvectors described by

(Keat, 1977; Shuster and Oh, 1981)

opt

= λ

max

opt

, (7)

where the optimal quaternion

opt

that minimizes the

cost function L(A) is the eigenvector associated to

maximum eigenvalue λ

max

of the matrix K, given by

K =



S− σI Z

Z σ



, (8)

where σ =

∑

i=1

, S =

∑

i=1

+ v

)

and Z =

∑

i=1

× v

7 INTEGRATION

Considering spatial applications, both the power reg-

ulation and the attitude estimation must be integrated

in an unique, compact and low consumption onboard

platform, which should read analog signals, compute

the present satellite attitude, and perform the power

control and energy management. This platform must

still execute other complementary functions of the

satellite such as telemetry, command, control, com-

munication and error analysis. In this context, an in-

teresting high performance and low cost option is a

DSP-based platform, which combines a high process-

ing speed processor, great amount of memory and

several peripheral devices for real time digital pro-

cessing signal, such as A/D converters, I/O ports,

PWM modules, parallel and serial communication in-

terfaces, and special modules to read encoders, coun-

ters, timers, etc. The programming uses high level

language, presenting several tools to develop complex

algorithms such as FFT (Fast Fourier Transform), ﬁl-

ters and other indispensable functions for the satel-

lite operation, such as attitude estimation and control,

power regulation and management, auto-diagnose,

communications, fail analysis, and data storage.

Figure 9: Experimental implementation.

8 EXPERIMENTAL RESULTS

The Q-method algorithm is experimentally imple-

mented using C language in a starter kit module based

in the Texas Instruments DSP TMS320F2808. A pho-

tography of this practical implementation is presented

in the Fig. 9. While reference vectors v

and v

are

considered ﬁxed and its values are directly inserted in

the code, the observation vectors w

and w

are ac-

quired using sample rate superior to 10 Hz. The vec-

tor w

is the magnetic ﬁeld produced by Helmholtz

coils, which is measured using the magnetometer cir-

cuit presented in Fig 8, while the vector w

is emu-

lated by potentiometers. The experimental results of

implementation considering two static known situa-

tions are shown in the table I, where is observed that

this DSP platform can provide satisfactory attitude es-

timations for this satellite application.

9 FINAL DISCUSSION

This paper presents a proposal to acquire the az-

imuthal position of the sun using the own power pho-

tovoltaic supply of an artiﬁcial satellite. Consider-

ing a box shape satellite, where all sides are cov-

ered by photovoltaic modules, the components of the

azimuthal position of the sun correspond to summa-

tions of the light-generated currents by opposite pho-

tovoltaic modules, which can be evaluated from the

operation of the SSR power converter. In the even-

tual absence of a photovoltaic module, photovoltaic

cells or photodiodes can substitute it in the satellite

conﬁguration. This information about the sun po-

sition and the measurement of other known vector,

such as the Geomagnetic Field, can be used to esti-

mate the attitude, allowing the integration of two of

the more important subsystems for the operation of

an artiﬁcial satellite. The integration of these subsys-

tems can be implemented in a DSP platform, which

would realize data acquisition, power regulation, bat-

tery management, attitude determination and others

important satellites functions. The simulation results

EVALUATION OF SUN POSITION USING THE PHOTOVOLTAIC GENERATION - An Application for Attitude

Estimation in Box-Shape Satellites

181

Table 1: Experimental results.

and w

are aligned with v

and v

x 0.0000 0.0000 0.0000 0.0000

y 1.0000 1.0000 0.0000 0.0000

z 0.0000 0.0000 1.0000 1.0000

Theoretical attitude matrix





1.0000 0.0000 0.0000

0.0000 1.0000 0.0000

0.0000 0.0000 1.0000





Experimental attitude matrix (DSP)





0.9994 0.0352 −0.0006

−0.0352 0.9992 −0.0179

0.0000 0.0179 0.9999





is inclined 45

in relation to v

while w

and v

are aligned.

x 1.0000 1.0000 0.0000 0.0000

y 0.0000 1.0000 0.0000 0.0000

z 0.0000 0.0000 1.0000 1.0000

Theoretical attitude matrix





0.7071 −0.7071 0.0000

0.7071 0.7071 0.0000

0.0000 0.0000 1.0000





Experimental attitude matrix (DSP)





0.7017 −0.7124 0.0028

0.7124 0.7013 0.0029

−0.0040 0.0000 1.0000





Reference and observation vectors

x 1.0000 0.70523 0.0000 -0.00793

y 0.0000 0.70884 1.0000 0.00881

z 0.0000 -0.01353 0.0000 0.99999

Theoretical attitude matrix (MATLAB)





0.70522 −0.00338 0.70897

0.70894 0.01337 −0.70513

−0.00709 0.99990 0.01183





Experimental attitude matrix (DSP)





0.70523 −0.00337 0.70896

0.70894 0.01339 −0.70513

−0.00711 0.99904 0.01183





shows that the azimuthal position of the sun can be

evaluated from the SSR operation with sufﬁcient ac-

curacy for attitude determination. The results of the

experimental implementation in a DSP platform of

the q-Method, an algorithm that involves a theoreti-

cally great computational effort, are satisfactory for

this satellite application. An experimental evaluation

of this proposal will realized using the little proto-

type of a box-shape satellite (Fig. 10), where the sub-

systems related to power regulation and attitude esti-

mation will be integrated by a DSP platform. Other

satellite conﬁguration will be also considered in fu-

ture studies related to this subject.

Figure 10: Box-shape structure.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the ﬁnancial sup-

port of the Federal University of Ouro Preto, National

Counsel of Technological and Scientiﬁc Development

(CNPq), State of Minas Gerais Research Foundation

(FAPEMIG) and Gorceix Foundation.

REFERENCES

Chen, F., Feng, J., and Hong, Z. (2006). Digital sun sen-

sor based on the optical vernier measuring principle.

Measurements Science and Technology, 17:24942498.

Garrig´os, A., Carrasco, J., Blanes, J., and Sanchis-Kilders,

E. (2006). A new sequential switching shunt regula-

tor - digital shunt regulator (S3R-DSR) for solar array

regulators. In 2006 IEEE International Symposium on

Industrial Electronics - ISIE 06.

Keat, J. (1977). Analysis of least-squares attitude deter-

mination routine DOAOP. Technical report, National

Aeronautics and Space Administration (NASA).

Patel, M. (1999). Wind and solar power systems. CRC

Press.

Santoni, F. and Bolotti, F. (2000). Attitude determination of

small spinning spacecraft using threeaxis magnetome-

ter and solar panels data. In 2000 IEEE Aerospace

Conference.

Shum, K. and Ashley, C. (1996). A new full shunt switch-

ing unit for solar array using coupled-inductor boost

converter. In 31st Intersociety Energy Conversion En-

gineering Conference - IECEC 96.

Shuster, M. and Oh, S. (1981). Three-axis attitude determi-

nation from vector observations. Journal of Guidance

and Control, 4(1):70–77.

Sityar, I. (1992). Sun sensor implementation using solar

power arrays. Master’s thesis, Naval Postgraduate

School, Monterey, USA.

Viscito, L. and Cerise, M. (2007). Rate and attitude deter-

mination using solar array currents. In 2007 Colorado

Space Grant Consortium’s: Undergraduate Space Re-

search Symposium.

Winetraub, Y., Bitan, S., Nativ, Y., and Heller, A. (2005).

Attitude determination advanced sunsensors for pico-

satellites. In 17th European Union Contest for Young

Scientists.

ICINCO 2009 - 6th International Conference on Informatics in Control, Automation and Robotics

182