**9. Design and simulation examples**

The following two examples will show how a spacecraft solar array, composed of one or more panels having different orientations, provide the needed power during the mission. The examples reported consider body mounted panels, having a fixed orientation with respect to the satellite body axes. This kind of panels is typically used for small and medium satellites, with a power demand less than 1 kW. If on one hand they are relatively cheap and easy to realise, on the other they may require additional efforts for the proper assessment of the energy budget throughout the orbits. This is particularly true in case of the power bus is an unregulated one, having wide voltage variations because of the battery

Architectural Design Criteria for Spacecraft Solar Arrays 181

**Satellite Ground Track: 1st June 2012, 24h**

Figure 23 shows the calculated temperatures for the three panels. Finally, figure 24 reports the available power from the array, the power exchanged by the battery, and the power required by the loads; from this plot it can be clearly seen the power delivered by the battery

**Solar Panels Illumination [W/m2]**

0 1 2 3 4 5 6 7 8 9

Time [sec]

**Solar Panels Temperatures [deg C]**

0 1 2 3 4 5 6 7 8 9

Time [sec]

x 104

panel #1 panel #2 panel #3

x 104

panel #1 panel #2 panel #3

Longitude [deg]

0 50 100 150 200 250 300 350

Fig. 21. Ground station visibility and eclipses


Latitude [deg]

is adequately balanced by the power used for recharging them.

Fig. 22. Illumination of solar panels over 24 hours period

Illumination [W/m2]

Fig. 23. Temperature of solar panels over 24 hours period


Temp [deg C]

charge and discharge cycling. In conclusion their design may be particularly challenging because of their typical small size, many times conditioned by the allowed dimensions and mass of the satellite, and the irregular illumination along the orbit.

The first example concerns an Earth observation satellite made as a cube. Three lateral sides are covered by solar cells; the fourth one accommodates the instruments and is Nadir pointing. The last two sides of the cube are parallel to the orbital plane. This configuration of the satellite is such that the illumination of each panel results to be almost sinusoidal, when the sun-light is incident on the panel itself. The temperatures will follow the same type of law, and the available electrical power as well. The orbit is sun-synchronous, and the transmitters are working when the ground stations are visible. The satellite is small; its required power is about 160W, and 60W are consumed by two different transmitters at different transmission frequencies. Each panel accommodates 8 strings of 18 cells each; the power conditioning is based on the S3R regulator with a battery power bus (battery directly connected to the distribution bus. This architecture is the one which can be prone to the lock-up of the power bus previously described, due to over-discharge of the battery after eclipse periods. The problem is however mitigated by the possibility to have a sun-bathing mode when the satellite passes over the oceans and in any case in the southern hemisphere. In this operative mode two of the three panels will have the common edge oriented towards the Sun, the sunlight incidence will be 45 deg. Figure 20 shows when these sun-bathing phases can occur (red ground-track).

Fig. 20. Satellite ground track

As said, the required power is mainly function of the duty cycle of the transmitters when the ground stations are visible. In this example the three ground stations, typically used for earth observation missions are Kiruna (light blue), Fairbanks (magenta), and Redu (yellow). Figure 21 shows when these stations are visible, together with the eclipse periods (blue ground track). The illuminations of the panels for 24 hours (14 orbits) simulation are reported in figure 22. It can be clearly seen when the sun bathing occurs: panel #3 shows a constant illumination of about 950 W, while the panel #2 (magenta) has a slight increase due to the albedo effect; the panel #1 results to be not illuminated.

charge and discharge cycling. In conclusion their design may be particularly challenging because of their typical small size, many times conditioned by the allowed dimensions and

The first example concerns an Earth observation satellite made as a cube. Three lateral sides are covered by solar cells; the fourth one accommodates the instruments and is Nadir pointing. The last two sides of the cube are parallel to the orbital plane. This configuration of the satellite is such that the illumination of each panel results to be almost sinusoidal, when the sun-light is incident on the panel itself. The temperatures will follow the same type of law, and the available electrical power as well. The orbit is sun-synchronous, and the transmitters are working when the ground stations are visible. The satellite is small; its required power is about 160W, and 60W are consumed by two different transmitters at different transmission frequencies. Each panel accommodates 8 strings of 18 cells each; the power conditioning is based on the S3R regulator with a battery power bus (battery directly connected to the distribution bus. This architecture is the one which can be prone to the lock-up of the power bus previously described, due to over-discharge of the battery after eclipse periods. The problem is however mitigated by the possibility to have a sun-bathing mode when the satellite passes over the oceans and in any case in the southern hemisphere. In this operative mode two of the three panels will have the common edge oriented towards the Sun, the sunlight incidence will be 45 deg. Figure 20 shows when these sun-bathing

As said, the required power is mainly function of the duty cycle of the transmitters when the ground stations are visible. In this example the three ground stations, typically used for earth observation missions are Kiruna (light blue), Fairbanks (magenta), and Redu (yellow). Figure 21 shows when these stations are visible, together with the eclipse periods (blue ground track). The illuminations of the panels for 24 hours (14 orbits) simulation are reported in figure 22. It can be clearly seen when the sun bathing occurs: panel #3 shows a constant illumination of about 950 W, while the panel #2 (magenta) has a slight increase due

to the albedo effect; the panel #1 results to be not illuminated.

mass of the satellite, and the irregular illumination along the orbit.

phases can occur (red ground-track).

Fig. 20. Satellite ground track

Fig. 21. Ground station visibility and eclipses

Figure 23 shows the calculated temperatures for the three panels. Finally, figure 24 reports the available power from the array, the power exchanged by the battery, and the power required by the loads; from this plot it can be clearly seen the power delivered by the battery is adequately balanced by the power used for recharging them.

Fig. 22. Illumination of solar panels over 24 hours period

Fig. 23. Temperature of solar panels over 24 hours period

Architectural Design Criteria for Spacecraft Solar Arrays 183

Lisa PF Solar Array Lay-out

Figure 28 shows the illumination and the temperature reached by the solar panel in the first orbits after launch, the temperature over the panel is now considered as constant. It can be observed that the illumination takes into account also the contribution of the albedo just before and after an eclipse (no illumination), as expected from a solar panel always pointing


X axis position [mm]

The figure 29 shows now the extended temperature profile over a period of 24 hours, together with output voltage and current; to be observed that from the fourth orbit onwards the temperature shows an slight increase after 70% of sunlight period has elapsed; this happens because when the battery is fully charged; the maximum power is not required anymore, the operating voltage of the array shifts toward the open circuit value. At the same time it can be seen that the output current decreases. This temperature increase is due to the difference between the maximum available power and the required one; the unused power

Solar Array I-V Curve

Curve @ 78 deg C Curve @ 108 deg C Curve for LISA-PF Temp. profile

<sup>0</sup> <sup>10</sup> <sup>20</sup> <sup>30</sup> <sup>40</sup> <sup>50</sup> <sup>60</sup> <sup>0</sup>

Solar Array output voltage [V]

Fig. 26. Solar array layout

warms up the array.

towards to the sun throughout the orbit.



0

Y axis position [mm]

500

1000

1500

Fig. 27. LISA Pathfinder Solar array, V-I curve

5

10

Solar Array Output Current [A]

15

20

25

Fig. 24. Power Balance

The second example concern the design of a body mounted solar array which output power is conditioned by a MPPT control system. This is the case of LISA Pathfinder, which solar array is composed of 39 strings of 24 cells each, for 650W required power in EOL conditions. The nominal attitude during the mission is sun pointing, and the limited surface available for the solar array is due to mission and spacecraft configuration constraints. At a certain stage of the project it was decided to separate the solar panel from the rest of the structure by dedicated supports. This solution introduced the possibility to have different working temperatures between the strings and cells belonging to the same string, because of different thermal exchange modalities among centre and periphery of the panel.

Fig. 25. LISA Pathfinder artistic impression

Therefore it was worth to analyse whether a temperature gradient of 30 °C between centre and periphery may originate knees in the I-V curve that may be recognised as false maximum power points by the MPPT control loop, leading to a block of the working point of the array in a non optimal position. Figure 26 shows the layout of the solar cells within their strings, adjacent rows of cells of the same colour belong to the same string. The resulting I-V curve (green) of the whole array is showed in figure 27, as term of comparison the two V-I curves calculated considering constant temperature are also reported as term of comparison. To be observed that the cell with the lowest temperature in a string rules the maximum current flowing trough the string itself. From the plot it can be concluded there are no knees between the open circuit voltage and the maximum power knee such to provoke the lock of the MPPT tracker around a false maximum power working condition.

Fig. 26. Solar array layout

Solar Array Available Power

0 1 2 3 4 5 6 7 8 9

Battery Power (<0 during discharge)

0 1 2 3 4 5 6 7 8 9

Load Required Power

0 1 2 3 4 5 6 7 8 9

Time [sec]

x 104

x 104

x 104

The second example concern the design of a body mounted solar array which output power is conditioned by a MPPT control system. This is the case of LISA Pathfinder, which solar array is composed of 39 strings of 24 cells each, for 650W required power in EOL conditions. The nominal attitude during the mission is sun pointing, and the limited surface available for the solar array is due to mission and spacecraft configuration constraints. At a certain stage of the project it was decided to separate the solar panel from the rest of the structure by dedicated supports. This solution introduced the possibility to have different working temperatures between the strings and cells belonging to the same string, because of different

Therefore it was worth to analyse whether a temperature gradient of 30 °C between centre and periphery may originate knees in the I-V curve that may be recognised as false maximum power points by the MPPT control loop, leading to a block of the working point of the array in a non optimal position. Figure 26 shows the layout of the solar cells within their strings, adjacent rows of cells of the same colour belong to the same string. The resulting I-V curve (green) of the whole array is showed in figure 27, as term of comparison the two V-I curves calculated considering constant temperature are also reported as term of comparison. To be observed that the cell with the lowest temperature in a string rules the maximum current flowing trough the string itself. From the plot it can be concluded there are no knees between the open circuit voltage and the maximum power knee such to provoke the lock of the MPPT tracker around a false maximum power working

thermal exchange modalities among centre and periphery of the panel.

Fig. 25. LISA Pathfinder artistic impression

condition.

Fig. 24. Power Balance


> Figure 28 shows the illumination and the temperature reached by the solar panel in the first orbits after launch, the temperature over the panel is now considered as constant. It can be observed that the illumination takes into account also the contribution of the albedo just before and after an eclipse (no illumination), as expected from a solar panel always pointing towards to the sun throughout the orbit.

> The figure 29 shows now the extended temperature profile over a period of 24 hours, together with output voltage and current; to be observed that from the fourth orbit onwards the temperature shows an slight increase after 70% of sunlight period has elapsed; this happens because when the battery is fully charged; the maximum power is not required anymore, the operating voltage of the array shifts toward the open circuit value. At the same time it can be seen that the output current decreases. This temperature increase is due to the difference between the maximum available power and the required one; the unused power warms up the array.

Fig. 27. LISA Pathfinder Solar array, V-I curve

Architectural Design Criteria for Spacecraft Solar Arrays 185

**LISA-PF; Battery Depth of Discharge, first mission day**

Fig. 30. Battery Depth of Discharge (DOD %) for launch phase and first mission day.

by triple junction solar cells capable to have a bulk efficiency of more than 30%.

AZUR SPACE Solar Power GmbH, 3G-28% Solar Cell Data-sheet

http://azurspace.de/index.php?mm=89

Konstanz, Germany, Sept. 2008.

Portugal, May 2002.

Heidelberg, 1980.

Objective of this chapter was to provide guidelines for the design at system level of a solar array for satellites. Such kind of application has to be compliant with severe requirements mainly dictated by the harsh space environment mainly in terms of temperature levels, cosmic radiations which provoke wide variations of the performances together with their continuous degradation. Mass and size of the panels are main constraints with respect to the required power as well as optimal orientation towards to the sun, several times limited by other requirements at spacecraft and mission level. The actual state of the art is represented

0 1 2 3 4 5 6 7 8 9

Time [sec]

x 104

Typical accommodations of these arrays have been illustrated and a few design examples provided. These examples have been chosen among those may be considered as particularly challenging with respect to the required power and energy budgets coupled with mission

Strobl, G. et al.; (2002). Advanced GaInP/Ga(In)As/Ge Triple junction Space Solar Cells*,* 

Neugnot, N. et al.; (2008). Advanced Dynamic Modelling of Multi-junction Gallium

Tada, H. and Carter, J., Solar Cell Radiation Handbook*, JPL Report* 77-56, Caltech, Pasadena,

Mottet, S., Solar Cells Modelisation for Generator Computer Aided Design and Irradiation

*Proceedings of ESPC 2002 6th European Space Power Conference*, ESA-SP 502, Oporto,

Arsenide Solar Arrays*, Proceedings of ESPC 2008 8th European Space Power Conference*,

Degradation, *ESA Symposium on Photovoltaic Generators in Space*, pagg. 1-10,

**10. Conclusions** 

Depth of Discharge [%]

constraints.

**11. References** 

1977

Fig. 28. Solar Array Illumination and temperature, launch phase and first 3 orbits

Fig. 29. Solar array temperature, output voltage and current

Finally, figure 30 shows the Depth Of Discharge (DOD %) of the battery from launch. The DOD is progressively recovered the first four orbits. After the fourth one, a stable charge– discharge cycling is reached.

Fig. 30. Battery Depth of Discharge (DOD %) for launch phase and first mission day.
