Power Production Calculations

## Abstract

We have calculated the maximum and minimum power we can get out of the solar cells over an orbit, considering the efficiency of the power supply unit too. The actual power production is expected to lie between these two extreme values. These values are Pmin=1.19W and Pmax=4.39W.

## Introduction

In order to estimate the power available for the subsystems of the satellite the following need to be considered:

• The solar cell efficiency
• The efficiency of the power supply unit
• The effective area of the solar cells

The solar energy flux is inversely proportional to the square of the distance from the Sun. The equation that describes the relationship between the solar luminosity L and the flux at a distance R from the sun is

(1)
\begin{align} \left \phi =\left. \ L \over{4 \pi R ^2} \end{align}

We require the extraterrestrial solar irradiance distribution at a distance of 1 AU from the Sun, which is known as the air mass zero AM0. The value recommended by the American Society of Testing and Materials (ASTM) is 1366.1 Wm-2.

## Solar Cell Efficiency ε

Clyde Space will supply the solar panels for the PLUME CubeSat. Clyde Space uses two types of solar cells, EMCORE’s Advance Triple Junction cells (ATJ) with efficiency 27.5% and Spectrolab’s Triangular Advanced Solar Cells (TASC) with efficiency 27.0%.

## Efficiency of the Power Supply Unit k

The power supply unit consists of components such as the battery charge regulators and the two power bus regulators that dissipate energy. This reduces the power available for the subsystems. According to Clyde Space who is our power supply unit’s provider, the total efficiency of the power supply unit is 90%.

## Effective Area of the Solar Panels A

The effective area of the solar panels is the total area of the solar panels exposed to the Sun. Obviously, the effective area will depend on the way the satellite is spinning. The team has decided that the best way to deal with this is to consider the two extreme cases. The area is minimum when axis of rotation of the satellite is pointing always to the Sun, thus, only one side of the satellite is exposed. The area is maximum when the corner between 3 faces points towards the Sun. In this case the effective area is equal to the area of a hexagon.

Figure 1. Configuration for minimum (left) and maximum (right) effective area.

The minimum effective area Amin is the area of one face, equal to
m2 

The maximum effective area Amax is the area of a regular polygon,
m2 

In both cases we need to multiply by the fraction of the faces that is covered with solar cells since 3 out of six faces will not be completely covered with solar cells. In fact, 3 faces will have 100% of their area covered in with solar cells, 2 faces will have 84% of their area covered in solar cells (faces with the detector) and 1 face will have 96% of its area covered with solar cells (face with the camera).

Calculations
The power available for the satellite is calculated using the following equation combined with the data listed above


where the symbols used have been defined above. The following Excel Spreadsheet can be used to calculate the power production, both when in sunlight and averaged over the orbital period for the two extreme cases discussed above, when we have a maximum exposed area and a minimum exposed area.

page revision: 2, last edited: 26 Nov 2008 16:15