How to (I): Size a Satellite Solar Array

Mini Series: Designing a Satellite for Dummies

Are you an aspiring aerospace engineer, a space enthusiast, a parent checking your child’s homework or simply interested in the specifics of how to design certain satellite parts? Then this is the place to be.

In this mini series we will go through the basics of designing and scaling a satellite, ranging from solar arrays to propellant tanks and even orbital parameters. If you would like us to cover other space-related topics, feel free to reach out to engineering@valispace.com.

Part 1: How to size a Solar Array

We will start this series with a tutorial on how to determine the size of the solar panels of a satellite, being one of the parts that almost every satellite needs. The solar arrays are part of the power subsystem of a satellite and normally act as the main source of power. Firstly, we show how the required power will be calculated, after which the other factors influencing the required size of the arrays will be discussed. In the end, you will be able to fully perform the sizing of your own satellite solar array!

The required power

The power subsystem of a satellite has to provide power to the satellite both in sunlight (subscript d) and in eclipse (subscript e). Usually, this is done by a combination of batteries and solar arrays. When the satellite is in eclipse (so no sunlight reaches the satellite), the batteries are drained to power the satellite. In sunlight, the solar arrays both power the satellite and recharge the batteries.

This means that the power required from the solar arrays $P_{SA}$ depends on the power required by the satellite during daylight, the time of daylight, the power required by the satellite during the eclipse, the time of eclipse and the efficiencies of the power transfers (from the arrays directly to the satellite parts (loads) $\chi_d$ and indirectly, so via the batteries $\chi_e$):

$$P_{SA} = \frac{P_d \cdot t_d / \chi_d + P_e \cdot t_e / \chi_e}{t_d} \; \; [W]$$

The required solar array size

Now that we know how much power the solar arrays have to provide for the satellite, we will use this as input to find the required size of the solar arrays.

The ideal  flux

The first step in this process is to find the amount of power that the solar array will provide per square meter in ideal circumstances ($\Phi_{ideal}$). This is dependent on the amount of solar radiation (in Earth orbit generally taken to be $J_S = 1367 \; \;  [W/m^2]$) and the efficiency of the solar cells (e.g. for Ga-As cells $\eta_{cell} = 36\% $). This results in the following ideal flux equation:

$$\Phi_{ideal} = J_S \cdot \eta_{cell} \; \; [W/m^2]$$

The Beginning of Life (BOL) flux

The actual flux at the start of the satellite’s life is dependent on two more parameters, namely the inherent degradation ($I_d$) and the highest solar incidence angle ($\theta_{max}$). The inherent degradation is directly proportional to the amount of area of the array that is not directly used for power generation. The highest solar incidence angle is the maximum to be expected angle between the normal of the solar array plane and the incoming solar radiation.

The Flux at BOL will look like this:

$$\Phi_{BOL} = \Phi_{ideal} \cdot I_d \cdot cos(\theta_{max}) \; \; [W/m^2]$$

The End of Life (EOL) flux

Over the lifetime of a solar array the individual cells start degrading, mainly due to continued exposure to radiation. The amount by which the entire array is degraded is normally calculated using the lifetime degradation factor ($L_d$):

$$L_d = (1-F_d)^{N_{y}} \; \; [-] $$

Here, $F_d$ is the yearly degradation factor (For Ga-As cells around 2.75%) and $N_{y}$ is the amount of years until EOL is reached. The flux at EOL will then be:

$$\Phi_{EOL} = \Phi_{BOL} \cdot L_d \; \; [W/m^2] $$

Sizing of the solar array area

Since at the end of the satellite’s life it still requires the same amount of power, the EOL flux eventually determines the total area of the arrays. The total solar array area is calculated as follows:

$$A_{SA} = \frac{P_{SA}}{\Phi_{EOL}} \; \; [m^2]$$

If you followed the steps correctly, you have now performed the sizing of your own solar arrays, congratulations!

 

We hope you liked this mini-tutorial! If you want to learn how the solar array and the power subsystem are related to other subsystems in a satellite or  how to design a complete satellite using Valispace and practical examples, also check our Satellite Tutorial by Calum Hervieu and Paolo Guardabasso. Stay tuned for more and feel free to give us feedback at contact-us@valispace.com!