# 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 2: How to size a Battery

In the first part of this series we learned how to size the solar arrays of a satellite. We will now continue with another main part of the power subsystem: The battery pack! The batteries of an Earth orbiting satellite are primarily used to power the satellite during eclipse, so when the Earth is in between the satellite and the Sun. Another use case for batteries is when the system has a high power demand for short periods of time. In this case, it is not useful to size the solar arrays to meet this demand, so batteries are used. However, to keep this tutorial simple, we will focus on the battery usage during eclipse. We will start this tutorial by finding the required capacity of the batteries, after which we will perform the sizing of the batteries itself. Throughout this tutorial we will assume parameters for Lithium-Ion (Li-Ion) batteries. That is because, as can be seen in the figure below, Li-Ion batteries currently have the highest volumetric and specific energy density compared to other batteries, which make them very suitable for space applications.

### The required capacity

In eclipse, the solar arrays cannot provide power to the satellite. This means that for the duration of the eclipse the batteries must provide power continuously to the satellite. The amount of energy the battery must be able to store is called the capacity ($C_{req}$). This is expressed as follows:

$$C_{req} = P_{req} \cdot t_e \; \; [Wh]$$

In here, $P_{req}$ is the expected maximum average power required during eclipse. This average can be accurately found by calculating a weighted average of all power modes. However, for initial sizing purposes an estimate of the average required power is sufficient. $t_e$ is the time of eclipse and is dependent on your satellite orbit.

#### The capacity at End of Life (EOL)

To evaluate the capacity which the battery must actually have, it is necessary to take into account its inherent efficiency ($\eta_{bat}$) and the Depth of Discharge( $DOD$). Values for these parameters obviously change along with the type of battery. For example, for Li-Ion batteries they can be assumed to be $DOD = 40 \; \%$ and $\eta_{bat} = 95 \; \%$. As this is the capacity that is also required at the end of the satellites life, this is called the EOL capacity ($C_{EOL}$), which then is:

$$C_{EOL} = \frac{C_{req}}{\eta_{bat} \cdot DOD} \; \; [Wh] $$

#### The capacity at Beginning of Life (BOL)

Over the lifetime ($N_{years}$) of a satellite, the batteries will degrade. There is a strong link between the DOD and the degradation of the batteries, a higher DOD results in higher degradation. This is one of the reasons that choosing what batteries are suitable for your mission is not as straightforward as just choosing the highest values at BOL. The fact that the batteries will degrade means that the EOL capacity will be significantly lower than the BOL capacity. This is taken into account by using the fading factor ($F_{fading}$), which can be assumed to be $0.92 \; \% / year$ for Li-Ion batteries. The BOL capacity will then be:

$$ C_{BOL} = \frac{C_{EOL}}{F_{fading} \cdot N_{years}} \; \; [Wh] $$

### The required mass and size

Now that we know the required capacity of the batteries, we can go on to determine the mass and size of the batteries. This is done using empirical relations, using the specific mass ($m_{sp}$) and the energy density ($e_{density}$). For Li-Ion batteries they can be assumed to be $m_{sp} = 170 \; [Wh/kg]$ and $e_{density} = 300 \; [Wh/liter]$ . The mass of the battery is then:

$$M_{bat} = \frac{C_{BOL}}{ m_{sp}} \; \; [kg]$$

And the volume of the battery is:

$$V_{bat} = \frac{C_{BOL}}{e_{density} } \; \; [liter]$$

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

*We hope you liked this mini-tutorial! If you want to learn how the batteries 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!*

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