This article introduces some of the basic concepts of batteries with particular applications for hobby-level small aircraft projects and similar. My aim for this article is to supplement my students' research for their senior design projects and provide an introductory walkthrough of the topic.
I will not be going over the prerequisite physics concepts in detail and I assume the reader has some high school or college level physics background. I also will not cover the inner workings of batteries as that is not a topic I have studied sufficiently.
Physics Background
Recall from high school or college physics that electrical power is defined as
where P is power (W), I is current (A), and V is voltage (V). Power refers to the time rate of change energy. With that understanding, we can show that mathematically as
where E is energy (J), P is power (w), and t is time (s). Now, joules and seconds are not always the most convenient measures to use, so we sometimes use Watt-hours to represent energy instead.
Battery Characteristics
Some of the things we care about when looking at batteries are:
Voltage. A battery's voltage is determined by two factors: the battery chemistry and the number of cells in series (denoted by the "S" number on the battery). The chemistry drives the voltage of the individual cells and the "S" number tells us how many cells the battery has in series. Recall from physics that voltages add in series.
Capacity. More often than not, capacity is given in amp-hours (Ah) or milliamp-hours (mAh). This only tells half the story. Remember that energy is in units of watt-hours not amp-hours. By applying our formula above, we need to multiple the amp-hour value by the battery voltage to get the capacity in watt-hours. Without knowing the voltage, amp-hours is a meaningless value.
Chemistry. In addition to influencing the voltage, battery chemistry influences a few other characteristics about a battery like depth of discharge, energy density, and more. I'm not an expert in battery chemistry, so I won't deep into the topic here, but there are a number of useful resources and reference materials online.
"S" Number. Most batteries have a number on them followed by the letter "S". This refers to the number of cells in series. For example a 3S LiPo battery will have a nominal voltage of 11.1 V (3.7 + 3.7 + 3.7).
C-Rating. The C-Rating tells us about the maximum current draw, and therefore the maximum instantaneous power draw. We'll cover this in more detail in a later section.
Depth of Discharge. The Depth of Discharge (DoD) of a battery refers to what percentage of the battery can safely be used. Discharging the battery beyond the DoD risks damaging the battery.
Power Budgets
In aerospace systems engineering, we often capture information about the power use in a system in the form of a power budget. A power budget captures how much power every component of your system uses. At a high level, it may look something like this:
| Component | Power |
|---|---|
| Propulsion | 300 W |
| EPS | 50 W |
| Structures | 0 W |
| ADCS | 30 W |
| TT&C | 15 W |
| C&DH | 5 W |
| Payload | 100 W |
| Total | 500 W |
The example above is loosely based on the power budget examples provided in Space Mission Analysis and Design, 3rd edition. A power budget simply totals up the power needs of every subsystem (and can and should be broken down into more detailed components) and gives you an understanding of the total power requirements of your system.
In this case, our system requires 500 W of power.
Power System Sizing
Given a power requirement, we can size our power system. We need some other assumptions or target values for things like time of operation and system voltage, but with those we can compute the energy required and ultimately the specifications we need to look for in a battery.
Let's look at an example.
Example
This example is applicable for a small unmanned aircraft (or similar system) that relies entirely on its battery for power. Suppose we have a system that requires 400 W of power. Let's say we want the system to fly for 30 minutes.
Now we have an energy requirement. From the power requirement and time, we know that our system needs 200 Wh of energy total.
Now we have to consider our depth of discharge. Let's say the battery we're looking at has a depth of discharge of 80%. This means we need to get our 200 Wh from only 80% of the battery capacity. We do this as follows:
Finally we can determine the battery we need once we know our target voltage. Suppose we've decided to use a 22.2V 6S LiPo battery. We can take our energy in Wh divided by the battery voltage to determine the required battery capacity in amp-hours.
Note that this changes if we choose a different voltage battery. If we chose an 11.1V 3S LiPo battery, we'd need a 22.5 Ah battery.
Instantaneous Power Draw and C-Rating
A battery also has a C-rating which tells you about the maximum discharge rate. To calculate the maximum discharge current, you multiply the C-rate by the capacity in amp-hours. This means this C-rate has units of . I've always found that to be a bit unintuitive, so let's look at the math.
Suppose we have a 14.8 V 2200 mAh battery with a C-rate of 30C. We can calculate the maximum discharge current as
Great! But what do we do with that? It might be more intuitive to take that number and determine our maximum power draw by accounting for the battery voltage.
This means for our 500 W example above, this would be just fine. But for a system that requires, say, 1000 W this battery wouldn't be able to provide sufficient instantaneous power.
Avoiding Common Mistakes
The most common mistakes I see from students make is to add up the current (A) value of all their components while overlooking the fact that different components run at different voltages. It helps to look at the power (W), rather than the current, of individual components when determining the total system power requirement.