# Julian Straub

## creations and thoughts

Energy storage is an important topic for solar-powered devices such as explored in the harvesting light series. The two main vehicles for energy storage are (super) capacitors and lithium ion batteries. The former because of the ease of use and the fact that most small circuits and harvesters do not need a larger energy storage. Lithium ion batteries have desirable properties such as ease of use, high power density and fast charge and discharge rates. This make them widely used for modern energy storage in devices ranging from smartphones, and laptops to whole cars. In the following we compare the two forms of energy storage. A more comprehensive comparison can be found at the battery university.

The energy stored in a capacitor follows the equation

$$E = \frac{1}{2} U Q = \frac{1}{2} U^2 C$$

where $U$ is the voltage [V], $Q$ is the charge [As] and $C$ is the capacitance [F] of the device.

A super capacitor of $C = 1F$ at a voltage of $U=5.5V$ (such as this one) stores about $E = 15J$. There are larger super caps that with capacities in the range of multiple 100s F for a voltage of 2.7V. Such capacitors reach energies in the range of $E=1.8kJ$ (for the example of a capacitance of 500F).

The energy stored in a lithium ion battery can be calculated from the rated voltage $U$ and charge $Q$ as:

$$E = U Q$$

For a small LiPoly cell of $U = 3.7V$ and $Q=800mAh$ the energy is $$E = 3.7V \cdot 0.8A \cdot 3600s =10.6kJ$$ Note that we had to convert the charge to $As$ from the usually specified $Ah$. The factor of $3600$ comes from the fact that one hour has 3600 seconds.

### Using Capacitors

Charging and discharging a capacitor is straight forward and not much care has to be taken other than to not exceed the voltage rating. Super caps have internal resistance in the order of $30\Omega$ and thus the maximum discharge rate is limited.

### Using Lithium Ion

Charging a lithium ion battery should happen in two stages: first constant current charge and, once the maximum voltage is reached, constant voltage charge until the charging current has dropped to close to $0A$.

There are dedicated charging ICs to handle this process. For the purpose of charging a cell from a solar panel, for the use in a light harvester, we are however interested in the simplest possible (safe) way of slowly charging a lithium ion cell. In general the second step is not needed if we are okay potentially not charging the cell top 100%. In fact if the cell is charged slowly then the cell is charged more fully when the voltage reaches the maximum of $4.2V$.

This suggests a simple charging mechanism whereby we simply ensure that the voltage over the lithium ion cell does not exceed $4.2V$. We can even leave a buffer of $0.2V$ and design the charging circuit to keep the voltage below $4.0V$ at all times.