As described, This is a normal operation. But I think the charging profile is not suitable for Lithium batteries.

In fact, there are different charging profiles.

When you first apply the solar power the battery will be charged to a threshold value which is 13.4V in your case. Then the controller will wait till the voltage drops below another threshold (which is below 13.1V in your case).

Charging profiles change depending on the type of the battery. The following is for instance the profile used by Deepsea chargers (not designed for lithium batteries):

[![enter image description here][1]][1]

the **float voltage** definition fits with your 13.1 V.  


To find out if it is really working as needed, apply a continuous load and wait to check below which threshold it will restart charging.

the following graph is an example of a charging profile for a lithium battery that is **not voltage float charged** and where the current is kept constant instead of the voltage (here the voltages are different than in your case) :


[![enter image description here][2]][2]

Some battery chargers are profile configurable either by software or simply by a button like the following:

[![enter image description here][3]][3]


Choosing the right profile increase the lifetime of the battery.


  [1]: https://i.sstatic.net/2pYVy.png
  [2]: https://i.sstatic.net/rR3Cz.png
  [3]: https://i.sstatic.net/1usGG.png