Why did you receive the error?
In order to install the game you downloaded, PlayStation 3/4 needs more free space than the file size of the game on the system hard drive. Generally speaking, it needs twice disk space of the content itself for you to download and install it successfully. For example, if the game you want to install is 10GB in size, you will need about 20GB of free space on the system hard drive. Once the game is installed, the installation file will be deleted thus you will get the extra space back.
2 ways to solve this
There are basically two ways to manage this when ps3 system storage not enough to install games. One is to backup your PS3 hard drive to an external storage device, and the other is to upgrade your PS3 drive with a larger one. As you use the PS3, you are most likely will install more games, and the growing quality of games will require more disk space. Therefore, it is recommended to upgrade PS3 hard drive with a larger one to solve this problem once for all. If you do not want to lose the games you purchased and installed on your PS3, you can use a cloning software to clone the original PS3 hard drive to a larger one and then replace the old one that PS3 says not enough space available.
How to upgrade hard drive without losing data
You need to take out of your original PS3 hard drive that has no enough space and game was forced to quit, and then connect both the original hard drive and the new larger hard drive to a Windows computer. For the hard drive cloning software, you can use AOMEI Backupper which is capable of cloning PS3/4 hard drive to a new one without losing data. You can follow the following steps to finish the clone.
1. Download and run AOMEI Backupper after connecting both hard drives.
2. At the Home screen, select “Disk Clone” under the “Clone” tab.
3. Select the original hard drive as the source disk in “Step 1” and the new hard drive as the destination disk.
4. Then it will bring you the Operation Summary screen. If no problem, click “Start Clone” to start the clone process.
This cloning process will be complete in the background, so you can still use the computer to do other things. When the clone is done, you can installed the cloned hard drive to your PS3/4, and then the problem there is not enough free space on the system storage will not bother you again, at least for a long while.