Hi,
>Reviewing I found that PROCEDURE pub.MSP_WEB_SP_SEC_PSMODE_PERM_SYNC_DeleteAllOldPermissionStates is the culprit, and table MSP_WEB_SECURITY_PSMODE_PERMISSION_SYNC_STATES grows too from less 1 gb to 51 gb
The database growth you said seems to be because the table is inserted into a large amount of data every night. So the data files and transaction logs of the database grow rapidly in a short period of time.
As for why the table accumulates a large amount of data, it is necessary to clarify whether this is a normal data record. If it is not, you may need to consult an expert in Project Server to diagnose the cause. I am not familiar with Project Server.
If the log file continues to grow even when the database is set to the simple recovery model, you need to consider whether there is a transaction that has not been committed for a long time or a large transaction is running on the database.
Please check the following update for Project Server 2013, it mentioned the table MSP_WEB_SECURITY_PSMODE_PERMISSION_SYNC_STATES. Also make sure to install the latest updates for your Project Server 2013.
https://support.microsoft.com/en-us/topic/february-21-2017-update-for-project-server-2013-kb3141525-4a5bd35c-7c45-7883-2365-fc51a0f71194