When you are using SSH to access the switch you are using a certain username and password. The fact that you need to elevate your privilege level by using the super command means that the account you are using doesn't have the highest privilege level.
So in order to prevent elevating your privilege level via the super command you should already have a sufficient privilege level to begin with.
In Comware 5, the OS running on the HP 5500 series switches, the privilege levels are defined as follows:
0-VISIT, 1-MONITOR, 2-SYSTEM, 3-MANAGE
Privilege level 3, also know as manager level, is the highest privilege level.
In order to successfully login with privilege level 3, which is equal to super, you would need to specify that for the user account you are using.
Configuring a privilege level for a local user goes as follows:
- < HP 5500 > system-view
- [ HP 5500 ] local-user
- [ HP 5500-luser-The_name_of_your_user_account ] authorization-attribute level 3
This in term means that you would authenticate locally on the switch which is know as "Local level switching authentication". If you however are using a RADIUS server, HWTACACS server, you are authenticating remotely which is know as "Remote level switching authentication". In that scenario the remote authentication server should be configured to provide your user with level 3 privileges.
For further information regarding the Authentication Authorization Accounting, also know as AAA, implementation on the HP 5500 I would redirect you to the "HP 5500 EI & 5500 SI Switch Series Security Configuration Guide":
For more information regarding the privilege level I would redirect you to: