The alternator output volatge as measured at the battery terminals is a function of temperature and battery condition.
Normally this will be 13.8 to 14.2 volts. As the temperature gets near freezing it will go up to 15 volts.
When the RPM's are raised above idle the voltave may come up a little since charging is marginal at idle. The voltage should never continue to climb as RPM's are raised. When the voltage goes over 15.5 volts you are in danger of blowing the cars electronics.
A good battery will absorb the extra current and keep the voltage from climbing, but this will "boil" water out of the battery. Check that. If all of the cells are loosing water this is a sure sign of overcharging,
As the battery goes bad from this, it will not be able to keep the charging voltage down.
The alternator must be removed and opened to replace the regulator, sorry.