I would change your sentence in a following way:
"For next year, we will start using this program to calculate tax for each branch that HAS INSTALLED the system."
start to do something is equal to start doing something
each is also a synonim of every
but as for using active and passive voice - here you do mistakes: each branch WHERE the system has been installed (by someone unknown)
or each branch that has installed the system (it is the branch that installed the system itself!)