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You are on the right track with this code:

i=1
while i<=3:
    psspy.case('savcnv.sav')
    psspy.rstr('savnw.snp')
    psspy.strt(outfile='i.out')
    psspy.run(tpause=1.0)
    psspy.dist_machine_trip(ibus=101, id='1 ')
    psspy.run(tpause=1.05)
    psspy.dist_clear_fault()
    psspy.run(tpause=5.0)
    i=i+1

But that line outfile='i.out' won't do what you think it does. 'i.out' is just a string, it doesn't know about the i variable you created. You must explicitly tell Python to substitute the i value into the string. e.g.

filename = '%s.out' % i
psspy.strt(outfile=filename)

the %s will be replaced with the i variable so it will change each time in your loop.