string of good luck

string of good luck AND a run of good luck (a series of lucky events, lucky streak ) — полоса удач, полоса везения, счастливая полоса

Example: He isn't the best pitcher. He's just having a string of good luck this season. (HomeIdiom)

also
[winning streak]
[on a roll]
[на гребне волны],
[на волне успеха]

opp.:
[bad patch]
[dry spell]
[down on one's luck]
a run of bad luck
[бутерброд всегда падает маслом вниз]