Republican Mayor Kevin Faulconer is facing one of the biggest decisions in his more than four years as head of the city of San Diego — whether to approve a government-run alternative to San Diego Gas & Electric. The choice, expected in coming weeks, represents a sharp fork on the road to fulfilling the mayor’s ambitious pledge of running the city on 100 percent renewable energy by 2035. The success of the city’s Climate Action Plan largely hinges on meeting the target. Within two decades, nearly half of all annual greenhouse-gas reductions achieved by the city are expected to come from increased use of renewable energy.