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As combating climate change has become a top priority and as many countries are taking steps to make their power generation sustainable, there is a marked increase in the use of renewable energy sources (RESs) for electricity generation. Among these RESs, solar photovoltaics (PV) is one of the most popular sources of energy connected to LV distribution networks. With the greater integration of solar PV into LV distribution networks, utility providers impose caps to solar penetration in order to operate their network safely and within acceptable norms. One parameter that restricts solar PV penetration is unbalances created by loads and single-phase rooftop schemes connected to LV distribution grids. In this paper, a novel method is proposed to mitigate voltage unbalance in LV distribution grids by optimally re-phasing grid-connected rooftop PV systems. A modified version of the discrete bacterial foraging optimization algorithm (DBFOA) is introduced as the optimization technique to minimize the overall voltage unbalance of the network as the objective function, subjected to various network and operating parameters. The impact of utilizing the proposed PV re-phasing technique as opposed to a fixed phase configuration are compared based on overall voltage unbalance, which was observed hourly throughout the day. The case studies show that the proposed approach can significantly mitigate the overall voltage unbalance during the daytime and can facilitate to increase the usable PV capacity of the considered network by 77%.