This paper presents the concept of provision of differentiated quality of electricity supply based on customers' requirements in distribution networks. To fulfill this concept, five new gap indices are proposed to reflect the satisfaction of the received power-quality (PQ) performance compared to the thresholds which are set based on customers' requirements regarding the performance of individual PQ phenomenon or the aggregated PQ performance. Using these new indices as objective functions, an optimization-based mitigation strategy is proposed to carry out the strategic placement of different flexible ac transmission systems devices based on the analysis of PQ performance and sensitivity analysis. In this methodology, a greedy algorithm is applied to search the optimal mitigation scheme in order to enable the provision of differentiated PQ levels. The feasibility of the proposed mitigation methodology is demonstrated using a large-scale generic distribution network. The advantages and disadvantages of using the proposed indices as the optimization objective functions are also analyzed in this paper.