Rooftop photovoltaic (PV) systems and plug-in electric vehicles (PEVs) will be increasingly utilized by residential customers due to their economic and environmental benefits. However, the intermittent power produced by PVs and the additional loads required for the PEV charging can cause power quality disturbances in the low-voltage distribution networks (LVDN). An adaptable correlated control (ACC) is proposed for the decoupled optimization of the active and reactive power, where energy cost can be minimized through the local demand-side management (DSM) of residential loads. Further, the optimal allocation of the sparse capacity of inverters for reactive power compensation to maintain the voltage variations and the mitigation of voltage unbalances within the allowable limits is proposed. The proposed ACC provides a supervisory control to observe and modify the voltage quality of the LVDN without the need for real-time collaboration between controllers. The impacts of the integration of installed rooftop PVs and PEV charging for unbalanced three-phase LVDNs are assessed rigorously using a versatile simulation platform. Also, the suitability of the proposed control strategy for DSM and the alleviation of voltage fluctuations and unbalances are assessed.