The current injection power flow method is commonly used by the power distribution industry in real-time distribution management systems. The inclusion of reactive power control adjustments that simulate local voltage controllers is known to create multiple power flow solutions. The state-of-the-art for simulating local voltage controllers computes the most likely operational solution by considering the different precedences of the controlled devices, based on their speeds of response. This paper presents a novel sensitivity-based approach for simulating local controllers, which directly accounts for both controller interactions and the way in which the system state is reached. Numerical results are reported on networks with up to 3146 nodes and voltage dependent load models; the results show that the proposed approach yields probable power flow solutions that are virtually identical to those given by an implementation of the state-of-the-art time-coordinated method and with a speed-up factor around three on the large network cases.