The occurrence of voltage violations are a major deterrent for absorbing more roof-top solar power to smart Low Voltage Distribution Grids (LVDG). Recent studies have focused on decentralized control methods to solve this problem due to the high computational time in performing load flows in centralized control techniques. To address this issue a novel sensitivity matrix is developed to estimate voltages of the network by replacing load flow simulations. In this paper, a Centralized Active, Reactive Power Management System (CARPMS) is proposed to optimally utilize the reactive power capability of smart photo-voltaic inverters with minimal active power curtailment to mitigate the voltage violation problem. The developed sensitivity matrix is able to reduce the time consumed by 48% compared to load flow simulations, enabling near real-time control optimization. Given the large solution space of power systems, a novel two-stage optimization is proposed, where the solution space is narrowed down by a Feasible Region Search (FRS) step, followed by Particle Swarm Optimization (PSO). The performance of the proposed methodology is analyzed in comparison to the load flow method to demonstrate the accuracy and the capability of the optimization algorithm to mitigate voltage violations in near real-time. The deviation of mean voltages of the proposed methodology from load flow method was; 6.5*10^-3 p.u for reactive power control using Q-injection, 1.02*10^-2 p.u for reactive power control using Q-absorption, and 0 p.u for active power curtailment case.