The evolution of power distribution grids from passive to active systems creates reliability and efficiency challenges to the distribution system operators. In this paper, an energy management and control scheme for managing the operation of an active distribution grid with prosumers is proposed. A multi-objective optimization model to minimize (i) the prosumers electricity cost and (ii) the cost of the grid energy losses, while guaranteeing safe and reliable grid operation is formulated. This is done by determining the active and reactive power set-points of the photovoltaic and storage systems integrated in the grid buildings. The resulting optimization model is non-convex, thus a convex second-order cone program is developed by appropriately relaxing the non-convex constraints which yields optimal results in most operating conditions. The convexified model is further utilized to develop an algorithm that yields feasible solutions to the non-convex problem under any operating conditions. Moreover, a second novel algorithm to find the operating point that provides fairness between the prosumers and the grid costs is proposed. Simulation results demonstrate the effectiveness and superiority of the proposed scheme in managing an industrial distribution grid compared to a self-consumption approach.