Increasing numbers in distributed generation units and growing electrification of the transportation sector leads to new challenges in electrical distribution grids. In this thesis, a holistic approach, including different functional layers for the operation, monitoring, and control of low voltage grids, is presented. Power flow methods are usually used to monitor the grid, but for control purposes, their implicit and non-linear character is quite challenging. This work introduces a linear explicit power flow approximation. It exploits on-line information combined with pseudo measurements to adapt to operating points of the grid. The lack of this functionality is a primary source of error in standard off-line methods. Needed grid parameters for the approximation, are calculated with an approach that combines a dynamic thermal model of the power cables with a mean value estimation of the impedance. Thus, resistive parameter changes due to load currents can be tracked during grid operation. The first operational layer is designed as a distributed model predictive control (DMPC). Its purpose is to better unify three-phase generation units, charging facilities, and dominant consumers in low voltage grids. It maximizes the transport capacity of the network, keeps sensitive data from each controller private, and considers the limitation of grid assets. A secondary layer deals with the inherent unbalance in low voltage grids. The approach uses a Jacobi based distributed optimization algorithm to coordinate local, flexible electric power. With the developed power flow approximation, it is possible to formulate a local optimization problem, that does not scale with grid size. Additionally, it can directly reduce the negative- and zero-sequence components without the need for additional measurements.