The volatility of renewable energy sources pose a significant challenge for Distribution Network Operators (DNOs) as it makes planning and maintaining a reliable electricity grid more complex. An essential tool in dealing with the uncertain behavior of renewable energy resources is the load flow simulation, i.e., the standard electricity network simulation in network design and operation. There is, however, still much untapped potential of applying these kind of simulations. The thesis presents improvements to the theory on linear load flow approximations. The resulting algorithms are then applied to various real world problems: control of a community battery, handling very large simulations, coping with low sensor coverage and evaluating strategic scenario's with high uncertainty. Firstly, theory is presented for the control of a community battery. It is shown how such a battery can be used for grid congestion reduction, backed up by a live experiment. A charge path optimization problem is posed as a linear problem and subsequently solved by an Linear Programming (LP) algorithm. It was found that the voltages and currents can be controlled to a great degree, increasing the grid capacity significantly. Network design formulas are described with which a DNO can quickly estimate the potential (de)stabilizing effect caused by a community battery on the steady-state voltages and currents in the grid. Next, load flow simulations are improved by applying numerical analysis techniques and the accuracy and efficiency of a linear load flow approach is investigated. The resulting fast load flow algorithm is then applied to a very large problem: integrally simulating the low and medium voltage network of Alliander DNO, a grid with over 22 million cable segments with a total combined length of over 88,000 km, built according to international standards. It is shown that this integral simulation can identify voltage problems much more accurately. Next, Bayesian state estimation is considered. A mathematical model is proposed to complement a limited set of real-time measurements with voltage predictions from forecast models. This method relies on Bayesian estimation formulated as a linear least squares estimation problem. The model is then applied to an IEEE benchmark and on a real network test bed. An observability analysis suggests strategies for optimal sensor placement. Next, theory is presented on coping with uncertain long-term scenarios for strategic simulations. A stochastic profile model is proposed based on copulas which can be calibrated by technology adoption data. Using a Monte Carlo approach, the stochastic profiles of all DNO assets are then simulated, identifying parts of the network with heavy loads. Finally, the thesis concludes by demonstrating additional applications of the presented methods, such as fast network capacity checks and reducing losses via network reconfiguration. It concludes by giving suggestions for future research.