Modeling low voltage networks poses a challenge to Distribution System Operators (DSOs) because the low voltage networks generally consists of millions of cables. This paper provides a method to model congestion problems and applies this to such a large low voltage network. By modifying the load model of a customer, a linear load flow model was created. Using a custom sparse solver model, all instantaneous currents and voltages were calculated for the network of Liander DSO, containing over 20 million cables and 3 million power customers. The model took only 30 seconds to simulate the entire network. The results shows that the network of Liander DSO can accommodate quite a large number of solar power installations with relative ease. Also, stepchange transformers are shown to have quite some potential to solve voltage issues that can arise due to solar power.@en