This paper addresses the day ahead network constrained thermal unit commitment problem under uncertainty. In this problem the electrical network is considered by a DC power flow model with phase angles represented directly into the model and the associated flow limit constraints dynamically introduced through an iterative process. The uncertainty regards to the stochastic demand to be supplied by thermal plants, possibly due to a configuration with high wind penetration. Two main contributions are presented: the first is a new compact mixed-integer formulation for unit commitment constraints such as minimum up/down times, by defining "multi-node constraints" that comprise integer variables related to all nodes in given sub-trees of the original scenario tree. The second is the application of a local branching strategy instead of a standard branch-and-cut algorithm to solve the problem. Computational experiments are carried out with an IEEE 118 buses system, assuming severe constraints on transmission lines capacities, in two scenarios trees for a 24 hour period.