In this paper we focus on solving the graph problem of the spanning distribution forest of a power network (SDFPN). The interest for the SDFPN comes from the fact that it well represents practical problems related to the partitioning of power distribution systems. It is closely related to the problem of maximal partitioning of supply demand graphs (MPGSD) and the capacitated spanning forest (CSF) problem that are used for modeling similar real-world systems. It has an advantage, compared to these problems, that it incorporates constraints related to ampacity, radiality, and the balance of consumption/generation in a partition. In this work, a mixed integer program (MIP) is developed for finding optimal solutions for the SDFPN. Next, a greedy constructive algorithm is designed for finding feasible solutions for large problem instances at low computational costs. In the computational experiments, we evaluate the size of graphs that can be solved to optimality using the MIP. The solutions acquired in this way are used to assess the performance of the proposed greedy algorithm.