AC-Feasibility on Tree Networks is NP-Hard
  Recent years have witnessed significant interest in convex relaxations of the power flows, several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that AC-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-Hard for tree networks. 
Karsten Lehmann, Alban Grastien, and Pascal Van Hentenryck
cs.CC math.OC