This paper studies the optimal power flow problem for resistive DC networks. The gradient method algorithm is written in a port-Hamiltonian form and the stability of the resulting dynamics is studied. Stability conditions are provided for general cyclic networks and a solution, when these conditions fail, is proposed. In addition, the results are exemplified by means of numerical simulations.
Benedito, E., del Puerto-Flores, Doria-Cerezo, A., Scherpen, J. Optimal power flow for resistive DC networks: a port-hamiltonian approach. "IFAC-PapersOnLine", 1 Juliol 2017, vol. 50, núm. 1, p. 25-30.