Optimal power flow models using network flow method

The network flow method is used in many areas and also in power system problems. The main application in power system is optimal power flow calculation, and this article presents three approaches complementing early developments: direct current optimal power flow, direct current optimal power flow with explicit losses and alternating current optimal power flow. We detail the mathematical formulation of each approach and test it to a simple system describing the constraint matrices. Then we compare the three approaches showing the advantages of each model.