This paper applies two methods of mathematical decomposition to carry out an optimal reactive power flow (ORPF) in a coordinated decentralized way in the context of an interconnected multiarea power system. The first method is based on an augmented Lagrangian approach using the auxiliary problem principle (APP). The second method uses a decomposition technique based on the Karush-Kuhn-Tucker (KKT) first-order optimality conditions. The viability of each method to be used in the decomposition of multi-area ORPF is studied and the corresponding mathematical models are presented. The IEEE RTS96, the IEEE 118-bus test systems and a 9bus didactic system are used in order to show the operation and effectiveness of the decomposition methods.