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 multi-area 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 RTS-96, the IEEE 118-bus test systems and a 9-bus didactic system are used in order to show the operation and effectiveness of the decomposition methods.771622303312