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An important step in the development of synchrophasor-based wide area monitoring and control system is to optimally place the phasor measurement units (PMUs) in the network. Optimal number of PMUs, to fully observe the power system network, may be large. Owing to their relatively high cost, utilities may like to install these devices in stages. A technique is proposed here for placing the PMUs in multiple stages over a given time period that ensures complete power system observability even under a branch outage or a PMU failure. The proposed scheme is based on integer linear programming (ILP) and a multi-criteria decision-making (MCDM) approach. The ILP is used to obtain the optimal PMU locations in the system to completely observe the system and, subsequently, the MCDM model is developed to prioritise these PMU locations. Three indices are proposed to develop the MCDM model, viz. bus observability index, voltage control area observability index and tie-line oscillation observability index. Finally, the PMU placement is carried out in stages based on the ranking of these optimal locations. The proposed method is applied on three test systems - IEEE 14-bus system, New England 39-bus system and Northern Regional Power Grid 246-bus Indian system.