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This paper presents a hybrid topological/numerical method for power system observability analysis, using conventional measurements, provided by SCADA, as well as synchronized phasor measurements, provided by phasor measurement units (PMUs). A PMU placed at a bus can measure the voltage phasor at that bus, as well as the current phasors in some or all the lines connected to that bus. Branch power flow and current phasor measurements are used to build topologically flow islands that, in turn, are used to construct a reduced network. A gain matrix associated with this reduced network is built, considering boundary injections at flow islands and all bus voltage phasors. Observability checking is carried out analyzing the pivots in the triangular factors of this gain matrix and observable islands are identified in a noniterative manner, by performing back substitutions. Additional measurements for observability restoration are provided by a direct method, using the triangular factors of a reduced Gram matrix associated with existing and candidate injections as well as PMUs at boundary buses of the observable islands. The IEEE 14 and 30 bus systems illustrate the steps of the proposed method.