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The topological observability of a Power System State Estimation (PSSE) problem is considered. The PSSE observability is decoupled into two separate problems using the well-known P-Â¿/Q-V decouple characteristic of power systems. Using a linear decoupled model for the measurements, the proposed method tries to find an observable spanning tree of the P-Â¿measurement graph (and subsequently for the Q-V measurement graph) using an algorithm for the search of matroid intersections. The method is first applied to six well- known examples of the technical literature, and then is used to study six different cases of a realistic system comprising 121 buses.