Conventional tools to provide steady-state power network solutions rely on bus-branch models, in which a "bus" is actually the result of merging internal electrical nodes pertaining to given substation. The corresponding network solutions are thus unable to readily provide information about variables internal to the substations, such as power Àows through circuit breakers and bus-section nodal voltages. Since the knowledge of such variables is important to several applications, such as real-time topology estimation and corrective switching methods, the need then arises to re-examine the power Àow formulation in order to obtain detailed solutions at the substation level. This paper addresses that problem by extending the decoupled power Àow formulation in order to allow the representation of selected parts of the network at the substation level. For that purpose, the state vector is expanded so as to include power Àows through switching branches as new state variables, in addition to the conventional nodal voltages. Moreover, information regarding the status of switching branches is taken into account as additional linear equations to be solved along with the traditional power Àow equations. Simulating results considering several substation layouts and two IEEE test systems are used to illustrate and evaluate the proposed approach.

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This paper presents a hierarchical structure for decentralized power system state estimation whose lower level is conducted at each power network substation. The local level modeling is based on a nonlinear Coestimation algorithm which provides not only the nodal state variables, but also the substation topology. The higher hierarchical level, performed at the Regional Control Center, coordinates the local estimates by processing the active power flow measurements taken on the transmission lines connecting the substations. In addition to other attractive features, the proposed estimation architecture also allows a substantial reduction on the amount of data transmitted from substations to control centers. The proposed methodology is tested through a number of case studies performed on the IEEE 9-bus network modeled at bus section level.Index Terms-Hierarchical state estimation, power system state estimation, real-time power system modeling, state and topology coestimation.

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