Smart grid state estimation with PMUs time synchronization errors †

State Estimation (SE) is one of the essential tasks to monitor and control the smart power grid. This paper presents a method to estimate the state variables combining the measurement of power demand at each bus with the data collected from a limited number of Phasor Measurement Units (PMUs). Although PMU data are usually assumed to be perfectly synchronized with the Coordinated Universal Time (UTC), this work explicitly considers the presence of time-synchronization errors due, for instance, to the actual performance of GPS receivers and the limited stability of the internal oscillator. The proposed algorithm is a recursive Kalman filter which not only estimates the state variables of the power system, but also the frequency deviations causing clock offsets which eventually affect the timestamps of the measures returned by different PMUs. The proposed solution was tested and compared with alternative approaches using both synthetic data applied to the IEEE 123 bus distribution feeder and real-field data collected from a small-size medium-voltage (MV) distribution system located inside the EPFL campus in Lausanne. Results show the validity of the proposed method in terms of state estimation accuracy. In particular, when some synchronization errors are present, the proposed algorithm can estimate and compensate for them.