Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.

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Accurate transmission line parameters are the basis of power system calculations. The measured phasor measurement unit (PMU) phase angle data at both ends of a line may contain large errors caused by synchronization problems, which can seriously affect the accuracy of parameter identification. This paper proposes a robust PMU-based method for calculating transmission line parameters from PMU data at both ends of a line in such a way that a synchronization error between the ends does not degrade the results. Specifically, a π -equivalent model for the transmission line is established, and a least square objective function with nonlinear equations for positive parameter identification is derived. Furthermore, to reduce the impact of noise and biased data, median estimation is used to obtain the final result. Finally, a simulation shows the effectiveness and robustness of the proposed method, and its practicality is demonstrated in a case study using measured PMU data.

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