Application of the complex algorithm in PMU-only state estimaiton

China's electrical grid has installed more than 2500 sets of phasor measurement unit (PMU), covering almost all the 500 kV and above and part of the 220 kV substations, which in sure observable of the ultra-high voltage power network and provide mass data for system analysis. However, PMU measurements may contain bad data and the precision of measurements especially phase need to be further improved. State estimation is an effective method to deal with data contaminated by noise and bias. Therefore, it's of great significance to study the PMU-only state estimation (POSE) problem. The real number equations based on the rectangular coordinate system and weighted least squares (WLS)algorithm are the general method to solve the POSE problem at present, which need to convert phasors into their real and imaginary parts, thus enlarging the size of the coefficient matrix which decreases the computational efficiency. In this paper, complex number equations for the POSE problem are established and the complex number weighted least squares (CWLS) estimation model is built to solve the equation directly in the complex domain which needs no phasor converting. The error characteristics of PMU measurements in the complex domain are analyzed in depth which give a guidance of choosing weights and illustrate the robustness of the CWLS to phase. Test results demonstrate the contrast analysis between the CWLS and the WLS from the perspectives of estimation time, estimation accuracy and adaptability to different error levels, which shows that the performances of the CWL Sare better than the WLS. The robustness of the CWLS to phase is also showed in the tests.