Analysis of Tan-Sun Coordinate Transformation System for Three-Phase Unbalanced Power System

This paper mainly analyzes the characteristics of Tan-Sun coordinate transformation system, which is an extended version of Clarke coordinate transformation system suitable to be applied in three-phase unbalanced power system. The main purpose of Tan-Sun coordinate transformation system is to convert three-phase unbalanced alternating-current quantities into two orthogonal alternating-current quantities with the same amplitude, and these two quantities can be further converted into two direct-current quantities without second harmonic components through Park transformation. Tan-Sun coordinate transformation system can realize the direct-current decoupling of three-phase unbalanced currents, and the strict decoupling of the model of three-phase unbalanced power system, so the control methods developed for three-phase balanced power system can be migrated into three-phase unbalanced power system perfectly. In this paper, Tan-Sun and inverse Tan-Sun coordinate transformation matrices are illustrated at first. The essence of Tan-Sun coordinate transformation system is then presented, which can be divided into two coordinate transformation processes, and the corresponding coordinate transformation matrices are provided by detailed analysis. The relationship between Tan-Sun and Clarke coordinate transformation systems is also discussed. Finally, the simulation and experimental results are provided to validate the effectiveness of the adaptive Tan-Sun phase-locked loop method and the superiority of Tan-Sun coordinate transformation system.