Graphical presentation of harmonic operating principles in voltage source converter with sparse vector methods

This study presents a graphical presentation of the harmonic operating principles in voltage source converter (VSC) with sparse vector methods and provides a visualisation method for analysing the harmonic operations of VSC. Based on the dynamic phasor sequence components model of the VSC, the operation analysis of VSC has been transformed into a solution of an algebraic equations. With the sparse characteristics of the vectors and coefficient matrix, the sparse vector method is applied into solving equations. The coupling from the ac-side to the dc-side can be represented by the forward substitution operations and the coupling from the dc-side to the ac-side can be represented by the back solution operations in the sparse vector method correspondingly. Therefore, the factorisation paths which describe the forward substitution and the back solution operations can describe the harmonic operating principles of VSC too. When the set of factorisation paths are presented as the weighted directed graphs based on graph theory, the harmonic operating principles of VSC can be displayed as the graphs, which is direct and clear. Finally, the simulation results testify the correctness of the studies.