Nonlinear control of FACTS and HVDC belonging to the voltage-source converter family

The nonlinear control method, associated with the books of A. Isidori (1989), and H. Nijmeijer and A. J. van der Shaft (1990), has so far been applied to the STATCOM (system order, N=3). There have been two hindrances to progress: (1) synthesizing the nonlinear transformation function which is the key to the method; (2) unfamiliarity with the advanced mathematical language. This paper describes the successful application off the method to the unified power flow controller (UPFC) (N=5). The paper is written in a tutorial form to give insights into how the nonlinear transformation function can be synthesized for voltage-source converters, where the bilinear nonlinearity has its origin from the power balance equation relating the ac-side power to the dc-side power. The objective is to explain the method in more accessible mathematical language so that more power electronic engineers can also use the nonlinear control method