The nonlinear control method, associated with the books of A. Isidori, H. Nijmeijer, and A. J. van der Shaft, has so far been applied to the STATCOM (system order, N = 3). There have been two impediments to progress in applying the method: 1) difficulty in synthesizing the nonlinear transformation which is the key to the method; 2) the advanced mathematical language which makes the aforesaid books generally inaccessible. This paper describes the successful application of the nonlinear control method to control systems based on back-to-back pulsewidth modulation voltage-source converter. This paper is written in a tutorial form to explain how the nonlinear control method can be applied without using the advanced mathematical language. The SSSC and the UPFC (system order, N = 5) are chosen as illustrative examples.
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Lu et al. (2007) studied this question.
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