Developing a Weakly Nonlinear Power System Model Using the Carleman Bilinearization Procedure

The paper considers the Carleman bilinearization procedure for developing weakly nonlinear models of electric power systems by representing the original nonlinear equations of the system in a bilinear form. In particular, we describe a general algorithm for representing a system of nonlinear differential equations in a bilinear form and proposed techniques for optimizing the dimension of the obtained bilinear system. An example of a single-machine infinite bus system demonstrates the bilinearization procedure and model order reduction.