Excitation system voltage regulator modeling with the use of fractional calculus

Abstract

The article presents a new and measurement-verified approach in the modeling of a voltage regulator, which is used in the power industry and applied for the purpose of regulation of generating units. The voltage regulator extended model, proposed in this paper, involves nonlinearities and the application of fractional calculus. The addition of these features has not only significantly increased the number of parameters determining the model response, it has also established a challenge of developing a solver capable of computing the resulting complex system of fractional differential–algebraic equations (FDAE). The mathematical formulation of a single simulation of a transient process for the model has been described. The application of the Oustaloup Recursive Approximation (ORA) of the fractional derivative has been considered in order to increase the speed of the model evaluation. Generalized equations leading to an approximating system of Differential–Algebraic Equations (DAE) have been presented in detail. In order to obtain the parameters for the fractional nonlinear model, a parameter estimation procedure has been applied, which consists of implementations of several algorithms that are executed sequentially. The usefulness and drawbacks of the application of the ORA has also been discussed.