Transfer Function with Nonlinear Characteristics Definition Based on Multidimensional Laplace Transform and its Application to Forced Response Power Systems

Osvaldo Rodríguez Villalón and Aurelio Medina-Rios
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Osvaldo Rodríguez Villalón: Departamento de Ingeniería Eléctrica, División de Ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Salamanca, Guanajuato 36885, Mexico
Aurelio Medina-Rios: División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Morelia, Michoacán 58030, Mexico

Energies, 2019, vol. 12, issue 21, 1-32

Abstract: In this research, the concept of nonlinear transfer function with nonlinear characteristics is introduced through the multidimensional Laplace transform and modal series (MS) method. The method of modal series is applied to the power systems dynamics analysis in order to consider nonlinear oscillations and modal interactions, which contribute to the response of the system’s dynamic following disturbances. The method of MS allows the inclusion of input excitation functions obtained as Laplace domain kernels superposed to obtain a transfer function. Applying the Volterra series expansion through kernels decomposition, a transfer function with nonlinear characteristics is obtained which incorporates some of the main modal characteristics of the nonlinear system. Following the same schematic procedure, it is possible to determine second and higher order transfer functions. Once the transfer functions both linear and with nonlinear characteristics are determined, a time domain and frequency response analyses can be performed. The methodology is exemplified by denoting the numerical and analytical properties with the application to a synchronous machine-infinite busbar test power system and to a three synchronous machines–nine buses test power system. Bode and Nyquist analysis are utilized to demonstrate the transfer functions accuracy and frequency response.

Keywords: nonlinear transfer function; modal series; multidimensional Laplace transform; forced response power systems (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2019
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