Time domain simulations of synchronous generator modelled by half-order system

This paper presents a methodology which allows to obtain a time domain response of synchronous generator modelled by the half-order systems. The machine is connected to an electrical network composed of RL circuit. From the Park d-q axis equivalent circuit containing impedances modelled by the half-order transmittances, a state space equation system has been built. Then, using the Grünwald-Letnikov approximation of the half-order derivatives, the state space equations have been solved using a program written in the Matlab® software. Simulation results of three phase short-circuit and power restoration have been compared with the corresponding measurements performed on a 3 kVA synchronous generator.

[1]  A. Oustaloup.  La dérivation non entière , 1995 .

[2]  I. Podlubny.  Fractional differential equations , 1998 .

[3]  Delphine Riu.  Modélisation des courants induits dans les machines électriques par des systèmes d'ordre un demi , 2001 .

[4]  Delphine Riu,et al.  Induced currents modeling by half-order systems application to hydro- and turbo-alternators , 2003 .

[5]  C. Forgez,et al.  Modeling diffusive phenomena using non integer derivatives , 2004 .

[6]  Xavier Moreau,et al.  A survey on the CRONE approach , 2005 .

[7]  A. Oustaloup.  Représentation et identification par modèle non entier , 2005 .

[8]  M. Usman Iftikhar,et al.  Dynamic modeling of proton exchange membrane fuel cell using non-integer derivatives , 2006 .

[9]  D. Cafagna,et al.  Fractional calculus: A mathematical tool from the past for present engineers [Past and present] , 2007, IEEE Industrial Electronics Magazine.

[10]  J. Diard,et al.  New approach of electrochemical systems dynamics in the time-domain under small-signal conditions. I. A family of algorithms based on numerical inversion of Laplace transforms , 2008 .

[11]  Piotr Ostalczyk.  Zarys rachunku różniczkowo-całkowego ułamkowych rzędów : teoria i zastosowania w automatyce , 2008 .

[12]  Octavian Enacheanu.  Modélisation fractale des réseaux électriques , 2008 .

[13]  N. Retiere,et al.  Non linear half-order modeling of synchronous machine , 2009, 2009 IEEE International Electric Machines and Drives Conference.

[14]  J. Diard,et al.  New approach of electrochemical systems dynamics in the time domain under small-signal conditions: II. Modelling the responses of electrochemical systems by numerical inversion of Laplace transforms , 2009 .

[15]  Khaled Jelassi,et al.  Fractional modeling of rotor skin effect in induction machines , 2010 .

[16]  Piotr J. Chrzan,et al.  Half-order modelling of ferromagnetic sheet , 2011, 2011 IEEE International Symposium on Industrial Electronics.

[17]  Szymon Racewicz.  Identification and non-integer order modelling of synchronous machines operating as generator , 2012 .

[18]  Khaled Jelassi,et al.  Fractional order modeling of rotor skin effect in induction machines , 2013 .