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Abstract
A simple two-axis (d-q) model of a saturated six-phase self-excited induction generator, aimed at a stand-alone renewable energy generation, is analyzed using mixed stator current and magnetizing flux as state-space variables. This new set of orthogonal transformation (dq0) is characterized with a four-saturation-element solely in-built system matrix. Selection of this model using proposed mixed variables is justified by its simplicity. Performance equations for the given machine use the magnetizing inductance (Lm) at steady state and the dynamic inductance (L). In view of simplifying the analysis, the effects of common mutual leakage inductance (Llm) and cross-saturation coupling (Lldq) across the d-q-axis of each stator have been pretermitted. The mathematical model presented herein has been verified by simulation results using a fourth-order Runge-Kutta subroutine. Analytical results were also validated by experimental results and were found to be in good agreement.
NOMENCLATURE
| 1/Ldd, 1/Lqq, 1/Ldq | = | saturation-dependent coefficient of system matrix A |
| Csh1, Csh2 | = | shunt capacitor per phase along stator sets I and II |
| cos φ,sin φ | = | angular displacements of the magnetizing current space vector with respect to the d-axis of the common reference frame |
| id1c, iq1c | = | d-q-axis current through shunt capacitor across winding set I |
| id2c, iq2c | = | d-q-axis current through shunt capacitor across winding set II |
| id1L, iq1L | = | d-q-axis current along resistive load across winding set I |
| id2L, iq2L | = | d-q-axis current along resistive load across winding set II |
| J | = | moment of inertia of rotor (kg.m2) |
| L | = | per phase dynamic inductance |
| Lldq | = | cross-saturation coupling between the d-q-axis of stator |
| Llm | = | common mutual leakage inductance between stator winding sets |
| Lm | = | per phase steady-state saturated magnetizing inductance |
| Lσ1 | = | stator leakage inductance per phase of set I |
| Lσ2 | = | stator leakage inductance per phase of set II |
| Lσr | = | rotor leakage inductance per phase referred to stator |
| P | = | number of poles |
| r1 | = | stator resistance per phase of set I |
| r2 | = | stator resistance per phase of set II |
| R1, R2 | = | resistive load per phase along stator sets I and II |
| rr | = | rotor resistance per phase referred to stator |
| Te | = | electromagnetic torque |
| TL | = | load torque |
| Tm | = | mechanical input torque |
| Vd2, Vq2. | = | q-axis voltage of winding set II |
| θr | = | electrical angular displacement of the rotor |
| ψqr, | = | q-axis rotor flux linkage per second referred to stator |
| ω | = | speed of the reference frame |
| ωb | = | base speed |
| ωr | = | rotor speed |
Additional information
Notes on contributors
Kiran Singh
Kiran Singh received her B.Tech. in electrical and electronics engineering from Veer Bahadur Singh (VBS) Purvanchal University, Jaunpur, Uttar Pradesh, India, in 2003 and her M.E. in electrical engineering with specialization in control and instrumentation from the Delhi College of Engineering, Delhi, India, in 2009. She is currently a Ph.D. student at the Department of Electrical Engineering, Indian Institute of Technology (IIT), Roorkee, India. Her research interests include modeling, analysis, and simulation of electrical machines and drives.
Girish Kumar Singh
Girish Kumar Singh received his B.Tech. from G.B. Pant University of Agriculture and Technology, Pantnagar, in 1981 and his Ph.D. in 1991 from Banaras Hindu University, Varanasi, in electrical engineering. He worked with various industries for over 5 years before joining Motilal Nehru Regional (MNR) Engineering College, Allahabad, in 1991 as lecturer; in 1996, he shifted to University of Roorkee. Currently he is a professor in the Electrical Engineering Department at Indian Institute of Technology, Roorkee (formerly known as University of Roorkee). His research interests include design and analysis of electrical machines, power apparatus, and electric drives.