Artificial Intelligence for Renewable Energy Systems. Группа авторов

1.22d. Hence, both rotor and damper winding behavior will be approximately the same for both three- and six-phase generator. Since, variation in real eigenvalue I was not noted, and hence not shown.

Figure 1.22 Change in real/real component of generator eigenvalue due to load variation. (a) stator eigenvalue, (b) rotor eigenvalue, (c) real eigenvalue II, (d) real eigenvalue III.

1.6 Conclusions

      This chapter deals with a detailed analysis of six-phase synchronous generator, applicable for wind power generation system. This includes the mathematical modeling of grid connected six-phase synchronous generator and its dynamic performance under load variation. Initially, machine was operated at no-load followed by the step increase in output power (i.e., active power increased at time t = 5 and 15 s from no-load to 50% of rated, to rated value). Hence, increase in active component (i.e., q-axis component) of current was noted to be increased with no change in reactive component (i.e., d-axis component) current, associated with both the three-phase stator winding. This has resulted in an overall increase in current of both stator winding sets. On the basis of performance results, it may be inferred that a stable operation is achieved with a step change in output power for a grid connected six-phase synchronous generator.

      Furthermore, a detailed small signal stability analysis was presented for grid connected six-phase synchronous generator with its three-phase counterpart. For this purpose, a linearized mathematical model was developed using Park’s variables, where eigenvalue criteria were used to access the stability under small disturbance. A larger effect was found with the change in stator resistance on both six-phase and three-phase generator. Six-phase generator was found to be more stable due to larger magnitude of negative component of both stator and rotor eigenvalues. Variation of stator leakage reactance also affects the machine stability. It was found that from rotor side, six-phase generator operation is tending toward stability, while three-phase generator is approaching toward instability. Hence, machine operation will remain more stable under stator leakage reactance variation in comparison with three-phase generator. On the field side, major effect was noted in smallest real eigenvalue III, where under variation in resistance rfr and leakage reactance xlfr, wherein six-phase generator remains stable with respect to its three-phase counterpart. From damper side also, operation of six-phase generator was found to have higher stability when compared with its three-phase equivalent.

      Hence, stability of generator operation can be enhanced with increased values of stator resistance and, on rotor side, with higher leakage reactance value of field winding circuit or/and by increased damper winding resistance along q axis.

References

      1. Singh, G.K., Self-excited induction generator research—a survey. Electr. Power Syst. Res., 69, 2, 107–114, 2004.

      2. Chinmaya, K.A. and Singh, G.K., Performance evaluation of multiphase induction generator in stand-alone and grid connected wind energy conversion system. IET Renewable Power Gener., 12, 7, 823–83, 2018.

      3. https://gwec.net/global-figures/wind-energy-global-status

      4. Singh, G.K., Multi-phase induction machine drive research survey. Electr. Power Syst. Res., 61, 2, 139–147, 2002.

      5. Levi, E., Multiphase electric machines for variable speed applications. IEEE Trans. Ind. Electron., 55, 5, 1893–909, 2008.

      6. Alger, P.L., Freiburghouse, E.H., Chase, D.D., Double windings for turbine alternators. AIEE Tans., 49, 1, 226–244, 1930.

      7. Kataoka, T. and Watanebe, E.H., Steady-state characteristic of a current-source inverter/double-wound synchronous machine system for AC power supply. IEEE Trans. Ind. Appl., 16, 2, 262–270, 1980.

      8. Fuchs, E.F. and Rosenberg, L.T., Analysis of an alternator with two displaced stator windings. IEEE Trans. Power Appar. Syst., 93, 6, 1776–1786, 1973.

      9. Hanna, R.A. and Macdonald, D.C., The six-phase generator and transformer into a three-phase power system. IEEE Trans. Power Appar. Syst., 102, 8, 2600–2607, 1983.

      10. Schiferl, R.F. and Ong, C.M., Six-phase synchronous machine with ac and dc stator connections, Part I: equivalent circuit representation and steady-state analysis. IEEE Trans. Power Appar. Syst., 102, 8, 2685–2693, 1983.

      11. Schiferl, R.F. and Ong, C.M., Six-phase synchronous machine with ac and dc stator connections, Part II: harmonic studies and a proposed uninterruptible power supply schemes. IEEE Trans. Power Appar. Syst., 102, 8, 2694–701, 1983.

      12. Sudhoff, S.D. and Wasynczuk, O., Analysis and average value modeling of line commutated converter-synchronous machine systems. IEEE Trans. Energy Convers., 8, 1, 92–99, 1993.

      13. Singh, G.K., Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation. Energy, 36, 9, 5621–5631, 2011.

      14. Singh, G.K., A six-phase synchronous generator for stand-alone renewable energy generation: experimental analysis. Energy, 36, 3, 1768–1775, 2011.

      15. Krause, P.C., Wasynczuk, O., Sudhoff, S.D., Analysis of electrical machinery and drive Systems, IEEE Press, A John Wiley & Sons, Inc. Publication, Piscataway, New Jersey, 2004.

      16. Stapleton, C.A., Root-locus study of synchronous-machine regulation. IEE Proc., 111, 4, 761–768, 1964.

      17. Lipo, T.A. and Krause, P.C., Stability analysis for variable frequency operation of synchronous machines. IEEE Trans. Power Appar. Syst., 87, 1, 227–234, 1968.

      18. Iqbal, A., Singh, G.K., Pant, V., Stability analysis of an asymmetrical six-phase synchronous motor. Turk. J. Elec. Eng. Comp. Sci., 24, 3, 1674–1692, 2016.

      19. Iqbal, A. and Singh, G.K., Eigenvalue analysis of six-phase synchronous motor for small signal stability. EPE J., 28, 2, 49–62, 2018.

      20. Singh, G.K. and Iqbal, A., Small Signal Stability of Three-phase and Six-phase Synchronous Motors: A Comparative Analysis. Chin. J. Electr. Eng., 6, 1, 22–40, 2020.

      21. Singh, G.K. and Iqbal, A., Modeling and analysis of six-phase synchronous motor under fault condition. Chin. J. Electr. Eng., 3, 2, 62–75, 2017.

      22. Iqbal, A., Singh, G.K., Pant, V., Steady-state modeling and analysis of six-phase synchronous motor. Syst. Sci. Control Eng., 2, 1, 236–249, 2014.

      23. Iqbal, A., Singh, G.K., Pant, V., Vector control of asymmetrical six-phase synchronous motor. Cogent Eng., 3, 1134040, 1–10, 2016.

      24. Alger, P.L., Induction machines, New York, Gorden and Breach, 1970.

      25. Aghamohammadi, M.R. and Pourgholi, M., Experience with SSSFR test for synchronous generator model identification using Hook-Jeeves optimization method. Int. J. Syst. Appl. Eng. Dev., 2, 3, 122–127, 2008.

      26. Jones, C.V., The unified theory of electric machine, Butterworths, London, 1967.

      27. Bojoi, R., Lazzari, M., Profumo, F., Tenconi, A., Digital field-oriented control of dual three-phase induction motor drives. IEEE Trans. Ind. Appl., 39, 3, 752–760, 2003.

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