Authors

Qing-Chang Zhong

Abstract

In science and engineering, many concepts are introduced without a clear physical meaning, e.g., imaginary numbers in mathematics and reactive power in electrical engineering. In this paper, a new operator, coined the ghost operator \\( g \\) , is introduced to physically construct the ghost of a system. It satisfies \\( g^{2}=-1 \\) but is different from the imaginary operator. With the help of the port-Hamiltonian systems theory, it is proved that the ghost of a system behaves exactly in the opposite way as the original system. This brings the ghost of a system into reality and paves the way to reveal the physical meaning of some imaginary concepts. Two applications are given as an example. One is to reveal the physical meaning of reactive power in electrical systems: it is the (real) power of the ghost system, which leads to a significantly simplified instantaneous power theory called the ghost power theory. The other is to define the reactive power for mechanical systems to complete the electrical–mechanical analogy. As a matter of fact, the resulting instantaneous power theory is generic and applicable to any dynamic system that can be described by the port-Hamiltonian model.

Citation

  • Journal: IEEE Access
  • Year: 2017
  • Volume: 5
  • Issue:
  • Pages: 13038–13045
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • DOI: 10.1109/access.2017.2720161

BibTeX

@article{Zhong_2017,
  title={{The Ghost Operator and Its Applications to Reveal the Physical Meaning of Reactive Power for Electrical and Mechanical Systems and Others}},
  volume={5},
  ISSN={2169-3536},
  DOI={10.1109/access.2017.2720161},
  journal={IEEE Access},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Zhong, Qing-Chang},
  year={2017},
  pages={13038--13045}
}

Download the bib file

References

  • Mizoguchi, T., Nozaki, T. & Ohnishi, K. The power factor in mechanical system. 2013 IEEE International Conference on Mechatronics (ICM) 576–581 (2013) doi:10.1109/icmech.2013.6519106 – 10.1109/icmech.2013.6519106
  • Holm, D. D. Geometric Mechanics. (IMPERIAL COLLEGE PRESS, 2011). doi:10.1142/p801 – 10.1142/p801
  • Holm, D. D. Geometric Mechanics. (IMPERIAL COLLEGE PRESS, 2011). doi:10.1142/p802 – 10.1142/p802
  • holm, Geometric Mechanics and Symmetry From Finite to Infinite Dimensions (2009)
  • tellegen, A general network theorem, with applications. Philips Res Rep (1952)
  • Carlin, H. J. Network theory without circuit elements. Proceedings of the IEEE vol. 55 482–497 (1967) – 10.1109/proc.1967.5570
  • Carlin, H. J. Correction to ‘Network theory without circuit elements’. Proceedings of the IEEE vol. 57 1171–1171 (1969) – 10.1109/proc.1969.7176
  • Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 45 1498–1502 (2000) – 10.1109/9.871758
  • Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
  • Erlicki, M. S. & Emanuel-Eigeles, A. New Aspects of Power Factor Improvement Part I—Theoretical Basis. IEEE Transactions on Industry and General Applications vol. IGA-4 441–446 (1968) – 10.1109/tiga.1968.4180920
  • Montanari, A. A. & Gole, A. M. Enhanced Instantaneous Power Theory for Control of Grid Connected Voltage Sourced Converters Under Unbalanced Conditions. IEEE Transactions on Power Electronics vol. 32 6652–6660 (2017) – 10.1109/tpel.2016.2627049
  • de Leon, F., Qaseer, L. & Cohen, J. AC Power Theory From Poynting Theorem: Identification of the Power Components of Magnetic Saturating and Hysteretic Circuits. IEEE Transactions on Power Delivery vol. 27 1548–1556 (2012) – 10.1109/tpwrd.2012.2188652
  • Zhong, Q.-C. Power-Electronics-Enabled Autonomous Power Systems: Architecture and Technical Routes. IEEE Transactions on Industrial Electronics vol. 64 5907–5918 (2017) – 10.1109/tie.2017.2677339
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
  • Control of motorcycle steering instabilities. IEEE Control Systems vol. 26 78–88 (2006) – 10.1109/mcs.2006.1700046
  • Jiang, J. Z. & Smith, M. C. Regular Positive-Real Functions and Five-Element Network Synthesis for Electrical and Mechanical Networks. IEEE Transactions on Automatic Control vol. 56 1275–1290 (2011) – 10.1109/tac.2010.2077810
  • Akagi, H., Watanabe, E. H. & Aredes, M. Instantaneous Power Theory and Applications to Power Conditioning. (2006) doi:10.1002/0470118938 – 10.1002/0470118938
  • rengifo, Reactive power compensation in mechanical systems. Proc 2nd Joint Int Conf Multibody Syst Dyn (2012)
  • Fang Zheng Peng & Jih-Sheng Lai. Generalized instantaneous reactive power theory for three-phase power systems. IEEE Transactions on Instrumentation and Measurement vol. 45 293–297 (1996) – 10.1109/19.481350
  • zhong, Control of Power Inverters in Renewable Energy and Smart Grid Integration (2013)
  • zhong, Power Electronics-Enabled Autonomous Power Systems Next Generation Smart Grids (2017)
  • Rezaei, E., Ebrahimi, M. & Tabesh, A. Control of DFIG Wind Power Generators in Unbalanced Microgrids Based on Instantaneous Power Theory. IEEE Transactions on Smart Grid vol. 8 2278–2286 (2017) – 10.1109/tsg.2016.2521644
  • Firestone, F. A. A NEW ANALOGY BETWEEN MECHANICAL AND ELECTRICAL SYSTEMS. The Journal of the Acoustical Society of America vol. 4 249–267 (1933) – 10.1121/1.1915605
  • Chua, L. Memristor-The missing circuit element. IEEE Transactions on Circuit Theory vol. 18 507–519 (1971) – 10.1109/tct.1971.1083337
  • Lev, F. M. Why is quantum physics based on complex numbers? Finite Fields and Their Applications vol. 12 336–356 (2006) – 10.1016/j.ffa.2005.07.006
  • Smith, M. C. Synthesis of mechanical networks: the inerter. IEEE Transactions on Automatic Control vol. 47 1648–1662 (2002) – 10.1109/tac.2002.803532