Authors

Martha Galaz, Romeo Ortega, Alessandro Astolfi, Yuanzhang Sun, Tielong Shen

Abstract

In this chapter we provide a solution to the long-standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances. More specifically, we consider the full 3 n -dimensional model of the n -generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well-defined estimate of the domain of attraction provided by a bona fide Lyapunov function. To design the control law we apply the recently introduced interconnection and damping assignment passivity-based control methodology that endows the closed-loop system with a port-controlled Hamiltonian structure with desired total energy function. The latter consists of terms akin to kinetic and potential energies, thus has a clear physical interpretation. Our derivations underscore the deleterious effects of resistive elements that, as is well known, hamper the assignment of simple “gradient” energy functions and compel us to include nonstandard cross terms. A key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system, which is obtained via the introduction of state-modulated interconnections.

Keywords

Power System; Energy Function; Lyapunov Function; Transient Stabilization; Power System Stabilizer

Citation

BibTeX

@inbook{Galaz,
  title={{Transient Stabilization of Multimachine Power Systems}},
  ISBN={9780817643836},
  DOI={10.1007/0-8176-4470-9_20},
  booktitle={{Current Trends in Nonlinear Systems and Control}},
  publisher={Birkhäuser Boston},
  author={Galaz, Martha and Ortega, Romeo and Astolfi, Alessandro and Sun, Yuanzhang and Shen, Tielong},
  pages={367--386}
}

Download the bib file

References

  • P. Anderson, Power systems control and stability (1977)
  • Bazanella, A. S., Kokotovic, P. V. & e Silva, A. S. A dynamic extension for L/sub g/V controllers. IEEE Trans. Automat. Contr. 44, 588–592 (1999) – 10.1109/9.751357
  • Hsiao-Dong Chang, Chia-Chi Chu & Cauley, G. Direct stability analysis of electric power systems using energy functions: theory, applications, and perspective. Proc. IEEE 83, 1497–1529 (1995) – 10.1109/5.481632
  • O. Dahl, Electric power circuits: theory and applications (1938)
  • C. Desoer, Feedback systems: input-output properties (1975)
  • Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
  • Galaz, M., Ortega, R., Bazanella, A. S. & Stankovic, A. M. An energy-shaping approach to the design of excitation control of synchronous generators. Automatica 39, 111–119 (2003) – 10.1016/s0005-1098(02)00177-2
  • Ghandhari, M., Andersson, G., Pavella, M. & Ernst, D. A control strategy for controllable series capacitor in electric power systems. Automatica 37, 1575–1583 (2001) – 10.1016/s0005-1098(01)00099-1
  • King, C. A., Chapman, J. W. & Ilic, M. D. Feedback linearizing excitation control on a full-scale power system model. IEEE Trans. Power Syst. 9, 1102–1109 (1994) – 10.1109/59.317620
  • Kirschen, D. S., Bacher, R. & Heydt, G. T. Scanning the issue - Special issue on the technology of power system competition. Proc. IEEE 88, 123–127 (2000) – 10.1109/jproc.2000.823993
  • P. Kundur, Power system stability and control (1994)
  • Q. Lu, Nonlinear excitation control of large synchronous generators (2001)
  • J. Machowski, Power system dynamics and stability (1997)
  • P. Magnusson, IEEE Transactions on Automatic Control (1947)
  • Mielczarski, W. & Zajaczkowski, A. M. Nonlinear field voltage control of a synchronous generator using feedback linearization. Automatica 30, 1625–1630 (1994) – 10.1016/0005-1098(94)90102-3
  • Moon, Y.-H., Choi, B.-K. & Roh, T.-H. Estimating the domain of attraction for power systems via a group of damping-reflected energy functions. Automatica 36, 419–425 (2000) – 10.1016/s0005-1098(99)00162-4
  • Narasimhamurthi, N. On the existence of energy function for power systems with transmission losses. IEEE Trans. Circuits Syst. 31, 199–203 (1984) – 10.1109/tcs.1984.1085484
  • Ortega, R. Some Applications and Extensions of Interconnection and Damping Assignment Passivity – Based Control. IFAC Proceedings Volumes 36, 41–50 (2003) – 10.1016/s1474-6670(17)38865-1
  • R. Ortega, Passivity-based control of Euler-Lagrange systems in Communications and Control Engineering (1998)
  • Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
  • Ortega, R., Stanković, A. & Stefanov, P. A Passivation Approach to Power Systems Stabilization. IFAC Proceedings Volumes 31, 309–313 (1998) – 10.1016/s1474-6670(17)40353-3
  • Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
  • Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
  • Pai, M. A. Energy Function Analysis for Power System Stability. (Springer US, 1989). doi:10.1007/978-1-4613-1635-0 – 10.1007/978-1-4613-1635-0
  • Rodríguez, H. & Ortega, R. Stabilization of electromechanical systems via interconnection and damping assignment. Intl J Robust & Nonlinear 13, 1095–1111 (2003) – 10.1002/rnc.804
  • Shen, T., Ortega, R., Lu, Q., Mei, S. & Tamura, K. Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems. Asian Journal of Control 5, 143–152 (2003) – 10.1111/j.1934-6093.2003.tb00105.x
  • Skar, S. J. Stability of Multi-Machine Power Systems with Nontrivial Transfer Conductances. SIAM J. Appl. Math. 39, 475–491 (1980) – 10.1137/0139040
  • Sun, Y. Z., Song, Y. H. & Li, X. Novel energy-based Lyapunov function for controlled power systems. IEEE Power Eng. Rev. 20, 55–57 (2000) – 10.1109/39.841351
  • van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
  • Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
  • Wang, Y., Hill, D. J., Middleton, R. H. & Gao, L. Transient stability enhancement and voltage regulation of power systems. IEEE Trans. Power Syst. 8, 620–627 (1993) – 10.1109/59.260819