On the stabilization of power systems with a reduced number of controls

  • Riccardo Marino
Session 5 Stability II
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 62)


The well-known nonlinear model for the stabilization problem of a power system network reduced at its generating nodes is considered. If active power controls can be employed at each node, the resulting control problem is not well defined since the location and the number of power controls are to be established: the aim is to use the least number of controls which allows the application of a stabilizing control scheme. We propose the recently developed technique of "feedback linearization".

Preliminary results establish that if the number of controls is equal to the number of generating nodes any power network is globally feedback linearizable; on the other hand if only one control is employed the power network is feedback linearizable if and only if its graph is a straight chain. Subsequently it is shown that, under mild conditions on the structure of a power network with n nodes, n/2 controls guarantee feedback linearizability. In those cases the explicit nonlinear state feedback stabilizing control laws are given.


Power System State Feedback Feedback Linearizability Power Network Linear Controllable System 
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6. References

  1. [1]
    J. ZABORSZKY, K.W. WHANG, K.V. PRASAD, Operation of the large interconnected power system by decision and control in emergencies, Report SSM7907, Dept. of System Science and Math., Washington University, St. Louis, MO, 1979.Google Scholar
  2. [2]
    R.W. BROCKETT, Feedback invariants for nonlinear systems, Proc. IFAC Congress, Helsinki, 1978.Google Scholar
  3. [3]
    B. JAKUBCZYK, W. RESPONDEK, On linearization of control systems, Bull. Acad. Pol. Sci. Vol. XXVIII, n.9–10, 517–522.Google Scholar
  4. [4]
    L.R. HUNT, R. SU, G. MEYER, Design for multiinput nonlinear systems, In Differential Geometric Control Theory, R. Brockett,.. ed. 268–298, Birkhäuser 1983.Google Scholar
  5. [5]
    R. MARINO, W.M. BOOTHBY, D.L. ELLIOTT, Geometric properties of linearizable control systems, Submitted to Int. J. of Math. System Theory.Google Scholar
  6. [6]
    J. ZABORSZKY, Towards a comprehensive analysis and operating practice of the large compound HV-AC-DC system, Report n.8203, Dept. of System Science and Math., Washington University, St. Louis, Mo, 1982.Google Scholar
  7. [7]
    R. MARINO, Feedback equivalence of nonlinear systems with applications to power system equations, Doctoral Dissertation, Washington University, St. Louis, Mo, 1982.Google Scholar
  8. [8]
    R. MARINO, Stabilization and feedback equivalence to linear coupled oscillators, To appear in Int. J. of Control.Google Scholar
  9. [9]
    W.M. BOOTHBY, Introduction to Differentiable Geometry and Riemannian Manifolds, Academic Press, N.Y., 1979.Google Scholar
  10. [10]
    R. MARINO, A geometric approach for state feedback stabilization of power system networks, Int. Conf. on Modelling, Identification and Control, I ASTED, Innsbruck, 1984.Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Riccardo Marino
    • 1
  1. 1.Dipartimento di ElettronicaSeconda Università di Roma, Tor VergataRomaItaly

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