Introduction
Energy functions, an extension of the Lyapunov functions, have been practically used in electric power systems for several applications. A comprehensive energy function theory for general nonlinear autonomous dynamical systems along with its applications to electric power systems will be summarized in this article.
We consider a general nonlinear autonomous dynamical system described by the following equation:
We say a function V : R n → R is an energy function for the system (1) if the following three conditions are satisfied (Chiang et al. 1987):
- (E1):
The derivative of the energy function V (x) along any system trajectory x(t) is nonpositive, i.e., \(\dot{V }(x(t)) \leq 0\).
- (E2):
If x(t) is a nontrivial trajectory (i.e., x(t) is not an equilibrium point), then along the nontrivial trajectory x(t) the set \(\{t \in R :\dot{ V }(x(t)) = 0\}\) has measure zero in R.
- (E3):
That a trajectory x(t) has a bounded value of V (x(t)) for t ∈ R...
Bibliography
Chiang HD (1989) Study of the existence of energy functions for power systems with losses. IEEE Trans Circuits Syst CAS-36(11):1423–1429
Chiang HD (1999) Power system stability. In: Webster JG (ed) Wiley encyclopedia of electrical and electronics engineering. Wiley, New York, pp 104–137
Chiang HD, Thorp JS (1989) Stability regions of nonlinear dynamical systems: a constructive methodology. IEEE Trans Autom Control 34(12):1229–1241
Chiang HD, Wu FF, Varaiya PP (1987) Foundations of direct methods for power system transient stability analysis. IEEE Trans Circuits Syst CAS-34(2):160–173,
Chiang HD, Chu CC, Cauley G (1995) Direct stability analysis of electric power systems using energy functions: theory, applications and perspective (invited paper)
Chiang HD, Li H, Tong J, Tada Y (2013) On-line transient stability screening of practical a 14,500-bus power system: methodology and evaluations. In: Khaitan SK, Gupta A (eds) High performance computing in power and energy systems. Springer, Berlin/New York, pp 335–358. ISBN:978-3-642-32682-0
Chu CC, Chiang HD (1999) Constructing analytical energy functions for network-reduction power systems with models: framework and developments. Circuits Syst Signal Process 18(1):1–16
Chu CC, Chiang HD (2005) Constructing analytical energy functions for network-preserving power system models. Circuits Syst Signal Process 24(4):363–383
Fouad AA, Vittal V (1991) Power system transient stability analysis: using the transient energy function method. Prentice-Hall, Englewood Cliffs
Sauer PW, Pai MA (1998) Power system dynamics and stability. Prentice-Hall, Upper Saddle River
Chiang HD (2011) Direct methods for stability analysis of electrical power system: theoretical foundation, BCU Methodologies and Application. Wiley, Hoboken
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Chiang, HD. (2014). Lyapunov Methods in Power System Stability. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_266-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_266-1
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Latest
Lyapunov Methods in Power System Stability- Published:
- 29 January 2020
DOI: https://doi.org/10.1007/978-1-4471-5102-9_266-2
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Original
Lyapunov Methods in Power System Stability- Published:
- 18 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_266-1