Structural stability in power systems. Final report
- Illinois Univ., Urbana, IL (United States). Dept. of Electrical and Computer Engineering
This report investigates the application of structural stability of nonlinear dynamic systems for power system problems. After a quick review of the mathematical literature, a single machine infinite bus problem with variable damping is shown to exhibit global bifurcation. This example validates the original result in structural stability by Andronov and Pontryagin. We next investigate the effect of varying load as a parameter on small signal behavior of a power system modeled as a differential-algebraic system. A complete analytical derivation of the small signal model is included. It is shown that singularity induced bifurcation occurs when the algebraic equation no longer is solvable for the algebraic variables. Next the limitation on the load indices k{sub p} and k{sub q} for existence of solution of the load flow equations is examined. Theoretically it is shown that for k{sub p}, k{sub q} {ge} 1, there always exists a solution for the load flow variables lending justification to the heuristic practice of allowing loads to be constant impedance whenever the load flow fails to converge during the course of dynamic simulation. In the case of dynamic load such as the induction motor, new phenomena such as nested limit cycles is observed depending on size of the motor. The report concludes with a brief application of Kharitonov`s theorem for robust stability of a power system with respect to uncertaintities in the load indices. The following conclusions are reached. Structural stability and bifurcations are related phenomena so far as large scale power systems are concerned. Load modeling is crucial for a proper analysis of different types of bifurcation phenomena. Future work will consist in extending the model formulation to include TCUL transformers, FACTS devices, etc.
- Research Organization:
- Electric Power Research Inst., Palo Alto, CA (United States); Illinois Univ., Urbana, IL (United States). Dept. of Electrical and Computer Engineering
- Sponsoring Organization:
- Electric Power Research Inst., Palo Alto, CA (United States)
- OSTI ID:
- 10143443
- Report Number(s):
- EPRI-TR-103870; ON: UN94010181
- Resource Relation:
- Other Information: PBD: Apr 1994
- Country of Publication:
- United States
- Language:
- English
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