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Slow dynamics simulation of power systems

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Abstract

This paper investigates the simulation of slow dynamics in two-time-scale power systems. A new approach is proposed to obtain the slow dynamics by projecting the trajectory of the post-fault system onto its slow manifold. This is achieved by a nonlinear projection of the full order system initial condition onto the slow manifold, such that the fast intraarea dynamics are not excited. A projection scheme is developed and applied to two-test power systems.

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References

  • Anderson P M, Fouad A A 1977Power system control and stability (Ames, IA: Iowa State University Press)

    Google Scholar 

  • Cheung K W 1991Manifold and stability analysis of singularly perturbed systems with applications to power networks, Ph D thesis, Rensselaer Polytechnic Institute, New York

    Google Scholar 

  • Cheung K W, Chow J H 1991 Stability analysis of singularly perturbed systems using slow and fast manifolds.Proceedings of the 1991 American Control Conference, pp. 1685–1690

  • Chow J H (ed.) 1982Time-scale modeling of dynamic networks with applications to power systems (New York: Springer-Verlag)

    MATH  Google Scholar 

  • Chow J H, Cheung K W 1992 A toolbox for power system dynamics and control engineering education and research.IEEE Trans. Power Syst. 7: 1559–1564

    Article  Google Scholar 

  • Chow J H, Kokotovic P V 1985 Time-scale modeling of sparse dynamic networks.IEEE Trans. Autom. Control AC-30: 714–722

    Article  MATH  Google Scholar 

  • deMello F P, Feltes J W, Laskowski T F, Oppel L J 1992 Simulating fast and slow dynamic effects in power systems.IEEE Comput. Appl. Power 5: 33–38

    Article  Google Scholar 

  • Fenichel N 1979 Geometric singular perturbation theory of ordinary differential equations.J. Differential Equations 31: 53–98

    Article  MATH  MathSciNet  Google Scholar 

  • Kelley A 1967 The stable, center-stable, center, center-unstable, unstable manifolds.J. Differential Equations 3: 546–570

    Article  MATH  MathSciNet  Google Scholar 

  • Kokotovic P V 1975 A Riccati equation of block-diagonalization of ill-conditioned systems.IEEE Trans. Autom. Control AC-20: 812–814

    Article  MATH  MathSciNet  Google Scholar 

  • Kokotovic P V, Khalil H K, O’Reilly J 1986Singular perturbation methods in control: Analysis and design (London: Academic Press)

    MATH  Google Scholar 

  • Kundur P 1985 Evaluation of methods for studying power system stability.Proceedings of the International Symposium on Power System Stability, Ames, Iowa

  • Kundur P, Rogers G J, Wong D Y, Wang L, Lauby M G 1990 A comprehensive computer program package for small signal stability analysis of power systems.IEEE Trans. Power Syst. 5: 1076–1083

    Article  Google Scholar 

  • Peponides G, Kokotovic P V, Chow J H 1982 Singular perturbations and time scales in nonlinear models of power systems.IEEE Trans. Circuits Syst. CAS-29: 758–767

    Article  MATH  MathSciNet  Google Scholar 

  • Schulz R P, Turner A E, Ewart D N 1974 Long term power system dynamics.EPRI Report 90-7-0, Palo Alto, California

  • Sobolev V A 1984 Integral manifolds and decomposition of singularly perturbed systems.Syst. Control Lett. 5: 169–179

    Article  MATH  MathSciNet  Google Scholar 

  • US DOE Report 1987 Development of a decoupling methodology for on-line detection of system instabilities. Systems Development and Engineering Department, General Electric Company, Schenectady, New York

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Cheung, K.W., Chow, J.H. Slow dynamics simulation of power systems. Sadhana 18, 749–760 (1993). https://doi.org/10.1007/BF03024223

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