A Model Reference Approach for Interarea Modal Damping in Large Power Systems

Part of the Power Electronics and Power Systems book series (PEPS, volume 3)


In this chapter, we present a set of results on the design of dynamic controllers for electromechanical oscillation damping in large power systems using Synchronized Phasor Measurements. Our approach consists of three steps, namely – (1) Model Reduction, where phasor data are used to identify second-order models of the oscillation clusters of the system, (2) Aggregate Control, where state-feedback controllers are designed to achieve a desired closed-loop transient response between every pair of clusters, and finally (3) Control Inversion, where the aggregate control design is distributed and tuned to actual realistic controllers at the generator terminals until the interarea responses of the full-order power system matches the respective inter-machine responses of the reduced-order system. Although a general optimization framework is needed to formulate these three steps for any n-area power system, we specifically show that model reference control (MRC) can be an excellent choice to solve this damping problem when the power system consists of two dominant areas, or equivalently one dominant interarea mode. Application of MRC to such two-area systems is demonstrated through topological examples inspired by realistic transfer paths in the US grid.


  1. 1.
    Chow JH, Peponides G, Kokotovic PV, Avramovic B, Winkelman JR (1982) Time-scale modeling of dynamic networks with applications to power systems. Springer, New YorkMATHCrossRefGoogle Scholar
  2. 2.
    Dobson I (1992) Observations on the geometry of saddle node bifurcation and voltage collapse in electric power systems. IEEE Trans Circuit Syst—Part 1 39(3):240–243Google Scholar
  3. 3.
    Willems JL, Willems JC (1970) The application of lyapunov methods to the computation of transient stability regions for multimachine power systems. IEEE Trans Power App Syst 89(5/6): 795–801CrossRefGoogle Scholar
  4. 4.
    Pai MA (1989) Energy function analysis for power system stability. Kluwer Academic Publishers, MACrossRefGoogle Scholar
  5. 5.
    Phadke AG, Thorp JS, Adamiak MG (1983) New measurement techniques for tracking voltage phasors, local system frequency, and rate of change of frequency. IEEE Trans Power App Syst 102:1025–1038CrossRefGoogle Scholar
  6. 6.
    Liu Y et al (2006) A US-wide power systems frequency monitoring network. In: Proceedings of the IEEE PES general meeting, Montreal, QC, Canada, June 2006Google Scholar
  7. 7.
    Hauer JF, Demeure CJ, Scharf LL (1990) Initial results in prony analysis of power system response signals. IEEE Trans Power Syst 5(1):80–89CrossRefGoogle Scholar
  8. 8.
    Messina AR, Vittal V, Ruiz-Vega D, Enriquez-Harper G (2006) Interpretation and visualization of wide-area pmu measurements using hilbert analysis. IEEE Trans Power Syst 21(4): 1760–1771CrossRefGoogle Scholar
  9. 9.
    Emami R, Abur A (2009) Reliable placement of synchronized phasor measurements on network branches. In: Proceedings of the IEEE PSCE, Seattle, WA, March 15–19, 2009Google Scholar
  10. 10.
    Dagle JE (2004) Data management issues associated with the August 14, 2003 Blackout Investigation. In: IEEE PES General Meeting, CO, June 2004Google Scholar
  11. 11.
  12. 12.
    Chakrabortty A, Chow JH, Salazar A (2011) A measurement-based framework for dynamic equivalencing of power systems using wide-area phasor measurements. IEEE Trans Smart Grid 1(2):68–81CrossRefGoogle Scholar
  13. 13.
    Pal B, Chaudhuri B (2005) Robust control in power systems. Springer, New YorkGoogle Scholar
  14. 14.
    Trudnowski DJ, Dagle JE (1997) Effects of generator and static-load nonlinearities on electromechanical oscillations. IEEE Trans Power Syst 12(3):1283–1289CrossRefGoogle Scholar
  15. 15.
    Oppenheim AV, Schafer RW (1989) Discrete-time signal processing. Prentice Hall, Upper Saddle River, NJMATHGoogle Scholar
  16. 16.
    Tao G (2003) Adaptive control analysis design and analysis. Wiley, New JerseyMATHCrossRefGoogle Scholar
  17. 17.
    Taylor CW, Erickson DC, Martin KE, Wilson RW, Venkatasubramanian V (2005) WACS—wide-area stability and voltage control system: R&D and online demonstration. Proc IEEE 93(5):892–906CrossRefGoogle Scholar
  18. 18.
    Kamwa I, Grondin R, Hebert Y (2001) Wide-area measurement based stabilizing control of large power systems—a decentralized/hierarchical approach. IEEE Trans Power Syst 16(1):136–153CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.North Carolina State UniversityRaleighUSA

Personalised recommendations