Expansion of system operating range by an interpolated LPV FACTS controller using multiple Lyapunov functions

Qian Liu, Vijay Vittal, Nicola Elia

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper, a new gain-scheduling control design approach is applied to a supplementary damping controller (SDC) design for a FACTS device in the IEEE 50-machine system. The power system model with the FACTS device is linearized at different operating points to obtain an LPV open-loop model, whose state-space entries depend continuously on a time-varying parameter vector. A synthesis procedure for an improved LPV controller using multiple parameter-dependent Lyapunov functions and an interpolation scheme is presented and applied to the static VAr compensator (SVC) SDC design. Comparisons from simulation results are presented among the interpolated LPV controller designed using multiple parameter-dependent Lyapunov functions (MLPV SDC), the LPV controller designed using a single parameter-dependent Lyapunov function (SLPV SDC), and a conventional controller designed using the Root-locus method (RL SDC), which show that with an interpolated MLPV SDC for the SVC device, the system can achieve better robustness in an extended operating range.

Original languageEnglish (US)
Pages (from-to)1311-1320
Number of pages10
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - Aug 2006
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received September 12, 2005; revised January 18, 2006. This work was supported in part by the National Science Foundation under Grants ECS-0338624 and EEC-9908690 and in part by the Power System Engineering Research Center. Paper no. TPWRS-00571-2005.


  • Damping controller
  • Gain-scheduling
  • IEEE 50-machine test system
  • Linear parameter varying (LPV)
  • Lyapunov function


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