Computation of time delay margin for power system small-signal stability

Ayasun S.

EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, vol.19, no.7, pp.949-968, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 7
  • Publication Date: 2009
  • Doi Number: 10.1002/etep.272
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.949-968
  • Keywords: electrical power system, small-signal stability, time delay, delay margin, Matlab, BIFURCATION-ANALYSIS, MODEL, RESONATOR
  • Gazi University Affiliated: No


With the extensive use of phasor measurement units (PMU) in the wide-area measurement/monitoring systems (WAMS), time delays have become unavoidable in power systems. This paper presents a direct and exact method to Compute the delay margin of power systems with single and commensurate time delays. The delay margin is the maximum amount Of time delay that the system can tolerate before it becomes unstable fora given operating point. First, without using any approximation or substitution, the transcendental characteristic equation is converted into a polynomial without the transcendentality such that its real roots coincide with the imaginary roots of the characteristic equation exactly. The resulting polynomial also enables us to easily determine the delay dependency of the system stability and the sensitivities of crossing roots with respect to time delay. Then, an expression in terms of system parameters and imaginary root of the characteristic equation is derived for computing the delay margin. The proposed method is applied to a single-machine-infinite bus (SMIB) power system with an exciter. Delay margins are computed for a wide range of system parameters including generator mechanical power, damping and transient reactance, exciter gain, and transmission line reactance. The results indicate that the delay margin decreases as the mechanical power, exciter gain and line reactance increase while it increases with increasing generator transient reactance Additionally, the relationship between the delay margin and generator damping is found be relatively complex. Finally, the theoretical delay margin results are validated using the time-domain simulations of Matlab. Copyright (C) 2008 John Wiley & Sons, Ltd.