An Accurate Method for Computing the Delay Margin in Load Frequency Control System with Gain and Phase Margins

Ashraf Khalil*, Dina Shona Laila

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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In traditional power systems, a dedicated communication channel is utilized to transfer the frequency measurements. With the deregulation and reconstruction of power systems, the information is sent through a shared communication network that makes time delays unavoidable in load frequency control (LFC) systems. With the existence of time delays, the LFC system becomes a standard time delay system that complicates the stability analysis and controller synthesis. In this paper, we present a new approach for analyzing the stability and determining the delay margin of the LFC system. By introducing a new variable, the transcendental equation is converted to nonlinear equations. To find the crossing frequencies, the nonlinear equations are solved, which is simpler than solving a set of linear matrix inequalities. A single-area and a multi-area LFC system are selected as case studies. The new method accurately determines the delay margin of the LFC system with phase and gain margin. The effect of the PI controller gains on the delay margin is also considered. A sensitivity analysis is conducted to discover the effects of the system parameters on the delay margin, and it is found that the primary loop parameters have a powerful influence on the delay margin. The stability region of the LFC system is also clearly identified through the proposed method. The influence of the system parameters on the stability region is studied. Compared to the published methods in the literature, the proposed method has a simpler structure while giving more accurate results.
Original languageEnglish
Article number3434
Issue number9
Number of pages21
Publication statusPublished - 2022


  • Delay-dependent stability margin
  • Delay margin
  • Load frequency control (LFC)
  • Power systems stability


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