Critical Loading Characterization for MTDC Converters Using Trajectory Sensitivity Analysis

Ahmed Moawwad*, Ehab F. El-Saadany, Mohamed Shawky El Moursi, Mohammed Albadi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This paper introduces a new technique to characterize the ac grids stability connected to multiterminal high-voltage direct current networks. The proposed method identifies the maximum active powers that converters can exchange with an ac network without losing the transient stability using trajectory sensitivity analysis. Therefore, the generators' rotor angles variations due to various converters active powers exchange are measured and normalized. Consequently, the norm of each trajectory vector is used as an indicator of the system proximity to instability. To enhance the accuracy of the method for online stability assessment applications, the steady-state initial conditions of the sensitivity network variables are precisely obtained using the Newton shooting method. For this purpose, the detailed differential and algebraic models representing the dynamics of the ac and dc networks have been formulated and analytically solved simultaneously with the sensitivity network. Comprehensive simulation studies on the IEEE 68-bus benchmark system are carried out using PSCAD/EMTDC for validation purposes. Results show that the modified approach provides more accurate results compared to the normal trajectory sensitivity analysis with less time compared to multiple time-domain simulations.

Original languageEnglish
Pages (from-to)1962-1972
Number of pages11
JournalIEEE Transactions on Power Delivery
Issue number4
Publication statusPublished - Aug 2018


  • AC-DC power flow
  • MTDC networks
  • deferential algebraic equations (DAE)
  • time-domain simulation
  • trajectory sensitivities
  • transient stability

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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