Critical Loading Characterization for MTDC Converters using Trajectory Sensitivity Analysis

Ahmed Moawwad, Ehab El-Saadany, Mohamed Shawky El Moursi, Mohammed Hamdan Albadi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


This paper introduces a new technique to characterize the AC grids stability connected to Multi-Terminal high voltage Direct Current (MTDC) 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 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 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
JournalIEEE Transactions on Power Delivery
Publication statusAccepted/In press - Feb 28 2018


  • AC-DC power flow
  • Deferential Algebraic Equations (DAE)
  • Load flow
  • Mathematical model
  • MTDC networks
  • Power system stability
  • Sensitivity
  • Stability analysis
  • time domain simulation
  • Trajectory
  • trajectory sensitivities
  • Transient analysis
  • transient stability

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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