Evaluation of numerical methods for TSCOPF in a large interconnected system Articles uri icon

publication date

  • June 2022

start page

  • 70562

end page

  • 70571


  • 10

International Standard Serial Number (ISSN)

  • 2169-3536

Electronic International Standard Serial Number (EISSN)

  • 2169-3536


  • Transient stability-constrained optimal power flow (TSCOPF) models comprehensively analyze the security and economic operation of power systems. However, they require a high computational effort and can suffer from convergence problems when applied to large systems. This study analyzes the performance of eleven numerical integration algorithms applied to ordinary differential equations that represent power system dynamics in a TSCOPF model. The analyzed algorithms cover a range of explicit and implicit methods, including the recently published semi-explicit and semi-implicit Adams-Bashforth-Moulton formulas, together with several initialization techniques. The integration methods are applied to a model of the Iberian Peninsula power system, and their performance is discussed in terms of convergence, accuracy, and computational effort. The results show that most implicit methods converge to the solution, even for large time steps. In particular, the Adams-Moulton method of order two and Simpson's rule, both initialized with RK4, outperform the trapezoidal rule, which is the default method in TSCOPF models.


  • Electronics
  • Industrial Engineering
  • Mechanical Engineering
  • Renewable Energies
  • Telecommunications


  • numerical methods; optimal power flow; power system stability; transient stability; tscopf