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<p>This contribution proposes a method for solving the non-sinusoidal steady-state of power systems through nodal modeling equations. The solution is based on companion-circuit analysis, using the nodal incidence matrix within a unified iterative process regardless of system size. A nodal model generally enables a more compact representation of power systems by modeling electrical components through their discrete Norton equivalent model. Furthermore, the companion-circuit analysis combines its own advantages with an enhanced numerical differentiation process, resulting in an efficient technique for the non-sinusoidal steady-state assessment in the time-domain, applied to power systems including time-varying components. The reduced and iterative computation of this combined method improves the numerical stability during the solution process. The efficiency and accuracy of the combined method is demonstrated using the modified IEEE 14- and 118-bus power systems, which include time-varying components (power electronics-based devices). The obtained results from the reported case studies have been successfully validated against the PSCAD/EMTDC<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="MediaObjects/202_2025_3407_IEq1_HTML.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="120" Type="Linedraw" Width="14" /> </InlineMediaObject> </InlineEquation> response, a simulator widely accepted by the power industry.</p>

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A method for an efficient non-sinusoidal steady-state solution of power systems based on discrete equivalent model and enhanced numerical differentiation

  • 期刊论文

  • 发表日期：

    2025年11月24日

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  • Julio Cesar Godinez-Delgado,
  • Aurelio Medina-Rios,
  • Rafael Cisneros-Magaña

摘要

This contribution proposes a method for solving the non-sinusoidal steady-state of power systems through nodal modeling equations. The solution is based on companion-circuit analysis, using the nodal incidence matrix within a unified iterative process regardless of system size. A nodal model generally enables a more compact representation of power systems by modeling electrical components through their discrete Norton equivalent model. Furthermore, the companion-circuit analysis combines its own advantages with an enhanced numerical differentiation process, resulting in an efficient technique for the non-sinusoidal steady-state assessment in the time-domain, applied to power systems including time-varying components. The reduced and iterative computation of this combined method improves the numerical stability during the solution process. The efficiency and accuracy of the combined method is demonstrated using the modified IEEE 14- and 118-bus power systems, which include time-varying components (power electronics-based devices). The obtained results from the reported case studies have been successfully validated against the PSCAD/EMTDC response, a simulator widely accepted by the power industry.