This is the second of the two chapters, dealing with the first objective. This chapter develops and discusses a propagation model. It begins with a presentation of standing wave definitions. The propagation model is defined and validated, and model elements for components are established. The chapter concludes with a section dedicated to propagation analyses, which contains a guideline for such studies as well as case studies demonstrating voltage propagation in a meshed system and an interpretation of the physical meaning. The Western Danish 400 kV transmission grid is used as a case study. Five key aspects are analysed: the effect of underground cable and overhead line combinations on voltage reflections, the impact of grid configuration changes on voltage propagation and amplification, the evaluation of standing voltage waves to determine voltage extremes, and the propagation of harmonic voltages from individual sources. Lastly, sensitivity analyses reveal that even short cable lengths significantly affect voltage reflections and propagation, with global impacts on the grid. The propagation model, utilising S-parameters, provides insights into the physical conditions influencing harmonic voltage waves, allowing for the assessment of optimal paths and the quantification of grid topology effects. The chapter concludes by emphasizing the model’s utility in understanding and mitigating harmonic propagation in meshed power systems.

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Propagation of Harmonics

  • Bjarne Søndergaard Bukh

摘要

This is the second of the two chapters, dealing with the first objective. This chapter develops and discusses a propagation model. It begins with a presentation of standing wave definitions. The propagation model is defined and validated, and model elements for components are established. The chapter concludes with a section dedicated to propagation analyses, which contains a guideline for such studies as well as case studies demonstrating voltage propagation in a meshed system and an interpretation of the physical meaning. The Western Danish 400 kV transmission grid is used as a case study. Five key aspects are analysed: the effect of underground cable and overhead line combinations on voltage reflections, the impact of grid configuration changes on voltage propagation and amplification, the evaluation of standing voltage waves to determine voltage extremes, and the propagation of harmonic voltages from individual sources. Lastly, sensitivity analyses reveal that even short cable lengths significantly affect voltage reflections and propagation, with global impacts on the grid. The propagation model, utilising S-parameters, provides insights into the physical conditions influencing harmonic voltage waves, allowing for the assessment of optimal paths and the quantification of grid topology effects. The chapter concludes by emphasizing the model’s utility in understanding and mitigating harmonic propagation in meshed power systems.