Module 3 — Transmission lines and cables

Module status: outline

This is the detailed outline for Module 3. The fully written core of the course is Module 1; chapter prose here is in development.

Lumped R, L, and C are not enough for long lines, where a disturbance takes real time to travel from one end to the other and reflects off the terminations. This module introduces distributed-parameter (travelling- wave) line models — arguably the most distinctive part of EMT simulation — and the determination of line and cable parameters.

What you will learn

• Why a long line cannot be modeled as a single lumped $\pi$-section for fast transients, and what "electrically long" means relative to the time step.
• The travelling-wave (Bergeron) model: a lossless line as two terminals coupled only by a propagation delay, implemented with history buffers.
• How losses and frequency dependence (the variation of line parameters with frequency) are added.
• Where overhead-line and underground-cable parameters come from (geometry, earth return, bundling, skin effect) at a conceptual level.
• The hard link between line length, wave speed, and time step.

Planned chapters

• 8. Travelling waves and the Bergeron line. The wave equation on a lossless line; characteristic impedance and travel time; the two-port history-source model and how reflections arise at the ends.
• 9. Losses and frequency-dependent lines. Lumping series resistance, then frequency-dependent models and why they matter for realistic waveshapes; a conceptual tour of phase- vs modal-domain modeling.
• 10. Line and cable parameters. What determines $R$, $L$, $C$ per unit length; bundled conductors, earth wires, and cable layers; the length/time-step constraint in practice.

Hands-on circuits

• Bergeron line demo — a step launched onto a distributed-parameter line so you can watch it propagate and reflect. (This sample uses the transmission-line component, which is a developer-tier feature; open it to see travelling waves in action.)

Course-specific examples will add a short open- vs short-circuited line to make reflection coefficients concrete, and a study of how the time step must track the line's travel time.

Practice themes

Expect problems on: computing a line's travel time and characteristic impedance from per-unit-length parameters; predicting reflection coefficients and the voltage doubling at an open end; and choosing a time step compatible with a given line length.

References

• H. W. Dommel, Electromagnetic Transients Program (EMTP) Theory Book, Bonneville Power Administration — overhead lines and underground cables.
• J. Arrillaga and N. R. Watson, Power Systems Electromagnetic Transients Simulation, IET Power and Energy Series 39 — Bergeron and frequency-dependent line models.

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