Appendices

Status: outline

Reference material that supports the chapters. This is the detailed outline; full text is in development. The fully written core of the course is Module 1.

These appendices collect the supporting theory and practical checklists that the chapters refer to, kept separate so the main narrative stays focused.

A. Numerical integration and stability

A deeper look at the integration rules behind EMT:

• Forward Euler, backward Euler, and the trapezoidal rule compared: accuracy order and stability region.
• What A-stability means and why an explicit rule can diverge on a stiff circuit while the trapezoidal rule cannot.
• Truncation error and the $(\mathrm{\Delta }t{)}^2$ global-error scaling used in Chapter 2.
• Trapezoidal chatter after discontinuities and the damping remedies introduced in Module 2.

B. The per-unit system

• Why power engineering normalizes quantities to per-unit, and the base relationships ($V_{base}$, $S_{base}$, $Z_{base}$, $I_{base}$).
• Converting element values (impedances, machine and transformer parameters) to and from per-unit, as used by NumaSim's unit selectors.
• Common pitfalls (base changes, three-phase vs single-phase bases).

C. Choosing the time step

A practical decision procedure:

• Identify the fastest phenomenon you must resolve (switching period, ringing frequency, line travel time).
• Apply the "an order of magnitude below the fastest period" rule of thumb, and tighten it for travelling-wave line models (the step must not exceed the shortest line's travel time).
• Trade accuracy against run time, using the $(\mathrm{\Delta }t{)}^2$ error scaling.
• Diagnose symptoms of too-large a step (distorted ringing, missed events) versus too-small (needlessly slow runs).

D. Verifying an EMT model

A checklist for trusting your results:

• Sanity-check steady-state values against hand calculations (Ohm's law, $V/R$, $\tau =L/R$ or $RC$, second-order ${\omega }_0$ and $\zeta$) — the technique used throughout Module 1.
• Confirm energy balance and that nothing floats (every island grounded).
• Refine the time step and confirm the answer converges.
• Compare against an independent method (a phasor/load-flow result for the steady state, or a closed-form transient) where one exists.

References

• H. W. Dommel, Electromagnetic Transients Program (EMTP) Theory Book, Bonneville Power Administration — appendices on ordinary differential equation solution, re-initialization at discontinuities, and per-unit quantities.
• J. Arrillaga and N. R. Watson, Power Systems Electromagnetic Transients Simulation, IET Power and Energy Series 39 — numerical integration and the analysis of continuous and discrete systems.

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