EMT Simulation of Power Systems

This course is a hands-on course on electromagnetic transient (EMT) simulation In this course, you will learn not just what an EMT program computes, but how it does it: how each resistor, inductor, capacitor, line, transformer, and machine becomes something the computer can solve, and how those pieces are assembled and advanced one time step at a time. Every idea is paired with a circuit you build and run in NumaSim.

Who this course is for

Electrical engineers and senior/graduate students who want to understand and apply EMT simulation. You should be comfortable with:

• AC circuit theory (phasors, impedance, RLC transients);
• basic differential equations (first- and second-order responses);
• per-unit and three-phase power fundamentals;
• elementary linear algebra (solving $\mathbf{A}\mathbf{x}=\mathbf{b}$).

No prior simulation experience is assumed. No programming is required — the "lab" for every chapter is a NumaSim circuit in your browser.

What you will be able to do

By the end of the course you will be able to:

1. Explain where EMT sits among power-system studies and when to reach for it instead of a load-flow or stability tool.
2. Derive the companion (discrete) model of R, L, and C elements from the trapezoidal rule, and predict the numerical error and stability of a chosen time step.
3. Assemble and solve the per-step network equations, including the handling of ideal sources and switches.
4. Model travelling-wave transmission lines and explain reflections and the line-length / time-step relationship.
5. Set up transformers, rotating machines, and their controls, and initialize them from a steady-state operating point.
6. Build, run, and critically check an EMT study of a small power system, choosing the time step and reading the results with confidence.

How to use this course

Work the modules in order; each builds on the previous one. For every chapter:

1. Read the theory and follow the derivations.
2. Open the chapter's circuit with the Open in app link, run it, and reproduce the figure described in the text.
3. Attempt the end-of-chapter problems before opening the solutions.

Circuits referenced in the text also appear in the sample gallery.

Course outline

Module 1 — Foundations of EMT (available now)

The core machinery every EMT program is built on.

• 1. What EMT simulation is and where it fits — transient time frames, EMT versus load-flow / stability studies, and the discretize-then-solve strategy.
• 2. Companion models: discretizing R, L, and C — the trapezoidal rule, the conductance-plus-history-source model, and a first look at numerical accuracy.
• 3. Building and solving the network each step — stamping the nodal system, updating history, the reference node, and switches.

Module 2 — Sources, switching, and power electronics (outline)

• Module 2 outline — sources and control signals, ideal switches, diodes / thyristors / IGBTs, numerical chatter and interpolation, and rectifier / converter examples.

Module 3 — Transmission lines and cables (outline)

• Module 3 outline — travelling waves, the Bergeron line model, frequency dependence, and line / cable parameter determination.

Module 4 — Transformers and rotating machines (outline)

• Module 4 outline — transformer models and saturation, the synchronous machine, and the induction machine.

Module 5 — Controls and machine controllers (outline)

• Module 5 outline — modeling control blocks in an EMT loop, excitation systems / AVRs, governors, power-system stabilizers, and controller auto-initialization.

Module 6 — System studies (outline)

• Module 6 outline — three-phase networks, faults, initialization from a load-flow, multi-rate subsystems, and the bridge to protection studies.

Appendices (outline)

• Appendices — numerical integration and stability, the per-unit system, choosing the time step, and a model-verification checklist.

Ready? Start with Chapter 1 — What EMT simulation is and where it fits.