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 simulator 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 (available now)

Extending the per-step solver to the switching devices and converters that dominate modern grids.

• 4. Sources and control signals — time-domain DC and AC sources, source impedance and soft-starts, and the control-domain blocks that sense and command electrical devices.
• 5. Switches and self-commutating devices — the ideal switch as a two-state conductance; how diodes, thyristors, and IGBTs decide their own state; and the in-step iteration that keeps them consistent.
• 6. Numerical issues of switching — switching-instant error and interpolation, trapezoidal chatter after a current interruption, and the damping remedies that tame it.
• 7. Rectifiers and converters — half- and full-wave rectifiers, the buck converter, and a closed-loop PWM power controller.

Module 3 — Transmission lines and cables (available now)

Where distance stops being negligible and a line becomes a delay rather than an impedance.

• 8. Travelling waves and the Bergeron line — the wave equation on a lossless line, surge impedance and travel time, the two-terminal history-source model, and reflections.
• 9. Losses, lumped lines, and the time step — lumping the series resistance, the nominal $\pi$ for short lines, and how the travel time constrains your choice of $\mathrm{\Delta }t$.
• 10. Multiconductor lines — phase coupling, modal decomposition, Clarke components, the aerial and ground modes, and the three ways to enter three-phase line data.
• 11. Frequency-dependent line models — what constant parameters miss, rational fitting and recursive convolution, and how to choose parameters for the study you are running.
• 12. Line and cable parameters — potential coefficients and images, Carson's earth return and complex depth, bundles and earth wires, cables, and reading a datasheet.

Module 4 — Transformers and rotating machines (available now)

The elements that store energy in iron and in a spinning mass, and the transformations that make them tractable.

• 13. Transformer models and parameters — coupled inductors and the T-equivalent, the trapezoidal companion, recovering $r$ and $x$ from factory tests, and three-phase vector groups.
• 14. Core saturation and inrush — the $\lambda$-$i$ curve, saturation as a current injection that keeps the matrix constant, the three curve definitions, and point-on-wave energization.
• 15. The synchronous machine — Park's transformation, speed and transformer emf, the standard parameters, the swing equation and multi-mass shaft, and reading a machine's datasheet off a short-circuit oscillogram.
• 16. The induction machine — slip and the cage rotor, the torque-speed characteristic, load characteristics, and why motors dominate dynamic load behaviour.

Module 5 — Controls and machine controllers (available now)

The second solver that runs alongside the network, and the standard generator controllers built on top of it.

• 17. Modeling control systems — the control domain as a signal-flow graph, forward-Euler discretization and its stability bound, the topological sort that fixes evaluation order, and the two-step delay across the control/electrical boundary.
• 18. Excitation systems and AVRs — the IEEE 421.5 front-end, the Type DC1A walked stage by stage with saturation and rate feedback, the Type AC4A contrast, and why $V_{REF}$ is back-calculated from the load flow.
• 19. Governors, turbines, and stabilizers — droop and load sharing, TGOV1 and GGOV1, why a fast AVR needs a power system stabilizer, and what system stiffness decides about which controller responds.

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.