Chapter 1 — What EMT simulation is and where it fits

Welcome to the course. Before we derive a single equation, this chapter sets the stage: what an electromagnetic transient (EMT) simulation actually computes, how it differs from the other studies a power engineer runs. You will also make your first two NumaSim runs.

Learning objectives

By the end of this chapter you should be able to:

• Define an electromagnetic transient and state what an EMT simulation produces (a time-domain waveform, not a phasor).
• Place EMT among the three classic network studies and choose the right one for a given question.
• Explain, at a high level, the "discretize, then solve a resistive network every step" strategy that the rest of Module 1 builds out.
• Run a circuit in NumaSim and read a signal off the scope.

1.1 What is a transient?

A power network spends most of its life in (or near) a steady state: voltages and currents are sinusoids of nearly constant amplitude and frequency. A transient is the network's response to a disturbance — a switch closing, a fault striking, a lightning surge, a load step — during the interval before it settles into a new steady state.

An electromagnetic transient is the fast part of that response, governed by the electric and magnetic energy stored in capacitances and inductances. Its waveforms contain far more than the fundamental 50/60 Hz tone: switching ripple, travelling-wave reflections, inrush, and high-frequency oscillations all live here.

An EMT simulation computes those instantaneous voltages and currents as functions of time — the actual $v(t)$ and $i(t)$ waveforms — by integrating the network's differential equations directly in the time domain. That is the defining feature: an EMT tool gives you the waveform, sample by sample, not a single complex phasor.

1.2 A spectrum of time scales

Different physical phenomena play out over wildly different time scales, and that is the single most useful thing to keep in mind when choosing a study. Roughly:

Transients span microseconds to hours; EMT studies live at the fast end of that range.

• Microseconds: lightning and steep-front surges, travelling waves on lines.
• Microseconds to milliseconds: breaker operations, power-electronic switching, fault inception. This is the heart of EMT work.
• Tenths of a second to seconds: generator rotor swings and system stability.
• Minutes and beyond: load growth, thermal limits, dispatch.

The faster the phenomenon you care about, the finer the time resolution your model needs — and EMT lives at the fast end.

1.3 Three classic network studies

Power engineers reach for different tools depending on the question. Three recur constantly:

• Power (load) flow — What are the steady-state bus voltages and line flows? A nonlinear algebraic solve at one frequency. (NumaSim has a dedicated solver; see Power flow.)
• Stability analysis — Does the system stay synchronized after a disturbance, over seconds? Usually a phasor (RMS) simulation: the network is assumed sinusoidal at the fundamental, and only the slow envelopes evolve.
• Electromagnetic transients (EMT) — What does the actual waveform look like, microsecond by microsecond? A full time-domain integration that makes no single-frequency assumption.

A phasor study collapses a sinusoid to one complex number (magnitude and angle) and is blind to harmonics and fast switching. An EMT study keeps the whole waveform, at the cost of much smaller time steps and longer run times. The art of EMT is partly knowing when that extra detail is worth it: capacitor-bank switching, converter and drive behavior, ferroresonance, surge protection, and protection-relay transients all demand it; a routine voltage-profile check does not.

Rule of thumb

If your question contains the words waveform, harmonic, switching, surge, or travelling wave, you almost certainly want EMT. If it contains steady-state, RMS, or MW/MVAr dispatch, you probably do not.

1.4 The big idea (preview of Module 1)

How can a computer integrate a whole network of inductors and capacitors fast enough to be useful? The strategy that every modern EMT engine uses, introduced by H. W. Dommel, has two moves:

1. Discretize in time. Pick a fixed time step $\mathrm{\Delta }t$ (often microseconds to tens of microseconds) and advance the solution one step at a time: $t=0,\mathrm{\Delta }t,2\mathrm{\Delta }t,3\mathrm{\Delta }t,\dots$
2. Replace every energy-storage element with a companion model — a plain resistor (conductance) in parallel with a current source whose value is known from the previous step. This comes from applying an implicit integration rule (the trapezoidal rule) to each element's differential equation.

The move every modern EMT engine makes: each energy-storage element (any $L$ or $C$) becomes a conductance $G_{\mathrm{eq}}$ in parallel with a history current source $I^{\mathrm{hist}}$ that is fixed by the previous step. Chapter 2 derives both quantities.

After the second move, the network at each individual step contains only conductances and current sources. That is a purely resistive circuit, and a resistive circuit is solved with one set of linear equations. So an EMT run becomes a loop:

The EMT time-step loop: update history sources from the previous step, solve the linear network, recover branch currents, then repeat.

Chapter 2 derives the companion models; Chapter 3 assembles and solves the per-step network. For now, just hold onto the shape of the idea: discretize, then solve a resistive network every step.

1.5 Lab: your first runs

Time to drive the simulator.

Lab 1A — a purely resistive circuit (no dynamics)

Open the voltage divider:

Open the voltage divider in app →

(Its full description lives at voltage divider.)

It is a 10 V DC source across two equal resistors. Press Run and look at the scope:

• V_src sits at 10 V.
• V_mid, the node between the resistors, sits at 5 V — exactly $V_{\text{src}}\cdot R_2/(R_1+R_2)$.

Both traces are flat lines. With only resistors there is no stored energy, so there is no transient: the circuit is in its final state from the first instant. Change one resistor and run again — the level moves, but it is still a flat line.

Lab 1B — add an inductor and watch time appear

Now open the R-L step response:

Open the R-L step response in app →

(Full description: R-L step response.)

This is the same kind of source, but the load is a resistor in series with an inductor. Press Run and watch I_L:

• It does not jump to its final value. It rises along a smooth curve, reaching about 63% of its final 1 A after 10 ms and levelling off near 1 A after ~50 ms.
• The inductor voltage V_mid does the opposite: it starts at the full 10 V and decays toward zero.

That curve is the electromagnetic transient. The inductor stores magnetic energy and resists sudden change, so the network needs time to reach its new steady state — and EMT computes every point along the way. Exactly why the curve has that shape, and how the simulator produces it one step at a time, is the subject of Chapter 2.

1.6 Summary

• A transient is the network's response to a disturbance; an electromagnetic transient is the fast part driven by L and C.
• An EMT simulation produces the time-domain waveform $v(t)$, $i(t)$, not a single phasor.
• Of the three classic studies — load flow, stability, EMT — EMT is the most detailed and the most computationally demanding, and is the right choice for waveform-, switching-, and surge-level questions.
• Every modern EMT engine works by discretizing time and turning the network into a resistive circuit it can solve once per step.

1.7 Problems

Try each before opening the solution.

Problem 1.1. For each question, name the most appropriate study (load flow, stability, or EMT):

(a) "Will bus voltages stay within ±5% at peak load next summer?" (b) "What is the peak transient overvoltage when this 200 km line is energized?" (c) "Does the generator remain in step after a three-phase fault is cleared in 100 ms?"

Solution 1.1

(a) Power (load) flow — a steady-state voltage-profile question. (b) EMT — energization produces travelling-wave / switching overvoltages that only a waveform simulation captures. (c) Stability — a seconds-scale electromechanical (rotor-angle) question, normally run as a phasor/RMS simulation.

Problem 1.2. A colleague proposes simulating power-electronic switching ripple with a phasor (RMS, single-frequency) tool to save time. Why will this fail?

Solution 1.2

A phasor tool assumes everything is a sinusoid at one frequency (the fundamental) and represents each signal by a single complex number. Switching ripple is, by definition, a collection of harmonics and fast edges around the fundamental — exactly the content a single-frequency phasor representation discards. You need a time-domain (EMT) simulation that keeps the full waveform.

Problem 1.3. In Lab 1B the current reached ~63% of its final value in about 10 ms. The circuit had $R=10\mathrm{\Omega }$ and $L=0.1\text{H}$. Compute $L/R$. What do you think that quantity represents? (We will prove it in Chapter 2.)

Solution 1.3

$L/R=0.1/10=0.01\text{s}=10\text{ms}$. This is the circuit's time constant $\tau$: the time to reach $1-e^{-1}\approx 63.2$ of the final change. After about $5\tau$ the response is within ~1% of its final value, which is why the current looked settled by ~50 ms.

Problem 1.4. Why must an EMT simulation generally use a much smaller time step than a stability (phasor) simulation of the same network?

Solution 1.4

EMT resolves the actual waveform, including the fundamental cycle and any faster switching or travelling-wave events, so its step must be a small fraction of the fastest period of interest (often microseconds). A phasor simulation only tracks the slow envelope of magnitudes and angles and can take much larger steps (milliseconds) because it never represents the fundamental waveform itself.

1.8 References

• H. W. Dommel, Electromagnetic Transients Program (EMTP) Theory Book, Bonneville Power Administration — the origin of the companion-model / nodal method.
• J. Arrillaga and N. R. Watson, Power Systems Electromagnetic Transients Simulation, IET Power and Energy Series 39 — Chapter 1 surveys the classification of transients and the range of applications.
• A. Greenwood, Electrical Transients in Power Systems, 2nd ed., Wiley — excellent physical intuition for transient phenomena.

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Next: Chapter 2 — Companion models: discretizing R, L, and C.