Inside the interrupter
Scrub through one opening at rated short-circuit current. The section uses the same geometry as the 3D model. Compare the GL 313 self-blast design with the classic puffer from the lecture.
Pressures come from a qualitative model (relative to filling pressure). They show the trend and are not GL 313 test data.
Arc physics and current zero
A breaker does not stop the current by parting the contacts. It parts them, lets an arc burn, and stops the current at a natural current zero, when cooling wins over arc heating.
1 · How the arc forms
2 · Minimum arcing time
The lecture example (slide 13) uses a breaker whose minimum arcing time is 9 ms. Move the contact-separation instant and see which current zero clears the arc.
3 · Two ways to fail after current zero
Thermal restrike
First microseconds. The gas blast is too weak, so arc input power (arc voltage × current) stays above the power removed. The gap never stops conducting. Voltage across the contacts stays at a few kV.
Dielectric restrike
Tens to hundreds of µs later. The gap has cooled, but its withstand is below the rising recovery voltage, so it breaks down again. The breaker tries again at the next current zero.
Try both in the simulator.
4 · Arc temperature and SF₆
- Arc core: 20 000–25 000 K. A cooler gas mantle surrounds it.
- Air becomes conducting by thermal ionisation at about 6000 K.
- SF₆ density falls rapidly above 1800 K as it dissociates into S and F.
- When the blast cools the gap, electrons attach to fluorine (electronegative), so conductivity collapses quickly. This is why SF₆ interrupts so well.
- Gas breakers: within a few µs after current zero the arc resistance rises to about 1 MΩ (slide 43).
5 · Interrupting media
SF₆ compared with air (slide 21)
Transient recovery voltage
After the arc goes out, the network forces a voltage back across the open gap. Its peak and rate of rise decide whether the interruption holds. Change the fault and network, then compare with the reference envelope.
The race after current zero
The gap recovers its strength while the TRV rises. If the TRV curve crosses the withstand curve, the arc re-ignites. Stronger gas blast shortens the thermal phase; wider contact gap raises the final withstand.
Reading the TRV
- Transformer-fed fault (no lines): L and C ring, giving the (1 − cos) shape of slide 45: VCB = √(2/3)·Vmax·(1 − cos t/√LC). Undamped peak is 2 × the recovery voltage.
- Lines on the bus: each line looks like its surge impedance Z. Z/n in parallel damps the ringing and gives the exponential start of a four-parameter TRV (slides 46–48).
- RRRV is the steepest slope. Low fault currents through transformers give high frequency and very steep RRRV.
- Thermal phase (first µs) depends on energy balance in the arc; the dielectric phase afterwards depends on gap withstand (slide 43).
- Type tests apply the recovery voltage for 300 ms after interruption.
Model: current injection into L ‖ C ‖ Z/n with network losses set by the amplitude factor; result scaled by kpp. Values are for teaching and are not a substitute for an EMT study.
Travelling waves
Lightning strokes and switching operations launch voltage steps that run along lines and cables at close to the speed of light. Wherever the surge impedance changes, part of the wave reflects and part passes on. Those reflections set the overvoltage that equipment, including circuit breakers, actually sees.
1 · When does a line become a wave guide?
Slide 5 asks for the wavelength of a 50 Hz signal. With λ = u / f and u ≈ 300 m/µs it is about 6000 km, so a 100 km line is electrically short at 50 Hz. Surges contain much higher frequencies.
Lumped or distributed?
- If the line is shorter than about λ/10, every point is at nearly the same phase and a lumped π-model is good enough.
- A surge front of duration T behaves like a frequency of roughly f ≈ 1/(4T). A 1.2 µs lightning front ≈ 200 kHz, so λ ≈ 1.4 km.
- Once the line is long compared with λ, the voltage at one end is not the voltage at the other end at the same instant. Travel time and reflections must be modelled.
- Slide 6 separates impulsive transients (one sharp spike, e.g. lightning) from oscillatory ones (ringing, e.g. switching). Both are travelling-wave events on long lines.
- Travel time on an overhead line is about 3.33 µs per km, on a cable about 5–7 µs per km.
2 · The distributed line and the wave equation
L, R, C and G are spread evenly along the line, per metre (slides 8–9). Each slice Δx carries a little series inductance and resistance and a little shunt capacitance and conductance.
Telegrapher’s equations for v(x,t) and i(x,t):
For a lossless line (R = G = 0) they reduce to the wave equation:
Its general solution is two shapes that keep their form while they move (slide 12):
Forward and backward waves
A forward wave carries i = +vf/Z and a backward wave carries i = −vb/Z (slides 13–14). Where they overlap, voltages add and currents subtract. Each wave passes through the other unchanged.
3 · Surge impedance and wave speed
Z = √(L/C) is a property of the geometry, not of length. A wave sees it as a pure resistance while it travels (slides 11, 14).
Typical values
| Plant | Z | Wave speed |
|---|---|---|
| Overhead line, single conductor (slide 15) | ≈ 450 Ω | ≈ 300 m/µs |
| Overhead line, twin bundle | ≈ 370 Ω | ≈ 300 m/µs |
| Overhead line, quad bundle | ≈ 350 Ω | ≈ 300 m/µs |
| Power cable (slide 16) | 5–70 Ω | 150–200 m/µs |
| Transformer winding (slide 31 example) | ≈ 1600 Ω | — |
Why is a cable’s Z so low? The conductor sits only millimetres from the earthed sheath, and the insulation has εr of 2.3–4. Both raise C a lot and lower L, so √(L/C) is small. The same εr slows the wave to c/√εr.
Bundles act like a fatter conductor, which lowers L and raises C, so Z drops.
4 · Reflection and transmission at a discontinuity
Waves reflect wherever Z changes: open ends, short circuits, branches, cable–line joints and shunt elements (slide 17). At the junction the voltages must match and the currents must balance, which gives e + e′ = e″ (slide 18).
5 · Capacitor or inductor at the end
A lumped C or L changes its apparent impedance with time, so the reflection is not a fixed number.
The 2e rule
Seen from a junction, an arriving wave e behaves like a source of 2e behind Z₁. Solve that small circuit and you have the junction voltage. It explains every case on this page:
- Open end: 2e across nothing → 2e.
- Short: 2e across Z₁ only → 0.
- Matched (Z₂ = Z₁): 2e split equally → e, no reflection.
- Line Z₂: 2e·Z₂/(Z₁+Z₂) → α·e.
- Capacitor: v = 2e(1 − e−t/Z₁C).
- Inductor: v = 2e·e−tZ₁/L.
The reflected wave is always the junction voltage minus the incident wave. This is also the basis of the Bergeron method used in EMT programs.
6 · Bewley lattice diagram
Distance runs across, time runs down (slides 25–26). Every time a wave reaches a node, multiply it by β to get the reflection and by α to get the transmission. A node’s voltage is the sum of everything that has arrived there. Pick the lecture example or build your own system.
| Segment | Z (Ω) | τ (µs) |
|---|
7 · Losses, attenuation and distortion
Real lines have R and G, so waves shrink and their fronts flatten as they travel (slide 17).
What changes on a real line
- Attenuation: amplitude falls as e−αx with α ≈ R/(2Z) + GZ/2. With Z = 400 Ω and 0.06 Ω/km the loss is under 1 % per 100 km, so series resistance alone does little.
- Skin effect raises R at surge frequencies, so steep fronts lose more than the tail.
- Corona adds charge around the conductor once the voltage exceeds the inception level. C rises, the wave slows, and the front flattens. This is the main reason lightning surges get less steep after a few km.
- Distortionless line: if R/L = G/C, the wave shrinks but keeps its shape. Real lines are not distortionless.
- Lossy surge impedance: Z = √((R + jωL)/(G + jωC)) (slide 13). At surge frequencies ωL ≫ R, so Z ≈ √(L/C).
8 · Where travelling waves matter
Direct stroke to a phase conductor
The stroke current splits in two, so each wave sees Z/2: V = I·Z/2 (slide 38).
Lecture example: 10 kA on a 450 Ω line gives 2.25 MV. This is why important lines carry overhead earth wires (slide 39).
Arrester separation distance
An arrester clamps the voltage at its own terminals. Equipment d metres away still sees reflections: Ut ≈ Up + 2·S·d/u.
Example values: Up = 400 kV, u = 300 m/µs, 750 kV lightning withstand.
Short-line fault at a breaker
For a fault a few km down the line, waves run between breaker and fault. The line-side voltage becomes a sawtooth with slope Z·di/dt and period 2d/u. It adds to the source-side TRV.
Z = 450 Ω, 50 Hz, peak factor 1.6. Compare with the bus-side TRV on the .
Lattice, discontinuity and termination models assume lossless lines with frequency-independent Z. Values are for teaching and are not a substitute for an EMT study. Lecture content: ELEC6320 Lecture 5, Abnormal Voltages and Travelling Waves, Dr Hui Ma, UQ.
First pole to clear
The three phases reach current zero at different instants. The pole that clears first sees the highest recovery voltage, because the neutral of the faulted side shifts once the system becomes unbalanced.
Clearing sequence
kpp at a glance
For systems up to 800 kV X₀/X₁ is taken as ≤ 3, so effectively earthed systems use kpp = 1.3 (slide 52).
Condition monitoring
Run a timing and travel test the way a TDR900 or CIBANO 500 would, read the SF₆ density monitor, and link each failure mode to the part that causes it.
Test result
Temperature-compensated density monitor
Example thresholds (fill 6.4, alarm 5.6, lockout 5.3 bar abs at 20 °C) are for illustration. Always use the nameplate values.
Leakage and CO₂-equivalent
GL 313 brochure: 12.7 kg SF₆, GWP100 = 24 300, so 309.1 t CO₂-eq per breaker.
Why −40 °C matters
At low temperature, SF₆ at high pressure liquefies and loses density in the gas phase. GL 313 is rated to −40 °C with pure SF₆; colder climates normally need a lower filling pressure or a gas mixture.
Check your understanding
Twenty-one questions on Lectures 5 and 10. Each answer comes with the reason and the slide it comes from.
Lecture map
Where each part of Lecture 5 (Travelling Waves) and Lecture 10 (High Voltage Circuit Breaker) lives in this lab.
GL 313 at a glance
Source: GE Vernova brochure GEA-33325 (GL 313 F1/4031 P and F3/4031 P).
About this model
The outline (phase spacing, heights, single F1 mechanism) follows the brochure drawing. The interior is a representative self-blast, double-motion interrupter built for teaching. Proportions and internal dimensions are illustrative, not manufacturer data.
All 3D, 2D and simulation code is modular, so the model, the section drawing and the simulators can be reused in other projects.