High Current Generation and Measurement

High voltage needs distance. High current needs the opposite.

Modules 3 through 7 built the complete generate-and-measure cycle for voltage. This module closes it with the sister quantity. A laboratory testing a metal-oxide surge arrester has to inject tens or hundreds of kiloamperes into it with a waveform controlled to the microsecond. A laboratory running a temperature rise test has to hold thousands of amperes circulating for hours with demonstrated thermal stability. Between the brutal transient and the patient steady state sits everything covered here: capacitor banks and RLC circuits, artificial transmission lines that manufacture rectangular waves, oscillating currents for synthetic testing, and the three sensor families that let you state with metrological pedigree how many amperes actually flowed.

There is a fundamental asymmetry between generating high voltage and generating high current. High voltage asks for insulation — clearances, bushings, oil, gas. High current asks for the opposite: the lowest possible impedance along the entire path. Massive busbars, torqued connections, minimum-inductance loops. A megavolt impulse generator can spread electrodes meters apart across a hall; a 100 kA current impulse generator packs its capacitors around the test object in a compact radially symmetric arrangement, because every stray microhenry lengthens the front and steals amplitude. In Module 6 a spark gap was a convenient switch. Here the geometry of the circuit is the dominant component.

What you will be able to do

• Characterize the standard current impulses — 8/20 µs and 4/10 µs in particular — and the long-duration rectangular wave, with their time parameters, tolerances and undershoot limits per IEC 62475:2010 and IEC 60099-4:2014.

• Explain capacitor-bank current impulse generators, derive the waveform of the series RLC circuit in all three damping regimes, and size C, L and R for an 8/20 wave — including the physical limit that makes the exact pair (8 µs, 20 µs) unreachable with low undershoot in a purely linear circuit.

• Describe long-duration rectangular wave generation with pulse forming networks and oscillating current generation for synthetic testing.

• Select the right sensor — low-impedance coaxial shunt, Rogowski coil, or Hall-effect and fluxgate device — considering current range, bandwidth, inductive pickup, galvanic isolation and i²t thermal capacity.

• Plan steady-state high current tests for temperature rise without falling into thermal self-deception: the stabilization criterion, temperature instrumentation and the treacherous role of connections.

Current impulse parameters are not voltage impulse parameters

IEC 62475:2010 is the mother standard of high current test techniques, the counterpart of IEC 60060-1 for voltage, and it defines the exponential current impulse with one difference that gets missed constantly. Voltage impulses use the 30% and 90% points to define the front. Current impulses use 10% and 90%: T1 = 1.25·(t90 − t10), with virtual origin O1 where that line crosses the time axis and T2 running from O1 to the 50% point on the tail. Tolerances are ±10% on peak and ±20% on the time parameters, wider than for voltage in explicit recognition of how hard the wave is to shape.

Beyond T1 and T2, three integral quantities carry the actual stress. Peak sets residual voltage. Charge Q = ∫i(t)dt governs electrode erosion and the energy deposited in a varistor, W ≈ U_res·Q. The action integral ∫i²(t)dt, in A²s, governs adiabatic heating of conductors and of the sensor itself. The same 100 kA peak carries radically different charge in a 4/10 and in a 2000 µs rectangular wave, which is why arrester standards migrated from discharge classes to charge. Undershoot is limited to 20% of peak, because reversal stresses the varistor in the opposite polarity and distorts the charge integral.

Each standard wave is a physical model frozen into a standard

The 8/20 represents the share of lightning current reaching a line arrester after division with conductor surge impedance. Under IEC 60099-4:2014 it defines the nominal discharge current In at 2.5, 5, 10 or 20 kA and is used to measure residual voltage, with an acceptance window tighter than the generic tolerance: 7 to 9 µs front, 18 to 22 µs tail. The 10/350 represents a direct-strike first return stroke. The 4/10 is a robustness test rather than a representative one — nearly twice the amplitude in less than half the time, classically 100 kA for In of 10 and 20 kA.

The long-duration rectangular impulse is not exponential. It is a near-constant plateau of hundreds of amperes to a few kiloamperes held for 500 to 3200 µs, reproducing a long charged line discharging through the arrester. IEC 62475 characterizes it by virtual peak duration Td (time above 90%) and total virtual duration Tt (time above 10%), with Tt ≤ 1.5·Td as the rectangularity criterion. This is the wave that moves real charge: 1 kA for 2000 µs is 2 C, the charge of twenty 10 kA 8/20 impulses. IEC 60099-4:2014 accordingly replaced line discharge classes with quantities measured on the varistor — repetitive charge Qrs, thermal energy Wth in kJ/kV of Ur, thermal charge Qth — labelled SH, SM, SL and DH, DM, DL.

The series RLC circuit and the 8/20 that cannot exist

Every current impulse generator is a bank C charged to V0, a switch, the loop inductance L and the total resistance R including the object. The response depends on α = R/2L against ω0 = 1/√(LC). Underdamped, i(t) = (V0/ωL)·e^(−αt)·sin(ωt): the first half cycle is the impulse, the second the undershoot. Critically damped, i(t) = (V0/L)·t·e^(−αt), peaking at Îp = V0/(e·Z0) with Z0 = √(L/C). Peak scales as V0/Z0, the whole time scale as √(LC), and stored energy is W = ½CV0².

Now the result that surprises everyone. A linear RLC circuit cannot deliver exactly T1 = 8 µs and T2 = 20 µs while holding undershoot at or below 20%. The minimum achievable T2/T1 at 20% reversal is about 2.7; the 8/20 asks for 2.5. IEC 62475 admits this in Annex E, which maps the reachable combinations against allowed undershoot, and that is why the time tolerance is ±20%. A worked compromise: C = 17.2 µF, L = 4.30 µH, R = 0.475 Ω (ζ = 0.48) at V0 = 100 kV, 86 kJ stored, gives 112 kA with T1/T2 of 8.0/21.8 µs and 18.3% undershoot. Three resources close the gap: the varistor under test adds current-dependent damping and eats the reversal; the crowbar circuit fires a second gap at peak and hands the current to a pure RL decay loop; and parallel stages with synchronized gaps sum tens of kiloamperes while radial symmetry keeps loop inductance down.

Manufacturing a rectangle, and the oscillating current

An RLC circuit will not produce a 2000 µs plateau — you have to emulate the line the wave represents. The pulse forming network is n identical LC sections in cascade; charged to V0 and discharged into a matched load it delivers approximately constant current I = V0/(Z + R_load) for Td ≈ 2·n·√(Ls·Cs), with Z = √(Ls/Cs) the per-section impedance. Five to ten sections give rectangularity compatible with Tt ≤ 1.5·Td. Mismatch is the enemy: a load below Z gives a reflected reverse step, a load above Z a stepped tail.

Between impulse and steady state sits oscillating current: a deliberately underdamped bank discharge through a reactor, a damped sinusoid of tens to hundreds of hertz and tens of kiloamperes. It is the backbone of the synthetic circuit breaker test, where a current circuit supplies the short-circuit current the breaker interrupts while a separate high-voltage low-energy circuit applies the transient recovery voltage at the exact current zero. Synchronization is on the order of microseconds.

Three sensor families, three physics

The coaxial shunt is the most direct measurement possible: 0.1 to 10 mΩ of manganin or constantan in a thin tube, with the return current in a concentric outer cylinder so the field where the voltage taps sit is essentially zero. That symmetry drives mutual inductance between power loop and signal loop to nanohenries or less, which is the whole point — at di/dt of 10¹⁰ A/s every stray nanohenry adds 10 V to the signal. Its dynamic limit is skin effect in the element: current crowds onto the outer face while voltage is sensed on the inner one, so response time grows with the square of wall thickness. Its thermal limit is adiabatic, ΔT = R·∫i²dt/(m·c_p). Drawbacks: no galvanic isolation, and it must be inserted in series.

The Rogowski coil is a uniformly wound air-cored toroid with output u(t) = −M·di/dt, reconstructed by an integrator. No iron means no saturation — the same coil measures 1 kA or 1 MA linearly — and bandwidth runs from fractions of a hertz, set by the integrator, to megahertz, set by coil resonance. It clamps on without breaking the circuit; watch winding uniformity, conductor position and integrator drift. With its integrator it classifies as a low-power passive current transformer under IEC 61869-10:2017. Hall-effect and fluxgate devices read the conductor's field and are, with the shunt, the only families that measure DC: open-loop Hall gives 1 to 2%, closed loop 0.1 to 0.5%, fluxgate comparators parts per million. The iron-core CT stays legitimate for steady sinusoidal current but is a double trap on impulse — the unidirectional component saturates the core by volt-second integral, and low-frequency response cannot hold flux through a 2000 µs tail. The symptom is a plausible peak with a shortened tail and understated charge.

Steady state, the 1 K/h rule, and the pedigree of the number

Temperature rise testing injects rated current for hours. The classic source is a current injection transformer with a few busbar turns delivering hundreds to thousands of amperes at a few volts into a nearly purely inductive load, so power is dominated by reactive and the secondary loop is itself part of the source. Thermal self-deception has three faces. Calling equilibrium too early: the criterion is a rise varying by no more than 1 K per hour, applied by IEC 60076-2:2011 to top-oil gradient and by IEC 61439-1:2020 to assemblies, and transformer thermal time constants run to hours. Measuring the wrong current: distorted source waveforms heat by true RMS including harmonics. And the connections, most treacherous of all — a 50 µΩ joint carrying 2,000 A dissipates 200 W, a soldering iron hidden inside the circuit that heats the neighbouring measurement point.

The chain ends at a digitizer, under the same IEC 61083-1:2021 that governs voltage work: 10 MS/s or more for an 8/20, 20 MS/s for a 4/10, 12 to 16 bits where the record will be integrated, and software validated per IEC 61083-2:2013. IEC 62475 sets approved-system targets at 3% expanded uncertainty (k = 2) on peak and 10% on time parameters, with a dedicated interference circuit for Rogowski systems because an air-cored sensor fails differently from a shunt. Keep two ideas apart: generation tolerance asks whether the wave sits inside its window, measurement uncertainty asks how much you doubt the number. And when integrating for charge, residual offset integrates too — 0.1% of full scale over a 2000 µs record corrupts the charge by an amount comparable to the Qrs tolerance. Record pre-trigger, subtract its mean, document the correction.

Syllabus

• Three regimes: impulse (microseconds), short-time (milliseconds to seconds), steady state (hours)

• Current impulse parameters: the 10%/90% front definition, T1 = 1.25·(t90 − t10), virtual origin, T2

• The integral quantities that measure stress: peak, charge Q = ∫i(t)dt, action integral ∫i²(t)dt

• Undershoot: the 20% polarity reversal limit and why it matters to a varistor

• The exponential family: 1/20, 4/10, 8/20, 10/350, 30/80 and their governing standards

• Arrester testing: In values, the 7–9 µs / 18–22 µs residual voltage window, the 4/10 high-current impulse

• Long-duration rectangular waves: Td, Tt and the Tt ≤ 1.5·Td rectangularity criterion

• From line discharge class to Qrs, Wth and Qth; the SH/SM/SL and DH/DM/DL classification

• Series RLC generator: underdamped, critically damped and overdamped solutions

• Sizing an 8/20 and the Annex E constraint map; crowbar circuits and parallel stages

• Pulse forming networks: section impedance, number of sections, mismatch effects

• Oscillating current and the synthetic breaker test; asymmetric peak factor

• Coaxial shunts: manganin tube construction, skin effect, adiabatic i²t limit

• Rogowski coils: u(t) = −M·di/dt, integrators, no saturation, IEC 61869-10 classification

• Hall-effect and fluxgate: open loop, closed loop, precision current comparators

• The iron-core CT saturation trap on impulse and long-tail waveforms

• Steady-state injection sources, reactive compensation and connection resistance

• The 1 K/h stabilization criterion, true-RMS measurement, thermal instrumentation

• Digital acquisition to IEC 61083-1:2021, uncertainty targets and offset removal before integration

Laboratory work

Five blocks on a real current impulse generator. Block 1, recognition and safety: identify bank, trigger gap, shaping inductor, return loop and fixed shunt; walk the earthing procedure and the bank discharge stick, because the 86 kJ of the worked example is lethal; review interlocks and the charging sequence. Block 2, an 8/20 wave with the coaxial shunt: fire into a reference resistive load, read peak, T1, T2 and undershoot in the software, and compare against the RLC prediction computed from the generator's nameplate C, L and R. Block 3, the same wave with a Rogowski coil around the return conductor: compare the two records point by point for phase, peak and integrated charge, then account for the deviations from coil position, integrator behaviour and shunt inductance. Block 4, the long-duration rectangular wave: fire the PFN into a resistor, verify Td, Tt and rectangularity, then deliberately mismatch the load and watch the reflected step appear — the travelling wave of Module 7 seen from the generation side. Block 5, integrals and reporting: compute Q and ∫i²dt from the records of blocks 2 to 4 with and without offset correction, estimate the adiabatic temperature rise of the shunt on the highest-energy shot, and run a short heating test on a training busbar with one joint deliberately left loose, located by thermography.

Key takeaway

Routine thermography flags a busbar joint 40 K above its neighbours under normal load. With this module you can close it out with numbers instead of parts. The physics is P = R_c·I², so 40 K under typical convection means tens to hundreds of watts and therefore tens to hundreds of microhms at a few thousand amperes. Confirm it de-energized with a four-wire micro-ohmmeter, because a two-wire reading measures the instrument leads and not the joint, and confirm with a split-core Rogowski that the circuit current is nominal and the problem is not overload. The root cause is lost contact pressure — torque relaxation, galvanic corrosion at a copper-aluminium interface, oxidation — and the prognosis is a feedback loop: more resistance, more temperature, more oxidation, thermal failure on a timescale of weeks. Fix it, re-torque to specification, re-measure the contact resistance and repeat the thermography under the same load. That is the difference between changing parts and doing engineering.

Module 8 of the Atlas Energy Academy · Generating & Measuring · about 6 hours · Video series plus hands-on laboratory practice · Prerequisites: Module 7 — Impulse Measurement and the Travelling Wave Problem