AC High Voltage Measurement

Generating 100 kV is useless if you cannot say how much is on the object.

There is a curious asymmetry in high voltage engineering. Generating kilovolts has been a solved problem for a century: cascades and resonant circuits produce hundreds of kilovolts as industrial routine. Measuring those kilovolts with a declared accuracy is still a discipline in motion, which is why IEC published a fourth edition of IEC 60060-2 in 2025, revising exactly the treatment of measurement uncertainty. The reason is physical. At low voltage the voltmeter connects directly and its burden is negligible. At high voltage no instrument survives full voltage, so a converting device has to be interposed — a divider, a voltage transformer or a sphere gap — that reduces the quantity to a measurable level.

That device interacts with the test circuit. It loads the source, it feels the stray capacitance of everything around it, it heats up, it ages. What appears on the display is not the voltage across the object; it is the voltage across the object seen through a chain of imperfect transformations. The craft of high voltage measurement consists of making those imperfections known, stable and small enough to fit inside the uncertainty the standard tolerates. And the standard tolerates little: withstand test values are applied within ±1% and measured with an expanded uncertainty no greater than 3%. A laboratory whose system errs by 5% can pass a transformer that would have failed the correct test, or fail a perfectly sound one at direct commercial cost.

What you will be able to do

• Choose between a resistive and a capacitive divider by application — voltage, frequency, test duration and required accuracy — and justify the choice by naming the dominant error mechanism in each: heating and stray capacitance in the resistive, cable and instrument loading in the capacitive.

• Measure crest voltage with sphere gaps per IEC 60052, applying air density and humidity corrections, respecting the tabulated clearances and the normative limit s ≤ 0.5·D.

• Build the calibration curve of a test transformer and explain why the turns ratio is not an acceptable measurement method.

• Decompose the measuring chain into its three blocks — converting device, transmission system, instrument — and assign the systematic error sources of each.

• Interpret the IEC 60060-2 requirements for an approved measuring system: assigned scale factor, calibration by comparison against a reference system at a minimum of five levels, expanded uncertainty ≤ 3% with k = 2, and a living performance record.

• Explain why the AC test value is the crest divided by √2 rather than the RMS value, and use the comparison between the two as a free waveshape diagnostic.

A measuring system, not a voltmeter

IEC 60060-2 does not speak of a high voltage voltmeter. It speaks of a measuring system: a complete set of devices intended to measure the test value, treated as a single metrological entity. The chain has three blocks. The converting device — divider, voltage transformer or sphere gap — turns high voltage into a proportional low-level signal. The transmission system, typically a coaxial cable with any attenuators and impedance matching, carries that signal from the test bay to the control room. The instrument — peak voltmeter, RMS voltmeter or digital recorder under the IEC 61083 series — displays or records the reading.

Each block multiplies the signal by a factor of its own, and the product of all of them is the scale factor F of the system. Instrument reading times F is the high voltage. The practical consequence is immediate: anything that changes one partial factor — swapping the coaxial cable for a longer one, replacing the instrument, changing input impedance — changes the scale factor of the whole system and invalidates the standing calibration. A measuring system is calibrated as assembled. There is no calibration of the divider alone that survives a change in the rest of the chain without verification.

The standard separates the reference measuring system, calibrated to within 1% for alternating voltages and used only to calibrate other systems, from the approved measuring system, the laboratory's working instrument, which must demonstrate an expanded uncertainty of the voltage value no greater than 3% with a coverage factor k = 2. Approval comes from calibration by comparison at a minimum of five levels spread between roughly 20% and 100% of the working range. But calibration is a photograph of one day. Keeping it valid is the job of the performance record: periodic calibration, intermediate scale factor checks, linearity, stability, temperature and proximity effects. That dossier, not the certificate on the wall, is what an ISO/IEC 17025 assessor asks to see.

The resistive divider has a frequency expiry date

A resistive divider is conceptually the simplest solution: a column of series resistors as the high arm R₁ and a low-value resistor R₂ from which the reduced voltage is taken, with U₁/U₂ = (R₁+R₂)/R₂. Sizing is a three-way compromise. First, thermal dissipation: at 100 kV a 100 MΩ column carries 1 mA and dissipates 100 W, which heats the resistors, shifts their resistance by tens to hundreds of ppm per kelvin, and therefore shifts the scale factor during the test itself. Practice limits column current to roughly 0.5 to 2 mA, which pushes R₁ into the hundreds of megohms at the higher voltages. Second, source loading: the divider current adds to the capacitive load current and, in high-Q resonant sources, can move the operating point.

Third, and decisive on AC, are the stray capacitances. Each section of the column presents a distributed capacitance to the grounded structures around it of the order of 10 to 20 pF per metre. On DC these are invisible. At 60 Hz they divert column current to earth unevenly along the height, the voltage distribution stops being uniform, and the division ratio becomes frequency dependent. The error grows with the product R₁·Ce, which is an elegant dead end: the higher resistance needed to limit heating and the greater height needed to hold off the voltage both make the response worse. Purely resistive dividers are therefore excellent on DC and usable on AC only to moderate voltages, of the order of 100 kV, or with guard shields at considerable cost.

The capacitive divider and the compressed-gas standard capacitor

In a capacitive divider the high arm is a small capacitor C₁, typically 40 to 100 pF, and the low arm is a much larger C₂, with U₁/U₂ = (C₁+C₂)/C₁. Column current is purely reactive: no dissipation, no heating, no self-induced thermal drift. That is the first advantage over the resistive. The second is the achievable quality of the high arm. A compressed-gas standard capacitor, with coaxial electrodes in SF₆ or nitrogen at roughly 10 to 15 bar, holds its capacitance within a few tens of ppm, shows a loss factor tan δ below 10⁻⁵, and behaves almost ideally from 50 Hz to hundreds of kilohertz. It is the same component that later serves as the reference capacitor in a Schering bridge for tan δ work and as the coupling capacitor for partial discharge measurement, so the laboratory amortises the investment three times.

No heating does not mean no error; the errors change address. The coaxial cable adds around 100 pF/m electrically to C₂, so a divider calibrated with 10 m and used with 25 m has a different scale factor — which is why IEC 60060-2 treats the cable as part of the measuring system. The instrument input impedance in parallel with C₂ forms a high-pass filter, harmless with 10 MΩ and 1 µF, worth checking with a 1 MΩ input. And the stray capacitances of the C₁ column change the effective capacitance with the geometry of the setup, so distance to the walls and height of the bus move the scale factor. That is the proximity effect, which IEC 60060-2 requires to be quantified in the performance record.

Sphere gaps: the physical standard of the crest

The sphere gap is the oldest and the most physically transparent measurement method in the field. Two polished metal spheres of diameter D, separated by a gap s, break down the air between them at a crest voltage that, with the geometry and atmospheric conditions held at reference, is reproducible within ±3%. There is no electronics to calibrate. The scale of the instrument is the dielectric strength of air itself, tabulated internationally in IEC 60052. As long as the gap does not exceed half the diameter, s ≤ 0.5·D, the field on the axis is quasi-uniform, breakdown follows the streamer criterion with minimal statistical scatter, and the voltage-spacing relation is nearly linear. Above 0.5·D the field becomes increasingly non-uniform, corona precedes breakdown, scatter rises and the tabulated values become merely indicative.

IEC 60052 standardises sphere diameters from 2 to 200 cm and assumes a controlled neighbourhood, tabulating the height A of the sparking point above the ground plane and a clear radius B around it. Ignoring those clearances is the classic beginner error: a nearby wall distorts the field, reduces the breakdown voltage and makes the gap read a few per cent low, a silent systematic error. Tabulated values hold at 20 °C, 101.3 kPa and 8.5 g/m³. Outside that, correct for relative air density, δ = (p/101.3)·(293/(273+t)) with p in kPa and t in °C; for 0.95 ≤ δ ≤ 1.05 the corrected value is simply U = δ·U₀. A laboratory at 900 m and 30 °C runs at δ ≈ 0.88 and breaks down some 12% below the table. Humidity works the other way, at about +0.2% per g/m³ above reference. The measurement is ritual: raise to breakdown repeatedly, discard the first sparks as conditioning, and take the mean of a consecutive series whose scatter stays within about 1%.

Hunting systematic error, and the number you actually sign

Random error announces itself: repeat the measurement and the scatter appears. Systematic error is the dangerous one, because it hides in constancy. The system errs by the same amount, in the same direction, every time, and no amount of repetition reveals it. The professional defence is deliberate confrontation — exposing the system to conditions that turn a systematic error into a visible discrepancy. Move the divider and measure the same voltage in both positions to expose proximity. Verify the scale factor whenever any component of the chain is replaced. Compare crest ÷ √2 against the measured RMS: a divergence beyond about 2% denounces a waveshape outside the IEC 60060-1 peak-to-RMS tolerance, and the oscilloscope confirms it. Measure the same voltage in the first minute and after thirty minutes of application to reveal the thermal signature of a resistive divider. One tempting shortcut deserves burial: reading 220 V on the primary of a 1:500 test transformer does not mean 110 kV on the secondary. Under capacitive load the leading current through the short-circuit reactance raises the secondary voltage above the turns ratio by 5 to 15%, and the error grows with the load. The correct procedure is the calibration curve, taken with a reliable high-side system at several levels for the load actually connected, redone whenever the load changes and never extrapolated past the last measured point.

When two independent systems disagree, the answer is procedural rather than aesthetic. Suppose the capacitive divider reads 98.2 kV and the sphere gap, after correction, reads 95.4 kV — a 2.9% deviation. It fits inside the combined uncertainties, so it is uncomfortable but not proof of a defect. Audit the weaker link first: a badly run sphere gap errs more often than a calibrated divider. Then interrogate the waveshape. Then sign the value from the approved measuring system with current traceable calibration, log the gap check in the performance record, and if the deviation persists, investigate before the next report. Mature laboratories never depend on a single path to the voltage value. The divider measures continuously, the gap verifies occasionally, and the crest against RMS comparison watches the waveshape.

Syllabus

• The measuring system as one metrological entity: converting device, transmission system, instrument

• Scale factor as the product of partial factors, and why changing any component invalidates the calibration

• Reference measuring system (≤ 1% for AC) versus approved measuring system (≤ 3%, k = 2)

• Calibration by comparison at five or more levels from about 20% to 100% of the working range

• The performance record: periodic calibration, linearity, short and long term stability, temperature and proximity effects

• Why the test value is crest ÷ √2 and the peak voltmeter is the canonical instrument

• Resistive dividers: column current between 0.5 and 2 mA, thermal drift, source loading

• Stray capacitance to earth of 10 to 20 pF per metre and the collapse of frequency response

• Guard shields and toroidal grading electrodes; where the resistive divider still wins

• Capacitive dividers: the compressed-gas standard capacitor, stability in tens of ppm, tan δ below 10⁻⁵

• Coaxial cable capacitance adding to the low arm, input impedance loading, and the proximity effect

• Sphere gaps per IEC 60052: quasi-uniform field, the s ≤ 0.5·D rule, sphere diameters and clearances A and B

• Atmospheric corrections: relative air density δ = (p/101.3)·(293/(273+t)) and the humidity correction

• Chubb-Fortescue peak measurement and modern digital recorders under IEC 61083-1 and -2

• Instrument voltage transformers in the laboratory: burden range, bandwidth and ferroresonance

• Systematic error hunting and the discipline of metrological redundancy

Laboratory work

Continue the AC bench setup from the previous module and add a confrontation between two independent measuring systems. Step one, preparation: check the grounding, delimit the area, verify sphere gap clearances A and B per IEC 60052, clean and visually inspect the spheres, and record ambient temperature, pressure and humidity with calibrated instruments. Step two, capacitive divider: energise in steps of 20, 40, 60, 80 and 100% of the test level, recording crest ÷ √2 and RMS at each step and checking the ratio against √2 ±5%. Step three, sphere gap: set s for the target level with s ≤ 0.5·D, raise smoothly to breakdown, discard the first two sparks, record five consecutive breakdowns with scatter within 1%, compute δ and the humidity correction, and obtain the corrected crest. Step four, confrontation: compute the percentage deviation between the two systems and compare against the sum of the uncertainties, discussing the cause if it exceeds expectation. Step five, calibration curve: with the divider as reference, record real high voltage against primary voltage at five points with the load connected, fit a line, and quantify the departure from the nominal turns ratio. Deliverable: a report with the measurement table, the atmospheric corrections worked step by step, the fitted calibration curve, and a half-page opinion answering which system you would sign, and with what uncertainty.

Key takeaway

High voltage measurement is not about choosing the friendlier number. It is about knowing which number has metrological backing and documenting the confrontation that proved it. Calibrate the system as assembled, keep the performance record alive, never infer the test voltage from the turns ratio, and build a second independent path to the same value so that a systematic error has somewhere to show itself.

Module 4 of the Atlas Energy Academy · Generating & Measuring · about 4 hours · Video series plus hands-on AC bench practice (part B) · Prerequisites: Module 3 — AC High Voltage Generation