Introduction to High Voltage Testing

Non-destructive tests check the quality and condition of insulation at voltages near or below the working voltage, without damaging it. They find moisture, contamination, voids and ageing early, so faults can be corrected before a destructive failure. The main tests are measurement of resistance, dielectric constant and loss ($\tan\delta$), and partial discharges.

1. Measurement of insulation (DC) resistance and resistivity

• A DC voltage (500 V – 10 kV, from a megger or DC source) is applied and the leakage current is measured with a sensitive galvanometer or electrometer.
• A three-terminal (guard ring) electrode system separates volume current from surface leakage, giving volume resistivity $\rho_v$ and surface resistivity $\rho_s$.
• Polarization index $PI = R_{10\,min}/R_{1\,min}$ shows moisture and dirt: $PI > 2$ is good, $PI < 1$ is dangerous.
• Used on transformers, machines, cables and insulator units.

2. Measurement of dielectric constant and loss factor ($\tan\delta$)

            HV
          /    \
     Cx,Rx      Cs (standard)
        |        |
        A--[D]---B
        |        |
       R3     R4 || C4
          \    /
          earth

• The high-voltage Schering bridge is balanced; then

$$C_x = C_s\frac{R_4}{R_3}, \qquad \tan\delta = \omega C_4 R_4$$

• $\varepsilon_r = C_x/C_0$ ($C_0$ = capacitance with vacuum/air). A rise in $\tan\delta$ with voltage ("tip-up") or with time indicates moisture, voids and ageing.
• The transformer ratio-arm bridge is used for higher accuracy and for earthed specimens.
• Used on bushings, cables, CTs, capacitors and machine windings.

3. Partial discharge (PD) measurement

• Partial discharges in voids, cracks or at sharp edges produce small current pulses. They are detected with a coupling capacitor and a detection impedance in parallel with the test object (straight detection or balanced bridge circuit), and displayed on a PD detector/oscilloscope.
• The result is the apparent charge in picocoulombs (pC), the inception and extinction voltages, and the pulse pattern (phase-resolved).
• Calibrated by injecting a known charge $q = V_0 C_0$.
• Acoustic (ultrasonic) and UHF sensors locate PD in transformers and GIS.

4. Other non-destructive tests

• DC leakage current / step voltage test on cables and machines.
• Dissolved gas analysis and oil BDV tests for oil-filled equipment.
• Visual, ultrasonic and infrared (thermography) inspection for cracks and hot spots in insulators.
• Leakage current monitoring of surge arresters (third-harmonic resistive current).

Tests by type of insulation

General tests on high voltage equipment

High voltage equipment is tested to prove that its insulation can withstand the stresses it will meet in service. By their nature, the general tests are:

1. Sustained low-frequency (power-frequency) tests – withstand and flashover tests at 50/60 Hz, dry and wet (rain), usually for 1 minute; done on insulators, bushings, transformers, switchgear, cables.
2. High-voltage DC tests – for cables, capacitors and rotating machines, where AC testing would need very large charging current; also leakage current measurement.
3. High-frequency tests – at kHz frequencies, for insulators used with carrier/radio frequencies and to check behaviour under high-frequency transients.
4. Surge or impulse tests – lightning impulse (1.2/50 μs), switching impulse (250/2500 μs) and chopped wave tests, to prove the basic insulation level (BIL/BSL).

By purpose, tests are grouped as type tests (on one design sample), routine tests (on every unit), sample/acceptance tests, and non-destructive tests (insulation resistance, $\tan\delta$, capacitance, partial discharge measurement) that check condition without damaging the insulation.

Measurement using series resistance micro-ammeter

A very high resistance $R$ is connected in series with a micro-ammeter between the high voltage terminal and earth. The current is proportional to the voltage:

$$V = I\,R$$

  HV (V)
    |
   [R]  very high R, in oil/SF6 tube
    |
  ( uA )----+
    |       |  protective gap
    |      ===  or zener
    |       |
  earth ----+

• $R$ is built from many wire-wound or metal-film resistors in series, inside an insulating tube filled with oil or SF₆, with corona-free end caps. It is chosen to pass a small current (a few μA to about 1 mA at full voltage).
• The micro-ammeter is at earth potential, so it can be read safely; it is calibrated directly in kV.
• A protective device (paper spark gap, neon tube or zener diode) across the meter bypasses the current if $R$ flashes over.
• Used mainly for DC; also for AC when the resistor's stray capacitance is small.

Measurement using resistance potential divider

  HV (V) ---+
            |
           [R1]   high-voltage arm
            |
            +-------> V2 (to electrostatic
            |              voltmeter / CRO)
           [R2]   low-voltage arm
            |
  earth ----+

$$V = V_2\,\frac{R_1 + R_2}{R_2}$$

The low-voltage output $V_2$ is read by a high-impedance meter (electrostatic voltmeter, digital voltmeter or CRO). For impulses the divider is connected by a matched coaxial cable to an oscilloscope.

Sources of error and remedies

Accuracy of about ±0.2% to ±2% is obtained with careful construction.

An electrostatic voltmeter measures voltage from the attractive force between two charged electrodes. Since the force depends on $V^2$, it reads the true rms value of AC (of any waveform) and the value of DC, and it draws almost no current.

Principle

For two parallel plates of area $A$ separated by $x$, the stored energy is $W = \frac12 CV^2$ with $C = \varepsilon_0 A/x$. The force between the plates is

$$\begin{aligned} F &= \frac{dW}{dx} = \frac12 V^2\frac{dC}{dx} \\ &= -\frac12\,\frac{\varepsilon_0 A V^2}{x^2}\quad(\text{attraction}) \end{aligned}$$

For AC, $V = V_m\sin\omega t$, and the moving system responds to the average force:

$$F_{av} = \frac{\varepsilon_0 A}{2x^2}\cdot\frac1T\int_0^T v^2\,dt = \frac{\varepsilon_0 A}{2x^2}V_{rms}^2$$

So the deflection measures $V_{rms}$.

Construction (attracted-disc type)

          HV electrode  (V)
   ===============================
                 |  gap x
   ======  [ movable disc ]  =====
   guard     |  (earthed)    guard
   ring      |               ring
             +-- spring / balance
             +-- mirror -> lamp & scale
                 |
               earth

• High-voltage electrode: a large plane disc (or sphere) connected to the voltage to be measured.
• Low-voltage electrode: an earthed plane with a guard ring; a small movable disc sits in a hole at its centre, flush with the plane.
• The guard ring keeps the field over the movable disc uniform, so the simple parallel-plate formula holds and edge effects are removed.
• The movable disc is held by a spring or a balance beam. Its small movement is magnified by a mirror and light beam on a scale, or the force is balanced by weights or a restoring spring (absolute instruments such as the Kelvin attracted-disc electrometer).
• The whole system may be enclosed in compressed gas (N₂, SF₆) or vacuum to raise the range.

Working

1. Voltage is applied between the HV electrode and the earthed plane.
2. The movable disc is attracted towards the HV electrode with force proportional to $V^2$.
3. The disc moves until the spring force balances the electrostatic force; the deflection is read on the scale, calibrated directly in kV.
4. For range change, the gap $x$ is adjusted (larger gap for higher voltage).

Features

Ranges of about 600 kV in air and up to about 1000 kV with compressed gas insulation are achieved.

Methods for measurement of high AC voltages

Electrostatic voltmeter

An electrostatic voltmeter measures voltage from the attractive force between two charged electrodes. Since the force depends on $V^2$, it reads the true rms value of AC (of any waveform) and the value of DC, and it draws almost no current.

Principle

For two parallel plates of area $A$ separated by $x$, the stored energy is $W = \frac12 CV^2$ with $C = \varepsilon_0 A/x$. The force between the plates is

$$\begin{aligned} F &= \frac{dW}{dx} = \frac12 V^2\frac{dC}{dx} \\ &= -\frac12\,\frac{\varepsilon_0 A V^2}{x^2}\quad(\text{attraction}) \end{aligned}$$

For AC, $V = V_m\sin\omega t$, and the moving system responds to the average force:

$$F_{av} = \frac{\varepsilon_0 A}{2x^2}\cdot\frac1T\int_0^T v^2\,dt = \frac{\varepsilon_0 A}{2x^2}V_{rms}^2$$

So the deflection measures $V_{rms}$.

Construction (attracted-disc type)

          HV electrode  (V)
   ===============================
                 |  gap x
   ======  [ movable disc ]  =====
   guard     |  (earthed)    guard
   ring      |               ring
             +-- spring / balance
             +-- mirror -> lamp & scale
                 |
               earth

• High-voltage electrode: a large plane disc (or sphere) connected to the voltage to be measured.
• Low-voltage electrode: an earthed plane with a guard ring; a small movable disc sits in a hole at its centre, flush with the plane.
• The guard ring keeps the field over the movable disc uniform, so the simple parallel-plate formula holds and edge effects are removed.
• The movable disc is held by a spring or a balance beam. Its small movement is magnified by a mirror and light beam on a scale, or the force is balanced by weights or a restoring spring (absolute instruments such as the Kelvin attracted-disc electrometer).
• The whole system may be enclosed in compressed gas (N₂, SF₆) or vacuum to raise the range.

Working

1. Voltage is applied between the HV electrode and the earthed plane.
2. The movable disc is attracted towards the HV electrode with force proportional to $V^2$.
3. The disc moves until the spring force balances the electrostatic force; the deflection is read on the scale, calibrated directly in kV.
4. For range change, the gap $x$ is adjusted (larger gap for higher voltage).

Features

Ranges of about 600 kV in air and up to about 1000 kV with compressed gas insulation are achieved.

Why routine measurement of insulation is necessary

Insulation is the part of electrical equipment that ages fastest. In service it is attacked by heat, moisture, dirt, oil vapour, vibration, corona and voltage surges, and its resistance and strength fall slowly without any outward sign. Routine measurement is needed to:

• Detect deterioration early (moisture ingress, contamination, cracks, ageing) before it leads to breakdown.
• Prevent unplanned outages and costly damage to transformers, motors, cables and generators.
• Ensure safety of people against leakage currents and shocks.
• Build a trend record: comparison with earlier readings shows the rate of ageing, which is more useful than a single value.
• Plan maintenance (drying, cleaning, rewinding, replacement) and check equipment after repair or long shutdown before energizing.

Interpretation from leakage current

When a DC test voltage is applied, the total current has three components:

 I
 |\
 | \  capacitive charging (dies in seconds)
 |  \
 |   \__  absorption (decays over minutes)
 |      \_____
 |            ------- conduction/leakage (steady)
 +------------------------------------> t

Insulation resistance $R = V/I$. Results are read as follows:

1. Current versus time (constant voltage)

• Current falls steadily with time and settles to a low value: absorption dominates, insulation is clean and dry.
• Current stays nearly constant from the start: leakage dominates, insulation is wet or dirty.
• Current rises with time or jumps erratically: serious defect, possible imminent breakdown.

This is expressed as the polarization index $PI = R_{10\,min}/R_{1\,min} = I_{1\,min}/I_{10\,min}$ (and dielectric absorption ratio $DAR = R_{60\,s}/R_{30\,s}$):

2. Current versus voltage (step-voltage test)

• Leakage current rises linearly with voltage (constant $R$): insulation is healthy.
• Current rises faster than voltage, with a "knee" in the curve: weak spots, cracks, moisture or contamination; the test is stopped before breakdown.

3. Comparison

• Compare with previous readings, with phases of the same machine and with similar equipment; a sudden fall in $R$ (rise in leakage) is more significant than the absolute value.
• Correct readings to a reference temperature (insulation resistance roughly halves for every 10 °C rise), since leakage current increases with temperature and humidity.

Gaseous and liquid insulation lose strength when impurities such as moisture, particles, air and decomposition products build up. They are therefore monitored periodically (and online) by sampling and by sensors fitted on the equipment. Rising impurity levels warn of internal faults (arcing, overheating, partial discharge) and of the need to filter, dry or replace the dielectric.

A. Gaseous dielectrics (mainly SF₆ in GIS and breakers)

• Moisture is critical: it condenses on spacers at low temperature and causes surface flashover, and reacts with arc products to form corrosive HF.
• High SO₂/SOF₂ indicates arcing or partial discharge inside the compartment.
• Gas is reclaimed (filtered, dried) using gas-handling carts when limits are exceeded.

B. Liquid dielectrics (transformer and cable oil)

1. Breakdown voltage (BDV) test

• Oil sample is placed in a test cell with two electrodes 2.5 mm apart (IEC 60156); voltage is raised at 2 kV/s until breakdown; mean of 6 readings.
• Low BDV indicates moisture and particles. Typical good oil: above about 50–60 kV.

2. Moisture content – Karl Fischer titration (IEC 60814), in ppm; online moisture sensors.

3. Dissolved gas analysis (DGA) – gases dissolved in oil are extracted and measured by gas chromatography (IEC 60599). The gas pattern identifies the fault:

Ratio methods (Rogers, IEC ratio, Duval triangle) are used for diagnosis.

4. Dielectric loss ($\tan\delta$) and resistivity – measured in a test cell at 90 °C; rise indicates polar contaminants and ageing products.

5. Acidity (neutralization number) and interfacial tension (IFT) – rising acidity and falling IFT show oxidation and sludge formation.

6. Furan analysis – furanic compounds (by HPLC) indicate ageing of paper insulation.

7. Others – particle count, colour, flash point, sludge content, and online sensors for hydrogen and moisture.

Oil found contaminated is treated by filtering, vacuum dehydration and degassing, or by regeneration with Fuller's earth.

Tests on high voltage equipment prove that its insulation withstands the voltages it will meet in service. The general tests are:

1. Sustained power-frequency tests – 50 Hz withstand and flashover tests, dry and wet, usually for 1 minute.
2. High-voltage DC tests – for cables, capacitors and machines, with leakage current measurement.
3. High-frequency tests – for insulators exposed to high-frequency (carrier, transient) voltages.
4. Impulse (surge) tests – lightning impulse 1.2/50 μs, switching impulse 250/2500 μs and chopped waves, to verify BIL.

By purpose they are done as type tests (one unit of a design), routine tests (every unit) and acceptance/sample tests, supported by non-destructive checks such as insulation resistance, $\tan\delta$ and partial discharge measurement.

Types of tests on high voltage equipment

• By purpose: type tests (on one sample of a design), routine tests (on every unit), sample/acceptance tests, and special tests.
• By voltage: power-frequency withstand and flashover tests (dry and wet), DC tests, high-frequency tests, and impulse tests (lightning 1.2/50 μs and switching 250/2500 μs); plus non-destructive tests such as $\tan\delta$ and partial discharge.

Measurement of high voltage using sphere gaps

A sphere gap consists of two identical polished metal spheres separated by an air gap. The uniform field between spheres gives a breakdown voltage that is accurately known (IEC 60052 / IEEE Std 4 tables) for a given sphere diameter $D$ and spacing $S$. By noting the spacing at which flashover occurs, the peak value of AC, DC or impulse voltage is found.

  HV test     R (series
  source ----/\/\/\----+
  (AC/DC/              |
  impulse)          ( HV )  upper sphere
     |               |  S   gap spacing
     |              ( E  )  lower sphere
     |               |      (earthed)
     +-------earth---+

Construction and arrangement

• Two equal spheres of copper, brass or aluminium, of standard diameters (2, 5, 6.25, 10, 12.5, 15, 25, 50, 75, 100, 150, 200 cm).
• Small spheres are mounted horizontally; large spheres (about 50 cm and above) vertically with the lower sphere earthed.
• Shafts, supports and nearby objects must keep the clearances given in the standard so that the field is not disturbed.
• A series resistor limits the current at flashover, protects the sphere surfaces from pitting and damps oscillations: about 100 kΩ to 1 MΩ for AC and DC; a low, non-inductive value (below about 500 Ω) for impulses so the wave is not distorted.

Procedure

1. Set the spacing $S$ larger than expected; apply the voltage.
2. For AC/DC, raise the voltage slowly (or reduce the gap) until flashover occurs; repeat several times and take the mean.
3. For impulses, find the 50% flashover voltage: the spacing at which half of the applied impulses cause flashover.
4. Read the standard breakdown voltage $V_s$ (kV peak) for that $D$ and $S$ from the table.

Correction for air density

Tables are for 20 °C and 760 mm Hg. Relative air density

$$\delta = \frac{b}{760}\times\frac{293}{273 + t} = \frac{0.386\,b}{273 + t}$$

($b$ in mm Hg, $t$ in °C). The actual breakdown voltage is $V = kV_s$, where $k$ is a correction factor; for $0.95 < \delta < 1.05$, $k \approx \delta$.

Factors affecting accuracy

• Spacing should not exceed $0.5D$ for ±3% accuracy (up to $0.75D$ with lower accuracy).
• Nearby earthed objects and the shaft affect the field.
• Dust, fibres and humidity cause erratic flashovers; spheres must be clean and smooth.
• For gaps below about 1 cm (and impulse tests) the gap is irradiated with UV light or a radioactive source to provide initiating electrons and reduce scatter.

Advantages: measures peak of AC, DC and impulse voltages; simple, rugged; used to calibrate other instruments. Limitations: the measuring process causes flashover, so it cannot monitor voltage continuously, and corrections are needed.

General tests on high voltage equipment

High voltage equipment is tested to prove that its insulation can withstand the stresses it will meet in service. By their nature, the general tests are:

1. Sustained low-frequency (power-frequency) tests – withstand and flashover tests at 50/60 Hz, dry and wet (rain), usually for 1 minute; done on insulators, bushings, transformers, switchgear, cables.
2. High-voltage DC tests – for cables, capacitors and rotating machines, where AC testing would need very large charging current; also leakage current measurement.
3. High-frequency tests – at kHz frequencies, for insulators used with carrier/radio frequencies and to check behaviour under high-frequency transients.
4. Surge or impulse tests – lightning impulse (1.2/50 μs), switching impulse (250/2500 μs) and chopped wave tests, to prove the basic insulation level (BIL/BSL).

By purpose, tests are grouped as type tests (on one design sample), routine tests (on every unit), sample/acceptance tests, and non-destructive tests (insulation resistance, $\tan\delta$, capacitance, partial discharge measurement) that check condition without damaging the insulation.

Electrostatic voltmeter

An electrostatic voltmeter measures voltage from the attractive force between two charged electrodes. Since the force depends on $V^2$, it reads the true rms value of AC (of any waveform) and the value of DC, and it draws almost no current.

Principle

For two parallel plates of area $A$ separated by $x$, the stored energy is $W = \frac12 CV^2$ with $C = \varepsilon_0 A/x$. The force between the plates is

$$\begin{aligned} F &= \frac{dW}{dx} = \frac12 V^2\frac{dC}{dx} \\ &= -\frac12\,\frac{\varepsilon_0 A V^2}{x^2}\quad(\text{attraction}) \end{aligned}$$

For AC, $V = V_m\sin\omega t$, and the moving system responds to the average force:

$$F_{av} = \frac{\varepsilon_0 A}{2x^2}\cdot\frac1T\int_0^T v^2\,dt = \frac{\varepsilon_0 A}{2x^2}V_{rms}^2$$

So the deflection measures $V_{rms}$.

Construction (attracted-disc type)

          HV electrode  (V)
   ===============================
                 |  gap x
   ======  [ movable disc ]  =====
   guard     |  (earthed)    guard
   ring      |               ring
             +-- spring / balance
             +-- mirror -> lamp & scale
                 |
               earth

• High-voltage electrode: a large plane disc (or sphere) connected to the voltage to be measured.
• Low-voltage electrode: an earthed plane with a guard ring; a small movable disc sits in a hole at its centre, flush with the plane.
• The guard ring keeps the field over the movable disc uniform, so the simple parallel-plate formula holds and edge effects are removed.
• The movable disc is held by a spring or a balance beam. Its small movement is magnified by a mirror and light beam on a scale, or the force is balanced by weights or a restoring spring (absolute instruments such as the Kelvin attracted-disc electrometer).
• The whole system may be enclosed in compressed gas (N₂, SF₆) or vacuum to raise the range.

Working

1. Voltage is applied between the HV electrode and the earthed plane.
2. The movable disc is attracted towards the HV electrode with force proportional to $V^2$.
3. The disc moves until the spring force balances the electrostatic force; the deflection is read on the scale, calibrated directly in kV.
4. For range change, the gap $x$ is adjusted (larger gap for higher voltage).

Features

Ranges of about 600 kV in air and up to about 1000 kV with compressed gas insulation are achieved.

The dielectric constant ($\varepsilon_r$) of an insulating material is the ratio of the capacitance of a specimen to its capacitance with vacuum (air) as dielectric. The loss factor is $\varepsilon_r\tan\delta$, where $\tan\delta$ (dissipation factor) is the ratio of the loss (resistive) current to the charging (capacitive) current. Both are measured by bridge methods at power and higher frequencies; the most common is the high-voltage Schering bridge.

  Ix     Ic (leading by 90 deg)
   \     |
    \    |   delta = angle between
     \   |   Ix and Ic
      \d |
       \ |
  ------+--------> Ir (in phase with V)

$$\tan\delta = \frac{I_R}{I_C}, \qquad \text{loss } P = V^2\omega C\tan\delta$$

1. High-voltage Schering bridge

              HV supply (V)
              /           \
      Arm 1  /             \ Arm 2
    Cx + Rx                 Cs (standard,
   (specimen)               loss-free)
          |                   |
          A------[ D ]--------B
          |                   |
      Arm 3: R3        Arm 4: R4 || C4
          \                  /
            ----- earth ----

• Arm 1: test specimen, represented as $C_x$ in series with $R_x$.
• Arm 2: standard compressed-gas capacitor $C_s$ (loss-free).
• Arm 3: variable non-inductive resistance $R_3$.
• Arm 4: fixed resistance $R_4$ in parallel with a variable capacitor $C_4$.
• D: vibration galvanometer or electronic null detector.
• Arms 3 and 4 are at low voltage (near earth), so adjustments are safe; protective gaps across them guard against a breakdown of $C_x$ or $C_s$. Earthed shields (Wagner earth) remove errors due to stray capacitance.

Balance condition $Z_1 Z_4 = Z_2 Z_3$:

$$\left(R_x + \frac{1}{j\omega C_x}\right)\frac{R_4}{1 + j\omega C_4R_4} = \frac{R_3}{j\omega C_s}$$

Equating real and imaginary parts:

$$\begin{aligned} C_x &= C_s\,\frac{R_4}{R_3} \\ R_x &= R_3\,\frac{C_4}{C_s} \\ \tan\delta &= \omega C_x R_x = \omega C_4 R_4 \end{aligned}$$

Usually $R_4 = \frac{1000}{\pi}\ \Omega$ so that at 50 Hz $\tan\delta = C_4$ in μF directly.

Dielectric constant: with specimen thickness $d$ and electrode area $A$, $C_0 = \varepsilon_0 A/d$, and

$$\varepsilon_r = \frac{C_x}{C_0} = \frac{C_x\,d}{\varepsilon_0 A}, \qquad \text{loss factor} = \varepsilon_r\tan\delta$$

A three-terminal (guard-ring) electrode system is used so that surface leakage and edge fringing do not affect the result.

2. Transformer ratio-arm bridge

• Uses a precision ratio transformer (ratio arms) instead of resistive arms; balance is set by turns ratios $N_s/N_x$.
• $C_x = C_s N_s/N_x$ and $\tan\delta$ from the conductance balance.
• Advantages: very high accuracy, unaffected by stray capacitances to earth, can test earthed specimens, works over a wide frequency range.

3. Other methods

• Resonance (Q-meter) method for high frequencies (kHz–MHz): change in resonance capacitance gives $C_x$, change in Q gives $\tan\delta$.
• Measurements versus voltage and temperature: $\tan\delta$ rising with voltage ("tip-up") indicates voids and partial discharge; rising with temperature indicates moisture and ageing.

A series impedance voltmeter measures a high AC voltage by passing a small current through a known high impedance (resistance or capacitance) in series with a low-range ammeter. The ammeter is at earth potential, and the voltage is calculated from the current.

Construction

  HV (V) ---[ Z: high R or C ]---+
                                  |
                              (  A  )  microammeter
                                  |    with protective
                             gap / zener across it
                                  |
  earth --------------------------+

• Series impedance $Z$: either
  • a very high resistance (wire-wound or carbon/metal-film resistors in series, housed in an insulating tube filled with oil or SF₆, with corona-free end caps), or
  • a capacitor (compressed-gas standard capacitor) for AC.
• Ammeter: a moving-coil microammeter (with rectifier for AC) or a sensitive AC ammeter at the earthed end.
• Protection: a spark gap, neon glow tube or zener diodes across the ammeter so that a flashover of $Z$ does not put full voltage across the meter.

Working principle

(a) Series resistance: current $I = V/R$, so

$$V = I\,R$$

With residual inductance $L$ the impedance is $Z = R + j\omega L$ and $V = I\sqrt{R^2 + \omega^2L^2}$; $R$ is chosen so that $\omega L \ll R$.

(b) Series capacitance: current $I = j\omega C V$, so

$$V = \frac{I}{\omega C}$$

If a rectifier and moving-coil meter is used in the capacitor arm, the meter reads the mean of the rectified charging current, $I_{av} = 2fCV_m$, from which the peak voltage $V_m = I_{av}/(2fC)$ is obtained (Chubb–Fortescue principle). The scale is calibrated directly in kV.

Typical currents are a few μA to about 1 mA, so the impedance is very high, e.g. about $10^{9}$–$10^{11}$ Ω for resistive arms at hundreds of kV.

Drawbacks

1. Stray capacitance and inductance: the long resistor has distributed capacitance to earth and residual inductance, so its impedance changes with frequency; errors increase for harmonics and high frequency.
2. Heating and temperature coefficient: power loss $I^2R$ heats the resistor; resistance changes with temperature, causing drift.
3. Corona and leakage: corona at terminals and leakage over the insulating surface add to the measured current, giving wrong readings at very high voltages.
4. Harmonics (capacitive type): current in a capacitor is proportional to frequency, so harmonics in the waveform cause large errors; also depends on exact supply frequency.
5. Waveform dependence: reads rms or mean, not peak (except the rectifier version), while breakdown depends on peak.
6. Bulky and costly for voltages above a few hundred kV; risk of damage to the meter on flashover without protection.