Measurement of High DC and AC Voltages

A multimeter reads a few hundred volts because the voltage sits comfortably across its internal resistance and the resulting current is small and safe. Scale that up to a hundred kilovolts and two things break at once. First, the insulation of any ordinary instrument flashes over long before the needle moves — the voltage simply jumps the air gap inside the case. Second, and more subtly, there is the loading problem: to read a voltage you must draw at least a little current, and at high voltage even a "little" current can be a significant load on a source whose own internal resistance is large. Connect the meter and the voltage you wanted to measure sags to a new, lower value — you have measured something, but not the thing you came to measure.

Every method in this chapter is therefore a way of scaling the voltage down by a known ratio while drawing as little from the source as possible. There are only three physical handles to pull, and the whole chapter is an exploration of them:

The simplest realisation of the first strategy puts a very large resistance \(R\) — typically hundreds of megohms — in series with a sensitive microammeter, the whole string connected across the voltage to be measured. The current that flows is tiny but perfectly proportional to the voltage, and Ohm's law turns the reading straight into volts:

The practical difficulties all live in that one large resistor. It must be subdivided into many short sections, often immersed in oil or fitted with grading shields, so that no single piece sees enough field to flash over or to bleed current away as corona. Its value must be stable with temperature, because a drifting \(R\) drifts the calibration directly. And it dissipates power \(V^2/R\): make \(R\) too small to keep the current readable and the resistor cooks; make it too large and stray leakage along its surface competes with the wanted current. For these reasons the series-resistance method is the standard up to a few tens of kilovolts, and is pushed higher only with care.

The second strategy keeps a resistor string but reads a voltage across part of it rather than the current through all of it. Two resistors in series, a large high-voltage arm \(R_1\) and a small low-voltage arm \(R_2\), share the same current; the voltage across the lower arm is therefore a fixed fraction of the whole, set by the ratio of the resistances:

The divider trades one problem for another. Choosing the current through the chain is now a balancing act: it must be large enough to swamp the leakage currents and the loading of the meter across \(R_2\), yet small enough that the arms do not overheat. The meter's own resistance must be far larger than \(R_2\), or it draws off part of the current and lowers the apparent ratio — the loading error in a new guise. Resistance dividers are natural for DC, where there is nothing for a capacitor to react against; for AC they suffer because stray capacitance to ground turns the clean resistive ladder into a frequency-dependent RC network, distorting the ratio. That is the cue to switch dielectrics.

Both methods so far draw a steady current, and so they load the source — fatal for a high-impedance HVDC supply whose voltage you must not disturb. The generating voltmeter sidesteps this entirely by drawing, on average, no current at all. It is a small capacitor formed between a fixed measuring electrode and a rotating, earthed vane that periodically covers and uncovers it. As the vane turns, the capacitance \(C\) between the electrode and the high-voltage plane swings cyclically; with the voltage \(V\) held constant, the charge \(q = C V\) on the electrode must rise and fall, and that flow of charge is a current proportional to the voltage:

The rectified, averaged current is proportional to \(V\) and to the speed of rotation, so once the geometry and speed are fixed the meter reads volts on a linear scale. Its great virtues are that it imposes essentially no load on the source and needs no direct conducting connection to the high-voltage conductor — the measuring head can sit at earth potential and "look" at the field. The same principle, with the rotating vane sampling the ambient field rather than a defined plane, becomes the field mill used to measure surface fields and atmospheric electricity. The price is a moving part and a calibration that depends on a fixed, repeatable geometry.

For alternating voltage the cleanest series element is not a resistor but a capacitor. A capacitor passes AC in proportion to frequency and capacitance, and — crucially — it dissipates no power, so it does not heat up the way a series resistor would. Place a known capacitance \(C\) in series with the source and an ammeter at the earthed end; the charging current is simply

This is the alternating-current mirror of the series-resistance microammeter: there \(V = IR\), here \(V = I/(\omega C)\). The reactance \(1/\omega C\) plays exactly the part the resistance played, and because it is lossless the method scales to higher voltages comfortably. Its accuracy hinges on knowing \(f\) and \(C\) well, and on the capacitor being free of loss and stray capacitance. Reading the rectified rather than the RMS current leads to a measurement of the peak value — the basis of the Chubb–Fortescue method we meet in the next chapter — but for now the message is just that for AC, capacitance replaces resistance as the natural series element.

Just as the resistance microammeter had its divider cousin, the capacitive method has one too. Two capacitors in series — a small high-voltage capacitor \(C_1\) and a large low-voltage capacitor \(C_2\) — carry the same charge, so the voltage across the lower one is a fixed fraction of the whole. Note the ratio inverts relative to the resistive divider, because for a given charge the smaller capacitor takes the larger voltage:

The capacitive divider is fast, lossless and stable, which makes it the workhorse for AC and the natural choice for impulse dividers in Chapter 17. Pushed one step further it becomes the capacitor voltage transformer (CVT) found on every high-voltage substation: the divider taps a manageable fraction of the line voltage, and a tuned inductor and small electromagnetic transformer then step that fraction down to the standard instrument level, with the inductor resonating against the divider capacitance so the burden of the connected meters and relays does not spoil the ratio. The CVT does double duty, also coupling power-line-carrier communication signals onto the line.

The third strategy abandons current and ratio altogether and reads the voltage from the force its field exerts. Two electrodes at different potentials attract one another; for a parallel-plate geometry of area \(A\) and spacing \(d\) the attractive force is

Three things follow from that one formula. First, the force depends on the square of the voltage, so on AC the instrument naturally averages \(V^2\) and reads the true RMS value — and it reads DC just as happily. Second, the moving electrode is purely a charged plate: in the steady state it draws no current at all on DC and only a vanishing charging current on AC, so the loading is negligible. Third, in the precision attracted-disc (Kelvin) absolute form, the voltage is recovered from nothing but a measured force, an area, a spacing and the constant \(\varepsilon_0\) — no calibrated standard of resistance or capacitance is needed, which is why it serves as an absolute reference. The square-law does crowd the low end of the scale, and the instrument spans roughly a few kilovolts up to a few hundred kilovolts, but for a direct, non-loading, true-RMS reading it is unmatched.

With AC there is a question that does not arise for DC: which value of the waveform are you measuring? The mean, the RMS and the peak are different numbers, and they coincide only for a pure sinusoid through the familiar factors \(V_{\text{rms}} = V_{\text{peak}}/\sqrt2\). The distinction is not academic — insulation breaks down on the peak, so for withstand and flashover work the peak is what matters, while heating and dielectric loss follow the RMS. Each method in this chapter has its own answer, and choosing an instrument means first deciding which value you need.

*The capacitor-and-ammeter route reports the RMS with a true-RMS meter, but the rectified version of it reports the peak — the Chubb–Fortescue circuit of Chapter 16.

For each item, first identify what it tests — the loading idea, a series formula, a divider ratio, the generating principle or the force law — then apply it. Difficulty rises down the list.