Selecting a VLF Tester Based on Cable Length and Capacitance

Selecting a VLF Tester Based on Cable Length and Capacitance

Most VLF enquiries open the same way: "I need a set for 15 kV cable." Voltage class is the easy question, and it is not the one that decides whether the test will run. Two 15 kV feeders, one 300 m long and one six kilometres long, are not the same test. What separates them is capacitance, and you get capacitance from length.

This article sets out the relationship between length, capacitance and the load a VLF set has to carry, works two examples through, and then covers what the numbers alone will not tell you. It is a sizing note, not a product catalogue.

Voltage class tells you how high the test voltage must go. Length tells you how much charge the set must move to get there, and therefore how much current it must deliver at the chosen frequency. A set that reaches 35 kV on a 400 m tail may be unable to reach the same voltage on five kilometres of the same cable, because the current limit is hit first.

This is why two instruments with the same voltage rating can behave very differently in the field, and why the capacitance figure matters more than the kilovolt figure on the front panel.

Sizing therefore has five inputs, not one: the required test voltage, the output current and load capability of the set, the frequency steps available, the actual capacitance of the cable, and the test procedure that governs voltage, duration and frequency. Length is the input that ties the last two together.

For a capacitive load, the current at test frequency f is:

Where I is current, C is the capacitance of the cable under test (all phases and accessories included), U is the test voltage actually applied, and f is the test frequency. Use consistent units: C in µF and U in kV give I in mA with a multiplier of 2πf.

The multiplier per frequency is therefore:

Four conditions apply to this relationship, and they matter more than the formula itself:

• Steady state, sinusoidal output. The expression describes the steady-state capacitive current. It does not describe the boost phase, the discharge, or transient behaviour at breakdown.
• Capacitance treated as constant. Capacitance varies slightly with voltage and temperature. For sizing purposes the data sheet value is adequate; for a marginal case it is not.
• Peak and RMS are not interchangeable. Standards usually express test voltage as an RMS value, while VLF sets are frequently rated in peak volts and peak milliamps. Converting between them with √2 is only valid for a sinusoidal waveform. VLF outputs are intended to be near-sinusoidal, but the conversion should be confirmed against the set's own specification and the standard edition in use rather than assumed.

That last point causes more sizing errors than any other. A "30 mA" set and a "42 kV RMS" test only become comparable after both are expressed in the same way.

Cable capacitance per phase is:

where c is the per-phase capacitance per kilometre from the cable manufacturer's data sheet, and L is the route length. As a first estimate only, XLPE cables commonly fall in the region of 0.2–0.35 µF/km per phase for 10–15 kV three-core constructions and 0.15–0.25 µF/km per phase for 35 kV single-core constructions. Paper-insulated lead-covered constructions are generally higher, although the difference depends on the individual cable. These ranges are indicative only: construction, conductor size and insulation thickness all move the figure, so they should not be treated as design values. The data sheet for the actual cable governs.

Three corrections get forgotten in practice:

• Paralleled phases. Three phases tested together carry three times the capacitance of one phase, and draw three times the current.
• Accessories. Joints, terminations and long tails of spare cable coiled at the far end all add capacitance, and the spare cable is usually the item nobody counts.
• Measurement beats estimation. During the test, voltage and current are displayed. C can be back-calculated from the same relationship and kept as a record. Over a few outages this is more reliable than any generic per-kilometre figure, and it makes the next sizing decision trivial.

The test voltages below are assumptions used to make the arithmetic visible. They are not recommendations. Take the actual test voltage, its duration and the frequency at which it applies from the standard edition or utility specification you work to.

Example A — 10 kV cable, 26 kV RMS test voltage, 0.1 Hz

At 26 kV RMS the corresponding peak value is about 36.8 kV, so the current per microfarad is approximately 0.628 * 36.8 ≈ 23 mA.

Example B — 35 kV cable, 42 kV RMS test voltage, 0.1 Hz

At 42 kV RMS the peak is about 59.4 kV, giving roughly 37 mA per microfarad.

Read against a set rated 30 mA peak, the practical message is compact: at 0.1 Hz, roughly five kilometres of 10 kV cable or four kilometres of 35 kV cable is where the current limit arrives — and moving to 0.05 Hz halves the current, doubling the reachable length.

That is the core of the sizing logic: on a capacitive load, the usable frequency range is as much a part of the specification as the voltage rating. The high-voltage source does not grow with the cable — the frequency comes down instead, provided the applicable test procedure permits it and the equipment supports it.

Sizing is necessary and not sufficient. Five things sit outside the formula and regularly decide whether a set is usable:

Weight and access. Higher-voltage sets are built from more than one unit. An 80 kV class instrument may arrive as two boosters connected in series plus a separate controller, while lower ratings need only one booster. If the cable is in a basement switch room with a narrow stair, the handling plan matters as much as the microfarads.

Field supply. These sets run from a single-phase mains supply of roughly 220 V at 50 Hz, with 110 V / 60 Hz variants available. On a generator, the supply has to sit within the set's input specification and stay stable, because an unstable supply affects the boost process.

Very small specimens. The opposite problem to a long feeder: below a very small capacitance the output waveform deteriorates, and the usual remedy is a small capacitor connected in parallel to restore a clean wave. Short factory leads and short motor windings are the common cases.

Test duration and the outage window. Duration and voltage step are set by the procedure you follow, not by the instrument. Confirm both before booking the outage, because a 0.02 Hz test on a long feeder occupies the circuit for far longer than the same test at 0.1 Hz.

Condition of the cable. A wet, aged or previously faulted cable may not survive the test voltage at all. If the circuit has already faulted, the sequence usually starts with fault location before the withstand test. That is a decision about the asset, not about the instrument, and it belongs in the test plan before the set is ordered.

• 1.List every circuit on the test schedule: voltage class, construction, route length, capacitance per kilometre, and whether the phases will be tested together or separately.
• 2.Convert each to capacitance per phase, including accessories and any spare cable.
• 3.Take the test voltage, duration and frequency from the applicable procedure.
• 4.Calculate the current at that frequency, in the same units as the set's rating, and compare with the set's output current — not with a catalogue capacitance figure alone.
• 5.Check the physical constraints: number of units, weight, access route, supply quality, and how long the circuit will be out of service.

If step 4 puts you over the limit, first check whether your procedure allows a lower frequency step and whether the set supports that step at the required voltage. Frequency may only be reduced where the standard, specification or equipment conditions permit it; otherwise a set with greater load capability is the correct answer.

Voltage class, cable construction, route length, capacitance per phase, and the highest test voltage you intend to apply. Four of those five are on the cable data sheet; the fifth is in your test procedure. With those numbers a supplier can confirm the voltage rating, whether one or two boosters are needed, and which frequency steps will cover the whole schedule — instead of quoting on voltage class and hoping the feeders are short.

Cable length decides capacitance, capacitance decides current, and current at a given frequency decides whether a particular set can complete the test. Voltage class only sets the target. Once that order is clear, most sizing disagreements resolve themselves: the question stops being "how many kilovolts" and becomes "how many milliamps at which frequency, on which circuits".

XZH TEST builds VLF AC hipot sets across a range of voltage and load ratings, including fixed-frequency and automatic frequency-sweep configurations, and can confirm a configuration against a specific test schedule. If you have the cable list, the capacitance per phase and the test voltage, we can check the fit before a purchase order is raised.