Surge arrester sizing: Uc, Ur, TOV capability and NBI protective margin

What surge arrester sizing is

A surge arrester is the last line of defence of insulation coordination. It is a voltage-dependent resistor — a stack of metal-oxide (zinc-oxide, ZnO) blocks — that behaves like an open circuit at normal voltage and like a near short circuit when an overvoltage appears, diverting the surge current to ground and clamping the voltage across the protected equipment.

Sizing it is a balancing act between two opposing requirements. On one hand, the arrester must tolerate the highest voltage that normal operation and temporary faults impose, or it ages and fails. On the other hand, it must clamp lightning and switching surges to a residual voltage low enough to protect the equipment insulation. The continuous voltage Uc and rated voltage Ur cover the first requirement; the residual voltage Up and its margin against the BIL cover the second.

The method below follows IEC 60099-4 / NBR 16050 and the application guidance of IEC 60099-5 and IEEE C62.22.

Step 1 — the voltage the arrester sees continuously

The arrester is connected phase-to-ground, so the steady-state voltage across it is the maximum phase-to-ground system voltage:

U_L-N,max = (Um/√3)·(1 + reg)

Here Um is the maximum system voltage (for a 13.8 kV nominal network, Um = 15 kV) and reg is the steady-state overvoltage from regulation or light-load conditions. The continuous operating voltage Uc must sit above this value with margin for harmonics and metering tolerance:

Uc_req = 1.05 · U_L-N,max

The 1.05 factor is not arbitrary: third-harmonic content and instrument tolerance routinely add a few percent to the fundamental. An arrester whose Uc only just equals the nominal phase-to-ground voltage will draw excessive resistive leakage current, heat up, and drift up the ageing curve. On isolated or resonant-grounded systems a ground fault can persist indefinitely, raising the sound phases toward line-to-line voltage; in that sustained-fault case the calculator references Uc to Um directly rather than to Um/√3.

Step 2 — from Uc to the rated voltage Ur

For standard metal-oxide arresters the continuous voltage is about 80% of the rated voltage, so the first lower bound on Ur is:

Ur(Uc) = Uc_req / 0.8 ≈ 1.25 · Uc_req

Ur is the 10-second power-frequency reference voltage that names the arrester (a “12 kV arrester”). But Uc is not the only constraint — the temporary overvoltage gives a second, independent one.

Step 3 — the temporary overvoltage (TOV) criterion

When a single phase faults to ground, the two healthy phases rise. The power-frequency overvoltage on the sound phases is:

Utov = k · U_L-N,max

where k is the earth-fault factor: about 1.3–1.4 on a solidly grounded system, climbing toward √3 ≈ 1.73 on an isolated or high-impedance system. The arrester can absorb this overvoltage only for a limited time before thermal runaway, and its TOV capability Tt (expressed per unit of Ur) decreases with duration — roughly 1.20 for sub-second events, 1.15 at 1 s, 1.10 at 10 s, and around 1.04 for very long faults. The rated voltage required by the TOV is therefore:

Ur(TOV) = Utov / Tt

The arrester must satisfy both criteria, so the design Ur is the next standard rating at or above the larger of the two:

Ur = next_standard(max(Ur(Uc), Ur(TOV)))

Once Ur is fixed at a catalog value, the actual arrester continuous voltage is recovered as Uc = 0.8·Ur, which must still cover Uc_req.

Step 4 — residual voltage and protective margin

The whole point of the arrester is the residual (protective) voltage Up — the voltage that remains across it while it discharges the nominal current In (an 8/20 µs impulse of 5, 10 or 20 kA depending on class). Up comes from the datasheet ratio Up/Ur, typically between 3.0 and 3.5:

Up = (Up/Ur) · Ur

This Up is compared against the equipment basic lightning impulse insulation level (BIL/NBI) to get the protective margin:

margin = (BIL/Up − 1) · 100 ≥ 20 %

A margin of at least 20% is the usual acceptance threshold. Cables, gas-insulated switchgear and rotating machines deserve more, because their insulation does not self-restore. Note that the effective margin at the equipment terminals is eroded by the inductance of the leads connecting the arrester — keep those leads short and direct.

Step 5 — the short-circuit (pressure-relief) rating

Finally, the arrester must fail safely. Its rated short-circuit / pressure-relief current Is must equal or exceed the prospective fault current Ik″ at the installation point:

Is ≥ Ik″

If the arrester is ever overstressed to failure, it should vent the fault current in a controlled way rather than rupture its housing violently. The calculator rounds Ik″ up to the next standard Is rating (5, 10, 16, 20, 31.5, 40 kA…).

How to read the result

The selection is consistent when all of the following hold:

• The adopted Ur is a standard value at or above both Ur(Uc) and Ur(TOV).
• The arrester Uc = 0.8·Ur still covers the required Uc.
• The protective margin (BIL vs Up) meets or exceeds the target (≥ 20%).
• The nominal discharge current In matches the application class.
• Is ≥ Ik″ so the failure mode is safe.

If the protective margin is negative or below target, the arrester clamps too high for that insulation level — you need a lower Up, which usually means a lower Ur (only possible if the TOV/Uc criteria allow) or a higher-energy arrester class with a better Up/Ur ratio. If instead the TOV criterion dominates and forces a high Ur, the protective margin shrinks; this is the classic tension on weakly grounded systems, where a higher Ur is unavoidable and the equipment BIL may have to be reconsidered.

Practical design considerations

• Always check both criteria. Uc protects against continuous duty and harmonics; TOV protects against the ground-fault overvoltage. The required Ur is the worse of the two — never just one.
• Match the earth-fault factor to the real grounding. Defaulting to k = 1.4 on an isolated system badly undersizes the arrester.
• Use the TOV capability for the actual clearing time. A relay that takes several seconds to clear demands a higher Ur than a fast one.
• Keep arrester leads short. Lead inductance adds to Up at the equipment terminals and quietly eats into the protective margin.
• Verify Is against the site fault level. A correct Up is worthless if the arrester cannot fail safely.

Following this chain — U_L-N,max, Uc, the two Ur criteria, the standard Ur, Up and its margin against the BIL, and finally Is — yields an arrester selection that is coordinated with the equipment insulation and robust against both continuous duty and temporary faults.