Capacitor Inrush and Outrush: Why Capacitor Fuses Are Rated Differently

Inrush: energizing an isolated bank

When a discharged bank is switched onto a bus with no other bank nearby, the source inductance and the bank capacitance ring together. A capacitor bank studies tutorial gives the circuit: peak inrush I_peak = V0 / sqrt(L / C) and frequency f = 1 / (2 pi sqrt(L C)), where L is source inductance, C the bank capacitance per phase and V0 the peak phase voltage, sqrt(2/3) times rated line voltage, adjusted for any trapped charge. Closing at the voltage peak is the worst case.

Two consequences follow, which a university switching-transients tutorial states directly: as bank size increases, peak inrush current increases and its frequency decreases. One switching device maker says single-bank inrush is generally less than 5 kA and 1 kHz, with natural frequencies tending to 200 to 800 Hz for banks sized for 1% to 4% voltage regulation. On the voltage side, USDA RUS Bulletin 1724D-112 gives a theoretical 2.0 per unit and typical transients of 1.3 to 1.5 per unit at 300 to 1,000 Hz.

For the fuse, an IEC-oriented fuse technical guide states the rule: the fuse must not operate during switching, and its pre-arcing I2t must be greater than the energy generated during energization. Its estimate of that energy rises with voltage and capacitance and falls as source inductance increases, which is why inserted inductance such as current-limiting reactors helps.

Worked example: isolated bank inrush

The same circuit can be written in terms of quantities on a one-line diagram: I_peak = 1.414 x sqrt(I_sc x I_1) and f = f_s x sqrt(I_sc / I_1), where I_sc is the available fault current, I_1 the bank's rated current and f_s the system frequency. This is circuit algebra, not a quoted standard; checked against the tutorial's 230 kV example, it gives 3,781 A and 852 Hz against the tutorial's 3,784 A and 851.84 Hz.

Take a 3,600 kvar three-phase bank on a 13.8 kV bus with 20,000 A available. Rated current is 3,600 / (1.732 x 13.8) = 150.6 A. Peak inrush is 1.414 x sqrt(20,000 x 150.6) = 1.414 x 1,735.5 = 2,454 A, at 60 x sqrt(20,000 / 150.6) = 60 x 11.52 = 691 Hz. The normal peak current is 1.414 x 150.6 = 213 A, so inrush peaks at about 11.5 times it, the same ratio as sqrt(I_sc / I_1). Those numbers sit inside the published single-bank range above.

Back-to-back switching

When a bank is switched on next to another bank that is already energized, the energized bank discharges into the new one through only the inductance between them, which an EPRI event report puts on the order of microhenries rather than millihenries in a substation. A switching device maker describes back-to-back inrush as on the order of tens of kiloamperes and tens of kilohertz, and a switchgear maker's FAQ puts the frequency range at 2 kHz to 30 kHz.

One manufacturer's capacitor fuse guide gives a quick estimate: peak current in kA = 1.333 x sqrt(kvar_eff / L), with L in microhenries and kvar_eff = kvar1 x kvar2 / (kvar1 + kvar2). For two 3,000 kvar banks, kvar_eff = 1,500. With 10 uH between them, 1.333 x sqrt(1,500 / 10) = 1.333 x 12.25 = 16.3 kA peak. Raise the inductance to 100 uH and it falls to 1.333 x sqrt(15) = 5.2 kA. Back-to-back switching is seldom the case for pole-mounted capacitors, a pole-bank fusing guide notes, so this is mainly a substation and metal-enclosed concern.

Outrush: discharge into a failed unit or a fault

Outrush is the reverse case. When an element or unit fails, the healthy parallel units discharge into it. A widely cited protection paper states the requirement: the fuse on the healthy elements must not blow when discharging into an adjacent faulted capacitor, but must quickly and effectively remove a failed element or unit.

A bank also discharges into a nearby system fault. The capacitor bank tutorial treats it like back-to-back switching with the inductance between bank and fault: its 230 kV example gives 6.201 kA at 1,398 Hz. A university tutorial warns that for a bus fault the inductance is on the order of tens of microhenries and outrush can be severe. PJM's guideline adds that discharge from several banks in parallel scales with the square root of the number of banks, and its 230 kV studies show 13.9 to 43.6 kA peak into a fault as inductance falls from 1,000 to 100 uH.

A pole-bank fusing guide lists the transient sources group fuses must withstand: bank switching, lightning surges and discharge into external faults, primarily on grounded wye systems, and warns that fuses can be damaged by high-magnitude, high-frequency currents. A power fuse maker uses the term sneakouts for nuisance fuse operations caused by inrush or outrush.

Inrush and outrush compared

The two events stress the same fuse property from different directions.

Why I2t is the measure

One manufacturer's capacitor fuse selection guide explains that I2t is used only for fuse operations faster than about 0.1 or 0.01 seconds, the region these pulses occupy. An IEC-oriented guide splits it in two: pre-arcing (melting) I2t up to arc initiation, plus arcing I2t, gives total operating I2t, which the selection guide notes is also the let-through I2t the failed capacitor sees. Two fuses in parallel have four times the I2t of one, since I2t scales with n squared for n parallel fuse-links.

To get a feel for the numbers, one undamped half cycle of a sine pulse with peak I_pk and frequency f carries I_pk squared x 1 / (4f). That is our arithmetic, not a published figure. For the isolated bank above: 2,454 squared / (4 x 691) = 6,022,000 / 2,764 = about 2,180 A2s through the bank's line fuse in the first half cycle; real inrush is a damped train of several cycles, and each unit fuse in the bank carries only its share. Compare the result with the fuse maker's published minimum melting I2t. No source reviewed for this guide gives a numeric margin between the two, so ask the fuse maker.

Repeated pulses and element fatigue

Inrush happens every time the bank closes. The selection guide warns that each time an element is heated near its melting point the fuse deteriorates slightly, that makers can plot how many operations a fuse survives at a given percent of its one-shot melting I2t, and that for applications with many such exposures it supplies elements with a higher I2t to melt.

Damage is hard to see. One fuse maker's I2t testing note says a nick halfway from the element edge to a hole cuts minimum melting I2t by 44% while changing resistance by only 0.75%, so resistance checks alone cannot find it. Its production test pulses each current-limiting fuse twice at 95% of published minimum melt I2t, and states that a good fuse withstands an indefinite number of such pulses.

Small units are the hard case. One manufacturer's capacitor fuse catalog notes that for 50 kvar capacitors it is difficult to choose reasonably sized fuses that will withstand the I2t outrush, because I2t withstand goes down exponentially with fuse rating rather than linearly.

Limiting inrush and outrush, and what to ask for

Most mitigation adds inductance or damping. Inrush and outrush reactors limit magnitude and frequency; one metal-enclosed bank maker fits 44 uH transient inrush reactors to each stage alongside one current-limiting fuse per capacitor. Pre-insertion inductors of 10 or 40 mH, one switching maker states, reduce back-to-back inrush to less than 3.5 kA and several hundred hertz, and the capacitor bank tutorial gives the optimum pre-insertion resistor as sqrt(L_source / C). A university design standard requires inrush reactors that keep high-frequency inrush below the I2t rating of the fuses and asks for peak inrush, rms inrush, frequency and duration in submittals. Breaker standards also set peak and frequency limits for capacitor switching.

Published guidance also builds switching duty into the continuous rating margin in different ways, and the fuse maker's I2t data closes the loop. Ask for the minimum melting I2t and total clearing I2t of each candidate rating with the time-current curves.

• One maker applies 1.65 times phase current for 600 V and 1.2 to 3 kV capacitor fuses, to protect against harmonics and switching currents.
• IEC-market guidance sets fuse rated current at about twice the operating current, citing inrush on power-up.
• For medium-voltage unit fuses, one manufacturer's selection guide uses 1.35 times capacitor current and checks I2t separately.
• For DENCO DNX (2.8kV to 38kV, 1C to 140C) and DNXC (8.3kV to 23kV, 10A to 65A), send unit kvar and voltage, units in parallel, source fault current and any back-to-back arrangement, and DENCO engineering will advise on the rating.

Common mistakes

These are the usual roots of sneakouts and weakened fuses.

• Checking only the fuse's continuous rating. Inrush and outrush are judged on melting I2t, a separate number.
• Calculating isolated-bank inrush for a bank that actually switches next to another energized bank.
• Ignoring adjacent banks in outrush. Discharge into a bus fault grows with every bank in parallel.
• Refitting the same rating after unexplained operations, without checking for element fatigue or higher switching duty.
• Upsizing the fuse to stop nuisance operations without rechecking the clearing curve against the case rupture curve.
• Re-energizing too fast. One bank manual says not to switch capacitors on, off and on again in less than 200 seconds.

Frequently asked questions