Reading Capacitor Fuse Time-Current Curves Against Case Rupture Curves

What a capacitor fuse curve shows

A fuse time-current characteristic (TCC) plots current on the horizontal axis and time on the vertical axis, both logarithmic. The tutorial presented with IEEE C37.48.1-2002 notes that TCC curves typically start at 0.01 s (10 ms) and end at 1000 s. Most fuse curves come as a pair: a minimum melt curve, the shortest time at which the element can melt at a given current, and a total clearing curve, the longest time the fuse takes to melt and then interrupt the arc.

Curves carry tolerance. One manufacturer's IEC technical guide gives TCC tolerance as plus or minus 20%, or plus or minus 10% with tight manufacturing control. That is why the minimum melt curve is used for the do-not-operate checks and the total clearing curve for the must-operate checks.

DENCO publishes DNXC time-current curves on p.73 of its catalog. Ask DENCO for the curve sheet that matches your rating before running the checks below.

Where the C number sits on the curve

For C-rated fuses the long-time end of the curve ties back to the rating. DENCO's catalog defines the DNX melting characteristic as melting in 1000 seconds at 1.7 to 2.4 times the C number. A 25C DNX therefore melts at 1000 s somewhere between 1.7 x 25 = 42.5 A and 2.4 x 25 = 60 A. The C rating is DENCO's catalog convention, not a standard rating, so compare it only within DENCO's catalog.

That 1000 s point is also where the capacitor's low-current exposure begins. A capacitively limited fault in an ungrounded bank can be only two or three times load current, so the fuse's long-time region is part of the protection, not an afterthought.

Below about 0.1 s: read I2t, not the curve

At high fault currents a current-limiting fuse operates in less than a cycle, and the curve stops being useful. One manufacturer's capacitor fuse selection guide says I2t is used only for fuse operations faster than about 0.1 or 0.01 seconds. It describes fuse melting as an energy function, notes that I2t to clear is always greater than I2t to melt, and that total clearing I2t is also the I2t let through to the failed capacitor.

Published current-limiting fuse catalogs list a minimum melt I2t and a maximum let-through I2t for each rating. The first is used for the inrush and outrush check, the second for the case rupture check at high currents. Where fuses are paralleled, one IEC guide gives the I2t of n fuses in parallel as n^2 times the single-fuse value, so two fuses carry four times the I2t of one. Ask DENCO for both values for the rating you are considering.

The upper boundary: tank rupture curves

When a capacitor element fails and arcs, gas pressure builds inside the sealed case. A protection software vendor's guide describes the case rupture curve as an internal gas pressure limit caused by an internal arcing fault, says it cannot be calculated by the engineer setting the protective device, and that faults cleared to the left of it indicate minimal likelihood of rupture. In the NEC 2023-cycle text, the safe zone is defined as low probability of damage other than a slight swelling of the case, as identified by the case rupture curve.

One capacitor maker's rule is that the fuse maximum clear TCC must fall below the tank rupture TCC at and below the available fault current, and that at high fault currents the rupture curve should be compensated for asymmetry. Its curve notes say to use asymmetrical rms amps for times shorter than 0.1 s, and mark a minimum clearing time of 0.8 cycle for safe coordination with expulsion fuses. The same curves print a minimum I2t for each duty class.

These I2t figures are what a current-limiting fuse's maximum let-through I2t is compared against in the sub-cycle region. The same software vendor's guide gives the reason fuses do this job: the relay and breaker combination is generally not fast enough to protect the capacitor from case rupture due to internal arcing faults.

Worked example: a 300 kvar, 13,800 V unit

A protection software vendor's guide publishes example rupture points for a 300 kvar, 13,800 V unit. Squaring current and multiplying by time shows the short-time part of the curve is close to constant I2t, about 1.3 x 10^6 A2s, which is the figure a fuse's let-through I2t must stay well below at high currents.

Unit current is 300 / 13.8 = 21.7 A, and with the 1.35 margin from published manufacturer guides the fuse must carry 29.3 A. Published tables place 13,800 V units on 15.5 kV fuses, where DENCO's DNXC15 ratings include 30 A. The checks are then: the 30 A total clearing curve passes to the left of each point in the table; at the 275 A, 300 s point, 275 / 21.7 = 12.7 times unit current, the fuse must already be clearing in under 300 s; and at the top of the range its maximum let-through I2t is well under 1.3 x 10^6 A2s. DENCO can supply the curve and I2t values for that check.

The lower boundary: inrush and outrush

The fuse must not melt during normal switching. Inrush flows when a bank is energized, and outrush flows from healthy units into a failed unit or a nearby fault. A published protection paper states the outrush requirement: the fuse on the healthy units must not blow when discharging into an adjacent faulted capacitor. One fuse maker calls nuisance operations from inrush or outrush sneakouts.

For an isolated bank, circuit theory gives the peak inrush as about 1.414 x sqrt(Isc x I1) and its frequency as the system frequency times sqrt(Isc / I1), where Isc is the available fault current and I1 the bank's rated current. For a 600 kvar, 12.47 kV bank drawing 27.8 A at a point with 8,000 A available: 1.414 x sqrt(8,000 x 27.8) = 667 A peak, at 60 x sqrt(8,000 / 27.8) = about 1,020 Hz. One switching-equipment maker describes single-bank inrush as generally less than 5 kA and 1 kHz, and back-to-back inrush as tens of kiloamperes at tens of kilohertz. One fuse guide's back-to-back estimate is 1.333 x sqrt(kvar_eff / L) kA peak, L in microhenries; two 3,000 kvar banks with 10 uH between them give 1.333 x sqrt(1,500 / 10) = 16.3 kA.

Because these events last a fraction of a cycle, the check is in I2t terms: the fuse's minimum melt (pre-arcing) I2t must exceed the I2t of the switching transient. One IEC-market guide gives this criterion for bank energization; confirm the calculation method in your study. Repetition matters as well as magnitude. One selection guide notes that each time an element is heated near its melting point it deteriorates slightly, and the sources reviewed for this guide give no numeric margin for repeated pulses, so ask the fuse maker.

A step-by-step overlay

With the curves on the same current scale, the check runs in this order. If no rating passes every step, the answer is a change to the bank or the fusing method, not a compromise on the curves.

• Plot the capacitor's tank rupture curve for its type and kvar size, from the capacitor maker.
• Mark the lowest and highest fault currents the fuse must clear, and the circuit X/R for asymmetry.
• Plot the candidate fuse's total clearing curve and confirm it lies in the safe zone between those currents.
• Below about 0.1 s, compare the fuse's maximum let-through I2t with the rupture curve's I2t instead of reading the curve.
• Estimate inrush and outrush and confirm they sit below the fuse's minimum melt I2t, with margin the fuse maker accepts for repeated switching.
• Confirm the rating still meets the continuous current and temperature derating checks.

Coordinating with unbalance protection and other fuses

A relay maker's distribution handbook, citing IEEE C37.99-2000, says the unbalance protection should coordinate with the unit fuses so that the fuses isolate the faulty unit before the protection trips the whole bank. IEEE's 2005 interpretation of IEEE 18-2002 reported user practice of alarming at 105% of rated voltage and tripping on unbalance above 110%.

Published delays show the time scale. One unbalance relay's lockout timer is factory-set at 10 seconds to let unit fuses respond to evolving faults, and its coordination assumes a fusing ratio of 1.25 or less. A relay maker's paper says for most applications an unbalance trip delay of 0.1 s should be adequate, and that longer delays increase the probability of catastrophic bank failure. The fuse curve therefore has to clear a failed unit well inside those delays.

Where a capacitor fuse sits downstream of another fuse, a municipal utility standard asks that the protecting fuse clear before the protected fuse reaches 75% of its melting time.

Common mistakes

These errors show up when curves are overlaid in a hurry.

• Comparing the minimum melt curve, not the total clearing curve, with the rupture curve.
• Reading the curve below 0.1 s instead of comparing I2t.
• Using symmetrical current against a rupture curve that asks for asymmetrical rms amps at short times.
• Using a typical rupture curve when the unit's duty class has its own curve.
• Checking only the high-current end and missing a crossing near the low fault current of a capacitively limited bank.
• Raising the fuse rating to stop sneakouts without rechecking the rupture curve.

Frequently asked questions