Capacitor Bank Unbalance Protection and How It Works with Fuses

Two layers: fuses and relays

A relay maker's paper on unbalance calculations describes the arrangement simply: banks are protected by a combination of fuses, which remove the failed unit or element, and protective relays, which alarm and trip the bank offline. In a fused bank, the unbalance protection is concerned with detecting the fail-open state after the fuse has removed the shorted unit.

A relay maker's paper on bank fundamentals adds that unbalance protection normally provides the primary protection for arcing faults within a bank, and that continuous overvoltage above 1.1 per unit on any unit should be prevented by relays that trip the bank. The fuse handles one unit. The relay handles the consequences for the others, and the faults a unit fuse cannot see.

What the relay is protecting: voltage on the healthy units

When a fuse removes a unit from a parallel group, that group's capacitance drops and it takes a larger share of the string voltage. For a grounded single wye, fused bank, the relay maker's unbalance paper gives kOV = SP / (SP - F(S - 1)), with P units per group, S series groups and F failed units in one group. For an ungrounded single wye, fused bank it gives kOV = 3SPR / (3SPR - F(3SR - 3R + 1)), with R strings per phase.

IEEE's 2005 interpretation of IEEE 18-2002 explains the 110% continuous overvoltage capability as the margin that lets a bank stay in service after the failure of at least one unit. Beyond that, the relay maker's paper warns, the internal overvoltage may cause more failures and eventually a cascading failure. It also notes the next failure is most likely to be in the group that already lost a unit.

Unbalance methods by bank configuration

A widely cited protection paper matches the method to the bank. One transmission organization's guideline, PJM's, approves neutral current unbalance, neutral current differential unbalance, summation of intermediate tap point voltages, and voltage difference schemes. A relay maker's paper notes that delta banks, built as a single series group, need no unbalance detection for the loss of a unit, because losing one does not overvoltage the others.

Worked example: neutral voltage on an ungrounded wye bank

A utility relay maker's instruction sheet gives formulas for an ungrounded single wye bank with one string per phase. Neutral voltage Vn = F x VL-n / (2F + 3S(P - F)), and voltage on the surviving units in the affected group Vo = 3P x VL-n / (2F + 3S(P - F)).

Its example uses S = 2 series groups, P = 10 units per group and VL-n = 20 kV. With one blown fuse, Vn = 20,000 / (2 + 6 x 9) = 357 V. With two in the same group, Vn = 40,000 / (4 + 6 x 8) = 769 V. The sheet sets the lockout at the midpoint, 563 V, so one blown fuse alarms and two lock the bank out.

The same formula shows why. Each group normally carries 10 kV. Survivors carry Vo = 30 x 20,000 / 56 = 10,714 V after one loss (1.071 per unit) and 30 x 20,000 / 52 = 11,538 V after two (1.154 per unit). The second loss takes them past 110%, which is where the lockout sits.

Worked example: how sensitive is the signal?

For a grounded single wye, fused bank, the relay maker's unbalance paper gives the unbalance current as 3I2 = (kOV - 1) / (R(S - 1)) per unit. With S = 4, P = 10 and R = 1, one failed unit gives kOV = 40 / 37 = 1.081, so 3I2 = 0.081 / 3 = 0.027 per unit, a 2.7% signal. Its quick estimate is the number of lost units divided by the units per phase; in its example, 180 units per phase and one lost gives 1 / 180 = 0.0056 per unit against an exact 0.0059.

The paper's conclusion is practical: it is better for protection sensitivity to have more units in a group than more strings in a phase. A large bank spreads one unit's loss over many units, so the signal shrinks, and the relay has to resolve it against standing errors. In its 138 kV ungrounded wye example, one failed unit moves the neutral by (1.063 - 1) / (3 x 3 + 1) = 0.0063 per unit, about 500 V on a 79.7 kV phase voltage.

Alarm and trip levels

Published practice converges on a few rules:

• Alarm on the first blown fuse. A relay maker's handbook, citing IEEE C37.99-2000, says the alarm level is selected according to the first blown fuse, and PJM's guideline says a single blown fuse should initiate an alarm.
• Trip when survivors would exceed 110%. The same handbook describes a delayed trip when further losses would push group overvoltage past 110% of unit rated voltage or the capacitor maker's recommendation; PJM trips when more than one fuse blows in a group and overvoltage on the remaining units exceeds 10%.
• A high-set stage for cascading or arcing faults, also from the handbook.
• Survey practice: IEEE's 2005 interpretation reports users alarming at 105% of rated voltage and tripping above 110%.
• Separate overvoltage protection: the unbalance paper states that unbalance protection does not substitute for phase overvoltage elements (59P).

Timing: let the fuse act first

The relay maker's handbook, citing C37.99-2000, says the unbalance protection should coordinate with the individual unit fuses so that the fuses isolate the faulty unit before the protection trips the whole bank. A utility relay maker's lockout timer is field adjustable from 2 to 30 seconds and factory set at 10 seconds, to allow time for the unit fuses to respond to evolving faults and so permit visual identification of the units to replace. That instruction sheet also says coordination assumes a fusing ratio of 1.25 or less for the unit fuses.

Trip delays pull the other way. A relay maker's paper says the delay should be minimized to reduce damage from an arcing fault, yet long enough to ride through inrush, system ground faults, nearby switching and non-simultaneous closing of the switch, and that for most applications 0.1 s should be adequate; longer delays increase the probability of catastrophic bank failure. A 2025 conference paper quotes C37.99-2012 suggesting 15 to 25 cycles may coordinate for faults external to the bank, and after spurious trips recommends negative-sequence delays not below 0.6 s on high-voltage banks. Alarm delays of 5 to 10 seconds are normal in another relay maker's simulations.

Fuseless banks remove one constraint: with no fuses, the unbalance protection does not have to be delayed to coordinate with them.

Standing unbalance, temperature and canceling failures

Every bank carries some unbalance with all units healthy. A relay maker's paper lists system voltage unbalance and capacitor manufacturing tolerance, plus sensing device tolerance and unit temperature differences, and says compensation should be provided if the inherent error approaches 50% of the alarm setting. Another relay maker's paper notes builders generally place units to limit unbalance to less than 0.5%, and that compensation should be re-nulled whenever a unit is changed. It reports a 10 °C variation from the bottom to the top of an outdoor cabinet on a sunny day, and relay operations observed when the rising sun hits one side of a bank.

Failures can also hide each other. If an equal number of units is lost from the same phase on both sides of a double wye, little neutral current flows. The suggested mitigation is a sensitive alarm, preferably at one fuse operation in a fused bank, so the first loss is never missed.

What this asks of the unit fuse

The relay scheme assumes the fuse behaves. It must operate reliably on a failed unit so the relay sees a clean fail-open state rather than a slowly worsening short. It must not operate on healthy units during the outrush into a failed neighbor or during switching, or the relay will count false losses. And it must clear within the unit's case rupture limit, because the relay and breaker are generally too slow for that; one software vendor's guide says the relay-breaker combination is generally not fast enough to protect the capacitor from case rupture, and that is the fuse's purpose.

Current-limiting unit fuses such as DENCO's DNX (clip style, 2.8 kV to 38 kV, 50 kA asymmetrical in DENCO's catalog) and DNXC (full-range, bus bar to lead mounting, 8.3 kV to 23 kV, 10 A to 65 A, 50 kA) are applied in this role. Which rating suits a bank depends on the capacitor maker's data and the protection study.

Common mistakes

• Setting the alarm so high that one blown fuse goes unnoticed. The next failure is most likely in the same group.
• Not re-nulling the inherent unbalance after replacing a unit or fuse.
• Using a trip delay shorter than the unit fuse's clearing time, so the bank trips for every unit failure and the failed unit is harder to find.
• Using long trip delays to avoid nuisance trips, which raises the chance of a catastrophic arcing failure.
• Treating unbalance protection as overvoltage protection. Phase overvoltage elements are still needed.
• Ignoring that unit fuse sizing and relay settings are coupled; one relay maker's coordination assumes a fusing ratio of 1.25 or less.

Frequently asked questions