In a bank with external fuses, each blown fuse removes one unit from its parallel group and raises the voltage on the units that remain. IEEE C37.99-2000 calculates that voltage and the unbalance signal with a few per-unit equations. With them you decide how many blown fuses should trip the bank, what signal the alarm should see, and how much margin the healthy units keep.
Short answer
In a bank with external fuses, each capacitor unit has its own fuse. When a unit fails and its fuse blows, the parallel group is left with one unit fewer and its capacitance drops. Voltage divides among the series groups according to the capacitance of each one, so the units remaining in that group carry more voltage.
IEEE C37.99-2000 (clause 8.3) calculates that voltage and the signal seen by the unbalance relay with a few per-unit equations. The result supports two decisions: how many blown fuses the bank can tolerate before tripping, and what signal the alarm should respond to.
What is calculated
For each number of blown fuses in a group, the standard tabulates these quantities:
- The voltage across the units in parallel with the blown fuses, which is the one compared with the unit limit.
- The neutral-to-ground voltage, in ungrounded wye banks.
- The neutral current between two wyes, in ungrounded double-wye banks.
- The change in ground current, in grounded wye banks. It is the same change that appears as a voltage on a low-voltage capacitor placed in the neutral.
- The difference current between two equal grounded wyes, measured with a current transformer between the neutrals.
The voltage-tap variant and the H-bridge have their own calculation in clauses 8.3.5 and 8.3.6 of the same standard. This guide covers the wye, the delta and the single-phase bank (clause 8.3.4).
The design this calculation applies to is the externally fused bank; for internal fuses use unbalance calculation with internal fuses, and for banks without fuses, fuseless and unfused unbalance calculation. The capacitor limits: 110 % voltage and 135 % kvar set how far the voltage on the healthy units may rise.
Input data
Everything is expressed in per unit: normal voltage, capacitance and current equal 1 with no blown fuses. You need this data from the bank:
| Data | What it is |
|---|---|
| S | Series groups, phase to neutral |
| Pa | Parallel units per phase in the affected wye |
| Pt | Parallel units per phase in the whole bank |
| n | Blown fuses in one parallel group |
| G | 0 if the bank is grounded; 1 if it is not |
In a single-wye bank, Pa equals Pt.
The equations in the standard
Table 2 of IEEE C37.99-2000 gives the equations for each column. For the affected group and phase:
- Capacitance of the group with blown fuses: Cg = (Pa − n) / Pa
- Capacitance of the affected wye: Cs = S × Cg / (Cg × (S − 1) + 1)
- Capacitance of the affected phase: Cp = (Cs × Pa + Pt − Pa) / Pt
- Neutral-to-ground voltage: Vng = G × (3 / (2 + Cp) − 1)
- Voltage across the affected phase: Vln = 1 + Vng
- Voltage across the units of the affected group: Vcu = Vln × Cs / Cg
Table 3 adds the protection signals:
- Change in ground current: Ig = (1 − G) × (1 − Iph), with Iph = Cp × Vln
- Neutral current between wyes: In = 3 × Vng × G / 2
- Difference current between equal wyes: Id = Vln × (1 − Cp)
The standard notes that special cases have different equations: a unit that fails before its fuse blows, and divisions by zero. Those cases are not in the tables and are solved separately.
A worked example
A single-wye bank with 4 series groups and 12 parallel units per group. With no blown fuses, the voltage on each unit is 1 per unit. Using the equations above, the voltage on the units of the affected group is:
| Blown fuses | Grounded (G = 0) | Ungrounded (G = 1) |
|---|---|---|
| 0 | 1.000 | 1.000 |
| 1 | 1.067 | 1.075 |
| 2 | 1.143 | 1.161 |
| 3 | 1.231 | 1.263 |
| 4 | 1.333 | 1.385 |
With the first blown fuse, the units stay below 110 %. With the second, they exceed it. The ungrounded bank rises a little more because the neutral shifts and the affected phase receives more voltage.
The change in ground current of the grounded bank is 0.022 with one fuse and 0.048 with two, in per unit of phase current. That is the signal the relay or the neutral capacitor sees in each case.
How to use the result
The standard gives the criterion, not the final setting:
- Limit. The healthy units must not exceed 110 % of rated voltage, or the value the manufacturer specifies (clause 8.3.1).
- Trip. Calculate the signal that appears with the fuse whose operation leaves more than 110 % and the one with one fuse fewer. The trip setting is placed halfway between the two. In the example, the trip corresponds to the second blown fuse.
- Alarm. It must operate with the first fuse. The standard normally places it between 50 % and 75 % of the signal that first fuse produces.
- Margin. The real signal also includes the natural unbalance of the bank and of the system. That is why the final setting is made from measurements on the installed bank.
For a larger bank, the standard notes that the same bank built as a single wye with 14 units per group stays below 110 % after the first fuse. In other words, the bank design decides how much margin you have.
Compare the calculated signal with the inherent unbalance and measurement error, and stage the alarm and trip according to the alarm and trip times of unbalance protection. The function that applies them is the capacitor bank unbalance protection (ANSI 60).
Common mistakes
- Using the number of units in one wye as if it were the whole phase. In an unequal double wye, Pa and Pt are different.
- Forgetting the neutral shift. In an ungrounded bank, the voltage on the affected unit rises more than in a grounded one.
- Comparing against 110 % without checking the nameplate. The unit limit may differ if the manufacturer says so.
- Setting from theory alone. Natural and system unbalance change the real signal. The setting is confirmed with the bank energized.
What we do at Tiza Group
In our engineering design and studies service we calculate the unbalance table for your bank from your nameplate data and deliver it for the protection settings. We work remotely, worldwide. Contact us and we will quote the calculation.
Related guides
- IEEE C37.99: shunt capacitor bank protection guide
- Capacitor bank with external fuses: design and limits
- Unbalance calculation for a bank with internal fuses
- Unbalance calculation for fuseless and unfused banks
- Capacitor bank at MV and HV: unbalance and tests
References
- IEEE Std C37.99-2000, IEEE Guide for the Protection of Shunt Capacitor Banks, clauses 8.3.1 to 8.3.4, Tables 2 and 3.
- IEEE Std 18-1992, IEEE Standard for Shunt Power Capacitors.
- IEEE Std 1036-1992, IEEE Guide for Application of Shunt Power Capacitors.
Frequently asked questions
Why calculate the unbalance if the relay already has a factory setting?
Because the factory value knows nothing about your bank. The signal a blown fuse produces depends on how many units are in parallel, how many groups are in series and how the neutral is connected. Without the calculation you cannot tell whether the first blown fuse already puts the healthy units above 110 % or whether there is still margin.
Do the same equations work for a delta-connected bank?
Yes. IEEE C37.99-2000 states that one leg of the delta is treated as one phase of a grounded wye. The equations are the same. Only the current reference changes: values given per unit of phase current are given per unit of leg current, that is, the phase current divided by the square root of 3.
How many parallel units should each series group have?
The standard recommends at least 10 parallel units per series group in high-voltage banks with several groups, so that the first blown fuse does not raise the voltage on the remaining units too much. With few parallel units, a single fuse can push the voltage past the 110 % limit.