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Capacitor Bank Grounded Wye Unbalanced Detection Discussion

In the late 1950’s Mr. Harold Stone of Line Material (later Line Material was merged by McGraw-Edison Company with Pennsylvania Transformer to become McGraw-Edison Power Systems, and is now (Cooper Power Systems), has developed and publish several papers on unbalance detection for capacitor banks.

For the grounded WYE connected bank the following formulas were developed:

For the neutral to ground current...

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia Amps
(1)
 %IN (of rated phase current) = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(2)
 The voltage on remaining units in one series section with "F" units removed:
 %Vr = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (3)
 Neutral current when one complete series section is shorted:

 %In (of rated phase current) = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia (4)

LEGEND
IN =  Neutral Current
I Rated current of one units
VT =  Applied line–to-neutral volts
V =  Rated voltage of capacitor units
VR= Voltage on remaining units in a group with "F" units removed.
S =  Number of series sections per phase
N =  Number of parallel units per series section
F =  Number of units removed from one section

METAL ENCLOSED CAPACITOR GROUNDED WYE APPLICATIONS

It is rare that more than one series group is used in metal enclosed applications. If we make that assumption we can simplify the above formulas.

Looking a balance load with two capacitors per phase, we have the following:

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let XC = 1 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 1V

Then gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 0.002653590254 farads = 1var

For 2 units in parallel will equal C1+C2 =0.00530519 farads =2vars

Or ZT = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

This gives us

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 2 amps or, gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 2amps

Each leg in a balanced grounded WYE capacitor bank as configured above will be 2 amps, and will be zero amps at the ground node point.

Looking at an unbalance load using the same parameters as the balance load given above we have the following:

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let XC = 1gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Let gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 1V

Then gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 2 amps

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia = 1amp

This means the current neutral to ground will be 1 amp and this will flow as unbalance current in the neutral.

Looking back at the formula for neutral current formula (1) we had:

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

IU = 1 amp

Let VT = V
N = 2
S =1
F = 1

This gives us 1 amp in the neutral, which confirms our numbers. However, we can really reduce this formula when S = 1.

This reduces to:

gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia and even further


 gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(5)
 or gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia
(6)

and if VT = V, this is really simplified to gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

Also the voltage on the remaining units given by:

%Vr = gilbert electrical systems, document library, basic electrical formulas, ungrounded, unbalance, calculation, capacitor, beaver, west virginia

with S = 1, and VT = V, %Vr will always be 100%

For the percentages and per unit values see Table 1 below.

Table 1 - Unbalance Verification
Grounded WYE
Ph-N Volts Cap Volts KVAR
Unit Current
Total Bank Current
N F
%Vn
% In Multiplier

In-Multiplier

1 1 1 1 1 1 1 100 100 1
1 1 1 1 1 2 1 100 50 1
1 1 1 1 2 2 2 100 100 2
1 1 1 1 1 1 1 100 33.33 1
1 1 1 1 2 2 2 100 66.67 2
1 1 1 1 3 3 3 100 100 3
1 1 1 1 1 1 1 100 25 1
1 1 1 1 2 2 2 100 50 2
1 1 1 1 3 3 3 100 75 3
1 1 1 1 4 4 4 100 100 4
1 1 1 1 1 1 1 100 20 1
1 1 1 1 2 2 2 100 40 2
1 1 1 1 3 3 3 100 60 3
1 1 1 1 4 4 4 100 80 4
1 1 1 1 5 5 5 100 100 5
1 1 1 1 1 1 1 100 16.67 1
1 1 1 1 2 2 2 100 33.33 2
1 1 1 1 3 3 3 100 50 3
1 1 1 1 4 4 4 100 66.67 4
1 1 1 1 5 5 5 100 83.33 5
1 1 1 1 6 6 6 100 100 6
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