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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...

 Amps (1) %IN (of rated phase current) = (2) The voltage on remaining units in one series section with "F" units removed: %Vr = (3) Neutral current when one complete series section is shorted: %In (of rated phase current) = (4)

 LEGEND IN = Neutral Current IU = 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:

Let XC = 1

Let  = 1V

Then  =

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

Or ZT =  =

This gives us

= 2 amps or,  =  =  = 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:

Let XC = 1

Let  = 1V

Then  =

= 2 amps

= 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 currentwe had:

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:

and even further

 (5) or (6)

and if VT = V, this is really simplified to

Also the voltage on the remaining units given by:

%Vr =

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