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Split WYE Unbalance Detection Detection Discussion (Page 2 of 2)

First I would like to mention that IEEE C37.99 covers a configuration similar to this. Their formulas are for the WYE sections to be equal.

These Formulas are as Follows (Unbalance Calculation Formula)
1. The amount of current flowing between neutrals of the two equal halves. Current transformer is assumed to have zero impedance.

 IN = (9) %IN = (PERCENT OF RATED TOTAL BANK CURRENT) (10)

2. The Voltage remaining on units in one series section with F units removed.

 %VR = (11)

3. Permissible number of units that can be removed from one series section to determine the result in a given %VR on the remaining units in that section.

 F = If F is fractional use the next lower whole number. (12)

 LEGEND Vt Applied line to neutral voltage. V Rated voltage of the capacitor unit Vr Voltage on remaining units in affected group with F units removed. IN Current between neutrals of two banks halves. IU Rated current of one unit. S Number of series sections per phase. N Number of parallel units in one series section. F Number of units removed from one series section.

 TABLE 3 SPLIT WYE UNBALANCE WITH CT CONNECTED BETWEEN NEUTRALS System Volts Capacitor Volts # Series Sections # of Units per Section per Phase # of Failed Units Unit KVAR Unit Current Current Between Neutrals Percent Volts on Remaining Units 1000 1000 1 1 1 1 1.00 0.600 120.00 1000 1000 1 2 1 1 1.00 0.545 109.09 1000 1000 1 2 2 1 1.00 1.200 120.00 1000 1000 1 3 1 1 1.00 0.529 105.88 1000 1000 1 3 2 1 1.00 1.125 112.50 1000 1000 1 3 3 1 1.00 1.800 120.00 1000 1000 1 4 1 1 1.00 0.522 104.35 1000 1000 1 4 2 1 1.00 1.091 109.09 1000 1000 1 4 3 1 1.00 1.714 114.29 1000 1000 1 4 4 1 1.00 2.400 120.00 1000 1000 1 5 1 1 1.00 0.517 103.45 1000 1000 1 5 2 1 1.00 1.071 107.14 1000 1000 1 5 3 1 1.00 1.667 111.11 1000 1000 1 5 4 1 1.00 2.308 115.38 1000 1000 1 5 5 1 1.00 3.000 120.00 1000 1000 1 6 1 1 1.00 0.514 102.86 1000 1000 1 6 2 1 1.00 1.059 105.88 1000 1000 1 6 3 1 1.00 1.636 109.09 1000 1000 1 6 4 1 1.00 2.250 112.50 1000 1000 1 6 5 1 1.00 2.903 116.13 1000 1000 1 6 6 1 1.00 3.600 120.00

Unequal WYE Consideration Figure 7

However, these formulas need modification in order to work when the WYE sections (halves) are not equal.

Actually this method with section 1 with 3 units and section 2 with 2 units will give us five (5) units in parallel. The voltage on the remaining units using (12) is for equal halves. Therefore, we have to force this to work for us by making N=2 ½.

This Gives us N=2 ½
S=1
F=1
VT=V=7200 Volts

However, this will not give us the exact current when units are lost in different WYE sections. We will now develop the neutral current by removing units in phase A from the different WYE section.

For our work we will again only consider one series group.

From Section 2 with one unit removed in phase "A" we have Removing one unit from "A" phase in section 2 we have the following

From (4) This gives "A" phase voltage (VA’N’) of The current in "A" phase (IA’N’) is To determine the voltage on phase B AND C we can use (8)  The effective KVAR for this phase will be The current in VB’N’ is Section 1 neutral current is 26.8AMPS – 23.84AMPS = 2.96AMPS.

From section 1 the neutral current will be

Phase A voltage is the same as section 2, at 7714.08 Volts.

The phase "A" current will be  For IB’N’ the VB’N’ will be the same as section 2 = 6795Volts, again  Section 1 neutral current is 44.6AMPS –40.26AMPS = 4.34AMPS.

The neutral current with one unit removed in section 2 is 4.34 + 3.7 = 8.04 AMPS.

From section 1 with one unit removed in phase "A" we have Removing one unit from "A" phase in section 1 we have the following

From (4) This gives "A" phase voltage (VA’N’) of The current in "A" phase (IA’N’) is To determine the voltage on phase B AND C we can use (8)  The effective KVAR for this phase will be The current in VB’N’ is Section 1 neutral current is 40.26AMPS – 35.714AMPS = 4.55AMPS.

From section 2 the neutral current will be as follows

Phase A voltage is the same, as section 1, at 7714.08 Volts and multipliers will be the same as above.

Therefore, phase "A" current will be

1.714 * 27.777 = 29.761 AMPS

Phase "B" current will be

For IB’N’ the VB’N’ will be the same as section 2 = 6795Volts, again  Section 2 neutral current is 29.76AMPS –26.84AMPS = 2.92AMPS.

The neutral current between sections with one unit removed in section (1) is 4.55 + 2.92 = 7.47 AMPS

If two units are remove in one of the phases we can see the effect.

Again using formula (2) we have This gives use 1.1538 times 7200 = 8308 Volts across the affected leg. We will continue with phase "A" in section (1).

The current in this leg we use formula (5) We will not go through the rigors of obtaining all the numbers but will look at the pertinent values.

The voltage on phase B and C will be 6714.55 Volts and the current in these legs will be 38.86 AMPS. The neutral current in this section is

38.86 Amps-28.846 Amps = 10.014 Amps.

In section (2) the phase "A" voltage 8303 Volts, the effective KVAR is 266 KVAR and current in this leg is 32.017 amps.

Phase "B" and "C" voltage will be same section (1), 6714 Volts and the effective KVAR is 173.94 KVAR. The current in phase "B" and "C" will be 25.9 amps.

The neutral current in section (2) is

32.017 amps – 25.9 amps = 6.11 amps

The neutral current between sections with two units removed in section (1) is 10.014 + 6.11 = 16.12 amps

If two units were removed in section (2) the neutral current between sections would be approximately 33amps.

This table is with uneven number of capacitor units in each wye section

System Voltage: 7200
Cap. Voltage:7200

 TABLE 4 - SPLIT WYE UNBALANCE WITH CT CONNECTED BETWEEN NEUTRALS #UNITS OF PAR. IN SEC. 1 #UNITS FAILED IN SECT.1 UNIT KVAR SECT.1 UNIT CURRENT SECT.1 VOLTAGE ON PH A #UNITS OF PAR. IN SEC. 2 #UNITS FAILED IN SECT.2 UNIT KVAR SECT.2 UNIT CURRENT 2 VOLTAGE ON PH A % VOLTS REMAING UNITS Total Neutral current 2 0 100 13.89 7200.00 3 0 100 13.89 7200.00 1.00 0.00 2 1 100 13.89 8307.69 3 1 100 13.89 8307.69 1.15 16.69 2 2 100 13.89 9818.18 3 2 100 13.89 9818.18 1.36 41.94 3 0 100 13.89 7200.00 4 0 100 13.89 7200.00 1.00 0.00 3 1 100 13.89 7957.89 4 1 100 13.89 7957.89 1.11 15.78 3 2 100 13.89 8894.12 4 2 100 13.89 8894.12 1.24 36.57 3 3 100 13.89 10080.00 4 3 100 13.89 10080.00 1.40 65.31 4 0 100 13.89 7200.00 5 0 100 13.89 7200.00 1.00 0.00 4 1 100 13.89 7776.00 5 1 100 13.89 7776.00 1.08 15.31 4 2 100 13.89 8452.17 5 2 100 13.89 8452.17 1.17 34.15 4 3 100 13.89 9257.14 5 3 100 13.89 9257.14 1.29 57.95 4 4 100 13.89 10231.58 5 4 100 13.89 10231.58 1.42 88.97 5 0 100 13.89 7200.00 6 0 100 13.89 7200.00 1.00 0.00 5 1 100 13.89 7664.52 6 1 100 13.89 7664.52 1.06 15.03 5 2 100 13.89 8193.10 6 2 100 13.89 8193.10 1.14 32.78 5 3 100 13.89 8800.00 6 3 100 13.89 8800.00 1.22 54.07 5 4 100 13.89 9504.00 6 4 100 13.89 9504.00 1.32 80.14 5 5 100 13.89 10330.43 6 5 100 13.89 10330.43 1.43 112.76 6 0 100 13.89 7200.00 7 0 100 13.89 7200.00 1.00 0.00 6 1 100 13.89 7589.19 7 1 100 13.89 7589.19 1.05 14.84 6 2 100 13.89 8022.86 7 2 100 13.89 8022.86 1.11 31.89 6 3 100 13.89 8509.09 7 3 100 13.89 8509.09 1.18 51.69 6 4 100 13.89 9058.06 7 4 100 13.89 9058.06 1.26 74.99 6 5 100 13.89 9682.76 7 5 100 13.89 9682.76 1.34 102.82 6 6 100 13.89 10400.00 7 6 100 13.89 10400.00 1.44 136.63

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