Economical Placement of Shunt Capacitors

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Where the most economical and where the best place to connect shunt capacitors to your plant may be two different things.  It all depends on the reason you want, or need, to add these capacitors.

It is always a good idea to have a good power factor at your facility.  My paper “Economics When Appling Shunt Capacitors” covers benefits of a good power factor.

If an efficient system isn’t motivation enough to add capacitors generally power factor penalties and/or releasing transformer capacity is.

Power factor penalties are normally imposed on KW demand with power factors below 90 to 95%.  Most utilities are increasing the demand charges and increasing the required power factor levels to 95% or higher.   Typical low voltage capacitor applications have multiple steps in an effort to keep the power factor fairly steady through out the changes in the load.  Some people are adapting this philosophy to the medium voltage side of the transformer.  I am not sure why this practice came into affect, especially on the medium voltage side.

The fact that the penalties are based on KW demand the customer definitely needs the banks on during this time.  However, the KVAR does not need to follow the load during lighter loads.  Caution should be employed when using multiple steps with medium voltage applications.  The cost of the equipment will increase substantially when steps are added.  Also, there is a greater potential of equipment problems.  This doesn’t mean multiple steps should not be applied, it means if they are to be used they should be used at a minimum.

Multiple steps should be applied if the bank becomes large and switching of this bank creates problems in the plants operation.  Such as sensitive drives dropping out because of the transients.  Another reason multiple steps may be considered is during lighter load periods, like lunch slow downs, larger banks may force the power factor leading, and switching the bank off completely may cause billing problems if loads ramp up before the bank switches back on during a 15 minute interval.

Let us look at an assumed system to see what the economics

would be by placing capacitors at different points on this assumed system.

Assumed System

We have selected a fairly large system with multiple transformation points.  This is to discuss the logic of placing capacitors at various points on this system.

Correcting the System Power Factor

The power factor is 70% and the penalty charge is anything below 90%.  We will correct the power factor to 92%

KW = 8000   and   PF =0.70

Then KVA =
And

Correcting to 0.92 power factor

Then we get

Therefore, to correct to power factor from 70% to 92% we need

Simply the formula is:

Where:

Pf = present power factor
Cf = Corrected power factor
KW = Kilowatts

Therefore, we will use 4800KVAR to the system power factor.

Correcting the power factor on the primary side of transformer 1 (Cap #1):

Correcting this system from 70% power factor to 92% power factor, as stated we will use a 4800KVAR bank.  This will be connected to the 34.5 KV side of the transformer and we will use 150 KVBIL.  The system we will use will be three phase, four wire, solidly and multi-grounded.  Therefore, we will connect the capacitors in a grounded wye configuration. Also, we will place the bank in a metal enclosure.

The basic Bill-of-Material will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase Capacitor Vacuum Switch
4 – 400KVAR, 19.92KV, single bushing capacitors per phase.
12 – Current limiting fuses one per capacitor
1 - Controller

The percent of voltage drop to transformer (T-1) based on the parameters we have selected for our system will be

%Voltage Drop =

Therefore, the voltage at the transformer will be approximately 34.22KV.

Place the 4800KVAR capacitor bank at location (CAP 1) on Figure 1 will have the following effect:

%Voltage Rise =

D = Line length
KV = phase to phase voltage
R = 0.699 Ohms/mile
X = 0.712 Ohms/miles

This will improve the voltage at the transformer to 34.31 KV

Savings: Using the fact that anything below 90% power factor is calculated as KVA demand means that the customer will be charged for 11,428 KW times 0.9 = 10,285KW-8000kw = 2285 times 7 ≈ $16,000.00 penalty charge per month.   Placing the capacitor bank at this point will save this penalty charge.

The cost of the capacitor bank will be approximately $75,000.00

Correcting the power factor on the secondary side of transformer (T-1) (Cap #2):

The 4800KVAR capacitor bank will be connected to the 13.8 KV side of the transformer.  The system we will use will be three phase, four wire, solidly and multi-grounded.  Therefore, we will connect the capacitors in a grounded wye configuration. Also, we will place the bank in a metal enclosure.

The basic Bill-of-Material will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch
4 – 400KVAR, 7.960KV, two bushing capacitors per phase.
12 – Current limiting fuses, 8.3 KV, one per capacitor
1 - Controller

The percent of voltage drop to transformer (T-1) on the secondary side will be slightly higher because we have chosen an additional 0.01 (D) of cable to the 13.8 KV capacitor bank.

%Voltage Drop =

 There will also be a voltage drop through the transformer

Therefore, adding both loses; the voltage at the transformer will be approximately 13.442KV

Placing the 4800KVAR capacitor bank at location (CAP 2) on Figure 1 will have the following effect:

%Voltage Rise =

D = Line length
KV = phase to phase voltage
R = 0.699Ohms/mile
X = 0.712 Ohms/miles

The voltage rise through the transformer will be

Kvar =Applied Kilo-vars
Kva = Kva of the transformer     
X_t = Transformer Reactance in %
The 10000 KVA transformer using 6.5% reactance we would have:

Adding these two values this will improve the voltage at the transformer from 13.44KV to 13.9 KV

We have forced the KVA on the 10000kva transformer to be above this value to 11,428.6 KVA.  Placing the capacitor bank on the secondary side of this transformer will release KVA and will now be 8696 KVA.

There will be an added savings in the energy used.  This will be a small amount but there is some savings. 

Energy Savings=

The 8760 factor is 365 days times 24 hours. Divide this by 12 for the monthly value.  The KVA factor should be represented by the typical 24 hour demand.  For our numbers we used a factor of 0.48 or 4800KVA average. 

At the transformer secondary the energy savings would be approximately 26,640 KWHR’s.  At $0.0325 per KWH the savings is $859.00.

Savings: Here again improving the power factor above 90% will save the $16,000.00 penalty charge per month, plus an additional $859.00 in energy charges.  Also, it will relieve the transformer KVA.

The total monthly savings will be as follows: 

The cost of the capacitor bank will be approximately $57,000.00

Correcting the power factor on the secondary side of transformer (T-2) (Cap #4) and at the primary of transformer (T-3) (Cap #3):

The 4800KVAR capacitor bank will split with 1800KVAR for (Cap 3) on the 13.8KV line of transformer (T-3) and 3300KVAR for (Cap 4) on the 4.16 KV secondary side on transformer (T-2).  This is a total of 5100KVAR which is slightly higher. But, the power factor on transformer (T-3) is 77% and the power factor on transformer (T-2) is 64%. We will correct both locations to 92%.  For conveniences we will leave the system as three phase, four wire, solidly and multi-grounded.  The connection will be a grounded wye configuration and in a metal enclosure.

The basic Bill-of-Material for the 1800 KVAR, 13.8KV bank will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch
2 – 300KVAR, 7.960KV, two bushing capacitors per phase.
6 – Current limiting fuses, 8.3 kv, one per capacitor
1 – Controller

The basic Bill-of-Material for the 3300 KVAR, 4.16KV bank, we will split in two stages will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch per stage
2 – 167KVAR, 2.77KV, two bushing capacitors per phase per stage.
      (This will give us 1126KVAR per stage at 4160 volts.)
12 – Current limiting fuses, 4.3 kv, one per capacitor
1 - Controller

The percent of voltage drop to transformer (1) on the secondary side will be slightly higher because we have chosen an additional 0.025 (D) of cable to the 13.8 KV capacitor bank. The voltage drop will be

%Voltage Drop =		at (T-3) primary.
%Voltage Drop =		at (T-2) secondary.

 There will also be a voltage drop through both transformers

This will be approximately 1.6082% at transformer (T-3) and 1.9367% at transformer (T-1) and 1.4525 for transformer (T-2).

Therefore, adding both loses; the voltage at transformer (T-2) secondary will be approximately 4.0165KV, and at transformer (T-3) the voltage will be 13.46KV.

Placing the 1800KVAR capacitor bank at location (CAP #4) on Figure 1 will have the following effect:

%Voltage Rise =

 Placing the 3300KVAR capacitor bank at location (CAP #3) on Figure 1 will have the following effect:

%Voltage Rise =

D = Line length
KV = phase to phase voltage
R = 0.699 Ohms/mile
X = 0.712 Ohms/miles

The (T-2) transformer is 7500KVA and the (T-3) transformer is 5000KVA with both having 6.5% reactance we would have the voltage rise percent will be:

	for (T-2)
	for (T-3)

Adding these values this will improve the voltage at

Transformer (T-2) from 4.0089KV to 4.1747KV.

Transformer (T-3) from 581 Volts to 598.6 Volts.

The KVA of transformer (T-2) loading will improve from 6563 KVA to 4565 KVA.

At the transformers the energy savings would be approximately 40,599 KWHR’s.  At $0.0325 per KWH the savings is $1,319.47.

Savings: The total monthly savings will be as follows: 

The cost of the capacitor banks will be approximately $98,000.00

Correcting the power factor on the secondary side of transformer 2 (Cap #4) and at the secondary side of transformer 3 (Cap #9): 

Here we will place the 1800KVAR (Cap 9) on the secondary side, 600 Volts, on transformer (T-3) and will leave the 3300KVAR for (Cap 4) on the 4.16 KV secondary side on transformer (T-2). 

The basic 1800 KVAR, will consist of three multiple step 600KVAR standard capacitors assemblies.

We will leave the banks as above for the 3300 KVAR, 4.16KV bank, we will split in two stages will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch per stage
2 – 184KVAR, 2.4KV, two bushing capacitors per phase per stage.
      (This will give us 1656KVAR per stage at 4160 volts.)
18 – Current limiting fuses, 4.3 kv, one per capacitor
1 - Controller

The percent of voltage drop to transformer (T-3) on the secondary side will be slightly higher because we have chosen an additional  (D) of cable to the capacitor bank. The voltage drop will be

%Voltage Drop =

The percent of voltage drop to transformer (T-2) on the secondary side will be slightly higher because we have chosen an additional  (D) of cable to the capacitor bank. The voltage drop will be

%Voltage Drop =

 There will also be additional voltage drop through transformers (T-2) and (T-3).

This will be approximately 1.9367% at transformer (T-1), 0.8041% at secondary transformer (T-3) and 1.4525 for transformer (T-2).

Therefore, adding both loses;

1. The voltage at transformer (T-2) secondary will be approximately 4.0089KV.

2. The voltage at transformer (T-3) secondary the voltage will be 581 volts.

%Voltage Rise =		for (T-2)
%Voltage Rise =		for (T-3)

The voltage rise through (T-2) 7500 KVA transformer and the (T-3) 5000 KVA transformer with both having 6.5% reactance we would have:

	for (T-2)
	for (T-3)

Adding these values this will improve the voltage at

Transformer (T-2) from 4.0089 to 4.1747KV.

Transformer (T-3) from 581 volts 598.6 volts.

The KVA of transformer (T-2) loading will improve from 6563 KVA to 4565 KVA and the KVA of transformer (T-3) loading will improve from 4800 KVA to 3913 KVA.

At the transformers the energy savings would be approximately 46,688 KWHR’s.  At $0.0325 per KWH the savings is $1,517.00.

Savings: The total monthly savings will be as follows: 

The cost of the capacitor banks will be approximately $125,000.00

Correcting the power factor on the primary side of transformer (T-4) (Cap #5), transformer (T-5) (Cap #6) and at the secondary side of transformer (T-3) (Cap #9): 

Here we will leave the 1800KVAR (Cap 9) on the secondary side, 600 Volts, on transformer (T-3), place  the 1500KVAR for (Cap 5) on the 4.16 KV primary side on transformer (T-4) and place  the 2100KVAR for (Cap 6) on the 4.16 KV primary side on transformer (T-5).. 

The 1800 KVAR, will stay as above.

We will use a single step 1500 KVAR, 4.16KV bank, and will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch per stage
3 – 167KVAR, 2.4KV, two bushing capacitors per phase per stage.
9 – Current limiting fuses, 4.3 kv, one per capacitor
1 - Controller

We will use a single step 2100 KVAR, 4.16KV bank, and will include:

1 – Main disconnect switch.
1 – Control power transformer
3 – Distribution arresters
3 – Single phase capacitor Vacuum Switch per stage
4 – 175KVAR, 2.4KV, two bushing capacitors per phase per stage.
12 – Current limiting fuses, 4.3 kv, one per capacitor
1 - Controller

The percent of voltage drop to transformer (T-3) on the secondary side will be same as above. The voltage drop will remain:

%Voltage Drop =

 The voltage drop through transformer (T-3) will also stay the same

The percent of voltage drop to transformer (T-3) on the secondary side will be slightly higher because we have chosen an additional  (D) of cable to the capacitor bank. The voltage drop will be

%Voltage Drop =

The percent of voltage drop to transformers (T-4) and (T-5) on the primary side will be slightly higher because we have chosen an additional  D) of cable to the capacitor bank. The voltage drop will be

(T-4) %Voltage Drop =
(T-5) %Voltage Drop =

 The additional voltage drop through transformers will be:

This will be approximately 1.6082% at transformer (T-1), 0.8589% at secondary transformer (T-3), 1.393% for transformer (T-4) and 1.4979% for transformer (T-5).

Therefore, adding loses;

1. The voltage at transformer (T-3) secondary will be approximately 581 Volts.
2. The voltage at transformer (T-4) primary will be 4.0672 KV.
3. The voltage at transformer (T-5) primary will be 4.063 KV.

%Voltage Rise =

4. The voltage rise at transformer (T-3) secondary will be approximately 0.0269%.
5. The voltage rise at transformer (T-4) primary will be approximately 0.0393%
6. The voltage rise at transformer (T-5) primary will be approximately 0.055%.

The voltage rise through (T-2) 7500 KVA transformer and the (T-3) 5000 KVA transformer with both having 6.5% reactance we would have:

	for (T-3)
	for (T-4)
	for (T-5)

Adding these values this will improve the voltage at

Transformer (T-3) from 581 volts 598.6 volts.

Transformer (T-4) from 4.0672 to 4.122 KV.

Transformer (T-5) from 4.0633 volts 4.1395 KV.

At the transformers the energy savings would be approximately 67,978 KWHR’s.  At $0.0325 per KWH the savings is $2,230.00.

Savings: The total monthly savings will be as follows: 

The cost of the capacitor banks will be approximately $145,000.00

Correcting the power factor on the secondary side of transformer (T-4) (Cap #7), transformer (T-5) (Cap #8) and at the secondary side of transformer (T-3) (Cap #9): 

Here we will leave the 1800KVAR (Cap 9) on the secondary side, 600 Volts, on transformer (T-3), place  the 1500KVAR for (Cap 7) on the 480 volt secondary side on transformer (T-4) and place  the 2100KVAR for (Cap 8) on the 480 volts secondary side on transformer (T-5).. 

The 1800 KVAR, will stay as above.

We will use a multiple step 1500 KVAR, 480 volt with two standard 600KVAR assemblies and one 300KVAR unit.

The 2100KVAR requirement will include three 600 KVAR assemblies and one 300 KVAR assemble.

The percent of voltage drop to transformer (T-3) on the secondary side will be same as above. The voltage drop will remain:

%Voltage Drop =

 The voltage drop through transformer (T-3) will also stay the same

The percent of voltage drop to transformers (T-4) and (T-5) on the primary side will be slightly higher because we have chosen an additional  D) of cable to the capacitor bank. The voltage drop will be

(T-4) %Voltage Drop =
(T-5) %Voltage Drop =

 The additional voltage drop through transformers will be:

This will be approximately 1.6082% at transformer (T-1), 0.8589% at secondary transformer (T-3), 1.393% for transformer (T-4) and 1.4979% for transformer (T-5).

Therefore, adding loses;

1. The voltage at transformer (T-3) secondary will be approximately 581 Volts.
2. The voltage at transformer (T-4) secondary will be 432 volts.
3. The voltage at transformer (T-5) secondary will be 431 volts.

%Voltage Rise =

4. The voltage rise at transformer (T-3) secondary will be approximately 0.0269%.
5. The voltage rise at transformer (T-4) secondary will be approximately 0.864%
6. The voltage rise at transformer (T-5) primary will be approximately 0.0617%.

The voltage rise through  the (T-3) 5000 KVA transformer will have a 6.5% impedance,  the transformer (T-4) the 3000 KVA and (T-5) the 3750 KVA with both having 5.75% reactance we would have:

	for (T-3)
	for (T-4)
	for (T-5)

Adding these values this will improve the voltage at

Transformer (T-3) from 581 volts 598.6 volts.

Transformer (T-4) from 432 volts to 445 volts

Transformer (T-5) from 431 volts to 445 volts.

At the transformers the energy savings would be approximately 70,978 KWHR’s.  At $0.0325 per KWH the savings is $2,307.00.

Savings: The total monthly savings will be as follows: 

The cost of the capacitor banks will be approximately $175,000.00