Why How Capacitor Switching How capacitor switching

8/13/2019 Why How Capacitor Switching How capacitor switching

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The Why and How ofPower Capacitor Switching Thomas Marx

4000 E. 116t St.Cleveland, OH 44105 Ph (216) 271-6600 Fax (216) 341-3615 Email: [email protected]

www.joslynhivoltage.com

AG 001June 2003


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Copyright 1991 Fisher Pierce

PROPRIETARY NOTICE

Fisher Pierce reserves the right to make changes without notice in the materialcontained herein, and shall not be responsible for any damages, including

consequential, caused by reliance on the materials presented.

The text, drawings, instructions and specifications contained herein are the property ofFisher Pierce and shall neither be reproduced in whole or in part without prior writtenapproval, nor be implied to grant any license to make, use or sell equipment inaccordance herein.

CAUTION

The equipment covered by this publication must be selected for a specific applicationand it must be installed, operated and maintained by qualified persons who arethoroughly trained and who understand any hazards that may be involved. Thispublication is written only for such qualified persons and is not intended to be asubstitute for adequate training and experience in safety procedures for this type ofequipment.

First Printing November 1990Second Printing March 1991Third Printing April 1992Fourth Printing May 2003


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AcknowledgementsThe author wishes to thank Steven R. Nurnberg, Joseph R. Thibodeau, Richard A.Girard, and John R. Keefe for their contributions to this book.


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Table of Contents

1.0 Introduction .......................... .......................... ........................... ........................... ......................... 52.0 Loss Reduction ........................ ........................... ........................... ........................... ....................63.0 Demand Reduction......................................................................................................................114.0 Voltage Profile.............................................................................................................................13

5.0 Total Cost Benefit........................................................................................................................176.0 Capacitor System Considerations................................................................................................176.1 VAr Controls................................................................................................................................186.2 Current Controls..........................................................................................................................196.3 Voltage Controls..........................................................................................................................196.4 Time and Temperature Controls .......................... ........................... ........................... .................. 196.5 Radio Controls ......................... ........................... ........................... ........................... .................. 196.6 Power Factor Controls.................................................................................................................197.0 Fisher Pierce Capacitor Switching Controls ........................... ........................... ........................... 227.1 VAr Controls (4600 Series)..........................................................................................................227.2 Current Controls (4800 Series) ....................... ........................... ........................... ....................... 237.3 Voltage Controls (2400 Series)....................................................................................................237.4 Time Controls (5600 Series)........................................................................................................247.5 Temperature Controls (5700 Series)............................................................................................247.6 Radio Controls ......................... ........................... ........................... ........................... .................. 247.7 Power Factor Controls.................................................................................................................247.8 Neutral Current Relay..................................................................................................................247.9 Combination Controls..................................................................................................................248.0 APPENDIX........................... .......................... ........................... ........................... ....................... 268.1 Conductor Data...........................................................................................................................268.2 Single-Phase Line-To-Neutral Capacitor Current ....................... ........................... ....................... 278.3 Capacitor Bank Worksheet ......................... ........................... ........................... ........................... 288.4 Capacitor Bank Worksheet Worked Example............................................................................308.5 Derivation of Loss Reduction Equation ......................... ........................... ........................... .........329.0 Field Tables ......................... .......................... ........................... ........................... ....................... 339.1 Single-Phase Line-to-Neutral Capacitor Current Field Table ........................ ........................... .....339.2 VAr Control Settings....................................................................................................................34

9.3 Single-Phase Reactive Current vs. A REAC Jack Vdc Reading ........................ ........................... 419.4 Three-Phase Line kVAr vs. A REAC Jack Vdc Reading........................... ........................... .........439.5 Power Factor vs. A REAC Jack Vdc and Line Current Vac....................... ........................... .........65


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1.0 Introduction

There are four reasons for using power capacitors:

1. Reducing avoidable losses caused by reactive load current.2. Reduce kVA demand.

3. Improve voltage profile.4. Increase revenue or decrease customer energy consumption.

All of these advantages can be evaluated on a financial basis. Generally, it can be stated that unless adistribution system has already been covered with switched capacitor banks on the feeders, addingswitched feeder capacitors produces the fastest pay-back of any equipment investment.

This book is intended to demonstrate the benefits provided by switched capacitor banks on distributionfeeders. The analysis outlined here requires only a simple pocket calculator to compute all of the factorsfor a section of feeder between a capacitor bank and the next upstream bank or substation. Typicalvalues are given for the various cost factors which can be used when no other data are available.

There is also a discussion of multiple capacitor feeders and the application of the various types ofswitching controls. However, this book is not designed for planning capacitor size and placement on amulti-tap system.

Finally, there is a brief guide to Fisher Pierce switching controls and some discussion of the products.


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2.0 Loss Reduction

The real energy loss due to utility line and transformer resistance is caused by the customers load, butthis energy is not registered by customers meters. There are two components to this loss; that caused bythe resistive component of the load, which cannot be avoided, and that caused by the reactive componentof the load, which can be avoided. Switched capacitor banks can be used to dramatically reduce the

avoidable losses.

About sixty percent of the system energy loss is caused by the resistance of the feeder conductors.Consequently, it is important to locate the power capacitors on the feeders as close to the loads aspractical. Substation capacitors cannot reduce feeder losses the reactive load current has alreadycaused heating of the feeders downstream of the substation. Reducing the reactive current at thesubstation cannot recover the heat lost on the on the feeders (Figure 1).

Figure 2.1: Feeder Resistive Losses

Substation

Substation

Substation

Substation

HeavyInductive

Load

Heavy

InductiveLoad

HeavyInductive

Load

HeavyInductive

Load

Line heating loss is caused by real and reactive load current.

A capacitor bank near the load greatly reduces the loss caused by the load

A capacitor bank located between the load and the substation saves line loss

A capacitor bank in the substation cannot recover any of the line heating loss.


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The appendix contains the derivation of the equation used here to calculate the loss reduction from acapacitor bank applied to a section of line from the bank to the next upstream capacitor or to thesubstation. This equation,

Loss reduction = 3RLINE[2IINDICAP) ICAP2], W,

Where: RLINE = single-phase line resistance (ohms)IIND = single-phase load inductive current (amps)ICAP = single-phase capacitor current (amps)W = three-phase line real power loss reduction (watts)

shows that reduction of avoidable losses depends on the reactive component of the load, but not on thereal component. Consequently, line power factor does not indicate how well loss reduction has beenaccomplished.

In the example give in section 8.4, the year-round industrial load current is 100A at 0.8 PF. Switching a900k Var bank onto the 5-mile section of #2 ACSR line reduced the power loss by 80.5kW. Now, supposethat a large housing development is added to the feeder and the winter load is increased by 40A resistive.The load power factor has been improved to 0.9PF, but the loss reduction caused by the capacitor bankis still 80.5kW. That is why this analysis is concerned with the reduction of reactive current, not theincrease in power factor.

As the size of a capacitor bank increases, the loss reduction increases until the leading current of thebank equals the lagging current of the load. However, as the capacitor current approaches the loadinductive current, each incremental capacitor results in less loss reduction. Figure 2.2 shows line losspower saving as a function of bank size for the example in 8.4. A good rule-of-thumb is to use a bank sizetwo-thirds of the value needed to reduce the peak load Vars to zero.

Another reason for using a capacitor bank that is not too large is to be able to set the capacitor control toswitch the bank onto the line early in the load cycle. The overall energy reduction is then usually greaterthan when using a large bank that is turned on for fewer hours per day.

There are several conditions that can reverse the loss reduction:Oversize fixed banks

Improperly controlled switched banksVoltage controlled switch banks

Figure 3 is a continuation of Figure 2 and shows the effect of bank sizes for which the capacitor current isgreater than the load inductive current. When the bank kVAr is two times the load kVar, there is no lineloss saving. Larger banks cause the line to go so far leading as to increase the loss over that of the loadwithout any bank on line. This condition is indicated by a minus sign in the loss reduction calculation.

The energy saved equals the power reduction times the time the bank is on the line (assuming anefficient switching method), and the cost saving equals that energy times the value of avoided energy.Usually, yearly figures are calculated so:

$SAVE/year = kWSAVEx h/year x $/kWh

In the example cited, the capacitor bank is on line 1,500/year, and energy is worth $.05/kWh, so,

$SAVE/year = 80.5kW x 1,500 h/year x $.05/kWh = $6,038


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Figure 1.2: Loss Reduction versus Bank Size

In assigning a value to the energy saved, it is important to consider that in most cases the bank will be onat the heavy load time of day, when peaking or purchased energy is most expensive.


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Figure 2.3: Losses for ICAPGreater than IIND

Figure 4 shows a typical daily load in which the reactive current increases more or less graduallydecreases towards evening. The avoidable losses can be reduced by 89% by installing a bank that is only2/3 as large as the peak load Kvars. Also, the Var sensing control is set to close the bank onto the linewhen the load inductive current equals 2/3 the bank capacitive current. Even though this scheme drivesthe line leading when the bank is first turned on and before it is turned off, the loss reduction is optimumfor a single bank.


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Figure 2.4: Effect on Power Capacitor on Daily Reactive Load

I LAG MAX

I LAG

TIME

Reactive Current Without Capacitor

Loss Reduction = 0%

Loss Reduction = 89%

ICAP

CAP ON= 2/3 ICAP

ICAP = 2/3 ILAG MAXILEAD MAX AT CAP OFF = 1/2 ICAP

Maximum Loss Reduction


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3.0 Demand Reduction

The reduction in reactive current caused by a power capacitor also reduces the total line current. Thisreduction in kVA demand during heavy load periods has a number of benefits:

1. The peak allowable loading is increased when it is most needed (that is the same as saying there

is released demand).2. The effective ampacity of the lines is increased.3. The operating temperatures of the lines and transformers are reduced, increasing equipment life.4. The necessity to upgrade lines and transformers may be delayed.

In the example cited in section 8.4, the line current before the bank was switched onto the line was 100A,and the demand was:

3 x 100A x 13.2kV = 2,286kVA3

When the bank is switched on, the line current is reduced to:

ILINE

=IRESIS

2

+ (IIND

-ICAP

)

2

, A

= 802= (60-39.4)2 = 82.6A

and the demand is:3 x 82.6A x 13.2kV = 1,888kVA

3

This reduction of 398kVA represents a release a 17.4% of the initial demand. In general, a 30% reductionin peak demand from the use of switched capacitors is not uncommon. The value of demand reductionvaries between utilities, but $80/year/kVA is typical, based on a five-year write-off cycle for capitalequipment. Using this figure, the savings in the example is:

398kVA x $80/year/kVA = $31,840/year saved.

In this example the cost savings from demand reduction is many times that of the energy reduction. Onthe other hand, the $80/year/kVA demand value may be more difficult to prove than the energy costsaving. The factors contributing to the value of demand reduction are:

Released generation capacityReleased transmission capacityReleased substation capacityReleased feeder capacity

Figure 3.1 shows the kVA demand as the capacitor bank size in the example is increased. The curveshows that the incremental released demand decreases as the bank leading current approaches the loadinductive current. Unlike line loss reduction, the demand reduction is affected by the magnitude of theresistive current; it is more difficult to reduce the kVA when the power factor is high.

As the curve in Figure 3.1 continues for capacitor sizes greater than the load inductive current, it swingsupwards. Fixed or oversize banks or improperly controlled switched capacitors cause an increase in kVAdemand if the line is allowed to go leading. Also, when power capacitors are used for voltage control, theline may be driven leading, and the kVA demand increases over that of the optimum loss and demandreduction case.


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Figure 3.1: Demand Reduction vs. Bank Size

Even when the line is not driven leading for voltage control, the bank increases the line voltage, and theresulting demand increase partially counteracts the demand reduction. The extent to which the voltagerise increases demand depends on the characteristics of the load. A purely resistive load that staysconnected to the line will cause a demand increase proportional to the square of the voltage. However,many loads will either not increase so sharply or the high increase will be temporary because controlaction, such as thermostats, will keep the energy constant.

As a rule of thumb, the maximum demand of a diversified load will increase by 1.6 times the increase of

voltage. That is, for every percent voltage increase, the maximum demand will increase 1.6 percent. Thelong-term average demand will increase one-third to one percent for each one percent voltage increase.

In the example given in the Voltage Profile section, the capacitor bank caused a 2.06V or 1.7% increase.If the long-term demand of the load changed by 0.7% demand per 1% voltage, then the demand increasewould be:

1.7%x 0.7%Demand = 1.19% demand increase%

Consequently, there is an increase in demand costs of:

.0119 x 1,888kVA x $80/year/kVA = $1,800/year cost

The net saving is $31,840 - $1,800 = $30,040/year saved.


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4.0 Voltage Profile

The demand capacity of distribution feeders is usually limited by voltage drop along the line rather than byconductor thermal ampacity. The service entrance voltage of all customers must be kept within certainlimits, usually +5 to +10%. If the feeder voltage profile can be flattened, there are several benefits tochoose from, the first two of which occur at heavy load periods when they are most needed:

1. The kVA demand can be increased to arrive at the original voltage drop. That is the same assaying that feeder demand has been released.

2. The substation voltage can be lowered to reduce peak demand and save energy.3. The service entrance voltage can be allowed to increase and, consequently, increase

revenue (but the kVA demand will not be optimum).

The voltage drop along the feeder conductor is composed of a number of components; Figure 4.1 showsthe voltage phasors for a section of line feeding a concentrated load. The phase angle between thevoltages at the ends of the line section is small, so all of the quadrature components are ignored. Thevoltage drop is caused by two load and line components that are in phase with the source voltage; Theline resistance times the resistive load current and the line reactance times the lagging load component.That is:

LOAD= (RLINEx IRESIS) + (XLINEx IREAC)

In the example shown:

LOAD = 8.45 X 80 + 3.33 X 60 = 876V

This drop is 11.5% of the source voltage, or 13.8V based on a 120V reference.

When the capacitor bank is added to the line, there is a voltage increase due to the line reactance timesthe bank capacitive current acting in the opposite direction from the load voltage drop:

CAP = XLINE X ICAP

In the example, this voltage recovery is:

CAP = 3.33 x 39.4 = 131V

or 2.06 based on 120V. Typically, the effect of a capacitor bank is in the range of 2-5V (120V reference).


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Figure 4.1: Conductor Voltage Drop


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When the purpose of a the capacitor bank is to control voltage, the bank may be sized so large that thecapacitive current exceeds the load inductive current. Therefore, the line current will swing leading, thekVA demand will increase and there may be instability problems, especially at light load (although, ifproperly controlled, the bank will probably not be on at light load).

The effect of voltage on demand is discussed in the Demand Reduction section; using the same guide forreal power as used for a long-term diversified demand, the power increases at a rate of 0.33 to 1 percentfor each percent increase in voltage, so the service entrance meter will register an increase in energy:

Energy = Power x Time

In the example, the load has a resistive component of 80A, so the power is:

3 x 80A x 13.2kV = 1,829kW

3

and the capacitor bank is on for 1,500 hours/year. The voltage increased by 1.7% and the load increased0.7% for each percent voltage increase, so the power increased 1.19%. Therefore,

.0119 x 1,829kW x 1,500h/yr. = 32,648kWh/yr. increase

If the charge for metered energy during heavy load periods is twice the cost of energy to the utility, thenthe utility in the example receives 2 x $0.5 = $.10kWh, and the revenue increase due to the voltage riseis:

$.10/kWh x 32,648kWh/yr. = $3,265/yr. increase


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Figure 4.2 shows the voltage profile of a uniformly loaded feeder; the end of the feeder is below theminimum acceptable voltage. When the bank is switched on, the entire feeder voltage, upstream anddownstream from the bank, is increased. (Although it is possible to suddenly change the current along afeeder, it is impossible to make a step change in voltage along a conductor.) Additional banks on the linewill add to the voltage rise, so that all active capacitors contribute to the shape of the voltage profile alongthe entire feeder.

Figure 4.2: Voltage Profile


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5.0 Total Cost Benefit

The financial benefit of a power capacitor can be balanced against the cost of the bank plus the switchingcontrol. Using the example cited:

Energy cost saving (transformer, substation,

and transmission savings not included): $ 6,038/yr.Demand reduction: $30,040/yr.Increased revenue: $ 3,265/yr.

The energy saving is tangible, but the demand value and increased metered energy are not so easy toassess this example ranges from $6,000 to $40,000 per year, depending on how the three factors areadded.

The cost of the 900kVAr bank, complete with switch and control, is on the order of $8/kVAr, or:

Bank cost = 900 x 8 = $7,200

Distribution equipment is often accounted for at a rate of 20%/year, so the yearly cost of the bank,allowing 10% interest, is:

Capacitor cost rate = .264 x $7,200 = $1,900/year

Obviously, properly switched power capacitors located on distribution feeders provide extreme financialbenefit to the utility.

6.0 Capacitor System Considerations

If there is to be only one capacitor bank on a uniformly loaded feeder, the traditional two-thirds, two-thirds rule gives optimum loss and demand reduction. That is:

The bank kVAr size should be two-thirds of the heavy load kVAr as measured at the substation, and thebank should be located two-thirds the length of the feeder from the substation. (If the objective is voltagecontrol, the bank should be farther from the substation.)

Using the example shown in Figure 2.4, this rule can be expanded to two-thirds, two-thirds, two-thirds:(the Fisher Pierce two-thirds

3rule):

1. The bank size should be 2/3 maximum load kVAr.2. The bank should be located 2/3 down the feeder.3. The control should be set up to close the bank onto the line when the lagging line

current reaches 2/3 the capacitor current.

In the case of concentrated industrial loads, there should be a bank, sized to almost equal the reactive

load current, located as close to each load as practical.

On a uniformly loaded feeder, located as close to each load as practical.

On a uniformly loaded feeder, greater savings can be achieved by using a number of banks distributedalong the feeder so that the load reactive current is compensated before it travels through much feederconductor. With more banks on the feeder, the total capacitor kVAr can more closely equal the total loadkVAr. Depending on the type of switching control, multiple banks on a feeder can lead to pumping as the


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controls affect the operating points of each other. Usually, no more than three or four switched banks areused on a feeder. Control interaction results from the change in line parameters when a bank is switched:

The reactive current between the substation and the bank is changed.

The total line current between the substation and the bank is changed.

The line voltage along the entire feeder is changed.

Figure 4.2 shows the effects of two banks on the voltage profile, and Figure 6.1 shows the reactivecurrent profile.

Reverse power flow will often cause efficient operation of a multiple capacitor system, because thecontrol settings will probably have been adjusted for increasing load towards the substation. Var andpower factor controls will operate in the wrong quadrant, so if reverse flow is possible, these controlsshould be equipped with a reverse power inhibit function.

Figure 6.1: Effect of Multiple Banks on Reactive Current

6.1 VAr Controls

In the case of a single bank per feeder, VAr controls are by far the most efficient for maximum loss anddemand reduction. Once the capacitor size has been selected, the capacitive current is known. Since aVAr control responds only to reactive current, it will switch the bank onto the line at the optimum point inthe load cycle regardless of any change in power factor, load growth, day of week, etc. (As explained in


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It would obviously be a mistake to turn on a large capacitor bank at light load in response to a low powerfactor. As previously discussed, loss reduction depends only on reactive current, not power factor.Therefore, if a control fails to turn the bank on at heavy load because the power factor is high, theopportunity to save the line losses is forfeited.

To guard against inappropriate operation, a power factor control might be protected with voltage and loadcurrent overrides. At this point it is probably better to use a VAr or current control in the first place. Powerfactor controls are susceptible to interaction from downstream capacitor banks.

The phasors in Figure 6.2 compare the operation of VAr and power factor controls when the loadcharacteristics change. Such changes may be a result from long-term load growth or due to weekly,seasonal, or even time of day variations. The point is that power factor is a measure only of phase angle,while a capacitor adds a fixed amount of leading current to the line regardless of the power factor. Thechange in power factor caused by the capacitor depends on the value of the line resistive current.

Summary of Capacitor Control Attributes

Type ofControl

Current SignalRequired

LossReduction

Efficiency

VoltageProfile

Improve

DemandReduction

Efficiency

InteractionBetween

Banks

VAr Yes Highest Moderate High High

Current Yes Moderate High High Moderate

Voltage No Moderate Highest Moderate High

Temperature No Problematic Problematic Problematic None

Time No Problematic Problematic Problematic None

Power Factor Yes Problematic Problematic Problematic High

RadioSCADANeeded

Can be High Can be High Can be High None


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Figure 6.2: VAr vs. Power Factor Control for Changing Load


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7.0 Fisher Pierce Capacitor Switching Controls

7.1 VAr Controls (4600 Series)

Fisher Pierce VAr controls are actually reactive current controls. Since line voltage is relatively constant

compared to reactive current, operation in response to Ar is almost identical to VAr. High and low voltageoverride and reverse power disable options are available on most models.

There is a Fisher Pierce control available for either current transformer or inductive current sensor inputsfor both four-wire wye and three-wire delta circuits. Figure 7.1

Figure 7.1: Types of Fisher Pierce VAr Controls

BASIC CURRENTMODEL SIGNAL AND

WIRING

4604 1301 Sensor Wye

4605 1301 Sensor Delta

4608 CT WYE

4609 CT DELTA


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Figure 7.2 shows the Fisher Pierce reactive current measuring method, which is similar for CT andcurrent sensor inputs, except that the current sensor signal is inherently 90 degrees out of phase with theline current. The signal conditioning circuit is critical to proper operation with inductive sensors.

Figure 7.2: Low Profile 4604 VAr Control Block Diagram

Measurement of reactive current requires a phase reference. Distribution lines usually have only a few

percent voltage distortion, so the voltage axis crossings can be used as a reliable phase reference. Thevoltage axis reference is used to drive an electronic switch which chops the current waveform. The DCcomponent of the chopped signal represents the quadrature (i.e. reactive) component of the current. Fora purely resistive signal, the DC value is zero. As the load becomes more lagging, the signal shifts tot ehright and the DC value becomes positive; leading current shifts the signal to the left and the DC voltagebecomes negative. The magnitude of the DC voltage is proportional to the amplitude and phase angle ofthe reactive current; that is, I sin .

7.2 Current Controls (4800 Series)

Fisher Pierce offers current controls for use with CT or inductive current sensor input. Signal conditioningis critical for inductive sensor signals. All Fisher Pierce low profile current controls utilize a true rmsmeasuring integrated circuit; modular current controls are average sensing.

7.3 Voltage Controls (2400 Series)

Fisher Pierce voltage controls utilize a tru rms measuring integrated circuit. Voltage controls are availablewith a step bias option.


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7.4 Time Controls (5600 Series)

Fisher Pierce offers 7-day and 365-day electronic time controls. All models contain batteries for poweroutage override.

7.5 Temperature Controls (5700 Series)

The typical range for high temperature controls, which close on increasing temperature, is 70-120F. Thetypical range for controls that close on decreasing temperature is 0-50F.

7.6 Radio Controls

Consult the Fisher Pierce Sales department for details of radio control systems.

7.7 Power Factor Controls

Fisher Pierce does not offer a power factor control.

7.8 Neutral Current Relay

Neutral current sensing controls are used to trip a capacitor bank off the line and lock out closeoperations if incipient capacitor failure is detected by the presence of unbalanced neutral current. FisherPierce offers both a stand-alone neutral current relay and a module that can be included in the modularcapacitor controls. The neutral current sensing circuit greatly attenuates harmonics.

7.9 Combination Controls

The modular controls can be configured with up to three control modules to perform the followingfunctions:

1. Basic voltage control with step bias, which shifts the cap on and cap off set points bya settable amount. The points at which the bias is enabled and disabled are set onthe auxiliary module or by an external contact. Note: The amount of bias is set on thebasic voltage module, which must be ordered with the bias option.

2. Basic control with close and/or trip override. A close override forces a close operationand inhibits a trip. A trip override forces a trip operation and inhibits a close. Separate

modules are used for each override, and the override threshold, and release pointsare set on those modules.

3. Basic control with neutral current lockout. A neutral current module can be added to abasic control; once activated, the neutral current relay will force a trip and lockoutfurther close operations until a manual reset button is pressed.


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Summary of Fisher Pierce Capacitor Switching Controls

Basic Model Type of Sensing Remarks

2406 Voltage No bias

2412 Voltage With bias

4604 VAr 1301-X1 sensor, 4-wire, Wye

4605 VAr 1301-X1 sensor, 3-wire, Delta

4608 VAr CT, 4-wire, Wye

4609 VAr CT, 3-wire, Delta

4614 VAr 4604 with reverse power disable

4615 VAr 4604 for 1301-X1 or X7 sensor

4616 VAr 4605 for 1301-X1 or X7 sensor

4617 VAr 4615 with reverse power disable

4620 VAr 1301-X7 sensor, 4-wire, Wye

4621 VAr 1301-X7 sensor, 3-wire, Delta

4844 Current 1301-X1 or X7

4846 Current Current transformer

5691 Time 7-day repeat cycle electronic clock

5695 Time 365-day programmable electronic clock

5732 Temperature Close on increasing temperature, electronic sensor

5733 Temperature Close on decreasing temperature, electronic sensor

1301-X1 refers to the standard current sensor.1301-X7 refers to the high accuracy current sensor.


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8.0 APPENDIX

8.1 Conductor Data

Size AWG or KCM TYPE AmpacityA

ResistanceRESIS/mile

ReactanceIND/mile

642

ACSRACSRACSR

100140180

3.982.571.69

0.6730.6590.665

11/02/0

ACSRACSRACSR

200230270

1.381.120.895

0.6650.6560.641

4/0267336

ACSRACSRACSR

340460530

0.5920.5520.306

0.5810.6050.451

398

477557

ACSR

ACSRACSR

600

670730

0.259

0.2160.186

0.441

0.4300.415

605636716795

ACSRACSRACSRACSR

760780840910

0.1720.1620.1440.138

0.4150.4120.4050.401

642

CUCUCU

130180240

2.411.520.955

0.6280.5990.571

11/02/0

CUCUCU

270310360

0.7570.6070.481

0.5570.5460.532

4/0250350

CUCUCU

480540670

0.3030.2570.184

0.5030.4810.460

450600750

CUCUCU

7809401090

0.1440.1100.089

0.4510.4320.417

21/02/0

AACAACAAC

160215250

1.410.8870.708

0.5760.5440.533

4/0336477

795

AACAACAAC

AAC

340465590

920

0.4440.2800.195

0.116

0.5020.4650.444

0.417


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8.2 Single-Phase Line-To-Neutral Capacitor Current

Distribution Voltage Capacitor Bank Size, kVAR

EL-LkV

EL-NkV

300 600 900 1200 1500 1800 2100 2400

4.16 2.4 41.7 83.3 125 167 208 250 292 333

8.32 4.8 20.8 41.7 62.5 83.3 104 125 146 167

12.0 6.93 14.4 28.9 43.3 57.7 72.2 86.6 101 115

12.47 7.2 13.9 27.8 41.7 55.6 69.4 83.3 97.2 111

13.2 7.62 13.1 26.2 39.4 52.5 65.6 78.7 91.9 105

13.8 8.0 12.5 25.0 37.5 50.0 62.5 75.0 87.5 100

14.56 8.4 11.9 23.8 35.7 47.6 59.5 71.4 83.3 95.2

20.78 12.0 8.3 16.7 25.0 33.3 41.7 50.0 58.3 66.7

22.9 13.2 7.6 15.2 22.7 30.3 37.9 45.5 53.0 60.6

24.94 14.4 6.9 13.9 20.8 27.8 34.7 41.7 48.6 55.6

27.6 15.9 6.3 12.6 18.9 25.2 31.4 37.7 44.0 50.3

34.5 19.9 5.0 10.1 15.1 20.1 25.1 30.2 35.2 40.2

ICAP= 1/3 x KVAR = 1/3 x KVAR = KVAR ; EL-Lin kVEL-N EL-L/3 EL-L/3

Example: Bank = 900kVAREL-L = 13.2kV

ICAP= 900 = 39.4A lead13.2 x 3


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8.3 Capacitor Bank Worksheet

List Line Conditions1. Distance to next upstream capacitor bank of to substation: __________ miles

2. Conductor size and type: _________/_________

3. Line voltage: __________ kVL-L

4. Bank size: __________ kVArCAP

5. Load current: __________ A, ILINE

__________ A, IIND

__________ A, ILINE

__________ PF

List Values For Computation

6. Cost of energy during heavy load time of day: __________ $ / kWh

7. Single-phase line resistance:

________ Miles x _________ RESIS/Miles = __________ RLINEStep 1 Table 1

8. Single-phase line inductance:

________ Miles x _________ IND/Miles = __________ IND Step 1 Table 1

9a. Single-phase capacitor current:

Step 4 and Table II: __________ A, ICAP

or 9b.

________ kVarCAP/ _________ kVL-L/1.73 = __________ A, ICAP Step 4 Step 3

10. Single-phase inductive load current:5A __________ A, ICAP

or 10b. __________ A, ICAP

11. Estimate hours per year capacitor bank is on:

____h/day x _____ day/wk x _____ wk/yr = ___________ hr/yr

or 11b. Use 10 h/day x 5 day/wk x 50 wk/yr = 2,500 hr/yr

Calculate Three-Phase Line Loss Reduction

12. 3 x _______ {(2 x _______ x _______) - ________2} / 1,000 = ___________ kWSAVERLINE IIND ICAP ICAPStep 7 Step 10 Step 9 Step 9

5A

5B

or

__________ (_________ x _________) =ILINE ILINE PF

Step 5B Step 5B Step 5B


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Calculate Yearly Energy Cost Savings

13. _______ kWSAVE X_______ hr/yr x ________ $/kWh = ___________ $SAVE/yrStep 12 Step 11 Step 6

Calculate Increase in Line Voltage (120V Reference)

14. _______ ICAP X________ IND X .120 X 1.73/________KV = __________ V,SEC

Step 9 Step 8 Step 3

Calculate Reduction in kVA Demand

15a. (_______ ILINEx ________ PF)2= __________ A2, IRESIS

2Step 5B Step 5B

15b. _______ 2- ________ 2= __________ A2, IRESIS2

ILINE IINDStep 5A Step 5A

16. Line current with capacitor bank on:

= + ( - )2 = ___________ ILINE/CAPIRESIS

2 IIND ICAPStep 15 Step 10 Step 9

17. Reduction in line current:ILINE- ILINE/CAP = ___________ A, I

Step 5 Step 16

18. Reduction in demand:

3 x _______ I x _________ kV + 1.73 = ___________ kVAStep 17 Step 3


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8.4 Capacitor Bank Worksheet Worked Example

List Line Conditions1. Distance to next upstream capacitor bank of to substation: 5 miles

2. Conductor size and type: #2 / ACSR

3. Line voltage: 13.2 kVL-L

4. Bank size: 900 kVArCAP

5. Load current: __________ A, ILINE

__________ A, IIND

100 A, ILINE

0.80 PF

List Values For Computation

6. Cost of energy during heavy load time of day: 0.05 $ / kWh

7. Single-phase line resistance:

5 Miles x 1.69 RESIS/Miles = 8.45 RLINEStep 1 Table 1

8. Single-phase line inductance:

5 Miles x 0.665 IND/Miles = 3.33 IND Step 1 Table 1

9a. Single-phase capacitor current:

Step 4 and Table II: 39.4 A, ICAP

or 9b.

________ kVarCAP/ _________ kVL-L/1.73 = __________ A, ICAP Step 4 Step 3

10. Single-phase inductive load current:5A __________ A, ICAP

or 10b. 60 A, ICAP

11. Estimate hours per year capacitor bank is on:

6 h/day x 5 day/wk x 50 wk/yr = 1500 hr/yr

or 11b. Use 10 h/day x 5 day/wk x 50 wk/yr = 2,500 hr/yr

Calculate Three-Phase Line Loss Reduction

12. 3 x 8.45 {(2 x 60 x 39.4 ) - 39.4 2} / 1,000 = 80.5 kWSAVERLINE IIND ICAP ICAPStep 7 Step 10 Step 9 Step 9

5A

5B

or

100 ( 100 x 0.80 ) =ILINE ILINE PF

Step 5B Step 5B Step 5B


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Calculate Yearly Energy Cost Savings

13. 80.5 kWSAVE X 1500 hr/yr x 0.05 $/kWh = $6038 $SAVE/yrStep 12 Step 11 Step 6

Calculate Increase in Line Voltage (120V Reference)

14. 39.4 ICAP X 3.33 IND X .120 X 1.73/ 13.2 KV = 2.06 V, SECStep 9 Step 8 Step 3

Calculate Reduction in kVA Demand

15a. ( 100 ILINEx 0.80 PF)2= 6400 A2,IRESIS

2

Step 5B Step 5B

15b. _______ 2- ________ 2= __________ A2, IRESIS2

ILINE IINDStep 5A Step 5A

16. Line current with capacitor bank on:

= 6400 + ( 60 - 39.4 )2

= 82.6 ILINE/CAPIRESIS

2IIND ICAP

Step 15 Step 10 Step 9

17. Reduction in line current:100 ILINE- 82.6 ILINE/CAP = 71.4 A, IStep 5 Step 16

18. Reduction in demand:

3 x 17.4 I x 13.2 kV + 1.73 = 398 kVAStep 17 Step 3


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8.5 Derivation of Loss Reduction Equation(Reduction in real power losses in distribution line resistance.)

Loss Reduction = Loss w/o cap Loss w/ capLoss w/o cap = (ILINEw/o cap)

2RLINE

Loss w/ cap = (ILINEw/ cap)2RLINE

Loss Reduction = (ILINEw/o cap)2RLINE (ILINEw/ cap)

2RLINE= RLINE [(ILINEw/o cap)2 - (ILINEw/ cap)2

(ILINEw/o cap)2 =IRESIS2+ IIND2(ILINEw/ cap)2 =IRESIS2+ (IIND ICAP)2

=IRESIS + IIND

2+ ICAP)

2- 2 IINDICAP

Loss Reduction= RLINE[(IRESIS

2+ IIND

2) - (IRESIS

2+

IIND

2+ ICAP

2- 2 IINDICAP)]

= RLINE(IRESIS2+ IIND

2- IRESIS

2-IIND

2- ICAP

2+ 2 IINDICAP)

= RLINE(-ICAP2+ 2 IINDICAP)

For the phases: Loss Reduction = 3 RLINE (-ICAP2 + 2 IINDICAP)

Note that the resistive current terms cancel out, so the loss reduction does not depend on power factor.


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9.0 Field Tables

Note: All of the tables are valid for both wye and delta services. All of the voltmeter readings are takenwith respect to the NEUT test jack.

9.1 Single-Phase Line-to-Neutral Capacitor Current Field Table

This shows the single-phase capacitor current for line voltages from 4.16 to 34.5kV and for bank sizesfrom 300 to 1800kVAr. The capacitor current is often needed when performing a complete field test asoutlined in the capacitor control Field Test Instructions.

Table 1: Single-Phase Line-to-Neutral Capacitor Current

CAPACITOR BANK SIZE, kVArE L-LkV

E L-NkV 300 600 900 1200 1500 1800 2100 2400

4.16 2.4 41.6 83.3 124.9 166.5 208.2 249.8 291.5 333.1

8.32 4.8 20.8 41.6 62.5 83.3 104.1 124.9 145.7 166.512.00 6.9 14.4 28.9 43.3 57.7 72.2 86.6 101.0 115.5

12.47 7.2 13.9 27.8 41.7 55.6 69.4 83.3 97.2 111.1

13.20 7.6 13.1 26.2 39.4 52.5 65.6 78.7 91.9 105.0

13.80 8.0 12.6 25.1 37.7 50.2 62.8 75.3 87.9 100.4

14.56 8.4 11.9 23.8 35.7 47.6 59.5 71.4 83.3 95.2

20.78 12.0 8.3 16.7 25.0 33.3 41.7 50.0 58.3 66.7

22.90 13.2 7.6 15.1 22.7 30.3 37.8 45.4 52.9 60.5

24.94 14.4 6.9 13.9 20.8 27.8 34.7 41.7 48.6 55.6

27.60 15.9 6.3 12.6 18.8 25.1 31.4 37.7 43.9 50.2

34.50 19.9 5.0 10.0 15.1 20.1 25.1 30.1 35.1 40.2


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9.2 VAr Control Settings

These tables show VAr control settings for line voltages from 4.2 to 34.5kV and for bank sizes from 300 to1800 kVAr when using a 1301 current sensor on the source side of the capacitor bank. The differencebetween the cap on and cap off points equals the single-phase capacitor current plus a 25% allowance toprevent cycling.

When using a current transformer, the VAr control is set for secondary current, so the CT ratio must beknown in order to relate the setting to the size of the capacitor bank. To find the dial settings, look up thesettings in the tables for the 1301 sensor and divide by the CT ratio. Be sure to use the ratio based on 1,not 5A; for example, use 80 for a 400:5 CT.

There are two sets of three tables each: one for controls with separate CAP ON and CAP OFF dials, andone set for controls with a CAP ON and a BANDWIDTH dial. The BANDWIDTH dial is the differencebetween the cap on and cap off reactive currents; once selected, this value remains the same regardlessof the CAP ON setting.

Each set contains a table for CAP ON settings at 1/3, 1/2, and 2/3 of the single-phase capacitor current. Ifthere is a single bank on a feeder, use the CAP ON = 2/3 Icap Table. If there is danger of pumping dueto multiple banks on a feeder, set the downstream controls to close at lower lagging reactive current (forexample, 1/3 or 1/2 Icap).

If the current sensor is downstream (load side) of the capacitor bank, set the CAP ON to the value shownin the tables. For bandwidth controls, set the BANDWIDTH knob to 25% (1/4) of the Icap value in Section9.0. For Cap On/Cap Off controls, set the CAP OFF knob more leading (less lagging) than the CAP ONsetting by the 25% of Icap value.


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Table 2: CAP ON/CAP OFF VAr Control SettingsCAP ON = 1/3 Icap

CAPACITOR BANK SIZE (kVAr)300 600 900 1200 1500 1800

On Off On Off On Off On Off On Off On Off

4.2 13.9 38.2 27.8 76.3 41.6 114.5 55.5 152.7 69.4 190.8 83.3 229.0

8.3 6.9 19.1 13.9 38.2 20.8 57.2 27.8 76.3 34.7 95.4 41.6 114.5

12.0 4.8 13.2 9.6 26.5 14.4 39.7 19.2 52.9 24.1 66.2 28.9 79.4

12.5 4.6 12.7 9.2 25.4 13.9 38.1 18.5 50.8 23.1 63.5 27.7 76.2

13.2 4.4 12.0 8.7 24.1 13.1 36.1 17.5 48.1 21.9 60.1 26.2 72.2

13.8 4.2 11.5 8.4 23.0 12.6 34.5 16.7 46.0 20.9 57.5 25.1 69.0

14.6 4.0 10.9 7.9 21.7 11.9 32.6 15.8 43.5 19.8 54.4 23.7 65.2

20.8 2.8 7.6 5.6 15.3 8.3 22.9 11.1 30.5 13.9 38.2 16.7 45.8

22.9 2.5 6.9 5.0 13.9 7.6 20.8 10.1 27.7 12.6 34.7 15.1 41.6

24.5 2.4 6.5 4.7 13.0 7.1 19.4 9.4 25.9 11.8 32.4 14.1 38.9

27.6 2.1 5.8 4.2 11.5 6.3 17.3 8.4 23.0 10.5 28.8 12.6 34.5

34.5 1.7 4.6 3.3 9.2 5.0 13.8 6.7 18.4 8.4 23.0 10.0 27.6

Note: Current sensor located on source (upstream) side of capacitor bank.

ON = A lag CAP ONOFF = A lead CAP OFFCAP ON OFF Difference between CAP ON and CAP OFF= I CAP x 1.25 to prevent hunting

Example: Bank = 900kVAr; E L-L = 13.2kVI CAP = 39.4A leadCAP ON = 1/3 x 39.4 = 13.1A lagCAP ON OFF = 1.25 x 39.4 = 49.2ACAP OFF = 13.1 - 49.2 = 36.1A lead


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4.2 20.8 31.2 41.6 62.5 62.5 93.7 83.3 124.9 104.1 156.1 124.9 187.4

8.3 10.4 15.6 20.8 31.2 31.2 46.8 41.6 62.5 52.0 78.1 62.5 93.7

12.0 7.2 10.8 14.4 21.7 21.7 32.5 28.9 43.3 36.1 54.1 43.3 65.0

12.5 6.9 10.4 13.9 20.8 20.8 31.2 27.7 41.6 34.6 52.0 41.6 62.4

13.2 6.6 9.8 13.1 19.7 19.7 29.5 26.2 39.4 32.8 49.2 39.4 59.0

13.8 6.3 9.4 12.6 18.8 18.8 28.2 25.1 37.7 31.4 47.1 37.7 56.5

14.6 5.9 8.9 11.9 17.8 17.8 26.7 23.7 35.6 29.7 44.5 35.6 53.4

20.8 4.2 6.2 8.3 12.5 12.5 18.7 16.7 25.0 20.8 31.2 25.0 37.5

22.9 3.8 5.7 7.6 11.3 11.3 17.0 15.1 22.7 18.9 28.4 22.7 34.0

24.5 3.5 5.3 7.1 10.6 10.6 15.9 14.1 21.2 17.7 26.5 21.2 31.8

27.6 3.1 4.7 6.3 9.4 9.4 14.1 12.6 18.8 15.7 23.5 18.8 28.2

34.5 2.5 3.8 5.0 7.5 7.5 11.3 10.0 15.1 12.6 18.8 15.1 22.6





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4.2 27.8 24.3 55.5 48.6 83.3 72.9 111.0 97.2 138.8 121.4 166.5 145.7

8.3 13.9 12.1 27.8 24.3 41.6 36.4 55.5 48.6 69.4 60.7 83.3 72.9

12.0 9.6 8.4 19.2 16.8 28.9 25.3 38.5 33.7 48.1 42.1 57.7 50.5

12.5 9.2 8.1 18.5 16.2 27.7 24.2 37.0 32.3 46.2 40.4 55.4 48.5

13.2 8.7 7.7 17.5 15.3 26.2 23.0 35.0 30.6 43.7 38.3 52.5 45.9

13.8 8.4 7.3 16.7 14.6 25.1 22.0 33.5 29.3 41.8 36.6 50.2 43.9

14.6 7.9 6.9 15.8 13.8 23.7 20.8 31.6 27.7 39.5 34.6 47.5 41.5

20.8 5.6 4.9 11.1 9.7 16.7 14.6 22.2 19.4 27.8 24.3 33.3 29.1

22.9 5.0 4.4 10.1 8.8 15.1 13.2 20.2 17.6 25.2 22.1 30.3 26.5

24.5 4.7 4.1 9.4 8.2 14.1 12.4 18.9 16.5 23.6 20.6 28.3 24.7

27.6 4.2 3.7 8.4 7.3 12.6 11.0 16.7 14.6 20.9 18.3 25.1 22.0

34.5 3.3 2.9 6.7 5.9 10.0 8.8 13.4 11.7 16.7 14.6 20.1 17.6





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Table 5: CAP ON/BANDWIDTH VAr Control SettingsCAP ON = 1/3 Icap


On BW On BW On BW On BW On BW On BW

4.2 13.9 52.0 27.8 104.1 41.6 156.1 55.5 208.2 69.4 260.2 83.3 312.3

8.3 6.9 26.0 13.9 52.0 20.8 78.1 27.8 104.1 34.7 130.1 41.6 156.1

12.0 4.8 18.0 9.6 36.1 14.4 54.1 19.2 72.2 24.1 90.2 28.9 108.3

12.5 4.6 17.3 9.2 34.6 13.9 52.0 18.5 69..3 23.1 86.6 27.7 103.9

13.2 4.4 16.4 8.7 32.8 13.1 49.2 17.5 65.6 21.9 82.0 26.2 98.4

13.8 4.2 15.7 8.4 31.4 12.6 47.1 16.7 62.8 20.9 78.4 25.1 94.1

14.6 4.0 14.8 7.9 29.7 11.9 44.5 15.8 59.3 19.8 74.1 23.7 89.0

20.8 2.8 10.4 5.6 20.8 8.3 31.2 11.1 41.6 13.9 52.0 16.7 62.5

22.9 2.5 9.5 5.0 18.9 7.6 28.4 10.1 37.8 12.6 47.3 15.1 56.7

24.5 2.4 8.8 4.7 17.7 7.1 26.5 9.4 35.3 11.8 44.2 14.1 53.0

27.6 2.1 7.8 4.2 15.7 6.3 23.5 8.4 31.4 10.5 39.2 12.6 47.1

34.5 1.7 6.3 3.3 12.6 5.0 18.8 6.7 25.1 8.4 31.4 10.0 37.7



Example: Bank = 900kVAr; E L-L = 13.2kVI CAP = 39.4A leadCAP ON = 1/3 x 39.4 = 13.1A lagBW = 1.25 x 39.4 = 49.2A REAC


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4.2 20.8 52.0 41.6 104.1 62.5 156.1 83.3 208.2 104.1 260.2 124.9 312.3

8.3 10.4 26.0 20.8 52.0 31.2 78.1 41.6 104.1 52.0 130.1 62.5 156.1

12.0 7.2 18.0 14.4 36.1 21.7 54.1 28.9 72.2 36.1 90.2 43.3 108.3

12.5 6.9 17.3 13.9 34.6 20.8 52.0 27.7 69.3 34.6 86.6 41.6 103.9

13.2 6.6 16.4 13.1 32.8 19.7 49.2 26.2 65.6 32.8 82.0 39.4 98.4

13.8 6.3 15.7 12.6 31.4 18.8 47.1 25.1 62.8 31.4 78.4 37.7 94.1

14.6 5.9 14.8 11.9 29.7 17.8 44.5 23.7 59.3 29.7 74.1 35.6 89.0

20.8 4.2 10.4 8.3 20.8 12.5 31.2 16.7 41.6 20.8 52.0 25.0 62.5

22.9 3.8 9.5 7.6 18.9 11.3 28.4 15.1 37.8 18.9 47.3 22.7 56.7

24.5 3.5 8.8 7.1 17.7 10.6 26.5 14.1 35.3 17.7 44.2 21.2 53.0

27.6 3.1 7.8 6.3 15.7 9.4 23.5 12.6 31.4 15.7 39.2 18.8 47.1

34.5 2.5 6.3 5.0 12.6 7.5 18.8 10.0 25.1 12.6 31.4 15.1 37.7





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4.2 27.8 52.0 55.5 104.1 83.3 156.1 111.0 208.2 138.8 260.2 166.5 312.3

8.3 13.9 26.0 27.8 52.0 41.6 78.1 55.5 104.1 69.4 130.1 83.3 156.1

12.0 9.6 18.0 19.2 36.1 28.9 54.1 38.5 72.2 48.1 90.2 57.7 108.3

12.5 9.2 17.3 18.5 34.6 27.7 52.0 37.0 69.3 46.2 86.6 55.4 103.9

13.2 8.7 16.4 17.5 32.8 26.2 49.2 35.0 65.6 43.7 82.0 52.5 98.4

13.8 8.4 15.7 16.7 31.4 25.1 47.1 33.5 62.8 41.8 78.4 50.2 94.1

14.6 7.9 14.8 15.8 29.7 23.7 44.5 31.6 59.3 39.5 74.1 47.5 89.0

20.8 5.6 10.4 11.1 20.8 16.7 31.2 22.2 41.6 27.8 52.0 33.3 62.5

22.9 5.0 9.5 10.1 18.9 15.1 28.4 20.2 37.8 25.2 47.3 30.3 56.7

24.5 4.7 8.8 9.4 17.7 14.1 26.5 18.9 35.3 23.6 44.2 28.3 53.0

27.6 4.2 7.8 8.4 15.7 12.6 23.5 16.7 31.4 20.9 39.2 25.1 47.1

34.5 3.3 6.3 6.7 12.6 10.0 18.8 13.4 25.1 16.7 31.4 20.1 37.7





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9.3 Single-Phase Reactive Current vs. A REAC Jack Vdc Reading

All Fisher Pierce VAr controls manufactured after 1980 have an A REAC test jack, which can be used tofind the present reactive current. Use the Vdc scale of any meter with an impedance greater than 10kOhm. This table is a single sheet with a section for 1301 sensors, which reads in reactive line current, and

a section for CT input controls, which reads in secondary reactive current. Observe the range setting onthe capacitor control, and use the corresponding column in the table. Note that readings greater than +/-5.0 Vdc are overrange, and may be in error. Also observe the maximum total current for the range;exceeding the total current may also cause errors. See section 5 for measuring total current.


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Table 8: Single-Phase Reactive Current vs. A Reac Jack Vdc Reading

1301 Current SensorLine Current

Current TransformerSecondary Current

Range RangeVdc X1 X4 X10 X1 X2 X40.1 0.6 2.4 6 0.01 0.02 0.04

0.2 1.2 4.8 12 0.02 0.04 0.080.3 1.8 7.2 18 0.03 0.06 0.120.4 2.4 9.6 24 0.04 0.08 0.160.5 3.0 12.0 30 0.05 0.10 0.200.6 3.6 14.4 36 0.06 0.12 0.240.7 4.2 16.8 42 0.07 0.14 0.280.8 4.8 19.2 48 0.08 0.16 0.320.9 5.4 21.6 54 0.09 0.18 0.361.0 6.0 24.0 60 0.10 0.20 0.401.1 6.6 26.4 66 0.11 0.22 0.441.2 7.2 28.8 72 0.12 0.24 0.481.3 7.8 31.2 78 0.13 0.26 0.521.4 8.4 33.6 84 0.14 0.28 0.56

1.5 9.0 36.0 90 0.15 0.30 0.601.6 9.6 38.4 96 0.16 0.32 0.641.7 10.2 40.8 102 0.17 0.34 0.681.8 10.8 43.2 108 0.18 0.36 0.721.9 11.4 45.6 114 0.19 0.38 0.762.0 12.0 48.0 120 0.20 0.40 0.802.1 12.6 50.4 126 0.21 0.42 0.842.2 13.2 52.8 132 0.22 0.44 0.882.3 13.8 55.2 138 0.23 0.46 0.922.4 14.4 57.6 144 0.24 0.48 0.962.5 15.0 60.0 150 0.25 0.50 1.002.6 15.6 62.4 156 0.26 0.52 1.042.7 16.2 64.8 162 0.27 0.54 1.08

2.8 16.8 67.2 168 0.28 0.56 1.122.9 17.4 69.6 174 0.29 0.58 1.163.0 18.0 72.0 180 0.30 0.60 1.203.1 18.6 74.4 186 0.31 0.62 1.243.2 19.2 76.8 192 0.32 0.64 1.283.3 19.8 79.2 198 0.33 0.66 1.323.4 20.4 81.6 204 0.34 0.68 1.363.5 21.0 84.0 210 0.35 0.70 1.403.6 21.6 86.4 216 0.36 0.72 1.443.7 22.2 88.8 222 0.37 0.74 1.483.8 22.8 91.2 228 0.38 0.76 1.523.9 23.4 93.6 234 0.39 0.78 1.564.0 24.0 96.0 240 0.40 0.80 1.60

4.1 24.6 98.4 246 0.41 0.82 1.644.2 25.2 100.8 252 0.42 0.84 1.684.3 25.8 103.2 258 0.43 0.86 1.724.4 26.4 105.6 264 0.44 0.88 1.764.5 27.0 108.0 270 0.45 0.90 1.804.6 27.6 110.4 276 0.46 0.92 1.844.7 28.2 112.8 282 0.47 0.94 1.884.8 28.8 115.2 288 0.48 0.96 1.924.9 29.4 117.6 294 0.49 0.98 1.965.0 30.0 120.0 300 0.50 1.00 2.00


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Table 9: Three-Phase Line kVAr vs. A Reac Jack Vdc Reading: 1301 Sensor, X1 Range

Line-to-Line Voltage, kVVdc 4.16 8.32 12 12.5 13.2 13.8 14.6 20.8 22.9 24.5 27.6 34.50.1 4.3 8.6 12.5 13.0 13.7 14.3 15.2 21.6 23.8 25.5 28.7 35.90.2 8.6 17.3 24.9 26.0 27.4 28.7 30.3 43.2 47.6 50.9 57.4 71.70.3 13.0 25.9 37.4 39.0 41.2 43.0 45.5 64.8 71.4 76.4 86.0 107.6

0.4 17.3 34.6 49.9 52.0 54.9 57.4 60.7 86.5 95.2 101.8 114.7 143.40.5 21.6 43.2 62.4 65.0 68.6 71.7 75.9 108.1 119.0 127.3 143.4 179.30.6 25.9 51.9 74.8 77.9 82.3 86.0 91.0 129.7 142.8 152.8 172.1 215.10.7 30.3 60.5 87.3 90.9 96.0 100.4 106.2 151.3 166.6 178.2 200.8 251.00.8 34.6 69.2 99.8 103.9 109.7 114.7 121.4 172.9 190.4 203.7 229.5 286.80.9 38.9 77.8 112.2 116.9 123.5 129.1 136.6 194.5 214.2 239.2 258.1 322.71.0 43.2 86.5 124.7 129.9 137.2 143.4 151.7 216.2 238.0 254.6 286.8 358.51.1 47.6 95.1 137.2 142.9 150.9 157.8 166.9 237.8 261.8 280.1 315.5 394.41.2 51.9 103.8 149.6 155.9 164.6 172.1 182.1 259.4 285.6 305.5 344.2 430.21.3 56.2 112.4 162.1 168.9 178.3 186.4 197.2 281.0 309.4 331.0 372.9 466.11.4 60.5 121.0 174.6 181.9 192.0 200.8 212.4 302.6 333.2 356.5 401.6 501.91.5 64.8 129.7 187.1 194.9 205.8 215.1 227.6 324.2 357.0 381.9 430.2 537.81.6 69.2 138.3 199.5 207.8 219.5 229.5 242.8 345.9 380.8 407.4 459.9 573.7

1.7 73.5 147.0 212.0 220.8 233.2 243.8 257.9 367.5 404.6 432.8 487.6 609.51.8 77.8 155.6 224.5 233.8 246.9 258.1 273.1 389.1 428.4 458.3 516.3 645.41.9 82.1 164.3 236.9 246.8 260.6 272.5 288.3 410.7 452.2 483.8 545.0 681.22.0 86.5 172.9 249.4 259.8 274.4 286.8 303.5 432.3 476.0 509.2 573.7 717.12.1 90.8 181.6 261.9 272.8 288.1 301.2 318.6 453.9 499.8 534.7 602.3 752.92.2 95.1 190.2 274.4 285.8 301.8 315.5 333.8 475.6 523.6 560.1 631.0 788.82.3 99.4 198.9 286.8 298.8 315.5 329.9 349.0 497.2 547.4 585.6 659.7 824.62.4 103.8 207.5 299.3 311.8 329.2 344.2 364.1 518.8 571.2 611.1 688.4 860.52.5 108.1 216.2 311.8 324.8 342.9 358.5 379.3 540.4 595.0 636.5 717.1 896.32.6 112.4 224.8 324.2 337.7 356.7 372.9 394.5 562.0 618.8 662.0 745.8 932.22.7 116.7 233.5 336.7 350.7 370.4 387.2 409.7 583.6 642.6 687.5 774.4 968.02.8 121.0 242.1 349.2 363.7 384.1 401.6 424.8 605.2 666.4 712.9 803.1 1003.92.9 125.4 250.7 361.7 376.7 397.8 415.9 440.0 626.9 690.2 738.4 831.8 1039.8

3.0 129.7 259.4 374.1 389.7 411.5 430.2 455.2 648.5 714.0 763.8 860.5 1075.63.1 134.0 268.0 386.6 402.7 425.3 444.6 470.4 670.1 737.7 789.3 889.2 1111.53.2 138.3 276.7 399.1 415.7 439.0 458.9 485.5 691.7 761.5 814.8 917.8 1147.33.3 142.7 285.3 411.5 428.7 452.7 473.3 500.7 713.3 785.3 840.2 946.5 1183.23.4 147.0 294.0 424.0 441.7 466.4 487.6 515.9 734.9 809.1 865.7 975.2 1219.03.5 151.3 302.6 436.5 454.7 480.1 501.9 531.0 756.6 832.9 891.1 1003.9 1254.93.6 155.6 311.3 448.9 467.7 493.8 516.3 546.2 778.2 856.7 916.6 1032.6 1290.73.7 160.0 319.9 461.4 480.6 507.6 530.6 561.4 799.8 880.5 942.1 1061.3 1326.63.8 164.3 328.6 473.9 493.6 521.3 545.0 576.6 821.4 904.3 967.5 1089.9 1362.43.9 168.6 337.2 486.4 506.6 535.0 559.3 591.7 843.0 928.1 993.0 1118.6 1398.34.0 172.9 345.9 498.8 519.6 548.7 573.7 606.9 864.6 951.9 1018.4 1147.3 1434.14.1 177.3 354.5 511.3 532.6 562.4 588.0 622.1 886.3 975.7 1043.9 1176.0 1470.04.2 181.6 363.1 523.8 545.6 576.1 602.3 637.3 907.9 999.5 1069.4 1204.7 1505.8

4.3 185.9 371.8 536.2 558.6 589.9 616.7 652.4 929.5 1023.3 1094.8 1233.4 1541.74.4 190.2 380.4 548.7 571.6 603.6 631.0 667.6 951.1 1047.1 1120.3 1262.0 1577.64.5 194.5 389.1 561.2 584.6 617.3 645.4 682.8 972.7 1070.9 1145.8 1290.7 1613.44.6 198.9 397.7 573.7 597.6 631.0 659.7 697.9 994.3 1094.7 1171.2 1319.4 1649.34.7 203.2 406.4 586.1 610.5 644.7 674.0 713.1 1016.0 1118.5 1196.7 1348.1 1685.14.8 207.5 415.0 598.6 623.5 658.5 688.4 728.3 1037.6 1142.3 1222.1 1376.8 1721.04.9 211.8 423.7 611.1 636.5 672.2 702.7 743.5 1059.2 1166.1 1247.6 1405.5 1756.85.0 216.2 432.3 623.5 649.5 685.9 717.1 758.6 1080.8 1189.9 1273.1 1434.1 1792.7


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Line-to-Line Voltage, kVVdc 4.16 8.32 12 12.5 13.2 13.8 14.6 20.8 22.9 24.5 27.6 34.50.1 17.3 34.6 49.9 52.0 54.9 57.4 60.7 86.5 95.2 101.8 114.7 143.40.2 34.6 69.2 99.8 103.9 109.7 114.7 121.4 172.9 190.4 203.7 229.5 286.80.3 51.9 103.8 149.6 155.9 164.6 172.1 182.1 259.4 285.6 305.5 344.2 430.2

0.4 69.2 138.3 199.5 207.8 219.5 229.5 242.8 345.9 380.8 407.4 458.9 573.70.5 86.5 172.9 249.4 259.8 274.4 286.8 303.5 432.3 476.0 509.2 573.7 717.10.6 103.8 207.5 299.3 311.8 329.2 344.2 364.1 518.8 571.2 611.1 688.4 860.50.7 121.0 242.1 349.2 363.7 384.1 401.6 424.8 605.2 666.4 712.9 803.1 1003.90.8 138.3 276.7 399.1 415.7 439.0 458.9 485.5 691.7 761.5 814.8 917.8 1147.30.9 155.6 311.3 448.9 467.7 493.8 516.3 546.2 778.2 856.7 916.6 1032.6 1290.71.0 172.9 345.9 498.8 519.6 548.7 573.7 606.9 864.6 951.9 1018.4 1147.3 1434.11.1 190.2 380.4 548.7 571.6 603.6 631.0 667.6 951.1 1047.1 1120.3 1262.0 1577.61.2 207.5 415.0 598.6 623.5 658.5 688.4 728.3 1037.6 1142.3 1222.1 1376.8 1721.01.3 224.8 449.6 648.5 675.5 713.3 745.8 789.0 1124.0 1237.5 1324.0 1491.5 1864.41.4 242.1 484.2 698.4 727.5 768.2 803.1 849.7 1210.5 1332.7 1425.8 1606.2 2007.81.5 259.4 518.8 748.2 779.4 823.1 860.5 910.4 1297.0 1427.9 1527.7 1721.0 2151.21.6 276.7 553.4 798.1 831.4 877.9 917.8 971.1 1383.4 1523.1 1629.5 1835.7 2294.6

1.7 294.0 588.0 848.0 883.3 932.8 975.2 1031.7 1469.9 1618.3 1731.4 1950.4 2438.01.8 311.3 622.5 897.9 935.3 987.7 1032.6 1092.4 1556.4 1713.5 1833.2 2065.2 2581.41.9 328.6 657.1 947.8 987.3 1042.6 1089.9 1153.1 1642.8 1808.7 1935.0 2179.9 2724.92.0 345.9 691.7 997.7 1039.2 1097.4 1147.3 1213.8 1729.3 1903.9 2036.9 2294.6 2868.32.1 363.1 726.3 1047.5 1091.2 1152.3 1204.7 1274.5 1815.7 1999.1 2138.7 2409.4 3011.72.2 380.4 760.9 197.4 1143.2 1207.2 1262.0 1335.2 1902.2 2094.3 2240.6 2524.1 3155.12.3 397.7 795.5 1147.3 1195.1 1262.0 1319.4 1395.9 1988.7 2189.5 2342.4 2638.8 3298.52.4 415.0 830.1 1197.2 1247.1 1316.9 1376.8 1456.6 2075.1 2284.6 2444.3 2753.5 3441.92.5 432.3 864.6 1247.1 1299.0 1371.8 1434.1 1517.3 2161.6 2379.8 2546.1 2868.3 3585.32.6 449.6 899.2 1297.0 1351.0 1426.7 1491.5 1578.0 2248.1 2475.0 2648.0 2983.0 3728.82.7 466.9 933.8 1346.8 1403.0 1481.5 1548.9 1638.7 2334.5 2570.2 2749.8 3097.7 3872.22.8 484.2 968.4 1396.7 1454.9 1536.4 1606.2 1699.3 2421.0 2665.4 2851.6 3212.5 4015.62.9 501.5 1003.0 1446.6 1506.9 1591.3 1663.6 1760.0 2507.5 2760.6 2953.5 3327.2 4159.0

3.0 518.8 1037.6 1496.5 1558.8 1646.1 1721.0 1820.7 2593.9 2855.8 3055.3 3441.9 4302.43.1 536.1 1072.2 1546.4 1610.8 1701.0 1778.3 1881.4 2680.4 2951.0 3157.2 3556.7 4445.83.2 553.4 1106.7 1596.3 1662.8 1755.9 1835.7 1942.1 2766.8 3046.2 3259.0 3671.4 4589.23.3 570.7 1141.3 1646.1 1714.7 1810.8 1893.1 2002.8 2853.3 3141.4 3360.9 3786.1 4732.73.4 588.0 1175.9 1696.0 1766.7 1865.6 1950.4 2063.5 2939.8 3236.6 3462.7 3900.9 4876.3.5 605.2 1210.5 1745.9 1818.7 1920.5 2007.8 2124.2 3026.2 3331.8 3564.6 4015.6 5019.53.6 622.5 1245.1 1795.8 1870.6 1975.4 2065.2 2184.9 3112.7 3427.0 3666.4 4130.3 5162.93.7 639.8 1279.7 1845.7 1922.6 2030.2 2122.5 2245.6 3199.2 3522.2 3768.2 4245.0 5306.33.8 657.1 1314.3 1895.6 1974.5 2085.1 2179.9 2306.3 3285.6 3617.4 3870.1 4359.8 5449.73.9 674.4 1348.8 1945.4 2026.5 2140.0 2237.3 2367.0 3372.1 3712.5 3971.9 4474.5 5593.4.0 691.7 1383.4 1995.3 2078.5 2194.9 2294.6 2427.6 3458.6 3807.7 4073.8 4589.2 5736.64.1 709.0 1418.0 2045.2 2130.4 2249.7 2352.0 2488.3 3545.0 3902.9 4175.6 5704.0 5880.04.2 726.3 1452.6 2095.1 2182.4 2304.6 2409.4 2549.0 3631.5 3998.1 4277.5 4818.7 6023.4

4.3 743.6 1487.2 2145.0 2234.3 2359.5 2466.7 2609.7 3718.0 4093.3 4379.3 4933.4 6166.84.4 760.9 1521.8 2194.9 2286.3 2414.3 2524.1 2670.4 3804.4 4188.5 4481.2 5048.2 6310.24.5 778.2 1556.4 2244.7 2388.3 2469.2 2581.4 2731.1 3890.9 4283.7 4583.0 5162.9 6453.64.6 795.5 1590.9 2294.6 2390.2 2524.1 2638.8 2791.8 3977.3 4378.9 4684.9 5277.6 6597.04.7 812.8 1625.5 2344.5 2442.2 2579.0 2696.2 2852.5 4063.8 4471.1 4786.7 5392.4 6740.44.8 830.1 1660.1 2394.4 2494.2 2633.8 2753.5 2913.2 4150.3 4569.3 4888.5 5507.1 6883.94.9 847.3 1694.7 2444.3 2546.1 2688.7 2810.9 2973.9 4236.7 4664.5 4990.4 5621.8 7027.35.0 864.6 1729.3 2494.2 2598.1 2743.6 2868.3 3034.6 4323.2 4759.7 5092.2 5736.6 7170.7


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Table 12: Three-Phase Line kVAr vs. A Reac Jack Vdc Reading: 50:5 CT, X1 Range


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Table 20: Three-Phase Line kVAr vs. A Reac Jack Vdc Reading: 200:5, X4 Range


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Table 30: Power Factor vs. A Reac Jack Vdc and Line Current Jack VacAll 1301 Sensor VAr Controls, X1 Range


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Table 33: Power Factor vs. A Reac Jack Vdc and Line Current Jack VacAll Modular CT VAr Controls, X1 Range


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Table 36: Power Factor vs. A Reac Jack Vdc and Line Current Jack VacAll Low Profile (70/80 Series) CT VAr Controls, X1 Range


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Table 38: Power Factor vs. A Reac Jack Vdc and Line Current Jack VacAll Low Profile (70/80 Series) CT VAr Controls, X4 Range

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