reference a fault

8/12/2019 Reference a Fault

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SKM Power*Tools for Windows

Power*Tools

for Windows

A_FAULT Reference Manual

Electrical Engineering Analysis Software

for Windows

Copyright 2006, SKM Systems Analysis, Inc

All Rights Reserved


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Contents1 A_FAULT STUDY 1-1

1.1 What is the A_FAULT Study? ........................................................................1-2

1.2 Engineering Methodology................................................................................1-31.2.1 ANSI Standard C37....................................................................................1-31.2.2 Comparing the ANSI and IEC Short Circuit Standards .............................1-31.2.3 Withstand, Closing and Latching, and Momentary Rating ........................1-41.2.4 Interrupting Ratings....................................................................................1-71.2.5 Adjusting Machine Contributions ..............................................................1-7

1.3 PTW Applied Methodology.............................................................................1-81.3.1 Before Running the A_FAULT Study .......................................................1-81.3.2 Running the A_FAULT Study ...................................................................1-81.3.3 A_FAULT Study Options ..........................................................................1-9

Fault Type ..............................................................................................................1-9

Faulted Bus.............................................................................................................1-9

Calculation Models...............................................................................................1-10

Transformer Tap...............................................................................................1-10

Pre-fault Voltage (pu).......................................................................................1-10

Low Voltage.........................................................................................................1-10

Momentary and Interrupting ................................................................................1-10

Solution Method...............................................................................................1-10

NACD Option ..................................................................................................1-111.3.4 Component Modeling...............................................................................1-11

Feeder Data ..........................................................................................................1-11

Transformer Data .................................................................................................1-12

Three-Winding Transformers...............................................................................1-12

Contribution Data.................................................................................................1-15

1.3.5 Low Voltage Duty Report ........................................................................1-151.3.6 Momentary Duty Report...........................................................................1-171.3.7 Interrupting Duty Report ..........................................................................1-19

Local and Remote Fault Contributions From Generators ....................................1-19

ANSI C37.5 Considerations (Total Rated Basis) .................................................1-19

ANSI C37.010 Considerations (Symmetrical Rating Basis) ................................1-20

Using the NACD Options ....................................................................................1-20

1.3.8 Modeling ANSI Decrement Curves .........................................................1-211.4 Application Examples ....................................................................................1-27

1.4.1 Induction Motor ac decrement Factors.....................................................1-27Case 1 ...................................................................................................................1-27

Case 2 ...................................................................................................................1-28

Case 3 ...................................................................................................................1-30

1.4.2 Modeling Transformers with Taps ...........................................................1-311.4.3 Calculating Interrupting Duties ................................................................1-34

Case 1 ...................................................................................................................1-34


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A_FAULT ii Reference Manual

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Case 2 .................................................................................................................. 1-361.4.4 Example from Plant ................................................................................. 1-41

Index A_FAULT i


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A_FAULT Study

This chapter examines the short-circuit current calculation procedures used in the

A_FAULT Short Circuit Study. The chapter includes a systematic methodology and

applies the methodology to numerous practical examples. You can also run a

Comprehensive Short Circuit Study (in the DAPPER Study Module) or an IEC Short

Circuit Study (in the IEC_FAULT Study Module). The IEC_FAULT Short Circuit Study

and the Comprehensive Short Circuit Study chapters discuss the Short Circuit

Methodology applied by each Study, and the standards followed by each; theIEC_FAULT Study is based on the IEC Standard 909, while the Comprehensive Short

Circuit Study is based on Thevenin equivalent circuit representation and Ohms law.

The A_FAULT Study follows the specifications of the American National Standards

Institute (ANSI) C37.010, C37.5, and C37.13, and IEEE Standard 141, also known as the

IEEE Red Book.

This chapter discusses:

Engineering Methodology.

PTW Applied Methodology.

Examples.

IN

T

H

IS

C

H

A

P

T

E

R

1.1 What is the A_FAULT Study? ....................................................................1-2

1.2 Engineering Methodology ........................................................................... 1-3

1.3 PTW Applied Methodology......................................................................... 1-8

1.4 Application Examples................................................................................ 1-27


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A_FAULT 1-2 Reference Manual

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1.1 What is the A_FAULT Study?

The A_FAULT Short Circuit Study (referred to hereafter as A_FAULT) models the

current that flows in the power system under abnormal conditions and determines the

prospective fault currents in an electrical power system. These currents must becalculated in order to adequately specify electrical apparatus withstand and interrupting

ratings. The Study results are also used to selectively coordinate time current

characteristics of electrical protective devices.Electrical apparatus manufactured in North America is predominantly tested and rated

against the ANSI, UL and NEMA equipment Standards; these Standards outline the

preferred method for calculating fault duties when specifying North American equipment.

Equipment must withstand the thermal and mechanical stresses of short-circuit currents as

described in the ANSI Standards. Both rms and peak short circuit withstand and

interrupting duties (referred to as making and breaking short-circuit current duties,

respectively) must be calculated and then compared to the protective device and electrical

apparatus ratings.

Define System Data

Define system topology and connections

Define feeder and transformer sizes

Define fault contribution data

Run A_FAULT Study

Study Setup

Cable LibraryTransformer Library

Study Setup

Saved in DatabaseThree-phase fault currents

Unbalanced fault currents

Calculated ANSI fault currents

Reports

Used by Time Current

Coordination (CAPTOR)

Datablocks


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A_FAULT Study A_FAULT 1-3


1.2 Engineering Methodology

Most often, North American engineers think of the American National Standards Institute

(ANSI) series of C37 equipment rating Standards when specifying electrical apparatus

withstand capabilities, and in the case of protective devices, equipment contact breaking

or interrupting ratings. The IEEE applies the C37 series of ANSI Standards. The C37series Standards deal with circuit interruption. Also, the IEEE has published theIEEE

Red Book,IEEE Standard 141 as an authoritative application guide for the selection of

equipment to withstand and interrupt short-circuit currents in an industrial/commercial

power system.

The ANSI C37 series Standards must be used in conjunction with other engineering

Standards, such as Underwriters Laboratory (UL) Standard 489, and the National

Electrical Manufacturers (NEMA) Standard AB-1. This following section outlines the

key principles in these Standards.

1.2.1 ANSI Standard C37Short-circuit current testing procedures and associated equipment ratings are based first on

the ability to withstand the maximum thermal and mechanical stresses during a fault.

Both thermal and mechanical stresses are proportional to the magnitude of the square of

the current flowing through the equipment during the fault condition. Short-circuit

currents are the largest during the first cycle of the fault, and high-magnitude short-circuit

currents can be sustained for several cycles, even up to 30 cycles in extreme situations.

Current carrying parts of electrical apparatus must be sized to withstand, or in the case of

switching and protective devices, close in and latch onto the faulted circuit. Besides the

thermal heating effects associated with large short-circuit currents, electrical apparatus

internal components and wiring must be mechanically braced to withstand the deleterious

magnetic stresses that can cause current-carrying parts to be stretched or repulsed from

one another during a fault condition.

Further, equipment designed to operate under fault conditionsthat is, designed to open

circuit breaker contacts and extinguish the associated arcing currents, or to separate fuse

links and control the associated arcing currentsmust be tested, and rated for such duty.

This second short-circuit current rating is known as an equipment interrupting rating.

Low-voltage devices often combine the withstand and interrupting ratings into a single

rating. On the other hand, high-voltage circuit breakers may have intentionally different

withstand and interrupting ratings, and may be specifically rated for delayed contact

separation. Engineers must compare the manufacturers published withstand and

interrupting equipment ratings against the calculated short-circuit current duties generated

by hand calculations or computer methods.

You may be most familiar with the ANSI, UL and NEMA Standards. However,

equipment manufactured in Europe is predominantly manufactured to the IEC group of

Standards. The following section highlights the significant differences between the ANSI

and IEC Standards as they pertain to short-circuit calculations.

1.2.2 Comparing the ANSI and IEC Short Circuit StandardsThere are three significant differences between the IEC methodology and ANSI

methodology.


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The first major difference involves calculating the dc decay component. ANSI requires

calculation of a single Thevenin equivalent fault point X/R ratio, based on separately

derived R and X values at the fault point. From that X/R ratio, a single equivalent dc

decay can be determined for multiple sources at the fault location. The IEC Standard uses

a unique R/X ratio, calculated from the complex form of the R and X values at the fault

location for each contribution, and uses this unique ratio for calculating the asymmetrical

fault currents from each machine to the fault point. It could be argued that the IECStandard is currentbased, while the ANSI Standard is impedancebased.

The second major difference also involves the dc decay component. Both Standards

recognize that calculating the dc decay (the transient solution to the short-circuit current

calculation) must be uniquely accomplished when parallel or meshed paths are involved.

Both Standards consider the nature of meshed or parallel paths when concerned with the

dc decay; however, the two Standards use completely different procedures for calculating

the dc decay current component when meshed or parallel paths are involved.

The third major difference involves the ac decrement component. The ANSI method

globally adjusts the machine subtransient impedances when considering different

moments of time during the fault. The IEC method modifies the prospective short-circuit

currents available from each machine based on the transfer impedance between the activesource and the specific fault location in question and the defined contact breaking time.

Clearly, the IEC methodology is more computationally intensive than the ANSI

methodology.

Both short circuit methodologies can be considered as quasi-steady-state solutions to the

short-circuit current problem, and both Standards acknowledge that a more dynamic

solution method might yield more accurate results. They do, however, claim sufficient

accuracy for specifying electrical equipment.

The results from IEC and ANSI calculations cannot be directly compared. While both

calculate a withstand duty, the IEC and ANSI methodologies are fundamentally different.

In the sample project, the ANSI closing and latching duty can, at times, be larger than the

IEC peak current duty. However, in other sections of the project, the opposite is true. Asimilar disparity can be found between the IECs breaking current and the ANSIs

symmetrical current interrupting duty. Thus, it can be concluded that when equipment is

rated in accordance with IEC Standards, then the IEC methodology must be used to

calculate the fault duties; and when equipment is rated in accordance with the ANSI

Standards, then the ANSI methodology must be used to calculate the fault duties.

1.2.3 Withstand, Closing and Latching, and Momentary RatingElectrical apparatus is usually rated to allow a continuous and short-time overload current

to be sustained for significant periods of time. Ratings are usually based on the ability of

the device to reject the Julian ( i t2 ) heating that occurs during the range of practical

operating conditions.

Equipment withstand ratings are based on the highest short-circuit current expected; this is

called the prospective short-circuit current. The prospective short-circuit current usually

occurs during the first half-cycle of the fault. Withstand currents are composed of a

symmetrical ac current and most likely, an aperiodic current component known as the dc

decay component. Withstand ratings may be published as equivalent first-cycle rms

currents, or more accurately, as peak or crest currents for the first half-cycle of the fault.


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As noted, the asymmetrical peak fault current consists of both ac and dc components, and

is a function of time. As shown in the following figure, the theoretical asymmetrical peak

to peak current is 2 2 multiplied by the initial symmetrical rms current. The initial

symmetrical rms current Ik is the ratio of the driving point voltage at the bus to the

Thevenin equivalent impedance. The asymmetrical nature of a fault current is best shown

by the following graph:

Current

Theoretical maximum

Peak at 1/2 cycle

(DC decay)

Bottom envelope

Top envelope

Decaying (aperiodic) component i

Time

2

2I"

i

k

p

2 2 I k

dcAsymmetrical values

including motor contributions

Steady state value

(no motor contributions)

dc

i

The first half-cycle asymmetrical peak current is the sum of the dc decay and ac

decrement components. This can be expressed in equation form as:

I = 2I 2I easymmetrical peak k k

2c

XR +

where

Iasymmetrical peak asymmetrical peak fault current;

Ik initial symmetrical rms fault current;

Idc dc decaying component of fault current;

c time in cycles into the fault.

Besides a withstand rating, electrical protective devices are rated on both their ability to

withstand a first-cycle short-circuit current, and to close and latch into a faulted circuit. In

older, high-voltage circuit breakers, this rating is known as the momentary rating. The

closing and latching current rating is also associated with the making current of a

switching device.

Low-voltage devices are usually rated to withstand and interrupt a specified symmetrical

rms current. Manufacturers test their protective devices against test asymmetrical

waveshapes, as noted in the following table of low-voltage test power factors and

asymmetrical current withstand capabilities:

Protective DeviceTest

PF (%)TestX/R

Tested AsymmetricalWithstand Capability

LV Power Circuit Breaker 15 6.6 1.62

LV Fuse 20 4.9 1.53

Molded Case Circuit Breaker GT 20 KA AIC 20 4.9 1.53


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Protective DeviceTest

PF (%)

Test

X/R

Tested Asymmetrical

Withstand Capability

Molded Case Circuit Breaker Between 10-20

KA AIC

30 3.2 1.38

Molded Case Circuit Breaker LT 10 KA AIC 50 1.7 1.15

When low-voltage protective devices are applied in a system with an X/R greater than thetest X/R ratios listed above, then special care must be taken when specifying the devices

symmetrical rating. In high X/R ratio situations, the symmetrical rating may not be

exceeded by the calculated short circuit symmetrical duty; however, there is a possibility

that the protective devices tested asymmetrical withstand value could be exceeded. Low-

voltage equipment is rated in symmetrical currents, but tested to a maximum asymmetrical

rms 1/2 cycle test current based on the following formula:

I I 1 2easym rms cycle rms symm

-2

12

XR= +

When low-voltage equipment is specified in a circuit with a calculated X/R ratio greater

than that for which the equipment was tested, you must ensure that both the symmetrical

and asymmetrical half-cycle rated currents are not exceeded.

To determine the low-voltage withstand (and interrupting) duty when the system X/R ratio

is greater than the test X/R for which the device is rated, the Standard calls for using the

following formula:

I Ie

e

symm LVF rms symm

-

system

-

test

XR

XR

=

+

+

1

1

p

p

Special care must be used when calculating system X/R ratios. The ANSI C37 series

Standards are explicit that the fault location X/R ratio must be calculated using the method

of separately-derived calculation. C37.13 and C37.010 require that the reactance at thefault point must be calculated ignoring resistance, and the resistance at the fault point

calculated ignoring reactance. Systems with looped paths, or multiple short-circuit

current contributions can exhibit a different X/R ratio when calculated using the

separately-derived method versus the conventional method of solving for the Thevenin

equivalent impedance, and then calculating the X/R ratio from knowing the angle between

the resistance and reactance of the Thevenin equivalent complex impedance.

High-voltage fuses may be rated to withstand either an rms symmetrical or asymmetrical

rms current. High-voltage fuses may be tested with a test X/R of either 15 or 25. The

manufacturer must be consulted to confirm the test X/R if only the symmetrical value is

published.

High-voltage circuit breakers manufactured since 1987 have a preferred closing andlatching rating expressed in the peak (crest) current. Breakers manufactured before 1987

are rated in rms amperes symmetrical, but tested to withstand an asymmetrical rms current

of 160% of the published symmetrical rms current.

When a three-phase bolted fault occurs, it is assumed that the fault occurs such that the

maximum asymmetric current occurs on Phase A. The other two phases are, respectively,

120and 240delayed from Phase A. Thus, the complex form of the maximum fault


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current in Phase A will be different than that in Phase B or C of a three-phase bolted fault.

The Phase A half-cycle asymmetrical fault current is:

I I 1 2easym rms cycle rms symm12

-2X

R= +

But the average fault current due to each of the three individual phase currents of a three-phase fault is:

I I 1 2e 2 1 easym rms cycle ave rms symm12

-2X

R

-2X

R= + + +

F

HG

I

KJ

1

30 5

.

It should be noted that the above equations are conservative, in that these equations are

based on the maximum fault current occurring at exactly one half-cycle into the fault. It

can be shown that this is only true in a purely-inductive circuit when the fault occurs at a

voltage zero.

1.2.4 Interrupting RatingsAs stated earlier, low-voltage protective devicesboth fuses and circuit breakersare

rated with a single interrupting rating. This is a symmetrical rating, usually in rms current.

Also, the manufacturer tests the low-voltage protective device in accordance with NEMA

Standard AB-1 to assure that the protective device will withstand, and operate under, a

specific (maximum) asymmetrical conditions.

Medium- and high-voltage circuit breakers are rated either on a Total Current or

Symmetrical Interrupting Current Rating. These ratings are usually specified along with a

maximum and minimum operating voltage, and a preferred contact opening time in cycles.

Circuit Breakers manufactured prior to 1964 base their short-circuit current interrupting

rating on ANSI Standard C37.5. This was known as the Total Current basis, and

considered both the ac decrement and dc decay characteristics of the calculated short-circuit current. Circuit breakers manufactured after 1964 are rated in accordance with

ANSI Standard C37.010, known as the Symmetrical Current basis. The primary

difference between the Standards is the specific multiplying factor used to adjust the initial

symmetrical rms current at the expected breaker opening time. These multiplying factors

are based on a series of figures in each Standard, and are influenced by the amount of

power system generation and the electrical distance between the power generation and the

fault location. The generation may be defined as local or remote. Remote generation has

no ac decrement (NACD). As such, the Standards define local generation when:

Equivalent System Impedance to Fault Excluding X gen

X gen

d

d


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Local generation and motors have an ac decrement; their symmetrical wave shape

decreases with the onset of the fault. For simplicity in the ANSI Standards, the time

varying ac decrement is modeled as a constant voltage source behind a time-varying

impedance. At the initial instant of the fault this impedance is known as the sub-transient

impedance, but this changes to the transient impedance two to three cycles into the fault.

The steady-state currents are modeled as the machines synchronous impedance. In large

machines, the resistance component of the machines internal impedance is ignored.

Within the C37 series Standards, there is a set of rotating-machine reactance multipliers to

be used to model the time varying nature of the machine reactance. This set is shown in

the following table:

Type of rotating machine Low-voltagenetwork

First-cyclenetwork

Interruptingnetwork

All turbine generators; all

hydrogenerators with amortisseur

windings; all condensers

1.0 Xd 1.0 Xd 1.0 Xd

Hydrogenerators without amortisseur

windings0.75 Xd 0.75 Xd 0.75 Xd

All synchronous motors 1.0 Xd 1.0 Xd 1.5 Xd

Induction motors above 1000 hp at 1800

r/min or less1.0 Xd 1.0 Xd 1.5 Xd

Induction motors above 250 hp at 3600

r/min1.0 Xd 1.0 Xd 1.5 Xd

All other induction motors 50 hp and

above at 1800 r/min1.0 Xd 1.2 Xd 3.0 Xd

All induction motors smaller than 50 hp 1.0 Xd neglect neglect

1.3 PTW Applied MethodologyPTW applies the methodology described in Section 1.2. Section 1.3 describes how to run

the A_FAULT Study, including explanations of the various options associated with the

Study.

1.3.1 Before Running the A_FAULT StudyBefore running the A_FAULT Study, you must:

Define the system topology and connections.

Define feeder and transformer sizes.

Define fault contribution data.

1.3.2 Running the A_FAULT StudyYou can run the Study from any screen in PTW, and it always runs on the active project.


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To run the A_FAULT Study

1. From the Run menu, choose Analysis.

2. Select the check box next to Short Circuit and choose the A_FAULT option button.

3. To change the Study options, choose the Setup button.

4. Choose the OK button to return to the Study dialog box, and choose the Run button.The Short Circuit Study runs, writes the results to the database, and creates a report.

1.3.3 A_FAULT Study OptionsThe A_FAULT Study dialog box lets you select options for running the Study.

Following is a list of the available Study options.

Fault Type

There are two options: Three Phase only, and 3 Phase-Unbalanced. The default is to

report only the Three-Phase Study results. The 3 Phase-Unbalanced option allows you to

study both the three-phase and the unbalanced fault networks (single-line-to-ground, line-to-line, and line-to-line-to-ground) in an abbreviated Report format.Faulted Bus

You can fault all buses or choose a specific bus to fault. If a fault is to be studied at a

single bus, then the faulted bus must be specified. The default is to study the fault

currents at all buses. If a single bus is faulted, then you can display the three-phase branch

fault contribution one branch away from the faulted location on a datablock.


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Calculation Models

These options further customize the Study.

Transformer Tap

You may model the primary transformer taps by selecting this check box. Secondary taps,

if modeled, are ignored in the A_FAULT calculations. No adjustment in pre-fault voltage,

associated with the transformer tap change, is automatically accomplished.

Pre-fault Voltage (pu)

The driving point voltage at the faulted bus or buses is defined in this box. The default

driving point voltage is 1.0 pu. The driving point voltage is not affected by the Swing Bus

per unit voltage, nor is it adjusted for transformer taps or the results from the Load Flow

Study.

Low Voltage

If you select the Low Voltage Duty check box, PTW will calculate the initial symmetrical

short-circuit currents at each specified bus, plus the half-cycle duty with no ac decrement.

Also, the Three-Phase Report calculates the low-voltage protective device symmetrical

duty required, based on the impact of the device test power factor. In the UnbalancedReport, the single-phase, and average three-phase (average Phase A plus Phase B and C)

asymmetrical duty is calculated. All motor and generator contributions are included in the

Study results, using the user-specified subtransient reactances entered in the ANSI

Contribution subviews for Motor and Generator components.

The Study Report format may be selected as Complete or Summary. The Complete

Report format is an extensive output format that includes a calculation of the branch

contributions to the faulted bus, whereas the Summary report format only includes a list of

the three-phase and single-line-to-ground short-circuit current duties and the associated

X/R ratios.

Because the low-voltage report calculates all motor contribution, and does not model

motor ac decrement factors, this report format most closely resembles the ComprehensiveShort Circuit Study results. Therefore, all bus fault currents are reported, regardless of

voltage.

Momentary and Interrupting

If you select the check box next to either or both of the Momentary and Interrupting

Duties, PTW will calculate the initial symmetrical short-circuit current at each specified

bus, modeling the reduction in motor fault current contribution (that is, considering motor

ac decrement) based on motor type, rated size, and speed (pole pairs). In the Three-Phase

Report, both the rms and peak (crest) asymmetrical current duty are calculated, based on

the 1.6 or 2.7 times test factor, and the asymmetrical rms and peak short-circuit current

duty based on the calculated X/R ratio at the fault location. In the InterruptingReport,each generator contribution is evaluated at each fault location to determine if itscontribution is considered remote or local to the fault location.

The Study Report format may be selected as Complete or Summary. The Complete

Report format is an extensive output format that includes a calculation of the three-phase

branch contributions to the faulted bus, whereas the Summary only includes a list of the

bus fault currents and the associated X/R ratios.

Solution Method


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You have the option of specifying an E/X or E/Z solution method. The Standards permit

the momentary fault currents to be calculated based on a value of E/X (voltage/reactance =

current) which is conservative, or calculated based on a value of E/Z (voltage/impedance

= current) which generally results in a smaller short-circuit current duty. The default

solution methodology is E/Z.

NACD OptionFor the Interrupting Duty Report, you can choose one of three operating modes, which

represent the most common interpretation of the ANSI Standards: All Remote,

Predominant, and Interpolated. In All Remote mode, the NACD factor is 1.0; all

generation is assumed to be remote; and the no ac decrement curves (dc decay curve only)

are used. This is the most conservative solution. In Predominant mode, if the NACD

factor is greater than or equal to 0.5, then the dc decay only curve is used. If the NACD

factor is less than 0.5, the curves which model both ac decrement and dc decay are used.

In Interpolated mode, interpolation between the dc decay curve and the ac decrement/dc

decay curves is used based on the percentage of generator contribution that is local and

remote.

Note: The ANSI C37 Standards do not specifically recognize the interpolation method

of calculation. Technical papers state that the interpolation of the data between the dc

decay only and the ac decrement/dc decay curves of the Standard may provide more

representative results. The interpolation is based on the X/R ratio and the NACD factor.

1.3.4 Component ModelingA_FAULT, IEC_FAULT, and the Comprehensive Short Circuit Study model electrical

passive devices identically. However, there are some key differences that should be

noted.

One major difference is that the Comprehensive Study models secondary transformer taps,

whereas A_FAULT and IEC_FAULT model only primary transformer taps. Another

major difference deals with the ac decrement for motors. A_FAULT modifies the motorsubtransient reactance using factors from the table in Section 1.2.5, Contributions,

whereas the Comprehensive Study does not alter the machine subtransient reactances for

ac decrement. IEC_FAULT uses a series of special equations for determining machine ac

decrement. Finally, the basis of the calculation of the fault location X/R is different.

A_FAULT uses the method of separately-derived R and X, whereas IEC_FAULT and the

Comprehensive Short Circuit Study use the complex (vector) solution of the impedance to

determine the X/R ratio.

When you run the A_FAULT Study, PTW checks for appropriate feeder sizes and

lengths, and transformer sizes in the Library. If the data is inappropriate or missing, error

and warning messages are shown in the Study Run dialog box and included in the Report.

The following sections describe the minimum data required for A_FAULT to run.

Feeder Data

You must specify a cables positive-sequence impedance and one-way circuit length.

PTW models the negative-sequence impedance as equal to the positive-sequence

impedance. If a cables zero-sequence impedance is zero, the Short Circuit Study uses the

positive-sequence value. Cable positive and zero sequence impedances may be selected

from the Cable Library, or you can define them in the Component Editor.


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If you make the cable User Defined, you can enter specific cable positive- and zero-

sequence impedance in ohms per 1000 feet or ohms per 1000 meters. Cable lengths must

be entered in the same units as the cable impedance data (feet or meters). If you switch

the Program Options from English to Metric units, PTW converts entered cable lengths

and impedances to the appropriate units. Cable impedances are unaffected by the wire

circuit description characteristics.

Transformer DataYou can select predefined two-winding transformers from the Transformer Library or you

can define them yourself in the Component Editor. PTW defines two-winding

transformers by their percentage leakage positive- and zero-sequence impedance value,

cooling capacity type, and the nominal kVA rating. If a transformer's zero-sequence

impedance is zero, PTW uses the positive-sequence value. Transformers' rated voltages

may differ from the bus nominal voltages. PTW models those off-nominal voltages as

ideal voltage shifters separate from any primary or secondary tap that is modeled. A

warning message appears in the Study Messages dialog box when PTW detects a

mismatch between the bus nominal voltage and the transformer rated voltage. You can

also define the transformer impedance in the Component Editor using the transformer's

resistance and reactance values in percent on the nominal or self-cooled kVA rating.

When you set the engineering standard for the PTW Project to IEC, user-definedtransformers can be defined in per unit on any kVA base, the Rated Short Circuit Voltage

percent or on Rated Ohmic voltage percent.

Transformer negative-sequence impedance always equals the positive-sequence value in

the Short Circuit Study. The primary and secondary transformer connections help

determine the effect of the zero-sequence Thevenin equivalent impedance.

The wye-grounded wye-grounded zero-sequence path appears as a non-shunt primary to

secondary leakage impedance. Grounding impedance may be placed on one or both of the

grounded points. PTW automatically multiplies this grounding impedance by three to

calculate the proper zero-sequence impedance on a per unit base. The wye-grounded

wye-grounded transformer is modeled in shell form, and is defined as an infinite

impedance when viewed from either connection.

Three-Winding Transformers

Three-winding transformers may be modeled. Off-nominal voltage and transformer taps

may be modeled in a manner similar to two-winding transformers. All three-winding

transformer data must be user defined in the Component Editor. PTW models the three-

winding transformer using conventional network reduction, and establishes a fictitious

center point bus. Also, PTW establishes a secondary to tertiary branch. This fictitious bus

and associated branch count against the total bus and branch limit in PTW.

There are two networks in the following one-line diagram. Transformer T1 is a three-

winding transformer with a primary, secondary and tertiary power rating of 15 MVA, 15

MVA and 5.25 MVA, respectively.


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GEN 1 GEN 2

BUS 1

C1

BUS 2

T2

BUS 3 BUS 4

T1

C2 C3

BUS 5 BUS 6

BUS 7

C4

BUS 8

BUS 9

T3

BUS 10

C5

BUS 11

27,856.53 A

22,405.02 A

11,150.80 A21,706.12 A

20,520.80 A 10,860.47 A

CENTER POINT

0.8790%

21,705.22 A

20,520.00 A

T4

BUS 12

C6

BUS 13

27,856.53 A

22,405.02 A

7199.51 A

6.0214%

9.9790%

11,150.56 A

10,860.25 A

The manufacturers published test data for Transformer T1 is:

Test#

ImpedanceMeasured

into Winding

WindingShort

Circuited

WindingOpen

Circuited

ShortCircuit

Voltage in %

ImpedanceBase for

Measure (MVA)

ImpedanceSymbol

1 Primary Secondary Tertiary 6.9 15 ZPS

2 Primary Tertiary Secondary 5.6 5.25 ZPT

3 Secondary Tertiary Primary 3.8 5.25 ZST

It is important to note that the preceding measurements are relative to different power

bases. In Test 1 when the tertiary circuit is open, short-circuit current flows only in

primary and secondary windings. Both of these windings have 15 MVA ratings. In the

test, the voltage across the primary winding is increased until 6.9 % rated voltage causes

the rated full current to flow in the secondary winding. By opening the tertiary circuit, nocurrent flows in this winding.

In Test 2, the tertiary winding is fully loaded based on its 5.25 MVA rating, even though

the primary carries only about one-third rated current on its 15.0 MVA rating. The test

stopped when the 5.6 % rated voltage was applied to the primary winding and full load

current was reached on the tertiary winding (corresponding to 5.25 MVA). It is critical to

know on what base the short circuit voltage takes place. The following drawing is an

equivalent impedance diagram for the three-winding transformer:

Z

ZPS

Z PT

T

S

PST


18/56


3/26/2006

You can convert this into an equivalent wye diagram using standard network reduction

techniques:

Z

Z2

Z 1

T

S

P

3

From the network reduction diagram, we can write:

Z = Z + Z

Z = Z + Z

Z = Z + Z

PS 1 2

PT 1 3

ST 2 3

Network reduction yields:

Z = (Z + Z - Z )

Z = (Z + Z - Z )

Z = (Z + Z - Z )

11

2 PS PT ST

21

2 PS ST PT

31

2 PT ST PS

You can solve the equations by substituting the manufacturers data expressed on a

common 15 MVA base:

Z = 6.9 + 5.615

5.25- 3.8

15

5.25

= 6.0214 %

Z = 6.9 + 315

5.25- 5

15

5.25

= 0.879 %

Z =15

5.25

15

5.256

= 9.978 %

11

2

21

2

31

2

j j j

j

j j j

j

j j j

j

FHG

IKJ

L

NM

O

QP

FHG

IKJ

L

NM

O

QP

FHG

IKJ+

FHG

IKJ

L

NM

O

QP

. .

. . .

8 6

56 38 9

The above values represent the two-winding transformer equivalent impedances that must

be used in the one-line diagram on page A_FAULT 1-12.

Contribution DataFault duty contributions to the power system originate from the motor generator and utility

source components. PTW provides default subtransient and X/R ratio values. You can

calculate the machine kVA and voltage base using the rated size and connected bus

nominal voltage. For example, if you enter a 50 hp motor with an 80% power factor and

92% efficiency, PTW calculates the rated kVA base as:


19/56



kVA =50 hp 746

1000 W

kW0.8 pf 0.92 efficiency

= 50.7 kVA

base

Whp

This is close to the rule-of-thumb that 1 hp is equal to 1 kVA. Of course, if you have a

1000 hp synchronous motor with a unity power factor, PTW calculates the motors kVAbase value as 746 kVA for short-circuit current purposes. The fault contribution

calculation remains unaffected by the motor load factor.

Fault contributions can be at any bus and there may be multiple contributions located at

any bus.

Important: .You may change the ANSI contribution calculated kVA base, for example to

model the 50 hp motor as 50.0 kVA. However in PTW, once the machine ANSI

contribution kVA base is selected (or automatically calculated by PTW if the base kVA

value is 0), it will not change. Therefore, if you enter the motor load as 50 hp, run a

Study, and then change the motors rating to 75 hp, the motors ANSI contribution base

kVA will remain 50 kVA. You must change the base kVA to 75 kVA manually.

Induction motors are modeled as delta-connected, whereas synchronous motors are

modeled as wye-connected. Neutral (grounding) impedance may be modeled.

1.3.5 Low Voltage Duty ReportFor low-voltage Studies, A_FAULT calculates the initial symmetrical short-circuit current

at each bus in the power system based on the contribution data derived from ANSI

C37.13. Under this Standard, the synchronous and induction motors are assumed to

contribute at 1.0 Xd". At each bus (including the high voltage bus records), the magnitude

of the fault current and the source of each contribution is reported.

In the partial one-line diagram and associated report below, the initial symmetrical short-

circuit current for a fault at Bus 15 is reported as 8.66 kA. Close inspection of the report

shows that 8.223 kA originates from Bus 14, and the remainder of the fault current is

generated from the four 25-hp motors directly connected to Bus 15, and contained in

MCC 15-1A.


20/56


3/26/2006

015-MCC 1A

I Symm 8.661 kAX/R 4.138

I Duty 9.265 kA

C14

Sub Feed #1

014-DSB 1

I Symm 9.993 kA

X/R 5.653

I Duty 11.459 kA

018-RA

I Symm 7.190 kA

X/R 2.313

I Duty 7.190 kA

MCC 15-1A

PNL 18 RA

MCCB1

LVP1

015-MCC 1A FAULT: 8.661 KA AT -74.64 DEG ( 7.20 MVA) X/R: 4.14

V O L T A G E : 4 8 0 . E Q U I V . I M P E D A N C E = . 0 0 8 5 + J . 0 3

L O W V O L T A G E P O W E R C I R C U I T B R E A K E R 8 . 6 6 1 K A

M O L D E D C A S E C I R C U I T B R E A K E R < 2 0 K A 9 . 2 6 5 K A

M O L D E D C A S E C I R C U I T B R E A K E R > 2 0 K A 8 . 6 6 1 K A

C O N T R I B U T I O N S : M 1 5 - 4 . 1 1 2 K A A N G : - 8

M 1 5 - 3 . 1 1 2 K A A N G : - 8 6 . 1 9

M 1 5 - 1 . 1 1 2 K A A N G : - 8 6 . 1 9

M 1 5 - 2 . 1 1 2 K A A N G : - 8 6 . 1 9

0 1 4 - D S B 1 8 . 2 2 3 K A A N G : - 7 4 . 0 2

Likewise, the bus initial symmetrical rms fault current at Bus 14 is 9.993 kA and at Bus 18

is 7.19 kA.

Inspection of the A_FAULT three-phase Low-Voltage Report shows that the X/R ratio at

Bus 15 is 4.14, which is below the 6.6 test X/R ratio if a LV Power Circuit Breaker

(LVPCB) is selected. The symmetrical bus duty for an LVPCB is 8.66 kA, the same as

the initial symmetrical rms short-circuit current bus. However, if a 14 kA AIC molded-

case circuit breaker is selected, then the prospective symmetrical rms bus duty iscalculated as 9.265 kA, since the 14 kA AIC breaker is tested at an X/R ratio of 3.2 in

accordance with the table in Section 1.2.5, Adjusting Machine Contributions, but

applied in a location where the X/R ratio is 4.14.

The low-voltage report includes the symmetrical rms fault current and the direction and

magnitude of all contributions at all points in the system. This provides required data for

determining the specific fault duty through the device versus the total fault duty at the bus.

The X/R value reported at the faulted bus is calculated by separate reduction of the X and

R networks. The magnitude and angle of the contributions are calculated using the

complex network.

An option in the Low-Voltage Report is the examination of unbalanced fault currents.A_FAULT will automatically generate the negative- and zero-sequence networks from the

input data specifications. The fault currents for single-line-to-ground, line-to-line, and

double-line-to-ground are reported. In addition, the maximum rms current (assumed to

occur on Phase A) at one half-cycle for the three-phase and the single-line-to-ground fault

conditions is reported, as shown in the following report:

U N B A L A N C E D F A U L T R E P O R T( FOR APPLI CATI ON OF LOW VOLTAGE BREAKERS)

PRE FAULT VOLTAGE: 1. 0000MODEL TRANSFORMER TAPS: NO


21/56



============================================================================== LOCATI ON FAULT KA X/ R EQUI VALENT ( PU) ASYM. KA AT 0. 5 CYCLES

VOLTAGE DUTI ES ( RMS) FAULT I MPEDANCE * MAX. RMS AVG. RMS *==============================================================================

015- MCC 1A 3 PHASE: 8. 661 4. Z1= 13. 8875 10. 387 9. 544

SLG DUTY: 8. 468 4. Z2= 13. 8875 9. 907480. VOLTS LN/ LN 7. 501 Z0= 14. 8453

LN/ LN/ GND 8. 673 ( 8. 282 GND RETURN KA)

In the low-voltage unbalanced report above, the three-phase fault at Bus 15 is reported

(8.661 kA), the three-phase and single-line-to-ground (SLG) duty X/R ratios are reported

(4), the positive-, negative-, and zero-sequence impedances on a 100 MVA pu base are

reported, and the asymmetrical rms three-phase and SLG values at one half-cycle are

reported. The maximum rms value is based on the assumption that the maximum

asymmetrical current flows on Phase A; the average symmetrical rms current is the

arithmetical mean current for Phase A plus Phase B and Phase C. For an SLG fault, there

is no current assumed to flow on Phase B or Phase C, thus no three-phase average value is

reported. Both the line-to-line fault current (7.501 kA) and the line-to-line-to-ground bus

fault current (8.673 kA) are reported. For a line-to-line-to-ground fault current, the

quantity of fault current flowing on the ground (i.e., the zero-sequence path) is also

reported (8.282 kA).

A fault summary is also provided. The fault summary contains the three-phase and single-

line-to-ground fault data, and the fault X/R ratios. Care must be taken when selecting

protective device ratings using strictly the three-phase report. In some cases, the

unbalanced fault current (SLG or LLG current) may be larger than the three-phase short-

circuit current. This is unlikely in most grounded low-voltage systems that have cables

with significant lengths.

1.3.6 Momentary Duty ReportThe momentary duty or the closing and latching duty is the current that flows through the

medium- and high-voltage system at one half-cycle after the fault occurs. This current

exhibits a dc decay from the symmetrical fault current, and the fault contribution from

motors rated less than 50 hp is ignored. The Standard also allows for a reduction ininduction motor contribution due to ac decrement. The values for momentary current are

found by first calculating the initial symmetrical rms current using the magnitude of the

available fault currents from the machine reactance values specified in the table in Section

1.2.5, Adjusting Machine Contributions, then applying a 1.6 symmetrical multiplier to

match the ANSI simplified momentary rms calculations, and then calculating the

momentary rms current based on the calculated fault circuit X/R value. Additionally, the

peak (crest) values are calculated:

I = I 1 2emomentary rms symm rms

-4c

XR +

Eq. 7-1

I 2 I 1 emomentary peak symm rms

2c

X R= +

F

HGG

I

KJJ

where

c 1/2 cycle.

A_FAULT solves Eq. 7-1 at a time equal to one half-cycle to calculate the momentary

current permitted by the Standard. The Standard also allows the simple multiplication of

the symmetrical current by a factor of 1.6 to determine the momentary rms current, and


22/56


3/26/2006

2.7 to determine the momentary peak (crest) current. It can be shown that at X/R = 25

and one half-cycle, Eq. 7-1 reduces to 1.6 times the symmetrical rms current.

The Standard requires separate reduction of the resistance and the reactance networks.

These separate values of X and R are used to calculate the X/R ratio. This X/R ratio can

be significantly different from the value obtained by the vector (complex) circuit

reduction. This is particularly true when there are significant parallel branches wheresignificantly different component X/R ratios are modeled.

While the separately reduced X/R ratio is used to calculate the momentary asymmetrical

duty, the complex network is used for calculation of the direction and magnitude of each

of the fault currents to the faulted bus.

A_FAULT will also calculate the unbalanced fault conditions for Momentary Duty

Studies. As with the low-voltage report, the single-line-to-ground, the line-to-line and the

double-line-to-ground fault currents are calculated. The momentary values for both the

three-phase and for the single-line-to-ground fault currents are calculated and reported.

BLDG 115 SERV

I C/L 11.409 kA

X/R 10.539 kAC10 C11

TX E

026-TX G PRI

I C/L 11.172 kA

X/R 9.423 kA

025-MTR 25

I C/L 10.989 kA

X/R 11.467 kA

007-TX E PRI

I C/L 18.666 kAX/R 5.236 kA

M25

SW1

MO/L#25

F3

In the above one-line diagram and the following report, the closing and latching

(momentary) three-phase short-circuit current duty at the Main Building 115 Service

Entrance is reported as 11.409 kA rms or 19.252 kA peak asymmetrical current based on

1.6 and 2.7 times multiplying factor in the Standard.

T H R E E P H A S E M O M E N T A R Y D U T Y R E P O R TPRE FAULT VOLTAGE: 1. 0000MODEL TRANSFORMER TAPS: NO

==============================================================================

BLDG 115 SERV E/ Z: 7. 130 KA AT - 82. 21 DEG ( 51. 38 MVA) X/ R: 10. 54SYM*1. 6: 11. 409 KA MOMENTARY BASED ON X/ R: 10. 337 KASYM*2. 7: 19. 252 KA CREST BASED ON X/R: 17. 568 KAVOLTAGE: 4160. EQUI V. I MPEDANCE= . 0456 + J . 3337 OHMSCONTRI BUTI ONS: 007- TX E PRI 5. 139 KA ANG: - 80. 39

026- TX G PRI . 393 KA ANG: - 84. 15025- MTR 25 1. 608 KA ANG: - 87. 57

This X/R ratio is below the manufacturers test case X/R of 25, thus the reason the

calculated duty (10.337 kA) is less than the reported initial symmetrical current 1.6


23/56



value of 11.409 kA. These asymmetrical currents are calculated as the bus total, and

contributions flow are from Bus 7 (5.139 kA), Bus 26 (0.393 kA), and Bus 25 (1.608 kA).

A_FAULT stores the 1.6 times initial symmetrical rms current duty in the database, as this

is the more conservative rms current duty in most industrial and commercial power

systems.

1.3.7 Interrupting Duty ReportThe interrupting duty Report generates short-circuit current duties for specification of

two-, three-, five-, and eight-cycle breakers. The calculations assume that the breakers

will open (contact parting time) in 1.5-, 2-, 3-, and 4-cycles respectively.

A_FAULT applies the tables and graphs in the C37.5 and the C37.010 Standards to

calculate the interrupting duties. These graphs, combined with the factors which reduce

motor fault contributions due to ac decrement, result in proper calculation of asymmetrical

interrupting rating values as required by either the Total Current Standard (C37.5) and the

Symmetrical Current Rated Standard (C37.010).

Local and Remote Fault Contributions From GeneratorsANSI requires short-circuit current contributions from generators to be classified as eitherlocal or remote. The definition of the contributions as local or remote will determine the

appropriate ANSI figures which are used for determination of the ac decrement and dc

decay in the power system.

Remote sources are treated by ANSI as having no ac decrement. (Motor contributions are

decremented in A_FAULT by use of factors multiplied by the motor reactance values.

Refer to the table in Section 1.2.5, Adjusting Machine Contributions). Contributions

specified as generators or utility sources are treated as either local or remote as described

in the following sections.

ANSI C37.5 Considerations (Total Rated Basis)

The following paragraphs refer to Figure 1-1 through Figure 1-3 in Section 1.3.8,

Modeling ANSI Decrement Curves. These figures are A_FAULT interpretations of the

ANSI Figures 1, 2, and 3 in ANSI Standard C37.5, para 3.2.1

A generator short-circuit current contribution is considered remote when the per-unit

reactance external to the generator is equal to or greater than 1.5 times the generator per

unit subtransient reactance on a common MVA base. Once the total generation

contribution at a faulted location is known, the appropriate interrupting factors may be

used from the Standards. For breakers tested in accordance with ANSI Standard C37.5

(pre-1964), use Figure 1-1 through Figure 1-3 to determine the appropriate interrupting

duty.

If the bus is determined to be remote from the generator, then Figure 1-3 is used for both a

three-phase and single-line-to-ground fault condition.

When generators are determined as local, then both the ac decrement and the dc decay

must be accounted for, Figure 1-1, from ANSI Standard C37.5, is used for determining

multiplying factors for three-phase fault conditions with local generation. Figure 1-2 is

used if a single-line-to-ground fault condition is studied.

The Standards recognize that the generation in a system may consist of both local and

remote contributions and therefore permit the interpolation between Figure 1-1 and Figure


24/56


3/26/2006

1-3 for three-phase multiplying factors, and between Figure 1-2 and Figure 1-3 for the

single phase factors in the total current rated Standard is possible. The interpolation is a

function of the X/R ratio and the ratio of remote fault current to total bus fault current.

In A_FAULT, each generator is evaluated as local or remote based on a determination of

the per-unit reactance external to the generator being equal to or greater than 1.5 times the

generator per unit Xd" on a common MVA base for each fault location. Then, thecontribution of each generator to the fault is determined.

ANSI C37.010 Considerations (Symmetrical Rating Basis)

The concepts of local, remote and interpolation methods discussed above also apply to the

ANSI Standard C37.010, para. 5.3.2. Three-phase fault multiplying factors, which

include the effects of both ac decrement and dc decay (local generation) are in Figure 8 in

ANSI Standard C37.010. The line-to-ground fault multiplying factors which include the

effects of the ac decrement and dc decay are shown in Figure 9 of the Standard.

Additionally, Figure 10 of the Standard illustrates the three-phase and the line-to-ground

fault multiplying factors which include the effects of the dc decay only (remote

generation). Figures 8, 9, and 10 of ANSI Standard C30.010 are reproduced as Figure 1-4

through Figure 1-15 in Section 1.3.8, Modeling ANSI Decrement Curves.

A_FAULT permits you to specify the generator contributions as All Remote,

Predominant, or Interpolated. The program methodology for the ANSI Standard C37.010

is the same as described for the ANSI Standard C37.5 in the previous sections.

Although the ANSI Standard C37.010 permits the use of a simplifying technique to

convert multiplying factors calculated by the ANSI Standard C37.5 to the ANSI Standard

C37.010 format, the results may differ from the multiplying factors taken from the curves

in the ANSI Standard C37.010. A_FAULT resolves this by using only the published

curves.Using the NACD Options

This following one-line diagram illustrates how A_FAULT uses the three NACD options:

BLDG 115 SERV

I init symm 6.330 kA

X/R 9.780 kA

I symm current 6.330 kA

I total current 6.352 kA

C10 C11

TX E

026-TX G PRI


X/R 8.888 kA



025-MTR 25

I init symm 6.082 kAX/R 10.001 kA



007-TX E PRI


X/R 4.844 kA



M25

SW1

MO/L#25

F3


25/56



In the above one-line diagram and the following Report, the interrupting three-phase

short-circuit current duty at the Main Building 115 Service Entrance is reported as an

initial symmetrical rms current of 6.33 kA at an X/R of 9.78.

T H R E E P H A S E I N T E R R U P T I N G D U T Y R E P O R TPRE FAULT VOLTAGE: 1. 0000MODEL TRANSFORMER TAPS: NONACD OPTI ON: I NTERPOLATED

==============================================================================

BLDG 115 SERV E/ Z: 6. 330 KA AT -81. 61 DEG ( 45. 61 MVA) X/ R: 9. 78VOLTAGE: 4160. EQUI V. I MPEDANCE= . 0554 + J . 3754 OHMSCONTRI BUTI ONS: 007- TX E PRI 5. 088 KA ANG: - 80. 19

026- TX G PRI . 173 KA ANG: - 85. 29025- MTR 25 1. 077 KA ANG: - 87. 74

GENERATOR NAME - - AT BUS - - KA VOLTS PU LOCAL/ REMOTE001- EDI SON 3. 615 . 97 R008- GEN 1 . 181 . 93 R020- GEN 2 . 418 . 90 L

TOTAL REMOTE: 3. 796 KA NACD RATI O: . 5997

SYM2 SYM3 SYM5 SYM8MULT. FACT: 1. 000 1. 000 1. 000 1. 002DUTY ( KA) : 6. 330 6. 330 6. 330 6. 344

TOT2 TOT3 TOT5 TOT8MULT. FACT: 1. 211 1. 052 1. 004 1. 000DUTY ( KA) : 7. 668 6. 656 6. 352 6. 330

At the BLDG 115 SERV Bus, the total fault current due to generators is 4.2 kA, of which

the generator 020-GEN2 at Bus 20 is considered local to the faulted bus. The total remote

generation is 3.796 kA which is 59.97% of the total fault current (6.33 kA) available at the

bus.

The output report lists the interrupting duty in accordance with both the symmetrical basis

and the total current basis. If a 5-cycle breaker is selected, the Symmetrical Current basisduty is 6.33 kA, but if a 5-cycle breaker is selected which is rated on a Total Current basis,

then it must be specified on a short circuit interrupting duty of 6.352 kA.

1.3.8 Modeling ANSI Decrement CurvesThe published ANSI figures used for determining the interrupting duty decrement factors

are, at best, difficult to read. During the creation of A_FAULT, the published curves were

photographically enlarged and data points interpolated. These data points were then

entered into a graphic utility program and the interpolated points plotted. The graphic

utility program permitted the output curves to be scaled to the same size as the enlarged

curves taken from the standard. The interpolated curves were then compared directly with

the published curves. The interpolated results agreed with the published curves.

The ac decrement/dc decay curves used by A_FAULT are discussed in this section. Figure

1-1, Figure 1-2, and Figure 1-3 represent the ac decrement/dc decay curves used by the

ANSI Standard C37.5. Figure 1-4 through Figure 1-15 represent the ac decrement/dc

decay curves used by the ANSI Standard C37.010. In Figure 1-4 through Figure 1-15, the

ac decrement/dc decay curves corresponding to the breaker contact parting time are

shown. The ac decrement/dc decay curves for contact parting at other than 1.5-, 2-, 3-,

and 4-cycles are not shown as they are not required for the A_FAULT solution. Sufficient

information in A_FAULT is provided to determine other multiplying factors from the

standards for breakers which may have slower contact parting times.

It should be noted that the ac decrement/dc decay curves published by ANSI Standard

C37.010 occasionally result in multiplying factors which are not always intuitive. For

example, careful examination of the symmetrical standard for three-phase faults with local

generation indicates multiplying factors for a five-cycle breaker (3-cycle parting time) at a


26/56


3/26/2006

value of X/R = 60 will result in a multiplying factor of 1.167. With the same X/R value,

an eight-cycle breaker (4-cycle parting time) will have a multiplying factor of 1.180.

Although the eight-cycle breaker opens under a lower asymmetrical current, the breaker

takes longer for contact parting, thus a higher asymmetrical rating requirement.

Examination of the dc decay curves (remote sources) further illustrates that the intuitive

understanding of asymmetrical current values does not correspond to asymmetrical ratingscalculated by the ANSI Standard C37.010. For example, examination of a system with an

X/R ratio of 30, the multiplying factors increase for slower operating breakers.

For all of the following drawings, the vertical axis is the X/R ratio based on the separate

reduction of the R and X networks. Likewise, for all of the following drawings, the

horizontal axis represents the ANSI multiplying factors.


27/56



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

Contact Parting of:

8-cycle breaker

6-cycle breaker

4-cycle breaker

2-cycle breaker

4 Hz

3 Hz 2 Hz

1 Hz

Figure 1-1. C37.5 Three-phase ac decrement/dc decay curves.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

4 Hz

3 Hz 2 Hz

1 Hz

Contact Parting of:

8-cycle breaker

6-cycle breaker

4-cycle breaker

2-cycle breaker

Figure 1-2. C37.5 Single-line-to-ground ac decrement/dc decay curves.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

4 Hz

3 Hz 2 Hz

1 Hz

Contact Parting of :

8-cycle breaker

6-cycle breaker

4-cycle breaker

2-cycle breaker

Figure 1-3. C37.5 Three-phase and single-line-to-ground DC decay curves

(dc decay only).


28/56


3/26/2006

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

4 Hz

Contact Parting of:

8-cycle breaker

Figure 1-4. C37.010 Three-phase ac decrement/dc

decay curve for 8-cycle breakers.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

3 Hz

Contact Parting of:

5-cycle breaker



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

2 Hz

Contact Parting of:

3-cycle breaker



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

1.5 Hz

Contact Parting of:

2-cycle breaker




29/56



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

4 Hz

Contact Parting of:

8-cycle breaker

Figure 1-8. C37.010 Single-line-to-ground ac

decrement/dc decay curve for 8-cycle breakers.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

3 Hz

Contact Parting of:

5-cycle breaker



1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

2 Hz

Contact Parting of:

3-cycle breaker

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

1.5 Hz

Contact Parting of:

2-cycle breaker


decrement/dc decay curve for 3-cycle breakers.Figure 1-11. C37.010 Single-line-to-ground ac



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1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

4 Hz

Contact Parting of:

8-cycle breaker

Figure 1-12. C37.010 Three-phase and single-line-to-ground dc

decay curve for 8-cycle breakers (dc decay only).

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

3 Hz

Contact Parting of:

5-cycle breaker

Figure 1-13. Three-phase and single-line-to-ground dc

decay curve for 5-cycle breakers (dc decay only).

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

2 Hz

Contact Parting of:

3-cycle breaker

Figure 1-14. Three-phase and single-line-to-ground dc

decay curve for 3- cycle breakers (dc decay only).

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7

0

10

20

40

30

50

60

70

80

90

100

110

120

130

140

150

1.5 Hz

Contact Parting of:

2-cycle breaker

Figure 1-15. Three-phase and single-line-to-ground

dc decay curve for 2 cycle breakers (dc decay only).


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1.4 Application Examples

The examples that follow illustrate how the A_FAULT Study calculates the various short-

circuit duties, given different project topologies. Unless otherwise specified, all per unit

values are expressed on a 100 MVA base at the bus system nominal voltage.

1.4.1 Induction Motor ac decrement FactorsThis first example comprises three separate cases in which different combinations of

induction motors are modeled to determine the impact of the ANSI ac decrement factor on

the ANSI fault current. The factors listed in the table in Section 1.2.5, Adjusting

Machine Contributions represent those modeled.

Case 1

In the following one-line diagram, a series of 4160 V 25 hp motors and a single 50 hp

motor are modeled as shown:

B1

C1

B2

C2

B3

M1

Size 25.0 hp

# of Mtrs: 2

U1

C3

B4

M2

Size 25.0 hp

# of Mtrs: 1

C4

B5

M4

Size 50.0 hp

# of Mtrs: 1

M3

Size 25.0 hp

# of Mtrs: 1

Note that the total motor short-circuit contribution from each of the three motor buses is

50 hp. A fault is created at Bus B2, and inspection of the following output Report shows

that the fault duty contributions from each of the three-motor branches are equal (47 A).

T H R E E P H A S E F A U L T R E P O R T( FOR APPLI CATI ON OF LOW VOLTAGE BREAKERS)


============================================================================== B2 FAULT: 13. 598 KA AT - 86. 14 DEG ( 97. 98 MVA) X/R: 14. 85

VOLTAGE: 4160. EQUI V. I MPEDANCE= . 0119 + J . 1762 OHMS


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3/26/2006

CONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16B3 . 047 KA ANG: - 84. 28B4 . 047 KA ANG: - 84. 28B5 . 047 KA ANG: - 84. 28

This is the expected result. In the Low-Voltage network Report all motors (regardless of

the rated voltage of the motor) are modeled with a machine reactance of 1.0 times the

rated subtransient reactance. This is compared to the medium/high-voltage momentary (or

closing and latching Report), where motors less than 50 hp are ignored. Note the output

results below:


==============================================================================

B2 E/ Z: 13. 496 KA AT - 86. 16 DEG ( 97. 24 MVA) X/R: 14. 89SYM*1. 6: 21. 593 KA MOMENTARY BASED ON X/ R: 20. 519 KASYM*2. 7: 36. 438 KA CREST BASED ON X/R: 34. 541 KAVOLTAGE: 4160. EQUI V. I MPEDANCE= . 0119 + J . 1776 OHMSCONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16

B5 . 039 KA ANG: - 84. 28

Note that the motor contributions from Bus B3 and Bus B4 are not included in the output

report. Also, note that the fault duty contribution from the 50 hp motor at Bus B5 is only

83% of the value reported in the low-voltage report. This is equivalent to increasing the

motors subtransient reactance by 1.2 times. Finally, note that the initial symmetrical rmsshort-circuit current is only 13.496 kA at Bus B2, compared to 13.598 kA in the previous

Report.

The Interrupting Report is printed below:


==============================================================================

B2 E/ Z: 13. 472 KA AT - 86. 16 DEG ( 97. 07 MVA) X/R: 14. 90VOLTAGE: 4160. EQUI V. I MPEDANCE= . 0119 + J . 1779 OHMSCONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16

B5 . 016 KA ANG: - 84. 29

GENERATOR NAME - - AT BUS - - KA VOLTS PU LOCAL/ REMOTEU1 13. 456 . 06 R

TOTAL REMOTE: 13. 456 KA NACD RATI O: . 9988

The fault duty contribution from the single 50 hp motor at Bus B5 is now only 34% of the

value reported in the Low-Voltage Report. This is equivalent to increasing the motors

subtransient reactance by 3.0 times and is consistent with a reduced ac decrement

component during interrupting. Also, observe that the initial symmetrical rms short-

circuit current is now 13.472 kA at Bus B2, reflecting the further reduction in motor

contributions. In each of the three Reports, the short-circuit current from the utility source

was 13.456 kA.

Case 2

This second example follows from the format of Case 1. The 4160 V motors have been

resized, as shown in the following one-line diagram:


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B1

C1

B2

C2

B3

M1

Size 100.0 hp

# of Mtrs: 1

U1

C3

B4

M2

Size 300.0 hp

# of Mtrs: 1

C4

B5

M4

Size 1250.0 hp

# of Mtrs: 1

First the Comprehensive Short Circuit Study is run for a fault at Bus B2:

*************** ** F A U L T A N A L Y S I S R E P O R T ********* *******

FAULT TYPE: 3PHMODEL I NDUCTI ON MOTOR CONTRI BUTI ON: YESMODEL TRANSFORMER TAPS: NO

MODEL TRANSFORMER PHASE SHI FT: NO

B2 VOLTAGE BASE LL: 4160. 0 ( VOLTS)I NI . SYM. RMS FAULT CURRENT: 15014. 0 / - 86. ( AMPS/ DEG )

THEVENI N EQUI VALENT I MPEDANCE: . 065 +j . 922 ( PU)THEVENI N I MPEDANCE X/R RATI O: 14. 105

ASYM RMS I NTERRUPTI NG AMPS1/ 2 CYCLES 3 CYCLES 5 CYCLES 8 CYCLES

22675. 9 16017. 4 15187. 5 15026. 0

B2 ==== I NI . SYM. RMS SYSTEM BRANCH FLOWS ( AMPS/ DEG ) ======= ALL BRANCHES REPORTED AT TI ME = . 5 CYCLES

VOLTS - - PHASE A- - - - - - PHASE B- - - - - - PHASE C

M1 4160. 94. 7/ - 84. 94. 7/ 156. 94. 7/ 36.M2 4160. 283. 9/ - 84. 283. 9/ 156. 283. 9/ 36.M4 4160. 1180. 1/ - 84. 1180. 1/ 156. 1180. 1/ 36.

*****************************************************************************

The results of A_FAULTs low-voltage report for the same fault bus (B2) are:



============================================================================== B2 FAULT: 15. 014 KA AT - 85. 94 DEG ( 108. 18 MVA) X/R: 14. 36

VOLTAGE: 4160. EQUI V. I MPEDANCE= . 0113 + J . 1596 OHMSCONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16

B3 . 095 KA ANG: - 84. 27B4 . 284 KA ANG: - 84. 22B5 1. 180 KA ANG: - 84. 02


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3/26/2006

Close examination of the two Reports shows that the bus initial symmetrical rms current

and each of the motor contributions are identical in magnitude. In fact, the only

significant difference between the two Reports is the reported X/R ratio. The

Comprehensive Study reported an X/R ratio of 14.11, whereas the A_FAULT study Low-

Voltage Report calculated the X/R ratio as 14.36. Indeed, even the difference in

calculated X/R ratio between the two methods is not particularly significant in this case.Next, A_FAULTs Momentary (closing and latching) Report is examined:


==============================================================================

B2 E/ Z: 14. 951 KA AT - 85. 95 DEG ( 107. 73 MVA) X/R: 14. 38SYM*1. 6: 23. 922 KA MOMENTARY BASED ON X/ R: 22. 634 KASYM*2. 7: 40. 368 KA CREST BASED ON X/R: 38. 137 KAVOLTAGE: 4160. EQUI V. I MPEDANCE= . 0113 + J . 1602 OHMSCONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16

B3 . 079 KA ANG: - 84. 27B4 . 237 KA ANG: - 84. 23B5 1. 180 KA ANG: - 84. 02

The 100 hp and 300 hp motors are modeled with a 1.2 times subtransient reactance ac

decrement factor, whereas the 1250 hp motor does not use a multiplying factor, based onthe ac decrement factors from the table in Section 1.2.5, Adjusting Machine

Contributions.

Case 3

This third example follows from the first two cases. The 4160 V motors have been re-

sized once again, as shown in the following one-line diagram:


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B1

C1

B2

C2

B3

M1

Size 300.0 hp

# of Mtrs: 1

U1

C3

B4

M2

Size 300.0 hp

# of Mtrs: 1

1800 rpm 3600 rpm

In this problem each of the two induction motors is rated 300 hp, but Motor M1 is rated at

1800 rpm, whereas Motor M2 is rated at 3600 rpm. The A_FAULT Momentary (closing

and latching) Report predicts the following ac decrement factors for the two motors:


==============================================================================

B2 E/ Z: 13. 976 KA AT - 86. 09 DEG ( 100. 70 MVA) X/R: 14. 72SYM*1. 6: 22. 362 KA MOMENTARY BASED ON X/ R: 21. 220 KASYM*2. 7: 37. 736 KA CREST BASED ON X/ R: 35. 732 KAVOLTAGE: 4160. EQUI V. I MPEDANCE= . 0117 + J . 1714 OHMSCONTRI BUTI ONS: B1 13. 456 KA ANG: - 86. 16

B3 . 237 KA ANG: - 84. 23B4 . 284 KA ANG: - 84. 22

As expected, the slower motor (Motor M1 on Bus B3) has a smaller momentary short-

circuit current contribution (237 A) than the faster motor attached to Bus B4 (284 A).

1.4.2 Modeling Transformers with TapsIn this example the impact of modeling transformer taps in A_FAULT is investigated.

The following one-line diagram posts the results of the Comprehensive Short Circuit

Study, modeling the effects of transformer taps.


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B1

14753.23 Amps 3P

13600.55 Amps SLG C1

B2

14266.92 Amps 3P

12999.28 Amps SLG

U1

G1

TX1

B3

35266.01 Amps 3P

37492.43 Amps SLG C2

B4

19772.67 Amps 3P

16101.20 Amps SLG

M1 L1

Because of a significant steady-state load flow voltage drop at Bus B4, a -2.5% primarytransformer tap is placed on Transformer TX1. The pre-fault no-load voltage used to

model the short-circuit current for a fault at Bus B4 is 1.0256 % of nominal due to the

-2.5% primary tap. The results of the Comprehensive Short Circuit Report are posted on

the one-line diagram. The calculated pre-fault, no-load voltage at Bus B4, given the

-2.5% primary tap, is 1.0256 pu V.

Rerunning the study using A_FAULT and modeling a 1.0256 pu driving point voltage

yields the same fault current magnitude at Bus B4, as compared to the Comprehensive

Short Circuit Study; this is noted in the following Report:


PRE FAULT VOLTAGE: 1. 0256

MODEL TRANSFORMER TAPS: YES==============================================================================B4 FAULT: 19. 772 KA AT - 55. 84 DEG ( 16. 86 MVA) X/ R: 2. 59

VOLTAGE: 480. EQUI V. I MPEDANCE= . 0081 + J . 0119 OHMSLOWVOLTAGE POWER CI RCUI T BREAKER 19. 772 KAMOLDED CASE CI RCUI T BREAKER < 20KA 19. 772 KAMOLDED CASE CI RCUI T BREAKER > 20KA 19. 772 KACONTRI BUTI ONS: M1 4. 208 KA ANG: - 84. 29

B3 16. 196 KA ANG: - 48. 7

The results between the Comprehensive Short Circuit Study and the A_FAULT Study

match.


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If the transformer tap is ignored, and the pre-fault voltage is reset to 1.0 pu, A_FAULT

predicts a slightly smaller fault current at Bus B4:



==============================================================================B4 FAULT: 19. 360 KA AT - 55. 63 DEG ( 16. 10 MVA) X/R: 2. 58

VOLTAGE: 480. EQUI V. I MPEDANCE= . 0081 + J . 0118 OHMSLOWVOLTAGE POWER CI RCUI T BREAKER 19. 360 KAMOLDED CASE CI RCUI T BREAKER < 20KA 19. 360 KAMOLDED CASE CI RCUI T BREAKER > 20KA 19. 360 KACONTRI BUTI ONS: M1 4. 103 KA ANG: - 84. 29

B3 15. 882 KA ANG: - 48. 52

This case may also be used to understand the significance of examining both the three-

phase and the single-line-to-ground fault Reports. It is important to understand that the

three-phase bolted fault may not be the largest fault current available at the bus. For

example, A_FAULT predicts that the single-line-to-ground fault current at Bus B3 will be

larger than the three-phase short-circuit current. Note the following one-line results from

A_FAULT:

B1

I Symm 14.733 kA 3 Ph

I Symm 13.589 kA SLG C1

B2


I Symm 12.988 kA SLG

U1

G1

TX1

B3


I Symm 36.864 kA SLG C2

B4

I Symm 19.360 kA 3 PhI Symm 15.732 kA SLG

M1 L1

Close in to the delta-wye-grounded transformer, the single-line-to-ground fault current is

larger than the three-phase short-circuit current.


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1.4.3 Calculating Interrupting DutiesThis example investigates how A_FAULT calculates the interrupting duties associated

with medium-voltage protective devices. Two issues of importance must be examined.

First, how the generator local/remove determination is made, and second, how A_FAULT

uses the various ac decrement figures to determine protective device Total Current and

Symmetrical Current duties.

Case 1

Consider the following one-line with the per unit impedances (expressed on a 100 MVA

base) as noted. Note that in this example resistances have been ignored:

B1

C1

B2

G1

X1 = 0.2 PU

C2

B3

C3

B4

C7

C4

B5

X1 = 0.4 PU

X1 = 0.6 PU

X1 = 0.9 PU

X1 = 0.1 PU

X1 = 1.0 PU

A portion of the A_FAULT three-phase interrupting report is reported below for the

impedances modeled above:


==============================================================================



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B3 3. 929 KA ANG: - 89. 65

GENERATOR NAME - - AT BUS - - KA VOLTS PU LOCAL/ REMOTEG1 8. 292 . 40 L

TOTAL REMOTE: . 000 KA NACD RATI O: . 0000




Inspection of this partial report shows that at for a fault at either Bus B4 or Bus B5,

A_FAULT has determined that the single generator at Bus B1 is considered local to the

faulted bus.

The impedance of the branch from Bus B4 to Bus B5 is now increased, as noted below:

B1

C1

B2

G1

X1 = 0.2 PU

C2

B3

C3

B4

C7

C4

B5

X1 = 0.4 PU

X1 = 0.6 PU

X1 = 0.9 PU

X1 = 0.95 PU

X1 = 1.0 PU


==============================================================================


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3/26/2006


B3 3. 929 KA ANG: - 89. 65



B5 E/ Z: 5. 290 KA AT - 89. 78 DEG ( 38. 12 MVA) X/R: 259. 76VOLTAGE: 4160. EQUI V. I MPEDANCE= . 0017 + J . 4540 OHMSCONTRI BUTI ONS: B4 5. 290 KA ANG: - 89. 78GENERATOR NAME - - AT BUS - - KA VOLTS PU LOCAL/ REMOTE

G1 5. 290 . 62 RTOTAL REMOTE: 5. 290 KA NACD RATI O: 1. 0000

As the impedance of the branch from Bus B4 to Bus B5 increased from 0.1 to 0.95 pu ,

A_FAULT determined that when the fault occurred at Bus B5, the Generator contribution

switched from being a local contribution, where ac decrement and dc decay is considered,

to a remote contribution where there is no ac decrement considered for the generator in

question.

Para 5.3.2 of ANSI Standard C37.010 states that a generator should be considered remote

to the fault location if the per-unit reactance external to the

reference a fault

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