3 Phase Short Circuit

Version 6.60.00 May 2011

Short Circuit Analysis Program

ANSI/IEC/IEEE &

Protective Device Evaluation

Users Guide

Power Analytics CORPORATION 16870 West Bernardo Drive, Suite 330.

San Diego, CA 92127 U.S.A.

Copyright 2011

All Rights Reserved

Short Circuit Analysis Program ANSI/IEC/IEEE

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Table of Contents

1 Unique Features of Paladin DesignBase Short circuit Program ........................................................ 1 1.1 WHATS NEW IN THIS RELEASE ......................................................................................................... 1

2 Introduction.............................................................................................................................................. 2 2.1 Type of Faults ............................................................................................................................... 2 2.2 Terminology .................................................................................................................................. 3 2.3 Sources in Fault Analysis ............................................................................................................. 6 2.4 ANSI/IEEE Standard .................................................................................................................... 7 2.4. 1Multiplying Factors (MF) ............................................................................................................. 7 2.4.2 Local and Remote Contributions .................................................................................................. 8 2.5 IEC 60909 .................................................................................................................................. 10 2.5.1 System Parameters .................................................................................................................... 10 2.5.2 Short Circuit Current Calculus .................................................................................................... 24

3 ANSI/IEEE Standard Based Device Evaluation (PDE IEEE) .............................................................. 30 3.1 Standard Ratings for HV and MV Circuit Breakers (CB) ............................................................ 30 3.2 Standard Ratings for Low Voltage Circuit Breakers (LV-CBs) ................................................... 34 3.3 Standard Ratings for Low/High Voltage Fuses, and Switches................................................... 36

4 IEC Standard Based Device Evaluation (PDE IEC) ............................................................................ 40 4.1 CIRCUIT-BREAKERS ................................................................................................................ 40 4.1.1 Rated characteristics to be given for all circuit-breakers ........................................................... 40 4.1.2 Circuit Breaker Name Plate Data ............................................................................................... 47 4.2 FUSES........................................................................................................................................ 48 4.2.1 General considerations .............................................................................................................. 48 4.2.2 Fuse IEC Characteristic Quantities [IEC 60269-1] ..................................................................... 49 Breaking range ........................................................................................................................... 49 Cut-off current ............................................................................................................................ 49 Cut-off current characteristic; let-through current characteristic ................................................ 49 Peak withstand current ............................................................................................................... 49 Pre-arcing time; melting time ..................................................................................................... 50 Arcing time of a fuse ................................................................................................................... 50 Operating time; total clearing time ............................................................................................. 50 I2t (Joule integral) ....................................................................................................................... 50 4.2.3 Fuse nameplate data .................................................................................................................. 51

5 Protective Device Evaluation Based on IEC Standard ...................................................................... 52 5.1 Fuses Evaluation ........................................................................................................................ 55 5.2 LVCB Evaluation ........................................................................................................................ 55 5.3 HVCB Evaluation ........................................................................................................................ 56

6. DesignBase Short Circuit Calculation Method ........................................................................................ 57 A. Calculation Methods and the Corresponding Tools............................................................. 57 B. AC ANSI/IEEE Standard Paladin DesignBase Short Circuit Tools: ................................. 58 C. AC Classical Short Circuit Method....................................................................................... 72 D. AC IEC 60909 Short Circuit Method .................................................................................... 73 E. AC IEC 61363 Short Circuit Method .................................................................................... 82 F. AC Single Phase Short Circuit Method ................................................................................ 94


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7. Managing the Paladin DesignBase Short Circuit Program ............................................................... 94 A. 3P, LL, LG, LLG Fault, Cycle ........................................................................................... 94 B. 3P, LL, LG, LLG Fault, 5 Cycle ............................................................................................ 97 C. 3P, LL, LG, LLG Fault, Steady state .................................................................................... 99 D. 3 Phase Fault, Steady State .............................................................................................. 101 E. Protective Device Evaluation (PDE) Tool Based on ANSI/IEEE Standard ....................... 103 F. Protective Device Evaluation (PDE) Based on IEC Standard ........................................... 112 G. Report Manager ANSI/IEEE ........................................................................................... 127 H. Short Circuit Back Annotation ............................................................................................ 142 I. Managing Schedule in Short Circuit .................................................................................. 145 J. Managing Utility / PCC Short Circuit contribution .............................................................. 159 K. Managing MOTOR CONTRIBUTION ................................................................................ 160 L. Managing UPS bypass function during a fault downstream UPS source ......................... 161 M. Three-phase Faults IEC 61363 Method ............................................................................ 163 N. Short Circuit Analysis Input Data ....................................................................................... 167

7.1 Power Grid Input Data .............................................................................................................. 167 7.2 Synchronous Generator Short Circuit Input Data .................................................................... 168 7.3 Induction Motor Short Circuit Input Data .................................................................................. 169 7.4 Synchronous Motor Short Circuit Input Data............................................................................ 170 7.5 High Voltage ANSI/IEEE Circuit Breaker Short Circuit Input Data .......................................... 171 7.6 Low Voltage ANSI/IEEE Circuit Breaker Short Circuit Input Data ........................................... 172 7.7 Low Voltage IEC Circuit Breaker Short Circuit Input Data ....................................................... 173 7.8 Low Voltage ANSI/IEEE Fuse Short Circuit Input Data ........................................................... 174 7.9 Medium / Low Voltage IEC Fuse Short Circuit Input Data ....................................................... 175

8 Network Reduction/Equivalent .......................................................................................................... 176 8.1 Introduction ............................................................................................................................... 176 8.2 Sample System Data ................................................................................................................ 176 8.3 How to Perform Equivalent/Reduction Calculations ................................................................ 177 8.4 Separating the Equivalent Part from the Rest of the System ................................................... 178 8.5 Specifying the Buses for the Equivalent ................................................................................... 179 8.6 Reporting of the Equivalent System ......................................................................................... 180 8.7 Computation of Equivalent System and Inspection of the Result ............................................ 183 8.8 Reconstructing the Original System by Using the Equivalent .................................................. 185 8.9 Validation and Verification of the Equivalent ............................................................................ 192

9 TUTORIAL: Conducting a Three-phase Short Circuit Study .......................................................... 195 9.1 The Calculation Tools ............................................................................................................... 196 9.2 Graphical Selection of Faulted Bus (Annotation) ..................................................................... 197 9.2.1 AC-ANSI/IEEE Method ............................................................................................................. 197 9.3 Short Circuit Annotation Tool ................................................................................................... 199 9.3.1 3-Phase Fault, 30 Cycles at Bus 18 ......................................................................................... 200 9.3.2 3-Phase Fault Current, Cycle Fault at Bus MAINBUS: ...................................................... 202 9.3.3 3-Phase Fault Current, 5 Cycle Fault at Bus MAINBUS: ....................................................... 204 9.3.4 Change the Fault Type displayed onto the drawing. ............................................................. 207 9.4 Professional Report .................................................................................................................. 215 9.4.1 All types of Faults at bus MAINBUS, 0.5 Cycle Symmetrical: .................................................. 215 9.4.2 All types of Faults at All buses, 0.5 Cycle Symmetrical: .......................................................... 219 9.4.3 All types of Faults at All buses, 5 Cycle Symmetrical: ............................................................. 222 9.4.4 All types of Faults at All buses, 30 Cycle Symmetrical: ........................................................... 224


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List of Figures

Figure 1: Device Evaluation, ANSI Standard, Page 1 .................................................................................... 38 Figure 2: Device Evaluation, ANSI Standard, Page 2 .................................................................................... 39 Figure 3: Percentage D.C. current component in relation to the time interval from initiation of

short-circuit current, for different time constant. ............................................................................ 44 Figure 4: PDE Flow Chart - IEC standard: ..................................................................................................... 52 Figure 5: Unbalanced system ......................................................................................................................... 66

List of Tables

Table 1: Recommended ANSI Source Impedance Multipliers for 1st Cycle and Interrupting Times ............. 6 Table 2: 30 cycles calculation impedance ....................................................................................................... 7 Table 3: Resistivity and equivalent earth penetration ................................................................................... 22 Table 4: IEC voltage factor ............................................................................................................................ 23 Table 5: CB rated interrupting time in cycles ................................................................................................ 30 Table 6: K factor ............................................................................................................................................ 33 Table 7: Default Device X/R Values Using EDSAs Library .......................................................................... 34 Table 8: n factor based on PF and short circuit level .................................................................................... 42 Table 9: Icu and k factor ................................................................................................................................ 46 Table 10: CB Name plate data ........................................................................................................................ 48 Table 11: IEC c factor ...................................................................................................................................... 81 Note: You can view this manual on your CD as an Adobe Acrobat PDF file. The file name is:

Short Circuit Analysis Program 3_Phase_Short_Circuit.pdf You will find the Test/Job files used in this tutorial in the following location:

C:\DesignBase\Samples\3PhaseSC

Test Files: ANSIYY1, IEC-YY; Busfault, EDM5, IEC1-60909, IEC2-60909, IEEE399, IEEEpde, MutualNet, SlidingFault, T123, T123PDE, testma1, Trib, TribNVTAP, UPSexpse, West

Copyright 2011

Power Analytics Corporation All Rights Reserved


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1 Unique Features of Paladin DesignBase Short Circuit Program

The salient features of the Paladin DesignBase advanced short circuit program:

9 Fault analysis of complex power systems having over 50,000 buses 9 Exact short circuit current and contributions computation using Three-Sequence Modeling 9 Simulate sliding and open conductor faults 9 High speed simulation by utilizing the state-of-the-art techniques in matrix operations (sparse

matrix and vector methods)

9 Automated reactor sizing for 3 Phase networks 9 Exporting and importing data from and to Excel 9 Import system data from Siemens/PTI format into Paladin DesignBase 9 Customize reports 9 Professional Reports 9 UPS source bypass 9 Support of ANSI and IEC standards for PDC (protective device coordination) 9 Support of ANSI and IEC standards for PDE (protective device evaluation) 9 Fully integrated with ARC flash program 9 Fully integrated with PDC

1.1 Whats new in this release

9 New PDE based on IEC Standards 9 New professional report tool based on Crystal Reports 9 New functions for UPS bypass and motors fed from VFD 9 Minimum and maximum utility fault contribution


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2 INTRODUCTION The short circuit is an accidental electrical contact between two or more conductors. The protective devices such as circuit breakers and fuses are applied to isolate faults and to minimize damage and disruption to the plants operation.

2.1 Type of Faults

Types of Faults depend on the power system grounding method. The most common faults are:

Three-Phase Fault, with or without ground (3P, or 3P-G) Single line to ground Fault (L-G) Line to Line Fault (L-L) Line to line to ground Fault (L-L-G)

Estimated frequency of occurrence of different kinds of fault in power system is:

3P or 3P-G: 8 % L-L: 12 % L-L-G: 10 % L-G: 70 %

Severity of fault: Normally the three-phase symmetrical short circuit (3P) can be regarded as the most severe condition. There are cases that can lead to single phase fault currents exceeding the three-phase fault currents; however, the total energy is less than a three-phase fault. Such cases include faults that are close to the following types of equipment:

The Wye side of a solidly grounded delta-wy transformer / auto-transformer The Wye-Wye solidly grounded side of a three winding transformer with a delta

tertiary winding A synchronous generator solidly connected to ground The Wye side of several Wye grounded transformers running in parallel


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Type of Short Circuits:

a):3P three-phase; b):L-L, line-to-line; c):L-L-G, line-to-line-to-ground; and d): L-G, line-to-ground

2.2 Terminology

Arcing Time - the interval of time between the instant of the first initiation of the arc in the protective device and the instant of final arc extinction in all phases. Available Short Circuit Current - the maximum short circuit current that the power system could deliver at a given circuit point assuming negligible short circuit fault impedance. Breaking Current - the current in a pole of a switching device at the instant of arc initiation (pole separation). It is also known as Interrupting Current in ANSI Standards. Close and Latch Duty - the maximum rms value of calculated short circuit current for medium and high-voltage circuit breakers, during the first cycle, with any applicable multipliers with regard to fault current X/R ratio. Often, the close and latching duty calculation is simplified by applying a 1.6 factor to the first cycle symmetrical AC rms short circuit current. Close and latch duty is also called first cycle duty, and was formerly called momentary duty. Close and Latch Capability - the maximum asymmetrical current capability of a medium or high-voltage circuit breaker to close, and immediately thereafter latch closed, for normal frequency making current. The close and latch asymmetrical rms current capability is 1.6 times the circuit breaker rated maximum symmetrical AC rms interrupting current. Often called first cycle capability. The rms asymmetrical rating was formerly called momentary rating. Contact Parting Time - the interval between the beginning of a specified over current and the instant when the primary arcing contacts have just begun to part in all poles. It is the sum of the relay or release delay and opening time. Crest Current / Peak Current the highest instantaneous current during a period. Fault an abnormal connection, including the arc, of relative low impedance, whether made accidentally or intentionally, between two points of different voltage potentials.


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Fault Point X/R the calculated fault point reactance to resistance ratio (X/R). Depending on the Standard, different calculation procedures are used to determine this ratio. First Cycle Duty the maximum value of calculated peak or rms asymmetrical current or symmetrical short circuit current for the first cycle with any applicable multipliers for fault current X/R ratio. First Cycle Rating the maximum specified rms asymmetrical or symmetrical peak current capability of a piece of equipment during the first cycle of a fault. Interrupting Current the current in a pole of a switching device at the instant of arc initiation. Sometimes referred to as Breaking Current, bI , IEC60909. Making Current the current in a pole of a switching device at the instant the device closes and latches into a fault. Momentary Current Rating the maximum available first cycle rms asymmetrical current which the device or assembly is required to withstand. It was used on medium and high-voltage circuit breakers manufactured before 1965; present terminology: Close and Latch Capability. Offset Current - an AC current waveform whose baseline is offset from the AC symmetrical current zero axis. Peak Current the maximum possible instantaneous value of a short circuit current during a period. Short circuit current is the current that flows at the short circuit location during the short circuit period time. Symmetrical short circuit current is the power frequency component of the short circuit current. Branch short circuit currents are the parts of the short circuit current in the various branches of the power network. Initial short circuit current IK" is the rms value of the symmetrical short circuit current at the instant of occurrence of the short circuit, IEC 60909. Maximum asymmetrical short circuit current Is is the highest instantaneous rms value of the short circuit current following the occurrence of the short circuit. Symmetrical breaking current Ia , on the opening of a mechanical switching device under short circuit conditions, is the rms value of the symmetrical short circuit current flowing through the switching device at the instant of the first contact separation. Rated voltage VR the phase-to-phase voltage, according to which the power system is designated; IEC UR the rated voltage is the maximum phase-to-phase voltage. Nominal Voltage UN (IEC) the nominal operating voltage of the bus. Initial symmetrical short - circuit power S "K is the product of 3 *I "*UK N


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System breaking power SB is the product of 3 *I * Ua N Minimum time delay t min is the shortest possible time interval between the occurrence of the short circuit and the first contact separation of one pole of the switching device. Dynamic stress is the effect of electromechanical forces during the short circuit conditions. Thermal stress is the effect of electrical heating during the short circuit conditions. Direct earthing / effective earthing is the direct earthing of the neutral points of the power transformers. Short circuit earth current is the short circuit current, or part of it, that flows back to the system through the earth. Equivalent generator is a generator that can be considered as equivalent to a number of generators feeding into a given system. DesignBase Short Circuit Analysis Program is based on ANSI/IEEE and IEC Standards and fully complies with the latest ANSI/IEEE/IEC Standards: ANSI/IEEE Std. 141 1993, IEEE Recommended Practice for Electric Power Distribution of

Industrial Plants (IEEE Red Book) ANSI/IEEE Std. 399 1997, IEEE Recommended Practice for Power Systems Analysis (IEEE

Brown Book) ANSI/IEEE Standard C37.010 1979, IEEE Application Guide for AC High-Voltage Circuit

Breakers Rated on a Symmetrical Current Basis ANSI/IEEE Standard C37.5-1979, IEEE Application Guide for AC High-Voltage Circuit Breakers

Rated on a Total Current Basis ANSI/IEEE Standard C37.13-1990, IEEE Standard for Low-Voltage AC Power Circuit Breakers

Used in Enclosures IEC-909 1988, International Electro technical Commission, Short Circuit Current Calculation in

Three-Phase Ac Systems UL 489_9 1996, Standard for Safety for Molded-Case Circuit Breaker, Molded-Case Switches,

and Circuit-Breaker Enclosures A Practical Guide to Short-Circuit Calculations, by Conrad St. Pierre IEC 60909-0/2001-07, Short-circuit currents in three-phase AC systems, Part 0: Calculation of

currents IEC 60909-3/2003, Short-circuit currents in three-phase AC systems, Part 3: Currents during two

separate simultaneous line-to-earth short-circuits and partial short-circuit currents flowing through earth

IEC 60947-1:2000-10, Low-voltage switchgear and controlgear Part 1: General rules IEC 60947-2:2003, Low-voltage switchgear and controlgear Part 2: Circuit breakers EN 60947-3:1999, Low-voltage switchgear and controlgear Part 3: Switches, disconnectors,

switch-disconnectors and fuse-combination units BS EN 62271-100:2001, High-voltage switchgear and controlgear Part 100: High-voltage

alternating-current circuit-breakers IEC 62271-111:2005-11, High-voltage switchgear and controlgear Part 111: Overhead, pad-

mounted, dry vault and submersible automatic circuit reclosers and fault interrupters for alternating current systems up to 38 kV


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2.3 Sources in Fault Analysis

Power utilities, all rotating electric machinery and regenerative drives are sources in fault calculation. Cycle Network Duty The decay of short circuit current is due to the decay of stored magnetic energy in the equipment. The main impedances for the first cycle is the sub-transient impedance. It is generally used for the first cycles up to a few cycles;

The cycle network is also referred to as the sub transient network, because all rotating machines are represented by their sub transient reactance. cycle short circuit currents are used to evaluate the interrupting duties for low-voltage power breakers, low voltage molded-case breakers, high and low voltage fuses and withstand currents for switches and high-voltage breakers. The following table shows the type of device and its associated duties using the cycle network. Type of Device Duty High voltage circuit breaker Closing and latching capability Low voltage circuit breaker Interrupting capability Fuse Bus bracing Switchgear and MCC Instantaneous settings Relay

Table 1: Recommended ANSI Source Impedance Multipliers for 1st Cycle and Interrupting Times

Source Type 1/2-Cycle Calculations

Interrupting Time

calculations (1.5 to 4 cycles cpt)

Reference

Remote Utility (equivalent) "sZ sZ ANSI C37.010

Local Generator "dvZ "dvZ ANSI C37.010

Synchronous Motor "dvZ 1.5*"dvZ ANSI C37.010

Large Induction Motors: >1000 HP or 250 HP and 2 poles

"Z

1.5* "Z

ANSI C37.010

Medium Induction Motors 50 to 249 HP or 250 to 1000 HP


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Harmonic Filters harmonicTunedZ

_100% =

Xd = 1 /LRC For Induction Motors

1.5-4 Cycle Network

This network is used to calculate the interrupting short circuit current and protective device duties (1.5 4) cycles after the fault.

Type of Device Duty

High voltage circuit breaker (>1.0 kV) Interrupting capability Unfused Low Voltage PCB without instantaneous Interrupting capability All Other Low voltage circuit breaker N/A Fuse N/A Switchgear and MCC bus N/A Steady State or 30-Cycle Network

This network is used to calculate the steady state short circuit current and duties for some of the protective devices 30 cycles after the fault occurs (delayed protective devices). The type of power system component and its representation in the 30-cycle network are shown in the following table. Note that the induction machines, synchronous motors, and condensers are not considered in the 30-cycle fault calculation.

Table 2: 30 cycles calculation impedance

Source Type 30 Cycle Calculation Impedance Power Utility /Grid "

sZ Generators '

dvZ Induction Motors Infinite impedance Synchronous Motors Xd

2.4 ANSI/IEEE Standard 2.4.1 Multiplying Factors (MF)

The short circuit waveform for a balanced three-phase fault at the terminal bus of a machine is generally asymmetrical and is composed of a unidirectional DC component and a symmetrical AC component. The DC component decays to zero, and the amplitude of the symmetrical AC component decays to constant amplitude in the steady-state. If the envelopes of the positive and negative peaks of the current waveform are symmetrical around zero axis, they are called Symmetrical. If the envelopes of the positive and negative peaks of the current are not symmetrical around the zero axis, they are called Asymmetrical. If the DC fault component is not considered in the fault current, the fault current has the AC component only, and it is symmetrical; if DC fault component is considered, then the fault current is asymmetrical and is called asymmetrical or total fault current.


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The multiplying factors MF converts the rms value of the symmetrical AC component into asymmetrical rms current or short circuit current duty. The MF is calculated based on the X/R ratio and the instant of time that the fault current happens. The X/R ratio for ANSI breaker duties is calculated from separate R and X networks.

First Cycle (Asymmetrical) Total Short Circuit Current MF (Circuit Duty): Is defined as:

RX

m eMF

221

+= , 1

For: X/R = 25, the MF is equal to 1.6. Note: In the short circuit option tab Control for ANSI/IEEE the user has the option to calculate MFm based on X/R or use MFm=1.6 Peak Multiplying Factor Is defined as:

)1(2 /2

RXPeak eMF

+= , 2

where is the instant of time when fault occurs, X/R for ANSI breaker duties are calculated from separate R and X network.

For: = Cycle, and X/R = 25 to one decimal place is 7.2=PeakMF . Note: In the short circuit option tab Control for ANSI/IEEE the user has the option to calculate MFpeak based on X/R or use MFpeak = 2.7.

2.4.2 Local and Remote Contributions

The magnitude of the symmetrical current (AC component) from remote sources remain essentially constant. No AC Decay (NACD) at its initial value or it may reduce with time toward a residual AC current magnitude (ACD). If the fault is close to a generator, then the AC component decays (ACD). In other words, when a generator is local or close to the faulted point, the short circuit current decays faster. If the generator is remote from the faulted point, the AC short circuit current decay will be slow and a conservative simplification is to assume that there is no AC decay (NACD) in the symmetrical AC component.


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Per ANSI Standards: A generator is a LOCAL SOURCE of the short circuit current if:

The per unit reactance external to the generator is less than 1.5 times the generator per-unit sub transient reactance on a common system base MVA

Its contribution to the total symmetrical rms Amperes will be greater than "*4.0d

G

XE

,

where the "d

G

XE

is the generator short circuit current for a three-phase fault at its terminal bus

A generator is a REMOTE SOURCE of a short circuit current if:

The per unit reactance external to the generator is equal to or exceeds 1.5 times the

generator per unit sub transient reactance on a common system base MVA

The generator short circuit contribution may be written as:

)( "dExternalG

GXX

EI += , 3

Its location from the fault is two or more transformations or Its contribution to the total symmetrical rms Amperes is less than or equal to "*4.0

d

G

XE

,

where the "d

G

XE

is the generator short circuit current for a three-phase fault at its terminal bus

The ANSI Standards provide multiplying factors (MF) based X/R ratio for three-phase faults and line-to-ground faults fed predominantly from generators and MF for faults fed predominantly from remote sources. No AC decay (NACD) Ratio The Total Short circuit Current is equal to:

moteLocalTotal III Re+= 4 and:

Total

mote

IINACD Re= 5

When all contributions are remote, or when there is no generator, then 1=NACD When all contributions are local, then 0=NACD


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2.5 IEC 60909 While using the IEC standard the following system components formulae are used: The network components like power transformers, reactors, feeders, overhead lines, cables and other similar equipment, positive-sequence and negative-sequence short-circuit impedances are equal:

)()( ZZ 21 = , 6

The zero-sequence short-circuit impedance,

)()()( I/UZ 000 = , 7

is determined by assuming an AC voltage between the three paralleled conductors and the joint return (for example earth, earthing arrangement, neutral conductor, earth wire, cable sheath and cable armoring). In this case, the three-fold zero-sequence current flows through the joint return. The impedances of generators (G), network transformers (T) and power station units (S) will be multiplied with the impedance correction factors KG, KT and KS or KSO when calculating short-circuit currents with the equivalent voltage source at the short-circuit location according to the standard [1].

2.5.1 System Parameters

Power transformer parameters

The impedance module ZT can be calculated from the rated transformer data as follows:

,S

UuZrT

rTkrT

=100

2

, 8

Where: UrT is the rated voltage of the transformer, on the high-voltage or low-voltage side. SrT is the rated apparent power of the transformer. ukr is the short-circuit voltage at rated current in percent.

The positive-sequence short-circuit resistance RT of a two-winding transformer is given by the relationship:

,I

PRrT

krTT 23 = , 9


11

Where: PkrT is the total loss of the transformer in the windings at rated current. IrT - the rated current of the transformer on the high-voltage or low-voltage side. Note:

The resistance RT is to be considered if the peak short-circuit current ip or the DC component iDC is to be calculated. For large transformers, the resistance is so small that the impedance is represented by the reactance only, when calculating short-circuit currents. The positive-sequence short-circuit reactance XT of a two-winding transformer results as follows:

.,RZX TTT 22 = , 10

The relative reactance of the transformer xT is given by the formula

TrT

rTT XU

Sx = 2 , 11

Note: The ratio RT/XT generally decreases with transformer size.

The impedance TZ of a two-winding power transformer is considered like positive-sequence

short-circuit impedance )(Z 1 , which is equal to the negative-sequence short-circuit impedance

)(Z 2 :

.,ZZZ )()(T 21 == , 12 The actual data for two-winding transformers (used as network transformers or in power stations) are given in IEC 60909-2.

The zero-sequence short-circuit impedance T)(Z 0 may be obtained from the rating plate or from

the manufacturer:

T)(T)(T)( jXRZ 000 += , 13 Zero-sequence impedance arrangements for the calculation of unbalanced short-circuit currents are given in IEC 60909-4.


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For two-winding power transformers with and without on-load tap-changer, an impedance correction factor KT is to be introduced in addition to the impedance evaluated according to equations (1.2) (1.4):

T

maxT x.

c.K601

950+

= , 14

where cmax (from table 2.2) is related to the nominal voltage of the network connected to the LV side of the network transformer and the transformer relative reactance is calculated with the relationship (11). The correction factor will not be introduced for unit transformers of power station units. The correction factor KT is multiplying all the components of the transformer positive-sequence impedance, according to the following relationship:

( ) ( )TTTTTTTK XKjRKZKZ +== , 15

The impedance correction factor will be applied also to the negative-sequence and the zero-sequence impedance of the transformer when calculating unbalanced short circuit currents. If the long-term operating conditions of network transformers before the short circuit are known for sure, then the following equation may be used instead of equation (1.10) in order to calculate the correction factor KT:

( ) bTrTbTT maxbnT sinI/Ix1c

UUK += , 16

Where:

cmax is the voltage factor from table 1.2, related to the nominal voltage of the network connected to the LV side of the network transformer. Ub - the highest operating voltage before short circuit.

bTI - the highest operating current before short circuit (this depends on network configuration

and relevant reliability philosophy). bt - the angle of power factor before short circuit.

The impedance correction factor will be applied also to the negative-sequence and the zero-sequence impedance of the transformer when calculating unbalanced short-circuit currents. The impedances between the star point of transformers and earth are to be introduced as (3 ZN) into the zero-sequence system without a correction factor. The rated transformation ratio tr of the power transformer:


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rTLV

rTHVr U

Ut = , 17

where UrTHV and UrTLV are transformer rated voltages of the HV and LV windings, respectively.

Reactors Assuming geometric symmetry, the positive-sequence, the negative-sequence and the zero-sequence short-circuit impedances of reactors are equal:

)()()( ZZZ 021 == , 18

Short-circuit current-limiting reactors will be treated as a part of the short-circuit impedance.

,I

UuXZrR

nkRRR

=3100 19

Where:

ukR and IrR are given on the reactor rating plate. UN the system nominal voltage.

Synchronous Generators and Motors The synchronous generator rated impedance is given by:

,SUZ

rG

rGrG

2

= , 20

The relative subtransient reactance "dx , related to the rated impedance is:

rG

"d"

d ZXx = , 21

The following values for the fictitious resistances RGf may be used for the calculation of the peak short-circuit current with sufficient accuracy:


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RGf = 0.05 "dX for generators with UrG > 1 kV and SrG 100 MVA;

RGf = 0.07 "dX for generators with UrG > 1 kV and SrG < 100 MVA;

RGf = 0.15 "dX for generators with UrG 1 kV.

In addition to the decay of the DC component, the factors 0.05, 0.07, and 0.15 also take into account the decay of the AC component of the short-circuit current during the first half-cycle after the short circuit took place. The influence of various winding-temperatures on RGf is not considered. The values RGf cannot be used when calculating the aperiodic component iDC of the short-circuit current. When the effective resistance of the stator of synchronous machines lies much below the given values for RGf, the manufacturers values for RG should be used.

The subtransient impedance GZ of the generator, in the positive-sequence system can be calculated with the formula:

"dGG jXRZ += , 22

When calculating initial symmetrical short-circuit currents in systems fed directly from generators

without transformers unit, the corrected impedance GKZ of the SG has to be used in the positive-sequence system:

( ) ( )"dGGGGGGK XKjRKZKZ +== , 23 with the correction factor KG for SG, given by the relationship:

( ) rGrG"d nmaxG UsinxUcK +=

1, 24

where:

cmax is the voltage factor according to table 2.2. UN - the nominal voltage of the system.

"dx - the relative subtransient reactance of the generator related to the rated impedance,

according to the (21) relationship.

rG is the phase angle between rGU and rGI . UrG - the rated voltage of the generator.


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The correction factor KG (equation 24) for the calculation of the corrected subtransient

impedance GKZ has been introduced because the equivalent voltage source ( )3/cUn is used instead of the subtransient voltage E behind the subtransient reactance of the synchronous generator. If the terminal voltage of the generator is different from UrG, it may be necessary to introduce:

( )GrGG pUU += 1 , 25

If the values of "dX and

"qX reactances are different, for the negative-sequence reactance

G)(X 2 of the SM, their arithmetical mean can be used:

2

""

)2(qd

G

XXX

+= , 26

The corrected short-circuit impedance of SG, GK)(Z 2 , is given, in the negative-sequence system,

by the following equation:

( ) ( )GGGGGK XKjRKZ )2()2( += , 27

For the short-circuit impedance G)(Z 0 of SG in the zero-sequence system, the following applies

with KG from equation (1.20):

( ) G)(G)(GGK)( jXRKZ 000 += , 28

When an impedance is present between the star-point of the generator and earth, the correction factor KG will not be applied to this impedance.

When calculating the initial symmetrical short-circuit current "kI , the peak short-circuit current ip,

the symmetrical short-circuit breaking current Ib, and the steady-state short-circuit current Ik, synchronous compensators are treated in the same way as SG. If synchronous motors have a voltage regulation, they are treated like synchronous generators. If not, they are subject to additional considerations.

Asynchronous Motors (AM) The rated apparent power of an AM can be calculated from the equation:


16

rMrM

rMrM cos

PS = , 29 where PrM, cosrM and rM are respectively the active rated power, rated power factor and rated efficiency of the motor, in accordance with its nameplate data. The rated current of the AM is given by the relationship:

rMrMrM

rMrM cosU

PI = 3 , 30 where UrM is the rated line voltage of the AM.

MV and LV motors contribute to the initial symmetrical short-circuit current "kI , to the peak short-

circuit current ip, to the symmetrical short-circuit breaking current Ib and, for unbalanced short circuits, also to the steady-state short-circuit current Ik. MV motors have to be considered in the calculation of maximum short-circuit current. LV motors are to be taken into account in auxiliaries of power stations and in industrial and similar installations, for example in networks of chemical and steel industries and pump stations.

The contribution of AM in LV power supply systems to the short-circuit current "kI may be

neglected if their contribution is not higher than 5 % of the initial short-circuit current "

MkI 0 , calculated without motors:

"MkrM I.I 0050 , 31

Where:

rMI is the sum of the rated currents of motors connected directly (without transformers) to the network where the short-circuit occurs;

"MkI 0 - the initial symmetrical short-circuit current without influence of motors.

In the calculation of short-circuit currents, those MV and LV motors may be neglected, providing that, according to the circuit diagram (interlocking) or to the process (reversible drives), they are not switched in at the same time. The impedance module ZM of AM in the positive- and negative-sequence systems can be determined by:


17

( )rMLRrMrM

rM I/ISUZ =

2

, 32

Where:

UrM is the rated voltage of the motor; SrM - the rated apparent power of the motor (see relationship (1.25)); (ILR/IrM) - the ratio of the locked-rotor current to the rated current of the motor.

The following relations may be used with sufficient accuracy in order to calculate AM parameters:

RM/XM=0.10, with XM=0.995ZM for MV motors with rated powers per pair of poles (PrM/p)1 MW;

RM/XM=0.15, with XM=0.989ZM for MV motors with rated powers per pair of poles (PrM/p)


18

303

100

80

.IUSc

.SP

"kQnQ

rTrT

rM

, 36

Where:

rMP is the sum of the rated active powers of the medium-voltage and the low-voltage motors which will be considered. rTS - the sum of the rated apparent powers of all transformers, through which the motors are directly fed.

"kQI - the initial symmetrical short-circuit current at the feeder connection point Q without

supplement of the motors. UnQ - the nominal voltage of the system at the feeder connection point Q.

Lines Constants The positive-sequence short-circuit impedance,

LLL jXRZ += , 37 may be calculated from the conductor data, such as the cross-section qn and the centre-distances d of the conductors. The following values for resistivity may be used:

m/mm541 2

Cu = for Copper; m/mm

341 2

Al = for Aluminum and m/mm311 2

Ala = for Aluminum alloy.

The effective resistance per unit length 'LrR of overhead lines at the conductor temperature 20C may be calculated from the nominal cross-section qn and the resistivity :

m/,q

Rn

'Lr = , 38

The line resistance RLr at the reference temperature r=20C can be determined if its length lL is known:


19

,lRR L'LrLr = , 39

Line Resistances RL (overhead lines and cables, line conductors and neutral conductors) will be

introduced at a higher temperature re , when calculating minimum short-circuit currents:

( )[ ] LrreL R1R += , 40

Where:

=0,004 K-1 is the temperature factor of resistivity, valid with sufficient accuracy for most practical purposes for copper, aluminum and aluminum alloy. e - the conductor temperature in degrees Celsius at the end of the short-circuit duration (for e, see also IEC 60865-1, IEC 60949 and IEC 60986).

r=20C - the reference conductor temperature in degrees Celsius. RLr - the resistance value at a reference temperature of 20C.

The geometric mean distance between conductors, or the center of bundles, in the case of overhead lines, is determined by the relationship:

3133221 LLLLLL dddd = , 41

Where: dL1L2, dL2L3 and dL3L1 are geometric distances between conductors. In the case of bundle conductor, the equivalent radius rB can be determined by the following formula:

n nB Rrnr

1= , 42

Where: n is the number of bundled conductors; r - the radius of a single conductor; R is the bundle radius (see IEC 60909-2).

The reactance per unit length 'LX for overhead lines may be calculated, assuming transposition,

from:

+=rdln

nfX 'L 4

10 , 43


20

Where:

0 = 410-7 H/m; f the nominal frequency of the power system; n - the number of bundled conductors, or n=1 for a single conductor; d - the geometric mean distance between conductors, according to (2.37) relationship; r - the radius of a single conductor or, in the case of conductor bundles, r is to be substituted by rB, from the (43) relationship.

The overhead line reactance XL follows to be determined, like in the resistance case, if its length lL is done:

,lXX L'LL = , 44 For measurement of the positive-sequence impedance

)()()( jXRZ 111 += , 45 and the zero-sequence short-circuit impedance,

)()()( jXRZ 000 += , 46 (see IEC 60909-4). Sometimes it is possible to estimate the zero-sequence impedances with the ratios R(0)L/RL and X(0)L/XL (see IEC 60909-2).

The impedances L)(Z 1 and L)(Z 0 of LV and HV cables depend on national techniques and

standards and may be taken from IEC 60909-2, from textbooks or manufacturers data. However, the impedance of a network feeder at the connection point Q is given by:

"kQ

nQ"kQ

nQQ I

UcSUc

Z3

2 == , 47

where "kQI is the initial symmetrical short-circuit current.

Earth Wire Impedance

The equivalent earth penetration depth is given by the following relationship:


21

0

851 E. = , m, 48

Where:

E is the earth type resistivity, having values in accordance with table 2.1 content. = 2f - angular frequency. 0 = 4107 H/m vide absolute magnetic permeability.

Resistivity E and equivalent earth penetration depth for different soil types


22

Table 3: Resistivity and equivalent earth penetration

Earth types Resistivity E,m

Equivalent earth penetration depth ,m

f=50 Hz f=60 Hz Granite Rocks Stony soil

>104 (310)103 (13)103

>9,300 (5.19.3)103

(2.945.1)103 >8,500

(4.658.2)103 (2.694.65)103

Pebbles, dry sand Calcareous soil, wet sand Farmland

(0.21.2)103 70200 50100

(1.323.22)103 (0.781.32)103

660930 (1.22.94)103 (0.711.2)103

600850 Clay, loam Marshy soil

1050


23

The mutual impedance per unit length between the earth wire and the parallel line conductors with common earth returns

WL

'WL d

lnfjZ 008 + , 52 Where: dWL is the geometric mean distance between the earth wire and the line conductors L1, L2 and L3, given by the formula

3321 WLWLWLWL dddd = , 53

when there is only one earth wire and by the next formula

6322212312111 LWLWLWLWLWLWWL ddddddd = , 54

when there are two earth wires.

Sources

As per IEC 60909 the equivalent voltage source (rms) is given by the relationship

3n

esUcU = , V, 55

where c is the voltage factor, having values according to the table 4:

Table 4: IEC voltage factor

Nominal voltage Un, V

Voltage factor c for the calculation of Tolerance, % Minimum short-circuit currents, cmin

Maximum short-circuit currents, cmax1)

Low voltage, [ ]kV,Un 1000100 0.95 1.05 6 1.10 10 Medium voltage, ( ]kV,Un 351 1.00 1.10 - High voltage2),

kVUn 35>


24

1) cmaxUn should not exceed the highest voltage Um for equipment of power systems:

mnmax UUc ; 2) if no nominal voltage is defined mnminnmaxm U,UcorUcU 90== should be applied. 2.5.2 Short Circuit Current Calculus Assumptions

All line capacitances and shunt admittances are neglected Non-rotating loads, except those of the zero-sequence system, are neglected Arc resistances are not taken into account For the duration of the short-circuit, there is no change:

o in the involved network o in the type of short-circuit involved

Additional calculations about all different possible load flows at the moment of the short-circuit are superfluous General rules

All network feeders, synchronous and asynchronous machines are replaced by their internal impedances

The equivalent voltage source is the only active voltage of the system When calculating short-circuit currents in systems with different voltage levels, it is necessary to

transfer impedances values from one voltage level to another, usually to that voltage level at which the short-circuit current is to be calculated

For p.u. system no transformation is necessary if these systems are coherent, i.e.

nLVnHVrTLVrTHV U/UU/U = , 56 for each transformer in the system with partial short-circuit currents. The impedances of the equipment in superimposed or subordinated networks are to be divided or multiplied by (tr)2, the square of the rated transformation ratio tr.; voltages and currents are to be converted by the rated transformation ratio tr. In general, two short-circuit currents, which differ in their magnitude, are to be calculated. In the case of a far-from-generator short circuit, the short-circuit current can be considered as the sum of the following two components:

- the AC component with constant amplitude during the whole short-circuit - the aperiodic DC component beginning with an initial value A and decaying to zero

Single-fed short circuits supplied by a transformer may be regarded as far-from- generator short circuits if

QtTLVK X2X , 57


25

with XQt calculated in accordance with 11 and

TLVTTLVK XKX = , 58 In the case of a near-to-generator short circuit, the short-circuit current can be considered as the sum of the following two components:

- the AC component with decaying amplitude during the short circuit - the aperiodic DC component beginning with an initial value A and decaying to zero

In the calculation of the short-circuit currents in systems supplied by generators, power-station units and motors (near-to-generator and/or near-to-motor short circuits), it is of interest not only to know the initial symmetrical short-circuit current "kI and the peak short-circuit current ip, but also the symmetrical short-circuit breaking current Ib and the steady-state short-circuit current Ik. In this case, the symmetrical short-circuit breaking current Ib is smaller than the initial symmetrical short-circuit current "kI . Normally, the steady-state short-circuit current Ik is smaller than the symmetrical short-circuit breaking current Ib. The type of short circuit which leads to the highest short-circuit current depends on the values of the positive-sequence, negative-sequence, and zero-sequence short-circuit impedances of the system. For the calculation of the initial symmetrical short-circuit current "kI the symmetrical short-circuit breaking current Ib, and the steady-state short-circuit current Ik at the short-circuit location, the system may be converted by network reduction into an equivalent short-circuit impedance Zk at the short-circuit location. This procedure is not allowed when calculating the peak short-circuit current ip. In this case, it is necessary to distinguish between networks with and without parallel branches. While using fuses or current-limiting circuit-breakers to protect substations, the initial symmetrical short-circuit current is first calculated as if these devices were not available. From the calculated initial symmetrical short-circuit current and characteristic curves of the fuses or current-limiting circuit-breakers, the cut-off current is determined, which is the peak short-circuit current of the downstream substation. Short-circuits may have one or more sources. Calculations are simplest for balanced short circuits on radial systems, as the individual contributions to a balanced short circuit can be evaluated separately for each source. When sources are distributed in meshed network and for all cases of unbalanced short-circuits, network reduction is necessary to calculate short-circuit impedances )()( ZZ 21 = and )(Z 0 at the short-circuit location.


26

Maximum and minimum short-circuit currents

When calculating maximum short-circuit currents, it is necessary to introduce the following conditions:

- voltage factor cmax , will be applied for the calculations of maximum short-circuit currents in the absence of a national standard

- choose the system configuration and the maximum contribution from power plants and network feeders which lead to the maximum value of short-circuit current at the short-circuit location, or for accepted sectioning of the network to control the short-circuit current

- when equivalent impedances ZQ are used to represent external networks, the minimum equivalent short-circuit impedance will be used which corresponds to the maximum short-circuit current contribution from the network feeders

- motors will be included if appropriate in accordance with 2.4, 2.5 and [1] - lines resistance RL are to be introduced at a temperature of 20C

When calculating minimum short-circuit currents, it is necessary to introduce the following conditions:

- voltage factor cmin for the calculation of minimum short-circuit currents will be applied according to table 3

- choose the system configuration and the minimum contribution from power stations and network feeders which lead to a minimum value of short-circuit current at the short-circuit location

- motors will be neglected - resistances RL of lines (overhead lines and cables, line conductors, and neutral conductors)

will be introduced at a higher temperature Initial symmetrical short-circuit current The highest initial short-circuit current will occur for the three-phase short circuit, because for the common case

)()()( ZZZ 210 => , 59 For short-circuits near transformers with low zero-sequence impedance, Z(0) may be smaller than Z(1). In that case, the highest initial short-circuit current " EkEI 2 will occur for a line-to-line short circuit with earth connection. This situation is described by the following relationships:

)()()()( ZZ;Z/Z 1202 1 => , 60

The initial symmetrical short-circuit current "kI will be calculated using the following general equation:


27

( )223 kkn"

kXR

UcI += , 61

where Rk and Xk are the sum of the series-connected resistances and reactances of the positive-sequence system respectively:

LTKQtk RRRR ++= , 62 LTKQtk XXXX ++= , 63

The impedance of the network feeder QtQtQt jXRZ += is referred to the voltage of the transformer side connected to the short-circuit location. Resistances Rk

kk X.R < 30 , 64 may be neglected.

When there is more than one source contributing to the short-circuit current, and the sources are unmeshed, the initial symmetrical short-circuit current "kI at the short-circuit location F is the sum of the individual branch short-circuit currents. Each branch short-circuit current can be calculated as an independent single-source three-phase short-circuit current in accordance with equation:

( )223 kkn"

kXR

UcI += , 65

In meshed networks, it is generally necessary to determine the short-circuit impedance

)(k ZZ 1= , 66 by network reduction (series connection, parallel connection, delta-star transformation) using the positive-sequence short-circuit impedances of electrical equipment. The impedances in systems connected through transformers to the system, in which the short-circuit occurs, have to be transferred by the square of the rated transformation ratio. If there are several transformers with slightly differing rated transformation ratios (trT1, trT2,..., trTn), in between two systems, the arithmetic mean value can be used.


28

The peak short-circuit current For three-phase short-circuits fed from non-meshed networks, the contribution to the peak short-circuit current from each branch can be expressed by:

"kp Ii 2= , 67

where the factor will be calculated by the following expression:

)X/R(e.. 3980021 += , 68 The peak short-circuit current ip at a short-circuit location F, fed from sources which are not meshed with one another, is the sum of the partial short-circuit currents:

=i

pip ii , 69

DC component of the short-circuit current

The maximum DC component iDC of the short-circuit current may be calculated with sufficient accuracy by equation:

)X/R(tf"k.c.d eIi

22 = , 70 Where:

"kI is the initial symmetrical short-circuit current

f - the nominal frequency t - the time R/X - the resistance/reactance ratio

Note: The correct resistance RG of the generator armature should be used and not RGf. Symmetrical short-circuit breaking current The breaking current at the short-circuit location consists in general of a symmetrical current Ib and a DC current iDC at the time tmin For some near-to-generator short circuits the value of iDC at tmin may exceed the peak value of Ib and this can lead to missing current zeros. For far-from-generator short circuits, the short-circuit breaking currents are equal to the initial short-circuit currents:

"kb

"EkEb

"kb

"kb II;II;II;II 112222 ==== , 71


29

For a near-to-generator short circuit, in the case of a single fed short-circuit or from non-meshed networks, the decay to the symmetrical short-circuit breaking current is taken into account by the factor according to equation:

"kb II = , 72

where the factor depends on the minimum time delay tmin and the ratio rG

"kG I/I and IrG is the

rated generator current, according to IEC 60909-0/2001-07 [1].

For three-phase short circuits in non-meshed networks, the symmetrical breaking current at the short-circuit location can be calculated by the summation of the individual breaking current contributions:

=i

bib II , 73

The short-circuit breaking current Ib in meshed networks will be calculated by:

"kb II = , 74

which is usually greater than the real symmetrical short-circuit breaking currents.


30

3 ANSI/IEEE Standard Based Device Evaluation (PDE IEEE)

3.1 Standard Ratings for HV and MV Circuit Breakers (CB)

The ANSI/IEEE Standards define the CB total interrupting time in cycles. However, the Contact Parting Time (CPT) needs to be known for application of breakers. The typical total rated interrupting time for Medium-Voltage Circuit Breakers is 5 cycles (ANSI C37.06 1987). However, the MV CBs interrupting time correspond to 3 cycle contact parting time for the short circuit current, in the 2 -8 cycle network.

Table 5: CB rated interrupting time in cycles

Circuit Breaker Rated Interrupting

Time, in Cycles CPT, in Cycles S

2 1.5 1.4 3 2 1.2 5 3 1.1 8 4 1.0

S is the breakers asymmetrical capability factor and is determined based on the rating structure to which the breaker was manufactured. Most breakers manufactured after 1964 are breakers rated on a symmetrical current basis. Those manufactured before 1965 were rated on a total current basis. Both the symmetrical and total current rated breakers have some DC interrupting capability included in their ratings and it is a matter of how it is accounted for in the total interrupting current. Note: For circuit breakers rated on Total Current S=1.0 Medium voltage breakers duty is based on:

1. Momentary rating (C&L) 2. Peak (Crest) 3. Interrupting

The Momentary and Peak formulae apply to both breakers symmetrical and total current rated breakers. The interrupting rating is calculated differently based on the formulae shown in the next sections.


31

Momentary Duty Calculation (C & L):

The CB Closing and Latching Capability defines the CB ability to withstand (close and immediately latch) the maximum value of the first-cycle short circuit current. The closing and latching capability of a symmetrical current-rated CB is expressed in terms of Asymmetrical, Total rms current, or peak current.

DesignBase uses the following steps to calculate the circuit breaker momentary duty:

1. Calculate the cycle symmetrical short circuit (Isym,rms). 2. Calculate asymmetrical current value using the following formula:

Imom,rms,asym = MFm*Isym,rms,

where:

RXmMF /-2

2e1

+= , 75 Note: In the short circuit option tab Control for ANSI/IEEE the user has the option to calculate MFm based on X/R or use MFm=1.6

3. Compare Imom,rms,asym against the medium voltage circuit breaker (C&L,rms ) value:

If Device C&L,rms rating Imom,rms,asym, then the device Pass or otherwise it fails

4. Calculate the % Rating = (Imom,rms,asym*100)/Device C&L,rms rating

Peak Duty calculation (Crest):

1. Calculate the cycle interrupting short circuit (Isym,rms). 2. Calculate the peak value of momentary SC using the following formula:

Imom,peak = MFp*Isym,rms

where:

2)e(1 /-2

RXMFp

+=,76

and

3-X/R

e*0.1-0.49 = 77


32

Note: In the short circuit option tab Control for ANSI/IEEE the user has the option to calculate MFpeak based on X/R or use MFpeak = 2.7.

3. Compare Imom,peak against the medium voltage circuit breaker (Creat,peak ) value. If Device

Creast,peak rating Imom,peak, then the device pass, or otherwise it fails 4. Calculate The % rating = (Imom,peak*100)/Device Crest,peak rating

Interrupting Duty Calculation

The Maximum Symmetrical Interrupting Capability for a Symmetrical Current-Rated CB is the maximum rms current of the symmetrical AC and DC component, which the CB can interrupt regardless of how low the operating voltage is.

The interrupting fault currents for the MV & HV circuit breakers is equal to 1.5-4 cycles short circuit current. For a system other than of 60 Hz adjust the calculated X/R as follows:

(Hz)Frequency System

60*(X/R) mod)/( =RX 78

The following steps are used to calculate the circuit breaker interrupting. There are three options:

All Remote i.e. NACD = 1.0. This is the most conservative solution All Local; i.e. NACD = 0 Adjusted, this is based on actual calculations

1. Determine if the generator is Local or Remote 2. Calculate total remote contribution, total local contribution, then the NACD (the current is

obtained by using the (1.5-4) cycle network impedance

3. Calculate NACD (No AC Decrement) ratio

Ilocal)(Iremote ItotalIlocal)-(Itotal Iremote +=NACD 79

4. Calculate the Multiplying factor based on the fault location (MFr, or MFl)

Remote If Generator current contribution to fault is less than 40% of a generator terminal fault then this generator is Remote, or equivalent impedance to generation terminals is > 1.5 times the Generator Zdv. For remote fault the multiplying factor is MFr:

SMFr

CRX /

-4

2e1

+= 80


33

Where C = CB Contact Parting Time in Cyc. Local For any local fault the multiplying factor MFl is calculated using the following formula within EDSA or look up tables. The equations are not given in ANSI C37.101, but are empirical equations to match the curves within the ANSI breaker standard.

SMFl

CRX /

-42 2eK

+= , 81

where:

Table 6: K factor

CPT K= 1.5 1.0278 - 0.004288(X/R) + 0.00002945(X/R)2 - 0.000000068368(X/R)3

2 1.0604 - 0.007473(X/R) + 0.00006253(X/R)2 - 0.0000002427(X/R)3 3 1.0494 - 0.00833(X/R) + 0.00006919(X/R)2 - 0.000000075638(X/R)3 4 1.0370 - 0.008148(X/R) + 0.0000611(X/R)2 - 0.0000002248(X/R)3

The Adjusted Multiplying Factor (AMFi) is equal to:

AMFi = MFl +NACD (MFr-MFl), 82 If AMFi is less than 1.0 then the program uses 1.0

5. Calculate Iint,

All Remote: Iint = MFr*Iint,rms,sym

All Local: Iint = MFl*Iint,rms,sym

Mixed local and remote: Iint = AMFi*Iint,rms,sym

6. Calculate 3 phase Device Duty by adjusting the device interrupting duty based on rated voltage using the following formula:

Rating)Int Max Device*kV Voltage Operating

kVMax Rated * RatingInt Device(Min Duty Device P3 = 7. Compare Iint against the CB 3P Device Duty.

If 3P Device Duty Iint, then the device Passes, otherwise it Fails.

8. Calculate % rating = (Iint *100)/ (3P Device Duty)


34

3.2 Standard Ratings for Low Voltage Circuit Breakers (LV-CBs)

For Low-Voltage CBs (LV-CBs) the time of short circuit current interruption occurs within the sub transient time interval. However, the interrupting capabilities of unfused LV-CBs are sensitive to the maximum peak magnitude of the total /asymmetrical fault current. If the device library does not have a value for X/R then the following default values are used as default by the EDSA program:

Table 7: Default Device X/R Values Using EDSAs Library

Breaker Type Test %PF Test X/R

Unfused Power Circuit (PCB) Breaker 15 6.59 Fused Power Circuit Breaker, MCCB, ICCB (Insulated Case CB)

20 4.9

Molded Case (MCCB), ICCB rated 10,000A 50 1.73 Molded Case MCCB), ICCB rated 10,001-20,000 A 30 3.18 Molded Case (MCCB), ICCB rated > 20,000 A 20 4.90

The following steps are used to calculate the low voltage circuit breaker interrupting:

1. Calculate the cycle interrupting short circuit (Isym,rms).

2. Calculate Low Voltage Multiplying Factor (LVF)

PCB: Power Circuit Breaker

ICCB: Insulated Case Circuit Breaker

Fused PCB / MCCB / ICCB

)7(

)e2(1

)e2(1 LVFasym

X/RTest 2-

X/R Calc2-

+

+= EQ

, 83

Unfused PCB / MCCB / ICCB with Instantaneous setting

)e(

)e( LVFp X/Rtest

T-

X/Rcalc-

2

2

1

1

++=

, 84


35

Where

3X/Rtest-

3-X/Rcalc

0.1e - 0.49

0.1e - 0.49

=

=

T

and

In Options of the short circuit Tab Control for ANSI/IEEE , the user can select to use

=T = 0.5 instead of using the empirical formula by selecting Applies 0.5 Cycles.

Unfused PCB without Instantaneous setting

If the breaker does not have an instantaneous setting then the breaker has two interrupting rating (peak and asymmetrical). Therefore the LVFp and LVFasym are calculated.

)e2(1

)e2(1 LVFasym

X/Rtest 4-

X/Rcalc 4-

t

t

++=

85 Where t is the breaker minimum short time trip in cycles at interrupting duty. The default value used by EDSA is 3 cycles. The peak interrupting rating is calculated as follows:

)e(

)e( LVFp X/Rtest

T-

X/Rcalc-

2

2

1

1

++=

86

Where

3

X/Rtest-

3-X/Rcalc

0.1e - 0.49

0.1e - 0.49

=

=

T

and


36

3. If any of the LVF is less than 1.0 then uses 1.0

4. Calculate adjusted Interrupting factor

Fused Breakers

Iint,adj = LVFasym* Isym,rms (the 3-8 cycle interrupting short circuit)

Unfused Breakers With Inst

Iint,adj = LVFp* Isym,rms (the cycle interrupting short circuit)

Unfused Breakers Without Inst

Iint,adj = LVFasym* Isym,rms (the 3-8 cycle interrupting short circuit)

Iint,adj = LVFp* Isym,rms (the cycle interrupting short circuit)

5. Compare Iint,adj against the CB symmetrical interrupting rating.

If Device Symmetrical rating Iint,adj, then the device passes, or otherwise it fails 6. Calculate The % rating = (Iint,adj*100)/Device Symmetrical rating

3.3 Standard Ratings for Low/High Voltage Fuses, and Switches The LVFs interrupting capability is the maximum symmetrical rms current which the fuse can interrupt and still remain intact. While the fuse has a symmetrical current rating it can also interrupt the DC component up to a value based on its test X/R ratio. The interrupting capabilities of LV-Fs are classified by the UL according to symmetrical current ratings in rms Amperes. In some rare cases the fuse asymmetrical rating is provided. Evaluation procedure:

3. Calculate the cycle interrupting short circuit (Isym,rms).

4. Calculate Iasym:

Iasym,adj = MFasym*Isym(1/2 Cyc)

If the fuse is symmetrical rated, then MFasym is calculated using the following formula:


37

)e2(1 MFasym X/R2- +=

87

If the fuse is asymmetrical rated, then MFasym is calculated using the following formula:

)e2(1

)e2(1 MFasym

X/RTest 2-

X/R Calc2-

++=

, 88

5. Compare Iasym,adj against the fuse symmetrical interrupting rating.

If Device Symmetrical rating Iasym,adj, then the device Pass otherwise it Fails 6. Calculate The % rating = (Iasym,adj*100)/Device Symmetrical rating.

Note: For standard switches the same formulae are used


38

Perform Short-Circuit Study & Update Answer File.For frequency other than 60 Hz, then adjust the X/R where,(X/R)mod=(X/R)*60/(System Hz)

y For LVCB, MVCB & Fuses Calculate the cycle short-circuit current(Isym,rms).

y For MVCB calculate the Iint,rms,sym.y Run the PDE analysis

Fused?

LVCB

Yes

IF LVF < 1,then LVF =1

MCCB/ICCB/PCBWith Instantaneous :Iint,adj =LVF*Isym,rmsPCB Without Instantaneous:Iint,adj =LVFp*Isym,rms( Cyc)int,adj =LVFasym*Isym,rms(3-8 Cyc)

CB X/R is known?

The X/R is equal to:

PCB, MCCB, ICCB = 4.9

Calculate LVF based on EQ-8 for PCB breaker withInstantaneous Setting, MCCB and ICCB.

For PCB without instantaneous use EQ-8 & EQ-9

Calculate LVFbased on EQ-7

NOYES

NO

YES

CB X/R is known?

NO

Is Device Symmetricalrating greater or Equal

to Iint,adj?

PassFail

YesNO

Calculate%rating=Iint,adj*100/

Device rating

ANSI DEVICE EVALUATION

Fuses/ Switches

Is Device rating greateror Equal to Iasym,adj?

PassFail

YesNO

Calculate%rating=Isym,adj*100/

Device rating

MVCB

Go toPage 2

The X/R is equal to:

PCB, ICCB = 6.59MCCB, ICCB rated 20,000 A = 4.9

Fuse / Switch Symmetrical Rating, selected:y Calculate MF based on EQ-1

Fuse / Switch Asymmetrical Rating selected:y Calculate MF based on EQ-10

Figure 1: Device Evaluation, ANSI Standard, Page 1


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ANSI DEVICE EVALUATIONPage 2MVCB From

Page 1

CalculateImom,asym=MFm*Isym,rms

Calculate MFp using EQ-2

Calculation Based on Generation:y All Remotey All Localy NACD

Calculatey MFr using EQ-4y Iint=MFr*Iint,rms,sym

Calculatey MFl using EQ-5y Iint=MFl*Iint,rms,sym

Calculate:y NACD using EQ-3y MFr using EQ-4y MFl using EQ-5y AMFi = using EQ-6.y If AMFl less than 1 use 1.0y Iint = AMFi*Iint,rms,sym/S

Is Device peak (crest)rating greater or Equal to

Imom,peak?

PassFail

YesNO

Calculate%rating=Imom,peak*100/device peak (crest) rating

Calculate 3 phase deviceduty using EQ-6a

Is Device Int rating greateror Equal to calculated Iint?

PassFail

YesNO

Calculate %rating=Iint*100/3P device Int rating

Is Device C&L,rms ratinggreater or Equal toImom,rms,asym?

PassFail

YesNO

Calculate%rating=Imom,rms,asym*100/

device C&L,rms rating

Calculate:y Total Remote Contributiony Total Local contributiony Total Contribution (Iint,rms,sym)y NACD using (EQ-3)y If NACD=0 then all contribution are Localy If NACD=1 then all contribution are Remote

ALL Remote

All Local

NACD

In the short circuit option tabControl for ANSI/IEEE the userhas selected the fixed MF factor

NO

NO

CalculateImom,peak=MFp*Isym,rms

Calculate MFm using EQ-1

YES

MFp = 2.7

YES

MFm = 1.6

Peak Duty(Crest)

MomentaryDuty (C&L)

Peak Duty(Crest)

MomentaryDuty (C&L)

Interrupting Duty

Figure 2: Device Evaluation, ANSI Standard, Page 2


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4 IEC Standard Based Device Evaluation (PDE IEC) 4.1 CIRCUIT-BREAKERS

Circuit-breaker design techniques have improved over time leading to benefits of technical performances, reduced size, weight, energy requirements and cost. This progression is also perceived to have led to an inevitable reduction in inherent design margins such that much of the older equipment, for which extensive operating experience is available, may have considerable margins in hand-over and above modern equipment. This trend is not problematic in itself but further emphasizes the need for future testing regimes to be fully representative of the system conditions in which the equipment needs to function correctly. In technologies where the interruption capability is fundamentally constant regardless of the switching duty, interpolation of test evidence is relatively simple and accepted. However, in technologies where the basic interruption characteristics of the device are duty dependent, such interpolations are far more difficult to achieve simply and it is quite conceivable that critical fault duties may be identified at fractional short-circuit levels. In principle, the high energies and relatively low di/dt values associated with an asymmetrical duty make it less onerous for such a device than an equivalent symmetrical duty. However, the effect of low energy minor loops and the possibility of extended arcing periods, in what are generally very short overall travel times, are factors which might prove particularly critical. Ultimately, equipment testing should consider the equipment under test to be a "black box" model regardless of the technology being employed, but this presents obvious difficulties if varying design technologies have specific sensitivities. It must be stressed at this point that there is no intention to cast doubt on the capabilities of particular equipment design philosophies merely to emphasize that as refined design techniques lead to minimized designs so the importance of well constructed and realistic testing regimes increases. An obvious, but non-preferred, solution to problems of asymmetric switching is to increase circuit-breaker operating times, although this does not alleviate the duty on other associated equipment and may be inconvenient from an overall system viewpoint. This contrary to the tendency for reducing protection times in modern equipment. High Voltage Breakers. Normally the interrupting current is a constant current at any voltage. However, some manufacturers do give a different current at various voltages. On the HV breakers it may to check if the breaker voltage rating is greater than the system voltage. The voltage rating of IEC breakers is the maximum voltage that the breaker can be applied at. Low Voltage Breakers. The same standards are used for LVPCB and MCCB.

4.1.1 Rated characteristics to be given for all circuit-breakers

a1) Rated voltage Ur.:

If the manufacturer indicates a few values for the rated voltage, then the greatest represents the maximum rated voltage; a2) Rated insulation level;


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a3) Rated frequency fr. The standard values for the rated frequency of high voltage circuit-breakers are 50 Hz and 60 Hz; a4) Rated normal current Ir: Current which the main circuit of a circuit-breaker is capable of carrying continuously under specified conditions of use and behavior; a5) Rated short-time withstand current Icw. The rated short-time withstand current Icw of a CB, disconector or swich-disconector means the rms value of a rated, admited, short-time current, indicated by a manufacturer, which the equipment can support without any damages. The testing determination of this current for a concret equipment is made in standard conditions [CEI 60947-1]. The rated short-time withstand current must be greater than twelve times the rated maximum operation current and, without other manufacturers indication, the current duration must be 1 s:

sT.pt,II cwecw 112 = , 89

A complete determination of the rated short-time withstand current is made, on the base of the mentioned standard, as follows:

( ){ } kA,I.pt,kA;IMaxI eecw 52512 = , 90

kA,I.pt,kAI ecw 5230 >= , 91

InAC the rated short-time withstand current is compearing with the rms value of the periodical short-circuit current component. It is necessary that the last mentioned value to be lower than the product between the short duration acceptable rated current and the factor n, indicated in table 3, in accordance with CEI 60947-1:

cwk InI , 92

Values of the power factor, the time constants and the ratio n between the peak value and the rated short-time withstand current.


42

Table 8: n factor based on PF and short circuit level

Short-circuit current,kA

Power FactorTime constant,

ms n factor

1,5 0,95

5

1,41 (1,5, 3] 0,9 1,42 (3, 4,5] 0,8 1,47 (4,5, 6] 0,7 1,53 (6, 10] 0,5 1,70 (10, 20] 0,3 10 2,00 (20, 50] 0,25

15 2,10

50 0,2 2,20

At the same time, the short duration acceptable rated current represents the upper limit value of the rms value of the short-circuit current periodical component which is presumed constant during the short timing , for which the following normalized values are recommended:

{ } s;,;,;,;, 15025010050

1. The rated short-time withstand current is equal to the rated short-circuit breaking current [5, p.33] - EN 60947-3:1999 Low-voltage switchgear and controlgear Part 3: Switches, disconnectors,

switch-disconnectors and fuse-combination units.

a6) Rated peak withstand current (Ip): It is equal to the rated short-circuit making current; a7) Rated duration of a short-circuit tk. A rated duration of a short-circuit need not be assigned to a self-tripping circuit-breaker provided that the following applies. When connected in a circuit the prospective breaking current of which is equal to its rated short-circuit breaking current, the circuit-breaker shall be capable of carrying the resulting current for the break-time required. This break time is that required by the circuit-breaker with the over current release set for the maximum time lag when operating in accordance with its rated operating sequence. Direct over current releases include integrated tripping systems. a8) Rated supply voltage of closing and opening devices and of auxiliary circuits Ua; a9) Rated supply frequency of closing and opening devices and of auxiliary circuits; a10) Rated pressures of compressed gas supply and/or of hydraulic supply for operation, interruption and insulation, as applicable;


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a11) Rated short-circuit breaking current Icn.

The rated short-circuit breaking current is the highest short-circuit current which the circuit breaker shall be capable of breaking under the conditions of use and behavior prescribed in standards. Such a current is found in a circuit having a power-frequency recovery voltage corresponding to the rated voltage of the circuit-breaker and having a transient recovery voltage equal to a specified value. For three-pole circuit-breakers, the AC component relates to a three-phases short-circuit. The rated short-circuit breaking current is characterized by two values: the rms value of its AC component; the percentage DC component. If the DC component does not exceed 20%, the rated short-

circuit breaking current is characterized only by the rms value of its AC component.

The circuit-breaker shall be capable of breaking any short-circuit current up to its rated short-circuit breaking current containing any AC component up to the rated value and, associated with it, any percentage DC component up to that specified, under the conditions mentioned above. The following applies to a standard circuit-breaker: - at voltages below and equal to the rated voltage, it shall be capable of breaking its rated short-

circuit breaking current - at voltages above the rated voltage, no short-circuit breaking current is guaranteed. The standard

value of the AC component of the rated short-circuit breaking current shall be selected from the R10 series specified in IEC 60059. The R10 series comprises the numbers

{1 1,25 1,6 2 2,5 3,15 4 5 6,3 8}

and their products by 10n. The value of the percentage DC component shall be determined as follows: - for a self-tripping circuit-breaker, the percentage DC component shall correspond to a time interval

equal to the minimum opening time of the first opening pole Top of the circuit breaker. Time Tr in the formula (6) is to be set to 0 ms

- for a circuit-breaker which is tripped solely by any form of auxiliary power, the percentage DC component shall correspond to a time interval equal to the minimum opening time of the first opening pole Top of the circuit-breaker plus one half-cycle of rated frequency Tr.

The minimum opening time mentioned above is that specified by the manufacturer. The minimum opening time is the shortest opening time, which is expected by the manufacturer to cover the entire population of the circuit-breaker concerned under any operational conditions when breaking asymmetrical currents. The percentage value of the dc component (iDC%) is based on the time interval (Top + Tr) and the time constant using the formula:

%,exp100%..

+=

ropcd

TTi


44

The graphs of the DC component against time given in figure 1 below are based on: a) standard time constant of 45 ms b) special case time constants, related to the rated voltage of the circuit-breaker: - 120 ms for rated voltages up to and including 52 kV - 60 ms for rated voltages from 72,5 kV up to and including 420 kV - 75 ms for rated voltages 550 kV and above

Figure 3: Percentage D.C. current component in relation to the time interval from initiation of short-circuit current, for different time constant.

These special case time constant values recognize that the standard value may be inadequate in some systems. They are provided as unified values for such special system needs, taking into account the characteristics of the different ranges of rated voltage, for example their particular system structures, design of lines, etc. In addition, some applications may require even higher values, for example if a circuit-breaker is close to a generator. In these circumstances, the required DC component and any additional test requirements should be specified in the inquiry.

a12) Rated ultimate short-circuit breaking capacity Icu The rated ultimate short-circuit breaking capacity Icu represents the highest rms value of the current that the device is able to interrupt without suffering significant damage

3 Phase Short Circuit

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