3 Phase Short Circuit

(1)

Short Circuit Analysis Program

ANSI/IEC/IEEE

&

Protective Device Evaluation

User’s Guide

Power Analytics CORPORATION

16870 West Bernardo Drive, Suite 330. San Diego, CA 92127

(2)

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 What’s 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

(6)

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 plant’s 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

(7)

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.

(8)

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”,

I

_b, 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.

(9)

System breaking power

S

B is the product of

3 * I * U

a 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

(10)

pad-2.3 Sources in Fault Analysis

Power utilities, all rotating electric machinery and regenerative drives are sources in fault calculation.

½ 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 ½ cycle is the sub-transient impedance. It is generally used for the first ½ cycles up to a few cycles;

The ½ cycle network is also referred to as the sub transient network, because all rotating machines are represented by their sub transient reactance.

½ 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 ½ 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) "

s

Z

s ANSI C37.010 Local Generator " dv

Z

" dv

Z

ANSI C37.010 Synchronous Motor " dv

Z

1.5* " dv

Z

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 <2poles 1.2*

"

Z

3*

_Z

" ANSI C37.010

Small Induction Motors

<50 HP 1.67*

"

(11)

Harmonic Filters

Z

_Tuned

_{_}

_harmonic

100 %

=

X”

d

=

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 "

s

Z

Generators '

dv

Z

Induction Motors Infinite impedance

Synchronous Motors

_X

_d

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”.

(12)

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: R X m

e

MF

π 2

2

1

−

+

=

, 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 R X Peak

e

MF

πτ −

+

=

, 2

where

τ

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

For:

τ

= ½ Cycle, and X/R = 25 to one decimal place is

MF

Peak

=

2 .

7

.

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.

(13)

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 .

0

d G

X

E

, where the _" d G

X

E

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:

) ( External _d" G G X X E I + = , 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

X

E

, where the " d G

X

E

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:

mote Local Total

I

=

+

_Re 4 and: Total mote

I

NACD

=

Re 5

(14)

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: ) ( ) (

Z

1

=

2 , 6

The zero-sequence short-circuit impedance,

) ( ) ( ) (

U

/

I

Z

₀

=

₀ ₀ , 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 sheathand 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-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:

Ω

,

S

U

u

Z

rT rT kr T

_⋅

⋅

=

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:

Ω

,

I

P

R

rT krT T 2

3 ⋅

=

, 9

(15)

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:

.

,

R

Z

X

_T

=

_T2

−

_T2

Ω

, 10

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

T rT rT T

X

U

S

x

=

₂

⋅

, 11 Note:

The ratio RT/XT generally decreases with transformer size.

The impedance

Z

T_{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 _:

.

,

Z

_T

=

₍₁₎

=

₍₂₎

Ω

, 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

Z

(0)T_{may be obtained from the rating plate or from} the manufacturer: T ) ( T ) ( T ) (

R

jX

Z

0

=

₀

+

₀ , 13

(16)

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 max T

x

.

c

.

K

6

0

1

95

0 +

⋅

=

, 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:

(

T T

) (

T T

)

T T

TK

K

Z

K

R

j

K

X

Z

=

⋅

=

+

, 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:

(

)

b T rT b T T max b n T

sin

I

/

I

x

1 c

U

K

ϕ

+

⋅

=

, 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. b

T

I

_{- the highest operating current before short circuit (this depends on network configuration} and relevant reliability philosophy).

b t

ϕ

_{- 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.

(17)

rTLV rTHV r

U

t

=

, 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:

) ( ) ( ) (

Z

1

=

2

=

0 , 18

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

Ω

,

I

U

u

X

Z

rR n kR R R

⋅

=

≅

3

100

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:

Ω

,

S

U

Z

rG rG rG 2

=

, 20

The relative subtransient reactance

x

"d_{, related to the rated impedance is:}

rG " d " d

Z

X

x

=

, 21

(18)

RGf = 0.05 " d

X

_{for generators with UrG > 1 kV and SrG ≥ 100 MVA;} RGf = 0.07

" d

X

_{for generators with UrG > 1 kV and SrG < 100 MVA;} RGf = 0.15

" d

X

_{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 manufacturer’s values for RG should be used.

The subtransient impedance

Z

G_{of the generator, in the positive-sequence system can be} calculated with the formula:

" d G

G

R

jX

Z

=

+

, 22

When calculating initial symmetrical short-circuit currents in systems fed directly from generators without transformers unit, the corrected impedance

Z

GK_{of the SG has to be used in the} positive-sequence system:

(

)

(

"

)

d G G G G G GK

K

Z

K

R

j

K

X

Z

=

+

, 23

with the correction factor KG for SG, given by the relationship:

(

"d rG

)

rG n max G

U

sin

x

U

c

K

ϕ

⋅

+

⋅

=

1

, 24 where:

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

" d

x

_{- the relative subtransient reactance of the generator related to the rated impedance,} according to the (21) relationship.

ϕrG is the phase angle between

U

rG_and

I

rG_. UrG - the rated voltage of the generator.

(19)

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

Z

GK_{has been introduced because the equivalent voltage source}

(

cU

n

/

3 )

_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:

(

G

)

rG G

U

p

U

=

1 +

, 25 If the values of " d

X

_and

X

"q_{reactances are different, for the negative-sequence reactance} G

) (

X

₂

of the SM, their arithmetical mean can be used:

2

" " ) 2 ( q d G

X

=

+

, 26

The corrected short-circuit impedance of SG,

Z

(2)GK_{, is given, in the negative-sequence system,} by the following equation:

(

_G _G

)

(

_G _G

)

GK

K

R

j

K

X

Z

(2)

=

+

(2) , 27

For the short-circuit impedance

Z

(0)G_{of SG in the zero-sequence system, the following applies}

with KG from equation (1.20):

(

G ( )G

)

( )G GK

)

(

K

R

jX

Z

0

=

₀

+

₀ , 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 " k

I

_{, 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.

(20)

rM rM rM rM

cos

P

S

ϕ

η

⋅

=

, 29

where PrM, cosϕrM and ηrM 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:

rM rM rM rM rM

cos

U

P

I

ϕ

η

⋅

=

3

, 30

where UrM is the rated line voltage of the AM.

MV and LV motors contribute to the initial symmetrical short-circuit current " k

I

_{, to the peak} short-circuit current ip, to the symmetrical short-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 " k

I

_{may be} neglected if their contribution is not higher than 5 % of the initial short-circuit current

" M k

I

₀ _, calculated without motors:

" M k rM

.

I

≤

0

05 ⋅

0

∑

, 31 Where:

∑

I

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

" M k

I

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:

(21)

(

LR rM

)

rM rM rM

I

/

I

S

U

Z

⋅

=

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=0.995⋅ZM for MV motors with rated powers per pair of poles (PrM/p)≥1 MW;

RM/XM=0.15, with XM=0.989⋅ZM for MV motors with rated powers per pair of poles (PrM/p)<1 MW;

RM/XM=0.42, with XM = 0.922⋅ZM for LV motor groups, with connection cables, where p is the pair of poles number.

If the ratio (RM/XM) is known, then the motor reactance XM will be calculated as follows:

(

)

2

1

_M _M M M

X

/

R

Z

X

+

=

, 33

However the motor resistance RM will be

(

M M

)

M

X

R

/

X

R

=

⋅

, 34

For the determination of the initial short-circuit current according to the short-circuit currents calculation method, AM are substituted by their impedances

Z

M_{, in the positive-sequence and} negative-sequence systems: " M M M

R

jX

Z

=

+

, 35

The zero-sequence system impedance Z(0)M of the motor will be given by the manufacturer, if needed.

(22)

3

0

3

100

8

0 .

I

U

S

c

.

S

P

" kQ nQ rT rT rM

−

⋅

≤

∑

, 36 Where:

∑

P

rM is the sum of the rated active powers of the medium-voltage and the low-voltage motors which will be considered.

∑

S

rT

-

the sum of the rated apparent powers of all transformers, through which the motors are directly fed.

" kQ

I -

the initial symmetrical short-circuit current at the feeder connection point Q without supplement of the motors.

U

nQ

-

the nominal voltage of the system at the feeder connection point Q.

Lines Constants

The positive-sequence short-circuit impedance,

L L

L

R

jX

Z

=

+

, 37

may be calculated from the conductor data, such as the cross-section

q

n and the centre-distances d of the conductors.

The following values for resistivity may be used:

m

/

mm

54

1

2 Cu

=

Ω

⋅

ρ

for Copper;

m

/

mm

34

1

2 Al

=

Ω

⋅

ρ

for Aluminum and

mm

/

m

31

1

2

Ala

=

Ω

⋅

ρ

for Aluminum alloy.

The effective resistance per unit length

R

'_Lr of overhead lines at the conductor temperature 20°C may be calculated from the nominal cross-section qn and the resistivity ρ:

m

/

,

q

R

n ' Lr

Ω

ρ

=

, 38

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

(23)

Ω

,

l

R

' _L Lr Lr

=

⋅

, 39

Line Resistances RL (overhead lines and cables, line conductors and neutral conductors) will be introduced at a higher temperature

θ

e

≠

θ

r_{, when calculating minimum short-circuit currents:}

(

)

[

e r

]

Lr

L

1 R

R

=

+

α

θ

−

θ

⋅

, 40

Where:

α=0,004 K

-1 is the temperature factor of resistivity, valid with sufficient accuracy for most practical purposes for copper, aluminum and aluminum alloy.

θ

e

-

the conductor temperature in degrees Celsius at the end of the short-circuit duration (for θe, see also IEC 60865-1, IEC 60949 and IEC 60986).

θ

r

=20°C

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

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

3 1 3 3 2 2 1L L L L L L

d

=

⋅

, 41 Where:

d

L1L2

, d

L2L3and

d

L3L1are geometric distances between conductors.

In the case of bundle conductor, the equivalent radius rB can be determined by the following formula:

n n

B

n

r

R

r

=

⋅

−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

X

'L_{for overhead lines may be calculated, assuming transposition,} from:

⎞

(24)

Where:

μ0 = 4π⋅10-7 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:

Ω

,

l

X

' _L L L

=

⋅

, 44

For measurement of the positive-sequence impedance

) ( ) ( ) (

R

jX

Z

1

=

1

+

1 , 45

and the zero-sequence short-circuit impedance,

) ( ) ( ) (

R

jX

Z

₀

=

₀

+

₀ , 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

Z

(1)L_and

Z

(0)L_{of LV and HV cables depend on national techniques and} standards and may be taken from IEC 60909-2, from textbooks or manufacturer’s data.

However, the impedance of a network feeder at the connection point Q is given by:

" kQ nQ " kQ nQ Q

I

U

c

S

U

c

Z

3

2

⋅

=

⋅

=

, 47

where

I

"_kQ is the initial symmetrical short-circuit current.

Earth Wire Impedance

(25)

0

85

1 ωμ

ρ

δ

₌

_.

_⋅

E _{, m,} ₄₈ Where:

ρ

Eis the earth type resistivity, having values in accordance with table 2.1 content.

ω

= 2πf

-

angular frequency.

μ

0

= 4π⋅10

−7H/m– vide absolute magnetic permeability.

(26)

Table 3: Resistivity and equivalent earth penetration

Earth types Resistivity ρE,

Ωm Equivalent earth penetration depth m δ,

f=50 Hz f=60 Hz Granite Rocks Stony soil >104 (3÷10)⋅103 (1÷3)⋅103 >9,300 (5.1÷9.3)⋅103 (2.94÷5.1)⋅103 >8,500 (4.65÷8.2)⋅103 (2.69÷4.65)⋅103

Pebbles, dry sand

Calcareous soil, wet sand Farmland (0.2÷1.2)⋅103 70÷200 50÷100 (1.32÷3.22)⋅103 (0.78÷1.32)⋅103 660÷930 (1.2÷2.94)⋅103 (0.71÷1.2)⋅103 600÷850 Clay, loam Marshy soil 10÷50 <20 295÷660 <415 270÷600 <380

The earth wire impedance per unit length

Z

'_W is:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

≈

WW r ' W ' W

r

ln

f

j

R

Z

δ

ν

μ

ωμ

4

8

0 0 , 49 Where: ' W

R

is the earth wires resistance per unit length;

⎩

⎨

⎧

=

;

Hz

f

for

,

km

/

.

;

Hz

f

for

,

km

/

.

60

06

0

50

05

0

8

0

Ω

ωμ

μ

r

-

relative permeability of earth wire. For Aluminum core steel reinforced (ACSR) wires with one layer of aluminum

,

μr ≈ 5 ... 10

;

for other ACSR wires

,

μr ≈ 1

;

for Steel wires

,

μr ≈ 75;

ν -

the earth wires number;

r

WW

-

equivalent earth wire radius, equal to the earth wire radius rW if there is just one earth

wire

W

WW

r

=

, 50

and calculated with following formula, if there are two earth wires:

W W

WW

r

d

r

=

⋅

, 51

(27)

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

WL ' WL

d

ln

f

j

Z

ωμ

0

μ

₀

δ

8 +

≈

, 52 Where:

dWL is the geometric mean distance between the earth wire and the line conductors L1, L2 and L3,

given by the formula

3 3 2 1 WL WL WL WL

d

=

⋅

, 53

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

6 3 2 2 2 1 2 3 1 2 1 1 1L W L W L W L W L W L W WL

d

=

⋅

, 54

when there are two earth wires.

Sources

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

3

n es

U

c

U

=

⋅

, 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

U

_n

∈

100 1000

0.95 1.05 6 1.10 10 Medium voltage,

(

,

]

kV

U

_n

∈

1

35

1.00 1.10 - High voltage2),

kV

U

>

35

(28)

1)_c

maxUn should not exceed the highest voltage Um for equipment of power systems:

c

_max

⋅

U

_n

≤

U

_m;

2)_{if no nominal voltage is defined}

m n min n max m

c

U

or

c

U

,

U

=

0

9

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.

nLV nHV rTLV

rTHV

/

U

/

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

Qt TLVK

2 X

(29)

with XQt calculated in accordance with 11 and

TLV T

TLVK

K

X

=

⋅

, 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

I

"_k 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

I

_k". 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

I

_k" 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

Z

₍₁₎

=

Z

₍₂₎ and

Z

₍₀₎ at the short-circuit location.

(30)

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 20°C

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 ) ( ) ( ) (

Z

₀

>

₁

=

₂ , 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

I

"_kE₂_E will occur for a line-to-line short circuit with earth connection. This situation is described by the following relationships:

) ( ) ( ) ( ) (

/

Z

;

Z

2 0

>

1

2

=

1 , 60

The initial symmetrical short-circuit current

I

"_k will be calculated using the following general equation:

(31)

(

2 2

)

3

_k _k n " k

X

R

U

c

I

+

⋅

=

, 61

where Rk and Xk are the sum of the series-connected resistances and reactances of the

positive-sequence system respectively:

L TK Qt k

R

=

+

, 62 L TK Qt k

X

=

+

, 63

The impedance of the network feeder

Z

_Qt

=

R

_Qt

+

jX

_Qt is referred to the voltage of the transformer side connected to the short-circuit location. Resistances Rk

k

.

X

R

< 3

0 ⋅

, 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

I

"_k 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:

(

2 2

)

3

_k _k n " k

X

R

U

c

I

+

⋅

=

, 65

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

) (

k

Z

=

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

(32)

The peak short-circuit current

For three-phase circuits fed from non-meshed networks, the contribution to the peak

short-circuit current from each branch can be expressed by:

" k

p

I

i

=

2 κ

, 67

where the factor κ will be calculated by the following expression: ) X / R (

e

.

3

98

0

02

1 +

⋅

−

=

κ

, 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 pi

p

i

, 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 ( t f " k . c . d

I

e

i

2π

2

−

=

, 70 Where: " k

I

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 circuit breaking currents are equal to the initial short-circuit currents: " k b " E k E b " k b " k b

I

;

I

;

I

;

I

=

₂

=

₂ ₂

=

₂ ₁

=

₁ , 71

(33)

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 μ according to equation:

" k

b

I

=

μ

⋅

, 72

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

I

"_kG

/

I

_rG 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 bi b

I

, 73

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

" k

b

I

=

, 74

(34)

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.

3 Phase Short Circuit

Short Circuit Analysis Program

ANSI/IEC/IEEE

&

Protective Device Evaluation

User’s Guide

Power Analytics CORPORATION

Table of Contents

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

9

Severity of fault:

Type of Short Circuits:

I

S

3 * I * U

t

½ Cycle Network Duty

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Z

Tuned

_

harmonic

100

%

=

X”

=

/

1.5-4 Cycle Network

Steady State or 30-Cycle Network

Z

Z

X

e

MF

2

1

+

=

)

1

(

2

e

MF

+

=

τ

τ

MF

=

2

.

7

*

_Z

_Z

_Tuned

_{_}

_harmonic

_X

_⋅