8698462 Short Circuit Calculations

Short Circuit Calculation

Sector Energy D SE PTI NC Steffen Schmidt

Purpose of Short-Circuit Calculations

 _{Dimensioning of switching devices}  _{Dynamic dimensioning of switchgear}

 _{Thermal rating of electrical devices (e.g. cables)}  _{Protection coordination}

 _{Fault diagnostic}  _{Input data for}

 _{Earthing studies}

 _{Interference calculations}  _{EMC planning}

Short-Circuit Calculation Standards

 _{IEC 60909:}

Short-Circuit Current Calculation in Three-Phase A.C. Systems

 _{European Standard EN 60909}

 _{German National Standard DIN VDE 0102}  _{further National Standards}

 _{Engineering Recommendation G74 (UK)}

Procedure to Meet the Requirements of IEC 60909 for the

Calculation of Short-Circuit Currents in Three-Phase AC Power Systems

 _{ANSI IIEEE Std. C37.5 (US)}

Short-Circuit Calculations Standard IEC 60909

IEC 60909 : Short-circuit currents in three-phase a.c. systems

Part 0: Calculation of currents

Part 1: Factors for the calculation of short-circuit currents

Part 2: Electrical equipment; data for short-circuit current calculations Part 3: Currents during two separate

simultaneous line-to-earth short circuits and partial short-circuit currents flowing through earth Part 4: Examples for the calculation of

Short-Circuit Calculations Scope of IEC 60909

 _{three-phase a.c. systems}

 _{low voltage and high voltage systems up to 500 kV}  nominal frequency of 50 Hz and 60 Hz

 _{balanced and unbalanced short circuits}  _{three phase short circuits}

 _{two phase short circuits (with and without earth connection)}  single phase line-to-earth short circuits in systems with solidly

earthed or impedance earthed neutral

 _{two separate simultaneous single-phase line-to-earth short circuits}

in a systems with isolated neutral or a resonance earthed neutral (IEC 60909-3)

 _{maximum short circuit currents}  _{minimum short circuit currents}

Short-Circuit Calculations Types of Short Circuits

3-phase

2-phase

Variation of short circuit current shapes

fault at voltage peak fault at voltage zero crossing fault located in

the network

fault located near generator

Short-Circuit Calculations

Far-from-generator short circuit

I_k” Initial symmetrical short-circuit current

i_p Peak short-circuit current

I_k Steady-state short-circuit current

Short-Circuit Calculations

Definitions according IEC 60909 (I)

initial symmetrical short-circuit current I_k”

r.m.s. value of the a.c. symmetrical component of a prospective

(available) short-circuit current, applicable at the instant of short circuit if the impedance remains at zero-time value

initial symmetrical short-circuit power S_k”

fictitious value determined as a product of the initial symmetrical short-circuit current I_k”, the nominal system voltage U_n and the factor √3:

NOTE: S_k” is often used to calculate the internal impedance of a network feeder at the

connection point. In this case the definition given should be used in the following form:

" k n " k

3

U

I

S

=

⋅

⋅

U

c

⋅

=

Short-Circuit Calculations

Definitions according IEC 60909 (II)

decaying (aperiodic) component i_d.c. of short-circuit current

mean value between the top and bottom envelope of a short-circuit current decaying from an initial value to zero

peak short-circuit current i_p

maximum possible instantaneous value of the prospective (available) short-circuit current

NOTE: The magnitude of the peak short-circuit current varies in accordance with the moment at which the short circuit occurs.

Short-Circuit Calculations

Near-to-generator short circuit

I_k” Initial symmetrical short-circuit current

i_p Peak short-circuit current

I_k Steady-state short-circuit current

A Initial value of the d.c component

I_B Symmetrical short-circuit breaking current

t_B

B

I 2 2⋅ ⋅

Short-Circuit Calculations

Definitions according IEC 60909 (III) steady-state short-circuit current I_k

r.m.s. value of the short-circuit current which remains after the decay of the transient phenomena

symmetrical short-circuit breaking current I_b

r.m.s. value of an integral cycle of the symmetrical a.c. component of the prospective short-circuit current at the instant of contact separation of the first pole to open of a switching device

Short-Circuit Calculations

Purpose of Short-Circuit Values

Minimum symmetrical short-circuit current I_k

Selective detection of partial short-circuit currents

Protection setting

Maximum initial symmetrical short-circuit current I_k”

Potential rise; Magnetic fields Earthing, Interference, EMC

Initial symmetrical short-circuit current I_k”

Fault duration Temperature rise of electrical

devices (e.g. cables) Thermal stress to equipment

Peak short-circuit current i_p

Forces to electrical devices (e.g. bus bars, cables…) Mechanical stress to

equipment

Symmetrical short-circuit

breaking current I_b

Thermal stress to arcing chamber; arc extinction Breaking capacity of circuit

breakers

Relevant short-circuit current Physical Effect

Standard IEC 60909

Simplifications and Assumption

Assumptions

 _{quasi-static state instead of dynamic calculation}

 _{no change in the type of short circuit during fault duration}  _{no change in the network during fault duration}

 _{arc resistances are not taken into account}

 _{impedance of transformers is referred to tap changer in main position}  neglecting of all shunt impedances except for C₀

Short-circuit

Equivalent voltage source at the short-circuit location

A Q Q _ZT _{A ZL} ZN F ~ I"K 3 .U_n c real network equivalent circuit

Operational data and the passive load of consumers are neglected Tap-changer position of transformers is dispensable

Excitation of generators is dispensable Load flow (local and time) is dispensable

Short circuit in meshed grid

Equivalent voltage source at the short-circuit location

Voltage Factor c

c is a safety factor to consider the following effects:

 _{voltage variations depending on time and place,}  _{changing of transformer taps,}

 _{neglecting loads and capacitances by calculations,}  _{the subtransient behaviour of generators and motors.}

1.00 1.10 Medium voltage >1 kV – 35 kV 0.95 0.95 1.05 1.10 Low voltage 100 V – 1000 V

-systems with a tolerance of 6% -systems with a tolerance of 10%

1.00 1.10

High voltage >35 kV

minimum short circuit currents maximum short circuit currents

Nominal voltage

Maximum and minimum Short-Circuit Currents shall be neglected shall be considered Motors Maximum impedance Minimum impedance Network feeders minimum short circuit currents maximum

short circuit currents

Minimum contribution Maximum contribution Power plants C_min C_max Voltage factor at maximum temperature at 20°C

Short Circuit Impedances

For network feeders, transformer, overhead lines, cable etc.

 _{impedance of positive sequence system = impedance of negative}

sequence system

 _{impedance of zero sequence system usually different}  _{topology can be different for zero sequence system}

Correction factors for

 _generators,

 _{generator blocks,}  _{network transformer}

Network feeders

At a feeder connection point usually one of the following values is given:

 the initial symmetrical short circuit current I_k”  the initial short-circuit power S_k”

If R/X of the network feeder is unknown, one of the following values can be used:

 _{R/X = 0.1}

 _{R/X = 0.0 for high voltage systems >35 kV fed by overhead lines}

" k 2 n " k n Q S U c I 3 U c Z = ⋅ ⋅ ⋅ = 2 Q Q ) X / R ( 1 Z X + =

Network transformer Correction of Impedance

Z_TK = Z_T K_T

 _general

 at known conditions of operation

T max T x 6 , 0 1 c 95 , 0 K ⋅ + ⋅ = b T rT b T T max b n T sin ) I I ( x 1 c U U K ϕ + ⋅ =

Network transformer

Impact of Correction Factor

The Correction factor is K_T<1.0 for transformers with x_T >7.5 %. _{Reduction of transformer impedance}

_{Increase of short-circuit currents} 0.80 0.85 0.90 0.95 1.00 1.05 0 5 10 15 20 x_T [%] K T cmax = 1.10 cmax = 1.05

Generator with direct Connection to Network Correction of Impedance

Z_GK = Z_G K_G

 _general

 for continuous operation above rated voltage: U_rG (1+p_G) instead of U_rG rG d max rG n G sin x 1 c U U K ϕ ⋅ ′′ + ⋅ =

Generator Block (Power Station) Correction of Impedance

Z_S(O) = (t_r2 _Z

G +ZTHV) KS(O)

 _{power station with on-load tap changer:}

 power station without on-load tap changers:

rG T d max 2 rTHV 2 rTLV 2 rG 2 nQ S sin x x 1 c U U U U K ϕ ⋅ − ′′ + ⋅ ⋅ = G Q

(

)

Asynchronous Motors

Motors contribute to the short circuit currents and have to be considered for calculation of maximum short circuit currents

If R/X is unknown, the following values can be used:

 _{R/X = 0.1 medium voltage motors power per pole pair > 1 MW}  _{R/X = 0.15 medium voltage motors power per pole pair ≤ 1 MW}

rM 2 rM rM LR M S U I / I 1 Z = ⋅ 2 M M M M ) X / R ( 1 Z X + =

Special Regulations for low Voltage Motors

 low voltage motors can be neglected if ∑I_rM ≤ I_k”

 _{groups of motors can be combined to a equivalent motor}  I_LR/I_rM = 5 can be used

Calculation of initial short circuit current Procedure

 _{Set up equivalent circuit in symmetrical components}  _{Consider fault conditions}

 _{in 3-phase system}

 _{transformation into symmetrical components}  _{Calculation of fault currents}

 _{in symmetrical components}

Calculation of initial short circuit current

Equivalent circuit in symmetrical components

positive sequence system

negative sequence system

zero sequence system

(1) (1) (1) (1) (1) (1) (1) (1) (2) (2) (2) (2) (2) (2) (2) (2) (0) (0) (0) (0) (0) (0) (0) (0)

Calculation of initial short circuit current 3-phase short circuit

L1 L2 L3 ~ _-Uf 012-system U_L1 = – U_f U_L2 = a2 _{(– U} f) U_L3 = a (– U_f) U₍₁₎ = – U_f U₍₂₎ = 0 U = 0 (1) r sc3 3 Z U c I ⋅ ⋅ = ′′ L1-L2-L3-system ~ ~ Z_(1)l Z_(1)r ~ ~ Z_(2)l Z_(2)r ~ ~ Z_(0)l Z_(0)r (1) (2) (0) network left of fault location network right of fault location fault location ~ c Un √3 ~ ~

Calculation of 2-phase initial short circuit current L1-L2-L3-system 012-system I_L1 = 0 I_L2 = – I_L3 I(0) = 0 3 n ) 2 ( ) 1 ( U c U U − = − ~ ~ Z_(1)l Z_(1)r ~ ~ Z_(2)l Z_(2)r ~ ~ Z_(0)l Z_(0)r (1) (2) (0) network left of fault location network right of fault location fault location ~ c Un √3 ( )1 ( )2 r sc2 Z Z U c I + ⋅ = ′′ ( ) 2 3 2 _sc3 sc2 1 r sc2 _′′ = ′′ ⇒ ⋅ = ′′ I I Z U c I L1 L2 L3 ~ -Uf

Calculation of 2-phase initial short circuit current with ground connection

L1-L2-L3-system 012-system 0 L1 = I 3 n 2 L2 U c a U = − 3 n L3 U c a U = − I = I = I ) 0 ( ) 1 ( n ) 2 ( ) 1 ( 3 U U U c U U − = − = − ~ ~ Z_(1)l Z_(1)r ~ ~ Z_(2)l Z_(2)r ~ ~ Z_(0)l Z_(0)r (1) (2) (0) network left of fault location network right of fault location fault location c Un √3 ~ ( )1 ( )0 r scE2E 2 3 Z Z U c I + ⋅ ⋅ = ′′ L1 L2 L3 ~ -U_f

Calculation of 1-phase initial short circuit current L1 L2 L3 L1-L2-L3-System 012-System I = 0 3 n L1 U c U = − 3 n ) 2 ( ) 1 ( ) 0 ( U c U U U + + = − ~ ~ Z_(1)l Z_(1)r ~ ~ Z_(2)l Z_(2)r ~ ~ Z_(0)l Z_(0)r (1) (2) (0) network left of fault location network right of fault location fault location ~ c Un √3 ~ -Uf _{(1) (2) (0)} r " sc1 3 Z Z Z U c I + + ⋅ ⋅ =

Largest initial short circuit current

Because of Z1 ≅ Z2 the

largest short circuit current can be observed

for Z1 / Z0 < 1

 _{3-phase short circuit}

for Z1 / Z0 > 1

 _{2-phase short circuit with}

earth connection

Feeding of short circuits

single fed short circuit

multiple fed short circuit

∑

∑

Calculation of short circuit currents by programs (1/3)

Basic equation

i = Y u Y: matrix of admittances (for short circuit)

                                ⋅ −                                 =                                 n r 2 1 nn n1 in i1 2n 21 1n 11 '' sci . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 . . . . . . 0 0 U U c U U Y Y Y Y Y Y Y Y I

Calculation of short circuit currents by programs (2/3)

Inversion of matrix of admittances

u = Y-1 _i                                                                 =                                 ⋅ − 0 . . . . . . 0 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . '' sci nn n1 in ii i1 2n 21 1n 11 r 2 1 I Z Z Z Z Z Z Z Z Z U U c U U

Calculation of short circuit currents by programs (3/3)

from line i:

⇒

from the remaining lines:

 _{calculation of all node voltages}

 _{from there -> calculation of all short circuit currents}

3 " sci ii r _{Z I} U c ⋅ = − 3 _ii r " sci Z U c I ⋅ − = " sci sci sc Z I U = ⋅

Short Circuit Calculation Results Faults at all Buses

Short Circuit Calculation Results Contribution for one Fault Location

Data of sample calculation Network feeder: 110 kV 3 GVA R/X = 0.1 Transformer: 110 / 20 kV 40 MVA u_k = 15 % P_krT = 100 kVA Overhead line: 20 kV 10 km R₁’ = 0.3 Ω / km X₁’ = 0.4 Ω / km

Impedance of Network feeder " k 2 n I S U c Z = ⋅

(

)

Impedance of Transformer n 2 n k T S U u Z = ⋅ Ω =1.5000 Z_T R_T = 0.0250 Ω X_T =1.4998 Ω

(

)

(

)

(

)

Impedance of Transformer Correction Factor T max T x 6 . 0 1 c 95 . 0 K ⋅ + ⋅ = 14998 . 0 6 . 0 1 1 . 1 95 . 0 K_T ⋅ + ⋅ = 95873 . 0 K_{T =} Ω =1.4381 Z_TK R_TK = 0.0240 Ω X_TK =1.4379 Ω

Impedance of Overhead Line  ⋅ =R' R_L Ω = 3.0000 R_L X_I = 4.0000 Ω km 10 km / 3 . 0 R_L = Ω ⋅  ⋅ = X' X_L km 10 km / 4 . 0 X_L = Ω ⋅

Initial Short-Circuit Current – Fault location 1 TK I R R R = + X = X_I + X_TK Ω + Ω = 0.0146 0.0240 R X = 0.1460Ω+1.4379Ω Ω = 0.0386 R X ₌1.5839_Ω

(

)

(

) (

)

Initial Short-Circuit Current – Fault location 2 L TK I R R R R = + + X = X_I + X_TK + X_L Ω + Ω + Ω = 0.0146 0.0240 3.0000 R X = 0.1460Ω+1.4379Ω+ 4.0000Ω Ω = 3.0386 R X ₌ 5.5839_Ω

(

)

(

) (

)

Peak Short-Circuit Current Calculation acc. IEC 60909

maximum possible instantaneous value of expected short circuit current equation for calculation:

_i

=

κ

⋅

₂

⋅

_I

X / R 3 e 98 . 0 02 . 1 + ⋅ − = κ

Peak Short-Circuit Current

Calculation in non-meshed Networks

The peak short-circuit current i_p at a short-circuit location, fed from

sources which are not meshed with one another is the sum of the partial short-circuit currents:

M G

M

Peak Short-Circuit Current

Calculation in meshed Networks

Method A: uniform ratio R/X

 _{smallest value of all network branches}  _{quite inexact}

Method B: ratio R/X at the fault location

 factor κ_b from relation R/X at the fault location (equation or diagram)  κ =1,15 κ_b

Method C: procedure with substitute frequency

 factor κ from relation R_c/X_c with substitute frequency f_c = 20 Hz 

 _{best results for meshed networks} f f X R X R _c c c ⋅ =

Peak Short-Circuit Current

Fictitious Resistance of Generator

 R_Gf = 0,05 X_d" for generators with U_rG > 1 kV and S_rG ≥ 100 MVA  R_Gf = 0,07 X_d" for generators with U_rG > 1 kV and S_rG < 100 MVA  R_Gf = 0,15 X_d" for generators with U_rG ≤ 1000 V

Peak Short-Circuit Current – Fault location 1 Ω = 0.0386 R X =1.5839Ω kA 0 . 8 I" k = 0244 . 0 X / R = " k p 2 I i = κ⋅ ⋅ X / R 3 e 98 . 0 02 . 1 _{+ ⋅} − = κ 93 . 1 = κ kA 8 . 21 i_p =

Peak Short-Circuit Current – Fault location 2 Ω = 3.0386 R X = 5.5839Ω kA 0 . 2 I" k = 5442 . 0 X / R = " k p 2 I i = κ⋅ ⋅ X / R 3 e 98 . 0 02 . 1 _{+ ⋅} − = κ 21 . 1 = κ kA 4 . 3 i =

Breaking Current Differentiation

Differentiation between short circuits ”near“ or “far“ from generator

Definition short circuit ”near“ to generator

 for at least one synchronous machine is: I_k” > 2 ∙ I_r,Generator

or

 I_k”_{with motor} > 1.05 ∙ I_k”_{without motor}

Breaking current I_b for short circuit “far“ from generator I_b = I_k”

Breaking Current

Calculation in non-meshed Networks

The breaking current I_B at a short-circuit location, fed from sources which are not meshed is the sum of the partial short-circuit currents:

M G

M

IB1 = μ∙I“k

IB = IB1 + IB2 + IB3 + IB4

Breaking current

Decay of Current fed from Generators

 I_B = μ ∙ I“_k

Factor μ to consider the decay of short circuit current fed from generators.

Breaking current

Decay of Current fed from Asynchronous Motors

 I_B = μ ∙ q ∙ I“_k

Factor q to consider the decay of short circuit current fed from asynchronous motors.

Breaking Current

Calculation in meshed Networks

Simplified calculation: I_b = I_k”

For increased accuracy can be used:

X“_diK subtransient reactance of the synchronous machine (i)

X“_Mj reactance of the asynchronous motors (j)

I“ , I“ " kMj j j j _n Mj " kGi i i _n Gi " k b (1 q ) I 3 / U c " U I ) 1 ( 3 / U c " U I I ⋅ −µ ⋅ ⋅ ∆ − ⋅ µ − ⋅ ⋅ ∆ − =

∑

∑

Continuous short circuit current

Continuous short circuit current I_k

 _{r.m.s. value of short circuit current after decay of all transient}

effects

 _{depending on type and excitation of generators}

 _{statement in standard only for single fed short circuit}  _{calculation by factors (similar to breaking current)}

Continuous short circuit current is normally not calculated by network calculation programs.

For short circuits far from generator and as worst case estimation I_k = I”_k

Short-circuit with preload Principle

A Load flow calculation that considers all network parameters, such as loads, tap positions, etc.

B Place voltage source with the voltage that was determined by the load flow calculation at the fault location.

Short-circuit with preload Example

A Load flow calculation

Short-circuit with preload Results 720V 336V 592.11V 1000V 192.0A 168A 197.37A 203.95A

Short-circuit with preload

~ ~ 365.37A 720V -0V 720V 700V -364V 336V 900. V -307.89V 592.11V 1000V -0V 1000V 10A 182A 192A 40A 208A 168A 40. A 157.37A 197.37A 50. A 153.95A 203.95A

Superposition: Load flow + feed back

~ ~ 365.37A 24A 6.58A 720V 1000V 40A 40A 50A Load flow ~ ~ 50A 10A Ω 2 3Ω 2Ω 10A 2Ω Ω 14 780V 900V Ω 90 700V 0V 0V 208.0A 365.3A 153.95A

Short-circuit: feed back 26A 3.42A 182A 780V 307.89V 364V 157.37A

Contact

Steffen Schmidt

Senior Consultant

Siemens AG, Energy Sector E D SE PTI NC Freyeslebenstr. 1 91058 Erlangen Phone: +49 9131 - 7 32764 Fax: +49 9131 - 7 32525 E-mail: [email protected]