Short circuit calculations

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) IEEE Guide for Calculation of Fault Currents for Application of a.c. High Voltage Circuit Breakers Rated on a Total Current Basis.

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

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 Steady-state short-circuit current I k A Initial value of the d.c component

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: " S 3 U I k n k NOTE: S k is often used to calculate the internal impedance of a network feeder at the connection point. In this 2 case the definition given should be used in the following form: c Un Z " Sk

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 shortcircuit 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 Symmetrical short-circuit breaking current I B 2 2 I B t B

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 Design Criterion Physical Effect Relevant short-circuit current Breaking capacity of circuit breakers Mechanical stress to equipment Thermal stress to equipment Protection setting Earthing, Interference, EMC Thermal stress to arcing chamber; arc extinction Forces to electrical devices (e.g. bus bars, cables ) Temperature rise of electrical devices (e.g. cables) Selective detection of partial short-circuit currents Potential rise; Magnetic fields Symmetrical short-circuit breaking current I b Peak short-circuit current i p Initial symmetrical shortcircuit current I k Fault duration Minimum symmetrical shortcircuit current I k Maximum initial symmetrical short-circuit current I k

Equivalent Voltage Source

Short-circuit Equivalent voltage source at the shortcircuit location real network Q A F equivalent circuit Z N Q Z T A Z L ~ cu. n I" K 3 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 real network equivalent circuit

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. Nominal voltage maximum short circuit currents Voltage factor c for calculation of minimum short circuit currents Low voltage 100 V 1000 V -systems with a tolerance of 6% -systems with a tolerance of 10% 1.05 1.10 0.95 0.95 Medium voltage >1 kv 35 kv 1.10 1.00 High voltage >35 kv 1.10 1.00

Short Circuit Impedances and Correction Factors

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 factors are valid in zero, positive, negative sequence system

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 Z N cu cu 2 n n " " 3 I S k k X N Z N 1 ( R / X 2 ) 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

Network transformer Correction of Impedance Z TK = Z T K T general K T cmax 0,95 1 0,6 x at known conditions of operation T K T U U n b 1 x T c (I max b T IrT )sin b T no correction for impedances between star point and ground

Network transformer Impact of Correction Factor 1.05 1.00 K T 0.95 0.90 0.85 cmax = 1.10 cmax = 1.05 0.80 0 5 10 15 20 x T [%] The Correction factor is K T <1.0 for transformers with x T >7.5 %. Reduction of transformer impedance Increase of short-circuit currents

Generator with direct Connection to Network Correction of Impedance Z GK = Z G K G general K G U U n rg 1 cmax x sin d rg for continuous operation above rated voltage: U rg (1+p G ) instead of U rg turbine generator: X (2) = X (1) salient pole generator: X (2) = 1/2 (X d " + X q ")

Generator Block (Power Station) Correction of Impedance Z S(O) = (t r 2 Z G +Z THV ) K S(O) G Q power station with on-load tap changer: K S U U 2 nq 2 rg U U 2 rtlv 2 rthv 1 x d c x max T sin rg power station without on-load tap changers: K SO U rg U nq (1 p G U ) U rtlv rthv 1 p t 1 cmax x sin d rg

Asynchronous Motors Motors contribute to the short circuit currents and have to be considered for calculation of maximum short circuit currents Z M I LR 1 /I rm U S 2 rm rm X M Z 1 (R M M / X M ) 2 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 R/X = 0.42 low voltage motors (including connection cables)

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

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 transformation into 3-phase system

Calculation of initial short circuit current Equivalent circuit in symmetrical components (1) (1) (1) (1) (1) (1) (1) (1) positive sequence system (2) (2) (2) (2) (2) (2) (2) (2) negative sequence system (0) (0) (0) (0) (0) (0) (0) (0) zero sequence system Copyright Siemens AG 2007. All rights reserved.

Calculation of initial short circuit current 3-phase short circuit L1-L2-L3-system L1 L2 L3 Z (1)l 012-system Z (1)r ~ ~ ~ c U n 3 (1) ~ ~ ~ -U f I sc3 c U 3 Z r (1) Z (2)l Z (2)r ~ ~ (2) Z (0)l Z (0)r ~ ~ (0) U L1 = U f U L2 = a 2 ( U f ) U L3 = a ( U f ) network left of fault location fault location U (1) = U f U (2) = 0 U (0) = 0 network right of fault location

Calculation of 2-phase initial short circuit current L1-L2-L3-system L1 L2 L3 Z (1)l 012-system Z (1)r ~ ~ ~ c U n 3 (1) ~ -U f I sc2 Z c U 1 r Z 2 Z (2)l Z (2)r ~ ~ (2) I sc2 cu I r sc2 2 Z sc3 1 I 2 3 Z (0)l Z (0)r ~ ~ (0) I L1 = 0 I L2 = I L3 U (1) U (2) I (0) = 0 c U n 3 network left of fault location fault location network right of fault location U L3 U L2 = U f I (1) = I (2)

Calculation of 2-phase initial short circuit current with ground connection L1-L2-L3-system L1 L2 L3 Z (1)l 012-system Z (1)r ~ ~ ~ c U n 3 (1) ~ -U f I sce2e Z 3 c U 1 2Z r 0 Z (2)l Z (2)r ~ ~ (2) Z (0)l Z (0)r ~ ~ (0) I L1 0 U a L2 U a L3 2 U n c 3 U n c 3 U (1) network left of fault location U (2) Un c 3 fault location U I (0) = I (1) = I (2) (1) U network right of fault location (0)

Calculation of 1-phase initial short circuit current L1-L2-L3-System L1 L2 L3 I " 3 c U sc1 ~ -U f Z (1) Z (2) Z (0) r Z (1)l 012-System Z (1)r ~ ~ Z (2)l Z (2)r ~ ~ c U n 3 ~ Z (0)l Z (0)r ~ ~ (1) (2) (0) U c L1 I L2 = 0 U n 3 U network left of fault location (0) U (1) U fault location (2) c U network right of fault location n 3 I L3 = 0 I (0) = I (1) = I (2)

Short Circuit Calculation Results Faults at all Buses

Short Circuit Calculation Results Contribution for one Fault Location

Example

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 R 1 = 0.3 Ω / km X 1 = 0.4 Ω / km

Impedance of Network feeder Z I c U S 2 n " k Z I 1.1 20kV 3GVA 2 Z I 0. 1467 R I 0. 0146 X I 0. 1460

Impedance of Transformer Z Z T T u k U S 2 n n 0.15 20kV 2 40MVA R R T T P krt U S 2 n 2 n 100 kva 2 20kV 40MVA 2 Z T 1. 5000 R T 0. 0250 X T 1. 4998

Impedance of Transformer Correction Factor K T K T cmax 0.95 1 0.6 x 1.1 0.95 1 0.6 0.14998 T K T 0.95873 Z TK 1. 4381 R TK 0. 0240 X TK 1. 4379

Impedance of Overhead Line R L R' X L X' R L 0.3 /km10km X L 0.4 /km10km R L 3. 0000 X I 4. 0000

Initial Short-Circuit Current Fault location 1 R R I R TK R 0.0146 0. 0240 X X I X TK X 0.1460 1. 4379 R 0. 0386 I " k 3 c U R 1 n j X 1 X 1. 5839 I " k 3 1.1 20kV 0.0386 2 1.5839 2 I " k 8.0kA

Initial Short-Circuit Current Fault location 2 R R I R TK R L R 0.0146 0.0240 3. 0000 X X I X TK X L X 0.1460 1.4379 4. 0000 R 3. 0386 I " k 3 c U R 1 n j X 1 X 5. 5839 I " k 3 1.1 20kV 3.0386 2 5.5839 2 I " k 2.0kA

Peak current

Peak Short-Circuit Current Calculation acc. IEC 60909 maximum possible instantaneous value of expected short " circuit current ip 2 I k equation for calculation: 1.02 0.98e 3R / X

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: G M M i p1 i p2 i p3 i p4 i p = i p1 + i p2 + i p3 + i p4

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 b from relation R/X at the fault location (equation or diagram) =1,15 b Method C: procedure with substitute frequency factor from relation R c /X c with substitute frequency f c = 20 Hz R X R X c c f f c best results for meshed networks

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 NOTE: Only for calculation of peak short circuit current

Peak Short-Circuit Current Fault location 1 I " k 8.0kA R 0. 0386 X 1. 5839 R/ X 0.0244 1.02 0.98e 1.93 3R / X i 2 " p I k i p 21.8kA

Peak Short-Circuit Current Fault location 2 I " k 2.0kA R 3. 0386 X 5. 5839 R/ X 0.5442 1.02 0.98e 1.21 3R / X i 2 " p I k i p 3.4kA

Breaking Current

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: G M M I B1 = μ I k I B2 = I k I B3 = μ q I k I B4 = μ q I k I B = I B1 + I B2 + I B3 + I B4

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: I b I " k i U" c U n / Gi 3 (1 i ) I " kgi j U" c U n / Mj 3 (1 q ) I j j " kmj U " Gi jx " dik I " kgi U " Mj jx " Mj I " kmj X dik subtransient reactance of the synchronous machine (i) X Mj reactance of the asynchronous motors (j) I kgi, I kmj contribution to initial symmetrical short-circuit current from the synchronous machines (i) asynchronous motors (j) as measured at the machine terminals and the

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