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  1. 1. EXPERT SYSTEMS AND SOLUTIONS Email: expertsyssol@gmail.com expertsyssol@yahoo.com Cell: 9952749533 www.researchprojects.info PAIYANOOR, OMR, CHENNAI Call For Research Projects Final year students of B.E in EEE, ECE, EI, M.E (Power Systems), M.E (Applied Electronics), M.E (Power Electronics) Ph.D Electrical and Electronics. Students can assemble their hardware in our Research labs. Experts will be guiding the projects. Copyright © Siemens AG 2008. All rights reserved.Page 1 28.06.2008 Steffen Schmidt E D SE PTI NC
  2. 2. Short Circuit CalculationSector EnergyD SE PTI NCSteffen Schmidt Copyright © Siemens AG 2008. All rights reserved.
  3. 3. Standards and Terms Copyright © Siemens AG 2008. All rights reserved.Page 3 28.06.2008 Steffen Schmidt E D SE PTI NC
  4. 4. 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  ….. Copyright © Siemens AG 2008. All rights reserved.Page 4 28.06.2008 Steffen Schmidt E D SE PTI NC
  5. 5. Short-Circuit CalculationStandards 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. Copyright © Siemens AG 2008. All rights reserved.Page 5 28.06.2008 Steffen Schmidt E D SE PTI NC
  6. 6. Short-Circuit CalculationsStandard 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 currents Copyright © Siemens AG 2008. All rights reserved.Page 6 28.06.2008 Steffen Schmidt E D SE PTI NC
  7. 7. Short-Circuit CalculationsScope 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 Copyright © Siemens AG 2008. All rights reserved.Page 7 28.06.2008 Steffen Schmidt E D SE PTI NC
  8. 8. Short-Circuit CalculationsTypes of Short Circuits 3-phase 2-phase 1-phase Copyright © Siemens AG 2007. All rights reserved. Copyright © 2008.Page 8 28.06.2008 Steffen Schmidt E D SE PTI NC
  9. 9. Variation of short circuit current shapes fault at voltage peak fault at voltage zero crossingfault located in the network fault locatednear generator Copyright © Siemens AG 2008. All rights reserved. Page 9 28.06.2008 Steffen Schmidt E D SE PTI NC
  10. 10. Short-Circuit CalculationsFar-from-generator short circuit Ik” Initial symmetrical short-circuit current ip Peak short-circuit current Ik Steady-state short-circuit current A Initial value of the d.c component Copyright © Siemens AG 2008. All rights reserved.Page 10 28.06.2008 Steffen Schmidt E D SE PTI NC
  11. 11. Short-Circuit CalculationsDefinitions according IEC 60909 (I)initial symmetrical short-circuit current Ik”r.m.s. value of the a.c. symmetrical component of a prospective(available) short-circuit current, applicable at the instant of short circuit ifthe impedance remains at zero-time valueinitial symmetrical short-circuit power Sk”fictitious value determined as a product of the initial symmetrical short-circuit current Ik”, the nominal system voltage Un and the factor √3:Sk = 3 ⋅ Un ⋅ Ik " "NOTE: Sk” is often used to calculate the internal impedance of a network feeder at theconnection point. In this case the definition given should be used in the following form: c ⋅ Un2Z= " Sk Copyright © Siemens AG 2008. All rights reserved.Page 11 28.06.2008 Steffen Schmidt E D SE PTI NC
  12. 12. Short-Circuit CalculationsDefinitions according IEC 60909 (II)decaying (aperiodic) component id.c. of short-circuit currentmean value between the top and bottom envelope of a short-circuitcurrent decaying from an initial value to zeropeak short-circuit current ipmaximum possible instantaneous value of the prospective (available)short-circuit currentNOTE: The magnitude of the peak short-circuit current varies in accordance with themoment at which the short circuit occurs. Copyright © Siemens AG 2008. All rights reserved.Page 12 28.06.2008 Steffen Schmidt E D SE PTI NC
  13. 13. Short-Circuit CalculationsNear-to-generator short circuit Ik” Initial symmetrical short-circuit current ip Peak short-circuit current Ik Steady-state short-circuit current A Initial value of the d.c component IB Symmetrical short-circuit breaking current 2 ⋅ 2 ⋅ IB tB Copyright © Siemens AG 2008. All rights reserved.Page 13 28.06.2008 Steffen Schmidt E D SE PTI NC
  14. 14. Short-Circuit CalculationsDefinitions according IEC 60909 (III)steady-state short-circuit current Ikr.m.s. value of the short-circuit current which remains after the decay ofthe transient phenomenasymmetrical short-circuit breaking current Ibr.m.s. value of an integral cycle of the symmetrical a.c. component of theprospective short-circuit current at the instant of contact separation ofthe first pole to open of a switching device Copyright © Siemens AG 2008. All rights reserved.Page 14 28.06.2008 Steffen Schmidt E D SE PTI NC
  15. 15. Short-Circuit CalculationsPurpose of Short-Circuit ValuesDesign Criterion Physical Effect Relevant short-circuit currentBreaking capacity of circuit Thermal stress to arcing Symmetrical short-circuitbreakers chamber; arc extinction breaking current IbMechanical stress to Forces to electrical devices Peak short-circuit current ipequipment (e.g. bus bars, cables…)Thermal stress to equipment Temperature rise of electrical Initial symmetrical short- devices (e.g. cables) circuit current Ik” Fault durationProtection setting Selective detection of partial Minimum symmetrical short- short-circuit currents circuit current IkEarthing, Interference, EMC Potential rise; Maximum initial symmetrical Magnetic fields short-circuit current Ik” Copyright © Siemens AG 2008. All rights reserved.Page 15 28.06.2008 Steffen Schmidt E D SE PTI NC
  16. 16. Standard IEC 60909Simplifications and AssumptionAssumptions  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 -> safe assumptions Copyright © Siemens AG 2008. All rights reserved.Page 16 28.06.2008 Steffen Schmidt E D SE PTI NC
  17. 17. Equivalent Voltage Source Copyright © Siemens AG 2008. All rights reserved.Page 17 28.06.2008 Steffen Schmidt E D SE PTI NC
  18. 18. Short-circuitEquivalent voltage source at the short-circuit location real network Q A F equivalent circuit ZN Q ZT A ZL ~ c.U 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 Copyright © Siemens AG 2008. All rights reserved.Page 18 28.06.2008 Steffen Schmidt E D SE PTI NC
  19. 19. Short circuit in meshed gridEquivalent voltage source at the short-circuit locationreal network equivalent circuit Copyright © Siemens AG 2008. All rights reserved.Page 19 28.06.2008 Steffen Schmidt E D SE PTI NC
  20. 20. Voltage Factor cc 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. Voltage factor c for calculation ofNominal voltage maximum short circuit currents minimum short circuit currentsLow voltage 100 V – 1000 V-systems with a tolerance of 6% 1.05 0.95-systems with a tolerance of 10% 1.10 0.95Medium voltage >1 kV – 35 kV 1.10 1.00High voltage >35 kV 1.10 1.00 Copyright © Siemens AG 2008. All rights reserved.Page 20 28.06.2008 Steffen Schmidt E D SE PTI NC
  21. 21. Maximum and minimum Short-Circuit Currents maximum minimum short circuit currents short circuit currentsVoltage factor Cmax CminPower plants Maximum contribution Minimum contributionNetwork feeders Minimum impedance Maximum impedanceMotors shall be considered shall be neglectedResistance of lines and cables at 20°C at maximum temperature Copyright © Siemens AG 2008. All rights reserved.Page 21 28.06.2008 Steffen Schmidt E D SE PTI NC
  22. 22. Short Circuit Impedances and Correction Factors Copyright © Siemens AG 2008. All rights reserved.Page 22 28.06.2008 Steffen Schmidt E D SE PTI NC
  23. 23. Short Circuit ImpedancesFor 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 systemCorrection factors for  generators,  generator blocks,  network transformer  factors are valid in zero, positive, negative sequence system Copyright © Siemens AG 2008. All rights reserved.Page 23 28.06.2008 Steffen Schmidt E D SE PTI NC
  24. 24. Network feedersAt a feeder connection point usually one of the following values is given: the initial symmetrical short circuit current Ik” the initial short-circuit power Sk” c ⋅ Un c ⋅ Un2 ZQ = = " 3 ⋅ Ik " Sk ZQ XQ = 1 + (R / X)2If R/X of the network feeder is unknown, one of the following values canbe used: R/X = 0.1 R/X = 0.0 for high voltage systems >35 kV fed by overhead lines Copyright © Siemens AG 2008. All rights reserved.Page 24 28.06.2008 Steffen Schmidt E D SE PTI NC
  25. 25. Network transformerCorrection of Impedance ZTK = ZT KT general c max K T = 0,95 ⋅ 1 + 0,6 ⋅ x T at known conditions of operation U c max KT = n ⋅ Ub 1 + x T (Ib IrT ) sin ϕb T Tno correction for impedances between star point and ground Copyright © Siemens AG 2008. All rights reserved.Page 25 28.06.2008 Steffen Schmidt E D SE PTI NC
  26. 26. Network transformerImpact of Correction Factor 1.05 1.00 0.95 KT 0.90 cmax = 1.10 0.85 cmax = 1.05 0.80 0 5 10 15 20 xT [%]The Correction factor is KT<1.0 for transformers with xT >7.5 %.Reduction of transformer impedanceIncrease of short-circuit currents Copyright © Siemens AG 2008. All rights reserved.Page 26 28.06.2008 Steffen Schmidt E D SE PTI NC
  27. 27. Generator with direct Connection to NetworkCorrection of Impedance ZGK = ZG KG general Un c max KG = ⋅ UrG 1 + x′′ ⋅ sin ϕrG d for continuous operation above rated voltage: UrG (1+pG) instead of UrG  turbine generator: X(2) = X(1)  salient pole generator: X(2) = 1/2 (Xd" + Xq") Copyright © Siemens AG 2008. All rights reserved.Page 27 28.06.2008 Steffen Schmidt E D SE PTI NC
  28. 28. Generator Block (Power Station)Correction of Impedance ZS(O) = (tr2 ZG +ZTHV) KS(O) Q G power station with on-load tap changer: 2 2 UnQ UrTLV c max KS = 2 ⋅ 2 ⋅ UrG UrTHV 1 + x′′ − x T ⋅ sin ϕrG d power station without on-load tap changers: UnQ U c max K SO = ⋅ rTLV ⋅ (1 ± p t ) ⋅ UrG (1 + pG ) UrTHV 1 + x′′ ⋅ sin ϕrG d Copyright © Siemens AG 2008. All rights reserved.Page 28 28.06.2008 Steffen Schmidt E D SE PTI NC
  29. 29. Asynchronous MotorsMotors contribute to the short circuit currents and have to be consideredfor calculation of maximum short circuit currents 2 1 UrM ZM = ⋅ ILR / IrM SrM ZM XM = 1 + (RM / XM )2If 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) Copyright © Siemens AG 2008. All rights reserved.Page 29 28.06.2008 Steffen Schmidt E D SE PTI NC
  30. 30. Special Regulations for low Voltage Motors low voltage motors can be neglected if ∑IrM ≤ Ik” groups of motors can be combined to a equivalent motor ILR/IrM = 5 can be used Copyright © Siemens AG 2008. All rights reserved.Page 30 28.06.2008 Steffen Schmidt E D SE PTI NC
  31. 31. Calculation of initial short circuit current Copyright © Siemens AG 2008. All rights reserved.Page 31 28.06.2008 Steffen Schmidt E D SE PTI NC
  32. 32. Calculation of initial short circuit currentProcedure 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 Copyright © Siemens AG 2008. All rights reserved.Page 32 28.06.2008 Steffen Schmidt E D SE PTI NC
  33. 33. Calculation of initial short circuit currentEquivalent 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. Copyright © 2008.Page 33 28.06.2008 Steffen Schmidt E D SE PTI NC
  34. 34. Calculation of initial short circuit current3-phase short circuit L1-L2-L3-system Z(1)l 012-system Z(1)r L1 ~ ~ L2 ~ c Un (1) √3 L3 Z(2)l Z(2)r ~ ~ ~ -Uf ~ ~ c ⋅ Ur ′′ I sc3 = (2) 3 ⋅ Z (1) Z(0)l Z(0)r ~ ~ (0) network left of fault location network right of UL1 = – Uf fault location fault location U(1) = – Uf UL2 = a2 (– Uf) U(2) = 0 UL3 = a (– Uf) U(0) = 0 Copyright © Siemens AG 2008. All rights reserved.Page 34 28.06.2008 Steffen Schmidt E D SE PTI NC
  35. 35. Calculation of 2-phase initial short circuit current L1-L2-L3-system Z(1)l 012-system Z(1)r L1 ~ ~ L2 ~ c Un (1) L3 √3 ~ Z(2)l Z(2)r -Uf c ⋅U r ~ ~ ′′ I sc2 = (2) Z ( 1) + Z ( 2 ) Z(0)l Z(0)r ~ ~ c ⋅U r ′′ I sc2 3 ′′ I sc2 = ⇒ = (0) 2 Z ( 1) ′′ I sc3 2 network left of network right of IL1 = 0 U fault location U (1) − U ( 2 ) = −c n fault location fault location 3 IL2 = – IL3 I(0) = 0 UL3 – UL2 = – Uf I(1) = – I(2) Copyright © Siemens AG 2008. All rights reserved.Page 35 28.06.2008 Steffen Schmidt E D SE PTI NC
  36. 36. Calculation of 2-phase initial short circuit currentwith ground connection L1-L2-L3-system 012-system Z(1)l Z(1)r ~ ~ L1 ~ c Un (1) L2 √3 L3 Z(2)l Z(2)r ~ ~ ~ 3⋅ c ⋅ U r -Uf ′′ I scE2E = (2) Z ( 1) + 2 Z ( 0 ) Z(0)l Z(0)r ~ ~ (0) I L1 = 0 network left of network right of fault location 2 Un fault location fault location U L2 = − a c 3 Un U (1) − U ( 2) = − c = U (1) − U ( 0) Un 3 U L3 = − a c 3 I(0) = I(1) = I(2) Copyright © Siemens AG 2008. All rights reserved.Page 36 28.06.2008 Steffen Schmidt E D SE PTI NC
  37. 37. Calculation of 1-phase initial short circuit current L1-L2-L3-System Z(1)l 012-System Z(1)r ~ ~ (1) L1 L2 Z(2)l Z(2)r L3 ~ ~ 3⋅ c ⋅ U r c Un I sc1 = " ~ (2) ~ -Uf Z (1) + Z ( 2 ) + Z ( 0 ) √3 Z(0)l Z(0)r ~ ~ (0) network left of network right of fault location Un fault location fault location U L1 = − c 3 Un U ( 0) + U (1) + U ( 2) = − c IL2 = 0 3 I(0) = I(1) = I(2) IL3 = 0 Copyright © Siemens AG 2008. All rights reserved.Page 37 28.06.2008 Steffen Schmidt E D SE PTI NC
  38. 38. 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 (current in earth connection) Copyright © Siemens AG 2008. All rights reserved.Page 38 28.06.2008 Steffen Schmidt E D SE PTI NC
  39. 39. Feeding of short circuits single fed short circuit " I sc ür:1 k3 S" kQ UnQ multiple fed short circuit G 3~ M 3~ ∑ I sc_part ≅ ∑ I sc_part " I“scG I“scN I“scM I sc = " " Fault Copyright © Siemens AG 2008. All rights reserved.Page 39 28.06.2008 Steffen Schmidt E D SE PTI NC
  40. 40. Calculation of short circuit currents by programs (1/3) Basic equation i=Yu Y: matrix of admittances (for short circuit) 0  Y 11 . . . . Y 1n   U1  0  Y  U     21 . . . . Y 2n    2   .   . .   .        .  .    . .    .   . .   .    =    Ur   I sci   Y i1 . . . . Y in  − c ⋅   3  .   . .       .   .   . .   .   .   .   .   .      0    Y n1  . . . . Y nn    U   n  Copyright © Siemens AG 2008. All rights reserved.Page 40 28.06.2008 Steffen Schmidt E D SE PTI NC
  41. 41. Calculation of short circuit currents by programs (2/3) Inversion of matrix of admittances u = Y-1 i  U1   Z 11 . . . . Z 1n  0   U  Z  2   21 . . . . Z 2n   0     .   . .   .        .    . .   .   .   . .   .   Ur  =     − c ⋅   Z i1 . Z ii . . Z in   I sci   3  . .   .   .       .   . .   .     .  .  .   .       U   Z n1  . . . . Z nn   0     n  Copyright © Siemens AG 2008. All rights reserved.Page 41 28.06.2008 Steffen Schmidt E D SE PTI NC
  42. 42. Calculation of short circuit currents by programs (3/3) from line i: − c Ur " ⇒I " = − c U r = Z ii ⋅ I sci 3 sci 3 ⋅ Z ii from the remaining lines: " U sc = Z sci ⋅ I sci  calculation of all node voltages  from there -> calculation of all short circuit currents Copyright © Siemens AG 2008. All rights reserved.Page 42 28.06.2008 Steffen Schmidt E D SE PTI NC
  43. 43. Short Circuit Calculation ResultsFaults at all Buses Copyright © Siemens AG 2008. All rights reserved.Page 43 28.06.2008 Steffen Schmidt E D SE PTI NC
  44. 44. Short Circuit Calculation ResultsContribution for one Fault Location Copyright © Siemens AG 2008. All rights reserved.Page 44 28.06.2008 Steffen Schmidt E D SE PTI NC
  45. 45. Example Copyright © Siemens AG 2008. All rights reserved.Page 45 28.06.2008 Steffen Schmidt E D SE PTI NC
  46. 46. Data of sample calculation Network feeder: Transformer: Overhead line: 110 kV 110 / 20 kV 20 kV 3 GVA 40 MVA 10 km R/X = 0.1 uk = 15 % R1’ = 0.3 Ω / km PkrT = 100 kVA X1’ = 0.4 Ω / km Copyright © Siemens AG 2008. All rights reserved.Page 46 28.06.2008 Steffen Schmidt E D SE PTI NC
  47. 47. Impedance of Network feeder c ⋅ Un2 ZI = " Sk 1.1⋅ ( 20 kV ) 2 ZI = 3 GVA ZI = 0.1467 Ω RI = 0.0146 Ω XI = 0.1460 Ω Copyright © Siemens AG 2008. All rights reserved.Page 47 28.06.2008 Steffen Schmidt E D SE PTI NC
  48. 48. Impedance of Transformer 2 Un 2 Un Z T = uk ⋅ R T = PkrT ⋅ 2 Sn Sn ( 20 kV ) 2 ( 20 kV ) 2 Z T = 0.15 ⋅ R T = 100 kVA ⋅ 40 MVA ( 40 MVA ) 2 Z T = 1.5000 Ω R T = 0.0250 Ω X T = 1.4998 Ω Copyright © Siemens AG 2008. All rights reserved.Page 48 28.06.2008 Steffen Schmidt E D SE PTI NC
  49. 49. Impedance of TransformerCorrection Factor c max K T = 0.95 ⋅ 1 + 0.6 ⋅ x T 1 .1 K T = 0.95 ⋅ 1 + 0.6 ⋅ 0.14998 K T = 0.95873 Z TK = 1.4381 Ω R TK = 0.0240 Ω X TK = 1.4379 Ω Copyright © Siemens AG 2008. All rights reserved.Page 49 28.06.2008 Steffen Schmidt E D SE PTI NC
  50. 50. Impedance of Overhead Line RL = R⋅ XL = X⋅ RL = 0.3 Ω / km ⋅ 10 km XL = 0.4 Ω / km ⋅ 10 km RL = 3.0000 Ω XI = 4.0000 Ω Copyright © Siemens AG 2008. All rights reserved.Page 50 28.06.2008 Steffen Schmidt E D SE PTI NC
  51. 51. Initial Short-Circuit Current – Fault location 1 R = RI + R TK X = XI + X TK R = 0.0146 Ω + 0.0240 Ω X = 0.1460 Ω + 1.4379 Ω R = 0.0386 Ω X = 1.5839 Ω c ⋅ Un Ik = " 3 ⋅ ( R1 + j ⋅ X1 ) 1.1⋅ 20 kV Ik = " 3⋅ ( 0.0386 Ω ) 2 + (1.5839 Ω ) 2 Ik = 8.0 kA " Copyright © Siemens AG 2008. All rights reserved.Page 51 28.06.2008 Steffen Schmidt E D SE PTI NC
  52. 52. Initial Short-Circuit Current – Fault location 2 R = RI + R TK + RL X = XI + X TK + XL R = 0.0146 Ω + 0.0240 Ω + 3.0000 Ω X = 0.1460 Ω + 1.4379 Ω + 4.0000 Ω R = 3.0386 Ω X = 5.5839 Ω c ⋅ Un Ik = " 3 ⋅ ( R1 + j ⋅ X1 ) 1.1⋅ 20 kV Ik = " 3⋅ ( 3.0386 Ω ) 2 + ( 5.5839 Ω) 2 Ik = 2.0 kA " Copyright © Siemens AG 2008. All rights reserved.Page 52 28.06.2008 Steffen Schmidt E D SE PTI NC
  53. 53. Calculation of Peak Current Copyright © Siemens AG 2008. All rights reserved.Page 53 28.06.2008 Steffen Schmidt E D SE PTI NC
  54. 54. Peak Short-Circuit CurrentCalculation acc. IEC 60909maximum possible instantaneous value of expected short circuit currentequation for calculation: ip = κ ⋅ 2 ⋅ Ik " κ = 1.02 + 0.98 ⋅ e −3R / X Copyright © Siemens AG 2008. All rights reserved.Page 54 28.06.2008 Steffen Schmidt E D SE PTI NC
  55. 55. Peak Short-Circuit CurrentCalculation in non-meshed NetworksThe peak short-circuit current ip at a short-circuit location, fed fromsources which are not meshed with one another is the sum of the partialshort-circuit currents: Copyright © Siemens AG 2008. All rights reserved.Page 55 28.06.2008 Steffen Schmidt E D SE PTI NC
  56. 56. Peak Short-Circuit CurrentCalculation in meshed NetworksMethod A: uniform ratio R/X smallest value of all network branches quite inexactMethod B: ratio R/X at the fault location factor κb from relation R/X at the fault location (equation or diagram) κ =1,15 κbMethod C: procedure with substitute frequency factor κ from relation Rc/Xc with substitute frequency fc = 20 Hz R R c fc = ⋅ X Xc f best results for meshed networks Copyright © Siemens AG 2008. All rights reserved.Page 56 28.06.2008 Steffen Schmidt E D SE PTI NC
  57. 57. Peak Short-Circuit CurrentFictitious Resistance of Generator RGf = 0,05 Xd" for generators with UrG > 1 kV and SrG ≥ 100 MVA RGf = 0,07 Xd" for generators with UrG > 1 kV and SrG < 100 MVA RGf = 0,15 Xd" for generators with UrG ≤ 1000 VNOTE: Only for calculation of peak short circuit current Copyright © Siemens AG 2008. All rights reserved.Page 57 28.06.2008 Steffen Schmidt E D SE PTI NC
  58. 58. Peak Short-Circuit Current – Fault location 1 Ik = 8.0 kA " R = 0.0386 Ω X = 1.5839 Ω R / X = 0.0244 κ = 1.02 + 0.98 ⋅ e −3R / X κ = 1.93 ip = κ ⋅ 2 ⋅ Ik " ip = 21.8 kA Copyright © Siemens AG 2008. All rights reserved.Page 58 28.06.2008 Steffen Schmidt E D SE PTI NC
  59. 59. Peak Short-Circuit Current – Fault location 2 Ik = 2.0 kA " R = 3.0386 Ω X = 5.5839 Ω R / X = 0.5442 κ = 1.02 + 0.98 ⋅ e −3R / X κ = 1.21 ip = κ ⋅ 2 ⋅ Ik " ip = 3.4 kA Copyright © Siemens AG 2008. All rights reserved.Page 59 28.06.2008 Steffen Schmidt E D SE PTI NC
  60. 60. Calculation of Breaking Current Copyright © Siemens AG 2008. All rights reserved.Page 60 28.06.2008 Steffen Schmidt E D SE PTI NC
  61. 61. Breaking CurrentDifferentiationDifferentiation between short circuits ”near“ or “far“ from generatorDefinition short circuit ”near“ to generator  for at least one synchronous machine is: Ik” > 2 ∙ Ir,Generator or  Ik”with motor > 1.05 ∙ Ik”without motorBreaking current Ib for short circuit “far“ from generator Ib = Ik” Copyright © Siemens AG 2008. All rights reserved.Page 61 28.06.2008 Steffen Schmidt E D SE PTI NC
  62. 62. Breaking CurrentCalculation in non-meshed NetworksThe breaking current IB at a short-circuit location, fed from sources whichare not meshed is the sum of the partial short-circuit currents: Copyright © Siemens AG 2008. All rights reserved.Page 62 28.06.2008 Steffen Schmidt E D SE PTI NC
  63. 63. Breaking currentDecay of Current fed from Generators  IB = μ ∙ I“kFactor μ to consider the decay of short circuit current fed fromgenerators. Copyright © Siemens AG 2008. All rights reserved.Page 63 28.06.2008 Steffen Schmidt E D SE PTI NC
  64. 64. Breaking currentDecay of Current fed from Asynchronous Motors  IB = μ ∙ q ∙ I“kFactor q to consider the decay of short circuit current fed fromasynchronous motors. Copyright © Siemens AG 2008. All rights reserved.Page 64 28.06.2008 Steffen Schmidt E D SE PTI NC
  65. 65. Breaking CurrentCalculation in meshed NetworksSimplified calculation: Ib = Ik”For increased accuracy can be used: ∆U"Gi ∆U"Mj Ib = I − ∑ ⋅ (1 − µi ) ⋅ IkGi − ∑ " " " k ⋅ (1 − µ jq j ) ⋅ IkMj i c ⋅ Un / 3 j c ⋅ Un / 3 " " " ∆UGi = jX " ⋅ IkGi diK " ∆UMj = jXMj ⋅ IkMj "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) and the asynchronous motors (j) as measured at the machine terminals Copyright © Siemens AG 2008. All rights reserved.Page 65 28.06.2008 Steffen Schmidt E D SE PTI NC
  66. 66. Continuous short circuit currentContinuous short circuit current Ik  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 bynetwork calculation programs.For short circuits far from generator and as worst case estimation Ik = I”k Copyright © Siemens AG 2008. All rights reserved.Page 66 28.06.2008 Steffen Schmidt E D SE PTI NC
  67. 67. Short-circuit with preload Copyright © Siemens AG 2008. All rights reserved.Page 67 28.06.2008 Steffen Schmidt E D SE PTI NC
  68. 68. Short-circuit with preloadPrincipleA 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.C Superposition of A and B Copyright © Siemens AG 2008. All rights reserved.Page 68 28.06.2008 Steffen Schmidt E D SE PTI NC
  69. 69. Short-circuit with preloadExampleA Load flow calculationB Short circuit calculation Copyright © Siemens AG 2008. All rights reserved.Page 69 28.06.2008 Steffen Schmidt E D SE PTI NC
  70. 70. Short-circuit with preloadResults Load flow Superposition: Load flow + feed back 50. A 40. A 40A 10A 153.95A 157.37A 208A 182A 2Ω 50A 40A 3 Ω 40A 2Ω 10A 2Ω 203.95A 197.37A 168A 192A 1000V 720V 10A 50A1000V -0V -0V 720V 1000V 720V 900V 780V 700V 900. V 700V 90 Ω 14 Ω ~ -307.89V -364V ~ ~ 592.11V 336V ~ 365.37A Short-circuit: feed back Short-circuit with preload 153.95A 365.3A 182A 203.95A 197.37A 168A 192.0A 157.37A 208.0A 26A 0V 3.42A 1000V 6.58A 24A 0V 720V 592.11V 336V 307.89V 780V 364V ~ ~ 365.37A Copyright © Siemens AG 2008. All rights reserved.Page 70 28.06.2008 Steffen Schmidt E D SE PTI NC
  71. 71. Break time! Copyright © Siemens AG 2008. All rights reserved. Copyright ©Page 71 28.06.2008 Steffen Schmidt E D SE PTI NC
  72. 72. ContactSteffen SchmidtSenior ConsultantSiemens AG, Energy SectorE D SE PTI NCFreyeslebenstr. 191058 ErlangenPhone: +49 9131 - 7 32764Fax: +49 9131 - 7 32525E-mail: steffen.schmidt@siemens.com Copyright © Siemens AG 2008. All rights reserved.Page 72 28.06.2008 Steffen Schmidt E D SE PTI NC
  73. 73. Thank you for your attention! Copyright © Siemens AG 2008. All rights reserved. Copyright ©Page 73 28.06.2008 Steffen Schmidt E D SE PTI NC

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