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In a cable a short circuit causes very extreme stresses which are proportional to the square of the current: • A temperature rise in the conducting components subjected to current flow such as conductor, screen, metal sheath, armour. Indirectly the temperature of adjoining insulation and protective covers also increases, • electro-magnetic forces between the current-carrying components. The temperature rise is important for its effect on ageing, heat pressure characteristics etc., and should be limited to a permissible short-circuit temperature. The thermo-mechanical effects of the current shall also be considered. For a given short-circuit duty therefore the short-circuit capacity of a cable installation is to be investigated with respect to all these parameters. For multi-core cables in most instances the thermal effect - related to the magnitude of fault current and clearance time - is the critical parameter, since the cable will normally have enough mechanical strength. With single-core cables however, in addition, the mechanical effect - related to the magnitude of the peak short-circuit current - is of such significance that, next to the thermal, the mechanical with- stand of both cable and its supports is to be investigated. Also accessories must be rated with respect to thermal and mechanical short-circuit stresses. The short-circuit withstand of a cable system is not quantitatively defined with regard to permissible number of repeated short circuits, degree of deformation or destruction or impairment quality. It is expected, however, that a cable installation will remain safe in operation and that any deformation remains within tolerable limits even after several short circuits.
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A short circuit causes very extreme stresses in a cable which are proportional to the square of the current: A temperature rise in the conducting components such as conductor, screen, metal sheath, armour. Indirectly the temperature of adjoining insulation and protective covers also increases, electro-magnetic forces between the current-carrying components. The temperature rise is important for its effect on ageing, heat pressure characteristics etc. and should be limited to a permissible short-circuit temperature. The thermo-mechanical effects of the current shall also be considered. For the given short-circuit condition the short-circuit capacity of a cable should be investigated with respect to all these parameters. For multi-core cables in most instances the thermal effect - related to the magnitude of fault current and clearance time - is the critical parameter, since the cable will normally have enough mechanical strength. With single-core cables however the mechanical effect - related to the magnitude of the peak short-circuit current - is of such significance that, next to the thermal, the mechanical strength of both cable and its supports should be investigated. Also accessories must be rated with respect to thermal and mechanical short-circuit stresses. The short circuit strength of a cable system is not quantitatively defined with regard to permissible number of repeated short circuits, degree of deformation or destruction or impairment quality. It is expected, however, that a cable installation will remain safe in operation and that any deformation remains within tolerable limits even after several short circuits. This course provides practical overview of short circuit performance of a cable.
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Copy of shortckt
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.
Short Circuit Calculation Sector
Energy D SE PTI NC Steffen Schmidt Copyright © Siemens AG 2008. All rights reserved.
3.
Standards and Terms
Copyright © Siemens AG 2008. All rights reserved. Page 3 28.06.2008 Steffen Schmidt E D SE PTI NC
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.
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. Copyright © Siemens AG 2008. All rights reserved. Page 5 28.06.2008 Steffen Schmidt E D SE PTI NC
6.
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 currents Copyright © Siemens AG 2008. All rights reserved. Page 6 28.06.2008 Steffen Schmidt E D SE PTI NC
7.
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 Copyright © Siemens AG 2008. All rights reserved. Page 7 28.06.2008 Steffen Schmidt E D SE PTI NC
8.
Short-Circuit Calculations Types 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.
Variation of short
circuit current shapes fault at voltage peak fault at voltage zero crossing fault located in the network fault located near generator Copyright © Siemens AG 2008. All rights reserved. Page 9 28.06.2008 Steffen Schmidt E D SE PTI NC
10.
Short-Circuit Calculations Far-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.
Short-Circuit Calculations Definitions 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 if the impedance remains at zero-time value initial 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 the connection point. In this case the definition given should be used in the following form: c ⋅ Un2 Z= " Sk Copyright © Siemens AG 2008. All rights reserved. Page 11 28.06.2008 Steffen Schmidt E D SE PTI NC
12.
Short-Circuit Calculations Definitions according
IEC 60909 (II) decaying (aperiodic) component id.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 ip 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. Copyright © Siemens AG 2008. All rights reserved. Page 12 28.06.2008 Steffen Schmidt E D SE PTI NC
13.
Short-Circuit Calculations Near-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.
Short-Circuit Calculations Definitions according
IEC 60909 (III) steady-state short-circuit current Ik r.m.s. value of the short-circuit current which remains after the decay of the transient phenomena symmetrical short-circuit breaking current Ib 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 Copyright © Siemens AG 2008. All rights reserved. Page 14 28.06.2008 Steffen Schmidt E D SE PTI NC
15.
Short-Circuit Calculations Purpose of
Short-Circuit Values Design Criterion Physical Effect Relevant short-circuit current Breaking capacity of circuit Thermal stress to arcing Symmetrical short-circuit breakers chamber; arc extinction breaking current Ib Mechanical stress to Forces to electrical devices Peak short-circuit current ip equipment (e.g. bus bars, cables…) Thermal stress to equipment Temperature rise of electrical Initial symmetrical short- devices (e.g. cables) circuit current Ik” Fault duration Protection setting Selective detection of partial Minimum symmetrical short- short-circuit currents circuit current Ik Earthing, 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.
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 -> safe assumptions Copyright © Siemens AG 2008. All rights reserved. Page 16 28.06.2008 Steffen Schmidt E D SE PTI NC
17.
Equivalent Voltage Source
Copyright © Siemens AG 2008. All rights reserved. Page 17 28.06.2008 Steffen Schmidt E D SE PTI NC
18.
Short-circuit Equivalent 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.
Short circuit in
meshed grid Equivalent voltage source at the short-circuit location real network equivalent circuit Copyright © Siemens AG 2008. All rights reserved. Page 19 28.06.2008 Steffen Schmidt E D SE PTI NC
20.
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. Voltage factor c for calculation of Nominal voltage maximum short circuit currents minimum short circuit currents Low voltage 100 V – 1000 V -systems with a tolerance of 6% 1.05 0.95 -systems with a tolerance of 10% 1.10 0.95 Medium voltage >1 kV – 35 kV 1.10 1.00 High 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.
Maximum and minimum
Short-Circuit Currents maximum minimum short circuit currents short circuit currents Voltage factor Cmax Cmin Power plants Maximum contribution Minimum contribution Network feeders Minimum impedance Maximum impedance Motors shall be considered shall be neglected Resistance 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.
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.
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 Copyright © Siemens AG 2008. All rights reserved. Page 23 28.06.2008 Steffen Schmidt E D SE PTI NC
24.
Network feeders At 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)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 Copyright © Siemens AG 2008. All rights reserved. Page 24 28.06.2008 Steffen Schmidt E D SE PTI NC
25.
Network transformer Correction 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 T no 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.
Network transformer Impact 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.
Generator with direct
Connection to Network Correction 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.
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.
Asynchronous Motors Motors contribute
to the short circuit currents and have to be considered for calculation of maximum short circuit currents 2 1 UrM ZM = ⋅ ILR / IrM SrM ZM XM = 1 + (RM / XM )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) Copyright © Siemens AG 2008. All rights reserved. Page 29 28.06.2008 Steffen Schmidt E D SE PTI NC
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.
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.
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 Copyright © Siemens AG 2008. All rights reserved. Page 32 28.06.2008 Steffen Schmidt E D SE PTI NC
33.
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. Copyright © 2008. Page 33 28.06.2008 Steffen Schmidt E D SE PTI NC
34.
Calculation of initial
short circuit current 3-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.
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.
Calculation of 2-phase
initial short circuit current with 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.
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.
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.
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.
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.
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.
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.
Short Circuit Calculation
Results Faults at all Buses Copyright © Siemens AG 2008. All rights reserved. Page 43 28.06.2008 Steffen Schmidt E D SE PTI NC
44.
Short Circuit Calculation
Results Contribution for one Fault Location Copyright © Siemens AG 2008. All rights reserved. Page 44 28.06.2008 Steffen Schmidt E D SE PTI NC
45.
Example
Copyright © Siemens AG 2008. All rights reserved. Page 45 28.06.2008 Steffen Schmidt E D SE PTI NC
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.
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.
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.
Impedance of Transformer Correction
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.
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.
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.
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.
Calculation of Peak
Current Copyright © Siemens AG 2008. All rights reserved. Page 53 28.06.2008 Steffen Schmidt E D SE PTI NC
54.
Peak Short-Circuit Current Calculation
acc. IEC 60909 maximum possible instantaneous value of expected short circuit current equation 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.
Peak Short-Circuit Current Calculation
in non-meshed Networks The peak short-circuit current ip at a short-circuit location, fed from sources which are not meshed with one another is the sum of the partial short-circuit currents: Copyright © Siemens AG 2008. All rights reserved. Page 55 28.06.2008 Steffen Schmidt E D SE PTI NC
56.
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 κb from relation R/X at the fault location (equation or diagram) κ =1,15 κb Method 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.
Peak Short-Circuit Current Fictitious
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 V NOTE: 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.
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.
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.
Calculation of Breaking
Current Copyright © Siemens AG 2008. All rights reserved. Page 60 28.06.2008 Steffen Schmidt E D SE PTI NC
61.
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: Ik” > 2 ∙ Ir,Generator or Ik”with motor > 1.05 ∙ Ik”without motor Breaking 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.
Breaking Current Calculation in
non-meshed Networks The breaking current IB at a short-circuit location, fed from sources which are 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.
Breaking current Decay of
Current fed from Generators IB = μ ∙ I“k Factor μ to consider the decay of short circuit current fed from generators. Copyright © Siemens AG 2008. All rights reserved. Page 63 28.06.2008 Steffen Schmidt E D SE PTI NC
64.
Breaking current Decay of
Current fed from Asynchronous Motors IB = μ ∙ q ∙ I“k Factor q to consider the decay of short circuit current fed from asynchronous motors. Copyright © Siemens AG 2008. All rights reserved. Page 64 28.06.2008 Steffen Schmidt E D SE PTI NC
65.
Breaking Current Calculation in
meshed Networks Simplified 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.
Continuous short circuit
current Continuous 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 by network 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.
Short-circuit with preload
Copyright © Siemens AG 2008. All rights reserved. Page 67 28.06.2008 Steffen Schmidt E D SE PTI NC
68.
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. 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.
Short-circuit with preload Example A
Load flow calculation B Short circuit calculation Copyright © Siemens AG 2008. All rights reserved. Page 69 28.06.2008 Steffen Schmidt E D SE PTI NC
70.
Short-circuit with preload Results
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 50A 1000V -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.
Break time!
Copyright © Siemens AG 2008. All rights reserved. Copyright © Page 71 28.06.2008 Steffen Schmidt E D SE PTI NC
72.
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: steffen.schmidt@siemens.com Copyright © Siemens AG 2008. All rights reserved. Page 72 28.06.2008 Steffen Schmidt E D SE PTI NC
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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