BS 7639 Short Circuit Current Calculation in 3Phase AC Syste

March 24, 2018 | Author: Aimee Rachel Dean Rabe | Category: Electrical Impedance, Alternating Current, Transformer, Electrical Network, Series And Parallel Circuits
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BRITISH STANDARDBS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI Short-circuit current calculation in three-phase a.c. systems — (Implementation of HD 533 S1) UDC 621.3.02.001 BS 7639:1993 Committees responsible for this British Standard The preparation of this British Standard was entrusted by the Power Electrical Engineering Standards Policy Committee (PEL/-) to Technical Committee PEL/104, upon which the following bodies were represented: British Cable Makers’ Confederation Electrical Installation Equipment Manufacturers’ Association Electricity Association Institution of Electrical Engineers GAMBICA (BEAMA Ltd.) Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI This British Standard, having been prepared under the direction of the Power Electrical Engineering Standards Policy Committee, was published under the authority of the Standards Board and comes into effect on 15 April 1993 © BSI 04-2000 The following BSI references relate to the work on this standard: Committee reference PEL/104 Special announcement in BSI News, July 1992 ISBN 0 580 21675 6 Amendments issued since publication Amd. No. Date Comments BS 7639:1993 Contents Committees responsible National foreword Foreword Text of HD 533 S1 National annex NA (informative) Original IEC text amended by CENELEC common modifications National annex NB (informative) Cross-references Page Inside front cover ii 2 5 Inside back cover Inside back cover Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI © BSI 04-2000 i It was derived by CENELEC from IEC 909:1988 Short circuit current calculations in three phase a.BS 7639:1993 National foreword This British Standard has been prepared under the direction of the Power Electrical Engineering Standards Policy Committee PEL/-. This will be indicated in the amendment table on the inside front cover. systems. pages i and ii. This standard has been updated (see copyright date) and may have had amendments incorporated. an inside front cover. Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy. © BSI Compliance with a British Standard does not of itself confer immunity from legal obligations. the HD title page. ii © BSI 04-2000 . published by the International Electrotechnical Commission (IEC). an inside back cover and a back cover. 12/02/2004.c. Summary of pages This document comprises a front cover. pages 2 to 86. Users of British Standards are responsible for their correct application. A British Standard does not purport to include all the necessary provisions of a contract. It implements Harmonization Document HD 533 S1:1991 which was published by the European Committee for Electrotechnical Standardization (CENELEC). Spain. B-1050 Brussels © 1991 Copyright reserved to CENELEC members Ref. Denmark. modified) Calcul des courants de court-circuit dans les réseaux triphasés à courant alternatif (CEI 909:1988. Finland.001 Descriptors: Calculation.3. Portugal. three-phase systems HD 533 S1 April 1991 English version Licensed copy:DRAKE & SCULL ENGINEERING LTD. Sweden. Uncontrolled Copy. German). modifiziert) This Harmonization Document was approved by CENELEC on 1990-03-05. short-circuit current. 12/02/2004. Netherlands.HARMONIZATION DOCUMENT DOCUMENT D’HARMONISATION HARMONISIERUNGDOKUMENT UDC 621. France. Switzerland and United Kingdom.c. systems (IEC 909:1988. Ireland. Germany. CENELEC members are the national electrotechnical committees of Austria. CENELEC European Committee for Electrotechnical Standardization Comité Européen de Normalisation Electrotechnique Europäisches Komitee für Elektrotechnische Normung Central Secretariat: rue de Stassart 35. HD 533 S1:1991 E . No. French. Norway. This Harmonization Document exists in three official versions (English. Belgium.02. modifiée) Berechnung von Kurzschlußströmen in Drehstromnetzen (IEC 909. Greece. Luxembourg. CENELEC members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for implementation of this Harmonization Document on a national level. Up-to-date lists and bibliographical references concerning such national implementation may be obtained on application to the Central Secretariat or to any CENELEC member. Italy. Iceland. © BSI Short-circuit current calculation in three-phase a. 1 General 12. © BSI (dop) 1991-11-01 — latest date of withdrawal of conflicting national standards (dow) 1991-11-01 16 16 16 16 17 23 23 23 27 30 30 31 31 33 33 33 33 37 37 37 37 2 © BSI 04-2000 . Finland and Norway. as HD 533 S1 on 5 March 1990. components (near-to-generator short circuits) 10 General 11 Short-circuit parameters 11.2 Balanced short circuit 11.1 Calculation method for balanced short circuits 9. has shown that some CENELEC common modifications were necessary for the acceptance as Harmonization Document. together with the common modifications prepared by the CENELEC Reporting Secretariat SR 73.5 Short-circuit impedances 11.2 Subscripts 4. currents and voltages 9 Calculation of short-circuit currents 9.2 Calculation method for balanced short circuits Page 2 5 5 5 8 8 9 10 11 12 Licensed copy:DRAKE & SCULL ENGINEERING LTD.BS 7639:1993 Foreword The CENELEC questionnaire procedure.1 Balanced short circuit 8. Systems with short-circuit currents having decaying a.3 The minimum short-circuit currents Section 2. component decay (far-from-generator short circuits) 7 General 8 Short-circuit parameters 8.2 Unbalanced short circuit 8. The text of the draft was approved by all CENELEC members. 12/02/2004.2 Calculation method for line-to-line and line-to-earth short circuits 9.3 Unbalanced short circuit 11. The reference document. currents and voltages 12 Calculation of short-circuit currents 12.3 Superscripts 5 Calculation assumptions 6 Equivalent voltage source at the short-circuit location Section 1.3 Short-circuit impedances 8.c. Systems with short-circuit currents having no a. The following dates were fixed: — latest date of announcement of the HD at national level (doa) 1990-09-01 — latest date of publication of a new harmonized national standard Contents Foreword 1 Scope 2 Object 3 Definitions 4 Symbols.4 Equivalent voltage source at the short-circuit location 11.4 Conversion of impedances. with the exception of Austria. was submitted to the CENELEC members for formal vote.1 General 11. subscripts and superscripts 4. Uncontrolled Copy. performed for finding out whether or not the International Standard IEC 909:1988 could be accepted without textual changes.6 Conversion of impedances.c.1 Symbols 4. I and I for a calculation of Ik p b k three-phase short circuit fed from non-meshed sources according to equations (55) to (58) Figure 23 — Example of the calculation of the initial symmetrical short-circuit 0 in a meshed network fed current Ik from several sources Figure 24 — Example for the estimation of the contribution from the asynchronous motors in relation to the total short-circuit current Figure 25 — Factor q for the calculation of the symmetrical short-circuit breaking current of asynchronous motors Page 28 31 32 35 Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12/02/2004.BS 7639:1993 Page 12.2 Series capacitors Appendix A (informative) Calculation of short-circuit currents Figure 1 — Short-circuit current of a far-from-generator short circuit (schematic diagram) Figure 2 — Characterization of short circuits and their currents.2 Asynchronous motors 13.1 Parallel capacitors 14. Uncontrolled Copy. (In some cases the impedance between busbar B and the short-circuit location F may be neglected) Figure 10 — Illustration of the calculation of the initial symmetrical 0 in a meshed short-circuit current I k network.1 Synchronous motors and synchronous compensators 13. b) ratio X/R Figure 9 — System diagram illustrating a short circuit fed from several sources which are independent of one another. The direction of current arrows is chosen arbitrarily Figure 3 — Illustration for calculating the initial symmetrical short-circuit 0 in compliance with the current I k procedure for the equivalent voltage source Figure 4 — Short-circuit impedance of a three-phase a.3 Calculation method for line-to-line and line-to-earth short circuits 12.c. i .4 The minimum short-circuit currents 13 Influence of motors 13. © BSI 37 38 39 40 11 13 41 14 42 15 18 43 19 22 24 44 45 25 48 49 26 © BSI 04-2000 3 . The short-circuit current at the short-circuit location F is supplied by the feeder connection point Q through transformers T1 and T2 46 46 47 47 47 50 51 51 51 52 Figure 11 — Chart indicating the type of short-circuit giving the highest current Figure 12 — Short-circuit current of a near-to-generator short circuit (schematic diagram) Figure 13 — Various short-circuit source connections Figure 14 — Phasor diagram of a synchronous generator at rated conditions Figure 15 — Example for the calculation of the initial symmetrical short-circuit 0 for a short circuit fed current Ik directly from one generator Figure 16 — Factor È for the calculation of short-circuit breaking current Ib Figure 17 — Factors Æmax and Æmin for turbine generators Figure 18 — Factors Æmax and Æmin for salient-pole machines Figure 19 — Example of the calculation of the initial symmetrical short-circuit 0 fed from one power-station current Ik unit Figure 20 — Example of the calculation of the initial symmetrical short-circuit 0 fed from non-meshed sources current Ik Figure 21 — Short-circuit currents and partial short-circuit currents for three-phase short circuits between generator and transformer of a power-station unit and at the auxiliary busbar A Figure 22 — Explanation of the 0 . system at the short-circuit location F Figure 5 — Measuring of zero-sequence short-circuit impedances of electrical equipment (examples) Figure 6 — System diagram and equivalent circuit diagram for network feeders Figure 7 — Three-winding transformer (example) Figure 8 — Factor x for series circuits as a function of: a) ratio R/X.3 Static converter fed drives 14 Consideration of non-rotating loads and capacitors 14. Transformers and low-voltage motor groups connected to the busbar C are identical Figure A. without the influence of asynchronous motors M1 and M2 (CB1 and CB2 are open) Table A. Transformers and groups of low-voltage asynchronous motors connected to the auxiliary busbar B.u. negative-sequence and zero-sequence systems with connections at the short-circuit location F1 for the 0 at a line-to-earth calculation Ik1 short circuit Figure A.BS 7639:1993 Page Figure A. with asynchronous motors M1 and M2 according to Figure A. Uncontrolled Copy. © BSI 62 58 64 61 67 66 76 72 81 79 80 82 84 15 50 4 © BSI 04-2000 .5 Table A. page 72.II — Collection of results for Example 1 (Un = 380 V) Table A.5 — Medium voltage 33 kV/6 kV system with asynchronous motors (complex calculation for Example 2) Figure A.VII — Data of low-voltage asynchronous motors and data of transformers 10 kV 0.693 kV and 10 kV/0. Partial short-circuit currents of the low-voltage motors at the short-circuit location F3 Page 52 54 59 55 Licensed copy:DRAKE & SCULL ENGINEERING LTD.6 — Network feeder.VI — Data of high-voltage motors and their partial short-circuit currents at the short-circuit location on busbars B or C respectively Table A.4 kV respectively connected to the auxiliary busbar B. Example 2 Figure A. Example 3 Figure A.8 — Detail of Figure A. power-station unit (PSU) — unit transformer and generator — with auxiliary transformer (AT). negative-sequence and zero-sequence short-circuit impedances Table A.7 — Positive-sequence system for the calculation of the partial 0 short-circuit current I kM–AT from high-voltage and low-voltage motors at the short-circuit location F2. Impedances are transferred to the high-voltage side of the auxiliary transformer AT with tr = 21 kV/10. high-voltage and low voltage asynchronous motors.1 — Low-voltage system with short-circuit locations F1. T2 ) for Example 2.3 — Positive-sequence. Example 1 Figure A.6. without the influence of asynchronous motors M1 and M2 (CB1 and CB2 open) Table A.]) for Example 2. page 52) for the 0 and i at the calculation of Ik p short-circuit location F1 Figure A.10 — Positive-sequence system 0 at the short-circuit for the calculation of Ik location F4 Table I — Voltage factor c Table II — Calculation of short-circuit currents of asynchronous motors in the case of a short circuit at the terminals Table A.9 — Positive-sequence system 0 at the for the calculation of Ik short-circuit location F3 Figure A.I — Data of equipment for Example 1 and positive-sequence.1. F2 and F3. 12/02/2004.IV — Calculation of *Xk (per unit [p.III — Calculation of Xk (7) for Example 2.V — Calculation of Z k ( T1.5 kV = 2 Figure A.4 — Medium voltage 33 kV/6 kV system with asynchronous motors.2 — Positive-sequence system (according to Figure A. if they give at least the same precision. adjusted to particular circumstances.c. treated in Section 1. based on the rated data of the electrical equipment and the topological arrangement of the system has the advantage of being possible both for existing systems and for systems at the planning stage. by a relatively low resistance or impedance. The calculation of the short-circuit impedance. an equivalent voltage source at the short-circuit location is considered. for example the superposition method. 12/02/2004. © BSI 04-2000 5 . practicable and concise procedure leading to conservative results with sufficient accuracy. the following definitions apply. — in high-voltage three-phase a. An application guide. as described under Clause 6. This does not exclude the use of special methods. This standardized procedure is given in such a form as to facilitate as far as possible its use by non-specialist engineers. One has to distinguish between — systems with short-circuit currents having no a. In existing low-voltage systems it is possible to determine the short-circuit impedance on the basis of measurements at the location of the prospective short circuit considered. For this purpose. This standard does not deal with installations on board ships and areoplanes. for example. by measurement on a network analyzer.2 short-circuit current an over-current resulting from a short circuit due to a fault or an incorrect connection in an electric circuit (IEV 441-11-07) NOTE It is necessary to distinguish between the short-circuit current at the short-circuit location and in the network branches.c. For the calculation of the thermal equivalent short-circuit currents see Section 2 of IEC Publication 865. systems and a technical report on the derivation of the parameters and various calculation factors of this standard are under consideration. Uncontrolled Copy.1 short circuit the accidental or intentional connection. Reference is made to the International Electrotechnical Vocabulary (IEV) [IEC Publication 50] when applicable. systems. This standard does not cover short-circuit currents deliberately created under controlled conditions (short-circuit testing stations). treated in Section 2. of two or more points in a circuit which are normally at different voltages (IEV 151-03-41) 3. for the selection of fuses and for the setting of protective devices and for checking the run-up of motors.c. or with a digital computer. © BSI 2 Object The object of this standard is to establish a general. systems with nominal voltages up to 380 kV operating at nominal frequency (50 Hz or 60 Hz). This section also includes the influence of motors. 3 Definitions For the purpose of this standard.BS 7639:1993 1 Scope This standard is applicable to the calculation of short-circuit currents: — in low-voltage three-phase a.c. — systems with short-circuit currents having decaying a. — the minimum short-circuit current which can be a basis. components (near-to-generator short circuit). There are two different short-circuit currents to be calculated which differ in their magnitude: — the maximum short-circuit current which determines the capacity or rating of electrical equipment. Short-circuit currents and short-circuit impedances may also be determined by system tests. 3. Licensed copy:DRAKE & SCULL ENGINEERING LTD.c. component decay (far-from-generator short circuit). dealing with non-meshed low-voltage three-phase a. Uncontrolled Copy. the aperiodic component of current.12 equivalent electric circuit a model to describe the behaviour of a circuit by means of a network of ideal elements (IEV 131-01-33) 6 © BSI 04-2000 . pages 11 and 31) 3. (aperiodic) component iDC of short-circuit current the mean value between the top and bottom envelope of a short-circuit current decaying from an initial value to zero according to Figure 1 and Figure 12 3.s. the nominal system voltage Un (see Sub-clause 3. current of an asynchronous motor with locked rotor fed with rated voltage UrM at rated frequency 3.m. if any.14).m. value of the a.3). value of an integral cycle of the symmetrical a.8 peak short-circuit current ip the maximum possible instantaneous value of the prospective (available) short-circuit current (see Figure 1 and Figure 12) NOTE The magnitude of the peak short-circuit current varies in accordance with the moment at which the short circuit occurs.C. Sequential faults are not considered. 3.5 0 initial symmetrical short-circuit current Ik the r. © BSI the r. 12/02/2004.6 0 initial symmetrical short-circuit (apparent) power S k 0 the fictive value determined as a product of the initial symmetrical short-circuit current Ik (see Sub-clause 3. value of the short-circuit current which remains after the decay of the transient phenomena (see Figure 1 and Figure 12.c.BS 7639:1993 3.10 steady-state short-circuit current Ik The r. The calculation of the peak three-phase short-circuit current ip applies for the phase conductor and moment at which the greatest possible short-circuit current exists.7 D. which can lead to higher aperiodic components of short-circuit current. 3. symmetrical component of a prospective (available) short-circuit current (see Sub-clause 3. and the factor 3 : 3. component of the prospective short-circuit current at the instant of contact separation of the first pole of a switching device 3.9 symmetrical short-circuit breaking current Ib the r.s. For three-phase short circuits it is assumed that the short circuit occurs simultaneously in all phase conductors.3) applicable at the instant of short circuit if the impedance remains at zero-time value (see Figure 1 and Figure 12.s. Investigations of non-simultaneous short circuits. symmetrical component of a prospective (available) short-circuit current (see Sub-clause 3. pages 11 and 31) 3.s.m. are beyond the scope of this standard.11 symmetrical locked-rotor current ILR The highest symmetrical r.m.3 prospective (available) short-circuit current the current that would flow if the short circuit were replaced by an ideal connection of negligible impedance without any change of the supply NOTE The current in a three-phase short circuit is assumed to be made simultaneously in all poles.s.5). value of the a. being neglected 3.c.m.4 symmetrical short-circuit current Licensed copy:DRAKE & SCULL ENGINEERING LTD.c. page 15]. Values are given in IEC Publication 38 Licensed copy:DRAKE & SCULL ENGINEERING LTD. page 15] 3.20.3 zero-sequence short-circuit impedance Z ( 0 ) of a three-phase a.14 nominal system voltage Un voltage (line-to-line) by which a system is designated and to which certain operating characteristics are referred. The 3.c.1 and Figure 4 c). This is the only active voltage of the network 3. 12/02/2004. component of prospective (available) short-circuit current remains essentially constant (see Clause 7) 3. — changing of transformer taps.20 Short-circuit impedances at the short-circuit location F 3. system the impedance of the zero-sequence system as viewed from the short-circuit location [see Sub-clause 8.13 (independent) voltage source an active element which can be represented by an ideal voltage source independent of all currents and voltages in the circuit. page 15] 3. system the impedance of the negative-sequence system as viewed from the short-circuit location [see Sub-clause 8.BS 7639:1993 3.19 near-to-generator short circuit a short circuit to which at least one synchronous machine contributes a prospective initial symmetrical short-circuit current which is more than twice the generator’s rated current. 3 . in series with a passive circuit element (IEV 131-01-37) 3.1 and Figure 4 b).16 voltage factor c the ratio between the equivalent voltage source and the nominal system voltage Un divided by values are given in Table I NOTE The introduction of a voltage factor c is necessary for various reasons. — the subtransient behaviour of generators and motors.c. or a short circuit to which synchronous and asynchronous motors contribute more than 5 % of the initial symmetrical short-circuit 0 without motors (see Clause 10) current I k 3. system the impedance of the positive-sequence system as viewed from the short-circuit location [see Sub-clause 8.s.20.3.c.3.1 and Figure 4 a).18 far-from-generator short circuit a short circuit during which the magnitude of the symmetrical a.m. value of the symmetrical internal voltage of a synchronous machine which is active behind the 0 at the moment of short circuit subtransient reactance Xd 3.1 positive-sequence short-circuit impedance Z ( 1 ) of a three-phase a.2 negative-sequence short-circuit impedance Z ( 2 ) of a three-phase a. © BSI 3.20.3. These are: — voltage variations depending on time and place. Uncontrolled Copy.15 equivalent voltage source cUn/ 3 the voltage of an ideal source applied at the short-circuit location in the positive-sequence system for calculating the short-circuit current according to Clause 6.17 subtransient voltage E¾: of a synchronous machine the r.c. — neglecting loads and capacitances by calculations according to Clause 6. It includes three times the neutral-to-earth impedance 3 Z NE © BSI 04-2000 7 . 3.s.22 0 of a synchronous machine subtransient reactance X d the effective reactance at the moment of short circuit.) Steady-state short-circuit current at the terminals (poles) of a generator with compound excitation Ew f Ib Ik IkP 8 © BSI 04-2000 .3. Uncontrolled Copy.3.) Steady-state short-circuit current (r.2) NOTE Index of symbol Z ( 1 ) may be omitted if there is no possibility of confusion with the negative-sequence and the zero-sequence short-circuit impedances.21 Short-circuit impedances of electrical equipment 3. for example.) Subtransient voltage of a synchronous machine Frequency (50 Hz or 60 Hz) Symmetrical short-circuit breaking current (r. It does not take into account adjustable time delays of tripping devices. if the three parallel phase conductors are used for the outgoing current and a fourth line and/or earth is joint return (see Sub-clause 8.c. 12/02/2004. 4.3.s.23 minimum time delay tmin of a circuit breaker the shortest time between the beginning of the short-circuit current and the first contact separation of one pole of the switching device NOTE The time tmin is the sum of the shortest possible operating time of an instantaneous relay and the shortest opening time of a circuit breaker.21.1 for the calculation of three-phase short-circuit currents 3.2) 3. the result in per unit is represented by a small letter x d '' = Xd '' / ZrG . The symbols represent quantities possessing both numerical values and dimensions that are independent of units.1 Symbols A c cU n / 3 Initial value of aperiodic component Voltage factor Equivalent voltage source (r. provided a coherent unit system is chosen.BS 7639:1993 3. system abbreviated expression for the positive-sequence short-circuit impedance Z( 1 ) according to Sub-clause 3. 3. voltage source.21.4 short-circuit impedance Z k of a three-phase a.3 zero-sequence short-circuit impedance Z ( 0 ) of electrical equipment the ratio of the line-to-earth voltage to the short-circuit current of one phase of electrical equipment when fed by an a.2) 3. 4 Symbols. All equations are written without specifying units. For the calculation of short-circuit currents the 0 is taken saturated value of X d 2 0 in ohms is divided by the rated impedance Z NOTE When the reactance X d rG = U rG / S rG of the synchronous machine.m. subscripts and superscripts Symbols of complex quantities are underlined.c.m. © BSI the ratio of the line-to-neutral voltage to the short-circuit current of the corresponding phase of electrical equipment when fed by a symmetrical positive-sequence system of voltages (see Sub-clause 8.20.m.s.21.20. the International System of Units (SI).2 negative-sequence short-circuit impedance Z ( 2 ) of electrical equipment the ratio of the line-to-neutral voltage to the short-circuit current of the corresponding phase of electrical equipment when fed by a symmetrical negative-sequence system of voltages (see Sub-clause 8. for example: Z = R + jX .1 positive-sequence short-circuit impedance Z ( 1 ) of electrical equipment Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12/02/2004. Xq XdP X″ q d resp.m. U(0 ) X resp. zero-sequence voltage Reactance. direct axis respectively quadrature axis Fictitious reactance of a generator with compound excitation in the case of steady-state short circuit at the terminals (poles) if the excitation is taken into account Subtransient reactance of a synchronous machine (saturated value). U( 2 ) .) Locked-rotor current of an asynchronous motor Decaying aperiodic component of short-circuit current Peak short-circuit current Correction factor for impedances Total loss in transformer windings at rated current Factor for the calculation of breaking currents of asynchronous motors Nominal cross section Resistance. È0 = 4.m. X ″ Xd est Z resp. r RG S″ k Sr tf tmin tr Un Ur uks uRr U( 1 ) . tr U 1 Nominal system voltage. line-to-line (r. direct axis respectively quadrature axis Reciprocal of the short-circuit ratio Impedance. system Positive-sequence short-circuit impedance Negative-sequence short-circuit impedance Zero-sequence short-circuit impedance Efficiency of asynchronous motors Factor for the calculation of the peak short-circuit current Factor for the calculation of the steady-state short-circuit current Factor for the calculation of the symmetrical short-circuit breaking current Absolute permeability of vacuum. Uncontrolled Copy./10–7 H/m Resistivity Phase angle ILR iDC ip K PkvT Licensed copy:DRAKE & SCULL ENGINEERING LTD. absolute respectively relative value Synchronous reactance.BS 7639:1993 I″ k or I ″ k3 Initial symmetrical short-circuit current (r.) Rated voltage.c. x Xd resp. z Zk Z( 1) Z( 2) Z( 0) ½ x Æ È È0 A Î 4.s.s.m. absolute respectively relative value Fictitious resistance of a synchronous machine when calculating I'' k and ip Initial symmetrical short-circuit power (apparent power) Rated apparent power of electrical equipment Fictitious transformation ratio Minimum time delay Rated transformation ratio (tap changer in main position). © BSI q qn R resp.s.) Rated short-circuit voltage in percent Rated ohmic voltage in percent Positive-.2 Subscripts (1) Positive-sequence component © BSI 04-2000 9 . line-to-line (r. negative-. absolute respectively relative value Short-circuit impedance of a three-phase a. high-voltage winding of a transformer Low-voltage. line current respectively earth current Licensed copy:DRAKE & SCULL ENGINEERING LTD. L2. Uncontrolled Copy. 2. kE2E Line-to-line short circuit with earth connection. low-voltage winding of a transformer Line Locked rotor Line 1. system Terminal. medium-voltage winding of a transformer Neutral of a three-phase a. L3 M ù MV N P PSU Q T 4. line-to-neutral short circuit Line-to-line short circuit without earth connection Maximum Minimum Nominal value (IEV 151-04-01) Rated value (IEV 151-04-03) Resulting Transformed value Auxiliary transformer Busbar Earth Fault. pole Power-station unit (generator and transformer) Feeder connection point Transformer k2E resp.c. 3 of a three-phase system Asynchronous motor or group of asynchronous motors Without motor Medium-voltage. © BSI max min n r rsl t AT B E F G HV LV L LR L1.BS 7639:1993 (2) (0) f k or k3 k1 k2 Negative-sequence component Zero-sequence component Fictitious Three-phase short circuit Line-to-earth short circuit. 12/02/2004. short-circuit location Generator High-voltage.3 Superscripts ¾ ½ Initial (subtransient) value Resistance or reactance per unit length 10 © BSI 04-2000 . 1.2. 9.c. In meshed networks there are several time constants.3. That is why it is not possible to give an easy exact method of calculating ip and iDC. pages 11 and 31). For the determination of the asymmetrical short-circuit breaking current the decaying aperiodic component iDC of the short-circuit current as shown in Figure 1 or Figure 12 may be calculated with sufficient accuracy by: (1) where: Ik '' f t = initial symmetrical short-circuit current = nominal frequency 50 Hz or 60 Hz = time R/X = ratio according to Sub-clause 9. In most practical cases a determination like this is not necessary. 12/02/2004. and is nearly reached if the short circuit starts at zero voltage.1.1.1. corresponding to the instantaneous value of the voltage at the beginning of short circuit (see Figure 1 and Figure 12. Special methods to calculate ip with sufficient accuracy are given in Sub-clause 9.3.s. it is of interest to know the r. Uncontrolled Copy. The value ip depends on the time constant of the decaying aperiodic component and the frequency f. © BSI Ik '' ip Ik iDC A = = = = = initial symmetrical short-circuit current peak short-circuit current steady-state short-circuit current decaying (aperiodic) component of short-circuit current initial value of the aperiodic component iDC Figure 1 — Short-circuit current of a far-from-generator short circuit (schematic diagram) 5 Calculation assumptions A complete calculation of short-circuit currents should give the currents as a function of time at the short-circuit location from the initiation of the short circuit up to its end. Depending on the application of the results. that is on the ratio R/X or X/R of the short-circuit impedance Z k .2.m. value of the symmetrical a. component and the peak value ip of the short-circuit current following the occurrence of a short circuit.2.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD.2 © BSI 04-2000 11 .2 or 9.1. 3. excitation of generators and so on are dispensable.3. 3) Arc resistances are not taken into account. that is.1).3. 2) Tap changers of the transformers are assumed to be in main position.1. shall be neglected. it is useful to calculate the short-circuit currents by the method of symmetrical components (see Sub-clause 8. Furthermore. tap changer position of transformers.2 — Method A — the right hand side of equation (1) should be multiplied by 1.15. with this method all line capacitances and parallel admittances of non-rotating loads. the recommended short-circuit calculations have acceptable accuracy. According to Sub-clause 9.3. synchronous and asynchronous machines are replaced by their internal impedances (see Sub-clause 8.092 < 25Ï 0. Operational data on the static load of consumers. © BSI where f = 50 Hz or 60 Hz. For balanced and unbalanced short circuits as shown in Figure 2.1 and 11. The equivalent voltage source is the only active voltage of the system. 12/02/2004.BS 7639:1993 In meshed networks according to Sub-clause 9. 6 Equivalent voltage source at the short-circuit location In all cases in Sections 1 and 2 it is possible to determine the short-circuit current at the short-circuit location F with the help of an equivalent voltage source. 12 © BSI 04-2000 . except those of the zero-sequence system (see Sub-clauses 8.27 < 5Ï 0. Furthermore.2 — Method B — the equivalent frequency should be selected as follows: 2Ïft fc/f < 2Ï 0.4).055 Licensed copy:DRAKE & SCULL ENGINEERING LTD.2). the calculation of maximum and minimum short-circuit currents is based on the following simplifications: 1) For the duration of the short circuit there is no change in the number of circuits involved. additional calculations about all the different possible load flows at the moment of short circuit are superfluous. a three-phase short-circuit remains three phase and a line-to-earth short circuit remains line-to-earth during the time of short circuit.1. page 13. While these assumptions are not strictly true for the power systems considered.15 < 10Ï 0. Uncontrolled Copy. All network feeders. page 14.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. and 3 . on average. it seems adequate to choose a voltage factor c according to Table I. Parallel admittances (e. is represented only by its internal impedance ZQ (see Sub-clause 8.3. © BSI a) Balanced three-phase short circuit. Figure 3. All other active voltages in the system are assumed to be zero. c) Line-to-line short circuit with earth connection.g. page 14. Thus the network feeder in Figure 3 a). by more than + 5 % (LV) or + 10 % (HV) approximately from the nominal voltage.5 % or + 4 %. The voltage factor c is different for the calculation of maximum or minimum short-circuit currents.1). The actual regulator or tap changer position of transformers in the case of far-from-generator short circuits may be disregarded without unacceptable loss of accuracy by use of this method. The direction of current arrows is chosen arbitrarily Finally high-voltage transformers in many cases are equipped with regulators and tap changers operating under load flow conditions. If there are no national standards.15) at the short-circuit location F is composed of the voltage factor c. considering that the highest voltage in a normal system does not differ. the nominal system voltage Un.3 applies in conjunction with the equivalent voltage source at the short-circuit location irrespective of whether a far-from-generator short-circuit according to Section 1 or a near-to-generator short-circuit according to Section 2 is involved. d) Line-to-earth short circuit. for example + 2.3. The equivalent voltage source cU n / 3 (see Sub-clause 3. line capacitances and passive loads) are not to be considered when calculating short-circuit currents in accordance with Figure 3 b). page 14. © BSI 04-2000 13 . The modelling of the system equipment by means of impedances according to Sub-clauses 8. shows an example of the equivalent voltage source at the short-circuit location F as the sole active voltage of the system in the case of a low-voltage system fed by a single transformer. Uncontrolled Copy. 12/02/2004. Figure 2 — Characterization of short circuits and their currents. b) Line-to-line short circuit without earth connection.2.2 and 11. whereas transformers feeding low-voltage systems have normally only a few taps.5. BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. b) Equivalent circuit diagram (positive-sequence system). 0 in Figure 3 — Illustration for calculating the initial symmetrical short-circuit current I k compliance with the procedure for the equivalent voltage source 14 © BSI 04-2000 . Uncontrolled Copy. © BSI a) System diagram. 12/02/2004. system at the short-circuit location F Table I — Voltage factor c Voltage factor c for the calculation of Nominal voltage Un maximum short-circuit current cmax minimum short-circuit current cmin Low voltage 100 V to 1 000 V (IEC Publication 38.05 1.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. Table I) a) 230 V/400 V b) Other voltages Medium voltage > 1 kV to 35 kV (IEC Publication 38. © BSI 04-2000 15 . © BSI Figure 4 — Short-circuit impedance of a three-phase a.00 1.00 1. Uncontrolled Copy.c. 12/02/2004.III) High voltage > 35 kV to 380 kV (IEC Publication 38.10 1.00 cUn should not exceed the highest voltage Um for equipment of power systems.IV) NOTE 1. Table A.00 1. Table A.10 0.95 1. 1 and XTLV in accordance with Sub-clause 8. page 13]. This assumption is generally satisfied in power systems fed from extended high-voltage systems through transformers.c.m.BS 7639:1993 In this way the equivalent voltage source for the calculation of the maximum short-circuit current can be established. In the event of a short circuit near to a transformer with neutral earthing or a neutral-earthing transformer. In three-phase systems the calculation of the current values resulting from unbalanced short circuits is simplified by the use of the method of symmetrical components which requires the calculation of three independent system components. Details of calculation are given in Clause 9. a quasi-stationary voltage condition). according to Table I. it is sufficient to take into account only the positive-sequence short-circuit impedance Z ( 1 ) = Z k as seen from the fault location (see Sub-clause 8.2 Unbalanced short circuit The following types of unbalanced (asymmetrical) short circuits are treated in this standard: — line-to-line short circuit without earth connection [see Figure 2 b). page 13.2. components I ″ k and Ik are r. avoiding any coupling of mutual impedances. Uncontrolled Copy.10 U n / 3 in medium and high-voltage systems. nor any significant change in the impedance of the circuit (i. 8 Short-circuit parameters 8.2.3. 12/02/2004. Therefore.05 U n / 3 in other low-voltage systems cU n / 3 = 1.1). gives schematically the general course of the short-circuit current in the case of a far-from-generator short circuit.3. page 13]. page 11. may a priori be regarded as far-from-generator short circuits if XTLV W 2 XQt with XQt to be calculated in accordance with Sub-clause 8. Systems with short-circuit currents having no a. page 14.3. component with constant amplitude during the whole short circuit.s. is of special interest. the three-phase short-circuit current is the largest. constant and linear impedances). 8. the line-to-earth short-circuit current may be greater than the three-phase short-circuit current. values and are nearly equal in magnitude. by: cU n / 3 = 1. 50 Hz cU n / 3 = 1. component decay (far-from-generator short circuits) 7 General This section refers to short circuits where there is no change for the duration of the short circuit in the voltage or voltages that caused the short-circuit current to develop (i.e. — the aperiodic component beginning with an initial value A and decaying to zero. — line-to-line short circuit with earth connection [see Figure 2 c). (2a) (2b) (2c) Licensed copy:DRAKE & SCULL ENGINEERING LTD.e. that is in the case of a far-from-generator short circuit.c. 16 © BSI 04-2000 .00 U n / 3 in low-voltage systems 230 V/400 V.or z-winding on the low voltage side of the transformer. As a rule. This applies in particular to transformer of vector group Yz. Dy and Dz when earthing the y. © BSI Section 1. In calculating the short-circuit current.c. Single-fed short-circuits supplied by a transformer according to Figure 3. because this kind of fault often leads to the highest values of prospective (available) short-circuit current and the calculation becomes particularly simple on account of the balanced nature of the short circuit. Figure 1.c. the prospective (available) short-circuit current can be considered as the sum of the following two components: — the a. The symmetrical a. system in accordance with Figure 2 a). — line-to-earth short circuit [see Figure 2 d). page 13].1 Balanced short circuit The balanced three-phase short circuit of a three-phase a.2. In this case Z k = Z ( 1 ) (see Sub-clauses 3. © BSI (3b) (3c) (4) Each of the three symmetrical component systems has its own impedance (see Sub-clause 8. The deviation depends on several parameters of the system. 12/02/2004.3 Short-circuit impedances For the purpose of this standard. Uncontrolled Copy.4). © BSI 04-2000 17 . earth system.3. When calculating short-circuit currents in accordance with Clause 9. When calculating unbalanced short-circuit currents in medium or high-voltage systems and applying an equivalent voltage source at the short-circuit location.1 and 3. the line zero-sequence capacitances and zero-sequence parallel admittances of non-rotating loads are to be considered for isolated neutral systems and resonant earthed systems. When calculating short-circuit currents in accordance with Clause 9. Neglecting the line zero-sequence capacitances in earthed neutral systems leads to results which are higher than the real values of the short-circuit currents. 8. In low-voltage systems. In this section. when a symmetrical system of voltages of negative-sequence phase order is applied to the short-circuit location F. Taking the line L1 as reference. page 15. if an a. voltage is applied between the short-circuited lines and the common returns (e. the currents in each line are found by superposing the currents of three symmetrical component systems: — positive-sequence current I ( 1 ) . for example the length of the line between transformers with neutral earthing. — zero-sequence current I ( 0 ) . The values of positive-sequence and negative-sequence impedances can differ from each other only in the case of rotating machines.g. page 15. negative-sequence and zero-sequence short-circuit impedances shall be considered. The results of the short-circuit calculation have an acceptable accuracy also in the case of untransposed lines.20. The method of the symmetrical components postulates that the system impedances are balanced. The zero-sequence short-circuit impedance Z ( 0 ) at the short-circuit location F is obtained according to Figure 4 c). 8. cable sheaths.BS 7639:1993 Using this method. page 15. all line capacitances and parallel admittances of non-rotating loads are neglected. IL2 and IL3 are given by: (3a) Licensed copy:DRAKE & SCULL ENGINEERING LTD. earth wires. all line capacitances and parallel admittances of non-rotating loads are neglected. For the calculation of balanced three-phase short circuits. neutral conductor. where far-from-generator short circuits are calculated. — negative-sequence current I( 2 ) . cable armouring). the currents IL1 .c. when a symmetrical system of voltages of positive-sequence phase order is applied to the short-circuit location F and all synchronous and asynchronous machines are replaced by their internal impedances. the positive-sequence impedance is the only relevant impedance. for example in the case of transposed lines.20. line capacitances and parallel admittances of non-rotating loads can be neglected. According to the calculation with symmetrical components positive-sequence. The negative-sequence short-circuit impedance Z ( 2 ) at the short-circuit location F is obtained according to Figure 4 b). it is generally allowed to take Z ( 2 ) = Z ( 1 ) . one has to make a distinction between short-circuit impedances at the short-circuit location F and short-circuit impedances of individual electrical equipment.3).1 Short-circuit impedances at the short-circuit location F The positive-sequence short-circuit impedance Z( 1 ) at the short-circuit location F is obtained according to Figure 4 a). page 19.1 Network feeders If a short circuit in accordance with Figure 6 a). earthing device. b) Transformer of vector group Yz.3. 12/02/2004. positive-sequence and negative-sequence short-circuit impedances are equal: When calculating the zero-sequence short-circuit impedance of a line. cables.c. 8. reactors and similar equipment.2.3. earth. c) Neutral-earthing transformer in zig-zag connection. d) Line (overhead line or cable).BS 7639:1993 Except for special cases.g. voltage between the three paralleled conductors and the joint return (e. Z ( 0 ) = U ( 0 ) ⁄ I( 0 ) is determined by assuming an a. for instance [see Figure 5 d). overhead lines. equal to or smaller than Z ( 1 ). JR: joint return. neutral conductor. Uncontrolled Copy. the zero-sequence short-circuit impedances differ from the positive-sequence short-circuit impedances. In this case. then the equivalent impedance ZQ of the network (positive-sequence short-circuit impedance) at the feeder connection point Q should be determined by: (5a) 18 © BSI 04-2000 .2 Short-circuit impedances of electrical equipment In network feeders. Licensed copy:DRAKE & SCULL ENGINEERING LTD. © BSI a) Transformer of vector group Dy. cable sheath and cable armouring). Normally the zero-sequence short-circuit impedances differ from the positive-sequence short-circuit impedances: Z ( 0 ) may be larger than. earth wire. Figure 5 — Measuring of zero-sequence short-circuit impedances of electrical equipment (examples) 8. the three-fold zero-sequence current flows through the joint return. transformers. page 18]. is fed from a network in which only the initial symmetrical short-circuit power S ″ kQ or the initial symmetrical short-circuit current I ″ kQ at the feeder connection point Q is known. the equivalent zero-sequence short-circuit impedance of network feeders is not required for calculations. then the equivalent kQ impedance ZQt referred to the low-voltage side of the transformer may be determined by: (5b) where: UnQ = nominal system voltage at the feeder connection point Q S″ kQ = initial symmetrical short-circuit apparent power at the feeder connection point Q I″ kQ = initial symmetrical short-circuit current at the feeder connection point Q c tr = voltage factor [see Sub-clause 3. In other cases.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. is fed by a transformer from a medium or high-voltage network in which only the initial symmetrical short-circuit power S ″ kQ or the initial symmetrical short-circuit current I ″ at the feeder connection point Q is known. Table I and Equation (2)] = rated transformation ratio at which the tap-changer is in the main position (see also Sub-clause 8. © BSI a) Without transformer. the equivalent impedance Z Q may be considered as a reactance. 12/02/2004. Figure 6 — System diagram and equivalent circuit diagram for network feeders If a short circuit in accordance with Figure 6 b). The initial symmetrical short-circuit power S ″ kQ or the initial symmetrical short-circuit current I ″ kQ on the high-voltage side of the supply transformers shall be given by the supply company. Z Q = 0 + j X Q . i. it may be necessary to consider this impedance.e. one may substitute RQ = 0. In general. page 19. however. if no accurate value is known for the resistance RQ of network feeders. In special cases. b) With transformer.1 XQ where XQ = 0.16.4) In the case of high-voltage feeders with nominal voltages above 35 kV fed by overhead lines. © BSI 04-2000 19 . Uncontrolled Copy.995 ZQ. The zero-sequence short-circuit impedances Z ( 0 ) T = R( 0 ) T + j X( 0 ) T of transformers with two or more windings may be obtained from the manufacturer.2. The resistive component can be calculated from the total loss in the windings at the rated current.05. Uncontrolled Copy. Special considerations are necessary. — the minimum short-circuit voltage uk min is considerably lower than the rated short-circuit voltage in the main position (uk min < ukr). page 22. The ratio X/R generally increases with transformer size.BS 7639:1993 8. or Figure 6 b). Z B and Z C referring to Figure 7. currents and voltages according to Sub-clause 8. 12/02/2004. NOTE It is sufficient for transformers with tap-changers to determine ZT in accordance with formula (6) for the main position and to convert the impedances. © BSI (8) where: UrT = rated voltage of the transformer on the high-voltage or low-voltage side IrT = rated current of the transformer on the high-voltage or low-voltage side SrT = rated apparent power of the transformer PkrT = total loss of the transformer in the windings at rated current ukr = rated short-circuit voltage. page 14. Resistance must be considered if the peak short-circuit current ip or the decaying aperiodic component iDC is to be calculated.2 Transformers The positive-sequence short-circuit impedances of two-winding transformers Z T = RT + j X T can be calculated from the rated transformer data as follows: (6) (7) Licensed copy:DRAKE & SCULL ENGINEERING LTD. page 19].3. In the case of three-winding transformers. — it is possible to change the transformation ratio of a transformer with the tap changer in a wide range. UTHV = UrTHV (1 ± pT) with pT > 0. in per cent uRr = rated ohmique voltage. the positive-sequence short-circuit impedances ZA . For large transformers the resistance is so small that the impedance may be assumed to consist only of reactance when calculating short-circuit current magnitude. can be calculated by the three short-circuit impedances (related to side A of the transformer): (9a) (9b) (9c) 20 © BSI 04-2000 . only if: — a single fed short-circuit current is calculated and the short-circuit current has the same direction as the operational current before the short-circuit occurs [short circuit on the low-voltage side of one transformer or parallel transformers with tap changers according to Figure 3. in per cent The necessary data may be taken from rating plates or obtained from the manufacturer. — the voltage during operation is considerably higher than the nominal system voltage (U W 1.4 using the rated transformation ratio tr corresponding to the tap-changer in the main position.05 Un). 2. between sides B and C 8.3 Overhead lines and cables The positive-sequence short-circuit impedances ZL = RL + j X L may be calculated from the conductor data. For measurement of the zero-sequence short-circuit impedances Z ( 0 ) = R( 0 ) + j X ( 0 ) . Sometimes it is possible to calculate the zero-sequence impedances with the ratios R(0)L/RL et X(0)L/XL. 12/02/2004.2 and Figure 5 d). The impedances Z ( 1 ) L and Z ( 0 ) L of low-voltage and high-voltage cables depend on national techniques and standards and may be taken from text-books or manufacturer’s data.3. page 18. given in percent. see Sub-clause 8. between sides A and C ukrBC = rated short-circuit voltage. © BSI (10c) where: UrTA = rated voltage SrTAB = rated apparent power between sides A and B SrTAC = rated apparent power between sides A and C SrTBC = rated apparent power between sides B and C ukrAB = rated short-circuit voltage. given in percent.3.BS 7639:1993 with the formulae: (10a) (10b) Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy. given in percent. such as the cross sections and the centre-distances of the conductors. between sides A and B ukrAC = rated short-circuit voltage. The effective resistance per unit length RL ′ of overhead lines at the medium conductor temperature 20 °C may be calculated from the nominal cross section qn and the resistivity Õ: (11) with: and © BSI 04-2000 21 . respectively the centre of bundles with the bundle radius R = radius of a single conductor. 8.2. assuming geometric symmetry.4 Short-circuit current limiting reactors The positive-sequence. Short-circuit current limiting reactors shall be treated as a part of the short-circuit impedance. 12/02/2004. 22 © BSI 04-2000 . b) Equivalent circuit diagram (positive-sequence system).5 Motors Synchronous motors are to be treated as synchronous generators (see Section 2). Figure 7 — Three-winding transformer (example) The reactance per unit length X ′L for overhead lines may be calculated.2. assuming transposition. In the case of conductor bundles. © BSI a) Denotation of winding connections. for single conductors n = 1 Taking È0 = 4Ï · 10–4 H/km as the permeability of a vacuum. the short-circuit currents of asynchronous motors decay rapidly. Asynchronous motors in low-voltage and medium-voltage systems supply short-circuit currents to the short-circuit location. In the case of three-phase balanced short circuits. from: (12a) where: d r n = geometric mean distance between conductors.3.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy.3. the negative-sequence and the zero-sequence short-circuit impedances are equal. r is to be substituted by = number of bundled conductors. equation (12a) may be simplified as follows: (12b) (12c) 8. 1.3.1) Resistances of the order of Rk < 0.1.1 Initial symmetrical short-circuit current I ″ k In accordance with Figure 3.2 Peak short-circuit current ip Because the short circuit is fed by a series circuit.4 Conversion of impedances. Voltages and currents are to be convened by the rated transformation ratio tr or t.2) Xk = XQt + XT + XL = sum of series-connected reactances in accordance with Figure 3 b) (see Sub-clause 8.1.2. currents and voltages from one level to the other [e. Uncontrolled Copy. corresponding to the actual position if it is known. see Figure 3 b). Sub-clause 11. 12/02/2004.5) Licensed copy:DRAKE & SCULL ENGINEERING LTD. The scope of Section 1 supports the following equation: Ik = I b = I ″ k (15) 9.3.1. 8. For per unit or other similar unit systems no conversion is necessary. the peak short-circuit current can be expressed by: ip = x 2 I″ k (16) © BSI 04-2000 23 . the three-phase initial symmetrical short-circuit current I ″ k becomes: (14) where: cU n / 3 = equivalent voltage source (see Clause 6) Rk = RQt + RT + RL = sum of series-connected resistances in accordance with Figure 3 b). page 14.3.5. © BSI I″ k = short-circuit current at the short-circuit location without the influence of motors In other cases see Section 2.1 Calculation method for balanced short circuits 9. page 14.2) = short-circuit impedance (see Sub-clause 8.1.1 Single fed three-phase short circuit 9. The impedances of the equipment in superimposed or subordinated networks are to be divided or multiplied by the square of the rated transformation ratio tr or in special cases by the square of the transformation ratio t. The impedance of the system feeder Z Qt = R Qt + j X Qt .1. The supplement of short-circuit currents of asynchronous motors to the current I ″ k may be neglected if: (13) where: CIrM = sum of the rated currents of motors in the neighbourhood of the short-circuit location (see Section 2. 9 Calculation of short-circuit currents 9. referred to the voltage of that transformer side where the short circuit occurs.3 Xk may be neglected. page 14].g.3.3. it is necessary to convert impedances.BS 7639:1993 It is not necessary to take into account asynchronous motors or groups of asynchronous motors which have a total rated current less than 1 % of the initial symmetrical short-circuit current I ″ k calculated without the influence of motors. is to be calculated according to equations (5a) and (5b) and additional information in Sub-clause 8. if these systems are coherent. currents and voltages When calculating short-circuit currents in systems with different voltage levels. RL is the line resistance for a conductor temperature of 20 °C (see Sub-clause 8. 1. fed from sources which are not meshed with one another in accordance with Figure 9.1.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. where the branch short-circuit currents flow together as shown in Figure 9. Impedances between the short-circuit location F and the busbar B. calculations are made in accordance with Sub-clause 9.1. In most cases the phase angles of the branch short-circuit currents are nearly the same. may be composed of the various separate branch short-circuit currents which are independent of each other: I″ k = I″ kT1 + I ″ kT2 Ik = Ib = I ″ k (17) (18) The branch short-circuit currents are to be calculated like a single-fed three-phase short-circuit current in accordance with Sub-clause 9. fed from sources which are not meshed with one another in accordance with Figure 9. b) ratio X/R The factor x for the ratios R/X and X/R is taken from Figure 8.3.1 Initial symmetrical short-circuit current I ″ k The initial symmetrical short-circuit current I ″ k . NOTE The short-circuit current at the short-circuit location F is the phasor sum of the branch short-circuit currents. 12/02/2004.2 Three-phase short circuit fed from non-meshed sources 9. Uncontrolled Copy.05 U n ⁄ ( 3 I ″ kB ) . The factor x may also be calculated by the approximate equation: 9.2.1. In all other cases. The short-circuit current at F is then equal to the algebraic sum of the branch short-circuit currents. the symmetrical breaking current Ib and the steady-state short-circuit current Ik at the short-circuit location F. page 25. © BSI Figure 8 — Factor x for series circuits as a function of: a) ratio R/X. may be neglected if they are smaller than 0.2. may be composed of the branch short-circuit currents ipT1 and ipT2: ip = ipT1 + ipT2 (19) 24 © BSI 04-2000 . where I ″ is the initial symmetrical short-circuit current on the busbar determined by equation (17) with kB a three-phase busbar short circuit. 9.1.1.2 Peak short-circuit current ip The peak short-circuit current ip at the short-circuit location F. ) 9. Uncontrolled Copy. according to Sub-clause 8.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12/02/2004. page 15 (positive-sequence short-circuit impedance at the short-circuit location F).3.3 Three-phase short circuits in meshed networks 9.3.3. The network feeder is treated in accordance with Sub-clause 8. by network transformation (e. page 26. It is generally necessary to ascertain the short-circuit impedance Z k = Z ( 1 ) . page 15 For the calculation of Ib and Ik.1.g. All impedances are referred to the low-voltage side of the transformers (see Figure 10).2. The calculation is to be carried out in accordance with Sub-clause 8. especially with Figure 4 a). © BSI Figure 9 — System diagram illustrating a short circuit fed from several sources which are independent of one another (In some cases the impedance between busbar B and the short-circuit location F may be neglected. © BSI 04-2000 25 . (20) where: cU n / 3 = equivalent voltage source (see Clause 6) Zk = short-circuit impedance. parallel connection and deltastar transformation) considering the positive-sequence short-circuit impedances of electrical equipment (see Sub-clause 8. series connection. the equivalent voltage source cU n / 3 is established at the short-circuit location as the only active voltage in the network.1 Initial symmetrical short-circuit current I ″ k In accordance with the example shown in Figure 10.1 and Figure 4 a).3.1.2).1.3.1. see Equation (15). Z T2 = impedances referred to the low-voltage side of the transformers. Method A — Uniform ratio R/X or X/R: use x = xa. the Method A is sufficient.2 Peak short-circuit current ip For the calculation of the peak short-circuit current ip in meshed networks Equation (16) is used and one of the following approximations A. Z Qt . The short-circuit current at the short-circuit location F is supplied by the feeder connection point Q through transformers T1 and T2 9. Z T1 . Uncontrolled Copy. page 24. If high accuracy is not needed. or C is chosen to find a suitable value for x. 12/02/2004. taking the smallest ratio of R/X or the largest ratio X/R of all branches of the network.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. © BSI a) System diagram. 26 © BSI 04-2000 .3. B. The factor xa is determined from Figure 8. b) Equivalent circuit diagram with the equivalent voltage source in accordance with Clause 6.1. Figure 10 — Illustration of the calculation of the initial symmetrical short-circuit current I ″ k in a meshed network. page 13.0. Figure 11. Any branch may be a series combination of several elements. if Z(2)/Z(1) < 1 (see Section 2). Method C — Equivalent frequency fc: use x = xc. © BSI 04-2000 27 .15 xb (21) Licensed copy:DRAKE & SCULL ENGINEERING LTD.15 xb is limited to 1. fc Lc is the impedance as seen from the short-circuit location if an equivalent voltage source with the frequency fc = 20 Hz (for a nominal frequency 50 Hz) or 24 Hz (for a nominal frequency 60 Hz) is applied there as the only active voltage. shows which type of short circuit leads to the highest short-circuit currents if the a.BS 7639:1993 It is only necessary to choose the branches which together carry 80 % of the current at the nominal voltage corresponding to the short-circuit location. Method B — Ratio R/X or X/R at the short-circuit location: The factor x is given by: x = 1. calculated with the frequency f = 50 Hz or f = 60 Hz. component decays. In Section 1 Z(2)/Z(1) = 1 is valid.8. © BSI where 1. The factor xc is found from Figure 8 for the ratio (22a) (22b) where: Zc Rc Xc = Rc + jXc = Re { Z } s R at power frequency c Equivalent effective resistance for the equivalent frequency fc as seen from the short-circuit location = lm { Z } s X at power frequency c Equivalent effective resistance for the equivalent frequency fc as seen from the short-circuit location The equivalent impedance Z c = R c + j2 .8 and in high-voltage networks to 2.c. In low-voltage networks the value xa is limited to 1. page 28. i. 9. Uncontrolled Copy. 12/02/2004.2 Calculation method for line-to-line and line-to-earth short circuits The types of short circuit considered are given in Figure 2 b) to Figure 2 d).e. In low-voltage networks the product 1.15 is a safety factor to cover inaccuracies caused by using the ratio R/X from a meshed network reduction with complex impedances. The factor xb is found from Figure 8 for the ratio R/X given by the short-circuit impedance Z k = Rk + j X k at the short-circuit location F. 1 Initial short-circuit current I ″ k2 Independent of system configuration. page 13] is calculated by: (23) Z( 1 ) = Z k is the positive-sequence short-circuit impedance at the short-circuit location F [see Figure 4 a). The ratio I ″ k2 to I ″ k according to Equations (20) and (23) is: (24) 28 © BSI 04-2000 . the initial short-circuit current of a line-to-line short circuit without earth connection [see Figure 2 b).BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD.2. Uncontrolled Copy. 12/02/2004.2. page 15].1 Line-to-line short circuit without earth connection 9.1. © BSI Figure 11 — Chart indicating the type of short-circuit giving the highest current 9. 2.2 depending on the system configuration. page 13. flowing to earth and/or grounded wires according to Figure 2 c). 12/02/2004. To calculate the value of I ″ k2E .1.2.2.2.2. the following formulae are given: (27a) (27b) with Z ( 1 ) = Z ( 2 ) a and a 2 are given in Sub-clause 8. The same value as used in the case of a three-phase short circuit may be taken.2 or 9.2. Equation (4).1. is calculated by: (29) In the case of a far-from-generator short circuit. the steady-state short-circuit current Ik1 and the breaking current Ib1 are equal to the initial short-circuit current I ″ k1 [see also Equations (15) and (25)]: I k1 = I b1 = I ″ k1 (30) © BSI 04-2000 29 . the steady-state short-circuit current Ik2 and the short-circuit breaking current Ib2 are equal to the initial short-circuit current I ″ k2 : I k2 = Ib2 = I ″ k2 9.2. one has to distinguish between the currents I ″ k2E and I ″ kE2E .1 Initial short-circuit currents I ″ k2E and I ″ kE2E According to Figure 2 c). The initial short-circuit current I ″ kE2E.2 Line-to-line short circuit with earth connection 9.2.3 Line-to-earth short circuit 9.1 Initial short-circuit current I ″ k1 The initial short-circuit current of a line-to-earth short circuit according to Figure 2 d).1. is calculated by: (28) 9.3.3.2. Uncontrolled Copy.2 Peak short-circuit current ip2 The peak short-circuit current can be expressed by: ip2 = x 2 Ik2 ″ (26) (25) Licensed copy:DRAKE & SCULL ENGINEERING LTD.1. page 13.BS 7639:1993 In the case of a far-from-generator short circuit. 9. page 13. 9.2 Peak short-circuit current ip2E It is not necessary to calculate ip2E because either: ip3 U ip2E or ip1 U ip2E. © BSI The factor x is calculated according to Sub-clause 9. 2.3. For simplification.1).3.3 The minimum short-circuit currents 9. The influence of motors is also taken into account. the same value as used in the case of a three-phase short circuit may be taken.BS 7639:1993 9. for example operational voltage of cables or overhead lines.2. Systems with short-circuit currents having decaying a. the values of Table I may be used. © BSI The value of the voltage factor c depends on many influences. Section 2. components.2 Initial symmetrical short-circuit current I ″ k When calculating three-phase short-circuit currents according to Sub-clause 9. When calculating unbalanced short circuits according to Sub-clause 9. aluminium and aluminium alloy. it is necessary to introduce the following conditions: — voltage factor c for the calculation of minimum short-circuit current according to Table I.c.1.2 or 9.2 Peak short-circuit current ip1 The peak short-circuit current can be expressed by: ip1 = x 2 Ik1 '' (31) The factor x is calculated according to Sub-clauses 9.1 are chosen. the minimum initial short-circuit current is given by: (33) Zk = Z ( 1 ) is the short-circuit impedance under the conditions of Sub-clause 9. phase conductors and neutral conductors) are to be introduced at a higher temperature: (32) where RL20 is the resistance at a temperature of 20 °C and Úe in °C the conductor temperature at the end of the short circuit.c.3. location of short circuit. 30 © BSI 04-2000 .3.2 depending on the system configuration. The factor 0. If there are no national standards. in some cases.3. 9.1. resistances RL of lines (overhead lines and cables. Uncontrolled Copy.3. components (near-to-generator short circuits) 10 General This section gives procedures for calculations in systems with short-circuit currents having decaying a. For lines in low-voltage systems it is sufficient to take Fe = 80 °C. the minimum contribution from sources and network feeders. — choose the system configuration and.1. Procedures for the calculation of short-circuit currents of synchronous and asynchronous motors are given if their contribution is higher than 5 % of the initial symmetrical short-circuit current I ″ k without motors (see Sub-clause 13.1.1 General When calculating minimum short-circuit currents.004/°C is valid for copper.1. 12/02/2004. which lead to a minimum value of short-circuit current at the short-circuit location. the equivalent voltage source cU n / 3 and impedances Z( 1 ) and Z ( 0 ) under the conditions of Sub-clause 9.2. Licensed copy:DRAKE & SCULL ENGINEERING LTD. 9. — motors are to be neglected. This is possible if the d. time constant of a synchronous machine is larger than the subtransient time constant.c. breaking current. some periods after the short circuit took place.c. the short-circuit current behaves generally as shown in Figure 12.c. The decaying aperiodic component iDC can be calculated according to Clause 5. In general the symmetrical short-circuit breaking current Ib is smaller than the initial symmetrical short-circuit current I ″ k . it is of interest not only to know the initial symmetrical short-circuit current I ″ k and the peak short-circuit current ip. This phenomenon is not dealt with in detail by short-circuit currents calculated in this standard. it will be necessary to determine the asymmetrical short-circuit breaking current from the a.1 General In the calculation of the short-circuit currents in systems supplied by generators. page 31. power-station units and motors (near-to-generator short circuits). In a near-to-generator short circuit. © BSI I'' k ip Ik = initial symmetrical short-circuit current = peak short-circuit current Figure 12 — Short-circuit current of a near-to-generator short circuit (schematic diagram) = steady-state short-circuit current iDC = decaying (aperiodic) component of short-circuit current A = initial value of the aperiodic component iDC © BSI 04-2000 31 . especially when dealing with the mechanical effects of short-circuit currents.c. Uncontrolled Copy. In the case of a near-to-generator short circuit the prospective short-circuit current can be considered as the sum of the following two components: — the a. Licensed copy:DRAKE & SCULL ENGINEERING LTD. but also the symmetrical short-circuit breaking current Ib and the steady-state short-circuit current Ik. component with decaying amplitude during the short circuit. In some special cases it could happen that the decaying short-circuit current reaches zero for the first time. 12/02/2004. — the aperiodic component beginning with an initial value A and decaying to zero. breaking current and the superimposed d. Normally the steady-state short-circuit current Ik is smaller than the symmetrical short-circuit breaking current Ib. Frequently.BS 7639:1993 11 Short-circuit parameters 11. 2.3 and 12.4. Z can be neglected if nB Z < 0. b) Short circuit fed from non-meshed sources.4.2. 12. Calculation according to Sub-clauses 12. d) Short circuit in meshed networks.4.3 and 12. 12/02/2004.05 -------------------- U 3 I kB ″ I kB ″ is calculated according to Figure 13 b) 1) Generators and motors can also be connected without transformers.2. The figure also specifies which clause of this section describes the short-circuit current calculation.1: 12.3. © BSI c) Short circuit fed from several sources with the common impedance Z . 12.2: for the case shown in Item 1) of Figure 13 a)  for the case shown in Item 2) of Figure 13 a)   single fed three-phase short-circuit.3 and 12. The main sub-clauses for the calculation of the three-phase short-circuit currents are: — — 12. Licensed copy:DRAKE & SCULL ENGINEERING LTD. Calculation according to Sub-clauses 12.4. 32 © BSI 04-2000 .BS 7639:1993 a) Singled fed short circuit. Calculation according to Sub-clauses 12. Uncontrolled Copy.1.2.2.2.3.2. page 32. Figure 13 — Various short-circuit source connections Short-circuit currents may have one or more sources as shown in Figure 13.4. 12. 12. 12.4. Calculation according to Sub-clauses 12.2.2.3 and 12. 12. The internal voltages of all synchronous and asynchronous machines are set to zero. 11. Motors and generators are dealt with in Sub-clauses 11. The short-circuit impedances of network feeders.5 to 11.2. 11. impedances of generators and motors are introduced.8. synchronous motors and synchronous compensators are treated as synchronous generators (see Sub-clauses 11.3.8.2 are valid.8 and Clause 12). and Figure 20.5.5.2.5.3. 12/02/2004.3 Overhead lines and cables Details given in Sub-clause 8.3.6.7.5.5.3.3.3.1 Short-circuit impedances at the short-circuit location F For the calculation of the initial symmetrical short-circuit current in a near-to-generator short circuit Sub-clause 8.1).6. are valid.5 Motors When calculating three-phase initial symmetrical short-circuit currents Ik ″ . 11.3.5.3.5. Details for the equivalent voltage source cU n / 3 are given in Clause 6 and Table I.3.5.5. Uncontrolled Copy.2 are valid.5.1. 11. page 37.3 are valid.5.3. 11.8.3 Unbalanced short circuit The details of Sub-clause 8. network transformers. Figure 13 c) respectively.1 and Figure 4.2 Short-circuit impedances of electrical equipment The general considerations made in Sub-clause 8.3.3.1 are valid. Furthermore in this method all line capacitances and parallel admittances of non-rotating loads except those of the zero-sequence system shall be neglected (see Figure 15.BS 7639:1993 — — 12. if correction factors are introduced for the impedances of generators and for the impedances of generators and transformers of power-station units (see Sub-clauses 11.2.4 Equivalent voltage source at the short-circuit location It is possible in all cases to determine the short-circuit current at the short-circuit location F by means of an equivalent voltage source cU n / 3 .4 are valid. overhead lines and cables as well as short-circuit limiting reactors are valid.5.4: for the cases shown in Figure 13 b).2 are valid. for the general case shown in Figure 13 d) (three-phase short circuit in meshed networks).3.3. 11.8 and 13. 11. Details for consideration of motors are given in Clause 13.7 and 11.2.2.3 Calculation of short-circuit impedances of electrical equipment 11.5. Therefore the synchronous machines are only effective with their subtransient impedances and the asynchronous motors are only effective with their impedances calculated from their locked-rotor currents. 11.2 Transformers The details given in Sub-clause 8.3.1 Network feeders The details given in Sub-clause 8.2. page 42).2. 11.3. 11.1 are valid.5.2 Balanced short circuit The details of Sub-clause 8.4 Short-circuit current limiting reactors Details given in Sub-clause 8.5 Short-circuit impedances In addition to Sub-clause 8.5.3. © BSI 04-2000 33 .7.7 and 11.3.3.5.3.3.5. 11.3.5.5.3. Unit transformers of power-station units are excluded and dealt with in Sub-clauses 11. 11.2.5. Additional calculations are given for power-station units in Sub-clauses 11. page 15. if the given inequality is fulfilled (three-phase short-circuit fed from non-meshed sources). 11.3. Licensed copy:DRAKE & SCULL ENGINEERING LTD. except for the special case given in Sub-clause 12. In this method the equivalent voltage source cU n / 3 at the short-circuit location is the only active voltage of the system.3. © BSI 11. 11.3: 12. © BSI SrM ILR/IrM = ratio of the locked-rotor current (Sub-clause 3.2.1. with XM = 0.922 ZM for high-voltage motors with powers PrM per pair of poles W 1 MW. Uncontrolled Copy. 12/02/2004.6 Generators directly connected to systems When calculating three-phase initial symmetrical short-circuit currents in systems fed directly from generators without unit transformers.995 ZM 11. for example in industrial networks or in low-voltage networks. The following applies for static converter fed drives: ZM UrM IrM = as in Equation (34) = rated voltage of the static converter transformer on the network side or rated voltage of the static converter.3. if no transformer is present = rated current of the static converter transformer on the network side or rated current of the static converter.42.989 ZM RM/XM = 0.BS 7639:1993 The impedance ZM = RM + jX M of asynchronous motors in the positive. with XM = 0. for high-voltage motors with powers PrM per pair of poles < 1 MW.sequence system can be determined by: (34) where: UrM IrM = rated voltage of the motor = rated current of the motor = rated apparent power of the motor SrM = PrM/(½r cos Îr) Licensed copy:DRAKE & SCULL ENGINEERING LTD.11) to the rated current of the motor The following may be used with sufficient accuracy: RM/XM = 0.995 ZM RM/XM = 0.10. with XM = 0. Details for consideration or omission of asynchronous motors or groups of asynchronous motors for calculation of short-circuit currents are given in Sub-clause 13.5. if no transformer is present ILR/IrM = 3 RM/XM = 0. for low-voltage motor groups with connection cables. Static converter fed drives are treated for the calculation of short-circuit currents in a similar way as asynchronous motors. the following impedance has to be used in the positive-sequence system: (35) with the correction factor: (36) where: cmax = voltage factor according to Table I Un = nominal voltage of the system UrG = rated voltage of the generator Z GK = corrected impedance of the generator ZG = impedance of the generator ( Z G = R G + j Xd ″) x″ d ÎrG = subtransient reactance of the generator referred to rated impedance ( x ″ d / Z rG ) d = X″ = phase angle between I rG and U rG / 3 34 © BSI 04-2000 .15.and negative.10 with XM = 0. 3. (38) For the calculation of short-circuit currents for line-to-line and line-to-earth short circuits (Sub-clause 12. also take account of the decay of the a. 12/02/2004.05 X ″ d for generators with UrG > 1 kV and SrG W 100 MVA RG = 0.07 and 0. component of the short-circuit current during the first half-period after the short circuit took place.5. The following values of sufficient accuracy may be used: RG = 0.3) the correction factor according to Equation (36) shall be taken into account. component. Uncontrolled Copy. 0.15.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD.c.15 X ″ d for generators with UrG u 1 000 V In addition to the decay of the d. For the impedances of synchronous generators in the negative-sequence system and the zero-sequence system the following applies: (37) For salient-pole synchronous machines with differing values of X ″ d and X ″ q.7 Generators and unit transformers of power-station units In this case correction factors for the impedances of generators and transformers of power-station units have to be introduced: (39) © BSI 04-2000 35 .c.1.2. the factors 0.1 instead of the subtransient voltage E¾ of the synchronous generator (see Figure 14). the correction factor KG [Equation (36)] for the calculation of the corrected impedance Z GK [Equation (35)] of the generator has to be introduced. © BSI Figure 14 — Phasor diagram of a synchronous generator at rated conditions Using the equivalent voltage source cU n / 3 according to Sub-clause 12.05. NOTE The effective resistance of the stator of synchronous machines lies generally much below the given values for RG.07 X ″ d for generators with UrG > 1 kV and SrG < 100 MVA RG = 0. 11. The influence of various winding-temperatures on RG is not considered. Uncontrolled Copy.3. PSU = corrected impedances of generators (G) and unit transformers (T) of power-station units ZG Z TLV x″ d .2.5.1.3. © BSI where: Z G. © BSI 04-2000 36 .2) = impedance of the generator Z = nominal system voltage at the connection point Q of the power-station unit = rated transformation ratio at which the tap-changer is in the main position = fictitious transformation ratio tf = Un/UrG = UnQ/UrG = (see Sub-clause 11. PSU = cmax (42) Licensed copy:DRAKE & SCULL ENGINEERING LTD. ÎrG = impedance of the generator Z G = R G + j Xd ″ (see Sub-clause 11.3. PSU are converted by the fictitious transformation ratio tf to the high-voltage side (see Sub-clause 12. 12/02/2004.2. 11.2.2). PSU . Special considerations are recommended if for a power-station unit having a transformer with a tap changer the operational voltage UQmin is permanently higher than UnQ (UQmin > UnQ).2) = (see Sub-clause 11.3. ÎrG xT NOTE 1 Equation (44) is valid if UQ = UnQ and UG = UrG.6) = impedance of the unit transformer related to the low-voltage side (see Sub-clause 8.3.5. NOTE 1 Equations (40) and (42) are valid if UQ = UnQ and UG = UrG. Special considerations are recommended if for a power-station unit having a transformer with a tap changer the operational voltage UQmin is permanently higher than UnQ (UQmin > UnQ). PSU and Z T.6) 2 ⁄ S . For the calculation of short-circuit currents at short circuits between generator and unit transformer of a power-station unit the equivalent voltage source cU rG / 3 at the short-circuit location is to be introduced.3.5.5. Z T.3. NOTE 2 Values for correction factors for negative-sequence impedances and zero-sequence impedances at unbalanced short circuits are under consideration.6) G = impedance of the unit transformer related to the high-voltage side (see Sub-clause 8.5. NOTE 2 Values for correction factors for negative-sequence impedances and zero-sequence impedances at unbalanced short circuits are under consideration. In this case the rated voltage of the generator is chosen. and/or UG differs from UrG (UG > UrG) or for a power-station unit having a transformer without a tap changer the voltage UG of the generator is permanently higher than UrG (UG > UrG). These cases are dealt with in Sub-clause 12.8 Power-station units For the calculation of short-circuit currents of power-station units for short circuits on the high-voltage side it is not necessary to deal with the correction factors according to Sub-clause 11. because the nominal system voltage cannot be determined.7. In this case the following formula for the correction of the impedance of the whole power-station unit (PSU) is used: (43) with the correction factor: (44) where: Z PSU ZG Z THV UnQ tr tf = corrected impedance of power-station unit related to the high-voltage side = R G + j Xd ″ (see Sub-clause 11.3.6) If necessary the impedances ZG.5.3. and/or UG differs from UrG (UG > UrG) or for a power-station unit having a transformer without a tap changer the voltage UG of the generator is permanently higher than UrG (UG > UrG).2. x = X ⁄ (U 2 ⁄ S ) = reactance of the unit transformer related to U rT rT T T rT rT x″ d .BS 7639:1993 with the correction factor: (40) (41) with the correction factor: KT. This procedure is not allowed when calculating the peak short-circuit current ip. 12/02/2004.1 General For the calculation of the initial symmetrical short-circuit current I ″ k .1 Short circuit fed from one generator 12.1.1 Initial symmetrical short-circuit current I ″ k The initial symmetrical short-circuit current for the examples of item 1) of Figure 13 a).6 Conversion of impedances.6. b) Equivalent circuit (positive-sequence system) with the subtransient voltage E¾ of the generator.3 and especially to Sub-clause 11.1. 9.3.2.BS 7639:1993 11. page 37. the value of the voltage factor c is chosen according to Table I. page 32. currents and voltages The details given in Sub-clause 8. © BSI 12.1 are to be regarded. 12.23) and the ratio I ″ k / I rG .2. Licensed copy:DRAKE & SCULL ENGINEERING LTD.5. Ib = È I ″ k where È is dependent on the minimum time delay tmin (see Sub-clause 3.the symmetrical short-circuit breaking current Ib and the steady-state short-circuit current Ik at the short-circuit location.3. (46) c) Equivalent circuit for the calculation with the equivalent voltage source (see Clause 6 and Sub-clause 11. 12 Calculation of short-circuit currents 12. 12.3. Exceptions in the Sub-clauses 12.2. Figure 15 — Example for the calculation of the initial symmetrical short-circuit current I ″k for a short circuit fed directly from one generator © BSI 04-2000 37 . the system may be converted by transformations into an equivalent short-circuit impedance Zk . NOTE Normally it can be presumed that the rated voltage UrG of the generator is 5 % higher than the nominal system voltage Un.1.2 Peak short-circuit current ip The calculation of the peak short-circuit current is done as shown in Sub-clause 9.2 Calculation method for balanced short circuits 12.1 and 12. is calculated with the equivalent source voltage cU n / 3 at the short-circuit location and the short-circuit impedance Z k = Rk + jX k : (45) For calculation of the maximum short-circuit current.3 Symmetrical short-circuit breaking current Ib The decay to the symmetrical short-circuit breaking current is taken account of with the factor È.2. a) System diagram.2).2.5.2 and 9. and of Figure 15. For the generator the corrected resistance KGRG and the corrected reactance KG X ″ d is used. Uncontrolled Copy. In this case it is necessary to distinguish between systems with and without parallel branches (see Sub-clauses 9.1.1.4 remain valid.1.2.4) and the impedances according to Sub-clause 11.2.2.1.1.2.1.2. The factor È may also be obtained from Figure 16 taking the abscissa for three-phase short circuit. If I ″ kG / I rG u 2. salient-pole generators and synchronous compensators are excited by rotating exciters or by static converter exciters (provided that for static exciters the minimum time delay is less than 0. Figure 16 — Factor È for the calculation of short-circuit breaking current Ib 38 © BSI 04-2000 . replace I ″ kG / I rG by I ″ kM / I rM (see Table II). apply È = 1 at every minimum time delay tmin. In the case of asynchronous motors.1 s. The calculation of low-voltage breaking currents after a time delay tmin > 0.1 s is not included in these procedures. (47) Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy.6 times the rated load excitation-voltage). For all other cases È is taken to be È = 1 if the exact value is unknown. © BSI The values I ″ kG (partial short-circuit current at the terminals of the generator) and IrG are related to the same voltage. generator manufacturers may be able to provide information. Figure 16 can also be used for compound excited low-voltage generators with a minimum time delay tmin u 0. 12/02/2004.BS 7639:1993 The values of È of the following equations apply to the case where medium voltage turbine generators. For other values of minimum time delay. linear interpolation between curves is acceptable.25 s and the maximum excitation-voltage is less than 1. 2.3 times the rated excitation at rated load and power factor for turbine generators [see Figure 17 a)] or 1. Uncontrolled Copy. Æmax-curves of Series One are based on the highest possible excitation-voltage according to either 1. Æmax-curves of Series Two are based on the highest possible excitation-voltage according to either 1.0 times the rated excitation for salient-pole machines [see Figure 18 b)].1.) © BSI 04-2000 39 .6 times the rated excitation at rated load and power factor for turbine generators [see Figure 17 b)] or 2. The methods of calculation given here can be regarded as a sufficient estimate for the upper and lower limits. a) Maximum steady-state short-circuit current Ik max The following may be set at the highest excitation of the synchronous generator for the maximum steady-state short-circuit current: Ik max = Æmax IrG (48) Æmax may be obtained from Figure 17 or Figure 18 for turbine generators or salient-pole machines. in the case when the short circuit is fed by one generator or one synchronous machine respectively.BS 7639:1993 12. Licensed copy:DRAKE & SCULL ENGINEERING LTD.4 Steady-state short-circuit current Ik Because the magnitude of the steady-state short-circuit Ik depends upon saturation influences and switching-condition changes in the system its calculation is less accurate than that of the initial symmetrical short-circuit current I ″ k . © BSI Figure 17 — Factors Æmax and Æmin for turbine generators (Definitions of Series One and Series Two are given in the text. xd sat (sat = saturated) is the reciprocal of the short-circuit ratio.6 times the rated excitation for salient-pole machines [see Figure 18 a)]. 12/02/2004. © BSI Figure 18 — Factors Æmax and Æmin for salient-pole machines (Definitions of Series One and Two are given in the text. constant no-load excitation of the synchronous machine is assumed.5. Uncontrolled Copy. 12/02/2004.8) in series with a line impedance Z L = R L + jX L according to Sub-clause 8.BS 7639:1993 b) Minimum steady-state short-circuit current Ik min For the minimum steady-state short-circuit current.3. 40 © BSI 04-2000 .2. NOTE For bus fed static exciters without current forcing the minimum steady-state short-circuit current for a three-phase bus short circuit is zero. and in Figure 19 the initial symmetrical short-circuit current is calculated with the equivalent voltage source cU n / 3 at the short-circuit location and the corrected impedances of the generator and the transformer of the power-station unit (Sub-clauses 11.5.3. Licensed copy:DRAKE & SCULL ENGINEERING LTD.2 Short circuit fed from one power-station unit 12.3.2.2.2.7 or 11.3. page 32.) 12. Ik min = Æmin IrG (49) Æmin may be obtained from Figure 17 or Figure 18 for turbine generators or salient-pole machines.1 Initial symmetrical short-circuit current I ″ k For the examples in Item 2) of Figure 13 a). 1. if Z < 0.3 with È according to Equation (47) or Figure 16. page 32].05 UnB/( 3 I ″kB ) holds [see Figure 13 c). Uncontrolled Copy.2.3.2 Peak short-circuit current ip The calculation is done as shown in Sub-clause 9. 12/02/2004. if the short circuit is fed by one power-station unit. page 38.2.3.3.1. Insert the transformed value I ″ kPSUt = t r I ″ kPSU in place of I ″ . © BSI a) System diagram.3 Three-phase short circuit fed from non-meshed sources 12.2.8 are used.5.7: (50) Z G.4 Steady-state short-circuit current Ik The calculation can be done as shown in Sub-clause 12. Both impedances are to be transformed to the high-voltage side with the fictitious transformation ratio tf = Un/UrG.1 General In addition to short circuits fed from non-meshed sources [see Figure 13 b).1.2.5. b) Equivalent circuit diagram of the positive-sequence system for the calculation with the equivalent voltage source at the short-circuit location and the corrected impedances of the generator and the transformer of the power-station unit.PSU from Equation (41).3 Symmetrical short-circuit breaking current Ib The calculation of the symmetrical short-circuit breaking current is done as shown in Sub-clause 12. Figure 19 — Example of the calculation of the initial symmetrical short-circuit current I ″ k fed from one power-station unit For the calculation of the initial symmetrical short-circuit current Equation (45) should be used. Insert the transformed value I ″ kPSUt = t r I ″ kPSU in place of I ″ kG .PSU is taken from Equation (39) and Z T.2. For power-station units the corrected resistances and the corrected reactances according to Sub-clause 11. © BSI 04-2000 41 . can be calculated by the procedure given in this sub-clause.2.5.2.5.8 the short-circuit impedance for the example in Figure 19 is given by: (51) Z PSU is taken from Equation (43). 12.2.4.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12.2. Following Sub-clause 11.3.1. all short circuits directly fed through a common impedance Z .2.7 and 11. The short-circuit impedance for the example in Figure 19 is given by the following in accordance with Sub-clause 11.3. 12.2. kG 12. page 32]. BS 7639:1993 In general the equivalent voltage source cU n / 3 is introduced [see Figure 20 c)] at the short-circuit location. Un is the nominal voltage of the system in which the short circuit occurs. Generators, feeding the short circuit directly (without transformers) are to be treated as given in Sub-clause 11.5.3.6, power-station units according to Sub-clauses 11.5.3.7 or 11.5.3.8 and 12.2.2 and asynchronous motors as shown in Sub-clause 11.5.3.5, taking into account Clause 13. Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI a) System diagram. b) Equivalent circuit diagram of the positive-sequence system with the subtransient voltages E¾. c) Equivalent circuit diagram of the positive-sequence system for the calculation with the equivalent voltage source cU n / 3 at the short-circuit location. Figure 20 — Example of the calculation of the initial symmetrical short-circuit current I ″k fed from non-meshed sources 42 © BSI 04-2000 BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI Figure 21 — Short-circuit currents and partial short-circuit currents for three-phase short circuits between generator and transformer of a power-station unit and at the auxiliary busbar A (see also Sub-clause 12.2.4.1) For calculating, the partial, short-circuit currents I ″kG and I ″ kT at a short circuit in F1 in Figure 21, the initial symmetrical short-circuit currents are given by: (52) (53) where: Z G,PSU Z T,PSU Z Q min = according to Sub-clause 11.5.3.7, Equation (39) = according to Sub-clause 11.5.3.7, Equation (41) tf = UnQ/UrG = fictitious transformation ratio, Sub-clause 11.6 = minimum value of the impedance of the network feeder, corresponding to S ″ kQ max For S ″kQ max the maximum possible value expected during the life time of the power station is to be introduced. For the calculation of the short-circuit current I ″ k at the short-circuit location F2, for example at the connection to the high-voltage side of the auxiliary transformer AT in Figure 21, it is sufficient to take: (54) The short-circuit current I ″ kAT at the short-circuit location F3 has to be treated according to Sub-clause 12.2.4.1. © BSI 04-2000 43 BS 7639:1993 12.2.3.2 Initial symmetrical short-circuit current I ″ k The initial symmetrical short-circuit current at the short-circuit location F can be calculated from the sum of the partial short-circuit currents as shown in Figure 22. Motors are taken into account by the application of Clause 13. (55) A simpler result, to be on the safe side, is gained by using the algebraic sum of values instead of the geometric sum. Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI Figure 22 — Explanation of the calculation of I ″ k, ip, Ib and Ik for a three-phase short circuit fed from non-meshed sources according to equations (55) to (58) 12.2.3.3 Peak short-circuit current ip, symmetrical short-circuit breaking current Ib and steady-state short-circuit current Ik If the three-phase short circuit is fed from several non-meshed sources according to Figure 22 the components of the peak short-circuit current ip and the symmetrical short-circuit breaking current Ib at the short-circuit location F are added: ip = ipPSU + ipT + ipM + . . . Ib = IbPSU + I ″ kT + IbM + . . . Ik = IbPSU + I ″ kT + . . . (56) (57) (58) The simple formulae (57) and (58) give results which are on the safe side. The partial short-circuit currents should be calculated as follows: — network feeders according to Sub-clause 8.3.2.1, — generators without transformers between the generator and the short-circuit location as in Sub-clause 12.2.1, — power-station units as in Sub-clause 12.2.2, taking into account Sub-clauses 11.5.3.7 and 11.5.3.8, — motors as in Sub-clause 11.5.3.5 and Clause 13. This directive does not apply to the steady-state short-circuit current Ik. It is assumed that generators fall out of step and produce a steady-state short-circuit current IkG . IbG or IkPSU . IbPSU. For network feeders I k = I b = I ″ k is valid. There is no motor supplement to the three-phase steady-state short-circuit current (see Table II). 44 © BSI 04-2000 12/02/2004. the arithmetic mean value can be used. The impedances of electrical equipment are calculated according to Sub-clause 11..4 Three-phase short circuit in meshed networks 12. trn. tr2. © BSI 04-2000 45 . © BSI a) System diagram.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. page 43 (short-circuit 2 and to transform this impedance by t rAT . For the calculation of the partial short-circuit current I ″ location F3). Equation (45) is used.1 Initial symmetrical short-circuit current I ″ k The initial symmetrical short-circuit current is calculated with the equivalent voltage source cU n / 3 at the short-circuit location. it is permitted to take Z rsl from Equation (54) kAT in Figure 21. Figure 23 — Example of the calculation of the initial symmetrical short-circuit current I ″k in a meshed network fed from several sources 12. b) Equivalent circuit diagram for the calculation with the equivalent voltage source cU n / 3 at the short-circuit location. If there are several transformers with slightly differing rated transformation ratios tr1. Figure 13 d). page 32.2. Uncontrolled Copy. and Figure 23 show examples for meshed networks with several sources. between two systems..5.3 (see also Sub-clause 12. * Impedance of a motor or an equivalent motor of a motor group. The impedances in systems connected beyond transformers to the system in which the short circuit occurs have to be transformed by the square of the rated transformation ratio.2).2.4. .2. 1. © BSI NOTE A more accurate calculation can be done with the following equations: (60) (61) (62) where: cU n ----------3 = equivalent voltage source at the short-circuit location = initial symmetrical short-circuit current.4.BS 7639:1993 12.2 to 12.1.2.2. page 38) with I ″ kGi ⁄ I rGi or I ″ kMj ⁄ I rMj respectively = (see Sub-clause 13.2.3 Symmetrical short-circuit breaking current Ib The following may be set for the short-circuit breaking current in meshed networks: Ib = I ″ k (59) Currents calculated with Equation (59) are larger than the real symmetrical short-circuit breaking currents.4.3.4. (42) and (44). 12/02/2004. symmetrical short-circuit breaking current with influence of all network feeders. Uncontrolled Copy. page 49) I″ k . 12.4. consider Sub-clauses 12. Licensed copy:DRAKE & SCULL ENGINEERING LTD.4. 12. % U ″Mj = initial voltage difference at the connection points of the synchronous machine i and the asynchronous motor j I″ kGi .2.3 Calculation method for line-to-line and line-to earth short circuits The details given in Sub-clause 9.3 remain valid.2. 46 © BSI 04-2000 .1 and Figure 25. 12. Careful reflection is necessary for the impedance correction factors in the equations (36).2. especially in the case of underexcited operation.4 The minimum short-circuit currents 12.2 remain valid. Ib % U ″Gi . (40). synchronous machines and asynchronous motors = parts of the initial symmetrical short-circuit current of the synchronous machine i and the asynchronous motor j = (see Sub-clause 12.4. 12. I ″ kMj È q The values of Equations (61) and (62) are related to the same voltage.4.1 General The details given in Sub-clause 9. In addition.4 Steady-state short-circuit current Ik The steady-state short-circuit current Ik may be calculated by: (63) is the initial symmetrical short-circuit current calculated without motors.2 Peak short-circuit current ip The calculation can be done as given in Sub-clause 9.3 and Figure 16. 4.4 Initial short-circuit currents at unbalanced short circuits The initial short-circuit currents at unbalanced short circuits are calculated according to Sub-clauses 9. This procedure is also applied for short circuits.1 Short-circuit fed from one generator If a short circuit is fed from one generator as shown in Figure 15. 12. Use the voltage factor cmin according to Table I. page 37.2 and 12. according to the circuit diagram (interlocking) or to the process (reversible drives).4. apply Sub-clause 12.2 Initial symmetrical short-circuit current I ″ k 12.2 Short circuit in meshed networks For the calculation use Sub-clause 12. 12. This value IkP should be obtained from the manufacturer. for example in networks of chemical and steel industries and pump-stations.2.2. Low-voltage motors are to be taken into account in auxiliaries of power-stations and in industrial and similar installations.4.2. and for unbalanced short circuits also to the steady-state short-circuit current Ik. which. motors may have constant field voltage and no regulators. fed by one or several similar and parallel working generators with compound excitation. In the calculation of short-circuit currents those high-voltage and low-voltage motors may be neglected. which are fed by several similar generators. 13. to the symmetrical short-circuit breaking current Ib. operated at one point in parallel. the symmetrical short-circuit breaking current Ib and the steady-state short-circuit current Ik. the peak short-circuit current ip.1 General High-voltage motors and low-voltage motors contribute to the initial symmetrical short-circuit current I ″ k. is done as follows: (64) For the effective reactance of the generators introduce: (65) Ikp is the steady-state short-circuit current of a generator with a three-phase terminal short circuit. © BSI 04-2000 47 .2.BS 7639:1993 12.4.1 and introduce a voltage factor cmin according to Table I for the calculation of the minimum short-circuit current. Motors in low-voltage public power supply systems may be neglected. Uncontrolled Copy. are not switched in at the same time. Motors and compensators with terminal-fed static exciters do not contribute to Ik.3 Steady-state short-circuit current Ik min fed from generators with compound excitation The calculation for the minimum steady-state short-circuit current in a near-to-generator short circuit. to the peak short-circuit ip. High-voltage motors have to be considered in the calculation of short circuit.4.2 Asynchronous motors 13. Exceptions are: no modification for internal voltage. © BSI 12. the synchronous motors and synchronous compensators are treated in the same way as synchronous generators. 12/02/2004.4 and a voltage factor cmin according to Table I.3. Licensed copy:DRAKE & SCULL ENGINEERING LTD. 13 Influence of motors 13.1 Synchronous motors and synchronous compensators When calculating the initial symmetrical short-circuit current I ″ k .2. © BSI ×PrM ×SrT = sum of the rated active powers of the high-voltage and the low-voltage motors which should be considered = sum of the rated apparent powers of all transformers.BS 7639:1993 High-voltage and low-voltage. 12/02/2004. Figure 24 — Example for the estimation of the contribution from the asynchronous motors in relation to the total short-circuit current 48 © BSI 04-2000 . through which the motors are directly fed = initial symmetrical short-circuit power at the feeder connection point Q without supplement of the motors S″ kQ The estimation according to Equation (66) is not allowed in the case of three-winding transformers. may be neglected in the calculation of currents for a short circuit at the feeder connection point Q (see Figure 24). Uncontrolled Copy. motors which are connected through two-winding transformers to the network in which the short circuit occurs. if: (66) where: Licensed copy:DRAKE & SCULL ENGINEERING LTD. groups of motors including their connection cables may be combined to an equivalent motor. For these equivalent asynchronous motors including their connection cables the following may be used: ZM IrM = [according to Equation (34)] = sum of the rated currents of all motors in a group of motors (equivalent motor) ILR/IrM = 5 RM/XM = 0.02 s  with m:  q = 0.05 s  the rated active power of motors (MW) q = 0.57 + 0.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. For simplification of the calculation. respectively XM = 1. see motor M4 in Figure 24.12 in m for tmin = 0. © BSI Figure 25 — Factor q for the calculation of the symmetrical short-circuit breaking current of asynchronous motors The factor q for the calculation of the symmetrical short-circuit breaking current for asynchronous motors may be determined as a function of the minimum time delay tmin: q = 1. 12/02/2004. The factor q may also be obtained from Figure 25.25 s   (67) If the calculation in Equation (67) provides larger values than 1 for q.26 + 0.12 in m for tmin = 0.10 s  per pair of poles  q = 0.03 + 0. Uncontrolled Copy.10 in m for tmin W 0.12 in m for tmin = 0. Low-voltage motors are usually connected to the busbar by cables with different lengths and cross-sections.3 m = 0. assume that q = 1.05 MW if nothing definite is known © BSI 04-2000 49 .79 + 0.42. g. short-circuit locations Q or A in Figure 24) it is possible to simplify the calculation of ZM according to Equation (34) with the rated current of the transformer T3 (IrT3. page 48.15) for motor powers per pair of poles < 1 MW xM = 1.3 Static converter fed drives Static converter fed drives (e. with I ″ kM / I rM q according to equation (67) or Figure 25. Table II — Calculation of short-circuit currents of asynchronous motors in the case of a short circuit at the terminals Short circuit Balanced short circuit Line-to-line short circuit Initial symmetrical short-circuit current Peak short-circuit current (69) (70) (73) (74) High-voltage motors: xM = 1.2.BS 7639:1993 For a short circuit at the busbar B in Figure 24.65 (corresponding to RM/XM = 0.3 and 12. Uncontrolled Copy.5. is the initial symmetrical short-circuit current at the short-circuit location B without supplement of the equivalent motor M4. as in rolling mill drives) are considered for three-phase short circuits only.5 for the equivalent motor of the static converter fed drive. In the case of a short circuit on the high-voltage side (e.10) for motor powers per pair of poles W 1 MW Low-voltage motor groups with connection cables xM = 1.g. 13.75 (corresponding to RM/XM = 0. © BSI 13. They do not contribute to the symmetrical short-circuit breaking current Ib.2 Terminal short circuit of asynchronous motors In the case of balanced and line-to-line short circuits at the terminals of asynchronous motors the currents I″ k .3. Ib and Ik are evaluated as shown in Table II.2. ip. (72) (76) 50 © BSI 04-2000 . For solid grounded systems the influence of motors on the line-to-earth short-circuit current cannot be neglected.4. page 49 Steady-state short-circuit Ik3M = 0 current 13. LV) in Figure 24 instead of the rated current IrM4 of the equivalent motor M4.2.3 Short circuit beyond an impedance For the calculation of the initial short-circuit currents according to Sub-clauses 12. Apply Sub-clause 11.3 (corresponding to RM/XM = 0. the partial short-circuit current of the low-voltage motor group M4 may be neglected.42) Symmetrical short-circuit I b3M = È qI ″k3M breaking current (71) (75) È according to equation (47) or Figure 16. if the rotational masses of the motors and the static equipment provide reverse transfer of energy for deceleration (a transient inverter operation) at the time of short circuit. page 38. Then they contribute only to the initial symmetrical short-circuit current I ″ k and to the peak short-circuit current ip. if the following condition holds: (68) IrM4 is the rated current of the equivalent motor M4.2. asynchronous motors are substituted by their impedances ZM according to Equation (34) in the positive-sequence and negative-sequence system. Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12/02/2004. BS 7639:1993 14 Consideration of non-rotating loads and capacitors Calculation methods are given in Sub-clauses 12.2 and 12. Uncontrolled Copy. the discharge current of the capacitors may be neglected for the calculation of the peak short-circuit currents.2 Series capacitors The effect of capacitors in series can be neglected in the calculation of short-circuit currents. acting if a short-circuit occurs. if they are equipped with voltage-limiting devices in parallel. © BSI © BSI 04-2000 51 . Licensed copy:DRAKE & SCULL ENGINEERING LTD. 14.3 which allow. as stated in Clause 6. 14.1 Parallel capacitors Regardless of the time of short-circuit occurrence. line capacitances and parallel admittances of non-rotating loads to be neglected. 12/02/2004. 1 Example 1: Calculation of short-circuit currents in a low-voltage system A. © BSI Figure A.1 Network feeder According to Equation (5b) with cQ = 1.1. negative-sequence and zero-sequence systems are given in Table A.I. Example 1 A. Uncontrolled Copy. (7) and (8) it follows that: Transformer T1: 52 © BSI 04-2000 .1. and ip shall be determined at the short-circuit locations F1 to F3 according to Section 1 (Systems with short-circuit currents having no a.2. The short-circuit currents I ″ k.1. component decay).2 Transformers According to equation (6).2 Determination of the positive-sequence impedances A.2.BS 7639:1993 Appendix A (informative) Calculation of short-circuit currents A.1 Problem A low-voltage system with Un = 380 V and f = 50 Hz is given in Figure A.1.1 (see Table I) it follows that: A. F2 and F3. The equipment data for the positive-sequence. Licensed copy:DRAKE & SCULL ENGINEERING LTD.1 — Low-voltage system with short-circuit locations F1.1. 12/02/2004.c. BS 7639:1993 Transformer T2: According to the calculation for transformer T1 it follows that: Licensed copy:DRAKE & SCULL ENGINEERING LTD.1.3 Lines (cables and overhead lines) Line impedances: Z L = Z ′L l Line L1 (two parallel cables): Line L2 (two parallel cables): Line L3 (cable): Line L4 (overhead line): © BSI 04-2000 53 .2. © BSI A. Uncontrolled Copy. 12/02/2004. 4 × 70 mm2 Cu 7 Z ′ L = ( 0. Dy 5 Two parallel four-core cables l = 10 m. X(0)L = 1. PkrT = 4.7 RL.6 kW.62 + j 9. d = 0.32 ZL1 = 4.1 Transformers For the transformers T1 and T2 with the vector group Dy5 the following relations are given by the manufacturer: Transformer T1: Transformer T2: A. Uncontrolled Copy.715 L2 Two parallel three-core cables l = 4 m.5 kW..BS 7639:1993 Table A.077 + j 0.55 ZL4 = Z (0)L4 = A. 12/02/2004. Dy 5 SrT = 400 kVA. 3 × 150 mm2 Al 7 Z ′ L = ( 0.297 ) -------kM 18.52 + j 14. UrTLV = 0.271 + j 0. qn = 50 mm2 Cu. UrTHV = 15 kV.995 ZQ (5b) 0.1.82 ZT2 = 2.I — Data of equipment for Example 1 and positive-sequence.4 kV ukr = 4 %.4 m 7 Z ′ L = ( 0.070 + j 0. ------------RL XL 0. cQ = 1.3 Determination of the zero-sequence impedances A.3704 + j 0.26 + j 7.60 + j 15.1.33 Z (0)T2 = (6) to (8) 4.4 kV ukr = 4 %.208 + j 0. PkrT = 6.740 16.60 + j 14. UrTHV = 15 kV.425 + j 0.420 + j 1.40 + j 44.62 + j 9.3.2 Lines (cables and overhead lines) The zero-sequence impedances are to be calculated with the relations R(0)L/RL and X(0)L/XL obtained from the manufacturer.136 1.1 · XQ with XQ = 0. © BSI Transformers T1 T2 SrT = 630 kVA. negative-sequence and zero-sequence short-circuit impedances Equipment Data of equipment Data and equation for the calculation of Z ( 1 ) and Z ( 0 ) Z(1) = Z(2) (m7) Z(0 ) (m7) Network feeder UnQ = 15 kV. S ″kQ = Q 250 MVA RQ = 0.760 + j 0.55 Z (0)L1 = lines L1 Data and ratios R( 0 ) L X( 0 ) L ------------.1. UrTLV = 0.700 ZT1 = Z (0)T1 = ZQt = Licensed copy:DRAKE & SCULL ENGINEERING LTD.068 ) -------kM given by the manufacturer 0.76 ZL3 = Z (0)L3 = L4 Overhead line (11). — Line L1: R(0)L = 3.395 1. (12a) l = 50 m.1.087 ) -------kM 5.385 + j 0.079 ) -------kM (6) to (8) 2.416 + j 0.81 XL with return circuit by the fourth conductor and surrounding conductor: 54 © BSI 04-2000 . 4 × 240 mm2 Cu 7Z ′ L = ( 0.165 ZL2 = Z (0)L2 = L3 Four-core cable l = 20 m.3.85 37. 23 RL.1 Short-circuit location F1 Short-circuit impedance at the short-circuit location F1 according to Figure A.4 Calculation of the short-circuit currents I ″ k and ip for balanced short circuits at the short-circuit locations F1. X(0)L = 3 XL. X(0)L = 4.2. when calculating the maximum short-circuit currents: Licensed copy:DRAKE & SCULL ENGINEERING LTD.1. it is sufficient to choose the conservative Method B or for higher accuracy Method C of Sub-clause 9.3.21 XL with return circuit by sheath: — Line L3: R(0)L = 3 RL.BS 7639:1993 — Line L2: R(0)L = 4.2: Figure A.1.05 (see Table I): Peak short-circuit current ip according to Sub-clause 9.1.2. © BSI A. Uncontrolled Copy.3. F2 and F3 A.4.1. © BSI 04-2000 55 .2 — Positive-sequence system (according to Figure A. X(0)L = 1.1. Because the calculation of Z k is carried out with complex values. 12/02/2004. page 52) for the calculation of I ″ k and ip at the short-circuit location F1 Maximum initial symmetrical short-circuit current according to Equation (20) with c = 1.46 XL with return circuit by the fourth conductor. sheath and earth: — Line L4: Overhead line with R(0)L = 2 RL. 12/02/2004.274 can be found and with the equation for x in Sub-clause 9. the ratios R/X of the parallel branches Z T1 and Z T2 + Z L1 + Z L2 are to be considered. These can be calculated as: Additionally. but taking the following values: In order to interpret this result.2 with an equivalent source voltage of the frequency fc = 20 Hz (fn= 50 Hz).857 m7/6.2 it follows that: Licensed copy:DRAKE & SCULL ENGINEERING LTD. Equation (16) with R/X according to Equation (22a)]: The impedance Z c = R c + j X c is calculated according to the comments of Method C of Sub-clause 9. The breaking current Ib and the steady state short-circuit current Ik at all three short-circuit locations need not be calculated since they are equal to the corresponding initial symmetrical short-circuit current I ″ k [see Equation (15)].3. 56 © BSI 04-2000 . Uncontrolled Copy.1. Equation (21)]: From the short-circuit impedance Z k = Rk + j Xk the ratio Rk/Xk = 1.1.1. © BSI Method C [equivalent frequency fc. two-thirds of the short-circuit current are taken by the transformer T1.BS 7639:1993 Method B [impedance ratio at the short-circuit location.771 m7 = 0. The calculation procedure is similar to the calculation of Z k . 3 Short-circuit location F3 with: Calculated according to Equation (21) of Method B (see Sub-clause 9.1. xb © BSI 04-2000 57 .852 7 = 0.2): therefore: xc = 1.4.05 .2847 Using the equation for x in Sub-clause 9.2: Licensed copy:DRAKE & SCULL ENGINEERING LTD.3.BS 7639:1993 A.4.29 F xb = 1. these two relations are similar to Rk/Xk = 1.1. Moreover.2 Short-circuit location F2 The peak short-circuit current can be calculated from Sub-clause 9.1. 12/02/2004.44 thus: The decisive ratio R/X is mostly determined by those of the branches Z T1 + ZL1 and ZT2 + Z L2 with (RT1 + RL1)/(XT1 + XL1) = 0.1.43.2: xc = 1. © BSI This leads to R/X ratio of: R/X = 0.29 and (RT2 + RL2)/(XT2 + XL2) = 0.1.1.3.953 7/6. A.32. Uncontrolled Copy. © BSI Figure A.3 — Positive-sequence. negative-sequence and zero-sequence systems with connections at the short-circuit location F1 for the calculation I ″ k1 at a line-to-earth short circuit Short-circuit impedances: 58 © BSI 04-2000 .5 Calculation of the short-circuit currents I ″k1 and ip1 for line-to-earth short circuits at the short-circuit locations F1.5. Uncontrolled Copy.BS 7639:1993 A.1 Short-circuit location F1 Licensed copy:DRAKE & SCULL ENGINEERING LTD. F2 and F3 A.1.1. 12/02/2004. 5.33 6. Uncontrolled Copy.1.2.03 0.125 34.41 4.89 34.04 1.81 32.59 70.07 68.2 for xc): Licensed copy:DRAKE & SCULL ENGINEERING LTD.93 6.42 65.82 1.BS 7639:1993 Initial short-circuit current for a line-to-earth short circuit according to Equation (29) (see Sub-clause 9.2.60 67.10 33.3.3.1.67 32.24 6.021 7.1): Peak short-circuit current ip1 according to Equation (31) of Sub-clause 9.1.c (kA) I″ k1 (kA) ip1.1.04 6.84 9.II — Collection of results for Example 1 (Un = 380 V) Short-circuit location Z( t ) = Z k (m7) Z(0) (m7) a I″ k ip.70 In all cases I ″ k = Ib = Ik (far-from-generator short circuit).5. calculated with the same value for xc in the case of a balanced three-phase short circuit (see Sub-clause 9.2.c (kA) I″ k1 / I ″ k — (kA) F1 F2 F3 a 7.46 80.2 Short-circuit location F2 A.6 Collection of results Table A.3 Short-circuit location F3 A.3. © BSI A. 12/02/2004. © BSI 04-2000 59 . 2 Example 2: Calculation of balanced short-circuit currents in a medium-voltage system. To show the difference between a real and a complex calculation and to demonstrate the decaying of the aperiodic component of the short-circuit current an additional calculation is given in Sub-clause A. Uncontrolled Copy.2. when calculating the short-circuit current I ″ k with absolute quantities or with quantities of a per unit system. 60 © BSI 04-2000 .BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD.2 of Section 2. see Sub-clause 9.1 (according to Table I for the maximum short-circuit currents): Xk is taken from Table A. As the short-circuit resistance is small in comparison with the short-circuit reactance (Rk < 0. page 61. both calculations are carried out (see Sub-clause A.4 if the circuit breakers CB1 and CB2 are open (without influence of the asynchronous motors M1 and M2).III demonstrates the calculation of the short-circuit reactance Xk at the short-circuit location F in Figure A.2. 12/02/2004.1 Problem A medium-voltage system 33 kV/6 kV (50 Hz) is given in Figure A.2 Calculation with absolute quantities Table A.1) it is sufficiently accurate to calculate only the short-circuit reactances of the electrical equipment and the short-circuit reactance Xk at the short-circuit location F in Figure A. The initial symmetrical short-circuit current without the influence of the asynchronous motors M1 and M2 becomes with c = 1. To demonstrate the difference.4. The calculations are to be carried out without asynchronous motors according to Sub-clause 9.3 Xk.4.1. A.1. The 33-kV-/6-kV-sub-station with two transformers each of SrT = 15 MVA is fed through two three-core solid type 33-kV-cables from a network feeder with S ″ kQ = 750 MVA and UnQ = 33 kV.III. influence of motors A.3 for the calculation with per unit quantities).1 of Section 1 and with the influence of asynchronous motors according to Sub-clause 13. © BSI A.2.2.4. 12/02/2004. Uncontrolled Copy.4 — Medium voltage 33 kV/6 kV system with asynchronous motors. © BSI Figure A.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. Example 2 © BSI 04-2000 61 . ZT) 0. without the influence of motors.(XL1t + XT1) 2 0.4) is: According to Sub-clause 12. 12/02/2004.4. Motor M1: where: Motor M2 (three motors with equal data F equivalent motor): 62 © BSI 04-2000 .2. Uncontrolled Copy.III — Calculation of Xk (7) for Example 2.3 (three-phase short circuit fed from non-meshed sources and Equation (55) it is possible to add the partial symmetrical short-circuit current at the short-circuit location (see Figure A.3969 4 5 6 L1 + T1 (L1 + T1) (L2 + T2) in parallel Short-circuit reactance Xk XL1t + XT1 = XL2t + XT2 Two equal branches in parallel 1 -.2655 The initial symmetrical short-circuit current.582 Licensed copy:DRAKE & SCULL ENGINEERING LTD. Equipment Equations and calculations Reactance (7 ) 1 Network feeder Equation (5b): 0. at the short-circuit location (see Figure A.5.BS 7639:1993 Table A.0177 0. © BSI 2 3 Cable L1 Transformer T1 Equation (6) (XT .5 for the short-circuit impedances of asynchronous motors.4146 0.3. page 61): The partial short-circuit currents I ″kM1 and I ″kM2 (CB1 and CB2 are closed) are calculated from Equation (69) in Table II and Equation (34) in Sub-clause 11. without the influence of asynchronous motors M1 and M2 (CB1 and CB2 are open) No.2073 0. 05 the values ÈM1 = 0. Uncontrolled Copy.1 s.68 and qM2 = 0.4. Sub-clause 12. When calculating the partial short-circuit current fed from the network.5 MW and mM2 = 1 MW the values qM1 = 0.40 and I ″kM2 / IrM2 = 6.3 is used: For the calculation of Ib3M the factor È has to be determined according to Equation (47) and q according to Equation (67) with tmin = 0.3.72 are calculated. With active power per pair of poles mM1 = 2.) quantities two reference quantities (Index R) have to be chosen.2. page 61. With I ″kM1 / IrM1 = 4.57 are found. According to Equation (71) the partial breaking currents are: The symmetrical short-circuit breaking current becomes: According to Equation (72) there is no contribution of the asynchronous motors to Ik: A. 12/02/2004.BS 7639:1993 where: Partial short-circuit currents according to Equation (69): Licensed copy:DRAKE & SCULL ENGINEERING LTD.3 Calculation with per unit quantities For the calculation with per unit (p. © BSI Short-circuit current at the short-circuit location F in Figure A.2.80 and ÈM2 = 0.3 of the value without motors. For Example 2 those quantities shall be: UR = Un = 6 kV or 33 kV and SR = 100 MVA © BSI 04-2000 63 . including the influence of the motors M1 and M2: The influence of the asynchronous motors raises the short-circuit current to 1.u. then the rated transformation ratio related to p.) 1 Network feeder Equation (5b): 0. ZT) 1.0491 3 Transformer T1 Equation (6) (XT .u.7375 64 © BSI 04-2000 . Uncontrolled Copy. without the influence of asynchronous motors M1 and M2 (CB1 and CB2 open) No.III.1516 0.u.) quantities (with an asterisk [*] as a superscript) therefore are defined as follows: If the system is not coherent as indicated in Sub-clause 8.u.M.1025 4 5 L1 + T1 (L1 + T1) (L2 + T2) in parallel Two equal branches in parallel 1.IV in a similar manner as in Table A.IV — Calculation of *Xk (per unit [p. M2) at the short-circuit location in Figure A. voltages becomes: Licensed copy:DRAKE & SCULL ENGINEERING LTD. © BSI The procedure for the calculation of the initial symmetrical short-circuit current without the influence of the motors is given in Table A. page 61.5758 6 Short-circuit reactance *Xk 0.]) for Example 2. is: From this the short-circuit current in kiloamperes is calculated: Table A.4. that means UrTHV/UrTLV s UnHV/UnLV.1617 2 Cable L1 0. 12/02/2004.4. The initial symmetrical short-circuit current * I ″ k (without M1.BS 7639:1993 Per-unit (p. Equipment Equations and calculations Reactance (p. 4.5. A.4 Calculation with complex quantities In this Sub-clause the short-circuit calculation is done with complex quantities for the medium voltage system according to Figure A.BS 7639:1993 The short-circuit impedances in p.u. Uncontrolled Copy.2. © BSI 04-2000 65 .2.2. © BSI Partial short-circuit currents according to Equation (69): The results are the same as in Sub-clause A. of the asynchronous motors are: Licensed copy:DRAKE & SCULL ENGINEERING LTD. This figure indicates the partial short-circuit currents of the branches and their addition at the short-circuit location. 12/02/2004. page 61. The complex impedances of electrical equipment are calculated from the data given in Figure A. 5 — Medium voltage 33 kV/6 kV system with asynchronous motors (complex calculation for Example 2) 66 © BSI 04-2000 . © BSI Data of asynchronous motors M1 and M2 given in Figure A.4 Figure A. Uncontrolled Copy. 12/02/2004.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. BS 7639:1993 Table A.V — Calculation of Zk (T1, T2) for Example 2, with asynchronous motors M1 and M2 according to Figure A.5 No. Equipment Equations et calculations Impedance (7 ) 1 Network feeder (see Table A.III) Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI 0.0058 + j 0.0579 2 Cable L1 0.0177 + j 0.0177 3 Transformer T1 (see Table A.III) 0.01588 + j 0.3966 4 5 6 L1 + T1 (L1 + T1) (L2 + T2) in parallel Short circuit impedance 0.03358 + j 0.4143 0.01679 + j 0.2072 0.02259 + j 0.2651 Short-circuit impedances of asynchronous motors M1 and M2: Motor M1: (see Sub-clause A.2.2) © BSI 04-2000 67 BS 7639:1993 therefore: XM = 0.995 ZM et RM = 0.1 XM (see Sub-clause 11.5.3.5) Motor M2 (three motors with equal data F equivalent motor): (see Sub-clause A.2.2) Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI PrM/p = 1 MW/1 = MW [ W 1 MW] therefore: Short-circuit current I ″ k at the short-circuit location F in Figure A.5, page 66, according to Equation (55) in Sub-clause 12.2.3.2: (see Sub-clause A.2.2) Peak short-circuit current ip at the short-circuit location F in Figure A.5 according to Equation (56) in Sub-clause 12.2.3.3: ip = (ipT1 + ipT2) + ipM1 + ipM2 68 © BSI 04-2000 BS 7639:1993 According to Sub-clause 9.1.1.2: Licensed copy:DRAKE & SCULL ENGINEERING LTD, 12/02/2004, Uncontrolled Copy, © BSI Decaying aperiodic component iDC according to Equation (1) at f = 50 Hz: Symmetrical short-circuit breaking current Ib according to Equation (57) in Sub-clause 12.2.3.3: (according to Sub-clause 12.2.3.3, far-from-generator short circuit) © BSI 04-2000 69 3.92 kA Ib = (14. Impedance correction factor A.1 Problem The balanced short-circuit currents at the short-circuit locations F1 to F4 in Figure A. 12/02/2004.54 kA = 1. Low-voltage asynchronous motors shall be handled as motor groups.2.VI or Table A. are to be calculated according to Section 2.80 · 0.2) Asymmetrical short-circuit breaking current Ib asym with the help of iDC: Licensed copy:DRAKE & SCULL ENGINEERING LTD.68 · 2.38 + 0. 70 © BSI 04-2000 .92) kA = 16.32 + 1.BS 7639:1993 With a minimum time delay tmin = 0.72 · 0.6. A power-station unit (PSU) is connected to a 220 kV system with the actual. © BSI Steady-state short-circuit current Ik according to Equation (58): A. The auxiliary transformer AT is of the three-winding type feeding two auxiliary busbars B and C with Un = 10 kV.1 s and the already calculated values for È and q: IbM1 = 0.38 kA and corresponding for the motor M2: IbM2 = 0.VII. page 72. The influence of asynchronous motors on the short-circuit currents is to be taken into account when calculating short-circuit currents at the short-circuit locations F2.3 Example 3: Calculation of balanced short-circuit currents in the case of near-to-generator short circuits. The terminal short-circuit currents of the high-voltage or low-voltage motors are calculated within the Table A. initial short-circuit power S″ kQ = 8 000 MVA of the network feeder. Uncontrolled Copy.24 kA = 0. F3 and F4.62 kA (see Sub-clause A.57 · 2. Uncontrolled Copy.2.2 Unit transformer From the data given in Figure A. 12/02/2004. S ″ kQ max is to be estimated from the future planning of the power-system.3.3. ZQ min (corresponding to S ″ kQ max ) is found according to Sub-clause 12.BS 7639:1993 A.1 from the actual symmetrical short-circuit power at the feeder connection point. that: Licensed copy:DRAKE & SCULL ENGINEERING LTD.3. © BSI For the calculation of the maximum short-circuit current at the short-circuit locations F2 and F3.2. A.2.2.2 yield: Converted to the low-voltage side of the unit transformer with tr = 240 kV/21 kV: © BSI 04-2000 71 .1.2 Short-circuit impedances of electrical equipment A.1 it follows.2. with c = 1.3.1 Network feeder According to Sub-clause 8.3. page 72.3.6. Equations (6) to (8) according to Sub-clause 8. VI. Uncontrolled Copy. ** For details see Figure A. 12/02/2004. © B 72 * For details see Table A.6 — Network feeder. high-voltage and low voltage asynchronous motors.8 and Table A. © BSI 04-2000 BS 7639:1993 Figure A. power-station unit (PSU) — unit transformer and generator — with auxiliary transformer (AT).VII. Example 3 .Licensed copy:DRAKE & SCULL ENGINEERING LTD. Substituting the data presented in Figure A. the calculation according to Sub-clause 11.6) can be performed as: Licensed copy:DRAKE & SCULL ENGINEERING LTD.5. and therefore: A.3.7 can. ZB and ZC according to Figure 7.2.5.7 with c = 1.6 in Equation (9).2.8 are used with cmax = 1. page 72) the equations in Sub-clause 11.6. the positive-sequence short-circuit impedances of the transformer are calculated as follows (related to the 21 kV side A): © BSI 04-2000 73 .3.3.3 Generator With the data given in Figure A.2.05 X ″ d (see Sub-clause 11.3. 12/02/2004. page 22. Uncontrolled Copy.4 Auxiliary transformer The positive-sequence short-circuit impedances ZA .2.1 (see Table I) and RG = 0. be found: therefore: In order to calculate the short-circuit current on the high-voltage side of the transformer (F1 in Figure A.BS 7639:1993 A. © BSI The correction factor according to Sub-clause 11. can be determined with the equations of Sub-clause 8.6. tf = Un/UrG = 220 kV/21 kV and tr = 240 kV/21 kV.5.5.3.3.1.3. 3.6 MVA According to Figure A.VII it follows that: 74 © BSI 04-2000 .8.2.4 kV. page 72. Uncontrolled Copy.5 MVA and UrTHV/UrTLV = 10 kV/0.693 kV connected to each of the two auxiliary busbars 10 kV and in addition one transformer with SrT = 1. and Figure A.2 and the data in Table A. 12/02/2004. the impedances of the three-winding transformer AT are: A. © BSI Using Equation (10) and referring the impedances to UrTA = 21 kV: Converted to the 10.5 Low-voltage transformers 2.6. With the equations in Sub-clause 8.5 kV (side B or C) with tr = 21 kV/10.2. Each of these transformers feeds a group of low-voltage asynchronous motors.5 kV.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. there are five transformers with SrT = 2. UrTHV/UrTLV = 10 kV/0. page 80.5 MVA and 1.3.6 MVA. Using Equations (69) and (34) and bearing in mind that UrM is equal to Un in this special case.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. 12/02/2004.VI.2 are given in Table A. © BSI Converted to the low-voltage side With tr = 10 kV/0.3.VII.5 and 13. the following expression can be found for I ″ k3M : Data and calculation of the short-circuit impedances of the low-voltage motor groups including their supply cables according to Sub-clauses 11.2 are given in Figure A.4 kV: A. and Table A.6 Asynchronous motors Data and calculations of the short-circuit impedances of the high-voltage motors M1 to M14 according to Sub-clauses 11. © BSI 04-2000 75 .5.8 page 80.3.2.5 and 13. Uncontrolled Copy.3.5. 3 Calculation of short-circuit currents A.3.1. tmin = 0. © BSI 1) 2) 3) The values for xM are given in Table II of Sub-clause 13. contribution of motors smaller than 5 %).BS 7639:1993 Table A.VI — Data of high-voltage motors and their partial short-circuit currents at the short-circuit location on busbars B or C respectively Licensed copy:DRAKE & SCULL ENGINEERING LTD.2. Equation (67). tmin = 0.1 s. The initial symmetrical short-circuit current is calculated according to Equation (55): 76 © BSI 04-2000 .2. Equation (47).3.2. Uncontrolled Copy.2.1 Short circuit at the short-circuit location F1 The calculation is done according to Sub-clause 12.3. 12/02/2004. It is not necessary to take the asynchronous motors into account (see Sub-clause 13.3. A.1 s. 2. tmin = 0.3 and 12.1 s: Power-station unit (see Sub-clauses 12. © BSI Network feeder: Equation (57).2.3. page 43. the initial symmetrical short-circuit current at the short-circuit location F2 (without the influence of asynchronous motors) is derived from the partial short-circuit currents I ″kG [see Equation (52)] and I ″ kT [see Equations (53) and (41)]. Uncontrolled Copy.3): with: A. 12/02/2004.2 Short circuit at the short-circuit location F2 First of all.BS 7639:1993 Equation (56): ip = ipPSU + ipQ Power-station unit: Licensed copy:DRAKE & SCULL ENGINEERING LTD.3.3.2. © BSI 04-2000 77 . according to Figure 21. BS 7639:1993 Using Equation (54) Z rsl is calculated from Z G.0205 F xT = 1. © BSI Normally it is sufficient to calculate as follows (because R ¤ X): ipG calculated with R G / X ″ d = 0.05 (see Sub-clause 11.86 ipT calculated with R/X = 0. 12/02/2004.3.PSU and Licensed copy:DRAKE & SCULL ENGINEERING LTD.94 78 © BSI 04-2000 .00645 7/0.5. Uncontrolled Copy.6) F xG = 1.3152 7 = 0. BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD.7 — Positive-sequence system for the calculation of the partial short-circuit current I ″kM – AT from high-voltage and low-voltage motors at the short-circuit location F2.3. so that only the current IbT = I ″ kT is of interest.2.4) related to the HV-side of the transformer AT. 12/02/2004. Uncontrolled Copy. Impedances are transferred to the high-voltage side of the auxiliary transformer AT with tr = 21 kV/10. © BSI Normally. Figure A.5 kV = 2 © BSI 04-2000 79 . The additional short-circuit currents fed from the asynchronous motors can be calculated from the results of Table A.VII and from the impedances of the auxiliary transformer (see Sub-clause A.VI and Table A. there is no circuit breaker provided to switch off the total breaking current. Transformers and groups of low-voltage asynchronous motors connected to the auxiliary busbar B.BS 7639:1993 Licensed copy:DRAKE & SCULL ENGINEERING LTD. page 72.8 — Detail of Figure A.6. Uncontrolled Copy. Transformers and low-voltage motor groups connected to the busbar C are identical 80 © BSI 04-2000 . 12/02/2004. © BSI Figure A. 693 0.3 1.5 1.0270 0.883 5.64 15.5 1.96 kA as calculated before. © BSI 04-2000 81 .00 7.625 2.3.66 0. that is equal to the value given above.0697 0.BS 7639:1993 Table A.5 5.377 4..376 2.1   Data   given by  the manufacturer    Data   given by  the manufacturer  0.693 kV and 10 kV/0.42 kA.1 This partial short-circuit current has to be considered because its magnitude reaches approximately 7 % of the current I ″ kG + I ″ kT = I ″ k = 86.3 1. 12/02/2004.20) Remarks Licensed copy:DRAKE & SCULL ENGINEERING LTD.4 6 16. When calculating ipM–AT with Method C of Sub-clause 9.41 kA = 15. c = 1.0081 0.75 or x = 1. Account has been taken of the fact that IbG + IbM–AT is smaller than I bT = I ″ kT .42 XM XM = 0.862 0..42 14.72 5 0.69 16.25 2. partial peak short-circuit currents and breaking currents fed from the asynchronous motors are to be added to the above calculated currents ip and Ib.38 kV.39 6. c = 1.6445 3.3) and IbM – AT = I ″ kM – AT as a conservative approach.40 0.41 kA with x = 1. 15 16 17 18 19 × (15.806 2.VI.05  Converted to the   high-voltage side  of the transformer  2 Z Mt = ZM ⋅ t r R Mt = XMt = RTHV + RMT XTHV + XMT Z THV + Z Mt I″ kT ( × I ″kT ) 1.VII.66 kV.0208 0.75 0.72 5 0. so that the breaking capacity for a circuit breaker between the unit transformer and the generator may be IbT = 42.19) 20 × (15.264 Un = 10 kV.5 kW MW kV — — — — MVA 7 7 7 7 7 7 kA 7 7 7 7 7 7 kA R M ⋅ t2 r X M ⋅ t2 r 12.62 13.1 Sub-clause 11. Uncontrolled Copy. © BSI SrT UrTHV UrTLV ukT PkrT PrM (motor group) UrM cos Îr½r ILR/IrM RM/XM xM SrM ZTHV RTHV XTHV ZM RM XM MVA 2.VII — Data of low-voltage asynchronous motors and data of transformers 10 kV/ 0.42 1.65. Motor group No.8 · 0.5 and Table II Table II SrM = PrM/(cos Îr½r)      Equations (6) to (8) I″ k3M Equation (34) RM = 0.701 is found and therefore ipM–AT = 15.67 Sub-clause 13. These are i pM – AT = Ä 2 I ″ kM – AT = 1.7 as a first approach (high-voltage motors have x = 1.372 1.694 0.5 6.693 kV 6 % 23.00 12. The sum of the short-circuit current × I ″ k reaches: Additionally.20 3. the factor xc = 1.00 5.9 = 0.39 3.991 2..4 kV respectively connected to the auxiliary busbar B..9 0.5.5 10 kV 0.2.0192 11.2 taking the impedances of the motors from Table A.00 15.74 14. 0.152 3.1.51 5.0 0.30 kA.3704 0.3.25 1.38 0.VI and Table A. low-voltage motor groups are to be considered with x = 1.0643 5.381 0. see Table A.8 13.7 2 ⋅ 6.922 ZM Un = 0.76 16. Partial short-circuit currents of the low-voltage motors at the short-circuit location F3 Transformer No.6 10 0. BS 7639:1993 A.3 Short-circuit at the short-circuit location F3 The initial symmetrical short-circuit current at the short-circuit location F3 can be calculated from the partial short-circuit currents as shown in Figure A.3.9: Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy.3. © BSI Figure A.9 — Positive-sequence system for the calculation of I ″k at the short-circuit location F3 Calculation of I ″ kAT : where: 82 © BSI 04-2000 . 12/02/2004. 3 MW and p = 2 (pair of poles). 5 (see Sub-clause 13. that I ″ is already smaller than twice IrG.3.3438 7) = 1. Uncontrolled Copy.3. © BSI 04-2000 83 .98 e–3 (0.1) and q . As a medium effective value x is found: If the short-circuit current I ″ kAT is transformed to the side A of the auxiliary transformer AT it becomes obvious.0121 7/0.1 s) according to I ″kM / IrM . so that IbAT = I ″kAT is valid [see Equation (18).VII.2.1. Method B) and the ratio R/X of the low-voltage motors including the transformers 15 to 20 according to Table A. Method B: 1.15 · 1.0) with 1.15 · xAT = 2 (see Sub-clause 9. 0.02 + 0. 12/02/2004.90 (see Sub-clause 9. © BSI It follows for the short-circuit power (see Sub-clause 3.342 derived from the conservative estimation that the low-voltage asynchronous motors of the motor group have rated powers u 0. kATt far-from generator short circuit].77 (tmin = 0.9 > 2.2. with È = 0.1.6): The peak short-circuit current ip can be derived with the following x-factors: xAT = 1.BS 7639:1993 the current I ″k can be calculated: Licensed copy:DRAKE & SCULL ENGINEERING LTD.2. BS 7639:1993 A. © BSI Figure A.61 = 1.4 Short-circuit at the short-circuit location F4 I″ k is calculated with the help of Figure A. 12/02/2004.10.2. Licensed copy:DRAKE & SCULL ENGINEERING LTD.8.10 — Positive-sequence system for the calculation of I ″ k at the short-circuit location F4 The peak short-circuit current is calculated from: According to Method B of Sub-clause 9.3.3.3.15 · xb = 1. it is necessary to take 1.15 · 1. Uncontrolled Copy. In this case for a low-voltage short circuit the maximum for 1. 84 © BSI 04-2000 .1.15 xb is limited to 1.85. © BSI © BSI 04-2000 85 . so that the ratio RT20/XT20 of the transformer will determine x for the calculation of ipT20. From the ratio RT20/XT20 = 1.60 can be determined and therefore for the whole peak short-circuit current at the short-circuit location F4: Licensed copy:DRAKE & SCULL ENGINEERING LTD.BS 7639:1993 (When considering the calculation of ipT20 it can be recognized that the impedance of the low-voltage transformer T20 gives the main part of the impedance Z P + Z T20LV . 12/02/2004.910 m7 = 0.031 m7/5.174 the factor x = 1. Uncontrolled Copy. Licensed copy:DRAKE & SCULL ENGINEERING LTD. Uncontrolled Copy. © BSI 86 blank . 12/02/2004. Appendix A. “230 kV” has been replaced by “380 kV”. Calculation of short-circuit currents In the title. © BSI National annex NB (informative) Cross-references Publication referred to Corresponding British Standard BS 4727 Glossary of electrotechnical power. electronics. Licensed copy:DRAKE & SCULL ENGINEERING LTD. Voltage factor c In the last box of column 1.BS 7639:1993 National annex NA (informative) Original IEC text amended by CENELEC common modifications 1 Scope In line 3. lighting and colour terms IEC 50(131):1978 IEC 50(151):1978 IEC 50(441):1984 Part 1:Group 01:1983 Fundamental terminology Part 1:Group 02:1980 Electrical and magnetic devices terminology Part 2:Group 06:1985 Switchgear and controlgear terminology (including fuse terminology) © BSI 04-2000 . telecommunication. “Appendix A” has been replaced by “Appendix A (informative)”. 12/02/2004. Table I. “230 kV” has been replaced by “380 kV”. Uncontrolled Copy. For details of these and other benefits contact Membership Administration. Contact the Information Centre. 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