4.0 Short-Circuit Effects David Chapman & Professor Toby Norris

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1 4.0 Short-Circuit Effects Dvi Chpmn & Professor Toy Norris 4.1 Introuction Like ll electricl circuits, usrs nee to e protecte ginst the effects of short-circuit currents. The open construction of usrs increses the risk of fults, e.g. y the ingress of foreign oies into ir gps, n the risk of consequent mge is high ue to their high norml operting currents n the mount of energy ville. Very high currents le to rpi n extreme overheting of the rs with consequent softening of the mteril n mge to the support structure. At the sme time, the electromgnetic forces generte will istort the softene conuctors which my rek free from their supports. Resonnce effects my mke the sitution worse. 4.2 Short-Circuit Heting of Brs The mximum potentil short-circuit current epens on the source impence of the supply n reuces long the length of the r s the impence increses. For the purpose of ensuring the sfety n integrity of the r, the short circuit current shoul e initilly clculte close to the fee en of the r, mking no llownce for r impence, to estlish the worst cse. When fult occurs, the short-circuit current will e mny times the norml operting current n will flow until the protective evice opertes. Becuse the time urtion is smll few secons t most it is usul to ssume itic heting, in other wors, tht, over the time scle of interest, there is no significnt cooling effect n tht ll the het generte y the current flow is retine in the r. Therefore it is ssume tht the temperture rise of the r is simply liner - this simplifies the clcultion significntly n yiels conservtive result. 1 The mount of het energy require to rise the temperture of unit mss of mteril y one egree Centigre is clle the specific het. For copper, t room temperture, the vlue is 385 Joule/kg/K. Knowing the mss of the r n the energy prouce y the short circuit current, the temperture rise cn e clculte: or Q is the mount of het e to the r (Joule) S is the specific het of the r mteril (J/kg/K) m is the mss of the r (kg) tr is the temperture rise. The mount of energy issipte in the r is: Therefore, P is the power issipte in the r (W) T is the time for which the power is issipte (secons). or where Dtr is the rte of temperture rise in egrees C per secon. The power issipte in the r is given y or 1 A similr simplifiction is me in etermining cle ehviour uner fult conitions. COPPER FOR BUSBARS 69

2 R is the resistnce of the r (Ω) r is the resistivity of the r mteril (Ωm) l is the length of the r (m) A is the cross-sectionl re of the r (m 2 ). Sustituting for W n M gives: D is ensity (kg/m 3 ). Two of the physicl constnts, specific het n resistivity, vry consierly with temperture so it is not ovious which vlues shoul e use. Resistivity increses with temperture (y fctor of 1.6 from 20ºC to 300ºC) so incresing the energy issipte s the temperture increses, while specific het flls y roun 8% over the sme rnge. Using room temperture vlues, n justing to use convenient units, gives the initil rte of temperture rise s: I is current in ka A is the cross-sectionl re in mm 2. At higher tempertures in other wors, s the fult current continues to flow until the protective evice opertes the rte of temperture rise will increse s the resistnce of the r increses. The worst cse rte of rise t the fee en of the r is pproximtely: However, if the short circuit is t some istnce from the fee en, the fult current mgnitue will e lower ue to the resistnce of the r n will reuce further s the r temperture rises. In prctice, wht is importnt is tht the finl temperture of the r remins lower thn the limiting esign temperture throughout the short circuit event. The limiting temperture for copper usrs is etermine y the temperture resistnce of the support mterils ut, in ny cse, shoul not excee ~ 200ºC. The mximum circuit reker tripping time is 200/Dtr secons. Busrs tht hve een suject to short circuit shoul e llowe to cool n inspecte efore eing returne to service to ensure tht ll joints remin tight n tht the mountings re secure. Note tht, lthough the heting time the urtion of the fult is quite short, the r will remin t high temperture for consierle length of time. Also, ecuse of the very high therml conuctivity of copper, prts of the r eyon the fult will lso hve ecome hot. 4.3 Electromgnetic Stresses Busrs re suject to mechnicl forces since ech is crrying current though the mgnetic fiels cuse y currents in other rs. When lternting currents re flowing, the forces hve stey component, ut lso virtionl component t twice the frequency of the lternting current. Uner norml working conitions these forces re of little consequence. However, if the rs re mounte on supports, ech section will hve resonnt frequency. If this frequency is close to twice the supply current (or ny significnt hrmonic current), then resonnt virtion of these ems my occur. This rther specil n uncommon circumstnce cn le to high virtionl isplcements n possily to metl ftigue or loosening of joints n connections. The prolem my e voie y choosing n pproprite spcing of the supports or cure y introucing itionl intermeite supports. Methos of estimting mechnicl resonnt frequencies re given lter. 70 COPPER FOR BUSBARS

3 If lrge currents flow, such s when short circuit occurs, the forces cn e more importnt. The uniirectionl component of the forces, excerte y the virtionl component, cn le to permnent ening n istortion of the rs or mge to, n even rekge of supports. The pek, or fully symmetricl, short-circuit current is epenent on the power fctor (cos f) of the usr system n its ssocite connecte electricl plnt. The vlue is otine y multiplying the rms symmetricl current y the pproprite fctor given in lnce three-phse shortcircuit stresses. The pek current, I, ttine uring the short circuit, vries with the power fctor of the circuit (see Tle 13): Tle 13 - Power Fctor n Pek Current Power Fctor Pek Current s Multiple of Stey Stte rms The theoreticl mximum for this fctor is 2 2 or where cos f = 0. If the power fctor of the system is not known, then fctor of 2.55 will normlly e close to the ctul system vlue, especilly where genertion is concerne. These pek vlues reuce exponentilly n, fter pproximtely 10 cycles, the fctor flls to 1.0, i.e. the symmetricl rms short-circuit current. As shown in Figure 45, the pek forces therefore normlly occur in the first two cycles (0.04 s). Theoreticl pek current Pek current (fully symmetricl) I Symmetricl current t Figure 45 Short-circuit current wveform COPPER FOR BUSBARS 71

4 Brs crrying like prllel currents re ttrcte towrs ech other. Thus, if the currents in one phse re crrie in seprte conuctors in prllel in the sme phse, then the gp etween them my e reuce y the mechnicl forces. More usully we el with rs crrying nti-prllel currents when the rs repel ech other. Ey current effects in rs crrying nti-prllel currents ring the current flow in r closer to the sies fcing the other conuctor. This will le to n increse in the repulsive force. Precise formule for this re not ville ut n over-estimte of the mgnitue of the force uner these circumstnces my e me y replcing the centre line istnce in the formul for the force per unit length y the istnce etween the fces Estimting the Forces Between Prllel Sets of Brs Assuming tht the rs re roun will give vlues for the forces which, use with fctor of sfety in estimting strength, re normlly relile. If there re mny rs in the configurtion then the forces etween iniviul pirs of rs my e simply e together, tking into ccount their irection. In the cse of c, one my nee to tke into ccount the phses of the currents. Br shpe usully hs minor effect unless the rs re very close together, s will e illustrte in the exmple of rectngulr rs Roun Brs For two rs with spcing n crrying prllel currents I1 n I2, the repulsive force per unit length is is spcing in mm µ o is solute permeility = 4π x10-7 Henrys per metre F is force per unit length in N/m. For two rs, t spcing, crrying nti-prllel irect currents (i.e. go n return currents) of mgnitue I, the repulsive force per unit length is For two rs t spcing,, crrying nti-prllel lternting currents (i.e. go n return currents) of mgnitue I, the repulsive force per unit length is is spcing in mm = 2πf f is frequency in Hz. Thus we hve stey repulsive force, together with force lternting t twice the frequency of the current of mplitue equl in mgnitue to the stey component of force. The result cn lso e seen s perioic force vrying from zero to twice the verge force. 72 COPPER FOR BUSBARS

5 For lnce three phse currents of rms vlue I t frequency = 2π f ( in r/s, f in Hz), the currents re: The stnr tringulr n inline rrys re shown in Figure 46. C y F BA A 30 x A F CB B F AB C F BC F AC B F CA x () () Tringulr Arry Figure 46 - Three phse system with spcings (mm). () tringulr rry, () inline rry The net force per unit length in the x-irection on r A in Figure 46() The net force in the y-irection on r A in Figure 46() The net result is stey force outwrs long the perpeniculr to the line BC of mgnitue The lternting forces in the x n y irection re in phse qurture n of equl mgnitue n so constitute force tening to move the conuctor in circle. The mgnitue is the sme s tht of the stey force. COPPER FOR BUSBARS 73

6 In-Line Arry The force per unit length in the x-irection (i.e. n outwr repulsive force) on r C in Figure 46() is This is stey outwr force with superpose 2 n hrmonic virtion. The mplitue of the hrmonic force is slightly greter thn the stey force. The force per unit length on the centre r, B, is purely virtionl. In the x-irection it hs mgnitue The force per unit length in the x-irection on r A is This too is on verge repulsive force outwrs in the negtive x-irection Brs of Rectngulr Section For rs of rectngulr section set out orerly, the force etween the two my e expresse s the force compute s if they were roun rs multiplie y correction fctor. Thus the force, in N/m, etween two rectngulr rs with centre line spcing, is The fctor K epens on the length of the sies, n, of the rectngulr cross-section n the spcing,, of the centre lines. K is shown in Figure 47 s function of Note tht the curves lelle / = 0 n / = 0 represent limiting vlues. 74 COPPER FOR BUSBARS

7 Fctor, K = 0 = 5 = = 1 = = = = Figure 47 - Fctor K for clculting the force etween two rs of rectngulr section For pir of rectngles whose long sies fce ech other, it will prove helpful to use the equtions elow in which is replce y n fctor K replce y K which is plotte in Figure 48. Form Fctor, k () Form Fctor, k () Figure 48 - Form fctor K. () low vlues of / (long sies fcing ech other) () high vlues of /. COPPER FOR BUSBARS 75

8 An pproximte formul for K ccurte to within 4% for n is: 4.4 Mounting Arrngements The mountings re require to restrin the usrs uner ll conitions to ensure tht: the mteril is not over stresse sfe istnce is mintine etween rs in norml service n uner short-circuit conitions y limiting mximum eflection the rs o not virte excessively (which woul impir the long term efficcy of joints) Mximum Permissile Stress The mximum permissile stress in conuctor is the resultnt of: its own nturl weight (Fm) n in the cse of usrs instlle out of oors, the itionl forces of win (Fw) n ice (Fi) loings n the mgnetic forces resulting from short circuit, noting tht the irection of short-circuit force (Fs) epens on the position of jcent phses n the irection of the currents in them. In generl cse, the resultnt cn e clculte y the following metho: F S Ø F w R F m +F 1 76 COPPER FOR BUSBARS

9 n The mximum skin stress in the conuctor cn then e clculte using the following formul: f is mximum skin stress, N/mm 2 L is spn, mm I is moment of inerti, mm D is imeter or epth of rectngulr section, mm. This eqution is vli for uniformly loe single em which is freely supporte t oth ens or freely supporte t one en n fixe t the other. For em which is horizontlly fixe t oth ens, mximum skin stress is reuce to one thir t the centre n to two-thirs t its ens. The mximum permissile stress is epenent on the conuctor mteril, temper, etc. ut must not excee the mteril proof stress otherwise permnent eformtion will occur. For conuctor mnufcture from hr rwn copper, the vlue is pproximtely 245 N/mm Moment of Inerti In the ove formul the moment of inerti, I, for the section of the em hs to e clculte out the neutrl xis which runs prllel to the em where the em hs zero tensile forces. In most cses this is the sme xis of the centre of cross-section. Shpe profiles hve much higher vlues of moment of inerti thn simple rs n ros (see Section 5.0 Busr Profiles). For rectngulr section of epth D mm n reth B mm For circulr section of imeter D mm or For tuulr section of internl imeter mm n externl imeter D mm or It shoul e note tht the vlue of I for given cross-section is epenent on the irection in which ech iniviul force is pplie. COPPER FOR BUSBARS 77

10 4.4.2 Deflection It is importnt to know how fr r will eflect so tht the necessry clernces etween rs n other structures cn e mintine. The mximum eflection of em crrying uniformly istriute lo, n freely supporte t ech en, is given y the formul: D is mximum eflection, mm Fm is weight per unit length of loe em, N/mm L is em length etween supports, mm E is moulus of elsticity (124 x 10 3 N/mm 2 ) I is moment of inerti of em section, mm 4. If one en of em is rigily fixe in horizontl position, the eflection is times tht given y the ove formul. If oth ens of em re rigily fixe in horizontl position, the eflection is 0.2 times tht given y the ove formul. Thus, with continuous em freely supporte t severl points, the mximum eflection in the centre spns my e ssume to e 0.2 times tht given y the formul, while the eflection in the en spns is times. Therefore, the eflection in the en spns my e ssume to e twice tht in the centre spns, ssuming equl spn istnces Nturl Frequency The nturl frequency of em simply supporte t its en is: n for em with oth ens fixe horizontlly it is: fn is nturl frequency, Hz D is eflection, mm. As the eflection with fixe ens is 0.2 times the vlue with freely supporte ens, it follows tht the nturl frequency is increse y times y en-fixing; fixing one en only increses the nturl frequency y out 50%. Busr systems shoul e esigne to hve nturl frequency which is not within 30% of the virtions inuce y the mgnetic fiels resulting from the currents, incluing ny significnt hrmonic currents, flowing in jcent conuctors. Where equipment is to e mounte outsie, nturl frequencies of less thn 2.75 Hz shoul e voie to prevent virtion ue to win eies. 78 COPPER FOR BUSBARS

COPPER FOR BUSBARS CHAPTER 4: SHORT-CIRCUIT EFFECTS

European Copper Institute COPPER FOR BUSBARS CHAPTER 4: SHORT-CIRCUIT EFFECTS David Chapman August 2011 ECI Available from www.leonardo-energy.org Document Issue Control Sheet Document Title: Publication