EXPERIMENTAL STUDY ON HEATING OF UNINSULATED ELECTRICAL CONDUCTORS

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1 EXERIMENTAL STUDY ON HEATING OF UNINSULATED ELECTRICAL CONDUCTORS Gheorghe HAZI +, Anet HAZI +, Sorin-Gbriel VERNICA + + VASILE ALECSANDRI UNIVERSITY OF BACAU, Romni Rezumt. În est lurre utorii prezint rezulttele obinute în lbortor privind înlzire i rire ondutorelor eletrie neizolte. Este desris instli experimentl utilizt i rezulttele obinute l msurtori. Temperturile obinute prin msurtori sunt omprte u ele determinte nliti utilizând proedurile preizte în stndrde internionle. Se rt modul de determinre onstntei de timp pentru regimul trnzitoriu. Cuvinte heie: înlzire, ondutore eletrie, determinri experimentle Abstrt. In this pper the uthors present the results obtined in the lbortory on heting of uninsulted eletril ondutors. It is desribed the experimentl system used nd the results obtined in mesurements. Tempertures obtined by mesurements re ompred with those determined nlytilly using the proedures speified in interntionl stndrds. It shows how to determine the time onstnt of the trnsitionl regime. Keywords: heting, eletri ondutors, experimentl determintions 1. INTRODUCTION Tempertures stedy of the uninsulted eletril ondutors re relevnt to determining the mximum permissible urrent supportble by urrent pths, prtiulrly for overhed lines. Mximum llowed in the stedy stte by the ondutor re given by their mnufturers. It is rrnged so, s the ondutors not to lose mehnil properties irreversibly under the effet of het. For onventionl steel-luminum ondutor, the mximum llowble is ºC, while the modern ondutors is over 00 ºC, [1], [],[3]. Temperture of the ondutors depends on the: urrent RMS vlue resistivity mteril / mterils Environmentl onditions (, wind, humidity, solr irrdine). Determintion of the mximum permissible is importnt both in the design phse, to verify tht overhed lines n rry eletril power projeted, nd in opertion phse, to hek the possibility of tking over the lines in degrded modes or withdrwl from servie for their revision. Estimted s rehed during the design phse is bsed on the methodology estblished by interntionl stndrds [], [5]. The influene of environmentl onditions on the of the ondutor is shown in [6]. The onditions of use of the ondutor t s bove 100 C is disussed in [7]. In [8] it is given own methodology for estimting by numeril simultion. In this pper, the uthors present experimentl results for n Al ondutor nd ompres them with results of the methodologies presented in [], [5]. It lso shows method for estimting time onstnt in the trnsient regime.. EXERIMENTAL INSTALLATION USED AND RESULTS Figure 1 shows shemti digrm of the experimentl instlltion. The urrent djustment through the ondutor is mde by hnging the supply voltge of the urrent kit with utotrnsformer. Tests were done in the lbortory, in old wether, with the window open. The results of the mesurements obtined for three vlues of the urrent setting re given in the Tbles I,II,III. TERMOTEHNICA Supliment 1/013 79

2 T101 T10 CURRENT KIT 100/5 A, 0 V mx 100 A C DIGIAL MULTIMETER DT C +0.75% ATR-8A 101 A DIGIAL MULTIMETER UT A, +1.5% Aluminum ondutor =.5 mm l=.9 m Fig. 1. Sheme of experimentl instlltion Tble I t 51A urrent Tble II t.5a urrent Tble III t 60.A urrent From the Tbles it is observed tht the urrent vlue ws not stritly onstnt due to ondutor resistne hnges with. It is noted tht the stbilized vlue is rehed within 300 s. 3. DETERMINATION OF THE TIME CONSTANT IN THE HEATING REGIME If it is estimted theoretil urve of vrition during the trnsition period by reltionship of the form: T e ( t) 0 mx 0 (1) 0 is initil, mx - finl Determintion of the time onstnt T ws done by the method of lest squres, requiring tht the t 80 TERMOTEHNICA Supliment 1/013

3 differene between the theoretil urve nd the urve determined prtil to be s smll s. We solve the optimiztion problem: Ferr( T ) ( t i, T n min! i1 msi ) () the ft tht, for the theoretil urve, the rdition losses is integrted into the onvetion losses, tht re liner with. From minimizing the funtion of the time onstnt T is obtined the vlues given in the Tble IV. Tble IV Theoretil time onstnt for the 3 tests 0 mx T Grphil representtion of the experimentl nd theoretil urves is given in Figures,3,. Fig.. The heting urve for I=60.A. THEORETICAL ESTIMATION OF THE FINAL TEMERATURE This estimte ws mde by the CIGRE methodology [] nd by the IEEE methodology [5]. The two methodologies, while tking into ount environmentl ftors similrly, they re distinguished. Thus CIGRE methodology uses the invrints Reynolds nd Nusselt to determine het trnsfer oeffiient, while the IEEE method uses experimentl ftors to the lultion of the het flux trnsferred by onvetion. Overll het blne eqution is: Fig.. The heting urve for I=51A Fig. 3. The heting urve for I=.5A Sme differene is observed in the 3 theoretil nd experimentl urves. This n be explined by j m s r r W (3) : j joule heting [W/m] m mgneti heting, [W/m] s solr heting, [W/m] r oron heting, [W/m] onvetive ooling, [W/m] r rditive ooling, [W/m] w evportive ooling, [W/m]. In our lbortory sitution, our only three terms in reltion (3): j, i r. Joule loss is determined by the reltion (W/m) : 0 () j 1 R 0 I S 0 luminum resistivity t ºC, S - ondutor ross setion, [m ] TERMOTEHNICA Supliment 1/013 81

4 R oeffiient of vrition of resistne with, [ºC -1 ] I urrent in iruit,. Convetion losses (W/m) re determined differently in the two methodologies. In the se of the method from referene []: (5) trnsfer oeffiient by onvetion, [W/m ºC] mbient, The oeffiient is determined bsed on the flow regime of ooling fluid (ir). Ws ttempted first, lulus with ir speed v = 0 (nturl onvetive ooling) but were obtined too lrge error. Being room with open windows, ws tken veloity v = 0.18 m / s, the reommended vlue in [9]. The trnsfer oeffiient by onvetion,, is determined using invrints Reynolds nd Nusselt: - emissivity with vlues reommended by 0.5. In ll mesurements mde, rdition losses re bout 10% of the het generted by the Joule effet, the differene being overed by onvetive losses. Determining the finl is itertive, strting from eqution (3) simplified: j r (10) Initilly ondutor ws imposed equl to the mesured nd it ws orreted in itertions, until terms of the eqution (10) were equl to n error of up to 0.01 W/m. The lultion lgorithm for both methodologies is shown in Figure 5. Nu B 1 Re n (6) B 1 nd n re given in tble in the methodology [] depending on the vlue of Re. Nu (7) is the therml ondutivity of ir. In the methodology of [5], it is presented diret reltionship to lulte the onvetion loss, of the form: K ngle v 0. 5 (8) ondutor dimeter, [mm], dynmi visosity, [ s], Kngle oeffiient tht is lulted (by empiril reltionship) depending on the inidene ngle of the ir on ondutor. It should be noted tht in both methodologies, ir prmeters depend on through empiril reltionships given in the stndrd. Rdition losses (W/m) re determined in both methodologies by Stefn-Boltzmnn reltionship: r B is the Stefn-Boltzmnn onstnt, B (9) Fig. 5. The lgorithm for lulting the finl The results obtined for the finl s,, re given in Tble V. Tble V Finl s obtined from mesurements in the 3 ses Mesurement 1 3 Mesured (ºC ) CIGRE method (ºC ) IEEE method (ºC) (A) Air speed (m/s) Note, from Tble 5, there is good orreltion of mesured nd lulted vlues by the two methodologies. 8 TERMOTEHNICA Supliment 1/013

5 5. CONCLUSIONS From the results presented it n be onluded: Experimentl heting urve re pproximtely exponentil, with smll devitions due to the wy in whih the rdition loss re onsidered in the theoretil urve. The time onstnt T in the heting regime for the ondutor used in the lbortory is bout 90 s The results obtined by the two methodologies (CIGRE nd IEEE) re very lose to those obtined experimentlly. The errors re up to 1- degrees. The differenes n be explined by the ft tht methodologies CIGRE nd IEEE re mde for ondutor rope, onsisting of mny wires threds, with the hert of steel, typilly. In the lb we used single wire ondutor of Al. REFERENCES [1] Nexns - Bre Overhed s. AAC, ACSR, ACSR II. 003, [] De Angeli rodotti - Bre Overhed s, [3] I. Ardelen, G. Flore, M. Olten, E. Mteesu, D. Mrginen,. Kilyeni, C. Brbulesu - Reondutorre LEA 0 kv Iernut-Bi Mre 3, utilizând tehnologii de LST. THE 8th INTERNATIONAL OWER SYSTEMS CONFERENCE, SC 009, November -6, 009, Timior, Români [] CIGRE - Brohure on therml behviour of overhed ondutors. Cigré Study Committee, Working Group 1. September 001. [5] IEEE - Stndrd for lulting the urrent of bre overhed ondutors. IEEE Std Trnsmission nd Distribution Committee of the IEEE ower Engineering Soiety. [6] T. Krontiris, A. Wsserrb nd G. Blzer, Wether-bsed Loding of Overhed Lines Considertion of s Het Cpity. Modern Eletri ower Systems 010, Wrolw, olnd, submission/dt/ppers/01.5.pdf [7] CIGRE- Guide to Opertion of Conventionl Systems bove 100ºC. CIGRE Working Group B- Stokholm, Sweden1 My 010 [8] F. Álvrez Gómez, J.M. Grí De Mrí, D. Grí uerts, A. Bri, R. Grnizo Arrbé, Numeril study of the therml behviour of bre overhed ondutors in eletril power lines, 011, [9] I Normtiv privind proietre i exeutre instliilor de ventilre i limtizre, probt prin ordinul Ministerului Dezvoltrii Regionle i Turismului, nr din TERMOTEHNICA Supliment 1/013 83