METODOLOGIE DE CALCUL A PIERDERILOR DE PUTERE SI ENERGIE ELECTRICA IN LINIILE DE JOASA TENSIUNE CU SARCINI ECHIDISTANT REPARTIZATE
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1 METODOLOGE DE ALUL A PERDERLOR DE PUTERE S ENERGE ELETRA N LNLE DE JOASA TENSUNE U SARN EHDSTANT REPARTZATE POWER, ATVE ELETR ENERGY LOSSES ALULATON AT A LOW VOLTAGE DSTRUTON LNE WTH EQUDSTANT DTRUTED LOADS. TOADER P. POSTOLAHE. NOARĂ Facultatea de Eergetică, Uiversitatea Politehica ucureşti, Româia.. SLVAS. VLAD A. APOSTOLESU FDFEE Muteia Nord - SDFEE Ploieşti, Româia. Rezumat. lucrare sut deduse relaţiile de calcul petru evaluarea pierderilor de putere active si eergie electrică petru liiile electrice de distribuţie de joasă tesiue moofilare. Totodata se propue u model matematic petru liiile electrice de distribuţie de joasă tesiue trifazate cu sau fără coductor de ul de exploatare. fie este iclus u cuprizator studiu de caz petru o reţea de distribuţie de joasă tesiue di cadrul FDFEE Muteia Nord (oraş Ploieşti). Summary. the paper they are deduced the calculus relatios to estimate the active eergy ad active power losses for the sigle phase low voltage distributio lies. At the same time it is proposed a mathematical model for three phase low voltage distributio lies with or without ull coductor. the ed it is icluded a ample case study for a low voltage distributio etwork from FDFEE Muteia Nord (tow Ploieşti).. alculul pierderilor de putere şi eergie petru o reţea cu sarcia echidistat distribuită Această situaţie se apropie cel mai mult faţă de realitate, î ipoteza că sarcia oricărui cosumator este egală cu. Această situaţie este redată î fig... The power ad eergy losses calculatio for a etwork with equidistat distributed load This situatio is the closest oe to the reality, supposig that each cosumators load is equal with. This is preseted i fig. 0 3 k - k - ( a ) [ A ] c c c c c c c c ( - ) c ( - ) c ( - 3 ) c ( - k + ) c ( - k + ) c ( b ) ( - k ) c c c 0 l 0 l 0 3 l 0 ( k - ) l 0 k l 0 ( - ) l 0 l 0 Fig. Schema reţelei cu sarciă echidistat distribuită: (a) schema moofilară; (b) distribuţia cureţilor. Fig. The electric etwork diagram with equidistat distributed load: (a) the sigle phase diagram;(b) the currets distributio Expresia complexă a curetului c al fiecărei sarcii se admite de forma primei relaţii (), iar curetul di trosoul (k-, k) este: cosϕ j siϕ ăderea de tesiue logitudială U este dată de relaţia: c c ( ); ( ) c U Prelucrarea algebrică a ultimei relaţii coduce la expresia [ m ] The complex expressio of curret c of each load is admitted like the relatio (), ad the curret from the portio of lie (k-, k) is: k, k k + () The logitudial voltage drop U is give by the relatio: cl0 0 0 k ( r ϕ + x si ϕ) ( k + ) cos () The algebrical processig of the last relatio leads to the expressio:
2 496 The 5 th teratioal Power Systems oferece + U c ( r 0 cosϕ + x 0 si ϕ) (3) ude ll 0 desemează lugimea totală a reţelei electrice. where ll 0 desigates the whole legth of the electric Pierderile de putere activă se vor determia cu relaţia: etwork. The active power losses will be established by the relatio: ed r l0c k ( k + ) 0 (4) care după efectuarea prelucrărilor algebrice devie: which, after the algebraical processigs becomes: ( + ) ( + ) r0 c (5) 6 iar pierderile de eergie se calculează cu relaţia: ad the eergy losses are calculated usig the relatio Wa kf t (6) f î care k f este coeficietul de formă al curbei de sarciă, where k f is the shape coefficiet of the load curve, ad t f iar t f este timpul de fucţioare al cosumatorului is the workig time of the cosumer Î cazul reţelei electrice di fig.., diagrama cureţilor the case of the electrical etwork from fig.., the se obţie di diagrama di fig..b. pri traslatarea currets diagram is obtaied from the diagram from acesteia cu mărimea 0. Dacă se admite petru curetul 0 fig..b. through traslatio of this oe of the size 0. f it relaţia următoare: is admitted for the curret 0 the ext relatio Î care N este umărul cosumatorilor reprezetaţi de 0 şi care trazitează reţeaua di fig.. uretul pri trosoul (k-, k) î acest caz devie: N c (7) J k, k 0 + k, k Where N is the umber cosumers represeted by 0 ad which trasit the etwork from fig.. The curret from the portio of lie (k-, k) i this case will be: (8) 0 3 k- k - c c c c c c c Fig.. Schema moofilară cu sarciă echidistat distribuită peste care se suprapue sarcia de trazit 0 Fig.. The sigle phase diagram with equidistat distributed load o which the trasit load 0 is superposed. Ţiâd cot de relaţiile () şi (7) curetul J k-,k di (8) Accordig to the relatios () ad (7), the curret J k-,k are expresia from (8) has the expressio: J k, k [( N + + ) k] c (9) ăderea de tesiue logitudială petru reţeaua di fig.. este dată de The logitudial voltage drop for the etwork from fig. is give by U ed cl0 k ( r0 cos + x0 siϕ) [ N + ( k + )] ϕ (0) care după efectuarea prelucrărilor matematice coduce la expresia which after the mathematical processig leads to the expressio: N + + U ed c ( r 0 cosϕ + x 0 si ϕ) () Petru pierderile de putere activă este valabilă ecuaţia For the active power losses followig equatio is valid: ed r l0c k care, după efectuarea sumei aalitice, permite evideţierea relaţiei codesate următoare: ed r0lc Pierderile de eergie electrică W aferete reţelei di fig. se calculează cu expresia (6).u relaţiile () şi (3) se poate aborda calculul acestor mărimi şi petru o reţea fără sarcii uiform echidistat distribuite ( 0), dar care este trazitată de o sarciă 0. Î acest caz căderea de tesiue U şi pierderea de putere au expresiile [ N + ( k + )] 0 () ad, after we do the aalytic sum, it allows us to otice the followig shortcut relatio: ( ) ( + ) ( + ) N + N + + (3) 6 The electric eergy losses W afferet to the etwork from fig. are calculated usig the expressio (6).With the relatios () ad (3) we ca attack the calculatio of these sizes ad for a etwork without equidistat uiform distributed loads ( 0), but which is trasited by a load 0.: this case the voltage drop U ad the power losses have the expressios: 0
3 , Timişoara, Romaia 497 U î timp ce pierderile de eergie W sut î cotiuare defiite de (6). ( r0 cosϕ + x0 si ϕ) r l N ( N + ) 0 l while the eergy losses W are still defied by (6). (4). Discuţie calitativă a modelelor sarciilor Modelul sarciilor uiform distribuite coduce la erori mari faţă de ultimul model propus şi prezetat î paragraful. Astfel, dacă î relaţiile () şi (3) se admite otaţia (7) ca şi: atuci acestea devi: + r cos ϕ + si ϕ + c o xo l o ; Se observă că difereţa ditre cele două relaţii poate fi semificativă î fucţie de mărimea sarciii c. Astfel petru căderea de tesiue, eroarea absolută este:. Qualitative debate o the loads models The model of uiform ditributed loads leads to great errors compared to the last model proposed ad itroduced i paragraf. So, if i the relatios () ad (3) we itroduce the otatio (7) as: c (5) the these become: U ( ) ( ) ( + )( + ) c r c o l o o c 6 (6) t is oticed that the differece betwee the two relatios ca be sigificatly varyig with the size of the load c. So, for the voltage drop, the absolute error is: ( ) ( 0 cos 0 si δ U r ϕ + x ϕ) c (7) sau, dacă ţiem cot de (5) î modul avem otherwise, accordig to (5) i modulus we have: δ ( U ) ( r0 cosϕ + x0 si ϕ) (8) iar petru pierderea de putere activă eroarea absolută este ad for the active power losses the absolute error is ( ) 3c + c δ r + 0l 0c 6 (9) care î situaţia itroducerii modulului relaţiei (5) devie: which, i the situatio of isertig the modulus of relatio (5), becomes: 3 + δ( ) r l ) Di aalizarea relaţiilor (8) şi (9) rezultă că erorile Aalysig the relatis (8) ad (9) it results that the sut cu atât mai mici cu cât umărul de sarcii echidistat errors grow smaller by the ecreasig of the umber of distribuţie este mai mare, î acest mod rezultâd şi o the equidistat ditributed loads, i this maer resultig a scădere a erorilor de calcul ditre cele două modele. Astfel dimiutio of the calculatio errors betwee the two models. petru 0, rezultă δ( U ) 5%, iar ( ) 6,67% δ P, dacă 0 0, altfel eroarea este mai mare. Î cocluzie susţiem că modelul matematic cel mai adecvat, după evaluarea cazurilor aterior prezetate, este uul di cele prezetate î această lucrare. So for 0 result δ( U ) 5%, ad ( ) 6,67% δ P, if 0 0, otherwise the error is greater. coclusio we agree that the most adequate mathematic model, after the evaluatio of the aterior preseted cases, is oe of these preseted i this paper. 3. Particularităţi topologice ale reţelei de joasă tesiue. Exemple de calcul. Î cotiuare meţioăm faptul că la joasă tesiue majoritatea cosumatorilor sut moofazaţi adoptâdu-se racordarea lor ître faze şi ulul de fucţioare. Meţioăm că metoda propusă se poate aplica umai PT-urilor ce deservesc cel puţi 3 cosumatori moofazaţi. Astfel sut redate doar două moduri de legare a acestora la reţeaua de distribuţie a eergiei electrice ( euiform, echidistat ). Evidet că umărul de posibilităţi de repartizare coectare este impresioat de mare, dar dispuerea lor se va realiza astfel îcât cureţii să fie, practic, cât mai echilibraţi. R A, R, R, R N sut rezisteţele fazelor (A,, ) şi a ulului N parcurse de cureţii de sarciă A,,, N afereţi fazelor (A,, ) şi ulului N; A,,, N umărul de cosumatori racordaţi pe fazele reţelei de distribuţie aalizate; N t - suma tuturor sarciilor reţelei aalizate, defiită de relaţia (), astfel: 3. The topology peculiarities of the low voltage etwork. alculatio examples Further o we metio that most of the costumers at a low voltage are sigle phase, that leads to their coectio betwee the phases ad the workig ull. We metio that the proposed method ca be applied oly to the statios which work for at least three sigle phases costumers. So are show oly two ways of coectig these at the electric eergy distributio etwork ( o-uiform, equidistat ). t s clear that the umber of distributio coectio possibilities is very large, but the disposig of them will be implemeted so that the currets to be as balaced as possible. R A, R, R, R N are the resistace of phases (A,, ) ad of the ull N crossed by the load currets A,,, N afferet to the phases(a,, ) ad to the ull N; A,,, N umber of costumer coected o the phases of the aalysed distributio etwork;
4 498 The 5 th teratioal Power Systems oferece Ître valoarea cureţilor ( A,,, N ) şi umărul acestora (N A, N, N, N t ) se pot defii relaţii aproximative. Astfel: N N t - sum of all the aalysed etwork loads, defied by the relatio N t N A + N + N () etwee the currets values ( A,,, N ) ad the umber of these (N A, N, N, N t ) we ca defie the approximate relatios. N ; ; i A,, N () i i t e e i, i ofiguraţia echidistat optimă, costă î aşezarea sarciilor echidistat, difereţiat pe fazele reţelei de distribuţie, ca î fig.3, adică: pe trosoul A cureţii celor N A sarcii alocate fazei A, sut aşezaţi la o distaţă egală cu 3 l, iar sarcia specifică aferetă sarciilor distribuite este i A pe trosoaele A şi A 3 3, umărul de sarcii echidistat distribuite este egal de asemeea cu N A, plasate la distaţa 3 l, iar cureţii alocaţi sarciilor este i, respectiv i ; pe trosoaele -D şi -D, umărul de sarcii echidistate este (N -N A ), fiid plasate la distaţa l, iar valoarea sarciilor este i, respectiv i ; pe trosoul E -F umărul de sarcii echidistate este (N -N ) ce sut plasate la distaţa l ître ele, iar mărimea sarciilor este i ; pe circuitul coductorului de ul itră curetul N. Distaţa l este defiită de relaţia: The equidistat optimum cofiguratio, costited i the arragemet of loads equidistat by, differeced o the phases of distributio etwork, like i fig.3, so: o portio of lie A the curret of N A allocated loads for phase A, are placed at a distace equal with 3 l, ad the specific load, affereted to the distributed loads, is i A ; o portios of lie A ad A 3 3, the umber of equidistat distributed loads is also equal with N A, placed at a distace of 3 l, ad the allocated currets for the loads is i, respective i ; o portios of lie -D ad -D, the umber of equidistat loads is (N -N A ), beig placed at a distace of l, ad the value of loads is i, respective i ; o portio of lie E -F, the umber of equidistat loads is (N -N ) that are placed at a distace of l betwee them, ad the size of loads is i ; o the ull coductor circuit the curret N gets i. The distace l is defied by the relatio: l L N + N + N (3) Referitor la mărimea sarciilor fiecărui aboat relaţiile de calcul sut ().Î cotiuare, precizăm valorile cureţilor ce trazitează trosoaele: A-A A - A 3 - -D D -E -F Î aceste codiţii pierderile de putere activă, pe fiecare troso, sut: ( ) A Relatig to loads sizes of each costumer, the calculus relatios are ().Further o, we specify the curret values which cross the portios of lie: A A A (4) A N A N (5) A 3 N A N (6) D (7) D E N N (8) F (9) [ r0 l ( N A ) ( N A ) A] ( N A ) r N ( N ) ( N ) A [ 0 A A A ] ( N ) [ r0 l N A ( N A ) ( N A ) ] ( N ) A these coditios the active power losses, o each portio of lie, are: ; (30) ; (3) ; (3) A3 3 P A r 0 l N A N ; (33) [ r0 l ( N A ) ( N A ) A] ( N A ) r N ( N ) ( N ) A [ 0 A A A ] ( N ) [ r0 l N A ( N A ) ( N A ) ] ( N ) A ; (30) ; (3) ; (3) A3 3 P A r 0 l N A N A r0 N A N 3 PE D r 0 N N PA A r0 ( N + N N A + 3) ; (33) ; (34) ; (35) ; (36) A
5 , Timişoara, Romaia 499 D ( N N + ) ( N + N + N + ) ( N + N + N + ) /[ ( N + N N )] r ; (37) 0 r0 6 + ; (38) N A A N A D 0 3 r l ( N N A ) ( N N A ) ( N N A ) ( N ) ( N N ) ( N N ) ( N N ) ( N ) ; (39). (40) D 0 3 r l A A A A A N A F (N - N ) E D (N - N A ) D A N A A 3 3 (N - N A ) N A fig.3 Mod de aşezare echidistat-optim a uui umăr oarecare de aboaţi casici la reţeaua electrică de j.t. fig.3 The equidistat-optimum lyig type, of a certai umber of low voltage domestic costumer. N (N - N ) (N - N A ) 4. Exemple umerice Î cotiuare sut prezetate rezultatele calculelor petru reţelele precizate de către serviciul tehic al SDFEE Ploieşti. Astfel î tabelele, sut cuprise rezultatele măsurătorilor cureţilor ca şi a datelor de material, ca şi a umărului de aboaţi casici (moofazaţi) racordaţi la aceste reţele. Î tabelele sut cuprise rezultatele calculului pierderilor de putere activă petru reţelele ale căror date au redate î tabelele. N A 4. Numerical examples Further o there are preseted the calculatio results for the specifed etworks by the egieerig departamet of SDFEE Ploieşti. So i the tables, the results of the currets mesuremets ad also the material data are icluded, ad the umber of sigle phase domestic costumers which are coected to these etworks. the table the results of active power losses calculatio for the etworks whose data are writte i the tables are icluded. Tab. DATE NTALE reţelele de joasă tesiue ale posturilor de trasformare PT PT 50 PT 43 PT 40 PT 506 PT 35 PT 438 Numar de cosumatori racordati la PT N tot abo uretul moitorizat pe faza A A 49,43 7,75 6,6 99,07 35,36 55,8 A uretul moitorizat pe faza 54,4 00,8 8,44 89,6 8,46 33,93 A uretul moitorizat pe faza 73,88 97,5,3 00, 6,78 43, A uretul moitorizat pe Nul N 54,5 37,58 8,45 3,8 3, 7, A Număr de aboati racordate la faza A N A abo Număr de aboati racordate la faza N abo Număr de aboati racordate la faza N abo Rezisteta specifica a coductorului faza (3x70mm ) r 0 0,437 0,08 0,874 0,437 0,437 0,437 Ω/km Rezisteta specifica a coductorului de ul (50mm ) r 0 0,6 0,6,4 0,6 0,6 0,6 Ω/km Lugimea retelei L m Tab. SHEMA DE ALUL pierderi de putere î reţelele de joasă tesiue ale PT-urilor Trosoul retelei PT 50 PT 43 PT 40 PT 506 PT 35 PT 438 UM A - 337,8 65, 54,35 7,6 69,70 90,78 W A - 3,58 3,96,95 44,78 4,4, W A3-3,90,5,94 50,65 6,43, W - A 8,80 30,5 4,3 98,6 9,8 4,46 W - A3 7,36 6,3 4,09,54 4,08 4,43 W E - D 5,86 3,90,50 70,58 0,75 3,68 W A - A 47,99 57,60 8,70 65,04 95,05 35,5 W - D 7,09 8,4 7,70 87,3 7,4 48,5 W Nul de exploatare 79,43 86,54,78 3,09 33,85 36,60 W D - 0,04 6,86 0,03 0,39 0,45 0,95 W D - 0,0 6,38 0,0 0,35 0,4 0,58 W - E 3,68,36 0,9,6 0,3 0,97 W TOTAL 634,56 03,67 38,38 4,04 97,64 80,6 W
6 500 Precizăm că la aceste reţele electrice sut racordaţi umai cosumatori casici, care au umai receptori moofazaţi. Î tabelul 3 sut cetralizate rezultatele calculului pierderilor de putere activă petru 6 cofiguraţii de reţele electrice de distribuţie de joasă tesiue, di patrimoiul SDFEE Ploieşti, precizate şi alese împreuă cu acordul serviciului tehic al acestei sucursale de distribuţie şi furizare a eergiei electrice precizate. The 5 th teratioal Power Systems oferece We specify that at these electric etworks oly domestic costumers are coected, who have oly sigle phase receivers. the table 3 the results for 6 active power losses calculatio of low voltage distributio etworks are cetralized, property of SDFEE Ploieşti, specified ad chose together with the egieerig departamet from SDFEE Ploieşti. Tab.3.omparaţie ître valorile pierderilor cu cosumatorii cocetraţi la capătul liiei şi valorile pierderilor cu cosumatorii echidistat distribuiţi. Tab.3 ompariso betwee the values of the loses ad the cocetrated cosumers at the ed of the lie ad the values of the loses ad the equidistat distributed cosumers. Puterea cosumată osumed power osumatorii echidistat distribuiţi The equidistat distributed cosumers osumatorii cocetraţi î capătul liiei The cocetrated cosumers at the ed of the lie PT P faze ul total ε tot ε ul faze ul total ε tot ε ul kw kw kw kw % % kw kw kw % % ocluzii Î urma efectuării calculelor pierderilor de putere activă petru câteva reţele electrice reale, di cadrul FDFEE Muteia Nord, se pot remarca următoarele cocluzii: utilizarea algoritmului propus î lucrare petru câteva reţelele electrice reale, coduce la valori ale pierderilor de putere activă cuprise î domeiul ε tot є [0,54;,36]%; pierderilor aferete coductorului de ul, raportat la puterea acivă totală, este cuprisă î itervalul ε ul є [0,06; 0,68]%, petru reţelele electrice de joasă tesiue reale; poderea pierderilor de putere activă aferete coductorului de ul ε ul faţă de pierderile de putere activă totale ε tot, este cuprisă î domeiul ε ul εtot [ 3,9;34,4 ]%; cometâd rezultatele di tabelul 3, precizăm că valoarea pierderilor de putere activă procetuale totale este acceptabilă (<5%). 5. oclusios As a result of the calculatio of the active power losses for some real electric etworks, from FDFEE Muteia Nord, we ca remark the followig coclusios: the utilizatio of the suggested algorithm i this paper for some real electric etworks, leads to values of the active power losses that are icluded i the rage ε tot є [0,54;,36]%; the ull coductor losses, reported to the total active power, are icluded i the rage ε ul є [0,063; 0,68]%, for the real low voltage electric etworks; the share of the active power losses afferet to the ull coductor ε ul compared to the total active power losses ε tot, is icluded i the rage ε ul εtot [ 3,9;34,4 ]%; discussig the results from table 3, we specify that the value of the total percetage of the active power losses is acceptable (<5%). ibliografie (Refereces). Albert, H., Mihăilescu, A. - Pierderi de putere şi eergie i reţelele electrice. Editura tehică, ucureşti, Albert, H. - Pierderi de putere şi eergie i reţelele electrice. Metodologie de calcul. Editura tehică, ucureşti, Albert, H., Florea,. Alimetarea cu eergie electrică a itrepriderilor idustriale. vol. Editura tehică, ucureşti, oescu, G.T., Pop, O. - gieria sistemelor de distribuţie a eergiei electrice. Editura tehică, ucureşti, * * * - PE 39/997. strucţiue privid determiarea PT î reţelele electrice. etrul de formare şi Documetare Eergetică (DE). EMENERG, ucureşti, acobescu, Gh., ordăescu,., Eremia, M., Tudose, M., Dumitriu,., Toader,., Ţeovici, R., Eache, R. - Reţele electrice petru alimetarea îtrepriderilor. ulegeri de probleme petru igieri. Editura tehică, ucureşti, Georgescu, Gh., Gavrilaş, M., Rădăşau, D. - alculul şi reducerea pierderilor de putere şi eergie î reţelele electrice. Editura Spectrum. aşi ordăescu,., Toader,., Dumitriu,., Scutariu, M., Triştiu,. - Determiarea pierderilor de putere şi eergie pe coturul SD lfov. otract de cercetare ştiiţifică MM 09 / Postolache, P., Toader,., Surdu,., ătrâu, F. - mpactul tehico-ecoomic al îcǎrcǎrii eutrului reţelelor de joasǎ tesiue asupra fucţioǎrii acestora şi a calitǎţii serviciului de furizare a eergiei electrice î cadrul S.D. ostaţa. Lucrare de cercetare ştiiţifică r.edu-0-0 di
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