{"id":9112,"date":"2016-06-17T15:30:03","date_gmt":"2016-06-17T15:30:03","guid":{"rendered":"https:\/\/automation-electric.com\/corectia-factorului-de-putere\/"},"modified":"2026-01-17T20:57:16","modified_gmt":"2026-01-17T20:57:16","slug":"corectia-factorului-de-putere","status":"publish","type":"post","link":"https:\/\/automation-electric.com\/ro\/corectia-factorului-de-putere\/","title":{"rendered":"Corec\u021bia factorului de putere"},"content":{"rendered":"

Eficien\u021ba energetic\u0103 a fost, este \u0219i va fi unul dintre subiectele de mare interes ale societ\u0103\u021bii moderne. \u00cen absolut orice industrie, indiferent de domeniul de activitate, fiecare companie \u00ee\u0219i propune, prin intermediul produselor pe care le comercializeaz\u0103, ca acestea s\u0103 consume c\u00e2t mai pu\u021bin\u0103 energie electric\u0103 \u0219i s\u0103 ofere performan\u021be c\u00e2t mai ridicate. Factorul de putere<\/strong> poate afecta serios aceast\u0103 eficien\u021b\u0103 energetic\u0103, \u00een diferite sisteme electrice, dac\u0103 nu se iau m\u0103suri corespunz\u0103toare, dup\u0103 cum o s\u0103 vedem \u00een continuare. <\/span><\/p>\n

\u00cenainte s\u0103 trecem la partea tehnic\u0103, am s\u0103 \u00eencerc s\u0103 prezint o analogie, astfel \u00eenc\u00e2t s\u0103 \u00een\u021belegem ce este de fapt acest factor de putere<\/strong>. \u00cen micul nostru experiment, o s\u0103 consider\u0103m un c\u0103rucior, care merge pe \u0219ine asemenea unui tren \u0219i poate fi tractat de o persoan\u0103 (fig.1). Dup\u0103 cum bine \u0219tim, indiferent de pozi\u021bia persoanei fa\u021b\u0103 de \u0219ine, c\u0103ruciorul nu o s\u0103 \u00ee\u0219i schimbe direc\u021bia, bine\u00een\u021beles excludem ideea c\u0103 sare de pe \u0219ine. <\/span><\/p>\n

\"\"<\/span><\/p>\n

fig. 1<\/span><\/p>\n

\u00cen cazul \u00een care persoana care tracteaz\u0103 nu se afl\u0103 exact pe mijlocul \u0219inelor, tot timpul \u00eentre pozi\u021bia persoanei \u0219i direc\u021bia de deplasare a c\u0103ruciorului o s\u0103 existe un unghi, pe care \u00een fig. 1 l-am notat cu . <\/strong>Acum o s\u0103 propunem ni\u0219te situa\u021bii posibile \u00een care se poate afla persoana respectiv\u0103, \u00een timp ce tracteaz\u0103 c\u0103ruciorul.<\/span><\/p>\n

Situa\u021bia 1<\/strong>. \u00cen aceast\u0103 situa\u021bie consider\u0103m c\u0103 unghiul dintre pozi\u021bia persoanei care tracteaz\u0103 c\u0103ruciorul \u0219i direc\u021bia de deplasare a acestuia este foarte mare, tinde undeva spre 90 de grade (fig. 2). C\u00e2nd persoana o s\u0103 \u00eenceap\u0103 s\u0103 tracteze c\u0103ruciorul nu \"\"<\/span><\/p>\n

fig.2<\/span><\/p>\n

o s\u0103 fie deloc surprins\u0103 c\u0103 o s\u0103 depun\u0103 un efort serios, adic\u0103 o s\u0103 consume destul de mult\u0103 energie \u0219i c\u0103ruciorul o s\u0103 se deplaseze foarte pu\u021bin, ba mai mult \u00een cazul \u00een care unghiul <\/strong>este de exact 90 de grade o s\u0103 depun\u0103 toat\u0103 energia care o de\u021bine \u0219i c\u0103ruciorul nu o s\u0103 se deplaseze deloc. Dac\u0103 am avea instalat un contor de energie, acesta o s\u0103 \u00eenregistreze frumu\u0219el \u0219i bini\u0219or toat\u0103 energia consumat\u0103, chiar dac\u0103 c\u0103rucirul o s\u0103 cam stea pe loc. <\/span><\/p>\n

Situa\u021bia<\/strong> 2<\/strong>. <\/strong>Afl\u00e2ndu-se \u00een situa\u021bia 1. <\/b>cu siguran\u021b\u0103 interlocutorului nostru nu o s\u0103 \u00eei prea convin\u0103 ideea s\u0103 tracteze c\u0103ruciorul \u00een asemenea condi\u021bii, complet defavorabile pentru el \u0219i o s\u0103 se deplaseze u\u0219or u\u0219or spre centrul \u0219inelor unde unghiul <\/strong>dintre pozi\u021bia lui \u0219i direc\u021bia de deplasare a c\u0103ruciorului o s\u0103 tind\u0103 spre zero grade (fig. 3). Cu c\u00e2t se deplaseaz\u0103 mai \"\"<\/span><\/p>\n

fig. 3<\/span><\/p>\n

Cu c\u00e2t este mai aproape de centrul \u0219inelor, cu at\u00e2t \u00ee\u0219i va da seama c\u0103 efortul depus se reflect\u0103 \u0219i \u00een deplasarea c\u0103ruciorului, ba mai mult, c\u00e2nd unghiul devine zero, \u00ee\u0219i d\u0103 seama c\u0103 toat\u0103 energia depus\u0103 \u00een tractarea c\u0103ruciorului se reflect\u0103 \u0219i \u00een deplasarea acestuia \u0219i, bine\u00een\u021beles, va \u00eencerca s\u0103 men\u021bin\u0103 aceast\u0103 pozi\u021bie \u00een jurul valorii zero. De data aceasta, contorul nostru va \u00eenregistra energia consumat\u0103, dar \u0219i c\u0103ruciorul s-a deplasat dup\u0103 a\u0219tept\u0103ri.<\/span><\/p>\n

Situa\u021bii similare se \u00eent\u00e2mpl\u0103 \u0219i \u00een sistemele electrice care con\u021bin elemente neliniare de circuit (bobine, condensatoare, diode, tranzistoare, etc) acestea fiind \u00eemp\u0103r\u021bite \u00een elemente pasive(bobine, condensatoare) \u0219i elemente active (diode, tranzistoare, etc). Noi o s\u0103 ne ocup\u0103m exclusiv de elementele pasive, pentru c\u0103 acestea sunt prezente \u00een diferite circuite electrice pe scar\u0103 larg\u0103 (ex. motoare asincrone) \u0219i sunt mari consumatori de energie. <\/span><\/p>\n

\u00cen circuitele electrice \u00een care tensiunea \u0219i curentul sunt m\u0103rimi alternative \u00een func\u021bie de natura sarcinii puterea poate fi definit\u0103 astfel:<\/span><\/p>\n

– putere aparent\u0103 [VA]<\/span><\/p>\n

– putere activ\u0103 [W]<\/span><\/p>\n

– putere reactiv\u0103 [VAR]<\/span><\/p>\n

acestea sunt valorile puterilor pentru tensiune monofazat\u0103, \u00een cazul tensiunii trifazate avem:<\/span><\/p>\n

– putere aparent\u0103 [VA]<\/span><\/p>\n

– putere activ\u0103 [W]<\/span><\/p>\n

– putere reactiv\u0103[VAR]<\/span><\/p>\n

Dac\u0103 facem un calcul simplu \u0219i raport\u0103m puterea aparent\u0103 la puterea activ\u0103 ob\u021binem factorul de putere:<\/strong><\/span><\/p>\n

<\/strong>Acum dac\u0103 arunc\u0103m o privire la situa\u021bia cu c\u0103ruciorul vedem foarte clar c\u0103 cu c\u00e2t unghiul a fost mai aproape de 90 de grade s-a consumat o anumit\u0103 cantitate de energie dar deplasarea a fost foarte mic\u0103, sau chiar nul\u0103 c\u00e2nd = , rezult\u0103 un factor de putere cos foarte mic sau chiar zero dac\u0103 unghiul ajunge la 90 grade, dup\u0103 care \u00een situa\u021bia 2 c\u00e2nd unghiul s-a redus \u0219i a tins spre grade, energia consumat\u0103 s-a reflectat \u00een deplasarea c\u0103ruciorului = , rezult\u0103 un factor de putere cos= 1, pe scurt am consumat aceea\u0219i energie ca \u0219i \u00een cazul precedent dar c\u0103ruciorul s-a deplasat mult mai mult. Deci \u00een concluzie, pentru ca s\u0103 fim c\u00e2t mai eficien\u021bi din punct de vedere al consumului energetic trebuie s\u0103 g\u0103sim solu\u021bii astfel \u00eenc\u00e2t s\u0103 men\u021binem acest unghi c\u00e2t mai aproape de grade, adic\u0103 un factor de putere cos c\u00e2t mai aproape de 1. Acest factor de putere este puternic influen\u021bat de prezen\u021ba elementelor reactive de circuit bobina \u0219i condensatorul, care sunt principalii vinova\u021bi c\u0103 valoarea sa este diferit\u0103 de 1. Bobina conduce deta\u0219at acest top deoarece este prezent\u0103 \u00een construc\u021bia motoarelor electrice, deci \u00een marea majoritate a cazurilor vom avea de corectat un factor de putere de tip inductiv. Dac\u0103 privim rela\u021biile celor trei puteri pur matematic vedem c\u0103 exist\u0103 urm\u0103toarea egalitate care mai este cunoscut\u0103 \u0219i sub denumirea de triunghiul puterilor: <\/span><\/p>\n

Cele dou\u0103 elemente de circuit (bobina \u0219i condensatorul) au un comportament diferit dar am\u00e2ndou\u0103 introduc un defazaj de 90 de grade \u00eentre tensiune \u0219i curent, tensiunea la bornele condensatorului este \u00een urma curentului cu 90 grade iar intensitatea curentului electric prin bobin\u0103 fiind \u00een urma tensiunii cu 90 grade, ceea ce este foarte util \u00een cazul nostru deoarece dac\u0103 dorim s\u0103 corect\u0103m un factor de putere inductiv vom introduce \u00een circuit un condensator \u0219i \u00een mod similar pentru un factor de putere capacitiv vom introduce o bobin\u0103 (fig. 4).<\/span><\/p>\n

\"\"<\/p>\n

fig. 4<\/span><\/p>\n

De fapt din punct de vedere electric a corecta factorul de putere<\/strong> \u00eenseamn\u0103 a “for\u021ba” cele dou\u0103 m\u0103rimi alternative tensiune \u0219i curent s\u0103 oscileze \u00een faz\u0103, adic\u0103 defazajul dintre ele s\u0103 fie c\u00e2t mai aproape de 0.<\/span><\/p>\n

Exemplu de calcul<\/strong><\/span><\/p>\n

Dup\u0103 cum am pomenit deja \u00een marea majoritate a cazurilor avem de corectat un factor de putere inductiv care este creat de bobine, cel mai des \u00eent\u00e2lnit exemplu este cel al motoarelor electrice. De obicei pe pl\u0103cu\u021ba cu informa\u021bii dat\u0103 de produc\u0103tor acest factor de putere este marcat av\u00e2nd valori \u00eentre (0.6-0.9), \u00eempreun\u0103 cu alte date legate de motorul respectiv. A\u0219adar s\u0103 lu\u0103m ca exemplu un motor electric asincron cu o putere activ\u0103 de 30 kW, alimentat la o tensiune de 400 de vol\u021bi la frecven\u021ba de 50 Hz \u0219i un factor de putere cos=0.8. Dup\u0103 cum deja am afirmat mai sus fiind vorba de corec\u021bia unui factor de putere inductiv va trebui s\u0103 introducem \u00een circuit un condensator pentru a aduce valoarea lui cos c\u00e2t mai aproape de 1. Pentru acesta trebuie s\u0103 afl\u0103m care este puterea reactiv\u0103 \u0219i bine\u00een\u021beles care este valoarea condensatorului care trebuie introdus \u00een circuitul motorului. Din formula triunghiului puterilor putem simplu deduce valoarea puterii reactive: <\/span><\/p>\n

Deocamdat\u0103 \u00een aceast\u0103 rela\u021bie nu cunoa\u0219tem valoarea puterii aparente dar o putem deduce foarte simplu din formula puterii active:<\/span><\/p>\n

<\/span>
\nDe aici scoatem puterea aparent\u0103:<\/span><\/p>\n

<\/span>
\nRevenind la puterea reactiv\u0103:<\/span><\/p>\n

<\/span><\/p>\n

\u00cen concluzie va fi necesar s\u0103 introducem \u00een circuit \u00een paralel cu bobinele motorului un condensator care s\u0103 produc\u0103 echivalentul a 22.5 [kVAR] putere reactiv\u0103 capacitiv\u0103. Cum afl\u0103m valoarea condensatorului ? ei bine destul de simplu, dac\u0103 ne \u00eentoarcem la sistemul de ecua\u021bii aferent celor 3 tipuri de puteri \u0219i rescriem sub alt\u0103 form\u0103 ecua\u021bia puterii reactive vom avea urm\u0103toarea formul\u0103 echivalent\u0103: <\/span><\/p>\n

<\/span><\/p>\n

Dup\u0103 cum se vede \u00een ecua\u021bia de mai sus, am introdus un nou termen care poart\u0103 denumirea de reactan\u021b\u0103 \u2013 acesta put\u00e2nd fi, \u00een func\u021bie de natura elementului reactiv, inductiv\u0103 \u00een cazul bobinelor \u0219i capacitiv\u0103 \u00een cazul condensatoarelor. Ecua\u021biile celor dou\u0103 reactan\u021be sunt astfel:<\/span><\/p>\n

reactan\u021ba inductiv\u0103: <\/span><\/p>\n

reactan\u021ba capacitiv\u0103:<\/span><\/p>\n

<\/span><\/p>\n

unde:<\/span><\/p>\n

-viteza unghiular\u0103 [rad\/s]<\/span><\/p>\n

L-inductan\u021ba bobinei [henry]<\/span><\/p>\n

C- capacitatea condensatorului [F]<\/span><\/p>\n

f-frecven\u021ba [Hz]<\/span><\/p>\n

\u00cen cazul nostru, suntem interesa\u021bi de reactan\u021ba capacitiv\u0103 pe care o vom introduce \u00een ecua\u021bia puterii reactive, de unde vom deduce valoarea condensatorului:<\/span><\/p>\n

Din:<\/span><\/p>\n

rezult\u0103 valoarea capacitorului:<\/span><\/p>\n

Valoarea lui sin va fi egal\u0103 cu 1, deoarece, dup\u0103 cum am amintit mai sus, indiferent de elementul de circuit introdus, bobin\u0103 sau condensator, acesta va introduce \u00een circuit un defazaj \u00eentre tensiune \u0219i curent de 90 de grade. \u00cen final, dup\u0103 calcule simple, s-a ob\u021binut:<\/span><\/p>\n

<\/span><\/p>\n

Se va alege o valoare standard c\u00e2t mai aproape de valoarea calculat\u0103, dac\u0103 exist\u0103, sau se vor monta mai multe condensatoare \u00een paralel.<\/span><\/p>\n

Tehnologia s-a supus cerin\u021belor \u0219i mai multe companii au dezvoltat controlere speciale pentru a men\u021bine acest factor de putere la un nivel c\u00e2t mai aproape de 1. \u00cen mediul industrial, unde exist\u0103 zeci sau sute de motoare \u0219i acest factor variaz\u0103 continuu \u00een func\u021bie de c\u00e2te motoare func\u021bioneaz\u0103 la un moment dat, un asemenea controler este foarte important. Func\u021bionarea unui asemenea controler este destul de simpl\u0103, un num\u0103r de condensatoare de diferite valori vor fi montate \u00eentr-un dulap, iar controlerul va cupla sau decupla tot timpul num\u0103rul necesar de condensatoare, astfel c\u0103 valoarea factorului de putere va fi men\u021binut\u0103 aproape de 1. <\/span><\/p>\n

O schem\u0103 simpl\u0103 de conectare a acestor condensatoare la un motor este prezentat\u0103 \u00een schema de la \u00eenceputul articolului.<\/span><\/p>\n

<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Eficien\u021ba energetic\u0103 a fost, este \u0219i va fi unul dintre subiectele de mare interes ale societ\u0103\u021bii moderne. \u00cen absolut orice industrie, indiferent de domeniul de activitate, fiecare companie \u00ee\u0219i propune,<\/p>\n","protected":false},"author":1,"featured_media":9113,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[934],"tags":[],"class_list":["post-9112","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-corectia-factorului-de-putere"],"acf":[],"yoast_head":"\nCorec\u021bia factorului de putere | Automation-Electric<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/automation-electric.com\/ro\/corectia-factorului-de-putere\/\" \/>\n<meta property=\"og:locale\" content=\"ro_RO\" \/>\n<meta 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