Fig.1. Dependenţele
rezistenţelor
Problema 1.8 La un post de transformare urban e=
ste
instalat un transformator trifazat de putere de tipul ТМ – 40/10/0,4. De determinat parametrii schemei echivalente a acestui
transformator şi de estimat dacă se poate de neglijat componenta
activă a tensiunii de scurtcircuit.
Rezolvare: Din literatura tehnică se aleg
datele caracteristice (de paşaport) a acestui transformator şi an=
ume:
pentru ТМ – 40/1=
0/0,4:=
sub> MVA; =
sub> kV;
=
sub> kV;
=
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă=
a
transformatorului se determină cu următoarea relaţie:=
o:p>
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
=
sub>;
=
&nb=
sp; =
=
sub>.
<=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>Conductanţa
activă a transformatoarelor se determină cu expresia:<=
/span>
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a
transformatorului se determină cu relaţia:
=
&nb=
sp; =
sub>;
=
&nb=
sp; =
=
sub> kvar.<=
/o:p>
Pentru a estima d=
acă
se poate de neglijat componenta activă a tensiunii de scurtcircuit =
sub> se fac
următoarele calcule (se consideră =
sub>):
=
&nb=
sp;
=
sub>;
Eroarea se determină cu expres=
ia:
=
&nb=
sp; =
=
sub>.
Din calcule se observă=
bine
că la calculul reactanţei a transformatorului trebuie de luat
în consideraţie componenta activă a tensiunii de scurtcircu=
it =
sub>, deoarece se obţine =
sub>.
Problema 1.9 La un post de transformare al unei=
uzine
este instalat un transformator trifazat de putere de următorul tip ТM – 1600/10/0,4. Se =
cere
să se determine parametrii schemei echivalente a acestui transformator
şi de estimat dacă se poate de neglijat componenta activă a
tensiunii de scurtcircuit.
Rezolvare: Din literatura tehnică se aleg
datele caracteristice (de paşaport) a acestui transformator şi an=
ume:
pentru ТM – 1600/10/0,=
4: =
sub> MVA; <=
!--[if gte vml 1]>
=
sub> kV; =
sub> kV;
=
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă a transformatorulu=
i se
determină cu următoarea relaţie:
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp; =
sub>;
=
&nb=
sp; =
=
sub>;
=
&nb=
sp; =
=
sub>.
<=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>Conductanţa
activă a transformatorului se determină cu expresia:=
span>
=
=
&nb=
sp; =
sub>.
Susceptanţa inductivă a
transformatorului se determină cu expresia:
=
&nb=
sp; =
=
sub>;
=
&nb=
sp; =
=
sub> kvar.<=
/o:p>
Pentru a estima dacă se
poate de neglijat componenta activă a tensiunii de scurtcircuit <=
!--[if gte vml 1]>
=
sub> se fac
următoarele calcule (se consideră =
sub>):
=
&nb=
sp; =
=
sub>;
=
&nb=
sp;
=
&nb=
sp;=
sub>
Din analiza rezultatelor
calculelor se observă bine că la calculul reactanţei a
transformatorului trebuie de luat în consideraţie componenta
activă a tensiunii de scurtcircuit =
sub>, deoarece se obţine =
sub>.
Problema 1.10 Staţia principală
coborâtoare (SPC) a unei uzine industriale este echipată cu
două transformatoare trifazate de putere de tipul ТМ – 630/35/10. De determinat parametrii schemei echivalente a acestui transfo=
rmator
şi de estimat dacă se poate de neglijat componenta activă a
tensiunii de scurtcircuit.
Rezolvare:=
Din literatura tehnică se aleg
datele caracteristice (de paşaport) a acestui transformator şi an=
ume:
pentru ТМ – 630/=
35/10:
=
sub> MVA; <=
!--[if gte vml 1]>
=
sub> kV;
=
sub> kV;
=
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă=
a
transformatorului se determină cu următoarea relaţie:=
o:p>
=
=
&nb=
sp; =
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
=
sub>;
=
=
=
sub>.
<=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>Conductanţa
activă a transformatoarelor se determină cu expresia:<=
/span>
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a
transformatorului se determină cu relaţia:
=
=
=
sub>;
=
&nb=
sp;
=
sub> kvar.<=
/o:p>
Pentru a estima d=
acă
se poate de neglijat componenta activă a tensiunii de scurtcircuit =
sub> se fac
următoarele calcule (se consideră =
sub>):
=
&nb=
sp;
=
sub>;
Eroarea se determină cu expres=
ia:
=
&nb=
sp; =
=
sub>.
Din calcule se observă=
bine
că la calculul reactanţei a transformatorului trebuie de luat
în consideraţie componenta activă a tensiunii de scurtcircu=
it =
sub>, deoarece se obţine =
sub>, se recomandă de neglijat când =
sub>.
Problema 1.11 Să se determine parametrii sc=
hemei echivalente
şi de estimat dacă se poate de neglijat componenta activă a
tensiunii de scurtcircuit a transformatorului de tipul
=
058;ДН
–16000/35/10.
Rezolvare:=
Din literatura tehnică se aleg
datele caracteristice (de paşaport) a acestui transformator şi an=
ume:
pentru ТДН
–16000/35/10: =
sub>MVA; =
sub>kV; =
sub>kV; =
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă=
a
transformatorului se determină cu următoarea relaţie:=
o:p>
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
=
sub>.
<=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>Conductanţa
activă a transformatoarelor se determină cu expresia:<=
/span>
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a transformato=
rului
se determină cu relaţia:
=
&nb=
sp;
=
sub>;
=
sub> kvar.<=
/o:p>
Pentru a estima d=
acă
se poate de neglijat componenta activă a tensiunii de scurtcircuit =
sub> se fac
următoarele calcule (se consideră =
sub>):
=
&nb=
sp;
=
sub>;
Eroarea se determină cu expres=
ia:
=
&nb=
sp; =
=
sub>.
Din calcule se observă=
bine
că la calculul reactanţei a transformatorului componenta activ=
59;
a tensiunii de scurtcircuit =
sub> poate fi
neglijată deoarece se obţine =
sub>. De aici se poate de făcut următoarea concluzi=
e:
pentru transformatoarele de puteri mari se poate de neglijat componenta
activă a tensiunii de scurtcircuit =
sub>.
Problema 1.12 La staţia electrică din =
satul
Răduleni sunt instalate două transformatoare trifazate de putere =
de
tipul ТМН –
6300/110/10. De determinat parametrii schemei echivalente a acestor
transformatoare şi de estimat dacă se poate de neglijat componenta
activă a tensiunii de scurtcircuit.
Rezolvare:=
Din literatura tehnică se aleg
datele caracteristice (de paşaport) a acestor transformatoare şi
anume: pentru ТМН
– 6300/110/10: =
sub> MVA; <=
!--[if gte vml 1]>
=
sub> kV; =
sub> kV;
=
sub> %; =
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă a transformatorulu=
i se
determină cu următoarea relaţie:
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
=
sub>;
=
&nb=
sp; =
=
sub>.
Conductanţa activă=
; a
transformatorului se determină cu expresia:
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a
transformatorului se determină cu relaţia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
=
sub> kvar.<=
/o:p>
Pentru a estima d=
acă
se poate de neglijat componenta activă a tensiunii de scurtcircuit =
sub> se fac
următoarele calcule (se consideră =
sub>):
=
&nb=
sp;
=
sub>;
Eroarea se determină cu expres=
ia:
=
&nb=
sp; =
=
sub>.
Din calcule se observă bine că la
calculul reactanţei a transformatorului componenta activă a tensi=
unii
de scurtcircuit =
sub> poate fi
neglijată deoarece se obţine =
sub>.
=
Problema
1.13 La staţia electric=
9; din
satul Burlăceni sunt instalate două transformatoare trifazate de
putere de următorul tip i=
8;ДН
– 16000/110/10. De determinat parametrii schemei echivalente a
acestor transformatoare.
Rezolvare: Din literatura
tehnică se aleg datele caracteristice (de paşaport) a acestor
transformatoare şi anume: pentru ТДН
– 16000/110/10: =
sub> MVA; <=
!--[if gte vml 1]>
=
sub> kV; =
sub> kV;
=
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă a transformatorulu=
i se
determină cu următoarea relaţie:
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>.
Conductanţa activă=
; a
transformatorului se determină cu expresia:
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a
transformatorului se determină cu relaţia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp;
=
sub> kvar.<=
/o:p>
=
Problema
1.14 La staţia electric=
9;
”Ciocana” din mun. Chişinău sunt instalate două
transformatoare trifazate de putere cu înfăşurări scin=
date
(divizate) de următorul tip &=
#1058;PДН
– 40000/110/10/10. De determinat parametrii schemei echivalente a
acestor transformatoare.
Rezolvare: Din literatura
tehnică se aleg datele caracteristice (de paşaport) a acestor
transformatoare şi anume: pentru ТPДН
– 40000/110/10/10:=
sub> MVA; =
sub> kV;
=
sub> kV;
=
sub> %;
=
sub> %;
=
sub> kW;
=
sub> kW;
=
sub> %.
Rezistenţa activă a transformatorulu=
i se
determină cu următoarea relaţie:
=
&nb=
sp; =
=
sub>Ω.
Reactanţa inductivă a transformatoru=
lui
se determină cu expresia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp;
=
sub>.
Conductanţa activă=
; a
transformatorului se determină cu expresia:
=
&nb=
sp;
=
sub>.
Susceptanţa inductivă a
transformatorului se determină cu relaţia:
=
&nb=
sp;
=
sub>;
=
&nb=
sp;
=
sub> kvar.<=
/o:p>
Problema 1.15 Pentru transforma=
torul
trifazat cu trei înfăşurări, montat la staţia
electrică din oraşul Floreşti, de tipul ТДТН–25000/110/35/10 cu raportul
puterilor 100/66,7/66,7% se cere să se calculeze parametrii schemei
echivalente raportaţi la tensiunea înfăşurării
primare.
Rezolvare<=
/u>: Transformatorul=
dat are
următoarele caracteristice:
Un1=3D=
115 kV, DPsc=3D145 kW, DP0=3D=
36 kW, usc12%=3D10,5%,<=
span
style=3D'mso-spacerun:yes'> usc13%=3D17%, usc23%=3D6%, I0%=3D1,0%.=
Pentru acest tip constructiv de transformator rezistenţele
înfăşurărilor se determină:
=
; =
;
.
Reactanţa se determină pe baza tensiunilor de scurtcircuit
între perechile de înfăşurări (=
sub>) care sunt indicate în fişa tehnică a tr=
ansformatorului,
pentru care la început se calculează tensiunea de scurtcircuit a
înfăşurărilor:
=
sub>
Rezistenţele reactive se determină:
=
sub>,=
sub> ,
Calculele ne demonstrează, că rezistenţa activă
în transformatoarele de putere mare poate fi neglijată deoarece =
ea
are valori mici în comparaţie cu cea reactivă.=
span>
Conductanţa activă a transformatorului:
Susceptanţa se determină după puterea reactivă de m=
agnetizare
=
sub> kvar;<=
/o:p>
Problema 2.1=
O linie electrică aeriană simplu circuit cu
tensiunea 10 kV este echipată cu conductoare Al-Ol–95/16
(AC–95/16) dispuse pe stâlpi de beton cu coronamentul în
vârfurile unui triunghi echilateral, linia electrică are lungime=
a de
8 km
şi distanţa între conductoare este D =3D 1 m. LEA alimentează un consumator care necesită=
; o
putere P =3D 1 kW la un factor =
de
putere cosφ =3D 0,9. La intrare în linie este impusă tensiu=
nea U1 =3D 10 kV. Se cere de
calculat:
-
valorile aproximative ale soluţiilor =
sub> şi =
sub>;
-
factorul de putere în ipoteza că =
sub>;
-
factorul de putere în ipoteza că fazorul <=
sub>=
sub> coincide
după sens cu fazorul =
sub>.
Rezolvare: Deoarece avem Unom
=3D 35 kV utilizăm schema echivalentă din figura 1.3,d.
Rezistenţa activă poate fi determinată cu relaţia de
mai jos.
=
sub>.
Reactanţa inductivă la fel poate fi
determinată cu următoarea relaţie:
=
sub>.
1. &n=
bsp;
Calculul valorilor aproximative ale soluţiilor <=
sub>=
sub> şi =
sub>:
=
sub>,
Considerând că: =
sub> se obţ=
ine:
=
sub>;
│∙U2
=
sub>.
În continuare se rezolvă ecuaţ=
ia
de gradul doi.
P=
span>2 =3D 1 kW; Q2 =3D P2∙tgφ =3D 0,48 kvar.=
p>
=
sub>;
=
sub>3,627 =3D 0;
Δ =
span>=3D 102 –
4∙3,627 =3D 100 – 14,509 =3D 85,491;
=
sub> kV;
=
sub> kV.
2. Determinarea fact=
orului
de putere în ipoteza că =
sub>:
=
sub>.
Considerând=
că
=
sub> din
expresia de mai sus se obţine:
=
sub>;
=
sub>0; =
sub>; =
sub>; =
sub> cosφ=3D1.=
3. Determinarea fact=
orului
de putere în ipoteza că fazorul =
sub> coincide
după sens cu fazorul =
sub>:
Dacă fazorul =
sub> coincide
după sens cu fazorul =
sub> atunci:
=
sub>; =
sub>;
=
sub> kvar;<=
/o:p>
=
sub> kVA;=
o:p>
=
sub>.
Problema 2.2 =
span>O reţea
electrică simplu buclată cu tensiunea nominală Unom=3D 10 kV, graful c=
ăreia
este reprezentat în figura 1, este echipată cu conductoare de ti=
pul
Al-Ol-70/11, distanţa între conductoare este D =3D 1 m, lungimea tronsoanelor şi puterile absorbite de
consumatori sunt indicate în schemă; tensiunea în nodul de
echilibru este U0 =
=3D 10,5
kV. De determinat valoarea maximă a pierderii de tensiune.<=
/span>
Fig.1 Graful re=
355;elei
electrice
Rezolvare:=
Deoarece linia este executată=
din
acelaşi fel de material rezultă că impedanţa pentru o
unitate de lungime este constantă şi v-om utiliza cazul doi de ca=
lcul
electric.
Calculul acestei probleme p=
oate
fi divizat în două etape şi anume:
-
etapa directă
=
Determinarea fluxului de putere S01-?
=
sub>
Pentru a determina celelalte
fluxuri de putere (S23,
S32, S02) aplicăm
teorema întâi a lui Kirchhoff pentru fiecare nod.
nodul 1.
–S01 + S1
+ S13 =
=3D 0;
=
S23 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D S3 – S13
=3D 1,88+j∙1,37 – (1,2 + j∙0,9) =3D 0,68 + j∙=
0,47
MVA.
nodul 3.
–S13 + S3
– S23 <=
/sub>=3D
0;
=
S23 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D S3 – S13 =3D 1,5 + j∙1 – =
(0,68 +
j∙0,47) =3D 0,82 + j∙0,53 MVA.
nodul 2.
–S02 + S2
+ S23 =
=3D 0;
=
S02 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D S2 + =
S23
=3D 1 + j∙0,8 + 0,82 + j∙0,53 =3D 1,82 + j∙1,33 MVA=
.
Verificarea se face cu relaţia:
=
S01 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>+ S02 =3D S1
+ S2 + =
S3;=
span>
1,88 + j∙1,37 + 1,82 +
j∙1,33 =3D 1,2 + j∙0,9 + 1 + j∙0,8 + 1,5 + j∙1;
3,7 + j∙2,7 =3D 3,7 +
j∙2,7.
sau determinăm fluxul de putere S02
prin relaţia:
=
sub>=
sub>
Observăm că am
obţinut aceleaşi valori a fluxului de putere S02, ceea ce dă dovadă că
calculele au fost efectuate corect.
Considerând nodul “3” nod de separare putem prezenta
următoarea schemă echivalentă.
Fig.2 Schema echivalent=
9;
Calcularea parametrilor schemei echivalente:
R=
span>02 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D r0∙l=
i>02
=3D 0,420∙2 =3D 0,840 Ω;
X=
span>02 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D x0∙l=
i>02
=3D 0,341∙2 =3D 0,682 Ω;
R=
span>23 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D r0∙l=
i>23
=3D 0,420∙1 =3D 0,420 Ω;
X=
span>23 <=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>=3D x0∙l=
i>23
=3D 0,341∙1 =3D 0,341 Ω.
Considerăm că U3 =3D Unom =3D10
kV şi în baza lui S=
u>23
şi Unom
determinăm Δ=
S<=
sub>23-?
=
sub> MVA.=
o:p>
Determinarea fluxului de putere =
sub>-?
=
sub> MVA.=
o:p>
Aplicăm prima teoremă a lui Kirchhoff
pentru nodul “2”
=
sub>;
=
sub> MVA.=
o:p>
În baza lui =
sub> şi Unom determinăm pierderea de
putere Δ=
S<=
sub>02 - ? <=
/span>
=
sub> MVA.=
o:p>
Determinarea fluxului de putere =
sub>-?
=
sub>=
sub> MVA.=
o:p>
-
etapa inversă
În baza lui U0 şi =
sub> determin=
59;m
pierderile de tensiune în tronsonul – 02.
Considerăm că =
sub> (=
sub>);
=
sub> kV.
În baza lui U=
0
şi =
sub> determin=
59;m U2-?<=
/p>
=
sub> kV.
=
În baza lui U=
2
şi =
sub> determin=
59;m
pierderile de tensiune în tronsonul – 23
=
sub> kV.
=
În baza lui U=
2
şi =
sub> determin=
59;m U3-?<=
/p>
=
sub> kV.
Problema 2.3 =
span> Se consideră o LEA trifazat=
59;
simplu circuit cu tensiunea 110 kV cu lungimea l =3D 100 km, echipată cu conductoare Al-Ol-150/19 (AC-150/19) dispu=
se
pe stîlpi de beton cu modul de dispunere a conductoarelor orizontal.
Distanţa între conductoare este de 4,5 =
m. Se cere:
- de alcă=
tuit
schema echivalentă;
- de determinat
rezistenţa activă a lini=
ei;
- de determinat
reactanţa inductivă a lini=
ei;
- de determinat
susceptanţa capacitivă a lini=
ei;
- de estimat (=
evaluat)
dacă se poate neglija susceptanţa capacitivă Bl.
Rezolvare:
1. Deoarece avem =
sub> kV utiliz=
259;m
schema echivalentă în “π” care este reprezentat=
ă
în figura 1.3,b. =
2. Determinarea rezistenţei active <=
!--[if gte vml 1]>
=
sub>-?
=
sub>; =
sub>;
=
sub>.
3.
Determinarea reactan=
355;ei
inductive =
sub>?
=
sub>;
=
sub>.
- Determinarea
susceptanţei capacitive
=
sub> =
sub>;
- Pentru a eva=
lua
dacă se poate neglija susceptanţa Bl trebuie de
făcut următoarele operaţii:
- determinarea
puterii reactive de compensare Qc−?
Deoarece avem aceeaşi tensiune la capetele
liniei putem scrie:
Qc =3D Ql =3D (Unom)2∙Bl =3D 1102&=
#8729;2,67∙10−4
=3D 3,231 MVAr.
- determinarea
puterii aparente S−?
=
sub>; =
sub>;
jec –
densitatea economică, jec=
=3D1
=
sub> ;
&n=
bsp;
Il =3D 150 A;=
=
sub> MVA.=
o:p>
c. =
determinarea pute=
rii
active P şi puterii reacti=
ve Q la un factorul de putere
cosδ =3D0,9.
&n=
bsp;
=
sub>
&n=
bsp;
=
sub> MW;
=
sub> Mvar.<=
/o:p>
=
=
sub>;
Deoarece am obţinut un
procent mare (de 26 %), la calcule trebuie de luat în consideraţ=
ie
susceptanţa capacitivă.
Dacă avem o linie cu aceiaşi paramet=
ri
numai că lungimea ei este de 10 km obţinem:
=
Bl =3D 2,67=
8729;10-6∙10
=3D 2,67∙10-5 S.
&n=
bsp;
Puterea reactivă de compensare va fi:
=
Qc =3D Ql =3D (Unom)2∙Bl =3D 1102∙2,67∙10ͨ=
2;5
=3D 0,323 Mvar;
=
=
sub>
Făcând verificarea observăm
că am obţinut 2,6% şi putem neglija susceptanţa
capacitivă.
Observăm că cu cît lungimea liniei este mai mică=
; cu
atât eroarea este mai mică şi invers eroarea mai mare
când lungimea liniei este mai mare.
Problema 2.4 Se consideră o linie
electrică aeriană simplu circuit cu tensiunea 110 kV este
echipată cu conductoare Al-Ol-185/43 dispuse pe stîlpi de beton =
cu
modul de dispunere a conductoarelor orizontal, LEA are lungimea de 100 km şi dista=
nţa
medie geometrică este Dmg =3D 5 m. Aceast=
9; linie
alimentează un consumator care consumă o putere S2 =3D 30+j20 MVA, la intrare este impusă tensi=
unea U1 =3D 121 kV. De deter=
minat
tensiunea la ieşire U=
2
şi puterea la intrare S1.
De de analizat dacă se poate neglija componenta transversală a
căderii de tensiune =
sub> şi de
construit diagrama fazorială de tensiuni.
<=
span
lang=3DRO style=3D'font-size:12.0pt;mso-ansi-language:RO'>Rezolvare: =
span> Determinarea
parametrilor pasivi a LEA:
-
Rezistenţa activă
Rl =3D r=
0∙l =3D 0,154∙100 =3D 15,4 =
37;.
-
Reactanţa inductivă
Xl =3D x=
0∙l =3D 0,420∙100 =3D 42 Ω=
;.
-
Susceptanţa capacitivă
Bl =3D b=
0∙l =3D 2,82∙10–6=
sup>∙100
=3D 2,82∙10–4 S.
Considerăm că tensiunea U2
la pasul “zero” este =
sub>=3D112 kV;
Determinarea puterii reactive de compensare =
sub>?
=
sub>=3D=
sub> Mvar.
Aplicăm prima teoremă a l=
ui
Kirchhoff în nodul “1”
=
sub>;
=
sub>
=
Determinarea tensiunii la iesire U2
- ?
=
Pentru a ne simplifica calculele considerăm că =
sub>=3D0;
=
sub>
∙ U2
=
sub>;
=
sub>;
=
sub>.
Rezolvând ecuaţia de gradul doi obţinem:<=
/span>
=
sub> kV;
=
sub> kV.
=
În baza lui =
sub> şi =
sub> determin=
59;m =
sub>?
=
sub>=3D1,7 Mvar.
=
Determinăm =
sub>- ?
=
sub>30 + j20 – j1,7 =3D 30 + j18,3 MVA.
Determinăm U1calcul - ?
=
sub>;
=
sub>=3D11,2 kV;
=
sub>=3D8,91 kV;
U1calcul =3D 109,82 + 11,2 + j8,91 =
=3D 121,02
+ j8,91 kV;
=
sub>=3D=
sub>=3D121,35 kV;
=
sub>.
Se
observă bine că componenta transversală a căderii de
tensiune =
sub> puţin =
influenţează,
pe viitor o putem neglija.
=
Determinarea puterii la intrare S1-
?
=
Aplicăm prima teoremă a lui Kirchhoff în nodul ̶=
0;2”
=
sub>=
sub>;
=
sub>.
=
Determinăm =
sub>
=
sub>Mvar.
=
Determinăm <=
!--[if gte vml 1]>
=
sub>
=
sub>;
=
sub>
=
sub>0,428 + j1,116 + 30 + j18,3 =3D 30,428 + j19,466 MVA;
S1 =3D 30,428 + j(19,466 – 2,064) =3D 30,428 + j17=
,402
MVA.
=
Diagrama fazorială a tensiunilor este prezentată în
figura 1.
Fig.1 Diagrama
fazorială a tensiunilor
Problema 2.5 =
span>De determinat ce =
valoare
a tensiunii trebuie menţinută în nodul de alimentare (nodul=
0)
a reţelei la o sarcină maximă Smax şi la o sarcină minimă=
; Smin =3D 0,3∙Smax a LEA, reprezentate în
figura 1, dacă în nodul “c” tensiunea în cazul
sarcinii maximale să fie nu mai joasă de 110 kV, iar la o
sarcină minimală
–– 108 kV. Sarcinile în MVA, lungimile tronsoanelor
în kilometri şi tipul conductoarelor utilizate sunt indicate pe
desen.
Fig.1 Schema electrică=
de
principiu a reţelei electrice
=
Rezolvare:
Alcătuim schema echivalentă a reţelei.
Fig.2. Schema echivalent=
59; a
RE
=
Din
tabelul 7 pag.229 [11] se alege parametrii calculaţi la 100 km a tipur=
ilor
de conductoare şi
calculăm parametri reali a tronsoanelor: =
&nb=
sp;
-
tronsonul 1 (0 – a) ACK – 240 <=
/o:p>
r1 =3D 12
Ω; x1 =3D 40,1 Ω;=
b1 =3D 2,85∙10=
–4
S;
<=
/span>=
sub>=
sub> =
<=
/span>=
sub>
-
tronsonul 2 (a – b) ACK – 120 <=
/o:p>
r2 =3D 24,9
Ω; x2 =3D 42,3 Ω; b2 =3D 2,69∙10–4 S.
<=
/span>=
sub> =
sub>
=
sub>
-
tronsonul 3 (a – c) ACK – 95 =
o:p>
r3 =3D 31,4
Ω; x3 =3D 42,9 Ω; b3 =3D 2,65∙10–4 S.
<=
/span>=
sub> =
sub>
=
sub>
Deoarece cunoaştem tensiunile în nodul „c”, calc=
ulul
regimului liniei se începe din nodul „c”.
Determinăm puterea reactivă de
compensare a tronsonului 3.
=
sub> Mvar.<=
/o:p>
Jumătate din această putere este injectată la
sfârşitul tronsonului. Atunci puterea la sfârşitul li=
niei
se va determina în felul următor:
=
sub>MVA.
Pierderile de putere în tronson:
=
sub>MW;
=
sub> Mvar;<=
/o:p>
=
ce
constituie din puterea tranzitată prin linie:
=
sub>
=
sub>
Pierderile de putere în tronsonul 3 constituie mai puţin =
de 5
% din puterea tranzitată şi în calculele următoare ele=
pot
fi neglijate, atunci =
sub>MVA.
Puterea =
sub> trecâ=
nd
prin rezistenţele R3<=
/sub>
şi X3, duc la c=
rearea
căderilor de tensiune pe acest tronson, care se determină:=
o:p>
=
sub>kV;
=
sub>kV.
Tensiu=
nea
în nodul „a” se determină ca expresia:
=
sub>
=
sub> kV;
sau Ua se determină şi cu ajutorul relaţi=
ei:
=
sub> kV.
Se vede bi=
ne
că componenta transversală a căderii de tensiune practic nu
influenţează la calculul tensiunii în nodul „a”
şi poate să nu fie luată în consideraţie deoarece=
:
=
sub> kV.
De aceea e
destul pentru a determina componenta longitudinală a căderii de
tensiune şi tensiunea de determinat după expresia simplificat=
9;.
Deoa=
rece
nu cunoaştem tensiunea la finele tronsonului 2, determinarea puterii reactive de
compensare a acestui tronson se face după tensiunea nominală:
=
sub>Mvar.
Puterea la sfârşitul tronsonului 2:
=
sub>.
Deoarece n=
u se
cunoaşte tensiunea în nodul ”b” şi se cunoa#=
1;te
tensiunea în nodul ”a”, la determinarea pierderilor de pu=
tere
poate fi utilizată tensiunea nominală:
=
sub>MW; &nb=
sp;
=
sub>
=
sub> Mvar; =
sub>
La fel pot fi neglijate valorile pierderilor de putere în tron=
sonul
2 deoarece ele constituie mai puţin de 5 % din puterea tranzitată
prin tronson, atunci =
sub>
Cunoscând =
sub> şi Ua determinăm
căderea de tensiune în tronsonul 2:
=
sub>kV.
=
Tensiunea în nodul ”b” se determină:
=
sub> =
kV.
&n=
bsp;
Puterea reactivă de compensare sumară la sfârşi=
tul
tronsonului 1, începutul tronsoanelor 2 şi 3 se determină:<=
o:p>
=
sub> Mvar.<=
/o:p>
Puterea la sfârşitul tronsonului 1 este:
=
sub>
Pierderile de putere în tronsonul 1:
=
sub>=
sub> =
=
sub> =
sub>
Puterea la începutul tronsonului este:
=
sub>
<=
/span>
Căderea de tensiune longitudinală pe tronsonul 1:<=
/span>
=
sub>kV.
=
Căderea de tensiune transversală pe tronsonul 1:
=
sub>kV.
Tensiunea în nodul ”0”:
=
sub>kV.
Dacă la calcul
tensiunii în nodul ”0” neglijăm căderea de te=
nsiune
transversală atunci obţinem:
=
sub>kV.
Eroarea de calcul=
este:
=
sub>
&=
nbsp;
Calculul regimului de lucru a liniei la un consum de putere
minimală, calculul se începe la fel de la nodul ”c” =
.
Putere=
a la
sfârşitul tronsonului 3 se va determina în felul urmă=
tor:
=
sub>
Pierderile=
de
putere în tronsonul 3 nu le determinăm deoarece ele, ca şi
– n regimul când avem consun de putere maximală, au valori
mici.
Căderea de tensiune pe tronsonul 3 :
=
sub> kV.
Tensiunea în nodul ”a”:
=
sub>kV.
Putere=
a la
sfârşitul tronsonului 2:
=
sub>
Deoarece =
sub>, atunci căderea de tensiune longitudinală pe
tronsonul 2 se determină:
=
sub> kV.
=
Tensiunea în nudul ”b” se determină:
=
sub> =
kV.
Puterea reactivă de compensare sumară la sfârşi=
tul
tronsonului 1, începutul tronsoanelor 2 şi 3 se determină:<=
o:p>
=
sub>
Puterea la sfârşitul tronsonului 1 este:
=
sub> =
Căderea de tensiune longitudinală pe tronsonul 1:<=
/span>
=
sub> kV.
Tensiunea &i=
circ;n
nodul ”0”:
=
sub> kV.
În aşa mod, tens=
iunea
în nodul de alimentare trebuie să fie egală cu 117,2 kV la o
sarcină maximă, iar la o sarcină minimă –– egală cu 109,6=
kV,
pentru a menţine tensiunea în limitele date în nodul
”c”.
Problema 3.1=
O linie electric&=
#259;
aeriană cu tensiunea nominală Unom
=3D 110 kV este echipată cu conductoare de tipul Al-Ol-185/24
dispuse orizontal pe stâlpi de beton, distanţa medie geometric=
259;
dintre conductoare este Dmg=3D5,5
m, lungimea liniei este l =3D10=
0 km
şi alimentează un singur consumator care consumă o putere S2=3D30+j∙20 MVA, tensiunea la intrare este U1=3D121 kV. De determinat tensiunea la ieşire =
U2, utilizând met=
oda
Newton – Raphson.
Rezolvare: În primul rând=
se
alcătuieşte schema echivalentă care este prezentată
în figura 3.1.
Fig. 3.1. Schema echivalent=
ă
a LEA
În continuare se determină elemente=
le
pasive a liniei.
Rl =3D r0∙l <=
/i>=3D
0,154∙100 =3D 15,4 Ω;
Xl =3D x0∙l=
i> =3D
0,420∙100 =3D 42 Ω;
Bl =3D b0∙l=
i> =3D
2,82∙10-6∙100 =3D 2,82∙10-4 S;=
Determinarea admitanţelor:
=
sub>;
=
sub> S;
=
sub>S;
=
sub>. Ecuaţia alcătuită conform ecuaţiilor
nodale va avea forma următoare
=
sub>.
=
=
Bilanţul
puterilor, folosind varianta rectangulară de exprimare a tensiunilor
&n=
bsp;
Într-un nod generator avem +Pg
şi +Qg iar într-un nod consum=
ator
avem –Pc ş=
;i
–Qc.
Abaterile de tensiune se determină cu relaţia:
=
=
sub>.
Se consideră la pasul “zero”
că:
=
sub> kV;
=
sub>.
Abaterile de putere se determină utiliz&a=
circ;nd
expresiile (3.13) şi (3.14)
=
sub>
=
sub>
Elementele Jacobianului vor=
avea
valorile:
=
sub>
=
sub>
=
sub>
=
sub>
Determinăm tensiunea la ieşire la pasul ”1”.=
=
sub>;
=
sub>=
sub>.
În continuare pentru a efectua calculele=
se
utilizează calculatorul şi se obţin următoarele rezulta=
te
pasul ”2” &=
nbsp; =
sub>;
=
sub>.
pasul ”3” =
sub>;
=
sub>.
pasul ”4” =
=
sub>;
=
sub>.
Mai departe nu-i necesar de
efectuat calculele deoarece rezultatele sunt aceleaşi, deci soluţ=
ia
este rezultatul obţinut la pasul ”4”.
Dacă se ia în
consideraţie puterea reactivă de compensare atunci se obţin
următoarele rezultate: se modifică numai valoare abaterii de pute=
re
reactivă.
=
sub> =
=
&nb=
sp;
=
sub>;
=
&nb=
sp; =
sub>.
În continuare pentru a
efectua calculele la fel se utilizează calculatorul şi se obţ=
;in
următoarele rezultate:
pasul ”2” &=
nbsp; =
sub>;
=
sub>.
pasul ”3” =
sub>;
=
&nb=
sp;
=
sub>.
pasul ”4”
=
sub>;
=
sub>.
Aici se finisează calc=
ulele.
Analizând rezultatele în cazul când se neglijează
puterea reactivă de compensare rezultatele puţin diferă unul=
de
altul, de aceea în continuare nu trebuie de luat această putere
în consideraţie.
Pentru a determina puterea limită (maximă) =
care
poate fi cerută de consumator se efectuează următorul calcul=
:
Se cunoaşte bine
următoarea expresie:
=
sub>
∙U2
=
sub>;
=
sub>;
=
sub>.
În continua=
re
radicalul se egalează cu zero şi ţinând cont că <=
sub>=
sub> se obţ=
ine:
=
sub>.
=
sub>, puterea limită se obţine.=
p>
=
sub>MW;
=
sub> Mvar.<=
/o:p>
Această problemă poate fi rezolvată
şi prin următoarea metodă.
Se alcătuieşte sistemul de ecuaţ=
;ii
pentru schema din fig. 3.1.
=
sub> =
&nb=
sp; =
=
&nb=
sp; =
(1)
=
sub> =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(2)
sau
=
sub> =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(3)
=
sub> =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(4)
Vom face următoarele notaţii:=
o:p>
=
sub>;
=
sub>
=
sub>;
=
sub>;
=
sub>; =
sub>; =
sub>;
=
sub>; =
sub>.
Luând în consideraţie
notaţiile de mai sus din (4) obţinem:
=
sub>, =
&nb=
sp; =
&nb=
sp;
(5a)
=
sub>, =
&nb=
sp; =
&nb=
sp; =
(5b)
sau
=
sub> =
&nb=
sp;
(6)
de unde
=
sub> =
&nb=
sp; =
&nb=
sp;
(7)
(7) se ridică la pătrat şi se a=
dună
parte cu parte
=
sub>
sau
=
sub> =
&nb=
sp;
sau
=
sub> =
&nb=
sp; =
sau
=
sub>; =
&nb=
sp; =
(8)
=
sub>; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
sau
=
sub>. =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(9)
Soluţia ecuaţiei (8) este:
=
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(10)
=
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(11)
=
sub>
unde =
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
(13)
=
=
sub>. =
&nb=
sp; =
&nb=
sp; =
=
&nb=
sp; (14)<=
/p>
Luând în consideraţie (12)
şi (14) relaţia (8) se poate scrie în felul următor:
=
sub>. =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
(15)
Din relaţia (7) obţinem că:
=
sub>, =
&nb=
sp; =
&nb=
sp;
(16)
=
sub>. =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(17)
Din relaţia (9) rezultă că
soluţie există dacă se îndeplineşte condiţia=
:
=
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(18)
sau
=
sub>, =
&nb=
sp; =
=
&nb=
sp; =
&nb=
sp; =
(19)
=
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
(20)
sau
=
sub>. =
=
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; (21)
Relaţia (21) primeşte următoarea
formă:
=
sub>, =
&nb=
sp; =
&nb=
sp;
(22)
sau
=
sub>, =
&nb=
sp; =
&nb=
sp; =
&nb=
sp;
(23)
de unde se determină
=
sub>. =
&nb=
sp; =
&nb=
sp; =
&nb=
sp; =
(24)
Deoarece =
sub> din (24)
rezultă că puterea maximă absorbită de consumator va av=
ea
loc în ipoteza că =
sub>.
=
sub>.
Din relaţia (3) se
obţine:
=
sub>, =
&nb=
sp; =
&nb=
sp; =
(25)
sau
=
sub>, =
&nb=
sp; =
&nb=
sp; =
(26) =
sau
=
sub> =
&nb=
sp;
(27)
(27) se ridică la pătrat şi se
adună parte cu parte, ţinând cont că =
sub> se obţ=
ine:
=
sub>
sau
=
sub>, =
&nb=
sp;
(29)
sau
=
sub>, =
&nb=
sp;
(30)
sau
=
sub>. =
&nb=
sp;
(31)
Din relaţia (27) se
determină:
=
sub>. =
&nb=
sp; =
(32)
=
sub>; =
sub>rad.
=
sub>; =
sub>rad.
=
sub>; =
=
sub> rad.=
o:p>
Conform relaţiei (13) se obţine:
=
sub>;
Conform relaţiei (14) se determină:=
=
sub>.
Conform relaţiei (15) se determină modulul
tensiunii:
=
sub>.
=
sub>.
Unghiul δ se determin&=
#259;
cu relaţia (16) şi (17):
=
sub>;
=
sub>;
=
sub>.
=
sub> kV;
=
sub> kV.
Puterea limită se
determină:
<=
!--[if gte vml 1]>
=
sub>MW.
În baza relaţiil=
or
(15), (16), (31) şi (32) se pot construi următoarele dependen#=
5;e:
Problema 4.1 Se consideră o linie
electrică trifazată, curent alternativ, simplu circuit de 35 kV (fig=
.1).
Linia alimentează un consumator industrial care absoarbe, în ore=
le
de vârf ale curbei de sarcină, o putere activă de 3800 kW, =
la
un factor de putere cosφ =3D 0,85. LEA are 22 km şi este executat=
ă
cu conductoare din oţel–aluminiu de tipul AC – 70/11. Curb=
a de
sarcină este prezentată în fig.2. Să se determine
pierderile de putere şi de energie (exacte şi aproximative) &icir=
c;n
linie prin toate metodele.
Fig.1 Schema LEA
=
Fig.2 Curba de
sarcină anuală clasată
Rezolvare: Pentru a determina pierderile de p=
utere
activă şi reactivă în LEA mai întâi trebui=
e de
alcătuit schema echivalentă a liniei şi de determinat parame=
trii
ei.
Deoarece tensiunea
nominală a LEA este 35 kV se utilizează schema echivalentă
prezentată în fig.3.
Fig.3
Schema echivalentă a LEA
Utilizând literatura tehnic=
259;
se determină
valorile parametrilor schem=
ei
echivalente.
=
sub> Ω;
=
=
sub> Ω. =
&nb=
sp; =
Pierderile de putere se determină cu
relaţia:
=
sub> W;
=
sub> kvar;<=
/o:p>
=
sub> kvar.<=
/o:p>
Pentru a determina pierderile de energie
activă e necesar de analizat curba de sarcină.<=
/p>
1. Se determină=
durata
de utilizare a sarcinii maxime – Tmax.
=
sub>
2. Se determină=
sarcina
medie Smed şi m=
edie
pătratică Smp<=
/i>.
1
sarcina medie se determină cu relaţia:=
=
sub> kVA;=
o:p>
2
sarcina medie pătratică se determină cu
relaţia:
=
sub>
3. Se determină
pierderile de energie activă prin toate metodele.
3
=
sub> kW∙h/=
an;
&n=
bsp;
=
sub>– coeficientul de formă a curbei de sarcin=
9;;
=
sub>.
-&nb=
sp;
=
sub> kW∙h/=
an;
-&nb=
sp;
=
sub> kW∙h/=
an;
=
sub> h/an.<=
/o:p>
=
sub>– durata pierderilor maximale determinate exact;
=
&nb=
sp;
=
sub> kW∙h/=
an;
=
sub> h/an;<=
/o:p>
=
sub>– durata pierderilor maximale determinate aproximat=
iv;
Problema 4.2 La un post de transformare,
echipat cu două transformatoare de tipul
TM =
–
630/10/0,4, sunt conectaţi doi consumatori care au consumat 5000000 kW∙h.
Durata de utilizare a sarcinii maxime este 5000 h/an. Considerând c=
259;
transformatoarele funcţionează în paralel să se determ=
ine:
1. pierderile de put=
ere
şi de energie în transformatoare;
2. să se studie=
ze cum
variază valoarea procentuală a pierderii de energie în
funcţie de cantitatea de energie consumată;
Rezolvare:=
Din literatura tehnică se aleg
parametrii de paşaport a transformatoarelor şi anume: =
sub> kVA; <=
!--[if gte vml 1]>
=
sub> kV;
=
sub> kV;
=
sub> %;
=
sub> kW;
=
sub>kW; =
sub> %.
Pentru a determina
pierderile de putere şi de energie trebuie de determinat sarcina
consumatorilor la un factor de putere cosφ=3D1,0. Această sarcin&=
#259;
se determină cu relaţia:
=
sub> kVA;=
o:p>
Pierderile
de putere activă şi reactivă se determină cu relaţ=
ia:
=
sub> kW;
=
sub> kvar;<=
/o:p>
=
sub>; =
sub> kvar.<=
/o:p>
Pierderile de ene=
rgie se
determină în felul următor:
=
sub> kW∙h/=
an;
=
sub> h/an.<=
/o:p>
=
sub>.
Consumul tehnolog=
ic al
transformatoarelor constituie 1,19 % din toată energia electică
tranzitată prin ele.
Problema 4.3 Un consumator industrial care
necesită o putere maximă de 20 MVA, la un factor de putere cos =
66;
=3D 0,9, este alimentat de la o staţie electrică de transformare =
110/10
kV dotată cu două transformatoare de tipul ТДН =
16000/110/10
conectate la o LEA de 110 kV cu lungimea de 50 km (fig.1). LEA este
echipată cu conductoare din oţel–aluminiu de tipul AC ̵=
1;
240/32 dispuse orizontal cu distanţa dintre faze de 4,5 m. Durata de u=
tilizare
a sarcinii maxime este Tmax =
sub>=3D6000h/an.
Să se determine pierderile de putere şi de energie în linie
şi în transformatoarele staţiei.
Fig.1 Schema de p=
rincipiu
a reţelei electrice
Rezolvare:=
Din literatura tehnică se aleg
parametrii de paşaport a transformatoarelor şi anume: =
sub> MVA; <=
!--[if gte vml 1]>
=
sub> kV;
=
sub> kV;
=
sub> %;
=
sub> kW;
=
sub>kW; =
sub> %.
Pierderile
de putere activă şi reactivă într-un singur transforma=
tor
se determină cu relaţia:
=
sub> kW,
=
sub> kvar,<=
/o:p>
=
sub>; =
sub> kvar.<=
/o:p>
Pierderile de put=
ere
activă şi reactivă în transformatoarele SE (când
transformatoarele lucrează în paralel) se determină cu
relaţia:
=
sub> kW,
=
sub> kvar.<=
/o:p>
Pierderile de ene=
rgie
activă în cazul când transformatoarele funcţioneaz=
59;
separat şi în paralel se determină în felul urmă=
tor:
=
sub> kW∙h/=
an,
=
sub> kW∙h/=
an,
=
sub> h/an.<=
/o:p>
Din analiza rezul=
tatelor
se observă că la funcţionarea în paralel a
transformatoarelor pierderile de putere cât şi de energie au val=
ori
mai mici decât în cazul funcţionării separat.
Pentru a determina
pierderile de putere activă şi reactivă în LEA mai
întâi trebuie de alcătuit schema echivalentă a liniei
şi de determinat parametrii ei.
Deoarece tensiunea
nominală a LEA este 110 kV se utilizează schema echivalentă
în ”π”.
Utilizând
literatura tehnică se determină valorile parametrilor schemei
echivalente.
=
sub> Ω;
<=
/sub> Ω;
<=
/sub> S;
<=
/sub> Mvar.<=
/o:p>
Se consideră=
că
în staţie transformatoarele funcţionează în para=
lel,
atunci se obţine:
<=
/sub>
<=
/sub> MW;
<=
/sub> Mvar. =
Pierderile de putere se determină cu
relaţia:
<=
/sub> MW;
<=
/sub> Mvar;<=
/o:p>
Pierderile de energie în LEA se
determină cu expresia:
<=
/sub> kW∙h/=
an.
La determinarea pierderilor de putere şi =
de
energie în LEA pierderile corona se neglijează.
=
Problema 4.4 O uzină, ce consum=
59; o
putere de (40+j30) MVA, se alimentează, de la o staţie electric=
259;
ce se află la distanţa l<=
/i> =3D
180 km de la uzină, prin intermediu unei LEA, confecţionată =
din
conductor de tipul ACKП–240, cu tensiunea de 220 kV. Tensiunea =
la
sfârşitul liniei când avem consum maxim de putere este
egală cu U2 =3D=
215 kV.
De determinat pierderile de putere în linie.
Rezolvare: Din tabele şi acte normative
găsim:
<=
/sub>,
<=
/sub> şi <=
/sub>. Atunci
obţinem:
&=
nbsp;
<=
/sub>;
&=
nbsp;
<=
/sub>;
<=
/sub>.
Puterea reactivă de compensare a liniei se
determină în felul următor:
&=
nbsp;
<=
/sub> Mvar.<=
/o:p>
Determinăm puterea
aparentă la sfârşitul liniei ţinând cont de fapt=
ul
că jumătate din puterea reactivă de compensare a liniei este
injectată la sfârşitul liniei. Atunci avem:
<=
/sub>.
Pierderile de
putere în linie se determină:
<=
/sub>
<=
/sub>
Pierderile totale de putere se determină:=
<=
/sub>, care constituie din puterea totală
<=
/sub>
Problema 4.5 Să sere de obţinut
relaţiile <=
/sub> dacă s=
unt
cunoscute consumul propriu tehnologic procentual în RE de 110 kV R=
11; <=
/sub> =3D 4,5 %, =
RE 10 kV
–<=
/sub> =3D 5,5 % şi în RED 0,4 kV – <=
/sub> =3D 6,0 %. =
Puterea
activă maximă tranzitată prin LEA este Pmax =3D 2000 kW,&n=
bsp;
Tmax =3D 6000=
h/an
şi cosφ =3D 0,88. Tipul, lungimea, şi numărul LEA c&aci=
rc;t
şi a transformatoarelor din staţiile electrice sunt indicate &ici=
rc;n
schema de principiu prezentată în figura 1.
<=
!--[if gte mso 9]>
Fig.1 Schema de principiu a=
RE de
(0,4 – 110) kV
Rezolvare:
Consumul propriu tehnologic
procentual în RE de 110 kV se determină cu relaţia:
<=
/sub>, =
&nb=
sp; =
&nb=
sp;
(1) =
Iar consumul propriu tehnol=
ogic
în RE de 10 kV se determină:
<=
/sub>, =
&nb=
sp;
=
&nb=
sp; =
(2)
<=
/sub>;
Din relaţia (2)
rezultă:
<=
/sub>;
<=
/sub>;
<=
/sub>;
<=
/sub>
<=
/sub>;
<=
/sub>
<=
/sub> kWh;=
o:p>
<=
/sub> kWh;=
o:p>
<=
/sub> kWh;=
o:p>
<=
/sub> =
<=
/sub> kWh.=
o:p>
Pro=
bleme
propuse către rezolvare
Problema 1.
Să se calculeze rezistenţa activă şi reactan#=
5;a
inductivă a unei linii electrice aeriene cu simplu circuit de 35 kV,
echipată:
a) &n=
bsp;
cu conductorul de oţel-aluminiu (AC-95/16);=
b) &n=
bsp;
cu conductorul din oţel (ПМС-9=
5).
Distanţa între f=
aze
este de 3,5 m şi lungimea liniei este de 15 km.
Problema 2. Să se calculeze paramet=
rii
pasivi a unei linii electrice aeriene simplu circuit de 10 kV, echipată=
; cu
conductoare de oţel ПМС-50. Fazele sunt dispuse &ici=
rc;n
vârfurile unui triunghi echilateral pe capul unui stâlp, cu
distanţa de 1m între ele. Linia alimentează un consumator de
1000 kW la cosj =3D 0,85. Lungim=
ea liniei este
de 5 km.
Problema 3. De determinat rezistenţa activă a un=
ei
LEA cu tensiunea de 110 kV, îndeplinită cu conductor de tipul AC=
-120
cu lungimea de 65 km, la temperatura 0 şi 35 0C.=
Problema 4. De estimat pentru=
care
secţiuni ale LEC de 10 kV se poate neglija reactanţa inductiv=
9;
dacă secţiunea variază în limitele 16 ÷ 240 mm<=
sup>2.
Problema 5. O întreprindere industrială se
alimentează de la două surse cu tensiunea 10kV printr-o LEA ş=
;i o
LEC. Lungimea LEA este de 8,5 km şi este îndeplinită cu
conductor de tipul AC-120/19 cu distanţa medie geometrică î=
ntre
conductoare de 2 m. Lungimea LEC este de 5 km (cablu AAБ-95). Se cere
să se determine parametrii schemei echivalente a liniilor respective.<=
o:p>
Problema 6. Să se
întocmească schema echivalentă şi să se determine=
parametrii
LEA de 110 kV
„Floreşti2 - Şoldăneşti” executată din
conductor de tipul AC-150/24. Conductoarele sunt dispuse pe stâlpi
în vârful unui triunghi echilateral, cu distanţa înt=
re
ele de 4,5 m. Lungimea liniei este de 53,2 km..
Problema 7. Se consideră=
o LEA
de 35(110) kV. De trasat curbele de variere a rezistenţei active (r0) şi a reactan=
355;ei
inductive (x0) pentru unitatea de lungime în
funcţie de secţiunea transversală a conductoarelor.
Secţiunea variază de la 35 mm2 până la 240 =
mm2.
Unom =3D =
35 kV, Dmg=3D3,5 m; Unom =3D 110 kV, Dmg =3D 5 m.=
Problema 8. O linie de 110 k=
V,
simplu circuit, este echipată cu conductor din oţel-aluminiu
având secţiunea de 185/29 mm2. Conductoarele sunt dis=
puse
pe stâlpi în plan orizontal la distanţa dintre ele de 4 m.
Lungimea liniei este de 70 km. Să se întocmească schema
echivalentă şi să se determine parametrii ei.
<=
b>Problema 9. O linie electric&=
#259; cu
simplu circuit de 110 kV, echipată cu conductoare din oţel-alumin=
iu
de tip AC-120/19, alimentează un consumator la distanţa de 55 km.
Conductoarele sunt dispuse în vârful unui triunghi echilateral,=
cu
distanţa între ele de 3,5 m. Să se alcătuiască sc=
hema
echivalentă şi să se determine parametrii ei.
Problema 10. O linie electrică de 330 kV alimenteaz=
259;
o staţie de transformatoare a unui consumator situat la o
distanţă de 270 km. Linia este echipată cu conductoare din
oţel-aluminiu de tipul 2×ACO-300 cu distanţa de 9 m î=
ntre
faze. Să se calculeze parametrii pasivi ai LEA.
Problema 11. Pentru LEA cu sim=
plu
circuit de 400 kV şi lungimea de 350 km, echipată cu conductoare
fasciculare de tipul AC-450/50 se cere să se calculeze reactanţa
specifică în următoarele două cazuri: când &icir=
c;n
fiecare fază sînt două conductoare şi respectiv c&acir=
c;nd
în fiecare fază sunt trei conductoare dispuse în vâr=
ful
unui triunghi echilateral. Fazele sunt dispuse în plan orizontal, pe
capul unui stâlp portal, cu distanţa de 15 m între ele.
Distanţele între conductoarele aceleiaşi faze – 400 m=
m.
Problema 12. La un
post de transformare al unei uzine este instalat un transformator trifazat =
de
putere de tipul ТM –
1000/10/0,4. Se cere să se determine parametrii schemei echivalent=
e a
acestui transformator şi de estimat dacă se poate de neglijat
componenta activă a tensiunii de scurtcircuit.
Problema 13.
Să se determine parametrii schemei echivalente şi de estim=
at
dacă se poate de neglijat componenta activă a tensiunii de
scurtcircuit a transformatorului de tipul
=
058;ДН
–25000/35/6,3.
Problema 14. <=
/span>La staţia
electrică din Şerpeni sunt instalate două transformatoare
trifazate de putere de următorul tip ТДН
– 10000/110/10. De determinat parametrii schemei echivalente a
acestor transformatoare.
Problema 15. Pentru transforma=
torul
trifazat cu trei înfăşurări, montat la staţia
electrică din oraşul Anenii-Noi, de tipul ТДТН–16000/110/35/10 cu raportul
puterilor 100/66,7/66,7% se cere să se calculeze parametrii schemei
echivalente raportaţi la tensiunea înfăşurării
primare.
Problema 16. <=
/span>La staţia
electrică din Străşeni sunt instalate două
autotransformatoare trifazate de putere de următorul tip АТДЦТ=
1053;
– 200000/330/110/10. De determinat parametrii schemei echivalente=
a
acestor autotransformatoare.
Problema 17. La staţia electrică a Uzinei de
Tractoare din mun. Chişinău sunt instalate două transformato=
are
trifazate de putere cu înfăşurări scindate (divizate) =
de
următorul tip
=
058;PДН–25000/110/6,3/6,3. De determinat
parametrii schemei echivalente a acestor transformatoare.=
Problema 18. O linie electrică aeriană simplu cir=
cuit
cu tensiunea 10 kV este echipată cu conductoare Al-Ol–70/11
(AC–70/11) dispuse pe stâlpi de beton cu coronamentul în
vârfurile unui triunghi echilateral, linia electrică are lungime=
a de
6,5 km şi distanţa între conductoare este D =3D 1,5 m. LEA alimentează un consumator care necesit=
59; o
putere P =3D 0,85 kW la un fact=
or de
putere cosφ =3D 0,87. La intrare în linie este impusă tensi=
unea U1 =3D 10 kV. Se cere de
calculat:
-
valorile aproximative ale soluţiilor =
sub> şi =
sub>;
-
factorul de putere în ipoteza că =
sub>;
-
factorul de putere în ipoteza că fazorul <=
sub>=
sub> coincide
după sens cu fazorul =
sub>.
Problema 19. O linie electrică aeriană simplu circ=
uit
de 35 kV, alimentează un consumator situat la distanţa de 3 km, c=
are
necesită o putere de 26 MW. Linia este executată cu conductoare de
oţel-aluminiu de 95/16. Fazele sunt dispuse orizontal pe capul unui
stâlp, cu distanţa de 4 m. Rezistivitatea electrică a
aluminiului este 28,9 <=
/sub>. Tensiunea la intrare este U1=3D 36 kV.
Să se determine: factorul de putere în ipoteză că
fazorul U1 coincide
după direcţie cu fazorul U2, considerând că
linia funcţionează în gol.
Problema 20. Pentru o schemă cu trei patru circuite de ales sistem=
ul
principal de circuite şi de scris în mod desfăşurat
ecuaţiile curenţilor circulari.
Problema 21. O linie electrică aeriană de 35 kV cu
lungimea de 20 km funcţionează în gol. Tensiunea la ieş=
;ire
din linie este de 35 kV. Conductoarele sunt de 70/11 din oţel-aluminiu.
Să se determine U1 şi I1 pe c=
ale
grafică şi analitică.
Problema 22. O LEA simplu circuit de 110 kV, alimenteaz=
9;
un consumator situat la distanţa de 70 km, care necesită 0 putere=
de
70 MW, la un factor de putere cosφ =3D 0,8. Linia este echipată cu
conductoare din oţel-aluminiu de tipul AC – 185/29. Fazele sunt
dispuse orizontal cu distanţa între ele de 4.5 m. Tensiunea U1
=3D 115 kV. Să se determine:
1. parametrii schemei
echivalente;
2. valorile aproxima=
tive
şi exactă a pierderii de tensiune;
3. componentele acti=
vă
şi respectiv reactivă a curentului la barele consumatorului;=
4. valorile real=
9;
şi imaginară a curentului la barele consumatorului.<=
/p>
Problema 23. O LEA simplu circuit de 110 kV alimentează=
; un
consumator situat la distanţa de
80 km, care necesită o putere activă de 21 MW. Linia este
echipată cu conductoare de oţel-aluminiu de 150/24. Fazele sunt
dispuse orizontal pe capul unui stâlp cu distanţa de 4 m. Tensiu=
nea U1=3D 115 kV. Să se
determine: <=
/span>
1. parametrii schemei
echivalente;
2. factorul de putere
cosφ în ipoteză ca fazorul U1 să coincid=
59;
cu fazorul U2;
3. pentru fazorul
obţinut de determinat pierderile de tensiune (valoarea exactă =
51;i
aproximativă).
Problema 24. O uzină ce consumă o putere activ=
59;
de 18 MW ,la un factor de putere cosφ=3D0,82, este alimentată de =
la o
staţie electrică situată la o distanţă de 15 km, p=
rin
intermediul unei LEA de 35 kV executată din conductoare de tipul AC
– 70/11 cu distanţa medie geometrică între faze Dmg
=3D 3.5 m. La barele staţiei tensiunea este de 37 kV. Să se deter=
mine:
1. parametrii schemei
echivalente;
2. valorile aproxima=
tive
şi exactă a pierderii de tensiune;
3. componentele acti=
vă
şi respectiv reactivă a curentului la barele consumatorului;=
4. valorile real=
9;
şi imaginară a curentului la barele consumatorului.<=
/p>
Problema 25. Se consideră o linie electrică
aeriană simplu circuit cu tensiunea 110 kV este echipată cu
conductoare Al-Ol-240/32 dispuse pe stâlpi de beton cu modul de dispu=
nere
a conductoarelor orizontal, LEA are lungimea de 80 km şi distanţa
medie geometrică este Dm<=
/sub>=3D5
m. Această linie alimentează un consumator care consumă o pu=
tere
S2 =3D 35+j20 MVA, la
intrare este impusă tensiunea =
U1
=3D 121 kV. De determinat tensiunea la ieşire U2 şi puterea la intrare S1. De de analizat dacă se poate neglija compon=
enta
transversală a căderii de tensiune =
sub> şi de
construit diagrama fazorială de tensiuni.
Problema 26. La un post de transformare, echipat cu dou=
9;
transformatoare de tipul TM–=
1000/10/0,4,
sunt conectaţi doi consumatori care au consumat 5500000 kW∙h.
Durata de utilizare a sarcinii maxime este 5400 h/an. Considerând c=
259;
transformatoarele funcţionează în paralel să se determ=
ine:
1. pierderile de put=
ere
şi de energie în transformatoare;
2. să se studie=
ze cum
variază valoarea procentuală a pierderii de energie în
funcţie de cantitatea de energie consumată;
Problema 27. <=
/span>Se consideră=
o linie
electrică trifazată, curent alternativ, simplu circuit de 35 kV (fig.1). Linia
alimentează un consumator industrial care absoarbe, în orele de
vârf ale curbei de sarcină, o putere activă de 4200 kW, la =
un
factor de putere cosφ =3D 0,88. LEA are 26 km şi este executat=
59; cu
conductoare din oţel–aluminiu de tipul AC – 95/15. Curba de
sarcină este prezentată în fig.2. Să se determine
pierderile de putere şi de energie (exacte şi aproximative) &icir=
c;n
linie prin toate metodele.
<=
!--[if gte mso 9]>
Fig.1 Schema LEA
<=
!--[if gte mso 9]>
Fig.2 Curba de sarcină
anuală clasată
Problema 28 Un
consumator industrial care necesită o putere maximă de 14 MVA, la=
un
factor de putere cosφ =3D 0,9, este alimentat de la o staţie
electrică de transformare 110/10 kV dotată cu două
transformatoare de tipul Т=
1044;Н
10000/110/10 conectate la o LE=
A de
110 kV cu lungimea de 43 km (fig.1). LEA este echipată cu conductoare =
din
oţel–aluminiu de tipul =
AC – 240/32 dispuse orizontal cu distanţa dintre faze de =
5 m.
Durata de utilizare a sarcinii maxime este Tmax
=3D 5800 h/an. Să se determine pierderile de putere şi =
de
energie în linie şi în transformatoarele staţiei.
<=
!--[if gte mso 9]>
Fig.1 Schema de p=
rincipiu
a reţelei electrice
Problema 29. O staţie electrică de transformare =
este
echipată cu două transformatoare de tip
ТДТН –
25000/110/35/10 (Δ=
P=
0 =3D
ΔPFe =3D 36 kW, ΔPscJM =3D ΔPscÎJ =3D Δ=
span>PscÎM =3D 145 kW), la barele de =
35 kV
şi 10.5 kV sunt racordate plecări ale reţelei electrice de
distribuţie (RED) care alimentează diverşi consumatori a
cărei sarcină totală are un timp anual de utilizare a puterii
maxime Tmax =3D 4500=
h,
timpul pierderilor maximale este τ =3D 2500 h. Graficile de sarcin=
9;
prezintă maximile de 10 MVA la tensiunea de 35 kV şi de 14 MVA la
tensiunea de 10,5 kV la un factor de putere unitar (cosφ =3D 1) care c=
oincid
cu vârful de sarcină al sistemului energetic. Să se calcule=
ze
pierderile de putere şi de energie electrică în
următoarele variante:
-&nb=
sp;
toate întreruptoarele sunt conectate
înafară de 10Î2T şi 35Î1T;
-&nb=
sp;
toate întreruptoarele sunt conectate
înafară de 10ÎSşi 35ÎS;
-
transformatorul 2T este retras în rezervă
(rezerva rece) şi sunt deconectate întreruptoarele 110Î2T,
10Î2T şi 35Î2T;
-
sunt deconectate întreruptoarele 10Î2T
şi 35Î2T (transformatorul 2T funcţionează în reg=
im
de mers în gol).
Să se compare cele patru varia=
nte
din punct de vedere al pierderilor de putere şi energie activă
considerînd că timpul anual de funcţionare o unui transform=
ator
este Tf =3D 8400 h.<=
o:p>
<=
!--[if gte mso 9]>
Fig.1 Schema de p=
rincipiu
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