Module B3. VLoad = = V S V LN

Transcription

1 Mdule B Prblem The -hase lads are cnnected n arallel. One s a urely resste lad cnnected n wye. t cnsumes 00kW. The secnd s a urely nducte 00kR lad cnnected n wye. The thrd s a urely caacte 00kR lad cnnected n wye. The lne-t-lne ltage at the lad s 5k. -hase dstrbutn lne sulyng ths lad has an medance f 0j5 hms er hase. (a Calculate the currents drawn by each lad (magntude and hase. (b ndcate the wer factr f each lad. Remember that nn-unty wer factrs must als nclude whether they are laggng r leadng. (c What s the wer factr f the entre lad? That s, what s the wer factr seen by the transmssn lne at the lad end? (d Calculate the real and reacte wer suled at the sendng end f the dstrbutn lne. lutn t rblem 0 j5ω N k (a ad Nte that:, Therefre: φ 00 0 W, j00 0 R, j00 0 R. fr urely resste lad: fr urely nducte lad: fr urely caacte lad: ad j ad ad j

2 Nte n the abe that fr the resste lad, the current and ltage are n hase, fr the nducte, the current lags by 90 deg, and fr the caacte, the current leads by 90 deg. (b ad : f. 0 ad : ad : f 0 laggng f 0 leadng (c Need current angle wth resect t ad ad j4. 64 j s ad and ad f ad.0 are n hase! (d s ad ad ( Zt ( ( 0 j ( ( , φ s ad P φ 5. 99kW, Q φ 8. 0kR lternately, ne culd cmute lsses and add t lad : lss ( φ ( ad Zt ( ( 0 j5 5, j7, φ lad ( φ lss( φ 00 0 P φ 5.99kW Q φ 8.0kR 5,997.9 j7,998.9 Prblem three hase lad has a er hase medance, cnnected n Y, f 00 j 0Ω. The lne-t-lne ltage magntude at the lad s 500. The three-hase dstrbutn lne sulyng ths lad has an medance f 0 j 5Ω /φ. (a Calculate the lne-t-lne ltage magntude at the sendng end f the dstrbutn lne. (b Calculate the real and reacte wer suled at the sendng end f the dstrbutn lne. lutn t rblem (a 500 N N j Z 00 j0 sendng,n N endng,b Z ne OD j ( ( 0 j5 (b ( ( , j74. sendng,n a 7 P.706kW, Q 7. 5kR

3 Prblem three-hase lad cnsumes 00k at 0.7 f laggng. The lne-t-lne ltage magntude at the lad s 500. The three-hase dstrbutn lne sulyng ths lad has an medance f 0 j 5Ω / φ (a Calculate the lne-t-lne ltage magntude at the sendng end f the dstrbutn lne. (b Calculate the real and reacte wer suled at the sendng end f the dstrbutn lne. lutn t rblem (a Nte that θcs - ( deg (the angle s ste because the f s laggng, and sn( an , φ ( 0. 7 j0. 74 φ. 0 ( 0. 7 j an Z ( 0 j sendng,an sendng,b an (b ( ( ( ( sendng an,sendng Psendng 4. 09kW, Qsendng 9. 58kR Prblem 4 The cmlex wer absrbed by a three-hase lad s 500k at 0.8 f lag P Q / φ f the ne ltage at the lad n rblem s , what s the ltage magntude acrss each hase f the lad, f the lad s cnnected as fllws, d What s the magntude f lne current drawn by ths lad? / φ y lutn t rblem 4 The cmlex wer absrbed by a three-hase lad s 500k at 0.8 f lag

4 Nte that θcs - ( deg (the angle s ste because the f s laggng, and sn( Then P φ 500(0.8/400 kw, Q φ 500(0.6/00 kw. PØ 400 kw Q/Ø 00 kr f the ne ltage at the lad n rblem s , what s the ltage magntude acrss each hase f the lad, f the lad s cnnected as fllws, Δ y What s the magntude f lne current drawn by ths lad? x Prblem 5 n the crcut shwn belw, an,000 j 0 (rms. ssume ste hase sequence. The balanced surce sules.5 MW and 0. MR t the three hase balanced lad. Fnd: a The rms lne current. b Z a 5 cn Nn an bn Bb 5 B Z P B BC Z P C ZP C 5 lutn t rblem 5 6 (a φ (.5 j0. 0

5 6 φ (. 5 j0. 0 anan φ, 000an 6 (. 5 j0. x0 an , an (b Z Z y Z y an a N an, Z Py Z Py a 5, , x Ω Prblem 6 three hase surce s sulyng a balanced three hase lad er a transmssn lne hang medance f Z j0 hms er hase. The ltage at the surce end f the transmssn lne s lts lne t neutral. The current suled thrugh the transmssn lne s 00-0 ameres.. Determne the wer factr seen by the surce, and secfy whether t s leadng r laggng.. Determne the ltage (lne t neutral at the lad.. Determne the wer factr f the lad, and secfy whether the lad s a. leadng r laggng b. nducte r caacte 4. Determne the real and reacte wer cnsumed by the lad. lutn t rblem 6. fcs( , and t s laggng.. OD (j07.8-j f angleangle at whch ltage leads the current-4.6-(-0-.6, s fcs( , and the current s leadng the ltage! Ths means the wer factr s leadng (art a and the lad must be caacte (art b. 4. OD ( ( ( j k

6 Prblem 7 balanced, three-hase lad hang a wer factr f 0.8 laggng s suled by a transmssn lne carryng 00 ams at 5 k lne-t-lne. Cmute the three-hase real and reacte wer delered t the lad. lutn t rblem 7 φ ( ( 5 0 ( M f 0.8 θ cs ( sn ( θ 0.6 P ( ( MW Q ( ( MR Prblem 8 balanced, three-hase, delta-cnnected lad cnsumes 50-j0 k at a lne-t-lne ltage f.8 k. Cmute the er-hase medance f ths lad assumng a seres cnnectn between R and X. lutn t rblem 8 (. 8 0 Z 8 jω Z ( 50 j0 0 Z Δ ZY Z Δ ( 8 j 9849 j99ω R 9849Ω X 99Ω( Caacte Prblem 9 three-hase wye-cnnected lad hang medance f Z 00j50 hms er hase s cnnected n arallel wth a three hase delta-cnnected lad hang medance f Z 600j00 hms er hase. The lad s suled by a three-hase wye-cnnected generatr that s drectly ntercnnected wth the lads (.e., there s n transmssn lne between the generatr and the lads. The ltage magntude f the generatr s.8 k lne-t-lne. ssume that the hase t neutral ltage at the generatr s the angle reference.. Draw the three-hase crcut. Clearly dentfy the numercal alues f ne lne t neutral surce ltage hasr and ne-hase medance fr each f lads and.. Draw the er-hase crcut. Clearly dentfy the numercal alues f the surce ltage hasr and the er-hase medances f lads and.. Cmute the three-hase cmlex wer cnsumed by each lad and the ttal, cmlex three-hase wer cnsumed by the tw lads. 4. hw that the ttal, cmlex three-hase wer cnsumed by the tw lads can be cmuted usng the lne current and the lne-t-lne alue f the surce ltage.

7 lutn t rblem 9. N 7967 Z 00j50 Z 600j00. N 7967 Z 00j50 Z 00j00. We culd use N /Z, N /Z, r we culd get the current nstead. et s d t by gettng the current. N /Z 7967/(00j j9.79, N ( (7967( j9.79 ( j4.0ka P 896. kw, Q 4.0 kr N /Z 7967/(00j j5.940 N ( (7967(.8680 j5.940 (76.68ej80.84ka P 76.7 kw, Q 80.8 kr Ttal 657.8j P Ttal kw, Q Ttal kr 4. T j , ne,800 Ttal ( (,800(7.8{cs(0.05jsn(0.05} 657.8j604.9 Prblem 0 Cnsder a balanced three-hase surce sulyng a balanced Y- r Δ- cnnected lad wth the fllwng nstantaneus ltages and currents. cs( ωt θ cs( ωt θ an bn cn cs( ωt θ 0 cs( ωt θ 40 a b c cs( ωt θ 0 cs( ωt θ 40 where and are the magntudes f the rms hase ltage and current, resectely. hw that the ttal nstantaneus wer rded t the lad, as the sum f the nstantaneus wers f each hase, s a cnstant. lutn fr Prblem 0

8 Cnsder a balanced three-hase surce sulyng a balanced Y- r Δ- cnnected lad wth the fllwng nstantaneus ltages cs ω t θ an ( cs( ω t θ 0 bn ( ω t θ 40 cn cs Fr a balanced lad the hase currents are cs ω t θ where ( a b cs( t θ 0 (.4 ω ( ω t θ 40 c cs and are the magntudes f the rms hase ltage and current, resectely. The ttal nstantaneus wer s the sum f the nstantaneus wer f each hase, gen by φ an a bn b cn c ubsttutng fr the nstantaneus ltages and currents cs ω t θ cs ω t θ ( ( φ ( ω t θ 0 cs( ω t θ 0 ( ω t θ 40 cs( ω t θ 40 cs cs Usng the trgnmetrc dentty csx csy cs(x-y cs(xy cs θ θ cs ω t θ θ [ ( ( ] φ [ cs( θ cs( 40 ] θ ω t θ θ [ cs( θ θ cs( ω t θ θ 480 ] The three duble frequency csne terms are ut f hase wth each ther by 0 and add u t zer, and the three-hase nstantaneus wer s φ csθ θ s the angle between hase ltage and hase current r the medance angle. θ θ Prblem three-hase lne has an medance f j4 hms/hase, and the lne feeds tw balanced three-hase lads that are cnnected n arallel. The frst lad s Y-cnnected and has an medance f 0j40 hms/hase. The secnd lad s delta-cnnected and has an medance f 60-j45 hms/hase. The lne s energzed at the sendng end frm a three-hase balanced suly f lne ltage lts. Takng the hase ltage a as reference, determne: a. The current, real wer, and reacte wer drawn frm the suly. b. The lne ltage at the cmbned lads. c. The current er hase n each lad. d. The ttal real and reacte wers n each lad and the lne. lutn fr Prblem (a The Δ-cnnected lad s transfrmed nt an equalent Y. The medance er hase f the equalent Y s

9 60 j45 Z 0 j5 Ω The hase ltage s The sngle-hase equalent crcut s shwn n the fllwng fgure. The ttal medance s ( 0 j40( 0 j5 Z j4 ( 0 j40 ( 0 j5 j 4 j4 4 Ω wth the hase ltage an Z 4 The three-hase wer suled s (b The hase ltage at the lad termnal s 0 0 j4 5 0 as reference, the current n hase a s ( ( 800 W ( ( 0 0 j The lne ltage at the lad termnal s ab ( (c The current er hase n the Y-cnnected lad and n the equalent Y f the Δ lad s 0 j0 j Z 0 j40 0 j0 4 j Z 0 j5 The hase current n the rgnal Δ-cnnected lad,.e., ab ab s gen by (d The three-hase wer absrbed by each lad s W ( ( 600 ar ( 0. ( W ar j.8 j The three-hase wer absrbed by the lne s

10 ( R jx ( j4( 5 50 W j00 ar t s clear that the sum f lad wers and lne lsses s equal t the wer delered frm the suly,.e., ( 450 j600 ( 00 j900 ( 50 j W j0 ar Prblem three-hase lne has an medance f 0.4j.7 hms er hase. The lne feeds tw balanced three-hase lads that are cnnected n arallel. The frst lad s absrbng 560.k at wer factr laggng. The secnd lad absrbs kw at unty wer factr. The lne-t-lne ltage at the lad end f the lne s 80.5 lts. Determne: a. The magntude f the lne ltage at the surce end f the lne. b. Ttal real and reacte wer lss n the lne. c. Real wer and reacte wer suled at the sendng end f the lne. lutn fr Prblem (a The hase ltage at the lad termnals s The ttal cmlex wer s R j ( φ ( 96 j k Wth the hase ltage as reference, the current n the lne s R( φ 660, ( 00 0 The hase ltage at the sendng end s j The magntude f the lne ltage at the sendng end f the lne s ( (b The three-hase wer lss n the lne s ( ( ( ( ( φ R jx j.7 00 kw j8 kar (c The three-hase sendng wer s ( ( φ ( ( kw j477 kar t s clear that the sum f lad wers and the lne lsses s equal t the wer delered frm the suly,.e., 58 j96 j8 540 kw 477 φ j ( φ R( φ ( ( ( kar