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# [EP] MINTEGIA (2010/03/25) ariketa (ebazpena)

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### [EP] MINTEGIA (2010/03/25) ariketa (ebazpena)

1. 1. ISARE,  (I1)SARE   FSARE   (J1)1   (J1)2   Δ   ⎛ U1 ⎞ 6300 λ   ⎛ U1 ⎞ 6300 ⎜ ⎟ = ⎜ ⎟ = ⎝ U 2 ⎠1 370 ⎝ U 2 ⎠ 2 370 λ   λ   € € Ψ1=0o   Ψ2=30o   (IC)1  =  270A   (IC)2  =  270A
2. 2. Δ   ⎛ U1 ⎞ 6300 ⎛ n1 ⎞ U1 6300 ⎜ ⎟ = ⇒ ⎜ ⎟ = = = 17 3 ⎝ U 2 ⎠1 370 ⎝ n 2 ⎠1 U 2 370 λ   3 λ   ⎛ U1 ⎞ 6300 ⎛ n1 ⎞ U1 6300 3= 3 = 17 ⎜ ⎟ = ⇒ ⎜ ⎟ = ⎝ n 2 ⎠ 2 U 2 370 λ   ⎝ U 2 ⎠ 2 370 3 3 € ⎛ n 2 ⎞ ⎛ n 2 ⎞ ⇒ ⎜ ⎟ = 3 ⋅ ⎜ ⎟ ⎝ n1 ⎠ 2 ⎝ n1 ⎠1
3. 3. 30o 30o (V13)1 (V13)2
4. 4. (Ip1)1 ⎛ n 2 ⎞ ⎜ ⎟ ⋅ ( IC )1 = x (J1)1   ⎝ n1 ⎠1 € Δ   ⎛ n ⎞ − ⎜ 2 ⎟ ⋅ ( IC )1 = −x ⎝ n1 ⎠1 (Is1)1 € λ   IC -IC Ψ1=0o   (VL)1 (V32)1 (V12)1 (V13)1 (V23)1 (V21)1 (V31)1 (V32)1 (IC)1  =  270A   30 60 90 120 150 180 210 240 270 300 330 360
5. 5. (Ip3)1 ⎛ n 2 ⎞ (J1)1   ⎜ ⎟ ⋅ IC = x ⎝ n1 ⎠1 € Δ   ⎛ n ⎞ − ⎜ 2 ⎟ ⋅ IC = −x ⎝ n1 ⎠1 (Is3)1 € λ   IC -IC Ψ1=0o   (VL)1 (V32)1 (V12)1 (V13)1 (V23)1 (V21)1 (V31)1 (V32)1 (IC)1  =  270A   30 60 90 120 150 180 210 240 270 300 330 360
6. 6. (J1)3 = (Ip1)3 - (Ip3)3 2x x € (J1)1   € −x Δ   € −2x (Ip1)3 ⎛ n 2 ⎞ ⎜ ⎟ ⋅ IC = x € ⎝ n1 ⎠1 λ   € ⎛ n ⎞ − ⎜ 2 ⎟ ⋅ IC = −x ⎝ n1 ⎠1 Ψ1=0o   (Ip3)3 ⎛ n 2 ⎞ € ⎜ ⎟ ⋅ IC = x ⎝ n1 ⎠1 € (IC)1  =  270A   ⎛ n ⎞ − ⎜ 2 ⎟ ⋅ IC = −x ⎝ n1 ⎠1 30 60 90 120 150 180 210 240 270 300 330 360 €
7. 7. (J1)2 = (Ip1)2 ⎛ n 2 ⎞ ⎛ n 2 ⎞ ⎜ ⎟ ⋅ ( IC ) 2 = 3 ⋅ ⎜ ⎟ ⋅ ( IC )1 = 3 ⋅ x (J1)2   ⎝ n1 ⎠ 2 ⎝ n1 ⎠1 € λ   ⎛ n ⎞ ⎛ n ⎞ −⎜ 2 ⎟ ⋅ ( IC ) 2 = − 3 ⋅ ⎜ 2 ⎟ ⋅ ( IC )1 = − 3 ⋅ x ⎝ n1 ⎠ 2 ⎝ n1 ⎠1 (Is1)€ 2 λ   IC -IC Ψ2=30o   (VL)2 (V32)2 (V12)2 (V13)2 (V23)2 (V21)2 (V31)2 (IC)2  =  270A   30 60 90 120 150 180 210 240 270 300 330 360
8. 8. 2x (J1)1 x € € −x € −2x (J1)2 € 3⋅ x € − 3⋅ x ⎛ n ⎞ 1 x = ⎜ 2 ⎟ ⋅ ( IC )1 = ⋅ 270 = 9.17A ISARE ⎝ n1 ⎠1 17 3 (2 + 3) ⋅ x € (1+ 3) ⋅ x = (1+ 3) ⋅ 9.17 = 25A ( 1+ 3 ⋅ x ) x € (2 + 3) ⋅ x = (2 + 3) ⋅ 9.17 = 34.22A € 1 ⎡ π π π ⎤ € ISARE = ⋅ ⎢2 ⋅ ⋅ 9.17 2 + 2 ⋅ ⋅ 25 2 + 2 ⋅ ⋅ 34.22 2 ⎥ 2π ⎣ 3 3 3 ⎦ −x ( − 1+ 3 ⋅ x ) 9.17 2 + 25 2 + 34.22 2 = ( − 2+ 3 ⋅ x ) 3 € € 30 60 90 120 150 180 210 240 270 300 330 360 ISARE = 25A €
9. 9. (VLC )1 = (VLC 0 )1 − (ΔVX )1 = 500 − 60 = 440V Δ   3 3VO PD 3 ⎛ 2 ⎞ 3 3⎜ 370 ⎟ 3 ⎠ ⎝ (VLC 0 )1 = VLC 0 PD 3 = = = 500v π π λ   ⎛ ⎞ 2 VO PD 3 = 2 ⋅ ⎜U 2 ⎟ = 370 ⎝ 3 ⎠ 3 (VLC ) 2 = (VLC ') 2 = (VLC 0 ') 2 − (ΔVX ) 2 = 433 − 60 = 373V € (VLC 0 ') 2 = (VLC 0 ) 2 ⋅ cosψ 2 = 500 ⋅ cos 30º = 433V λ   ⎛ 2 ⎞ 3⋅ 3 ⋅ ⎜ 370 ⎟ λ   3 3VO PD 3 ⎝ 3 ⎠ (VLC 0 ) 2 = VLC 0 PD 3 = = = 500v π π ⎛ ⎞ 2 VO PD 3 = 2 ⋅ ⎜U 2 ⎟ = 370 ⎝ 3 ⎠ 3
10. 10. FSARE = (PLC )1 + (PLC ) 2 = [(V ) ⋅ (I ) ] + [(V ) LC 1 C 1 LC 2 ⋅ (IC ) 2 ] = [440 ⋅ 270] + [373⋅ 270] = 0.80 3 ⋅ U1 ⋅ ISARE 3 ⋅ U1 ⋅ ISARE 3 ⋅ 6300 ⋅ 25 ⎛ ΔV ⎞ € cos(ϕ1 )1 = 1− ⎜ X ⎟ ⎝ VLC 0 ⎠1 cos(ϕ1 )1 = 1− 0.12 = 0.88 (ϕ1 )1 ≠ (ϕ1 ) 2 (ϕ1)1 = arccos(0.88) = 28.35º VR ⎛ ΔVX ⎞ cos(ϕ1 ) 2 = cosψ 2 − ⎜ ⎟ €⎝ VLC 0 ⎠ 2 cos(ϕ1 ) 2 = cos 30º − 60 = 0.74 (I1)1 500 (I1)2 (ϕ1) 2 = arccos(0.74 ) = 41.75º €
11. 11. (VLC 0 )1 ⋅ (IC )1 500 ⋅ 270 (I1 )1 = = = 12.37A 3 ⋅ U1 3 ⋅ 6300 (VLC 0 ) 2 ⋅ (IC ) 2 500 ⋅ 270 (I1 ) 2 = = = 12.37A 3 ⋅ U1 3 ⋅ 6300 (I1 ) SARE = (I1 ) 2 2 SARE,X + (I1 ) SARE,Y = 20.112 + 14.112 = 24.56A € (I1 ) SARE,X = (I1 )1,X + (I1 ) 2,X = 10.88 + 9.23 = 20.11A (I1)2,X (I1)1,X (I1 )1,X = (I1 )1 ⋅ cos(ϕ1 )1 = 12.37 ⋅ cos28.35 = 10.88A (I1 ) 2,X = (I1 ) 2 ⋅ cos(ϕ1 ) 2 = 12.37 ⋅ cos 41.75 = 9.23A (I1)1,Y (I1)2,Y (I1)1 (I1 ) SARE,Y = (I1 )1,Y + (I1 ) 2,Y = 5.87 + 8.24 = 14.11A (I1)2 (I1 )1,Y = (I1 )1 ⋅ sin(ϕ1 )1 = 12.37 ⋅ sin28.35 = 5.87A (I1 ) 2,Y = (I1 ) 2 ⋅ sin(ϕ1 ) 2 = 12.37 ⋅ sin 41.75 = 8.24 A