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[EP] MINTEGIA (2010/03/04) ariketa (ebazpena)

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[EP] MINTEGIA (2010/03/04) ariketa (ebazpena)

  1. 1. ISARE   (J1)1   (J1)2   (J1)3   λ   ⎛ n1 ⎞ Δ   ⎛ n1 ⎞ Δ   ⎛ n1 ⎞ ⎜ ⎟ = 15 ⎜ ⎟ = 30 ⎜ ⎟ = 30 ⎝ n 2 ⎠1 ⎝ n 2 ⎠ 2 ⎝ n 2 ⎠ 3 λ   λ   λ   € € € (IC)1=  30A   (IC)2=  90A   (IC)3=  60A  
  2. 2. ⎛ n 2 ⎞ 1 ⎜ ⎟ = ⎝ n1 ⎠1 15 ⎛ n 2 ⎞ 1 ⎛ n 2 ⎞ 1 ⎛ n 2 ⎞ ⎜ ⎟ = ⇒ ⎜ ⎟ = ⋅ ⎜ ⎟ € ⎝ n1 ⎠ 2 30 ⎝ n1 ⎠ 2 2 ⎝ n1 ⎠1 (V1)2 ⎛ n 2 ⎞ ⎛ n 2 ⎞ 1 ⎛ n 2 ⎞ 1 ⎜ ⎟ = ⇒ ⎜ ⎟ = ⋅ ⎜ ⎟ 30o (V13)3 ⎝ n1 ⎠ 3 30 ⎝ n1 ⎠ 3 2 ⎝ n1 ⎠1 € 30o (V13€ )1 (IC)1= 30A (IC)2= 90A  (IC)2 = 3(IC)1 (IC)3= 60A  (IC)3 = 2(IC)1
  3. 3. (J1)1 = (Ip1)1 ⎛ n 2 ⎞ (J1)1 ⎜ ⎟ ⋅ ( IC )1 = x ⎝ n1 ⎠1 € λ ⎛ n ⎞ − ⎜ 2 ⎟ ⋅ ( IC )1 = −x ⎝ n1 ⎠1 ⎛ n1 ⎞ ⎜ ⎟ = 15 (Is1)1 ⎝ n 2 ⎠1 € λ (IC)1 -(IC)1 € (VL)1 (V32)1 (V12)1 (V13)1 (V23)1 (V21)1 (V31)1 (V32)1 (IC)1 = 30A 30 60 90 120 150 180 210 240 270 300 330 360
  4. 4. (Ip1)2 ⎛ 2 ⎞ ⎛ n 2 ⎞ ⎛ 2 ⎞ ⎡1 ⎛ n ⎞ ⎤ ⎡⎛ n ⎞ ⎤ ⎜ ⎟ ⋅ ⎜ ⎟ ⋅ ( IC ) 2 = ⎜ ⎟ ⋅ ⎢ ⎜ 2 ⎟ ⎥ ⋅ [ 3⋅ ( IC )1 ] = ⎢⎜ 2 ⎟ ⋅ ( IC )1⎥ = x (J1)2 ⎝ 3 ⎠ ⎝ n1 ⎠ 2 ⎝ 3 ⎠ ⎣2 ⎝ n1 ⎠1⎦ ⎣⎝ n1 ⎠1 ⎦ € Δ   ⎛ n1 ⎞ ⎛ 1 ⎞ ⎛ n ⎞ ⎛ 1 ⎞ ⎡1 ⎛ n ⎞ ⎤ 1 ⎛ n ⎞ 1 − ⎜ ⎟ ⋅⎜ 2 ⎟ ⋅ ( IC ) 2 = − ⎜ ⎟ ⋅⎢ ⎜ 2 ⎟ ⎥ ⋅ [ 3⋅ ( IC )1 ] = − ⋅ ⎜ 2 ⎟ ⋅ ( IC )1 = − x ⎝ 3 ⎠ ⎝ n1 ⎠ 2 ⎝ 3 ⎠ ⎣2 ⎝ n1 ⎠1⎦ 2 ⎝ n1 ⎠1 2 ⎜ ⎟ = 30 ⎝ n 2 ⎠ 2 (Is1)2 € λ (IC)2 € (VL)2 (V1)2 (V2)2 (V3)2 (IC)2 = 90A 30 60 90 120 150 180 210 240 270 300 330 360
  5. 5. (Ip3)2 (J1)2 x € Δ   1 − x 2 ⎛ n1 ⎞ ⎜ ⎟ = 30 € ⎝ n 2 ⎠ 2 (Is3)2 λ (IC)2 € (VL)2 (V1)2 (V2)2 (V3)2 (IC)2 = 90A 30 60 90 120 150 180 210 240 270 300 330 360
  6. 6. (J1)2 = (Ip1)2 - (Ip3)2 3 x 2 (J1)2 € Δ ⎛ n1 ⎞ 3 − x 2 ⎜ ⎟ = 30 ⎝ n 2 ⎠ 2 (Ip1)2 € λ x € 1 − x € 2 € (Ip3)2 x (IC)2 = 90A € 1 − x 2 30 60 90 120 150 180 € 210 240 270 300 330 360
  7. 7. (Ip1)3 ⎛ n 2 ⎞ ⎡1 ⎛ n ⎞ ⎤ ⎛ n 2 ⎞ ⎜ ⎟ ⋅ ( IC ) 3 = ⎢ ⋅ ⎜ ⎟ ⎥ ⋅ [2 ⋅ ( IC )1 ] = ⎜ ⎟ ⋅ ( IC )1 = x 2 (J1)3 ⎝ n1 ⎠ 3 ⎣2 ⎝ n1 ⎠1⎦ ⎝ n1 ⎠1 € ⎛ n ⎞ Δ − ⎜ 2 ⎟ ⋅ ( IC ) 3 = −x ⎝ n1 ⎠ 3 ⎛ n1 ⎞ (Is1)3 ⎜ ⎟ = 30 (IC)3 € ⎝ n 2 ⎠ 3 λ -(IC)3 € (VL)3 (V12)3 (V13)3 (V23)3 (V21)3 (V31)3 (V32)3 (IC)3 = 60A 30 60 90 120 150 180 210 240 270 300 330 360
  8. 8. (Ip3)3 ⎛ n 2 ⎞ ⎜ ⎟ ⋅ ( IC ) 3 = x (J1)3 ⎝ n1 ⎠ 3 € ⎛ n ⎞ Δ − ⎜ 2 ⎟ ⋅ ( IC ) 3 = −x ⎝ n1 ⎠ 3 ⎛ n1 ⎞ (Is3)3 ⎜ ⎟ = 30 € (IC)3 ⎝ n 2 ⎠ 3 λ -(IC)3 € (VL)3 (V12)3 (V13)3 (V23)3 (V21)3 (V31)3 (V32)3 (IC)3 = 60A 30 60 90 120 150 180 210 240 270 300 330 360
  9. 9. (J1)3 = (Ip1)3 - (Ip3)3 2x (J1) € x 3 € Δ ⎛ n1 ⎞ −2x −x ⎜ ⎟ = 30 € ⎝ n 2 ⎠ 3 (Ip1)3 λ x € € € −x (Ip3)3 € x (IC)3 = 60A € −x 30 60 90 120 150 180 210 240 270 300 330 360 €
  10. 10. 5x (J1)1 x 4x € 3x ISARE € € 2x € −x x € 3 € € x −x (J1)2 2 −2x € € −3x € −4 x 3 € −5x − x 2 € 30 60 90 120 150 180 210 240 270 300 330 360 (J1)3 € I SARE = 1 ⎡ π ⎛ 5 ⎞ 2 π ⎛ 7 ⎞ 2 π ⎛ 9 ⎞ 2 π 2 π 2 ⎤ ⋅ ⎢ 2⋅ ⋅ ⎜ x ⎟ + 2⋅ ⋅ ⎜ x ⎟ + 2⋅ ⋅ ⎜ x ⎟ + 2⋅ ⋅ ( 2x) + 2⋅ ⋅ ( x) ⎥ 2x € 2π ⎢ 6 ⎝ 2 ⎠ ⎣ 6 ⎝ 2 ⎠ 3 ⎝ 2 ⎠ 6 6 ⎥ ⎦ x € 1 ⎡ π 25 π 49 π 81 π π ⎤ = x⋅ ⋅ ⎢ 2⋅ ⋅ + 2⋅ ⋅ + 2⋅ ⋅ + 2⋅ ⋅ 4 + 2⋅ ⎥ 2π ⎣ 6 4 6 4 3 4 6 6 ⎦ € 1 ⎡ 50 98 162 8 2⎤ 1 ⎡ 512⎤ 32 = x⋅ ⋅ ⎢ + + + + ⎥ = x ⋅ ⋅ ⎢ ⎥ = x ⋅ 2 ⎣ 24 24 12 6 6⎦ 2 ⎣ 24 ⎦ 3 −x € −2x 32 ⎡⎛ n2 ⎞ ⎤ 32 ⎡ 1 ⎤ 35 I SARE = x ⋅ = ⎢⎜ ⎟ ⋅ ( I C )1⎥ ⋅ = ⎢ ⋅ 30⎥ ⋅ = 6.53A 30 60 90 120 150 180 210 240 270 300 330 360 3 ⎢⎝ n1 ⎠1 ⎣ ⎥ ⎦ 3 ⎣15 ⎦ 3 €

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