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Unformatted text preview: MVA := 1000kW MW := MVA MVAr := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927Hz ΟΜΑ∆Α 3 ΘΕΜΑ 1ο (4 βαθµοί)
A := 0.93 ⋅ e j⋅ 0.88 deg B := 152.5 ⋅ e 150 ⋅ kV ES := j⋅ 78deg Ω C := 0.001 ⋅ e j⋅ 90.2 deg S ES = 86.60254 kV 3 Ax := Re( A) Ax = 0.92989 Ay := Im( A) Ay = 0.01428 Bx := Re( B) Bx = 31.70653 Ω By := Im( B) By = 149.16751 Ω a := ( B ⋅ ES b := 2 ⋅ ( ES 4 )2 8 kg m
a = 174421875000000
12 6
s A ) 2 ⋅ ( Bx ⋅ Ay − By ⋅ Ax) 3 b = −2073848253341.72 6 kg m
9 4 s A
b := 2 ⋅ ( ES ) 2 ⎯
⋅ Im A ⋅ B ( ) 3 b = −2073848253341.72 6 kg m
9 4 s A
c := ( ES ⋅ A ) 2 − ( ES ) 2 2 c = −1013250000 4 kg m
6 2 s A
2 b + b − 4⋅a⋅c XL1 := 2⋅c XL1 = −80.90716 Ω 2 b − b − 4⋅a⋅c XL2 := L1 := L2 := 2⋅c
XL1 L1 = −0.25754 H XL2
ω ES := ⎡A + ⎛ −B ⋅ j ⋅
⎢ ⎜ ⎝ 1 ⎞⎤ ⋅ E
S
⎥ XL1 ⎠⎦ (rejected) L2 = 6.77248 H ω ⎣ XL2 = 2127.63625 Ω (per circuit & per phase) ES = 86.60254 kV
arg ( ES ) = 156.03547 deg ES := ⎡A + ⎛ −B ⋅ j ⋅
⎢ ⎜ ⎣ ⎝ 1 ⎞⎤ ⋅ E
S
⎥ XL2 ⎠⎦ ES = 86.60254 kV
arg ( ES ) = −0.03547 deg D := A ΘΕΜΑ 2o (3 βαθµοί)
A1 := A B1 := B C1 := C D1 := D A2 := A1 B2 := B1 C2 := C1 D2 := D1 A := ( A1 ⋅ B2 + A2 ⋅ B1)
( B 1 + B 2) B := ( A1 − A2) ⋅ ( D2 − D1) C := C1 + C2 + B1 + B2 D := A B1 + B2 A = 0.92989 + 0.01428j B1 ⋅ B2 B = 15.85327 + 74.58375j Ω C = −0.00001 + 0.002j S A = 0.93 arg ( A) = 0.88 deg B = 76.25 Ω arg ( B) = 78 deg C = 0.002 S arg ( C) = 90.2 deg D = 0.93 arg ( D) = 0.88 deg A := A1 B := B1
2 A = 0.92989 + 0.01428j C := 2C1 D := A B = 15.85327 + 74.58375j Ω C = −0.00001 + 0.002j S A = 0.93 arg ( A) = 0.88 deg B = 76.25 Ω arg ( B) = 78 deg C = 0.002 S arg ( C) = 90.2 deg D = 0.93 arg ( D) = 0.88 deg ER := 140 ⋅ ( kV) ⋅ e j⋅ 0 3 ER = 80.82904 kV ES := 150 ⋅ ( kV) ⋅ e j⋅ 12deg 3 ES = 84.71007 + 18.00568j kV
ES = 86.60254 kV ( ES − A ⋅ ER ) IR = 242.20419 − 76.5341j A IR = 254.00854 A arg ( IR) = −17.53602 deg ⎯
SR := 3 ⋅ ER ⋅ IR SR = 58.73139 + 18.55853j MVA SR = 61.5938 MVA arg ( SR) = 17.53602 deg IS := C ⋅ ER + D ⋅ IR IS = 225.75219 + 93.94823j A IS = 244.52059 A arg ( IS ) = 22.59495 deg ⎯
SS := 3 ⋅ ES ⋅ IS SS = 62.44525 − 11.68062j MVA SS = 63.52831 MVA arg ( SS ) = −10.59495 deg SL := SS − SR SL = 3.71386 − 30.23915j MVA SL = 30.46636 MVA arg ( SL) = −82.99821 deg IR := B ΘΕΜΑ 3ο (3 βαθµοί) MVA := 1000kW MW := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927 Hz MVAr := MVA
X := 70Ω
PR := 2400MW V := 400 ⋅ ( kV) ⋅ e j⋅ 0 V = 230.94011 kV (nominal phase voltage) 3 Ερώτηµα (α)
Bcmax := 1.9 ⋅ 10 −2 mho ⎛
⎝ Pmax_ideal_1circuits := 1 ⋅ ⎜ 3 ⋅ ⎞
X ⎠
2 2⋅V Pmax_ideal_1circuits = 4571.42857 MW Pmax_ideal_2circuits := 2 ⋅ Pmax_ideal_1circuits ⎡
⎢
⎢
⎣ Pmax_SVC_1circuits := 1 ⋅ ⎢ 3 ⋅ ⎤
⎥
X ⋅ Bcmax ⎞ ⎥
⎛
X ⋅ ⎜1 −
4
⎝
⎠⎥
⎦ Pmax_ideal_2circuits = 9142.85714 MW 2 V (για δ=900) Pmax_SVC_1circuits = 3424.29106 MW
Pmax_SVC_2circuits := 2 ⋅ Pmax_SVC_1circuits ⎛
⎝ δ A := 2 acos⎜ 1 − X ⋅ Bcmax ⎞
4 Pmax_SVC_2circuits = 6848.58213 MW δ A = 96.25119 deg ⎠ δA > π
2 ( ) Pmax_1circuits = 3403.9305 MW Pmax_2circuits := Pmax_SVC_2circuits ⋅ sin δ A ( ) Pmax_2circuits = 6807.861 MW Pmax_2circuits := 2 ⋅ Pmax_1circuits Pmax_2circuits = 6807.861 MW Pmax_1circuits := Pmax_SVC_1circuits ⋅ sin δ A ⎛ δA ⎞
⎝2⎠ Pmax_1circuits = 3403.9305 MW ⎛ δA ⎞
⎝2⎠ Pmax_2circuits = 6807.861 MW Pmax_1circuits := Pmax_ideal_1circuits ⋅ sin⎜ Pmax_2circuits := Pmax_ideal_2circuits ⋅ sin⎜ Ερώτηµα (β)
⎛ PR δ 1 := 2 asin⎜ ⎞ δ 1 = 30.43691 deg ⎝ Pmax_ideal_2circuits ⎠
⎛ PR δ 2 := 2 asin⎜ ⎞ δ 2 = 63.33649 deg ⎝ Pmax_ideal_1circuits ⎠ ( E1 := PR ⋅ δ 2 − δ 1 ) δ2 ⌠
⎛ δ ⎞ dδ
− Pmax_ideal_1circuits ⋅ ⎮ sin⎜
⎮
⎝2⎠
⌡δ
1 δ2 < δA ( E2A := −PR ⋅ δ A − δ 2 ) δA ⌠
+ Pmax_ideal_1circuits ⋅ ⎮
⎮
⌡δ ⎛ δ ⎞ dδ
⎝2⎠ sin⎜
2 E1 = 337.36494 MW ⎛ ⎞ PR δ 3 := asin⎜ δ 3 = 44.49725 deg ⎝ Pmax_SVC_1circuits ⎠ δ crit := π − δ 3 ( δ crit = 135.50275 deg ) E2B := −PR ⋅ δ crit − δ A ( ) E2B := −PR ⋅ δ crit − δ A δ crit ⌠
+ Pmax_SVC_1circuits ⋅ ⎮
⌡δ A δ crit ⌠
+ Pmax_SVC_1circuits ⋅ ⎮
⌡δ sin( δ ) dδ sin( δ ) dδ A E1 = 337.36494 MW
E2A = 299.9211 MW
E2 := E2A + E2B E2B = 425.46429 MW
E2 = 725.38539 MW E2 − E1 = 388.02046 MW ...
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 Spring '07
 Shmmygr

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