Unformatted text preview: MVA := 1000kW MW := MVA MVAr := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927Hz ΟΜΑ∆Α 2 ΘΕΜΑ 1ο (4 βαθµοί)
A := 0.91 ⋅ e j⋅ 0.8 deg B := 150 ⋅ e 150 ⋅ kV ES := j⋅ 82deg Ω C := 0.0009 ⋅ e j⋅ 90.12 deg S ES = 86.60254 kV 3 Ax := Re( A) Ax = 0.90991 Ay := Im( A) Ay = 0.01271 Bx := Re( B) Bx = 20.87597 Ω By := Im( B) By = 148.54021 Ω a := ( B ⋅ ES b := 2 ⋅ ( ES ) 2 ) 4 8 kg m
a = 168750000000000
12 6
s A 2 ⋅ ( Bx ⋅ Ay − By ⋅ Ax) 3 b = −2023397611011.82 6 kg m
9 4 s A
b := 2 ⋅ ( ES ⎯ ) 2 ⋅ Im( A ⋅ B) 3 b = −2023397611011.82 6 kg m
9 4 s A
c := ( ES ⋅ A )2 − ( ES )2 2 c = −1289250000 4 kg m
6 2 s A
2 b + b − 4⋅a⋅c XL1 := 2⋅c XL1 = −79.38399 Ω 2 b − b − 4⋅a⋅c XL2 := L1 := L2 := 2⋅c
XL1 L1 = −0.25269 H XL2
ω ES := ⎡A + ⎛ −B ⋅ j ⋅
⎢ ⎜ ⎝ 1 ⎞⎤ ⋅ E
S
⎥ XL1 ⎠⎦ (rejected) L2 = 5.24836 H ω ⎣ XL2 = 1648.82174 Ω (per circuit & per phase) ES = 86.60254 kV
arg ( ES ) = 163.99745 deg ES := ⎡A + ⎛ −B ⋅ j ⋅
⎢ ⎜ ⎣ ⎝ 1 ⎞⎤ ⋅ E
S
⎥ XL2 ⎠⎦ ES = 86.60254 kV
arg ( ES ) = 0.00255 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 = 0.90991 + 0.01271j B1 ⋅ B2 B = 10.43798 + 74.27011j Ω C = −0 + 0.0018j S A = 0.91 arg ( A) = 0.8 deg B = 75 Ω arg ( B) = 82 deg C = 0.0018 S arg ( C) = 90.12 deg D = 0.91 arg ( D) = 0.8 deg A := A1 B := B1
2 A = 0.90991 + 0.01271j C := 2C1 D := A B = 10.43798 + 74.27011j Ω C = −0 + 0.0018j S A = 0.91 arg ( A) = 0.8 deg B = 75 Ω arg ( B) = 82 deg C = 0.0018 S arg ( C) = 90.12 deg D = 0.91 arg ( D) = 0.8 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 = 244.89371 − 115.88265j A IR = 270.92751 A arg ( IR) = −25.32331 deg ⎯
SR := 3 ⋅ ER ⋅ IR SR = 59.38357 + 28.10005j MVA SR = 65.69643 MVA arg ( SR) = 25.32331 deg IS := C ⋅ ER + D ⋅ IR IS = 223.99919 + 43.16054j A IS = 228.11942 A arg ( IS ) = 10.90619 deg ⎯
SS := 3 ⋅ ES ⋅ IS SS = 59.25636 + 1.13138j MVA SS = 59.26716 MVA arg ( SS ) = 1.09381 deg SL := SS − SR SL = −0.1272 − 26.96867j MVA SL = 26.96897 MVA arg ( SL) = −90.27025 deg IR := B ΘΕΜΑ 3ο (3 βαθµοί) MVA := 1000kW MW := MVA f := 50 ⋅ Hz ω := 2πf ω = 314.15927 Hz MVAr := MVA
X := 75Ω
PR := 2345MW V := 400 ⋅ ( kV) ⋅ e j⋅ 0 V = 230.94011 kV (nominal phase voltage) 3 Ερώτηµα (α)
−2 Bcmax := 1.45 ⋅ 10 mho ⎛
⎝ Pmax_ideal_1circuits := 1 ⋅ ⎜ 3 ⋅ ⎞
X ⎠
2 2⋅V Pmax_ideal_1circuits = 4266.66667 MW Pmax_ideal_2circuits := 2 ⋅ Pmax_ideal_1circuits ⎡
⎢
⎢
⎣ Pmax_SVC_1circuits := 1 ⋅ ⎢ 3 ⋅ ⎤
⎥
X ⋅ Bcmax ⎞ ⎥
⎛
X ⋅ ⎜1 −
4
⎝
⎠⎥
⎦ Pmax_ideal_2circuits = 8533.33333 MW 2 V (για δ=900) Pmax_SVC_1circuits = 2929.89986 MW
Pmax_SVC_2circuits := 2 ⋅ Pmax_SVC_1circuits ⎛
⎝ δ A := 2 acos⎜ 1 − X ⋅ Bcmax ⎞
4 Pmax_SVC_2circuits = 5859.79971 MW δ A = 86.54113 deg ⎠ δA < π
2 ( ) Pmax_1circuits = 2924.56265 MW Pmax_2circuits := Pmax_SVC_2circuits ⋅ sin δ A ( ) Pmax_2circuits = 5849.12529 MW Pmax_2circuits := 2 ⋅ Pmax_1circuits Pmax_2circuits = 5849.12529 MW Pmax_1circuits := Pmax_SVC_1circuits ⋅ sin δ A ⎛ δA ⎞
⎝2⎠ Pmax_1circuits = 2924.56265 MW ⎛ δA ⎞
⎝2⎠ Pmax_2circuits = 5849.12529 MW Pmax_1circuits := Pmax_ideal_1circuits ⋅ sin⎜ Pmax_2circuits := Pmax_ideal_2circuits ⋅ sin⎜ Ερώτηµα (β)
⎛ PR δ 1 := 2 asin⎜ ⎞ δ 1 = 31.90075 deg ⎝ Pmax_ideal_2circuits ⎠
⎛ PR δ 2 := 2 asin⎜ ⎞ δ 2 = 66.68044 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 = 347.59386 MW ⎛ ⎞ PR δ 3 := asin⎜ δ 3 = 53.16532 deg ⎝ Pmax_SVC_1circuits ⎠ δ crit := π − δ 3 ( δ crit = 126.83468 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 = 347.59386 MW
E2A = 102.7413 MW
E2 := E2A + E2B E2B = 284.13237 MW
E2 = 386.87368 MW E2 − E1 = 39.27981 MW ...
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 Spring '07
 Shmmygr

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