Rcitation8 - Electric Energy Processing: Fundamentals and...

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1 18-618: Recitation #8 Dr. Nermeen Mahmoud October 15,2009 Review Electric Energy Processing: Fundamentals and Applications
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2 Problem 1 A 300 MVA, 20 kV, two poles three phase synchronous generator, it has a subtransient reactance of 20% and inertia J=0.017 MJ/MVA per mech rad . The generator supplies a number of synchronous motors over a 60-km transmission line having transformers at both ends, as shown on the line diagram of figure 1. The motors are in rated 13.8 kV, rated inputs to motors are 200 MVA and 100 MVA for M1 and M2, respectively. For both motors Xm =20%. The three phase transformer T1 is rated 350 MVA, 230/20 kV with leakage reactance of 10%. Three phase Transformer T2 is rated 350 MVA, 220/13.8 kV with leakage reactance 10%. Series reactance of transmission line is 0.4 /km. Draw the reactance diagram with all reactance marked in per unit. Select the generator rating as base in the generator circuit.[1]
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3 Problem 1-A Transformer T1 0.0857p.u 350 300 * 230 230 * 0.1 X S S * V V * Z Z Base new to Base old from convert 350MVA S 230kV V 230kV V 300MVA S 2 new p.u 1 T.f old 3 φ new 3 φ 2 LBase_new L LBase_old L old p.u T.f new 1p.u T.f 3 φφtrans Ltransf. - L Lbase - L base 3 φφsy
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4 Problem 1-A 0.0784p.u 350 300 * 230 220 * 0.1 X S S * V V * Z Z 350 S 220 V 230 V 300 S 2 new p.u 2 T.f old 3 φ new 3 φ 2 LBase_new L LBase_old L old p.u T.f new p.u T.f t 3 Ltransf. - L Lbase - L base 3 Base new to Base old from convert MVA kV kV MVA ransf sys Transformer T2
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5 Problem 1-A 0.3p.u 200 300 * 13.8 13.8 * 0.2 X S S * V V * Z Z Base new to Base old from convert 200MVA S 13.8kV V 13.8kV V 300MVA S 2 new p.u M1 old 3 φ new 3 φ 2 LBase_new L LBase_old L old p.u T.f new p.u M1 3 φφmotor Lmotor1 - L Lbase - L base 3 φφsy Motor M1
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6 Problem 1-A
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7 Problem 1-A G Gnew X X kV MVA 22 V 300 S Lbase - L base 3 The Generator has the X G =0.2 p.u referred to For the transmission Line The reactance of the transmission line= 60*0.4=24 3 . 176 300 ) 230 ( S V Z 230 V 300 S 2 base 3 LBase - L 2 Base Lbase - L base 3 kV MVA u p Z Z X Base line L T . 1361 . 0 3 . 176 24 .
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8 Problem 1-A Single line diagram for the problem (1) j0.13161 j0.0857 j0.0784 j0.3 j0.6
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9 If the motors M1 and M2 have inputs of 130 MW and 50 MW respectively at 13.8kV, and both operate at unity power factor, find the voltage at the terminal of the generator.
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Rcitation8 - Electric Energy Processing: Fundamentals and...

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