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Transients in Power Systems

by: Fredy Okuneva

Transients in Power Systems ECE 524

Fredy Okuneva
GPA 3.81

Brian Johnson

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Brian Johnson
Class Notes
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This 8 page Class Notes was uploaded by Fredy Okuneva on Thursday October 22, 2015. The Class Notes belongs to ECE 524 at University of Idaho taught by Brian Johnson in Fall. Since its upload, it has received 23 views. For similar materials see /class/227723/ece-524-university-of-idaho in ELECTRICAL AND COMPUTER ENGINEERING at University of Idaho.

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Date Created: 10/22/15
QT 39OU NOISSES SNELLSAS HEIMOCI NI SiNElISNVEIi VZS EDEI ECE 524 Session 15 Page 58 Transients in Power Systems Spring 2008 Equivalent circuit LS Neglect load for now Load Vm 2817kV 2 Vm I VLL 5 Vst 2 Vmsincot b i 2 90deg Approximate Solution As a rst pass we could look at just the transient circulating between the two capacitors Series combination of capacitors C1C2 1 quot C1 c2 Ceq 1433 HP 1 f 01 Cycz 27395 L2 C1 C2 Initial Voltage Conditions fm 2 959615Hz 39 leely to be damped severly by a resistance Vol 0 2 Vm V020 2 0V 142 Z01 E Z01 11589 eq La 91 ECE 524 Transients in Power Systems Session 15 Page 68 Spring 2008 Peak current Vc10 Vc20 Z01 ka1 2433 A Very large current at a high frequency ka1 2 Note This is circulating between the capacitors not through the source For comparison the steadystate current would be 22 J3 1SS 1155 47753A 1 Y1 j 39Xs J Xcl J X02 J 0sz Or with just 1 capacitor as we saw in lecture 13 VLL W3 Isslcap iIsswlcapl 3049A Now look at the voltage at the bus First look at the term at the above resonant frequency F h b 1 Vcl039Cl V02039C2 rorn c arge a ance Vm mty 2 Cl 2 Vin nity 18mm There will be an oscillating voltage based on this 6001 I Z n fm V02t 2 Vin nity Vinfinity39COS001t This represents the increase in voltage at that capacitor This represents the decrease t 39 39 V39 t V0 Vm mty Vm ln th cosltm01 in voltage at thls capaCItor F m ECE 524 Session 15 Page 78 Spring 2008 Transients in Power Systems Note that Vm Vin nity 1006 kV There will be 2 other terms in the response 1 The 60 Hz responsejust the steadystate solution 2 A term that is equivalent to the two capacitors adding in parallel resonatin with the source impedance l f 2 02 21t1LsiC14 C2i f02 43826 HZ Session 15 Page 1111 ECE 524 Spring 2008 Transients in Power Systems Now look at the current between the capacitors now the source voltage is not scaled 4323M 30 103 20 20 3930 I 1 1 I I l 10 20 30 4390 39103 50 file capswitpl4 x vart v VS 682 CZ Now the high frequency term dominates Zoom in on the current between caps Calculated 2433kA with high freq term alone 3 39 ka 2 2456kA 103 20 20 P 3930 I 1 I 1660 1665 163970 1675 1680 1685 103 16090 file capsvvitp4 xvart 3 32 cO 1 T1 2 0016693sec T2 2 0016797sec 961538Hz T2 T1 m Universityofldaho m Universityofldaho w para 54 We w 4 Broad g m Universityofldaho


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