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Midterm1-Solutions - Q‘C‘ L L l lC’lU g MIDTERM EXAM...

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Unformatted text preview: ,, Q‘C‘ L L) l lC’lU g MIDTERM EXAM 1 SPRING 2011 ECE 522 This exam is closed book and I will hand out an equation sheet. BE SURE TO SHOW YOUR WORK CLEARLY AND FULLY. 1. Power flow solutions — Fast Deeoupled Newton—Raphson algorithm (25 points): For the system below, use the fast decoupled Newton-Raphson algorithm to find the first update for the .- J A.-- A" A; 111 LVN“,~ n-,._“._._-~ A 131,“. ”4-5.4 ,,,1LAL-,~_,_.._,'AV,J-.. 1 VUlL‘agC lllaglutuuc tutu £1115ch aL c111 uuacc abbulllulé a 116“. mm L. Bus 1 Bus 2 (slack bus) V1 =1.00[_00 y = —j4 P2=2.0 V3=1.00 V (L 3 a _ 12 'g ~— , _ \, .L‘ . Iy3o=12 Bus 3 P3:-3.0 Q3z-05 (PQ bus) 2. Iterative solution to equations (15 points): It is desired to find the solution to the equation below. Assume a starting guess of x: 1 .0 and perform one iteration using (a) a Gauss-Seidel approach with A=2, and (b) the Newton-Raphson method. 2=Y3+2Y2_§ x g "2 't' «i (L/n \ (oi \ a). may, 0)) ‘-5 " \Z‘ s x 4 {A firm +2x u/xr) ,4 f x r q or: X03: L) s W (UL 3. Load frequency control (20 points): Consider a two area power system. Both areas have two generating units. In area A, the governors are adjusted for a 5% droop, and in area B for a 10% droop. The unit capacities and area load are given below: Area A Area B G1=200 MW G1=200 MW G2=300 MW G2=400 MW Load 2 150 MW Load:250 MW Initially, there is a 150 MW load transfer from Area B to Area A and the system is operating at 60 Hz. If the load increases by 50 MW in area A, find: a) the initial change in system frequency, b) the “ideal bias” values in MW/Ol.Hz for each area that would ensure proper coordination, c) the area control error (ACE) in both areas assuming the bias setting found in (b). State whether the ACE signal indicates an increase or a decrease is needed in that area. Clinic-36 VOL/MN? bask A P: 80/400 I 0325 PW Ami til 1 t2\ ._ 06 (4333‘ A: c-‘x {21: ,cé (2‘16” :~ (/2 067 1' .> U 1. 20¢. {\vt’ttfik fi-\ : ¢Q<Liéic>~fciy~ Ql:(\\ I 27 l J a 6 .0 I ’) A, / g— » /, «L /5/9 : E: 4 \i T C S pd‘ L37 121 + fzz / ( [\9\ Wm '—“ "2%“ (ML V36: t€ \su. :r \U Mid/OHM?- C 9f"\ £5 Mad ‘0 ' ‘ i e-ediéwcj C) flCE d“? LLB ‘4 Lg». Lj‘e’btecmlcws can?!) _ vi ‘9 qt’vue rt '7’” 9% vwi {CIECI\ it; E‘ (CL \‘ (OS ‘05.th % L [iat'tzflmrjz‘m ) "’ ‘ ‘A - «~50 MM," [intemwa .. - 7 ‘V\ (E R : D tVUVU (Ki 3% (SAC-EM? .t ; “SLZS + ("Spams") : -50 we. m (0 W875) : o :0 (w ”l J P 4'", 7“] :9 A :J R l 4. Power system reliability (20 points): For the system described below find (a) the LOLE on a yearly basis, i.e., the expected number of days/year, and (b) EUE on a yearly basis, i.e., the expected MWh/year. (For simplicity, assume exactly 52 weeks per year so 364 days). Generation Data 5Unit 'ékcépééi'ty _. . .W {Eon WWW 1 150 MW 10 05 2 120 MW ‘0 05 Load Data - Assume on peak lasts for 12 hours and off peak lasts for 12 hours each day. éDa gDaily Peak “Baflywomfilg‘eéiewm l y iLoad §Load : iMonday-Friday §160 MW ig75 MW ésaturdaf/Sunday :75 MW 360 MW 9 “lcflcj S , (.2 N,» L 1 l g," 7: ii, A up ‘2 V9,; \3 \ S l ‘ M (3 ~ 7 . 2 i i Z on 170 ‘4‘” Mo (1%) l C: v\ lét/ lull/v l? S ({xg‘)((’6> M—l: @7134 ‘JUMQ‘ ‘5 lac v hwy: ‘, MW \16‘8’ . 4 ~7)\;\UV lav}: ‘ j ‘4‘. l 11 OH 0 Yes \ to (“W A 4 ‘gvt/Ufi’l S LOL‘L: - Si titkbx‘ j>>K "7(:' M; ng LUVYtS :L MO (MW x 1W) —’ 3 Y g 6 Claus /Lj'eczr” 55' X g 7‘ lC‘Mu/‘X l7 land's X (Clg>y~(<((’€2 : x , _ L 5 El”; I ‘1 x 4 '7‘» LlOl/vt'ku' )c\Z\r\cu.v;‘7~ (ft/é) x £405- g‘- E )g (/éGMCJ’X/Y '4;- 75K1Z)(_C/S>(_06> _\.. figzfixy'z )L( ‘7 5/ all? f (3301/? \ (Cg )(JLS L _ :7 ““7. [C 63 COME}? 5. Short Answer (20 points) (a) True or false. In the transmission system, voltage levels are primarily dependent on the reactive power flow and reactive power loss. 11 \Me (b) Which of the two load flow algorithms (1. e fast decoupled or full Newton-Raphson) do you cxpccl l0 C011v61g€ 111 1CWCI 11c1aL‘1ui1a. QLaLC Icaauii fab“)“L;‘(LK\\S3\CLCCLW9 'llat sclulton) (J1 (civil/(gives (C) In the power system security framework what is meant by a secure operating point? (Be specific.) )[C //0u1, {A SEX/Cu e U vx 1km“. (.f (ml \ C7, C’C'Né LUl/L‘gv 6, L2 CD’H/ P(/((}1Qr \ €C'l 9% (C1C4lblf/EL/1C(( / /'/6 SC) J7me 1’sz 11111111411111 C/‘gqf {1011 WHO) 61 // {fun/”11w; / LO! 71‘1“ A 17¢,«511u I //L-//!/ g Q11: 77/15 ; (77$; 6; ,1 [(3 9/ Z r (d) Consider a small system with two areas say area A and area B Area A is leaning” on the frequency control with a bias setting smaller than the ideal setting (i. e. below the natural ovemor response) If Area B experiences a 100 MW morease in load then the Area Control Error (ACE) for area A will be: i) greater than ze1o (i .e., AGC sends lOvv ' er pul es to the generators in area A) / ii) Lem iii) less than zero (i.e., AGC sends raise pulses to the generators in area A) Q C W‘ );:;[email protected] WALK Ck (511/111 ll lfims <91ll1‘1177 1U1/1cg “lamCflL Mk1“; O‘Wfi uredé CM luallt C) ...
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