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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 NewtonRaphson algorithm to ﬁnd the ﬁrst update for the . J A. A" A; 111 LVN“,~ n,._“._._~ A 131,“. ”45.4 ,,,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 Q3z05
(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 GaussSeidel approach with A=2, and (b) the NewtonRaphson method. 2=Y3+2Y2_§
x
g "2 't' «i (L/n
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\Z‘ s x 4 {A ﬁrm +2x u/xr) ,4 f x r
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(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. Clinic36 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
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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 :
iMondayFriday §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‘
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l 11 OH 0 Yes \ to (“W A
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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 NewtonRaphson) 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
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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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 Summer '10
 Tomsovic
 Electrical Engineering

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