EE_387_200809SP_exam_1_solution

EE_387_200809SP_exam_1_solution - EE 387 Spring 2009...

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Unformatted text preview: EE 387 Spring 2009 Midterm Exam 1 '\ if: Last Name: 6”“ First Name: Instructions: 1. This is a closed—book, closed—note exam. There is a separate equation sheet. No other study materials should be visible or accessible during the exam. 2. Be certain to check all parameter values that you use, as many of the values differ slightly from the ones used in the lecture notes and/or homework assignments. 3. All phasor variables are specified in rms. Likewise, your answers for such variables should be in ms. 4. Voltage and current phasors should be reported in polar form, while complex power and immitances should be reported in rectangular form. 5. A significant fraction of your score for each problem will be based on the manner in which you develop your solution. It should be logical and neat. 6. You have 90 minutes to complete the exam. 7. You must turn in all pages of the exam. Do not write below this line: Problem 1 (20 points) Problem 2 (20 points) Problem 3 (20 points) Problem 4 (20 points) Problem 5 (20 points) TOTAL (100 points) Consider the single—phase system shown to the right. The value of the source voltage is I75 = 480 V. LoadA is 12 kW with 0.866 lagging power factor, and Load B is 10 kVA with 0.8 lagging power factor. The magnitude of the reactive power associated with capacitor C is 10 kVAR. Determine the following: a. The complex power supplied by the source, SS. b. The current drawn by Load A, IA. c. The impedance of an equivalent series network for Load B, 23. A ~ f’f /: < 2: L2 4, s ,‘L ‘ 91““ ,x/ 3 v A l 5% t 1 ! (/W 1 _,..____n! t» n» ‘a 7 «K ’ ‘t t I l; KW A: ' )2 F {a}, *“ s M“ “x; .e l :"\ '. _ ,' ’ .‘ DZ ” ' f w 1 ,. 1 3 re "” ‘ “ ~\ i i/ 3‘ .,_ if; ! V12. : ; “x .1 V / a a, w. '“ Q “a ,l x ”7 , \ w T Q Hi ’ W J p k? \l f w < "a ff“ 1 A $3; M JL “”3 3; v i: w / ) V (A “319% n ‘= E» J,” 1" 2 “v i :2 ”i “VA“ ’9 ff“ “i :3 W ”ng l Consider an inductor having a core that is constructed by stacking 25 laminations like the one shown to the right 'The thickness of each lamination is 1 mm, and the relative pennabflfiy of each lannnafion is 1000. The winding is wound around the center leg and has 100 turns. Estimate the value of the magnetizing inductance. A 5: m if .9 W ’i J _.,._ Wmflw \fix‘fl ., W , we? in, Q!" m ‘u” /\ 'f‘ x r,“ \u m 4 l ,1 517' .,. \Jl‘g'wi ' L/ fl 2) e U ‘ ‘ “ 77c. ' " iywpgflcjp ,5. (fly; ~ ‘ “r“ "\ l um" ' is» l ‘ {1&4 ”a: X 3/ st 513‘ j xv / ,1 L/fi/g 10mm 20 mm «tun—Guy 13mm (a: Natalia“: 2. (cont) 3. The single—phase transformer in the system shown to the right is rated at 50 kVA and 4800:240 V/V; its equivalent impedance is Z = 5 + leQ referred to the primary. The I7 1 values of the load voltage and current are V2223010°V and [222004—36.9°A, respectively. a. Draw an equivalent circuit for the source-transformer-load system with all quantities referred to the primary winding. b. Determine the value of I71. Determine the transformer voltage regulation. d. Determine the transformer efficiency. 4 " “ ‘ e «" z—B‘; “5‘5 f‘, U“ g——W'6““W If: G?) \Vjt ‘ a ft, m x x jg: / = « - “t 2" ”L a v. @Q Vi: w iv]; (é 4‘2; -» / / i r==- /’ f” c? ‘ ‘ ~-v ’; tam F ' f’\/~/x/ V? f : awe ” a; -- r k h a we: < ‘ R (My fv / ‘_ 9‘“: i2" .._ : f ' 3 C 1‘ if? , l U19? 5 3 \xaffii ‘ hm * V 3V “ 32x d“ ”i v w >< C53 :71» (cont) 3. Consider the (non—standard) 3—phase transformer shown to the right. Derive the positive—sequence voltage gain flab/17W]. Assume that each of the l-phase transformers is ideal and has a secondary— to primary—tums ratio of N2 /N1. y’w‘ r; y a t - UM t rye”: s: f“, ’\ .f‘m/ w W, ”a“? ”a x. , \‘ j / at W I ,, .o x," A 3:” Mr V ifi“ ‘A “ 35W"? ‘ u “‘7 4. (com) 5. Some problems requiring short solutions: a. For voltage and current phasors I?‘ 2120410" V and I: = 101 w 20° A , determine the component of I: that is in quadrature With 17X , qu' V4... Express the form of the phase admittance matrix for t/ v a symmetric 3-phase impedance. ‘ The ac current and flux linkage for a particular inductor can be expressed i(t) = x/EI cos(a)et) 1(1) = x/EA cos(a)et) where I =10A , A =O.1V's, and we :27r-60 rad/s. i. Express the induced voltage e(t) . ,/ , \\Y '9’” 1 / {I \. ’E ‘— t -. 3 w "1,“ 3A,”? ‘ ‘ "z a.“ l} e t j W A $331 is)? "" éi/z \"L‘UC Kw ,1‘ V ii. Calculate the peak value of energy stored in the inductor W L . l 4 A particular transformer is designed so that the copper losses and iron losses are equal to each other at full load and 0.7 lagging power factor. Determine the percentage change in total losses if the power factor of the load is corrected to unity. a ,fiesreai w... a 10 ...
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