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EE_387_200809FA_exam_1_IMPROVED_solution

EE_387_200809FA_exam_1_IMPROVED_solution - EE 387 Fall 2008...

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Unformatted text preview: EE 387 Fall 2008 Midterm Exam 1 Last Name: <x 11’? V . 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 ms. Likewise, your answers for such variables should be in rms. 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. You have 90 minutes to complete the exam. You must turn in all pages of the exam. >19 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) 9 my In the network shown to the right, I71 is adjusted automatically to maintain V2 at a constant value irrespective of P2 or pfz. a. Derive an expression for the real power loss in the feeder Pf as a function of pfg — treat I72 and P2 as parameters. Simplify the expression as much as possible. b. Plot Pf for values of pfz ranging from 1 to 0.5 lagging with V2 =140° p.u., P2 =O.5 p.u., and Rf = 0.01 p.u. Be certain to include a scale for Pf. Y 1. (cont) A 230—kV, 3—phase transmission line delivers 300 MVA at a power factor of 0.8 lagging to a delta—connected load. Calculate the following: The total real and reactive power delivered to the load. The real and reactive power per phase. The phase voltages. The phase currents. The phase impedances. The line currents. rump-9.65» ./ » I” ,2; y; W i V 4‘\,." ,' I‘\ 2‘ x”. ) 1 .EYV’XV , I ‘ \J - u- ’_ .‘\ I . A. T A/ ‘ jx / A 1"- \.;' f : r , W ' 1" M f «” ~ (/- T; '" ‘ v V A "‘ x I J”, " 7L . _, r I,» 1 { j. a, \v' \ ~ ’ ' [v w,. ‘ W m y . d r'x f" {,T fl. m- <«, \ / / 2X ,» , _ - v f- <’\ -— \. 7 ’ . \x - ’d .1 KN. - at F“ m . ’-‘=- t m”. { ~, .) x ‘ ~ . r. L w P» -( ~1' T“ “I m. " W . L m {x ‘ p g; L; L‘V V ” ‘ g9; ’ / f.“ l ‘. ~ It A .t M ——~, r VA VA a »« 1 « 5.. , , V,» ,\ ~— 1 z a 4 .1 1 r J N O C? - - 2. (cont) The single—phase transformer in the system shown to the right is rated at 50 kVA and 2400240 V/V; its equivalent impedance is Z = 2+ j5 Q referred to the primary. The K values of the load voltage and current are 172 = 230400 v and i2 = 2004—300 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. ‘2" ~ 1.- 1,, 4C: 5| 4: M iv 2‘, x : .4; \ ("w 1 ,_ m f “‘7 ‘ 7* K ,,,,, , ‘ ,W. \ / r r /'l n i . .11 r‘ [7/ K»? r «i e/ / / 1,. .1" w ,i/ I" 3,” a” g -' /‘ i". 2 H: . 3 L m “ v " l f {l \ W V 'j‘ 1/ : 7 ~* e 3»/ «c {— a / «VA ' (an; .. g’,,/\ (‘5: _ ., \ —. ,a N . ‘ _. 5" ._,‘e , VJ \J V. 74 N _~ J '\ ‘k/ C It," . m \- /,, , - y/ g ’ _ ,3 A v ~' N "‘ W 14' k w s / \ \./ \‘ 3. (cont) 4. A V) C/ U‘\ Consider the field plot for a simple 2—winding machine shown below. The parameters for the machine are rg =20 mm, g 21mm, [2 2100mm, NS =20 turns, N, =1 turn. a. b. c. d. Calculate the value of the stator magnetizing flux (am, from the field plot. Calculate the value of stator magnetizing inductance Lm. Calculate the value of stator leakage inductance Lb, Plot the radial component of the air-gap flux density Bgr as a function of position around the stator $3, on the axes provided on the facing page. Be certain to include a scale for By . is = 25 A, ir = 0 A, AAZ = 500 nT-m (38 field lines) n ; C . , (cont) 1/- 4. Some questions requiring short answers or problems requiring short solutions: a. What are the values of Va", Vb" , and 176", if Vab =345445° V and the line-to— neutral voltages are a balanced negative—sequence set? my ii» *0 ‘7’” “N _ rx ,‘ I “‘9' 77?" *‘r‘ , V‘- . v‘ V a 1*» “Kiwi i A A \f'en “ U83; ’i b it"; View ‘ Qt’ic if DO if b. For a 3—phase system with symmetric loads and lines, what condition on the three phase voltages of any wye—connected voltage sources ensures that there will be no neutral currents? For full credit give the most general condition. [a]: TA? 5% A” TJAW “' it; by“ J’ gram : 0. Why are the copper losses of a transformer load dependent, while the iron losses are not? i 2 "TX 1 Q £17730??? "IQ i4?! K ‘> 2 wax/‘x ¥g<5c< Ara Qyofigi ‘5 \r {Warm eélwk 0 V ., t (a “U d. The flux linkage equation for one winding of a particular three—winding rotating machine is expressed: 11m (Isa ’ lsb ’ Zr 7 6r) : L 33' [SH + Lsr (6r 10 ...
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