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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, closednote 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. rump9.65» ./ » I” ,2; y;
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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 sourcetransformer—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
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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 airgap 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 nTm (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 lineto— neutral voltages are a balanced negative—sequence set? my ii» *0 ‘7’” “N _ rx ,‘ I “‘9' 77?" *‘r‘ , V‘ . v‘ V a 1*»
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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
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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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 '08
 JEFFERYMAYER

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