ECE 325, Fall 2015, Test 1
Problem 1 (30 points): Short answer questions
a. (4 points) The top-3 energy resources of electricity generation for the overall US power grids
are coal, natural gas and hydro. True or false?
False (4 pts). Coal, natural gas and nuclear (reason is unnecessary)
b. (12 points) In the following generations,
1) Combined-cycle power plant
4)
2) Concentrated solar tower
5)
3) Pumped storage hydro-plant
6)
Pressurized water reactor
On-shore wind turbine generator
Photovoltaic solar farm
Which convert heat to electricity? (4 points) 1, 2, 4
(2 pts for one, 3 pts for two, 4 pts for three. Take 1 pt for each wrong one)
Which one usually has the highest overall efficiency? (4 points) 3 (4 pts)
Which two are more likely used as peak-generation plants? (4 points) 1, 3 (2 pts for one)
c. (4 points) Which are reasons for AC winning over DC for power transmission systems?
(2 pts for one; 4 pts for both; 4-1 pts if all three are given)
1) Voltage levels in AC systems can easily be transformed by transformers
2) AC generators and motors have simpler designs than DC generators and motors
3) AC transmission systems are always cheaper to build than DC transmission systems
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d. A circuit connecting devices A and B has current I and voltage E as indicated in the figure.
Waveforms of their instantaneous values, i and e, are given in the plot. Determine which
device is the active source and which is the reactive source. (10 points)
P<0, Q<0, so A is the active source, and A is the reactive source (2 pts each; If the answer is
wrong but steps are provided, give 1 pts for steps on each.)
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Problem 2 (35 points): The circuit connecting a j5 inductor, a -j10 capacitor and a 10 resistor
is powered by a 10V AC source. Calculate
a. Currents I1, I2 and I3
R=10, ZC=-j10, ZL=j5
Method 1:
Z= R//ZC+ZL = 10-j10/(10-j10) +j5
I1=E/Z=10/5=20o A
1 pt for angle)
KVL:
E - I1ZL+I2ZC=0,
(1 pt)
I2= (I1ZL-E)/ZC= -1 -j =1.41 -135o A
I2 ZC+I3R=0
(1 pt)
I3= - I2 ZC/R = 1 – j=1.41 -45o A
= 5 (1 pt)
(1 pt for RMS and
(1 pt for RMS and 1 pt for angle)
(1 pt for RMS and 1 pt for angle)
Method 2:
KVL: E - I1ZL+I2ZC=0
KVL: I2 ZC+I3R=0
KCL:
I1+I2-I3=0
I1= 20o A I2= -1 -j = 1.41 -135o A
I3= 1 – j=1.41 -45o A
(1 pt for each KVL/KCL equation, 1 pt for each RMS, 1 pt for each angle)
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b. The voltage ER across the resistor
ER=I3R=14.1 -45o V
(4 pts: 3 pts for RMS and 1 pt for angle)
c. Draw the phasor diagram about E, ER,
I1, I2 and I3
Phasor diagram (10 pts; two pts for
each phasor)
d. Calculate the active power and reactive power supplied by the source
S=EI1*=102=20W+ j0 var
(8 pts; 4 pts for each of P and Q)
e. Calculate the reactive power supplied by the capacitor
SC=ERI2*=14.1 -45o 1.41 135o=20j var
(4 pts)
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Problem 3 (35 points): A wye-connected motor
is connected to a 5780V (line-to-line) 3-phase,
60Hz transmission line. A wye-connected inductor
bank rated at QI=700kvar is also connected to the
line. If the motor produces an output of 1200kW at
an efficiency of 100% and a power factor of 80%
(lagging). IL, Im and II are respectively the
transmission line current, the line current drawn by
the inductor bank and the motor line current. Calculate the following
a. The reactive power Qm absorbed by the motor
m=cos-1(0.8)=36.9o
(2 pts)
Qm=Pmtan(m)=12003/4=900 kvar
(5 pts)
b. The complex power S=P+jQ supplied by the transmission line
Sm=1200+j900 kVA
S=Sm+j QI=1200+j1600 kVA
Q=1600 kvar (4 pts)
c. RMS values of IL, II and Im
|IL|=|S|/(EL1.73)=200 A
|Im|=|Sm|/(EL1.73)=150A
|II|=|QI|/(EL1.73)=70A
(4 pts)
(4 pts)
(4 pts)
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d. Draw a phasor diagram about IL, Im, II and ELN (line-to-neutral voltage of the transmission line)
for one phase
ELN =EL/1.73=3337 V
(2 pts)
= tan-1(Q/P)=tan-1(4/3)=53.1o
(2 pts)
Phasor diagram (8 pts; 2 pts per phasor)
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