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Name: _____Answers___________
ECE 476
Exam #1
Tuesday , October 6, 2015
Closed book, closed notes
One note sheet allowed
Scientific calculators allowed
1. ________ / 24
2. ________ / 24
3. ________ / 24
4. ________ / 28
Total
________ / 100
1.
(24 points total)
A new 3 phase, 60 Hz, 200 mile transmission line is to be built using Bluebird conductor.
Bluebird conductor has an outside diameter of 1.762 inches; stranding of 84/19 (Al/St)
yields a GMR for the conductor of 0.0588 feet. Resistance for each conductor is 0.0505
/mile. Bundling is to be used, with the three conductors per phase spaced
symmetrically 1 feet apart. A horizontal tower configuration is used, with a distance of
20 feet between adjacent phases (i.e., 20 feet between the left and center phases, 20 feet
between the center and right phases, and hence 40 feet between the left and right phases).
Assuming that the line is uniformly transposed, draw the medium length -equivalent
circuit for the line, showing the value of all parameters. For reference  = 4 x 10-7
H/m and 0 = 8.854 x 10-12 F/m. There are 1609 meters per mile.
R
0.0505
 200  3.367 
3
Rb  3 0.0588  1 1  0.389 ft
GMD  3 20  20  40  25.2 ft
 25.2 
7
L  2  107 ln 

8.342

10
H /m

 0.389 
X L  0.506  /mile  200 mile =101 
Rbc  3 0.0734  1 1  0.419 ft
2 0
 1.358  1011 F/m
 25.2 
ln 

 0.419 
YC 2 60  C  1609  200

 0.00082 S
2
2
C
2.
(24 points total)
Two three-phase generators supply a three-phase load through separate three-phase lines.
The load absorbs 30 kW (three-phase) at unity (1.0) p.f. The line impedance is 0 + 1j
ohms per phase between generator G1 and the load, and 0 + 2j ohms per phase between
generator G2 and the load. If generator G1 supplies 15 kW (three-phase) at unity p.f.,
with a terminal voltage of 460 V line-to-line, determine:
(12 pts) a.
The real power supplied by generator G2
(6 pts) b.
The line-to-line voltage at the load terminals
(6 pts) c.
The reactive power supplied by generator G2
(a)
15 kW
(b)
*
 15000 
I1  
  18.820 amps
 460 3 
460
Vload ,ln 
0  j  18.82  265.58  j18.82  266.2  4.05 volts
3
Vload ,ll  3  266.2  461.1 volts
(c)
*


10000
IL  
  37.46  j 2.65 amps
 265.58  j18.82 
I 2  I L  I1  18.64  j 2.65 amps, I 2  18.82 amps
G2 must be supplying all the reactive losses, so its
reactive power output is

3  1 I1  2  I 2
2
2
  3.18 kvars
3.
(24 points total)
True/False – Two points each. Circle T if statement is true, F if statement is False.
T
F
1.
Supplying reactive power locally leads to increased line current,
thus increased line losses.
T
F
2.
When a three-phase system is delta-connected, the phase currents
equal the line currents.
T
F
3.
Excepting a few small isolated systems, the electric grid in North
America consists of a single large synchronous 60 Hz system.
T
F
4.
The total real power losses of an ideal transformer are always zero.
T
F
5.
Transposition of high voltage transmission lines, particularly those
operating at over 345 kV, is practically always done on every
transmission line to keep the system blanced.
T
F
6.
Per unit values are always dimensionless.
T
F
7.
With balanced three-phase circuits, per-phase analysis is
commonly done after converting the Y-connected loads to Δconnected loads, thereby solving only one phase of the circuit
T
F
8.
LTC transformers can be used for controlling bus voltage
magnitudes.
T
F
9.
In the PowerWorld example shown in class the use of phase
shifting transformers was demonstrated for controlling the flow of
power in New York, NY.
T
F
10.
The area control error (ACE) for an electric balancing authority can
never be negative because transmission lines always have real
power losses.
T
F
11.
The ballpark figure given in class for the real power losses on a
high voltage transformer (e.g. 500 MVA) was about 5%.
T
F
12.
A load that consumes 100 kW and 50 kvar has a lagging power
factor.
4.
(28 points total)
Short Answer, seven points each
a)
For a three-phase system using a 100 MVA power base and a 138 kV voltage
base, what is the per unit impedance of Z = 5.06 + j23.7 Ω?
0.0266 + j 0.1244
b)
As discussed in class, a common power flow load model is to assume the load is
constant power. That is, with no voltage dependence. Why might this be an
appropriate model for a resistive heater in which the instantaneous power
consumed varies with the square of the voltage?
Electric heaters are often controlled by a thermostat, so in
aggregate they behave as constant energy loads, hence a constant
power model is appropriate for the power flow time frame;
c)
Give the 3 by 3 Bus Admittance Matrix (Ybus) for the three bus power system
shown below with the indicated short line model per unit line impedances
Bus 2
Bus 1
j0.2
j0.1
j0.1
Bus 3
Ybus
d)
10 
 15 5
 j  5 15 10 
 10 10 20 
For the equation 2 x  x  3  0 with an initial guess x(0) = 1, do two Gauss
iterations to determine x(2).
x(0) = 1, x(1) = 2.0, x(2) = 2.207