Transcribed Text
Figure 1 shows the results of a laboratory experiment. A current of 110A was applied to a Copper
cylindrical conductor during 30 minutes. The points represent the temperature rise measurements; the
continuous line represents a mathematical approximation found by the students who did the test using
the first order model described in class. The ambient temperature was approximately kept at an average
of 25 C.
a. Estimate the equilibrium temperature rise. (2p)
b. Estimate the time constant (2p)
c.
Write an expression for the estimated curve (theta as a function of time) using the numerical
results obtained in parts a and b. (2p)
d.
The wire diameter is 4.5 mm, approximately. Estimate a value for the equivalent convection
factor, h in W/(m2K). (2p)
e.
Your task is to predict the theta vs t curve using the same and laboratory setup but with a
current of 85 amps. Write an equation like the one you wrote in Part C for the new conductor
assuming that h has the same value determined in Part d. Plot the estimate theta as a function
of time. (2p)
Note: You do NOT have to use MATLAB to do Part e. You can do it with your calculator and plot the
curve on a linearscaled plot paper, or EXCEL, or any other method you have.
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Time in seconds
Figure 1: Results of a wire heating experiment (notice the temperature reaches burning levels)
a) A metallic wire of certain secret new alloy is known to have a coefficient alpha
a=0.0038K1 at 20°C. The density and specific heat of the metal are unknown. The wire
has circular section with an unknown diameter and is used to build a cable with a rated
temperature of 65°C and a damage temperature of 150°C. The damage 14t = Kd was
found experimentally using no initial current and an ambient temperature of 25°C. The
result was:
Kd = 2.5.106 amp².s
Find Kd using the rated temperature as initial value.
b) Find Kd for a wire with the same characteristics as the wire in a) but with a diameter 1.5
times the size of the wire used in part a. (Use the same initial temperature value used
to find the value of Kd given above.)
c) Plot the three damage curves using a loglog scale, indicating which curve corresponds
to each case.
a.
Determine the HVside fuses needed to protect a transformer bank with a total threephase
capacity of 3x333kVA, 13800480 V in connection YnynO. Show and explain step by step the
procedure you employ to solve this question. Choose between the type K and type T fuse curves
given in class. Assume the transformer has a damage curve as the one given in class. [3p]
b. Plot both, the fuse curves and the transformer damage curve on the same loglog graphic. Use
the loglog curve posted in the class web page. You do NOT need to use MATLAB to do this
problem. You can do it with your calculator and plotting the curve with pencil on the given log
log sheet. It is your choice. The current must be referred to HV side of the transformer bank.
[3p]
Note: assume the inrush can be represented by a point in the t vs I plot with
I = 12 x transformer rated current
t = 0.1 second
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Refing
Reting
a

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97
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=
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I

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,
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.06
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or
or
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.5 7

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$00
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(e)
CURRENT IN AMPERES
(b)
CURRENT IN AMPERES
Fig. 41Timecurrent characteristic curves for Type K (Fast) universal fuse links.
No arcing time is included. (b) Totalclearing curves. These curves show the time
(a) Melting curves. These curves show the minimum time required to melt the fusible
required for any given current to melt the fuse link and clear the circuit.
element, starting from an ambient temperature of 25C with no previous loading.
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Reting
Reting
ane
eng
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o
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is
*3
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,
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, ,

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5 7 o
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CURRENT IN AMPERES
CURRENT IN AMPERES
(a) Melting Curves
(b) Total Clearing Curves
Fig. 42Timecurrent characteristic curves for Type T (Slow) universal fuse links.
No arcing time is included. (b) Totalclearing curves. These curves show the time re
(a) Melting curves. These curves show the minimum time required to melt the fusible
quired for any given current to melt the fuse link and clear the circuit.
element, storting from on ambient temperature of 25C with no previous looding.
TIME va CURRENT CURVE
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10.00
1.00
0.10
0.01
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Current (Amps x
) e
Volts
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