HVE401E/101 9 ASSIGNMENT 2 Question 1: 1.1 The following observations were made in an experiment for...

Question

HVE401E/101 9 ASSIGNMENT 2 Question 1: 1.1 The following observations were made in an experiment for determining of dielectric strength of transformer oil. Determine the power law equation: Gap spacing: XXXXXXXXXXBreakdown Voltage (kV XXXXXXXXXX) 1.2 How is the breakdown voltage of an air gap affected by air density, air pressure and air temperature? XXXXXXXXXXDetermine the following: (a) The breakdown voltage of a uniform sphere gap in air with a uniform gap of 10mm and a 100mm under standard atmospheric conditions? (b) The correction factor to be applied to the breakdown voltage determined under standard atmospheric conditions if the tests are carried out at a Laboratory 1300m above sea level and 28ºC ambient temperature. (Assume the atmospheric pressure decreases by 1.32% per 100m altitude above sea level XXXXXXXXXXA steady current of 0.9 kA flows through a plane electrode separated by a distance of 6 mm when a voltage of 22 kV is applied. If a current of 75 A flows when the distance of separation is reduced to 1 mm and the field is kept constant at 22 kV, determine the following (a) Townsend’s first ionization’s coefficient (b) The saturation current XXXXXXXXXXCalculate at what speed a one meter width belt of a 22.5MV Van de Graaf generator must be driven to generate a maximum power output of 20kW if the medium surroundings the high tension terminal is air with an electric field strength of 3MV/m. (5) [29]
10 Question 2: 2.1 Derive an expression for maximum thermal voltage and show that the voltage is independent of thickness of specimen. Clearly state the assumptions made XXXXXXXXXXDerive an expression for critical electric field and show that the field is independent of the critical temperature of the dielectric. Clearly state the assumptions made XXXXXXXXXXWhen a dielectric material is subject to an electric field, charges of opposite nature is induced on the two opposite surfaces of the material and hence a force of attraction is developed and the specimen is subjected to electrostatic compressed forces and when these forces exceed the mechanical withstand strength of the material, the material collapses. If the initial thickness of the material is d0 and is compressed to a thickness d under the applied voltage V, then the compressed stress F developed due to electric flied is: F = 0.5I0 Ir (V2/d2) Where Ir is the relative permittivity of the specimen. If ? is the Young’s modulus, the mechanical compressive strength is: ? ln (d0 /d) Derive a formula for Ea, the highest apparent field strength under equilibrium conditions in terms of I0, Ir and Young’s modulus XXXXXXXXXXAn eight-stage Cockcroft-Walton circuit has all capacitors of 0.4?F. The secondary maximum voltage of the supply transformer is 88kV at a frequency of 310Hz. If the load current is 0.008A, determine:(a) The voltage regulation (b) The ripple (c) The optimum number of stages (d) The maximum output voltage (e) The no-load output voltage (f) Vomax under load conditions. (14)

005_1y0l85k-fvrdtvhb.pdf

David · Accepted Answer

Solution : 
Let us assume that the relation between gap spacing and breakdown 
voltage be given as
Using first and third reading 
4 93
8 176
n
n
k
k

  
8 176
1.892
4 93
2 1.892
n
n
n
 

 
Taking log on both sides  
N= 0.9199 = 0.92 
K = 93/4^n= 26 
Using  2nd and 4th reading 
6 139
10 222
6 139
0.626
10 222
0.6 0.626
0.9165
n
n
n
n
n
k
k
n


 


 
K= 26.9 
Taking average value 
N=0.918 
K= 26.45
The breakdown voltage depends on the air density, pressure and 
temperature. 
At STP the breakdown voltage is given by following empirical formula
So the breakdown voltage depends on the pressure by above empirical 
formula. 
Now the voltage obtain from the above formula depend on density and 
temperature of gas. So in order to obtain the breakdown voltage at 
other point , it is multiplied by the following correction factor
So it can be observed that the higher is the pressure , more is correcting 
factor. Higher temperature will result in lower correcting factor.
Using the following formula
Under stp P= 1bar    gap = 10mm = 1cm 
Vb= 26.48 kV 
Under stp P= 1bar    gap = 100mm = 10 cm 
Vb= 264.8 kV
Correction factor is given by
where b is the atmospheric pressure in cm of Hg and  t the temperature 
in °C 
t= 28 
pressure at zero altidude = 76 cm 
Now there is 1.32 % by every 100 m 
So p at 1300 m = 76*(.9868)^13  = 64.9 cm 
3.92*64.9
0.845
273 28
  

 
The correction factor is less then 1 and hence the brake down voltage  
Is less then the Vb at STP
Townsends law 
0
0.6
0
0.1
0
900 *
60 *
dI I e
I e
I e






  
Now dividing the above two equation we get 
0.6
0.1
0.5
900
15
60
15
e
e
e



 

 
Taking ln on both sides  
We get  5.416 
a) Townsends first ionization coefficient= 5.416 cm-1 
b) Saturation current 
0.6
0
0.6*5.416
0
0
900 *
900 *
34.91
I e
I e
I A




 
In graaf generator 
 
Wher sigma is survace charge density 
B is length 
V is the velocity 
V= 22.5 MV        P= 20 kW 
I= 0.889 mA
0
6
12 6 6
3*10 /
8.854*10 *3*10 26.562*10
E
E V m
 
  


 
 
b=1 
3
6
0.889*10
33.46 / sec
26.562*10 *1
I
v
b
v m




 

 
Let us assume that minimum voltage is applied for infinite time 
and thus breakdown takes place. For this, we assume that we 
have a thick dielectric slab that is subjected to constant ambient 
temperature at its surface by using sufficiently large electrodes as 
shown in above figure. 
In order to calculate maximum thermal voltage, let us consider a 
point inside the dielectric at a distance x from the central axis and 
let the voltage and temperature at the point are  Vx and T, respec- 
tively. We further assume that all the heat generated in the 
dielectric will be carried away to its surroundings through the 
electrodes. Therefore, neglecting the term 
 
the main equation reduces to
 
Integrating both sides with respect to x we get
Let us assume  
Then simplifying we get
 
 
This shows that the maximum thermal voltage depends upon the 
critical temperature Tc at the centre of dielectric and Vm is 
independent of the thickness of the insulating material.

HVE401E/101 9 ASSIGNMENT 2 Question 1: 1.1 The following observations were made in an experiment for determining of dielectric strength of transformer oil. Determine the power law equation: Gap...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment