Copyright by Bhargavi Devarajan 2010 - The University of Texas at ...

Copyright by Bhargavi Devarajan 2010

The Thesis committee for Bhargavi Devarajan Certifies that this is the approved version of the following thesis :

Modeling of a DC fuse for protection of semiconductor R devices using PSCAD /EMTDCTM

APPROVED BY SUPERVISING COMMITTEE:

Alexis Kwasinski, Supervisor William Mack Grady


by Bhargavi Devarajan, B.E.

THESIS Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of Master of Science in Engineering

THE UNIVERSITY OF TEXAS AT AUSTIN May 2010

Dedicated to the people who mean the most: my parents, my sister and my fianc´e

Acknowledgments

I would like to thank my advisor, Dr. Alexis Kwasinski, for his constant support and guidance during the implementation of the thesis. I shall forever cherish the friendship, support and guidance of Niveditha Reddy, Puja Kowley, Purva Jamdade and Pranav Bhandarkar. I would also like to thank Deepak Mohan and Mithun Vyas for their invaluable contribution towards my thesis.

v


Bhargavi Devarajan, M.S.E. The University of Texas at Austin, 2010

Supervisor: Alexis Kwasinski

This thesis presents a new simulation model for DC fuses used to protect R semiconductor devices using PSCAD /EMTDCTM . The basic construction

and operation of fuses is discussed, highlighting the difference between the operations of AC and DC fuses. The melting and arcing models of the fuse are implemented separately. The modeling concept is explained in detail and the model is validated with experimental results.

vi

Table of Contents

Acknowledgments

v

Abstract

vi

List of Figures Chapter 1.

viii

Introduction

1

Chapter 2. Construction and Operation of fuses 2.1 Fuse Ratings . . . . . . . . . . . . . . . . . . . . 2.2 Fuse Construction . . . . . . . . . . . . . . . . . 2.3 Fuse operation . . . . . . . . . . . . . . . . . . . 2.4 Fuse time current characteristic (TCC) curves . 2.5 Operating time of fuses . . . . . . . . . . . . . . 2.6 DC fuse selection criteria . . . . . . . . . . . . . 2.7 Basic fuse types . . . . . . . . . . . . . . . . . .

. . . . . . .

5 5 6 7 8 8 9 12

Chapter 3. Modeling of DC fuse 3.1 Melting model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Arcing Model . . . . . . . . . . . . . . . . . . . . . . . . . . .

14 15 18

Chapter 4. Validation of the Fuse model 4.1 Experimental setup to validate the Fuse model . . . . . . . . .

22 22

R 4.2 PSCAD /EMTDCTM model . . . . . . . . . . . . . . . . . . .

26

Chapter 5.

Conclusion

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28

Bibliography

30

Vita

33 vii

List of Figures

1.1

DC Architecture . . . . . . . . . . . . . . . . . . . . . . . . .

1

2.1 2.2 2.3

Fuse construction . . . . . . . . . . . . . . . . . . . . . . . . . TCC Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuse operating time . . . . . . . . . . . . . . . . . . . . . . . .

7 9 10

3.1 3.2

Fuse current and voltage curves for a fault in a DC system . . Melting model of DC fuse . . . . . . . . . . . . . . . . . . . .

15 16

3.3

R PSCAD /EMTDCTM implementation of melting model of DC fuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combined melting and arcing model of fuse . . . . . . . . . .

17 19

R PSCAD /EMTDCTM model of combined melting and arcing circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

3.4 3.5 4.1 4.2 4.3 4.4 4.5

Short circuit model . . . . . . . . . . . . . . . . . . . . . . . . Polycab wire catalogue DC resistance . . . . . . . . . . . . . . Cooper Bussman (BK-MDL5) TCC curves . . . . . . . . . . . Short circuit current (in blue) and voltage (in orange) waveforms across the fuse during the melting and arcing periods . . Fuse waveforms from simulation: (a)Fuse current (b)Fuse voltage (c)Zoomed in view of fuse current and (d)Zoomed in view of fuse voltage . . . . . . . . . . . . . . . . . . . . . . . . . . .

viii

22 23 24 26

27

Chapter 1 Introduction

DC power has a wide range of applications today because they provide continuous and reliable supply even during times of AC outages. DC power equipment is the lifeline for DC data centers, telecommunication equipment, UPS systems and switchgear. Thus it is imperative that DC equipment be protected adequately with minimum outages [22],[23]. The main objective of

Figure 1.1: DC Architecture

1

any power system is to supply power to the load continuously and reliably. However, occurrence of faults in the system can not only cause outages and damage to equipment but to personnel as well. To avoid these hazards, protection schemes are used in order to trip the faulty parts of the circuit quickly with no or minimum harm to personnel. Power system quantities such as voltage and/or current are continuously sensed by these protective devices. These devices compare the measured quantities with the threshold values and operate within a preset period of time if the measured quantities exceed the threshold values. This isolates the faulty part of the circuit from the healthy part of the system. An electric fuse is used to protect a circuit against over currents. A fuse essentially consists of a strip of alloy like copper or silver. Fuses are connected in series with the circuit that needs to be protected. As current flows through the strip, it generates heat. If this heat is high enough, it causes the strip to melt which opens the circuit thus interrupting the circuit current [2]. Reliability and safety of DC power systems is governed by the protective devices used in the circuit. With increase in the values of current handled by the system today, the voltage fluctuations resulting from the operation of the fuse due to a fault in the system also increase. These voltage fluctuations may cause damage to electronic equipment. Hence knowing the fuse blowing characteristics helps to see what effect these voltage changes have on the circuit equipment which are sensitive to these voltage changes [23]. Chapter 2 gives an overview of the construction and operation of fuses. 2

The characteristics of AC and DC protective devices differ. However, many protective devices are usually designed and tested to protect only AC systems. Although the rms value of an AC current is thermally equal to the DC current, many protective devices suited for AC circuits are used in DC systems also which results in inadequate protection of these DC systems. In a 60 Hz AC circuit as the fault current crosses zero, the fuse attempts to quench the arc. In DC systems, however, as the current never crosses zero, the voltage across the arc in a DC fuse is sustained until the voltage across the fuse equals the system voltage. Thus, DC fuses should be able to withstand the arcing energy. In DC circuits, the fault current also depends on the system inductance. Hence as the system inductance increases in magnitude, the rate of rise of the fault current is slower. This causes the melting time of the fuse also to increase and hence the let through energy of the fuse (I 2 t) is higher for high system inductance values [1],[10],[9]. R Chapter 3 deals with a DC fuse model developed in PSCAD /EMTDCTM .

Both, the melting and the arcing models are analyzed individually. The melting model of the fuse consists of an RL circuit in series with a DC power source along with a switch. The R in the circuit is the combined resistance of the cable and the fuse. The inductance is the inductance of the cable. The closing of the switch simulates a short circuit in the system. The short circuit current flowing in the circuit is compared with the time current characteristic (TCC) curves of the fuse entered in the look up table. The melting time is thus determined. The arcing model of the fuse is represented by an RC circuit. The

3

fuse voltage, current, melting and arcing times are obtained from the model [22],[23]. A short circuit test experiment is conducted with a DC power supply and a fuse. The fuse blowing characteristics are obtained from the readings on an oscilloscope. From the graphs, it can be found that the results of the fuse model are in fair agreement with the experimental results as shown in Chapter 4.

4

Chapter 2 Construction and Operation of fuses

Fuses are current interrupting devices used for circuit protection during overcurrent and short circuit conditions and are connected in series with the equipment to be protected. Due to a fault in a circuit, if the current flowing in the circuit exceeds the current rating of the fuse, it melts, creating an open circuit in the system which helps interrupt the flow of the fault current. Once the fuse has blown, it needs to be replaced to restore normal operation of the circuit.

2.1

Fuse Ratings According to IEEE Std 242-2001, a fuse has three ratings, voltage,

ampere and interrupting rating. • Voltage rating: ”The root-mean-square (rms) AC (or the DC) voltage at which the fuse is designed to operate. All low-voltage fuses function on any lower voltage, but use on higher voltages than rated is hazardous” [10]. • Ampere rating: ”The root-mean-square (rms) or DC current that the

5

fuse carries continuously without deterioration and without exceeding temperature rise limits specified for that fuse” [10]. • Interrupting rating:”The rating based upon the highest root-mean-square (rms) AC or DC current that the fuse is tested to interrupt under the conditions specified” [10]. The rating of the fuse selected should atleast be equal or higher than the ratings of the system.

2.2

Fuse Construction Typically, a fuse consists of an element (or link) surrounded by a filler

and enclosed by the fuse body. This element is welded to the fuse contacts called blades. The fuse elements are commonly constructed using either copper or silver. These elements have narrow sections known as bridges (or weak points) which have higher resistances than the rest of the link. The fuse characteristics depend on the material and shape of the element. The voltage rating of the fuse and whether the fuse is going to be used in AC or DC circuits decides the number of bridges in the element [2],[9]. When current flows through the element in the fuse, heat is generated in proportion to the resistance of the element and square of the current (I 2 t). This generated heat is absorbed by the filler and is exuded to the surroundings through the fuse body. The material used as the filler is usually quartz sand [2],[9]. 6

Figure 2.1: Fuse construction [2]

2.3

Fuse operation Under normal operating conditions, current flows through the fuse

which behaves like a small resistance thereby dropping a small voltage drop of the order of millivolts across the itself. During light overloads or short circuits, one or a few of the bridges melt causing an arc to be formed across the melted area. The filler absorbs the energy of the arc and passes it on to the surrounding air and the arc is thus extinguished [9]. If the fault is persistant, many bridges melt and the heat generated by the element is much more than that can be passed to the filler. The arcing is now continuous which causes the link to burn back, thereby lengthening the arc. This increase in the arc resistance reduces the current through the fuse. The arc will be sustained so long as there is enough system voltage to drive the arc until the fuse link completely melts. The fuse opens when the voltage across the fuse equals the system voltage [9].

7

2.4

Fuse time current characteristic (TCC) curves Fuses operate with an inverse time current characteristic, i.e. if the

current flowing through the fuse is higher, the element melts faster, causing the fuse to operate faster. The operating curves of fuses are called the Time current characteristics curves (TCC). These curves give the different overcurrent/short circuit current values on the abscissa (x-axis) and the corresponding time required for the fuse to operate on the ordinate (y-axis). While a fault is being cleared, a fuse lets out an energy called the let through energy which is equal to I 2 t. According to IEEE Std. 242-2001, I 2 t(ampere-squared seconds) is ”a factor of heat energy developed within a circuit during the fuses melting or arcing. The sum of melting and arcing I 2 t is generally stated as total clearing I 2 t” [10].

2.5

Operating time of fuses According to IEEE Std 242-2001, the operating time of fuses can be

split into two parts the melting time and the arcing time. • Arcing time: ”The time elapsing from the melting of the current-responsive element (e.g., the link) to the final interruption of the circuit. This time is dependent upon such factors as voltage and reactance of the circuit” [10]. • Melting time: ”The time required to melt the current-responsive element 8

Figure 2.2: TCC Curves [6]

on a specified overcurrent” [10]. It also defines the total clearing time as ”the total time between the beginning of the specified overcurrent and the final interruption of the circuit, at rated voltage. It is the sum of the minimum melting time plus tolerance and the arcing time” [10].

2.6

DC fuse selection criteria The following details about DC fuses should be considered while select-

ing a DC fuse: 9

Figure 2.3: Fuse operating time [7]

• Since the rms value of AC current equals DC current, the time-current curves of the AC fuse can be used for DC systems as well. Earlier, the common practice was to use AC rated fuses in DC circuits with half the voltage rating i.e. if the DC system voltage was 100V, then an AC fuse rated 200V was used. This, however, was not always effective. The voltage drop across the fuse has to equal the system voltage to interrupt the overcurrent in the circuit. With a reduction in the voltage rating, the arcing time required for the voltage across the fuse to build up reduces which also reduces the arcing I 2 t. Hence in order to use an AC fuse in a DC circuit, it must first be tested to ensure that the fault will be 10

interrupted [1],[9],[10]. • In a DC circuit, magnetic energy is stored in the inductance of the system computed as U = 12 Li2 . During the fuse operation, this stored energy (U) is given out by the inductor. This adds to the energy that the fuse has to break [9],[10]. • The highest voltage that can appear across the fuse during circuit interruption needs to be analysed. If fuses are not selected to withstand the highest system voltage, then this could result in inadequate protection to equipment [9]. • The rise in fault current depends on the DC time constant. As defined by UL 198L- 1995, the time constant of a DC circuit is the length of time, in seconds, it takes for the instantaneous current to reach 63.2% of its maximum value. It is expressed by the equation τ =

L . R

When the ratio

of circuit inductance to resistance is high in a system, higher voltages are induced across the inductances of the circuit during faults. The supply voltage and these induced voltages which are additive in nature try to maintain the current in the circuit [10],[17]. According to Std 1375-1998, ”When a fault occurs in a DC circuit with time constants of 2.5 ms or less, current increases at about the same rate as would occur in an AC circuit with current of the same magnitude. Fuses will open the circuit in about the same time as they would for an equivalent AC short

11

circuit. However, as time constants increase, especially when they are over 6 ms, current increases more slowly. The fuse is not in the adiabatic range and it is dissipating part of the energy being created by current flow. This increases the melting time of the fuse link significantly. The result is that the entire fuse is heated. Initially, only one bridge may open. This increases the fuses resistance and decreases current flow. The longer time constants also indicate increased inductance and therefore more stored energy which has to be discharged while the fuse is interrupting the overcurrent. Since the entire fuse has been heated, the fuse filler materials are also heated. At elevated temperatures, filler materials are not as effective at arc quenching. Consequently, unless the fuse has been designed and tested at the longer time constants, the fuse may sometimes be destroyed, with attendant equipment damage” [9].

2.7

Basic fuse types Basically, fuses are classified into the types as listed below:

1. Time Delay fuses: Time delays are built into a fuse to ensure that it carries inrush currents and harmless temporary overloads without tripping. Heat sinks are used in time delay fuses to incorporate the delay. The heat dissipated due to inrush and temporary overload currents is absorbed by the heat sink and released to the surroundings thereby delaying melting of the fuse element. During overloads which persist, the

12

heat generated by the fault is very high and hence the heat sink cannot absorb all of the heat resulting in the melting of the fuse element [9]. 2. Fast acting fuses: Fast acting fuses are designed to open very quickly in the event of an fault in the circuit. Semiconductor devices cannot withstand overcurrents and hence need to be protected by fast acting fuses. 3. Current limiting fuses: A current limiting fuse reduces the magnitude and duration of a fault current. The fuse melts in the first quarter cycle to prevent the peak current from reaching a value which would flow if the fuse were replaced with an equivalent resistance. This greatly reduces the total electrical energy delivered to the fault. According to IEEE 242-2001, DC fuses dont have a current limiting performance defined in standards [9].

13

Chapter 3 Modeling of DC fuse

The current and voltage waveforms during the blowing of the fuse in a DC system are shown in the figure 3.1. In an AC system, the rate of rise of the fault current depends on the frequency of the system. From the figure, it can be seen that during a fault in a DC system, the current rises suddenly till it reaches a certain value. In a DC system, this rate of rise of current is influenced by the circuit resistance and inductance values i.e. by the circuit time constant values given by τ =

L R

[1],[10].

When the heat produced by the current flowing in the fuse reaches a threshold value, the fuse link melts. The time from the beginning of the fault to when the fuse link melts is termed as the melting period. The melting of the fuse element produces an arc across itself. The resistance of this arc causes the current value to fall as seen in the figure. The arcing time is the time from when the element begins to melt till the current reaches zero [1],[10]. From the fuse voltage curve, it can be seen that during the melting time of the fuse, the voltage across the fuse slowly rises. As the arcing period starts, there is a sudden shoot in the fuse voltage across the arc after which it starts falling till it reaches the system voltage [7],[22],[23]. A model for the DC

14

Figure 3.1: Fuse current and voltage curves for a fault in a DC system [7]

R fuse has been developed in the PSCAD /EMTDCTM software. The melting

and arcing models are implemented as two independent parts of the circuit.

3.1

Melting model This section discusses the modeling of the melting circuit of the fuse. A

DC power supply whose outputs are connected to a short circuit switch (SC) through a cable is shown in Figure 3.2. In this DC circuit, the closing of SC simulates a short circuit. For the SC closed condition, applying Kirchoff’s

15

Figure 3.2: Melting model of DC fuse

voltage law to the circuit, we get [22],[23], Ri + Lcable

di =E dt

(3.1)

where R is the sum of cable (Rcable ) and fuse resistance (Rf use ). Lcable is the cable inductance E is the output voltage of the DC power supply.

Thus the current i is given by i(t) =

E (1 − e−t/τ ) R

where τ is the time constant of the DC circuit given by

(3.2) L R

R The melting model shown in Figure 3.2 was implemented in PSCAD /EMTDCTM .

In this model, the short circuit condition is simulated by closing switch S1. Switch S2 represents the protective device i.e. the fuse in this case.

16

R Figure 3.3: PSCAD /EMTDCTM implementation of melting model of DC fuse

Under normal operating condition of the circuit (i.e. in the absence of a fault), the short circuit switch S1 is open and the fuse switch S2 is closed.

17

To simulate a fault in the circuit, the two state switch (SC) is moved from the off position to the on position. The output of this two state switch (SC) is given as the gating signal to the short circuit switch S1 causing it to turn on. This causes a short circuit current (Idc ) to flow through the circuit and the value of this current can be computed by equation (3.2). If this short circuit current (Idc ) exceeds the current rating of the fuse (Iref ), the fuse begins to melt. The value of this short circuit current (Idc ) is given to a look up table. The look up table contains the TCC curves of the fuse. The table gives the melting time of the fuse for a corresponding value of short circuit current flowing in the circuit. At the end of the melting time, the control system turns off the gating signal to the fuse switch (S2). This causes the fuse switch to open which represents the opening of the fuse link at the end of the melting time.

3.2

Arcing Model From the current and voltage waveforms of the fuse as shown in Figure

3.1, the arcing model of the fuse can be represented by an RC circuit as shown in Figure 3.4 [22],[23]. The two way switch in position 1 is representative of the melting model of the fuse. When the switch is in position 2 at the end of the melting period, the arcing model is now inserted into the circuit. Applying Kirchoff’s voltage law to the circuit, we get [22], Ri + Lcable

di + Vc = E dt

18

(3.3)

Figure 3.4: Combined melting and arcing model of fuse

where R is the combined resistance of the arc (Rarc ) and the cable (Rcable ). C is the fuse capacitance Lcable is the inductance of the cable. Vc is the voltage across the capacitance. Vf use is the voltage across the fuse.

Solving for i, we get [22], i = −i0

p (z − a)2 + ω 2 ) · e−at · sin(ωt + φ) ( 2 ω

where φ = tan−1 (

ω ) z−a

R 2L p 1 R ω = (( ) − ( )2 ) LC 2L E z = Li0 a =

19

(3.4)

Thus, calculating the fuse voltage, we get [22], Vf use = Rarc i + Vc

Vf use = E + i0

(3.5)

p (z − a)2 + ω 2 ( ) · e−at · sin(ωt + φ) · ω2

(Rcable − Lcable ) · sin(ωt + φ) + Lcable ω · cos(ωt − φ)

(3.6)

The arcing model of the fuse was modeled using an RC circuit as shown in Figure 3.5. When the fuse switch (S2) opens at the end of the melting period, the arcing model is now connected to the circuit. The control system closes the arcing switch (S3) at the end of the melting time. Thus current now flows through the arcing circuit and the capacitor charges. The current that flows in this RC circuit (i.e. the arcing model) is as given by equation (3.4) and the voltage drop across the fuse can be calculated by the expression given in equation (3.6).

20

R Figure 3.5: PSCAD /EMTDCTM model of combined melting and arcing circuits

21

Chapter 4 Validation of the Fuse model

4.1

Experimental setup to validate the Fuse model In order to simulate a short circuit, the following test circuit was used.

The test system consists of a DC power source (GPR 3510H). Connected

Figure 4.1: Short circuit model

in series to this DC power source is a 100 µ Farad inductor and a Cooper Bussman (BK-MDL5) fuse using a 4 feet long AWG 14 wire. An oscilloscope (Tektronic TPS 2024) was connected across the fuse to measure the voltage across it during the short circuit. A current probe (TCP A300) was used 22

Figure 4.2: Polycab wire catalogue DC resistance [5]

23

Figure 4.3: Cooper Bussman (BK-MDL5) TCC curves [4]

24

to measure the current flowing through the fuse and this waveform was also recorded in the oscilloscope. The DC cable resistance for the AWG 14 (≈ 2.5mm2 ) wire from the Polycab Catalogue is 7.41 ohms/km. Hence, for 4 feet length, the value of the DC resistance Rwire is 9.03 ×10−3 ohms. The inductance of the wire is negligible. The DC source was operated in the constant current mode and the output current was set to 10.56 A. The voltage across the battery terminals at this time was found to be 36.9V. From the TCC curve of the fuse as seen in Figure 4.1, the melting time of the fuse was found to be 25 seconds at ≈ 10A. The current and the voltage waveforms recorded during the short circuit are as shown. Figure 4.4 shows the current (in blue) and voltage (in orange) during the melting period of the fuse. The bottom half of the figure shows the current and voltage during the arcing period of the fuse. From these values of current, voltage, melting and arcing times obtained, and substituting it in equation (3.4), the value of the RC time constant τ was calculated to be 40 µ seconds. From this, the values of Rarc and Carc were calculated to be Rarc =0.05 ohms and Carc =800 µ Farad.

25

Figure 4.4: Short circuit current (in blue) and voltage (in orange) waveforms across the fuse during the melting and arcing periods

4.2

R PSCAD /EMTDCTM model

The values of Rcable and Lcable obtained from the actual experimental R setup were used in the melting model in PSCAD /EMTDCTM . In the arcing R model in PSCAD /EMTDCTM , the values of Rarc and Carc calculated were

26

R used. From the PSCAD /EMTDCTM simulation, the voltage and current

waveforms during a short circuit in the fuse are as shown in Figure 4.5.

(a)

(b)

(c)

(d)

Figure 4.5: Fuse waveforms from simulation: (a)Fuse current (b)Fuse voltage (c)Zoomed in view of fuse current and (d)Zoomed in view of fuse voltage

27

Chapter 5 Conclusion

To simulate a short circuit, the fuse model is implemented in two parts - the melting model and the arcing model. The melting model implemented as an RL circuit is connected to the supply voltage at the instant of short circuit. This causes the current to rise and reaches a maximum value of 10.029 A as seen in Figure 4.5. This rate of rise in the current is dependent on the time constant of the RL circuit in the melting model given by τ =

L R

and calculated

to be 0.01104 seconds. From the experimental results seen in Figure 4.4, the maximum value of the current was found to be 10.5 A which is almost the same as the simulation results. During the melting period of the fuse, the voltage drop across the fuse in the simulation was found to be around 1.6 V as seen in Figure 4.5,which is close to the experimental result of 1.2V as seen in Figure 4.4. The melting period for the Cooper Bussman fuse found to be 25 seconds from Figure 4.3 and was approximately the same as measured by the stopwatch during the experiment. At the end of the melting period the arcing period begins. The arcing model is implemented as an RC circuit in the simulation. As seen in the

28

simulation results in Figure 4.5, the current starts to fall from 10.029A to zero with a time constant τ = RC calculated as 40µ seconds. This is close to the results obtained from the experiment seen in Figure 4.5. During this period, the fuse voltage rises to 36.89V in the simulation as seen in Figure 4.5. From the experimental results seen in Figure 4.4, the fuse voltage at the end of the arcing period was found to be 31.2V. Comparing the waveforms obtained from the experimental results (as R seen in Figure 4.4) and the PSCAD /EMTDCTM simulation (Figure 4.5), it

can be seen that the simulation results are in fair agreement with the experimental results. Hence the simulation model can be used as a tool to approximately predict the voltage excursions of the fuse during a short circuit in a DC circuit. This tells us what voltages the DC equipment will be subjected to. R The model developed for the DC fuse in PSCAD /EMTDCTM can

be extended to different DC fuse ratings. Consider that we have a fuse of a different rating that now needs to be used in the circuit. In order to incorporate the melting model of the new fuse in the circuit, the look up table will need to be updated with the TCC curves of the new fuse being used. In order to model the arcing period of the fuse, one fuse blowing experiment will need to be performed in order to obtain the Rarc and the Carc values to be used in the R arcing model. Once these values are inputted in the PSCAD /EMTDCTM

model, the model’s output can be analysed to study the behaviour of the fuse during short circuits or overload conditions. 29

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Vita

Bhargavi Devarajan was born in Mumbai, India on 19 Februay 1985, the daughter of Mr. R. Devarajan and Mrs. Uma Devarajan. She received the Bachelor of Engineering degree from Mumbai University. She worked with Uhde India Ltd., a German MNC in Mumbai before moving to the United States to pursue her Masters in Electrical and Computer engineering at the University of Texas at Austin in August, 2008.

Permanent address: C5 Voltas Society Shivshrushti, Kurla(E), Mumbai, Maharashtra, India 400024

This thesis was typeset with LATEX† by author. † A LT

EX is a document preparation system developed by Leslie Lamport as a special version of Donald Knuth’s TEX Program.

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