THE CALCULATION OF LOW-VOLTAGE

FAULT CURRENTS WITH RESPECT TO TIME

by

i W. Ronald Kilgore

B.S., Southern College of Technology, 1988

A thesis submitted to the

University of Colorado at Denver

in partial fulfillment

of the requirements for the degree of

Master of Science

Electrical Engineering

1996

Kilgore, W. Ronald (M.S., Electrical Engineering)

The Calculation of Low-Voltage Fault Currents with Respect to Time

Thesis directed by Professor Pankaj K Sen

ABSTRACT

This thesis explores the calculation of fault current in low-voltage (below 600 volts)

electric systems. A method is presented to calculate all practical circuit impedance

values by taking into account the change in resistance during a fault due to change in

conductor temperature. The purpose of the calculations is to present fault current

with respect to time rather than the maximum conceivable fault current that is

produced with standard calculation methods. Sample calculations and the source code

of a C++ computer program are provided to demonstrate the calculation methods

verified by experimental results

This abstract accurately represents the content of the candidates thesis. I recommend

its publication.

Signed

xv

CONTENTS

Chapter

1. Introduction...............................................................1

2. Calculation of Impedances .................................................4

2.1 Transformer Impedances...................................................4

2.1.1 Single-Phase Transformer ...............................................5

2.1.2 Single Transformer with a Center-Tapped Secondary......................7

2.1.3 Three-Phase Bank Connected Wye-Wye ....................................9

2.1.4 Three-Phase Bank Connected Delta-Wye................................. 11

2.1.5 Three-phase Bank Connected Wye-Delta (with a four-wire secondary) .... 13

2.2 Conductor Impedances................................................... 15

2.2.1 Resistance............................................................ 15

2.2.2 Capacitance...........................................................25

2.2.3 Inductance............................................................25

2.3 Impedance of Conductors in Conduit to a Ground Fault....................27

2.4 Resistance of Electric Arc..............................................28

3. Temperature Rise Calculations.............................................31

3.1 Calculation of Heat Produced in Conductor .............................31

3.2 Change of Conductor Temperature due to Heat Generated in Conductor .... 32

3.3 Calculation of Heating Efficiency ......................................33

3.4 Temperature Effect on Fault Calculations................................35

4. Calculation and Test/Measurement Verification ...........................36

5. Proposed Changes in the National Electrical Code ........................54

v

6. Proposed Product Changes...........................................56

7. Summary ...........................................................57

Appendix

A. Source Code for C++ Program ......................................58

B. Output of C++ Program.............................................87

C. Tabulation of Measured Fault Current..............................102

References........................................................... 103

vi

1. Introduction

Electric faults in low-voltage systems can be extremely costly to life and property. For

this reason, much effort has been spent on the calculation of available fault currents as

part of system design. The primary purpose of most fault calculations is to assure

proper protection coordination and equipment ratings. For this reason, most fault

calculations are interested in the maximum possible fault currents. Often, in the field

of failure analysis, the goal of fault calculations is not to find the maximum possible

fault current under the worst case scenario, but to find the probable fault current given

a set of circumstances. The methods commonly used to calculate available fault

current in electric systems make several very conservative assumptions (e.g. neglecting

the circuit resistance). Some methods do not neglect circuit resistance but assume the

circuit resistance is constant throughout the fault. This thesis examines the effects of

dynamic circuit resistance in low-voltage fault conditions.

The primary difficulty in determining probable fault currents is accurately determining

system impedances. In most fault-current calculations it is usually acceptable to use

conservatively low estimates of system impedances because the goal is to determine

the maximum possible fault current. One goal of this research is to locate and apply

calculation methods that will accurately depict the system impedances in order to

determine probable fault currents and compare results with common calculation

methods. The circuit impedances that will be examined include transformer

impedances with several common connection methods, circuit impedance, and fault

resistance (i.e., arc resistance).

1

The temperature of conductors during a short circuit can rise almost instantaneously

during fault conditions because circuit resistance is the largest part of the total

impedance and heat is generated within the conductors due to I2R losses. Because the

resistance of a conductor is directly proportional to the temperature of that conductor,

the temperature rise of the conductors greatly influences the total circuit impedance,

and therefore the total fault current. Also, as the resistance of the conductor

increases, the conductor heats more rapidly. This temperature rise effect on the time-

dependant fault current should be examined for proper protection coordination.

The temperature rise calculations will be modeled by calculating the heating efficiency

of the conductor. This heating efficiency is dependant on the fault duration and the

specific heat of the conductor material and cable insulation. Heat produced in the

cable is stored in the cable with less efficiency as time passes. This calculation method

has been successfully tested for fault durations of up to two seconds as part of this

thesis. The calculation method can be extrapolated beyond two seconds, but that has

not been tested. If the circuit has unusual thermal properties (i.e., immersed in water,

or gas insulated), special considerations must be made that are beyond the scope of

this research.

Presently the National Electrical Code (NEC) has no requirements for maximum

circuit lengths. The NEC does indicate minimum conductor sizes for branch circuits1;

however, the use of extension cords often decreases the conductor size, increases the

length, and limits the fault current to well below the instantaneous trip rating of the

circuit breaker. This thesis proposes changes to the NEC to include a maximum

circuit length for each conductor size protected by each circuit breaker rating and the

use of inline fuses in extension cords.

2

This thesis includes:

1. Method of calculation of equivalent impedances with several

different transformer connection methods.

2. Method of calculation of the impedances of electric circuits in most

typical installations.

3. Method of calculation of the impedances of electric conduits as

ground return circuit.

4. Method of calculation of instantaneous heating and associated

resistance change of insulated conductors during fault conditions.

5. Sample calculation of a faulted low-voltage circuit with laboratory

verification.

6. Proposed National Electrical Code and product design changes.

7. A C++ computer program to perform calculations presented in this

thesis.

The units presented in this thesis will be found to he inconsistent. This was done

purposely to accurately reproduce the calculation method of each reference. The

sample calculations were performed using a mathematical computation software that

automatically adjusts for units. The units are internally consistent in the sample

calculations.

3

2. Calculation of Impedances

Most impedances used in typical fault calculations are determined by looking for the

circuit device in standard tables. Due to the necessity of performing the calculations

described in this thesis by the use of a computer program, it is desirable to calculate all

cable impedances. This method will also enable more precise calculation of the

specific circuit in question rather than a general circumstance. The impedances applied

in the calculations will be applied in the ohmic values rather than per-unit values. This

is done because the faults examine will generally be only on the secondary of the

distribution transformer. The calculations could also be performed equally well in the

per-unit method.

2.1 Transformer Impedances

The name-plate impedance of most transformers is an adequate start to determine the

impedance of the transformer bank. When a transformer experiences a fault within or

electrically close to the secondary, the impedance of the transformer changes from the

steady-state value2. For purposes of this work, the fault current will be limited

primarily by the secondary cables. Short-circuit impedance of the transformers does -

not become a factor until the fault current reaches a level of 15 to 20 times the rated

current3. At 15 to 20 times the rated current, the transformer resistance value

increases due to winding temperature rise, and the reactance increases due to magnetic

forces causing winding movement. Because the current is greatly limited by the

secondary cables, the transformer impedance is not effected by faults deep within the

secondary distribution.

4

When two or three transformers are connected to form a three-phase bank, the system

must be modeled accommodating the particular connection scheme. The transformer

impedance must take into account the method chosen for connecting the transformer.

The connections that will be examined include:

1. Single-phase transformer

2. Single-phase transformer with a center-tapped Secondary

3. Three-phase bank connected Wye-Wye

4. Three-phase bank connected Delta-Wye

5. Three-phase bank connected Wye-Delta (with a four-wire secondary)

6. Three-phase bank connected Delta-Delta (with a four-wire secondary)

7. Three-phase bank connected Open Wye-Open Delta (with a four-wire

secondary)

2.1.1 Single-Phase T ransformer

The single transformer is handled using simple per-unit impedances using the name

plate data. The transformer is modeled as an impedance equal to the name plate

impedance as seen in Figure 2.1. If both resistive and reactive components are not

given, the impedance value can be assumed to be at an angle of between 75 and 80

(X/R ratio of 4 to 6). The larger the transformer, the greater the impedance angle:

5

Connection Diagram

Primary

(High Voltage)

Secondary

(Low Voltage)

3

Equivalent Impedance Model

Z=R+jX

Converted to

Ohmic values on

the secondary.

Figure 2.1

Model for single-phase transformer. Transformer impedance is that of the name-plate

converted to an ohmic value.

6

2.1.2 Single Transformer with a Center-Tapped Secondary

This connection is most commonly used for residential loads with a 120/240-volt

secondary. The neutral is derived by bonding the center tap to ground. The

determination of the transformer impedance to a ground fault must take into account

the half-winding impedance of the transformer. The impedance of the transformer to a

ground fault as seen in Figure 2.2 is calculated as follows:4

- 1.5 R{% + j 2.0 Xt % (2.1)

Where: R B is the resistive component of the nameplate per unit impedance

based on the transformer full winding KVA.

X 3 is the reactive component of the nameplate per unit impedance

based on the transformer full winding KVA.

The 1.5 and 2.0 multipliers found in equation 2.1 are rule of thumb values. Equation

2.1 is accurate for the majority of transformers that are wound in shell form If the

transformer is wound in core form the inductive multiplier is decreased from 2.0 to

1.15 due to the difference in winding geometry.

If the fault in question is between two energized conductors, the transformer is

modeled like the single-phase transformer in section 2.1.1 with the secondary voltage

equal to the line-to-line voltage.

7

Connection Diagram

Equivalent Impedance Model

\

% Z= Zhalf = 1.5Rt% + 2.0 Xt%

m Converted to

Ohmic values on

^ the secondary.

Figure 2.2

Schematic connections and equivalent circuit of single-phase transformer with

secondary center-tap grounded.

8

2.1.3 Three-Phase Bank Connected Wye-Wye

The three-phase bank of transformers connected Wye-Wye is modeled as one single-

phase transformer with a single-phase-to-ground fault as seen in Figure 2.3. If the

fault is phase-to-phase in nature, the transformer impedance must be doubled to

account for the two transformers involved in the fault. Also, care must be taken to use

the line-to-line voltage rather than the line-to-neutral voltage. Similar results can be

derived from the use of symmetrical components.

9

Connection Diagram

Equivalent Impedance Model

Z=R+jX for Line-to-Neutral

or Ground Faults.

Z=2R+j2X for Line-to-Line

faults.

Converted to Ohmic

values on the secondary.

Figure 2.3

Three-Phase Wye-Wye connected transformer with single-phase model.

10

2.1.4 Three-Phase Bank Connected Delta-Wye

The Delta-Wye transformer connection is modeled similar to the Wye-Wye

connection. The primary difference is that ground fault current will circulate within

the primary windings because there is neither a ground connection nor a neutral

conductor on the primary side of the transformer bank. The equivalent circuit model is

seen in Figure 2.4.

11

Connection Diagram

Z=R+jX for Line-to-Neutral

or Ground Faults.

Z=2R+j2X for Line-to-Line

faults.

Converted to Ohmic

values on the secondary.

Figure 2.4

Three-Phase Delta-Wye connected transformer with single-phase model.

12

2.1.5 Three-phase Bank Connected Wye-Delta (with a four-wire

secondary)

The delta connected secondary, seen in Figure 2.5, is often used for commercial three-

phase loads. One of the three transformers is center-tap grounded in order to provide

a secondary neutral for 120-volt loads. This provides for two lighting phases and one

power phase. The phase-to-phase faults are modeled like the single-phase fault in

section 2.1.1 with care taken to use the line-to-line voltage for the fault voltage.

The phase-to-neutral faults are modeled differently depending upon the faulted phase.

If the faulted phase is one of the two phases connected to the center-tapped

transformer (i.e., a lighting phase), the transformer bank is modeled using the half-

winding impedance discussed in section 2.1.2. If the faulted phase is the phase that is

not connected to the center-tapped transformer (i.e., the wild phase), the

transformer bank equivalent impedance is modeled as follows5:

Z + Z. ,,

Z = -!-----^ (2.2)

2

Where:

Z is the equivalent impedance of the transformer bank to a power

phase-to-ground fault.

Z, is the transformer nameplate impedance.

ZhalJ is the half-winding impedance of the center-tapped transformer.

13

Primary

(HV)

Connection Diagram

Secondary

(LV)

OOOOOOOOOOOOOOOQDOOOOOOr

Equivalent Impedance Model

Z =

Zt + Zhalf

Converted to Ohmic

values on the secondary.

Figure 2.5

Three-Phase Wye-Delta transformer with single-phase model.

14

Equation 2.2 is derived by observation that the fault current has two parallel paths in

the center-tapped transformer and the two power transformers. The total impedance

of each path is divided by two.

If the transformer bank is connected in an open wye-open delta, the system is modeled

identically except for the condition of the power phase-to-ground. In this condition

the sum of the half-winding and nameplate impedances are not divided by two because

there is no parallel path for the fault current.

2.2 Conductor Impedances

The secondary conductors from the service entrance conductors to the individual

branch-circuit conductors offer the greatest impedance to a bolted fault. For this

reason, the calculation of cable impedance is of paramount importance to proper fault

current calculations. For proper impedance calculation both the resistance and

reactance must be calculated.

2.2.1 Resistance

In order to calculate the total resistance the dc resistance must first be determined.

Then proper multipliers for skin and proximity effects must be calculated to determine

the ac resistance of a cable.

2.2.1.1 dc Resistance

The dc resistance of a conductor is calculated with the following formula:6

15

Where:

R is the resistance of the conductor (in ohms).

p is the resistivity of conductor (8.145 10"K------------------ for copper

and 1.254 x 10 K ^ x inch for aluminUm).

/ is the conductor length in feet,

a is the cross-sectional area of the conductor in inch2.

This dc resistance must then be adjusted to the conductor temperature with the

formula7:

^t2= ^/,0 + at^2~ *i)) (2.4)

Where: tj and t2 are conductor temperatures (in C)

R. is the conductor resistance at temperature tj (in ohms)

n

R. is the conductor resistance at temperature t2,C (in ohms)

a, is the temperature coefficient of resistance of the conductor

n

material at temperature tj (unitless)

The temperature coefficient of resistance (a) is dependent on temperature and must be

calculated for the conductor temperature. As the conductor temperature changes

during a fault, the coefficient of resistance must be recalculated using the following

equation:

a

h

1

1

+ (<2-'l)

(2.5)

Where: tl and t2 are the initial and final temperatures respectively (C).

a. is the resistance temperature coefficient at tx (unitless)

n

a. is the resistance temperature coefficient at t2 (unitless).

The previous equation assumes that the temperature coefficient of resistance is linear.

That assumption is valid in all but very cold temperatures.

2.2.1.2 ac Resistance

Due to the magnetic flux present due to alternating current flow, the ac resistance is

larger in magnitude than the dc resistance. This greater resistance is due skin and

proximity effects. The ac resistance is determined by first calculating the dc resistance,

and then multiplying this value by the skin and proximity effect multipliers (7^ and Ycp

respectively). The resistance change due to 60 Hz alternating current is greater for

larger conductors and can usually be ignored for conductors smaller than #6 AWG.8

2.2.1.2.1 Skin Effect

In a dc circuit the conductor can be modeled as a solid rod because the current density

is uniform throughout the cross-section of the conductor. Alternatively, the current in

17

an ac circuit actually travels largely along the circumference of the conductor. The

current density decreases from the surface of the conductor in inverse proportion to

the square root of the frequency. The greater concentration of current along the

circumference of the conductor lessens the effective cross-sectional area of the

conductor. Because the conductor resistance is inversely proportional to conductor

cross-sectional area, the ac resistance is greater than the dc resistance. The ratio of

to Rfc is called the skin-effect ratio (Y^).9 Skin effect is caused by magnetic lines of

flux internal to the conductor causing greater flux density toward the center of the

conductor. The increased flux density increases the inductive reactance of the center

portion of the conductor forcing the current to the outer conductor portion.10

The formula for the skin-effect ratio for a circular conductor is as follows:

Y=St

cs

nrJJnr)

IJfar)

(2.6)

Where is the skin-effect ratio

Si is the function indicating the real part of the argument

r is the radius of the conductor (meters)

JQ and Jj are Bessel functions of the first kind and of order zero and one

respectively

n =

\

-jyy-

P

(2.7)

18

where: 00 is the frequency (radians per second)

|i is the absolute permeability (4tt;x 10"A henrys per

meter if conductor is nonmagnetic, either copper

or aluminum)

p is the resistivity of the conductor material

(1.7241 x 10'* Q-meter for copper and

2.83 x 10"x Q-meter for aluminum)

2.2.1.2.2 Proximity Effect

When electric current flows in a

conductor an associated

magnetic field is formed around

the conductor. Two adjacent

conductors with identical current

flowing in opposite direction

form magnetic fields that attract

the current toward the adjacent

conductor. This is caused by the

vector addition of the magnetic

lines between the conductors

and cancellation on the external

sides of the conductors. This

effect causes additional inductive reactance in the external portion of the conductors

and an increased current density on the adjacent portion of the conductor (Figure 2.6).

19

The proximity effect also reduces the effective cross-sectional area of the conductor

thereby increasing the conductor resistance. This is calculated by determining a

multiplier (YC[) for the dc resistance of the conductor. Proximity effect for circular

conductors is calculated as follows:

Y F(x )

cp V P' s

1,18

F(xp) + 0.21

+ 0.312

( 2a\2

\

Where: Yf; is the proximity effect multiplier (no units),

a is the conductor diameter (inches).

s is the axial spacing between conductors (inches)

Ffej) is the function:

F(xp)=Bt

Xp/piXp)

2 J,(xp)

(2.8)

(2.9)

Where:

x =

p

\

izR

dc

(2.10)

A similar proximity effect takes place when a conductor is placed in a conductive

conduit. An increased resistance occurs because of the current that is induced in the

conduit. The resistance multiplier, Yp, for nonmagnetic conduit is determined as

follows:11

20

(2.11)

Where:

Y f(CI)

* 80 o

M

21

/ is the frequency (in hertz)

Cl is the conductor area (in circular inches)

p is the conductor resistivity

v Â£

Where:

1

p=e ve + 0

[a^+b*?- 2a*b *cos(nlAB)\ (2.12)

LAB is the angle formed between lines joining the

center of the pipe with the center of two

conductors (in degrees)

a and b are the distances between the center of the pipe

and the center of conductor the two conductors

(A and B) divided by the mean pipe radius

(unitless). See figure 2.7.

15.94 cor? __j

v =-----------x 10 1

P;

(2.13)

Where: r is the mean pipe radius (in inches)

t is the pipe thickness (in inches)

p. is the resistivity of the pipe material

(in microhm-inches)

21

22

A more straightforward simplified approximation for calculating the proximity effect in

a nonmagnetic pipe, Yp, is found in NEHER-McGRATH.12

Rdc is the dc resistance of the cable within the pipe (microhms per foot)

is the outside pipe diameter (inches)

/ is the frequency (Hz)

s = 0.578 D for close triangular spacing (inches)

D.- D

s = for wide triangular spacing (inches)

where: D is the inside pipe diameter (inches)

The model introduced in NEHER-McGRATH for the pipe proximity effect, Yp, for -

magnetic pipes is also used:13

for a three conductor cable:

(2.14)

Where: Rs is the conduit resistance (microhms per foot)

Ds is the outside cable insulation diameter (inches)

1.545- 0.115 D

p

(2.15)

R

dc

23

for a single conductor in close triangular configuration (see figure 2.8):

Y =

p

0.895 0.115 D,

R

dc

(2.16)

for a single conductor cable in cradled configuration:

Y =

p

0.345 0.175 D

___ p

R

dc

(2.17)

24

Where all variables are identical to those used for the nonmagnetic pipe proximity

effect.

2.2.2 Capacitance

Typically the capacitance within a low-voltage system is so little that the effect is

neglected.14 The only time that capacitance of a low-voltage system is crucial is when

calculation of fault current availability on a system with an ungrounded transformer

secondary (i.e., a Delta-connected secondary) is necessary. These systems are

designed to limit fault current to a value below a level that would cause equipment

damage during a fault. The ground-fault current available for a fault on an

ungrounded secondary system is determined by the capacitance to ground of the

system. This design is usually employed only on systems that require constant

operation under all circumstances.15 Ungrounded secondary systems are beyond the

scope of this thesis; therefore, the capacitance of the electrical components will not he

examined.

2.2.3 Inductance

In order to calculate the inductance of a single-phase electric circuit a return path must

be specified. The return path may be a neutral conductor, the grounding conductor, or

an unintended return path. The neutral and grounding conductors can be

mathematically modeled by standard inductance formulas. Any unintended path would

have to be considered independently but general formulas may apply.

The inductive reactance of one of two cables not routed in conduit and overhead

distribution lines is determined by the following general equation:16

25

h=

+ 2 In

D '

iAv

x 10

-7

(2.18)

Z,j is the inductance of one of two conductors (in henrys per

D is the distance between the center of each of two conductors (in

ry, r2 are the radii of each conductor (in meters).

If the radius of each conductor is the same, the preceding equation will simplify to the

following:17

2.57 S

Where: A

meter). D

meters). n,r2

X1 = kx log

D

(2.19)

Where: is the positive sequence reactance of one of two conductors with

both self and mutual inductance accounted for.

kx is a constant that adjusts for conductors in proximity to magnetic

pipes. For conductors routed in steel pipes k .= 60.9. For

conductors in nonmagnetic pipes or free air k .= 52.9. The

magnetic constant yields 15% higher results.

Sis the geometric mean spacing between the conductors. For cables in

close triangular configuration S=D (the diameter of cables

including insulation). For the more typical cradled

configuration:

26

\ 2

(2.20)

Where Dp is the inside diameter of the pipe.

2.3 Impedance of Conductors in Conduit to a Ground Fault

The impedance of cables in conduit is greatly influenced by the return path of a ground

fault. If current returns on a neutral or ground conductor, the impedance can be

calculated by methods outlined in previous equations. However, if the current returns

along conduit, the impedance is dependant upon the degree of conduit magnetism and

the magnitude of the ground-fault current.

The primary model of impedance of a ground-fault circuit involving conduit-current

flow is that developed by FISHER18. This method calculates a multiplier (M) to the

positive sequence impedance of the conductors within the conduit that adjusts for the

coaxial-type currents in this situation and the magnetic circuit of the conduit. This

calculation is an approximation developed by empirical data only.

The basic equation for the model is the following:

(2.21)

27

Where:

Zqj)U0 is the angle-phase line to housing impedance (ohms).

Zj is the positive sequence impedance of the conductor within the

conduit (ohms).

iy N

M= (2.22)

ix

Where: i is the RMS current within conductor/conduit

N and P are determined by table 2.1:

2.4 Resistance of Electric Arc

The resistance of a low-voltage electric arc has been the subject of a great many

studies. The primary model that will be used in this thesis is that of FISHER.19 This

simple model was developed using empirical data from many low-voltage arcing tests.

The resistance of the arc has been calculated with sufficient accuracy for low-voltage

arcs on 120-volt through 480-voh systems. The equation for the arc resistance is as

follows:

R

arc

25JL

i085

(2.23)

Where: Rarc is the resistance of the electric arc (in ohms).

L is the length of the arc (inches).

/ is the RMS current passing through the electric arc (amperes).

28

Table 2.1: Constants for calculation of ground fault impedance in conduit.

Cables in Alut nirnrm Conduit

Cable Size (AWG) Cables in Steel Conduit Copper Wire Aluminum Wire M

N P Minimum M Maximum M M Cable Size (AWG)

18 1.50 0.00 1.50 1.60 1.15 1.10 18

16 1.65 0.00 1.50 1.70 1.15 1.10 16

14 1.80 0.02 1.50 1.80 1.15 1.10 14

12 2.20 0.04 1.50 2.00 1.15 1.10 12

10 2.80 0.06 1.60 2.10 1.15 1.10 10

8 3.40 0.08 1.60 2.20 1.15 1.10 8

6 5.00 0.12 1.60 2.70 1.15 1.10 6

4 6.40 0.14 1.60 3.20 1.15 1.10 4

3 7.60 0.16 1.70 3.50 1.15 1.10 3

2 9.20 0.18 1.70 3.70 1.15 1.10 2

1 12.00 0.21 1.70 4.00 1.17 1.11 1

0 15.00 0.23 1.70 4.40 1.17 1.11 0

2/0 18.00 0.25 1.80 5.00 1.40 1.27 2/0

3/0 25.00 0.28 1.90 5.80 1.40 1.27 3/0

4/0 30.00 0.30 2.00 6.50 1.28 1.20 4/0

250 37.00 0.32 2.00 6.80 1.27 1.20 250

300 43.00 0.33 2.00 7.00 1.26 1.20 300

350 49.00 0.34 2.00 7.20 1.25 1.20 350

400 55.00 0.35 2.00 7.30 1.25 1.20 400

500 66.00 0.37 2.00 7.50 1.25 1.20 500

mo 80.00 ML- ml- 1 70 600

The length of the arc varies with each situation. For most self- extinguishing arcs, the

length is usually approximated between 0.1 and 0.2 inches. Arcing faults on 480/277-

volt systems are often not self-extinguishing and therefore the arc length can be up to

several inches. Each specific installation requires independent analysis and

assumptions.

Experimental results dictate that arcing faults on 120-volt systems are usually self-

29

extinguishing. In these situations an arcing fault will last from 0.5 to 15 cycles.20

Voltages at the 208-volt level and above are often not self extinguishing and can last

for several seconds or until the overcurrent protection operates.

30

3. Temperature Rise Calculations

3.1 Calculation of Heat Produced in Conductor

Conductor resistance is directly proportional to the temperature of the conductor

material. Because the conductor temperature during an electric fault can rise very

rapidly due to IeR losses, the temperature rise acts to increase the circuit resistance.

For this reason the temperature of the conductor must he determined before an

accurate determination of the circuit resistance can be calculated. The determination

of this temperature rise can be greatly simplified by the use of a model presented by

EICHORN.21 EICHORN has modeled the temperature rise in insulated conductors

for both adiabatic and nonadiabatic conditions.

To determine the instantaneous temperature rise of the cable first the heat generated in

the cable must be determined. This amount of generated heat is equivalent to the

following:

Q=I2Rt (3.1)

Where: Q is the heat generated in the conductor (joules)

/ is the current within the conductor (amperes)

R is the resistance of the conductor (ohms)

t is the time interval (seconds)

31

3.2 Change of Conductor Temperature due to Heat Generated in

Conductor

The value of heat generated (Q) previously calculated can be used to determine the

temperature rise by the following:

(3.2)

ffl V

Where: A T is the change in temperature for the time interval used to

calculate Q (Kelvin)

m is the mass of the conductor in which the heat is

generated (gram)

c is the specific heat constant:

c = 174 717 j e- for copper

lb C

c = 429 197 J0}1^ for aluminum

lbC

il ffQY- is the heating efficiency as calculated by the

EICHORN method (see section 3.3)

The mass of the conductor is determined by multiplying the volume of the conductor

by the density of the conductor material (0.32117 ^ for copper and

inch1

0.09765 for aluminum).

inch1

32

3.3 Calculation of Heating Efficiency

The heating efficiency of the conductor is the efficiency at which the heat produced in

the conductor is stored in the conductor. As the temperature increases during a short

circuit, heat is transferred to the cable insulation that is in direct contact with the

conductor. Because of this heat loss to the insulation all of the heat produced within

the conductor cannot be assumed to apply directly to temperature increases of the

conductor. To account for the heat loss to the insulation a heating efficiency factor

(y\heattn^ is applied. This factor is calculated as follows (see table 3.1):

T1

heating

1

1 etf(x)~ 1+2

(3.3)

I? n 2TtrJoX

Where: x Fyjt-------------

F is the contact factor that indicates the degree of thermal

contact between the conductor and the insulation

(usually 0.80 to 0.95)

t is the elapsed time into the fault (seconds)

r is the radius of the conductor (inches)

A is the insulation thermal conductivity

( 0.07 0.10 FTU_ for pyc insulation)

sec//1 F

a is the volumetric specific heat for the insulation

33

oc is the vohimetric specific heat for the conductor

q is the area of the conductor (square inches)

As seen from the equation, t\heating is dependant on the conductor and insulation

specifications, and elapsed time. For this reason i\heating can be calculated for the circuit

before any fault calculations are begun. Typical values of volumetric specific heat for

common conductor and insulation materials are shown in the following table:

Table 3.1: Volumetric Specific heat (a anda ) for various materials

Material Volumetric Specific Heat BTU \

{ inch1 F)

Copper 0.002948

Aluminum 0.022068

Polyvinyl Chloride (PVC) 0.014249

Polyethylene 0.01848

34

3.4 Temperature Effect on Fault Calculations

For each new temperature, the new temperature coefficient of resistance must be

calculated by the method outlined in equation 2.5. From this point in the calculation

the new resistance of each cable must be calculated due to the temperature rise. The

total fault current is then recalculated and additional heat is generated in the

conductor. The circular nature of these calculations continues until the fault can he

assumed to clear, or the temperature of the conductor exceeds the conductor melting

point of the metal (1981 F for copper and about 1200F for aluminum).

As can be expected, the change in resistance due to the instantaneous temperature rise

of the conductor can have a dramatic effect on the fault current with respect to time.

The analysis of this calculation includes comparison of the initial fault current and the

corresponding fault current decay with the time-current curves for the fuse or circuit

breaker protecting the circuit. If the ignition temperature for the insulation around the

smallest conductor within the circuit is exceeded before the overcurrent protective

device enters the operation region of the time-current curve, then a fire could result

from an electric fault on circuit in question.

35

4. Calculation and Test/Measurement Verification

A one-line diagram of the circuit that was used in the laboratory during verification of

this thesis is seen in figure 5.1. The measured values were obtained with a computer-

aided data acquisition system sampling the fault current at 2 kHz. The instantaneous

RMS value of the fault current was calculated and is presented in Appendix C. The

sample calculations were performed in MathCad (a registered trademark of Math Soft,

Cambridge, MA) and are seen as follows:

SOkVA 13.2 kV primary 208/120 V secondary 4% Impedance Pad-mounted transformer (r\y) jj 156 feet of #t AWGAI cable, In Al conduit, typeXHHW, 1/phase 10 feet of #18AWG lamp cord, PVC, no conduit

3 92 feet of500 kcmil Al a i_ cable In underground ZA/*sl PVC conduit, 1/phase, typeXHHW 137 feet of #12 AWG Copper conductor, 1/2 inch steel conduit, type THHN

Figure 4.1

One-line diagram of laboratory test circuit

36

Transformer Impedance:

ZpU := 4-%-Ej'85des Zpu = 0.00349 +0.03985j

V := 120-volt VA = 50000-volt amp

Z -V2

ZY:= Zv = 0.001 +0.01148j -ohm

x VA x

Number of segments:

Seg = 4 n = 1.. Seg -

Length of each segment :

lj = 92 ft 12 =156-6 ^ = 137-ft 14 = 10 ft

Diameter of conductor that makes up each segment:

dia^ := 708-mils dia^ = 289-mils dia^ = 80.8-mils dia^ = 40.3-mil

Insulation thickness for each conductor:

inSj := 95-mils ins^ = 40-mils in^ := 30-mils ins4 = 30-mils

Separation of conductors for inductance and proximity effect:

sep := dia + 2-ins

n n

Now die resistance of each segment is calculated at 20 degrees C:

p cu := 1.7241-10 6-ohmcm p aj := 2.8624-10 6-ohmcm

Pi = P al P2 := PJ

m Cl P cu P4 = P3

37

Sep

<------------->

Figure 4.2

Separation of conductors.

5.01264-105

a =

8.3521-104

6.52864-103

cmil

1.62409-103

a

3.43496-10

2.06154* 10~4

0.00159

0.00639

ohm

ft

The resistance of each segment is then calculated:

Rdc rdc

n n

R

dc total

:= XR

dc

Rdc =

Rdc_total = a31681ohm

38

0.00316

0.03216

0.21763

0.06386

ohm

The dc resistance must be adjusted for skin effect:

rad

a := 2-jc -60----

sec

p := 4-Jt 10 Permeability of free air

m

The Skin-effect ratio is seen in the following:

dia

The radius of each conductor.

90.96835 90.96835j

N :=

YCS :=

n

/

N -r Jn

n n U

K-r.)

2J

i I

Ycsn = RefYcsnj 1

N =

Yes =

90.96835 90.96835j

117.21259 - 117.21259j

117.21259 - 117.21259j

0.00926

2.58843-10

4.36028-10

-4

2.6983-10

-7

Yep is the adjustment factor for proximity effect to other conductors. This factor

is calculated for circuit segments that have the circuit conductor return path

rather than over conduit.

39

1.15676

0.47218

0.1701

0.08484

M o(x);= J o(x-j15) M i(x) =J i (x-j1:5)j2

0 0(x) = arg(M 0(x)) 0 ^x) := arg(M j(x))

M(x)

0 l(x) 0 0(x)

y%-m(xpJ-

/ dia

\Sq,n /

1.18

M/xp \ + 0.27

+ 0.312-

/dia

n

lsepJ

Ysp =

0.02543

7.23623-10"4

6.42297* 10-6

1.92572* 10"7

Now for the proximity effect contribution of a nonmagnetic pipe:

First the dc resistance of the pipe must be calculated. Segment #2 is the

only one that has a non-magnetic pipe.

^pipe^41 ODpipe:=415in t:=

pipe pipe

pipe''1

pipe -

it -

N.1

2 /

rs :=

Pal

pipe

40

. 2

apipe = 0-96015'in

r = 14.08442

pohm

ft

Ds = seP2

sm pipe

s := 1.55-in^ + 0.58-dia2

= n>

pipe

x

cp2

X

cp2

3-r

I

0.10901*%

Segment #3 has a magnetic conduit and the Xcp is

calculated as follows (assuming cradled arrangement):

a := 1.7 for steel conduit.

D_. = 0.7- in

P3

sep3 Dp3

0.34------- + 0.175----

xcp3

:= a-

m m

( ^3) (lohm

x

cp3

= 0.01823*%

cp

0

0.10901

0.01823

0

%

41

Rac_ = r dc_' (1 + Ycsn + YsPn + *q>rK

n n

Rac

0.00327

0.03223

0.21767

0.06386

ohm R ac totaj IR ac

Rac total =0-31703

The difference between ac and dc resistance can be seen as follows:

RaCj Rdc1

KdCj

ac3-Rdc3

= 3.46851 %

= 0.01931 %

R ac2 R dc2

dc

R

ac.

dc.

= 0.20726 %

= 4.62403*10~5

Rdc Rdc,

3 4

As seen in the previous calculation, the ac portion of the resistance can be

ignored for all circuit sized conductors (conductors smaller than #8 AWG).

The total ac resistance of the circuit is:

%

4

R ac tot ~ Yj Rac Rac tot=0-31703 'ohm

* -- n

n= 1

42

The total ac resistance can then be compared to the total dc resistance:

Rdctot = Y Rdc Rdctot = 0-31681-ohm

i i n

n= 1

^ ac tot dc tot

-dc tot

= 0.06891 -%

As seen the contribution of the ac portion of the

total circuit resistance is very minimal.

The inductance of each segment is calculated as follows:

k =52.9 =60.9 kv =60.9

1

*2

*3

S2==

1.26- sep

/ \ 2

sep2

DP ~sep2

P2 2j

kY := 52.9

X4

S3==

1.26-sep,

1 -

f sep3

S2 =0.46414 -in

S3= 0.17548 -in

Sj := sep1

S4 = sep4

Xn=kxH

2.57-S

dia

. polrnij

^ ift

X =

0.0025j

0.00585j

0.00623j

4.26336-10_4j

ohm

43

The X/R ratio of the circuit in question is seen as:

4

XoverR =

^ac tot

n= 1

XoverR= 0.0473257736

As seen in the preceeding equation, the X over R ratio is much less than 1.

For crude calculations the reactance can be neglected with similar answers

The initial fault current with all conductor temperatures at

20 deg.C is seen as the following:

The initial fault current has been calculated and now effects of change

in resistance as the conductor temperature rises during fault.

First the Temperature Coefficient of Resistance must be input:

^tot ^ ac tot+ ^ tot

Ztot = 0.31703 +0.015j -ohm

120- volt

i= 188.55823 *amp

l -

0.00403

a

degC

0.00393

3" degC

44

he specific heat of conductor material is as follows:

cal

0.092- c := 0.226

gm- degC

cl =cal c2:=cal

c3 = c cu C4 = C CU

cal

gmdegC

he density of the conductor material is used to calculate the mass

f the conductor as follows:

dencu = 8.87-

gm

cm

den^ := 0.09765-

lb

3

m

den1 := den ^

de^ := den al

der^ = den

cu

den4 :=dco

mass := a 1 den

n n n n

mass =

42.44218

11.99123

2.7013

0.04905

1

The thermal coefficient of resistance is as follows:

0.00403

degC

a

cu

0.00393

degC

The heating efficiency, as a function of short circuit time,

is calculated by the following method:

X fas := 0.08-

BTU

hr-ft -degF-ft

c ins

0.293

BTU

Ib-degF

45

a c c cu ^encu

F := 0.85

a ins c ins

1.35

62.247-

dia

2-71-

c ins^ ins

M = F-

n

m

n v

X :=M

n

n

240

sec

eff :=

n

1 erf(xn

eff=

0.9958

0.98977

0.96423

0.93052

46

The efficiency matrix can be set up before the calculation of the heating:

q = 1.. 480 dt =------sec

240

h i sec 500

eflj

: =

^3,1 efij

lv J efij

t + dt

q

1+2

mi'A

lq+l

\q+l

\q+l

n3,q+l

. ^4,q+ 1

M2'/q/

1 erf M,- t 1+2

1+2

m4.

i +,jr

1+2

47

The iterative calculation to determine the temperature rise, the resistance

increase, and the corresponding decrease of current is as follows:

q := 1.. 480 dt =

240

ll,l

2,1

3,1

l4,l

a

U

a

2,1

a

3,1

a4,l

RU

*2,1

*3.1

R

4,1

20- degC

20- degC

20- degC

20- degC

a al

aal

a

cu

a

cu

R

R

R

R

ac,

ac-

ac-,

ac.

sec

48

x,

dt-

T2,q-

masSj-Cj

MX,

mass/c

n.

'2,q

T3,q +

* w**

mas^'C3

:wx,

n

'3,q

dt-

4,q mass.-c. 4,

4 4

1, q+i

r

2, q+l

r3,q+l

r4,q+l

at,q+ 1

a2,q+l

3,q+l

X, 1

4,q + 1

^l,q+ 1

*2^+1

^3,q+ 1

R4,q+1

Vl .

masSj-Cj

1

/ 1 \ [*wx.l

(2,q/ + masSj-Cj '^.q

/ 1 \ \3,q/ + *wx, mas^*c3 *3*

i

/ 1 \ kq/ + *wx mass/c. 4 4 *U,q

\q 1+(l.q)- masSj-Cj \q

\q 1 + Kq) mas^Cj \q

V 1 + Kq) mas^Cj \q

V 1 + Kq)- *(/(%) mass/c. 4 4 j '\q

120-volt

49

he results of laboratory short-circuit tests on the identical circuit are read in from a data file a

ollows (See Appendix B for the tabulated results):

u = 1..100

imeas : =READ( data ) amp tmeas :=READ(time) sec

u u

*meas = 186.6312amp Ij = 188.55823amp

*i~*meas

----------- = 1.0219%

he results of the iterative calculation is seen in the following four graphs:

Time (Seconds)

Figure 4.3: Calculated Current vs. Time

50

(Amperes) Current (Amperes)

measu

Time (Seconds)

Figure 4.4: Measured Current vs. Time

51

As seen in the previous graph the measured value of fault current compares favorably to the

calculated value.

The temperature of the smallest conductor reaches over 300 deg. C in less than 2 seconds.

The circuit resistance has changed during the fault due to the conductor temperature change. T

total change is seen in the following calculation:

^finaltotal _Rl,480 + R5,480 + R3,480 + 4,480

Rfinal_total = 040846-ohm Rac_total =0.31703 ohm

Rac total Rfinal total ..

----=------------=---- =28.860?%

R dctotal

52

The 28.9% change in circuit resistance results in

the following change in total fault current:

Ij = 188.55823 amp

I4g0= 146.57978-amp

- =22.26286-%

>1

The 22.3% change in fault current can be very important in calculating proper circuit

protection and coordination of protective devices.

53

5. Proposed Changes in the National Electrical Code

Article 310 of the National Electrical Code (NEC) has provisions for minimum circuit-

breaker sizing for circuit size conductors.22 There is no provision indicating minimum

size of extension cord or maximum length of branch circuit conductors. This lack of

requirement can lead to situations where the maximum available fault current is below

the instantaneous trip level of the branch overcurrent protective device. This can lead

to a fault that lasts several seconds, heating the circuit conductors, and thereby

decreasing the fault current. As the fault current decreases circuit breaker tripping is

delayed even further.

The most common conductor insulation is PVC. When PVC reaches a temperature of

about 200 C the material begins releasing a flammable vapor that can be ignited with a

nearby open flame or electric arc. From the test conducted in the laboratory, the vapor

from the rapidly heating insulation is rapidly forced from the ends of the insulation.

Although at room temperatures PVC insulation will not sustain combustion, at

elevated temperatures the material usually will continue to bum freely due to the

increased heat supplied by the heating conductor.23 Although admittedly this is not a

typical situation, this problem can occur on circuits with the fault current limited

primarily by a single small conductor. The small conductor will heat rapidly while the

other larger conductors remain much cooler. The problem of short-circuit heating of

conductors can become much more apparent when the over-current protection of the

circuit is inadequate, fails to operate, or is defeated.

The NEC does contain a provision that states the circuit impedance shall not be of a

54

level that interferes with the proper operation of the over-current protection.24 The

NEC offers no guidelines or methods to insure this provision is met and most users of

the code do not perform analysis necessary to determine fault current levels. In order

to comply with this article of the NEC, an appendix could be referenced in which a

table is placed that outlines a method for calculating the maximum lengths of low-

voltage branch circuits given conductor sizes. The table could be as seen in Table 3.

Table #5.1: Unit resistance per 10 fee of circuit.

Conductor 15 A Circuit 20 A Circuit 30 A Circuit

Size Breaker Breaker Breaker

10 0.025 0.034 0.050

12 0.046 0.061 0.092

14 0.082 0.109 0.163

16 0.183 0.245 0.367

18 0326 0435 ... -usa

Table #3 is used by measuring the length of circuit necessary to feed desired load and

adding the number found in the table for each 10 feet of given circuit size. Care must

be exercised to include each cable within the circuit and expected appliance cords.

The sum total of all unit resistances must not be over 1.00. If the sum total exceeds

1.00, the fault current available at the load will likely he less than the instantaneous trip

region of the circuit breaker.

The values for Table #3 are obtained by calculating the single-phase, per-unit resis-

tance of the conductor on a 120-volt base. The current base is assumed to be 10 times

the circuit breaker rating, the level at which most circuit breakers enter the

instantaneous tripping region. The values of the resistance are then multiplied by 2 to

account for the return circuit.

55

6. Proposed Product Changes

The product design changes that result from the work surrounding this research are

primarily in the area of protection of extension cords. With current design practices,

nothing prevents the use of several extension cords in series, thereby greatly limiting

the fault current to well below the instantaneous trip level of a branch circuit breaker.

The branch circuit breaker is not designed to protect this situation.

A simple remedy for this problem is to insert a fuse in the male attachment plug on the

extension cord. This could protect the cord from continuous overload and fault

currents below the trip level of the branch circuit breaker. This fused plug design is

currently used in self-regulating heat cables and Christmas-tree lights. The attachment

plug for each device contains a fuse holder to hold a bayonet fuse. The same

arrangement could be installed on extension cords to limit the fault current and thereby

limit the short-circuit heating of the conductors. The fuse rating for this situation

should be a time-delay fuse. This will allow for starting of electric motor driven

appliances while protecting the cable from short-circuit heating.

56

7. Summary

Short circuit calculation methods that are common in engineering practice are very

useful but are overly conservative for predicting the response of low-voltage systems

under fault conditions. The two assumptions that lead to the greatest error are (1)

neglecting circuit resistance and (2) neglecting change in circuit resistance due to

temperature rise of faulted conductors. The calculation methods in this thesis address

both of these assumptions and present methods that more precisely calculate the

available fault current throughout the fault than commonly used methods. Some of the

applications of this analysis are as follows:

Calculation of the short circuit temperatures of faulted conductors in order to

determine possibility of conductor temperatures igniting conductor insulation.

Calculation of fault current with respect to time in order to determine proper

coordination of overcurrent protection devices.

Calculation of expected trip times for overcurrent devices.

The analysis has been compared very favorably to fault current measurements

completed in the laboratory.

57

Appendix A: Source Code for Gt+ Program

^include

#include

^include

^include

#include

struct proj_data{

char eng[40];

char comp [40];

char proj_name[40];

char file_name[10];

double priavai;

int avaljnput;

int calc_per_sec;

};

struct. seg_data{

char ident[40];

double length ;

double dia;

double rad;

double temp;

double row;

double alpha;

double sep;

int path;

int mail;

int ins_matl;

int conduit;

double rac;

double x;

int set;

double mass;

double density;

double spec heat;

58

double insspecheat;

double volspecheat;

//THIS IS THE AREA WHERE ALL FUNCTIONS ARE LISTED,

GENERALLY IN THE ORDER IN

//WHICH THEY APPEAR.

int graph();

int in_window();

int mscm();

int bhiscm (int 1, int t, int r, int b);

int seginput(int);

int segin();

int rac(int);

int drac(int, double);

int x(int);

int calc();

double erf(double); //this calcs the error function for the value x

//int ini_struct();

int total(int);

int load(); //this loads saved system data

int mass(); //this calcs the mass of the conductor

int save(); //this saves the system data to a file,

int heat efiQ; //this sets the heating efficiency variable.

//THESE ARE THE GLOBAL VARIABLES:

double i[481]; //the array that holds the current

int maxn; //the number of segments currently in system

extern seg data seg[10]; //the structure name that holds the segment data

extern projdata info;

extern FILE *fptr;

float eff[10][481];

float v; INoltage at fault

const float pi=3.1415926;

int calculated=0; //This is used as a flag for calculation

59

void main (void)

{

clrscr(); // this clears the screen

max_n=0;

in_window(); // this function is the first input screen//

return;

}

in_window()

{

register int i;

register int j;

int s;

bhiscm(20,5,60,22);

// this section writes the message to the screen

gotoxy(5,3);

cputs(" 1. Input System Data.");

gotoxy(5,5);

cputs("2. Input Segment Data. ");

gotoxy(5,7);

cputsC'3. Load System Data from File.");

gotoxy(5,9);

cputs("4. Calculate Fault Current.");

gotoxy(5,ll);

cputs("5. Graph Results to Screen.");

gotoxy(5,13);

60

cputs("6. Save System Data to File.");

gotoxy(5,15);

cputs("7. Exit Program.");

gotoxy(5,18);

cputs("Make Your selection: (1-7)");

s = (getch());

switch(s){

case'l': inscm ();break;

case'2': segin();break;

case '3': load();break;

case'4': calc();break;

case'5': graph();break;

case'6': save();break;

case 7': _exit(0);

default: break; }

in_window();

return 0;}

int calc() {

const cmax_n=max_n;

int n; //This is the segment number

int cps; //calculations per sec. This will not be here in final ver.

int q;

double dt;

double dT; //This is the change in temperature of the conductor,

double denominator;

double numerator;

double k; //This is the factor in the heating eff. calc

FILE *fptr;

float temp[10][481];

double heating_eff[10,481];

61

//area of each segment conductor

double area[10];

double bot;

float time=0; //this is the running time for output file

// double a; //temp for area

// double radius; //temp for radius

// double vsh; //temp for seg[n].vol_spec_heat

// double ef; //temp for efficiency

calculated=l;

mass();

bluscm(15,10,65,17);

gotoxy(5,3);

cout"What is the fault voltage?";

gotoxy(5,5);

cinv; // TfflS IS A GLOBAL VARIABLE.

bluscm(25,12,55,17);

gotoxy(5,3);

cout"One Moment Please....";

gotoxy(5,5);

cout"Results written to OUT.TXT";

cps=480;

dt=2.0/cps;

//This calculates the initial fault current,

for (n=l;n
temp [n] [ l]=seg[n] .temp;

rac(n);

x(n);

area[n]=pow(seg[n].dia/2,2)*pi;

};

total(l); //THIS FUNCTION CALCULATES THE FAULT CURRENT

FOR

//ITERATION #1

62

heat_efl(); //this function sets up the heating efficiency

//matrix

for (q=2;q
for (n=l ;n
numerator=dt*i[q- l]*i[q-1] *seg[n] ,rac*eff[n] [q];

denominator=seg[n] .mass* seg[n]. sp ec_heat;

dT=numerator/denominator;

seg[n] ,temp=seg[n] .temp+dT;

temp [n] [q]=seg[n] .temp;

drac(n,dT);

total(q); //This function will calc the fault current.

fptr=fop en( "out.txt"," w");

fprintf(fptr,"This program was written by W. Ronald Kilgore\n");

fprintf(fptr,"as a partial requirement for an MSEE degree\n");

fprintf(fptr,"from the University of Colorado at Denver.\n\n\n");

fprintf(fptr,"Project Name: %s.\n",info.proj_name);

fprintf(fptr,'"Engineer's Name: %s.\n",info, eng);

fprintf(fptr,"Comp any Name: %s.\n",info.comp);

fprintf(fptr,"____________________________\n");

for (n= 1 ;n
fprintf(fptr," Segment %iname: %s.\n",n,seg[n].ident);

fj)rintf(fptr,"Segment Length: %f feet.\n",seg[n].length);

fprintf(fptr,"Segment Diameter: %f inches.\n",seg[n].dia);

fprintf(ij)tr, "Final Conductor Temp: %f DegC.\n",seg[n].temp);

fprintf(fptr,"Conductor Separation: %finches.\n",seg[n].sep);

if (seg[n].matl=l)

fprintf(fptr,"Conductor material is Copper.\n");

if (seg[n].matl=2)

fprintf(fpfr,"Conductor material is Aluminum.\n");

63

if (seg[n].conduit=l)

lprintf(fptr,"Segment is not in conduit.W);

else

if (seg[n].conduit=2)

fprintf(fptr,"Segment is routed in magnetic conduit.W);

if (seg[n].conduit=3)

fprintf(fptr,"Segment is routed in nonmagnetic conduit.W);

if (seg[n].path=l)

fprintf(iptr,"Conduit is return path.W);

else

fprintf(fptr,"Conduit is not in return path.W);

if (seg[n].ins_matl=l)

fprintf(fptr, "Insulation is PVC.W);

if (seg[n].ins_matl=2)

fprintf(fptr, "Insulation is PE.\n");

fprintf(fptr,"\nW);

fprintf(fptr,"Time (sec)\tl (amps)\t");

for (n=l;n
fprintf(fptr,"Seg. %i\t",n);};

fprintf(fptr,"Seg. %iW,cmax_n);

for (q= 1 ;q
fprintf(fptr,"'%f\t%f\t",time,i[q]);

time=time+dt;

for (n=l ;n
^)rintf(Â§)tr,"%f\t",temp[n] [q]);};

fprintf^tr, "%f\n",temp [cmaxn] [q]);

};

fclose(fptr);

return 1;

}

64

//THIS FUNCTION CALCULATES THE CHANGE IN RESISTANCE

AND ALPHA

drac(int n, double dT) {

seg[n].rac=seg[n].rac (l.+seg[n],alpha (dT));

seg[n]. alpha=l/(( l/seg[n]. alpha)+(dT));

return 1; }

total(int q) {

complex ztemp;

complex ztot=0;

float itemp;

const complex j=sqrt(complex (-1));

intn;

for (n=l;n
ztemp =complex(seg[n].rac+ (seg[n].x)*j);

ztot=ztot+ztemp;

};

i[q]=v/(2 *(abs(ztot)));

return 1;

}

int x(int n) {

float k;

double arg;

//The next section adjusts X for magnetic conduit

if (seg[n]. conduit=2) {k=60.9;}

65

else

k=52.9;

arg=2.57* seg[n]. sep/seg[n]. dia;

seg[n].x=k (loglO(arg)) le-6 (seg[n],length);

return 1;

>

//This function calculates the initial dc resistance for each segment

int rac(int n) {

double area;

double r_20;

double alpha;

const double pi=3.1415926;

area=((pow(seg[n].dia/2,2) (pi)));

r_20=seg[n].row*seg[n].length/area;

if (seg [n] ,temp=20.) {

seg[n].rac=r_20;

return 1;}

else {

alpha=l/(( l/seg[n]. alpha)+(seg[n]. temp-20.));

seg[n].rac=r_20*(1.0+alpha*(seg[n].temp-20.0));

return 1;

}

mass() {

66

int n;

double num;

double den;

for (n=l;n
seg[n].mass=seg[n], length* 12.0*pow(seg[n].dia/2,2)*3.141592*seg[n]. density;

};

return 1;

}

double erf(double x) {

int n; //this is the counter

int q;

double total; //this is the running total

double top; //this is the numerator

double bot;

double next;

double inside;

double fact=l;

int p;

total=0;

top=l;

inside=0;

for (n=l;n<50;n++) {

fact=l;

top=l;

for (q=n;q>0;q~) {

fact=fact*q;};

p=2*n+l;

top=pow(x,p);

bot=p*fact;

next=pow(-1 ,n)*top/bot;

67

// cout"top= "top;

inside=inside+next;

total=(2.0/1.7724538509)*(x+inside);

// cout"erf(x)=";

// couttotal;

// getch();

return total;

};

int heat_efl() {

const float e=2.71828183;

double bot;

double top;

double k;

double vsh;

double area[20];

double a;

double radius;

float test;

float ef;

int q;

int cps;

double t; //this is the elapsed time in the heating eff

double dt;

int n;

cps=480;

dt=2.0/cps;

for (q=l;q
t=dt*q;

68

for (n=l;n<(max_n+l);n++){

radius=0.0254*seg[n]. dia/2;

area[n]=pow(radius,2)*pi;

k=0.85*sqit(t)*(2*pi*radius);

k=k*sqrt(seg[n] .insspecheat* 1.49036);

bot=area[n]*seg[n].vol_spec_heat;

k=k/bot;

eff[n] [q]=( 1.0/(k*k))*((pow(e,k*k)*( l-erf(k)))- l+(2*k)/sqr

t(pi));

};

return (1);};

69

/*

"BLUSCRN.CPP"

THIS FILE IS THE FUNCTION THAT DISPLAYS THE DIALOG WINDOW.

*/

#inchide

#include

int bluscm (int 1, int t, int r, int b)

{

int end;

register int i;

register int j;

int s;

int xmargin;

int left=l;

int top=t;

int right=r;

int bottom=b;

textmode(C80);

textbackground(BLACK);

clrscr();

textbackgroimd(BLUE);

textcolor(WHlTE);

70

window (left,top,right,bottom);

// this loop changes the background color to blue

for (i=l;i < 25; i++){

for(j=l J < 80j++){

gotoxy(j,i);

cprintf("");}}

return 10;

}

#include

#include

#include

#include

extern double i[480];

extern int calculated;

extern bhiscm (int 1, int t, int r, int b);

void graph ()

{

int driver,mode;

int max_x,max_y;

int left,right,top,bottom;

float max_i=0;

int count;

int temp;

int xl,x2,yl,y2;

float itemp;

71

char *yaxis[ll];

inty[ll];

float cnt;

char ychr[10];

if (calculated=0){

bhiscm(20,12,60,17);

gotoxy(5,3);

cout"You have to calculate the values";

gotoxy(5,5);

cout"before you graph them. Hit a key.";

getch();

return; }

for (count=l ;count< 100;count++) { //This loop finds the max I

if(i[count]>max_i) {

max_i=i[count];} }

//This loop sets max i to multiples of 50

for (count=0;coimt<100;count++){

temp=max_i+count;

if(temp%50=0) break;}

max_i=temp;

// This code initializes the graphics driver:

driver= DETECT;

mode= 0;

initgraph(&driver,&mode,"c:\\tc\\bgi");

72

// This gets the max values of x and y and stores them.

max_x=(getmaxx());

max_y=(getmaxy());

// Set colors and font:

setbkcolor(BLUE);

setcolor(WHITE);

settextstyle( SMALL_FONT,HORIZ_DIR, 5 );

// This code draws the outside box of the graph:

left=max_x/10;

top= max_y/10;

right=max_x-(max_x/10);

bottom=max_y-(max_y/9);

rectangle (left,top,right,bottom);

outtextxy(left,bottom+10,"0.0");

outtextxy((right-left)*0.1+left ,bottom+10,"0.2");

outtextxy((right-left)*0.2+left ,bottom+10,"0.4");

outtextxy((right-left)*0.3+left ,bottom+10,"0.6");

outtextxy((right-left)*0.4+left ,bottom+10,"0.8");

outtextxy((right-left)*0.5+left ,bottom+10," 1.0");

outtextxy((right-left)*0.6+left ,bottom+10,'T.2");

outtextxy((right-left)*0.7+left ,bottom+10,"1.4");

outtextxy((right-left)*0.8+left ,bottom+10," 1.6");

outtextxy((right-left)*0.9+left ,bottom+10," 1.8");

outtextxy(right,bottom+l 0,"2.0");

// This will label the y-axis:

xl=left*0.6;

for (count=10;count>-l;count~){

y[coimt]=bottom-(bottom-top)*(count)/10-(bottom-top)/50;}

73

for (count=0;count
yl=(count)*(max_i)/10;

itoa(yl,ychr,10);

outtextxy(xl,y[count],ychr);}

// This code lables all titles:

settextstyle(SANS_SERIF_FONT,HORIZ_DIR, 1);

outtextxy(max_x/2-50,bottom+30,"Time in Seconds");

settextstyle(SAN S_SERIF_FONT,HORIZDIR,2);

outtextxy(max_x/2-95 ,top/10, "Fault Current vs. Time");

settextstyle( SAN SSERIFFONT, VERTDIR, 1);

outtextxy(left*. l,max_y/2-75,"Current in Amperes");

// This changes the active window to inside the graph for

// ease of use

setviewport(left,top,right,bottom, 1);

max_x=right-left;

max_y=bottom-top;

setcolor(CYAN);

//Drawing vertical grids:

line(max_x*0.10, 0, max_x*0.1, max_y);

line(max_x*0.20, 0, max_x*0.2, maxjy);

line(max_x*0.30, 0, max_x*0.3, maxjy);

74

line(max_x*0.40, 0, max_x*0.4, max_y);

line(max_x*0.50, 0, max_x*0.5, max_y);

line(max_x*0.60, 0, max_x*0.6, max_y);

line(max_x*0.70, 0, max_x*0.7, max_y);

line(max_x*0.80, 0, max_x*0.8, max_y);

line(max_x*0.90, 0, max_x*0.9, max_y);

//Drawing horizontal grids

line(0,max_y*0.10, max_x, max_y*. 1);

line(0,max_y*0.20, max_x, max_y*.2);

line(0,maxjy*0.30, max_x, max_y*.3);

line(0,max_y*0.40, max_x, max_y*.4);

line(0,max_y*0.50, max_x, max_y*.5);

line(0,max_y*0.60, max_x, max_y*.6);

line(0,max_y*0.70, max_x, max_y*.7);

line(0,max_y*0.80, max_x, max_y*.8);

line(0,max_y*0.90, max_x, max_y*.9);

setcolor(LIGHTRED);

for (count=l;connt<240;count-H-){

cnt=count*2;

xl=((max_x)*cnt/480.);

y 1 =max_y-(max_y*i[cnt]/max_i);

x2=((max_x)*(cnt+1)/480.);

y2=max__y-(max_y*i[cnt+l]/max_i);

Iine(xl,yl,x2,y2); }

getch();

75

restorecrtmode;

return;

}

/*

"DMPUSCRN.CPP"

THIS FILE HANDLES THE INPUT OF DATA.

*1

#include

^include

#include

#include

#include

struct proj_data{

char eng[40];

char comp [40];

char proj_name[40];

char file_name[10];

double priaval;

int avalinput;

int calc_per_sec;

};

struct seg_data{

char ident[40];

double length;

76

double dia;

double rad;

double temp;

double row;

double alpha;

double sep;

int path;

int matl;

int insmatl;

int conduit;

double rac;

double x;

int set;

double mass;

double density;

double specheat;

double insspecheat;

double volspecheat;

};

struct projdata info;

struct seg_data seg[20];

int bluscm(int, int, int, int);

int seginput(int);

extern int max_n;

int inscm ()

{

FILE *fptr;

char end;

register int i;

register int j;

int s;

int xmargin;

77

bluscm(10,5,70,25);

xmargin=8;

gotoxy(20,2);

cputs("Input project data:'1);

gotoxy(xmargin,4);

cputs("Engmeer:");

gotoxy(xmargin,6);

cputs("Company:");

gotoxy(xmargin,8);

cputs("Project Name:");

gotoxy(xmargm, 10);

cputsC'DOS File name for data:");

gotoxy(xmargin, 12);

cputs("Primary Fault Current Available:");

gotoxy(xmargin, 14);

cputs("Primary Fault Current in MVA or Amperes?");

gotoxy(xmargin, 16);

cputs("How many Calculations Per Cycle? (1-20)");

gotoxy(xmargin, 18);

cputs("Is above information correct? (Y/N)");

/* The next code puts the cursor at each new place that it needs to be

to get next input*/

gotoxy(xmargin+l 1,4);

gets(info.eng);

78

gotoxy(xmargm+10,6);

get s(info. comp);

gotoxy(xmargin+15,8);

gets(info.proj_name);

gotoxy(xniargin+24,10);

gets(info.file_name);

gotoxy(xmargin+34,12);

cininfo .priaval;

gotoxy(xmargin+41,14);

cminfo. avalinput;

gotoxy(xmargin+40,16);

cminfo. calc_per_sec;

gotoxy(xmargin+45,18);

end = (getchQ);

if (end=y) {

return 1;

};

if(end=rY,){

return 1;};

inscm ();

return 10;

}

79

segin(){

strcpy(seg[0].ident,"fake name");

bluscm(25,10,55,15);

intn;

int insmatl;

cout"Highest Seg="max_n;

gotoxy(5,2);

cputs("Which Segment to edit?");

gotoxy(5,7);

cinn;

if(n>max_n){

max_n=n;}

seginput(n);

return 1;

}

seginput(int n) {

int xmargin=8;

int ins matl;

char end;

double thickness;

80

// this section writes the message to the screen

bluscm(10,1,70,24);

gotoxy(20,2);

cout" Segment #"n" of "max_n;

gotoxy(xmargin,4);

cputs("Segment Name:");

gotoxy(xmargin,6);

cputs( "Length (feet):");

gotoxy(xmargin, 8);

cputs("Conductor Diameter (inches):");

gotoxy(xmargin, 10);

cputs("Conductor Material (l=Cu, 2=A1):);

gotoxy(xmargin, 12);

cputs("Insulation Thickness (mils):");

gotoxy(xmargin, 14);

cputs("Insulation Material (1=PVC, 2=PE):");

gotoxy(xmargin, 16);

cputs("Circuit in conduit? (l=no,");

gotoxy(xmargin, 17);

cputs("2=magnetic, 3=nonmagnetic):");

gotoxy(xmargin, 19);

cputs("Conduit in return circuit? (l=Yes, 2=No)");

gotoxy(xmargin,21);

cputs("Conductor Temp (deg. C.):");

gotoxy(xmargin,23);

cputs("Is above information correct? (Y/N)");

/* The next code puts the cursor at each new place that it needs to be

to get next input*/

gotoxy(xmargin+15,4);

81

gets(seg[n] .ident);

gotoxy(xmargin+16,6);

cinseg[n].length;

gotoxy(xmargin+3 0,8);

cinseg[n].dia;

gotoxy(xmargin+34,10);

cinseg[n] .matl;

gotoxy(xmargin+30,12);

cinthickness;

seg[n]. sep=seg[n]. dia+2*thickness/1000;

gotoxy(xmargin+41,14);

cinseg[n].ins_matl;

gotoxy(xmargin+3 0,17);

cinseg[n]. conduit;

gotoxy(xmargin+45,19);

cinseg[n].path;

gotoxy(xmargin+26,21);

cinseg[n].temp;

gotoxy(xmargin+38,23);

end=(getch());

seg[n].set=l; // this will be the flag that tell me if

// the segment has been entered.

/* The next code sets the coefficient of resistivity

for the conductor material.*/

82

if (seg[n].matl=l){

seg[n].row=8.14535e-6; //TfflS IS FOR COPPER

seg[n].alpha=0.00393; // /DEGC

seg[n].density=0.32117;//#/INA3

seg[n]. spec_heat=l 74.717; //JOULE/#DEGC

seg[n].vol_spec_heat=3.4166*pow(10.,6.);}

// seg[n].ins_spec_heat=T.65129*pow(10.,6.);}

else if (seg[n].matl=2){

seg[n].row=1.3523 le-5; //TfflS IS FOR ALUMINUM

seg[n], alpha=0.00403;

seg[n]. density=0.09765;

seg[n].vol_spec_heat=3.4166*pow(10.,6.);

//seg[n].ins_spec_heat=1.65129*pow(10.,6.);

seg[n].spec_heat=429.197; }

else{

bluscm(15,5,65,19);

gotoxy(5,5);

cout"The value you entered for Material";

gotoxy(5,7);

cout"is out of bounds. Try again.(Hit a Key)";

getch();

seginput(n);

// THE FOLLOWING SETS THE VOLUMETRIC SPECIFIC

HEATS FOR

// BOTH THE CONDUCTOR AND INSULATION

if (seg[n].ins_matl=l){

seg[n].ins_spec_heat=1.65129*pow(10.,6.);}

//BTU/INA3 *DEGF

else if (ins_matl=2){

seg[n].ins_spec_heat=l.65129*pow( 10.,6.); }

else{

bluscm(15,5,65,19);

gotoxy(5,5);

83

cout"The value you entered for insulation material"

gotoxy(5,7);

cout"is out ofbounds. Try again.(Hit a Key)";

getch();

seginput(n);

};

if (end=y) {

return 1;

};

ifCend^^K

return 1;

};

seginput(n);

return 1;

}

save () {

FILE *fptr;

if ((fjptr=fopen(info.file_name,"wb"))=NULL) {

bluscm(10,12,70,17);

gotoxy(5,3);

cout"I couldn't save the file and I think it's your fault! !\n";

gotoxy(5,5);

cout"You may need to input system data.";

getch();

return 1;};

84

fwrite(&info, sizeof (info), 1,lptr);

fwrite(&max_n,sizeof (maxn), 1, fptr);

fwrite(&seg, sizeof(seg), 1, fptr);

fclose(fptr);

bluscm(15,12,65,17);

gotoxy(5,3);

cout"Input data has been written to "info.file_name".";

return 1;

}

intload() {

char *filename;

FILE *fptr;

bluscm( 15,5,65,20);

gotoxy(5,5);

cputs("What DOS file name is the data stored as?");

gotoxy(5,7);

cinfilename;

if((fptr=fop en(filename, "rb" ))=NULL) {

bluscm(20,5,60,20);

gotoxy(5,5);

cout"Can't open file "filename".";

getch();

return 1;

fread(4rinfo,sizeof(info), l,fptr);

fread(&max_n,sizeof(max_n), 1 ,fptr);

fread(&seg,sizeof(seg), l,fptr);

fclose(fptr);

85

bhiscm(25,5,55,20);

gotoxy(5,5);

cout"Loaded data for:

gotoxy(5,7);

coutinfo.proj_name;

gotoxy(5,10);

cout"Press any key...";

getch();

return 1;

}

86

Appendix B: Output of C++ Program

This program was written by W. Ronald Kilgore

as a partial requirement for an MSEE degree

from the University of Colorado at Denver.

Project Name: Master's Thesis: UCD.

Engineer's Name: W. Ronald Kilgore, P.E..

Company Name: Kilgore Engineering, Inc..

Segment 1 name: Transformer to Meter.

Segment Length: 92.000000 feet.

Segment Diameter: 0.708000 inches.

Final Conductor Temp: 20.008894 DegC.

Conductor Separation: 0.898000 inches.

Conductor material is Aluminum.

Segment is routed in nonmagnetic conduit.

Conduit is not in return path.

Insulation is PVC.

Segment 2 name: Meter to Panel.

Segment Length: 156.000000 feet.

Segment Diameter: 0.289000 inches.

Final Conductor Temp: 20.296771 DegC.

Conductor Separation: 0.379000 inches.

Conductor material is Aluminum.

Segment is routed in magnetic conduit.

Conduit is not in return path.

Insulation is PVC.

Segment 3 name: Panel to Receptacle.

Segment Length: 137.000000 feet.

Segment Diameter: 0.080800 inches.

87

Final Conductor Temp: 37.085621 DegC.

Conductor Separation: 0.140800 inches.

Conductor material is Copper.

Segment is routed in magnetic conduit.

Conduit is not in return path.

Insulation is PVC.

Segment 4 name: Zip Cord.

Segment Length: 10.000000 feet.

Segment Diameter: 0.040300 inches.

Final Conductor Temp: 324.624092 DegC.

Conductor Separation: 0.100300 inches.

Conductor material is Copper.

Segment is not in conduit.

Conduit is not in return path.

Insulation is PVC.

Time (sec)

0.000000

0.004167

0.008333

0.012500

0.016667

0.020833

0.025000

0.029167

0.033333

0.037500

0.041667

0.045833

0.050000

0.054167

0.058333

0.062500

0.066667

0.070833

I (amps)

189.221479

189.038273

188.858745

188.682234

188.508318

188.336704

188.167166

187.999529

187.833651

187.669414

187.506715

187.345469

187.185600

187.027040

186.869730

186.713618

186.558654

186.404794

Seg. 1

20.000000

20.000025

20.000051

20.000076

20.000103

20.000128

20.000153

20.000179

20.000204

20.000229

20.000254

20.000278

20.000303

20.000328

20.000355

20.000380

20.000404

20.000427

Seg. 2

20.000000

20.000919

20.001833

20.002743

20.003649

20.004551

20.005449

20.006346

20.007238

20.008127

20.009014

20.009897

20.010778

20.011658

20.012533

20.013405

20.014277

20.015144

Seg. 3

20.000000

20.065210

20.129585

20.193253

20.256296

20.318777

20.380739

20.442219

20.503246

20.563845

20.624039

20.683844

20.743279

20.802357

20.861090

20.919493

20.977573

21.035343

Seg. 4

20.000000

21.002895

21.986345

22.954220

23.908955

24.852253

25.785391

26.709364

27.624973

28.532885

29.433655

30.327768

31.215635

32.097626

32.974056

33.845219

34.711369

35.572739

88

Time (sec)

0.075000

0.079167

0.083333

0.087500

0.091667

0.095833

0.100000

0.104167

0.108333

0.112500

0.116667

0.120833

0.125000

0.129167

0.133333

0.137500

0.141667

0.145833

0.150000

0.154167

0.158333

0.162500

0.166667

0.170833

0.175000

0.179167

0.183333

0.187500

0.191667

0.195833

0.200000

0.204167

0.208333

0.212500

0.216667

0.220833

I (amps)

186.252000

186.100233

185.949460

185.799650

185.650774

185.502803

185.355714

185.209482

185.064085

184.919502

184.775713

184.632699

184.490443

184.348928

184.208137

184.068056

183.928670

183.789965

183.651928

183.514546

183.377807

183.241700

183.106214

182.971337

182.837059

182.703371

182.570263

182.437725

182.305749

182.174326

182.043449

181.913108

181.783296

181.654005

181.525230

181.396961

Seg. 1

20.000452

20.000477

20.000502

20.000526

20.000551

20.000576

20.000599

20.000624

20.000648

20.000673

20.000696

20.000721

20.000746

20.000769

20.000793

20.000816

20.000841

20.000864

20.000889

20.000912

20.000937

20.000959

20.000982

20.001007

20.001030

20.001053

20.001078

20.001101

20.001123

20.001148

20.001171

20.001194

20.001217

20.001240

20.001263

20.001287

Seg. 2

20.016010

20.016872

20.017735

20.018593

20.019449

20.020302

20.021154

20.022003

20.022852

20.023697

20.024540

20.025381

20.026220

20.027058

20.027893

20.028725

20.029556

20.030386

20.031214

20.032038

20.032862

20.033684

20.034504

20.035320

20.036137

20.036951

20.037764

20.038574

20.039383

20.040192

20.040997

20.041800

20.042603

20.043404

20.044201

20.044998

Seg. 3

21.092812

21.149986

21.206875

21.263485

21.319824

21.375896

21.431709

21.487270

21.542582

21.597649

21.652479

21.707073

21.761440

21.815580

21.869497

21.923199

21.976685

22.029961

22.083031

22.135895

22.188559

22.241024

22.293293

22.345371

22.397261

22.448961

22.500477

22.551811

22.602966

22.653942

22.704744

22.755373

22.805830

22.856117

22.906239

22.956196

Seg. 4

36.429546

37.281979

38.130219

38.974426

39.814754

40.651340

41.484314

42.313801

43.139912

43.962753

44.782421

45.599018

46.412621

47.223320

48.031197

48.836319

49.638760

50.438587

51.235867

52.030659

52.823017

53.613003

54.400669

55.186062

55.969231

56.750225

57.529087

58.305862

59.080589

59.853306

60.624058

61.392872

62.159790

62.924847

63.688068

64.449493

89

Time (sec)

0.225000

0.229167

0.233333

0.237500

0.241667

0.245833

0.250000

0.254167

0.258333

0.262500

0.266667

0.270833

0.275000

0.279167

0.283333

0.287500

0.291667

0.295833

0.300000

0.304167

0.308333

0.312500

0.316667

0.320833

0.325000

0.329167

0.333333

0.337500

0.341667

0.345833

0.350000

0.354167

0.358333

0.362500

0.366666

0.370833

I (amps)

181.269193

181.141918

181.015131

180.888825

180.762994

180.637632

180.512733

180.388292

180.264303

180.140761

180.017661

179.894997

179.772765

179.650961

179.529578

179.408613

179.288061

179.167918

179.048180

178.928842

178.809900

178.691351

178.573190

178.455414

178.338018

178.221000

178.104355

177.988080

177.872172

177.756628

177.641443

177.526615

177.412140

177.298016

177.184239

177.070806

Seg. 1

20.001310

20.001333

20.001356

20.001379

20.001402

20.001425

20.001448

20.001471

20.001493

20.001516

20.001537

20.001560

20.001583

20.001606

20.001629

20.001652

20.001673

20.001696

20.001719

20.001741

20.001762

20.001785

20.001808

20.001829

20.001852

20.001875

20.001896

20.001919

20.001940

20.001963

20.001984

20.002007

20.002028

20.002050

20.002071

20.002094

Seg. 2

20.045794

20.046587

20.047380

20.048170

20.048960

20.049747

20.050533

20.051317

20.052099

20.052881

20.053659

20.054438

20.055216

20.055990

20.056763

20.057535

20.058306

20.059074

20.059843

20.060608

20.061373

20.062138

20.062899

20.063660

20.064419

20.065176

20.065931

20.066687

20.067440

20.068192

20.068943

20.069693

20.070440

20.071186

20.071932

20.072676

Seg. 3

23.005987

23.055618

23.105089

23.154402

23.203560

23.252562

23.301411

23.350109

23.398657

23.447056

23.495308

23.543413

23.591375

23.639194

23.686872

23.734411

23.781809

23.829071

23.876196

23.923185

23.970041

24.016764

24.063354

24.109816

24.156145

24.202349

24.248425

24.294373

24.340197

24.385895

24.431471

24.476925

24.522257

24.567469

24.612562

24.657536

Seg. 4

65.209152

65.967064

66.723274

67.477798

68.230667

68.981903

69.731537

70.479591

71.226089

71.971054

72.714508

73.456467

74.196968

74.936012

75.673630

76.409843

77.144661

77.878105

78.610199

79.340958

80.070396

80.798531

81.525383

82.250961

82.975281

83.698357

84.420212

85.140854

85.860291

86.578552

87.295639

88.011566

88.726341

89.439995

90.152519

90.863930

90

Time (sec)

0.375000

0.379166

0.383333

0.387500

0.391666

0.395833

0.400000

0.404166

0.408333

0.412500

0.416666

0.420833

0.425000

0.429166

0.433333

0.437500

0.441666

0.445833

0.450000

0.454166

0.458333

0.462500

0.466666

0.470833

0.475000

0.479166

0.483333

0.487500

0.491666

0.495833

0.500000

0.504166

0.508333

0.512500

0.516666

0.520833

I (amps)

176.957715

176.844962

176.732545

176.620460

176.508706

176.397279

176.286176

176.175396

176.064935

175.954792

175.844962

175.735445

175.626237

175.517337

175.408742

175.300449

175.192457

175.084763

174.977365

174.870261

174.763448

174.656926

174.550690

174.444741

174.339075

174.233690

174.128585

174.023758

173.919207

173.814930

173.710925

173.607190

173.503724

173.400525

173.297590

173.194919

Seg. 1

20.002115

20.002138

20.002159

20.002180

20.002203

20.002224

20.002245

20.002268

20.002289

20.002310

20.002331

20.002354

20.002375

20.002396

20.002417

20.002438

20.002460

20.002481

20.002502

20.002523

20.002544

20.002565

20.002586

20.002607

20.002628

20.002649

20.002670

20.002691

20.002712

20.002733

20.002754

20.002775

20.002796

20.002817

20.002838

20.002859

Seg. 2

20.073420

20.074160

20.074900

20.075638

20.076376

20.077112

20.077847

20.078581

20.079313

20.080044

20.080774

20.081503

20.082230

20.082956

20.083681

20.084404

20.085127

20.085848

20.086567

20.087286

20.088003

20.088720

20.089434

20.090149

20.090860

20.091572

20.092283

20.092993

20.093700

20.094408

20.095114

20.095818

20.096521

20.097223

20.097925

20.098625

Seg. 3

24.702391

24.747129

24.791754

24.836262

24.880655

24.924934

24.969103

25.013159

25.057104

25.100939

25.144663

25.188278

25.231787

25.275188

25.318481

25.361671

25.404755

25.447733

25.490608

25.533381

25.576050

25.618618

25.661083

25.703449

25.745716

25.787884

25.829952

25.871922

25.913795

25.955572

25.997252

26.038836

26.080326

26.121719

26.163021

26.204227

Seg. 4

91.574249

92.283478

92.991638

93.698723

94.404762

95.109756

95.813713

96.516647

97.218567

97.919487

98.619408

99.318344

100.016304

100.713295

101.409325

102.104408

102.798553

103.491760

104.184036

104.875404

105.565857

106.255409

106.944061

107.631836

108.318718

109.004738

109.689888

110.374176

111.057617

111.740204

112.421959

113.102882

113.782974

114.462242

115.140709

115.818359

91

Time (sec)

0.525000

0.529166

0.533333

0.537500

0.541666

0.545833

0.550000

0.554166

0.558333

0.562500

0.566666

0.570833

0.575000

0.579166

0.583333

0.587500

0.591666

0.595833

0.600000

0.604166

0.608333

0.612500

0.616666

0.620833

0.625000

0.629166

0.633333

0.637500

0.641666

0.645833

0.650000

0.654166

0.658333

0.662500

0.666666

0.670833

I (amps)

173.092510

172.990360

172.888469

172.786835

172.685456

172.584330

172.483456

172.382832

172.282458

172.182330

172.082449

171.982812

171.883418

171.784265

171.685352

171.586678

171.488241

171.390040

171.292074

171.194341

171.096839

170.999569

170.902527

170.805713

170.709126

170.612765

170.516628

170.420713

170.325021

170.229549

170.134296

170.039262

169.944444

169.849843

169.755456

169.661283

Seg. 1

20.002880

20.002899

20.002920

20.002941

20.002962

20.002983

20.003002

20.003023

20.003044

20.003065

20.003084

20.003105

20.003126

20.003145

20.003166

20.003187

20.003206

20.003227

20.003246

20.003267

20.003286

20.003307

20.003328

20.003347

20.003368

20.003387

20.003408

20.003428

20.003447

20.003468

20.003487

20.003508

20.003527

20.003548

20.003567

20.003586

Seg. 2

20.099323

20.100021

20.100718

20.101414

20.102108

20.102802

20.103495

20.104185

20.104876

20.105564

20.106253

20.106939

20.107624

20.108309

20.108994

20.109676

20.110357

20.111038

20.111717

20.112396

20.113073

20.113750

20.114426

20.115099

20.115772

20.116446

20.117117

20.117786

20.118456

20.119125

20.119791

20.120459

20.121124

20.121788

20.122452

20.123114

Seg. 3

26.245342

26.286366

26.327295

26.368135

26.408884

26.449541

26.490110

26.530590

26.570980

26.611282

26.651497

26.691626

26.731665

26.771620

26.811489

26.851273

26.890970

26.930584

26.970114

27.009560

27.048923

27.088203

27.127401

27.166517

27.205553

27.244507

27.283379

27.322172

27.360886

27.399519

27.438074

27.476551

27.514948

27.553268

27.591511

27.629677

Seg. 4

116.495209

117.171257

117.846519

118.520996

119.194695

119.867622

120.539772

121.211166

121.881805

122.551682

123.220818

123.889214

124.556862

125.223785

125.889977

126.555443

127.220200

127.884232

128.547562

129.210190

129.872101

130.533325

131.193863

131.853699

132.512863

133.171341

133.829147

134.486282

135.142746

135.798553

136.453705

137.108185

137.762024

138.415207

139.067749

139.719635

92

Time (sec)

0.675000

0.679166

0.683333

0.687500

0.691666

0.695833

0.700000

0.704166

0.708333

0.712499

0.716666

0.720833

0.724999

0.729166

0.733333

0.737499

0.741666

0.745833

0.749999

0.754166

0.758333

0.762499

0.766666

0.770833

0.774999

0.779166

0.783333

0.787499

0.791666

0.795833

0.799999

0.804166

0.808333

0.812499

0.816666

0.820833

I (amps)

169.567322

169.473573

169.380034

169.286704

169.193582

169.100667

169.007959

168.915455

168.823156

168.731059

168.639164

168.547470

168.455976

168.364681

168.273584

168.182684

168.091980

168.001471

167.911156

167.821034

167.731105

167.641367

167.551820

167.462462

167.373293

167.284312

167.195518

167.106909

167.018486

166.930248

166.842193

166.754321

166.666630

166.579121

166.491792

166.404642

Seg. 1

20.003607

20.003626

20.003645

20.003666

20.003685

20.003704

20.003723

20.003744

20.003763

20.003782

20.003801

20.003822

20.003841

20.003860

20.003880

20.003899

20.003918

20.003939

20.003958

20.003977

20.003996

20.004015

20.004034

20.004053

20.004072

20.004091

20.004110

20.004129

20.004148

20.004168

20.004187

20.004206

20.004225

20.004244

20.004263

20.004282

Seg. 2

20.123775

20.124435

20.125095

20.125753

20.126411

20.127068

20.127724

20.128378

20.129030

20.129684

20.130335

20.130987

20.131636

20.132286

20.132933

20.133581

20.134228

20.134872

20.135517

20.136160

20.136803

20.137444

20.138084

20.138725

20.139364

20.140001

20.140638

20.141275

20.141911

20.142546

20.143179

20.143812

20.144444

20.145075

20.145704

20.146334

Seg. 3

27.667767

27.705778

27.743715

27.781576

27.819363

27.857073

27.894711

27.932272

27.969761

28.007175

28.044518

28.081787

28.118984

28.156109

28.193161

28.230143

28.267054

28.303892

28.340662

28.377361

28.413990

28.450550

28.487040

28.523460

28.559813

28.596098

28.632315

28.668463

28.704544

28.740557

28.776505

28.812386

28.848200

28.883947

28.919630

28.955248

Seg. 4

140.370895

141.021530

141.671524

142.320892

142.969635

143.617752

144.265259

144.912155

145.558441

146.204102

146.849182

147.493637

148.137512

148.780777

149.423462

150.065552

150.707062

151.347977

151.988312

152.628067

153.267258

153.905869

154.543915

155.181396

155.818298

16.454651

157.090439

157.725677

158.360367

158.994492

159.628067

160.261108

160.893600

161.525543

162.156952

162.787827

93

Time (sec)

0.824999

0.829166

0.833333

0.837499

0.841666

0.845833

0.849999

0.854166

0.858333

0.862499

0.866666

0.870833

0.874999

0.879166

0.883333

0.887499

0.891666

0.895833

0.899999

0.904166

0.908333

0.912499

0.916666

0.920833

0.924999

0.929166

0.933333

0.937499

0.941666

0.945833

0.949999

0.954166

0.958333

0.962499

0.966666

0.970833

I (amps)

166.317671

166.230878

166.144262

166.057822

165.971558

165.885469

165.799553

165.713811

165.628241

165.542843

165.457615

165.372559

165.287671

165.202953

165.118402

165.034019

164.949803

164.865752

164.781867

164.698147

164.614590

164.531197

164.447966

164.364898

164.281990

164.199243

164.116656

164.034229

163.951960

163.869849

163.787895

163.706098

163.624457

163.542972

163.461642

163.380466

Seg. 1

20.004301

20.004320

20.004339

20.004356

20.004375

20.004395

20.004414

20.004433

20.004452

20.004469

20.004488

20.004507

20.004526

20.004543

20.004562

20.004581

20.004601

20.004618

20.004637

20.004656

20.004673

20.004692

20.004711

20.004728

20.004747

20.004766

20.004784

20.004803

20.004820

20.004839

20.004858

20.004875

20.004894

20.004911

20.004930

20.004948

Seg. 2

20.146963

20.147591

20.148216

20.148842

20.149467

20.150091

20.150715

20.151337

20.151958

20.152580

20.153200

20.153818

20.154436

20.155054

20.155670

20.156286

20.156902

20.157516

20.158129

20.158741

20.159353

20.159964

20.160574

20.161184

20.161793

20.162399

20.163006

20.163612

20.164217

20.164822

20.165426

20.166029

20.166632

20.167233

20.167833

20.168432

Seg. 3

28.990799

29.026287

29.061708

29.097067

29.132362

29.167591

29.202759

29.237862

29.272902

29.307880

29.342794

29.377647

29.412439

29.447168

29.481834

29.516441

29.550987

29.585472

29.619896

29.654259

29.688562

29.722807

29.756990

29.791117

29.825182

29.859188

29.893137

29.927027

29.960857

29.994633

30.028347

30.062006

30.095608

30.129150

30.162638

30.196068

Seg. 4

163.418167

164.047974

164.677246

165.306000

165.934219

166.561920

167.189102

167.815765

168.441910

169.067535

169.692657

170.317261

170.941360

171.564957

172.188049

172.810638

173.432724

174.054321

174.675415

175.296005

175.916122

176.535736

177.154877

177.773514

178.391678

179.009354

179.626541

180.243256

180.859497

181.475266

182.090561

182.705383

183.319733

183.933609

184.547012

185.159973

94

Time (sec)

0.974999

0.979166

0.983333

0.987499

0.991666

0.995833

0.999999

1.004166

1.008333

1.012499

1.016666

1.020833

1.024999

1.029166

1.033333

1.037500

1.041666

1.045833

1.050000

1.054167

1.058333

1.062500

1.066667

1.070833

1.075000

1.079167

1.083334

1.087500

1.091667

1.095834

1.100001

1.104167

1.108334

1.112501

1.116667

1.120834

I (amps)

163.299444

163.218574

163.137858

163.057293

162.976879

162.896616

162.816504

162.736540

162.656726

162.577060

162.497543

162.418172

162.338948

162.259870

162.180938

162.102151

162.023509

161.945011

161.866656

161.788444

161.710374

161.632446

161.554660

161.477014

161.399509

161.322144

161.244918

161.167831

161.090882

161.014071

160.937397

160.860860

160.784459

160.708194

160.632065

160.556070

Seg. 1

20.004967

20.004984

20.005003

20.005020

20.005039

20.005056

20.005074

20.005093

20.005110

20.005129

20.005146

20.005163

20.005182

20.005199

20.005219

20.005236

20.005253

20.005272

20.005289

20.005306

20.005323

20.005342

20.005360

20.005377

20.005394

20.005413

20.005430

20.005447

20.005465

20.005484

20.005501

20.005518

20.005535

20.005552

20.005569

20.005589

Seg. 2

20.169031

20.169630

20.170227

20.170824

20.171421

20.172016

20.172609

20.173204

20.173796

20.174389

20.174980

20.175571

20.176161

20.176750

20.177338

20.177925

20.178513

20.179098

20.179684

20.180269

20.180853

20.181437

20.182018

20.182600

20.183182

20.183762

20.184341

20.184921

20.185499

20.186077

20.186653

20.187229

20.187805

20.188379

20.188953

20.189528

Seg. 3

30.229443

30.262760

30.296022

30.329227

30.362377

30.395472

30.428513

30.461496

30.494427

30.527302

30.560122

30.592888

30.625601

30.658260

30.690865

30.723415

30.755915

30.788361

30.820753

30.853092

30.885380

30.917614

30.949799

30.981928

31.014008

31.046036

31.078012

31.109938

31.141811

31.173635

31.205408

31.237129

31.268801

31.300423

31.331995

31.363518

Seg. 4

185.772446

186.384476

186.996033

187.607147

188.217789

188.827972

189.437714

190.046997

190.655838

191.264221

191.872162

192.479660

193.086700

193.693314

194.299469

194.905197

195.510483

196.115326

196.719742

197.323715

197.927261

198.530365

199.133057

199.735306

200.337128

200.938538

201.539505

202.140060

202.740189

203.339905

203.939194

204.538055

205.136520

205.734558

206.332184

206.929398

95

Time (sec)

1.125001

1.129168

1.133334

1.137501

1.141668

1.145834

1.150001

1.154168

1.158335

1.162501

1.166668

1.170835

1.175002

1.179168

1.183335

1.187502

1.191668

1.195835

1.200002

1.204169

1.208335

1.212502

1.216669

1.220835

1.225002

1.229169

1.233336

1.237502

1.241669

1.245836

1.250003

1.254169

1.258336

1.262503

1.266669

1.270836

I (amps)

160.480210

160.404484

160.328891

160.253431

160.178104

160.102909

160.027845

159.952913

159.878111

159.803440

159.728898

159.654486

159.580202

159.506047

159.432020

159.358121

159.284349

159.210703

159.137184

159.063791

158.990523

158.917380

158.844362

158.771468

158.698698

158.626051

158.553527

158.481126

158.408847

158.336689

158.264653

158.192738

158.120944

158.049269

157.977715

157.906280

Seg. 1

20.005606

20.005623

20.005640

20.005657

20.005674

20.005692

20.005709

20.005726

20.005743

20.005760

20.005777

20.005796

20.005814

20.005831

20.005848

20.005865

20.005880

20.005898

20.005915

20.005932

20.005949

20.005966

20.005983

20.006001

20.006018

20.006035

20.006052

20.006069

20.006086

20.006102

20.006119

20.006136

20.006153

20.006170

20.006187

20.006203

Seg. 2

20.190100

20.190672

20.191242

20.191813

20.192383

20.192951

20.193520

20.194088

20.194654

20.195221

20.195787

20.196352

20.196917

20.197481

20.198044

20.198606

20.199167

20.199728

20.200289

20.200848

20.201406

20.201965

20.202522

20.203079

20.203636

20.204191

20.204746

20.205301

20.205854

20.206408

20.206961

20.207512

20.208063

20.208614

20.209164

20.209713

Seg. 3

31.394989

31.426413

31.457787

31.489111

31.520386

31.551613

31.582790

31.613920

31.645000

31.676035

31.707020

31.737957

31.768847

31.799688

31.830482

31.861231

31.891932

31.922585

31.953192

31.983753

32.014267

32.044735

32.075157

32.105530

32.135860

32.166145

32.196384

32.226578

32.256725

32.286827

32.316883

32.346897

32.376865

32.406792

32.436668

32.466503

Seg. 4

207.526199

208.122589

208.718567

209.314133

209.909302

210.504059

211.098419

211.692368

212.285919

212.879059

213.471817

214.064163

214.656113

215.247665

215.838821

216.429596

217.019974

217.609955

218.199539

218.788742

219.377548

219.965973

220.554016

221.141663

221.728928

222.315811

222.902313

223.488434

224.074173

224.659531

225.244522

225.829117

226.413345

226.997208

227.580688

228.163788

96