Development of an Application Program to Calculate
Short-Circuit Temperature Rise in OPGW
by Ryuzo Kimata *, Koji Yoshida*2, T.A.Schéhade *2, Dr. László Varga *3,
and Dr. Ottó Günter *3

Composite cables with optical-fiber ground wire (OPGW) support both power trans-

ABSTRACT mission and data communication, making more effective use of real estate and line
facilities. The inclusion of optical fibers within the cable structure, however, means that the temperature rise limit differs from that of conventional overhead ground wires. Specifically, in power line
ground faults, virtually all of the short-circuit current flows in the ground wire, resulting in large
instantaneous rises in temperature that are a major factor in power line design. Further the OPGW
structure incorporates elements not previously used in power lines, such as pipes, spacers, etc.,
and this increases the error in calculating ordinary short-circuit temperature rise. A study was therefore carried out to calculate short-circuit temperature rise, taking into account the structural features
specific to OPGWs, and personal computer software was developed. Comparisons with resultsfrom short-circuit tests at a representative conductor size confirmed that calculations were accurate
to within 5%.

1.

INTRODUCTION

An overhead ground wire is installed to protect phase conductors from lightning and to reduce electromagnetic interference against telecommunication lines during the
grounding of power lines. The construction of overhead
ground wires having the above purposes, is generally composed of relatively small-sized, mechanically excellent
wires such as Aluminum Clad wires, Steel stranded wires,or AACSR. Recently, an optical fiber composite groundwire (OPGW) has been widely used for effective utilization of land and equipment. An optical fiber can transmit alarge amount of information in high speeds and suffers noelectromagnetic interference because of its non-metallic
characteristics. This advantageous feature makes it possible to construct long distance telecommunication lines
with high reliability. The OPGW must have the same mechanical strengths and electrical characteristics of theconventional overhead ground wire, and there are many
construction ways to built-in optical fiber. The basic construction of OPGW is: an optical fiber unit is placed at thecenter of stranded ground wires, this unit itself is accommodated in a preventive aluminum pipe housing, Aluminum Clad wires and aluminum alloy wires are arranged
peripherally to obtain intended characteristics. An example* Development Dept., Bare Wire Div.
* 2 Phillips Fitel Inc., Canada* 3 Research Institute of Electric Power Co. (VEIKI Kft),
Hungaryof typical construction and characteristics of the OPGW is
illustrated in Table 1.

2.

TEMPERATURE-CURRENT
CHARACTERISTICS OF OPGW

2.1 Current through Overhead Ground Wire
A steady current that is electromagnetically induced by
the phase conductors always runs through the overhead
ground wire. A shunt current from the phase conductors is
to be superimposed to the induced current in case ofgrounding. The induced current and this shunt current arecalculated from factors such as: distance from the phaseconductor, grounding resistance, soil resistance and wire
conductivity. The relationship between these currents andthe temperature rise in the ground wire is obtained by calculating such factors: (1) the heat generated by induced
steady current, (2) the heat absorption from the sun, (3)the heat radiation from the wire, (4) the equilibrium stateof heat (initial temperature) through the above absorption
and radiation, (5) the heat generated by the superimposedcurrent when grounded, and (6) calculation of the transient state including (1) through (5).
The relationship between the induced current and wire
temperature in a steady state has been investigated in thepast and summarized as the calculation of current carrying capacity in the overhead transmission wires1)~2).
The transient temperature rise due to short-circuit cur-45

rent is calculated by adding the temperature rise in the
short-circuit to the steady state temperature rise. The following equation shows the relationship between the temperature change dθ and lapse of time dt. The ratio of bothparameters is calculated by dividing the difference (which
is obtained by the addition of heat generated by current
flowing and heat absorbed from the sun and subtracting
radiating heat from the wire) with the heat capacity of thewire C.

) + 0e -t/
I R dc(20)× 1 0 -5{ 1 + ( T + 2 0 ) } + W sdm=
d K m- I 2 R dc(20)× 1 0 -5CT=
d K m- I 2 R dc(20)× 1 0 -5=

Where,
I : Current (A)β : The ratio of AC to DC resistanceRdc: Conductor DC resistance (Ω/km)
Ws: Solar radiation (W/cm2)
d : Conductor outer diameter (cm)
η : Absorptivity = Emissivity
Km: A coefficient according to the Stephan-Boltzmanlawθ : Temperature rise (°C)
C : Heat capacity (J/cm.°C)

Table 2

Maximum operating temperature of bare wire
conductor
Maximum operating temperature (T+θ)˚C
Type

Solving the above differential equation, the transient temperature rise is obtained as follows.

Continuous

Short time

Instantaneous

Aluminum clad steel wire (AC)

200

230

400

Galvanized steel wire

200

230

400

I -aluminum alloy steel
reinforced (IACSR)

90

100

150

Aluminum conductor steel
reinforced (ACSR)

90

120

180

Thermo-resistant aluminumalloy conductor steel
reinforced (TACSR)

150

180

260

Construction and characteristics of OPGW

OPGW60mm2

OPGW80mm2

OPGW170mm2

OPGW290mm2

30AC
OPGW500mm2

40AC
OPGW500mm2

Outer layer

23AC 8/3.2

23AC 7/3.9

27AC 12/3.5

40AC 12/4.5

30AC 30/4.2

40AC 30/4.2

Inner layer——

40AC 8/SB(2.89)

40AC 8/SB(4.0)

40AC 8/SB(3.62)

40AC 8/SB(3.62)

OP unitOP1/5.0

OP1/5.0

OP1/6.0

OP1/6.5

OP1/6.5

OP1/6.5

73.5{7,490}

95.6{9,750}

144.6{14,750}

179.9{18,340}

381.0{38,850}

307.4{31,350}

Aluminum clad
steel wire

64.34

83.65

168.0

291.4

497.8

497.8

OP unit

13.55

13.55

20.36

23.39

23.39

23.39

Total

77.89

97.2

188.4

314.69

521.1

521.1

Aluminum clad
steel wire

411.4

535.0

940.0

1,372

2,770

2,358

OP unit

42.57

42.57

62.97

72.88

72.88

72.88

Total

454.0

577.6

1,003

1,445

2,843

2,431

11.4

12.8

17.5

22.5

29.4

29.4

Product code

Items

-t/

Where,
Rdc(20) : DC resistance at 20°C (Ω/km)
α : Resistance temperature coefficientt :Time (sec)θ 0: Initial temperature of wire (°C)
Km: hrη+hw (wind)
Km: hrη+hc (no wind)d
I 2 R dc ×10 -5 + W s d - d K m=
dtCTable 1m( 1 - e2Construction
Stranded wire
construction
No. / Dia.(mm)* Minimum tensile load kN{kgf}Reference

Cross
sectional area
(mm2)

Mass
(kg/km)Outer diameter (mm)2*Modulus of elasticity GPa{kgf/mm }*Linear expansion coefficient (1/km)*Electrical resistance (Ω/km)

149.1{15,200}–6

149.1{15,200}–6

130.4{13,300}–6108.9{11,100}–6

128.5{13,100}–6

108.9{11,100}–6

12.9×1412.9×1414.0×1415.5×1414.0×1415.5×14

1.19

0.914

0.336

0.150

0.112

0.0884* optical fiber not included

46

Furukawa Review, No. 18. 1999

This equation is a general formula, therefore, the temperature is calculated by substituting t =∞ at steady state,
t=0 at transient current flowing. For the flowing current in ashort-circuited state, the time lapsing is regarded extremely
short. Heat generated by Joule's Law in the short-circuit
only affects the temperature rise of the wire. Therefore theinstant heat absorption and radiation of the wire itself canbe negligible factors.
At present, the calculation method for steady state current temperature rise has been reexamined internationally by IEEE and CIGRE. In Japan, a technical committee
in JIEE has been held to collect the recent results of theinvestigation5). The calculation formula by CIGRE is relatively in good agreement with the measured results, therefore, this equation will be widely used from now on.
2.2 Permissible Temperature of Conductors
The permissible temperature of conductors is normallydetermined by the following factors: mechanical deterioration affected by the heat hysteresis of a conductor, equipment conditions, and heat characteristics of accessory
parts. Among these, a predominant factor is the annealing property of the wire. The existing level of the acceptable deterioration range in tensile strength is less than
10% of normal value considering the material's properties, vibration fatigue and corrosion.
When strength deterioration occurs, the relation between
temperature and the lapse of time becomes to differ bymaterials. On the other hand, the instantaneous permissible temperature is defined as a temperature which does
not cause the wire's annealing by instantaneous current
upon failure. As a concrete example, it is the temperaturewhen the tensile strength of the conductor does not decrease in a flowing current under 1/4 tensile strength ofthe conductor for two seconds. The data is shown in Table
2. An OPGW has optical fibers inside its construction,
therefore, the permissible temperature of OPGW must be
determined by taking into consideration not only the deterioration of the mechanical properties but also the thermal
deterioration of the optical fiber. The permissible temperature of an optical fiber is determined by the heat resistantproperty of a buffer material which plays a role in protecting the optical fiber. The allowable temperature of a silicon
buffer type wire is defined as 300°C, and 180°C in UV
acrylic type wires. In other words, in designing the OPGW,
it is required that the maximum temperature absorbed in
an aluminum pipe (spacer) should be less than the above
temperature, i.e. 300°C or 180°C, respectively. In actuallines, the OPGW is used, assuming that the short-circuitcurrent in failure will flow scarcely in full amount estimatedin the designing stage.
2.3 Temperature Rise in Short -Circuit Current
The instantaneous temperature rise of a ground wire is
obtained, as mentioned above, by solving the differential
equation which expresses a transient state, i.e., occurrence of instantaneous heat by ohmic loss in the groundwire based on Joule's Law and the temperature rise of thewire(which has a certain thermal capacity) with the dura-tion of time. The running time of a short-circuit is regarded
so short that heat radiation or absorption from and into
the wire will not occur. The next equation gives the instantaneous temperature rise.

I=

C log e (

+1

)

0 +1
-5

t R dc(20) ×10
I : Short circuit current (A)t : Time (sec)In the case that the conductors are made of a single
material, current distribution is relatively uniform. The temperature difference between the conductors is small, andthe measured value and the calculated value are in agreement with each other. An OPGW does include optical fibers in itself, however, its construction is composed ofseveral materials and is rather complicated in general.
Thus, the composite conductor like OPGW has materials
whose conductivities are also different from each other.
The instantaneous current which flows through the composite conductor is distributed to each wire in proportion
to the wire's own conductivity due to the contact resistance between wires. Each wire has its own specific heatand heat capacity, thus each wire has a different temperature rise. The temperature of each conductor is different
under the initial condition during the short-circuit current
flowing , and gradually falls into an equilibrium state throughthermal heat transfer. As mentioned above, the temperature difference by the conductors creates a new problem
in OPGW designing. It is necessary to calculate the maximum temperature rise of the unit which accommodates
optical fibers because the rise is extremely important. An
actual conductor is spiral-shaped with stranded pitches
and has impedance against an alternative current. It must
Ti/i–1

Ri/2

Ti

Ci

Figure 1

Ri/2

Φi

Ti/i+1

Ti : Temperature
Ri : Thermal resistance
Ci : Heat capacity
Φi : Generated heat

Equivalent circuit for heat conduction in OPGW

Figure 2

Experiment on heat transfer

47

be considered that each wire has a mutual inductance.
When the wire is an aluminum clad which contains ferromagnetic steel, the iron losses due to the hysteresis property and eddy-current affect the temperature rise of thewire. Because OPGW is so complicated, there were several cases that the data measured had shown more than
a 30% deviation from the experimental value by using themethod of the conventional short-circuit temperature risecalculation.
2.4

Short Circuit Temperature Rise Calculation
Program
As mentioned above, in order to calculate the temperature rise of OPGW precisely, the following must be considered:. Each wire has its own impedance to the AC current,
and therefore the current distribution in the conductor
is not uniform,. The heat in each wire is produced by the resistivity
and current based on Joule's Law and also producedby the iron losses due to its magnetic characteristics.
This heat moves from a wire to another wire with timeby the temperature difference.
In order to design OPGW reasonably, a personal com-puter program has been developed which makes it possible to calculate the precise short-circuit temperature riseby taking into consideration the above effects. The impedance of each wire is estimated by calculating magnetic
fields produced by the distributed currents which are affected by the geometric construction of conductors andthe conductivity of each wire. This estimated impedanceis used to again calculate current distribution. This algorithm is iterated and the ultimate current distribution in the
conductor is obtained by converging these outputs in steps.
The temperature rise in the conductor is derived from theconductor's thermal capacity and the heat which is generated by the current and wire's resistance based on Joule's
Law and by the iron losses due to magnetic field.Then theheat generated by each wire begins to move by temperature difference. The heat transfer between each wire isimpeded by each contact condition and surface condition.
Figure 1 shows a heat flow of the OPGW in a form ofelectrical equivalent circuit. The temperature change in the
conductor can be calculated from a transient state in theequivalent circuit. Heat transfer constant differs by contact
conditions (wire shape, stranded wire structure etc.), therefore, theoretical calculation is difficult. The constant is obtained by an actual short-circuit test in which the temperature rise is measured using actual wires. Figure 2 shows aheat transfer test.
The temperature rise of the wire in short-circuit tests

START

Shunt current to a component
wire (DC model calculation)

Heat transfer
between wires**

Figure 3

Experiment on magnetic characteristics of AC
wire

NO

2

R(T)I tj
Tj+1= ————+T
c.m.hδTHeat2
Φ=R(T)I ————
δT<cool∆T≤ε1Heat transfer is calculated
from above equation

YES
Magnetic fieldcalculationi

Shunt current to a component
wire(AC model calculation)

Parallel to axis
Ua

Heat transfer
between wires*

Resistance calculation

Perpendicular to axis

NO

∆T≤ε2

Ut
YES
END

Figure 5
Figure 448

Waveform of induced voltage on OPGW

Program flow chart for calculation of OPGW
temperature in short-circuit conditions

Furukawa Review, No. 18. 1999

Optical fibre units

Figure 6

Data output of OPGW calculation

Aluminum spacer
Aluminum tube

increases each wire resistance with time (the temperature coefficient of resistance is assumed constant), andboth the current distribution and the magnetic fields arecalculated in the next step. Thus, iteration of these procedures brings out the actual nearest temperature rise in
short-circuit failure. As mentioned above, an aluminum cladwire used in the OPGW produces iron losses and the values must be included in the calculation as additionalamounts of heat.
The magnetic field produced by the current which flows
through the stranded wire has magnetic flux of the both
axial and line directions, and the total magnetic field acting on the wire is gained by composing both directional
forces. The magnetic characteristics of aluminum clad wires
placed in this magnetic field are difficult to theoreticallycalculate. Therefore, the B-H curve is obtained experimentally using an actual wire. In this experiment, both magnetic saturation characteristics of a coiled aluminum cladwire and magnetic field originated by the current which
Table 3

Aluminum-clad steel wires
Aluminum alloy wires

Figure 7

Construction of OPGW

flows through the stranded wire are measured by a sensor coil. Figure 3 shows the experiment for the magnetic
characteristics of an aluminum clad wire, and Figure 4
shows the wave form samples of the induced voltage inthe stranded wire.
The short circuit temperature rise calculation has been
programmed using Turbo-Pascal, and is available for a personal computer(Windows version). By inputting such data:
initial temperature, short-circuit current, short-circuit time,
duration etc., a tabulating and graphing output of the relationship between rise in temperature and the elapse oftime is obtained. Figure 5 and 6 show a flow chart andoutput of the calculation.

Comparison of measured and calculated results for OPGW under short-circuit conditions

Calculated

Measured

Calculated

Measured

OPGW

Short circuitcurrent
I [kA]
33.5
33.3
33.5
33.2
32.41
32.02
34.24
33.01
14.3
14.3
14.4
14.4
10.8
11.0
11.1
1.0
14.60
14.48
15.32
14.59
1.15
10.99
10.86
10.91

Time
t [sec]
0.38
0.56
0.70
0.96
0.38
0.56
0.70
0.96
0.30
0.30
0.16
0.46
0.30
0.40
0.50
0.80
0.30
0.30
0.16
0.46
0.30
0.40
0.50
0.80

Initialtemperature
Ti [˚C]
50
50
50
50
50
50
50
50
19
24
25
25
25
47
41
41
19
24
25
25
25
47
41
41

Ambient
temperature
Ta [˚C]
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20

Spacertemperature
Tsp [˚C]
145
185
248
305
145
185
248
305
135
140
90
220
90
139
154
235
135
140
90
220
90
139
154
235

Aluminum clad
Aluminum wire
wire temperature temperature
Tac [˚C]
Taa [˚C]
75
140
88
180
117
235
135
292
75
140
91
180
116
242
147
298
66
132
70
138
50
86
107
215
—
86
—
136
—
152
—
230
63
132
67
136
48
88
102
215
48
88
79
135
82
150
117
230

49

2.5 OPGW Short-Circuit Test
To verify the calculation data, a short-circuit test for a typical OPGW was carried out. The OPGW was produced byPhilips-Fitel Inc., Canada, and the construction is shownin Figure 7. The test was conducted at VEIKI Kft in Hungary. The length of OPGW is approximately 10 m, and thetension applied is about 10% UTS.
2.6 Evaluation
The calculated data, given by the developed software, andmeasured results are compared and they are in close
agreement with each other within 5% as shown in Table 3.
This is considered satisfactory in consideration of the test
precision. In the temperature measurement, it was foundthat the rising was extremely fast, so the time-lag of thetransient response must be considered in the measurement system. The thermocouple used in the test was smallenough in thermal capacity, but should inevitably include
a small margin of error. Also, the wave form deformationof the current might exist. Taking all factors of errors into
consideration, this calculation data is accurate and satisfactory.
From the test results, the temperature of the optical unit
seems to be high regardless of the surface temperature
being low. This trend must be taken into account beforehand in transmission line designing.

3.

REFERENCES

1) Technical Committee for Aluminum Bare Wire Current Carrying Capacity; "Aluminum Bare Wire Current Carrying Capacity", Electrical Technology Research Association 4, No.6
(1949). (in Japanese)2) Committee for Studying Transmission Line; "Report on Improvement of Transmission Line, Part-1, Overhead Transmission Line", Central Research Institute of Electric Power Industry (1965). (in Japanese)
3) IEEE; "IEEE Standard for Calculating the Current-Temperature Relationship of Bare Overhead Conductors", IEEE Standard 738-1993 (1993).
4) CIGRE; "The Thermal Behavior of Overhead Conductors",
CIGRE WG12, ELECTRA No.144 (1992).
5) JIEE, Technical Committee for Investigation of Current Carrying Capacity Calculation by Probabilistic Method; " Current Carrying Capacity of Overhead Transmission Line", JIEE,
Technical Report 660, (1997). (in Japanese)6) R. Kimata; "The Current Rating of OPGW under Fault Condition", CIGRE SC22-WG12 Sendai Meeting, (1997).
Manuscript received on July 22, 1998.

IN SUMMARY

It is found that the short circuit temperature rise calculation program for a conductor makes it possible to estimate
the momentum temperature of an OPGW with sufficientaccuracy. A reasonable design for the OPGW is expected
to be carried out for overhead transmission line by various
customers, using the program to obtain necessary mechanical characteristics and a satisfactory tolerable temperature of the optical fiber cable in the unit. Recently, alarger capacity of transmission is required and the number of optical fibers involved is now increasing. The spacer
type OPGW in the conventional design, therefore, suffers
unfitting in OPGW designing. The development of a new
construction of OPGW is urgently required. This programis intended to be used for examination of the operating
current capacity of the new construction design.
This study has been carried out by VEIKI in Hungary
who subcontracts Phillips-Fitels Inc. in Canada. The analysis of test data was done in cooperation with FETI in Hungary. The outline of this study is reported to CIGRE SC22
WG12, and will be soon reported to ELECTRA.

50

Furukawa Review, No. 18. 1999