Energy and Power Engineering, 2013, 5, 1235-1239
doi:10.4236/epe.2013.54B234 Published Online July 2013 (http://www.scirp.org/journal/epe)
Effects of Harmonics on Power Loss in XLPE Cables
W. Z. Gandhare1, K. D. Patil2
1Principal, Governme nt College of Engineering Amravati, India
2Research Scholar, Government College of Engineering Aurangabad, India
Email: wz_gandhare@yahoo.co.in, kesharsingp@rediffmail.com
Received February, 2013
ABSTRACT
Harmonics in power systems is increasingly at high level. Also, there has been an incredible growth in the use of cross
linked polyethylene (XLPE) cables in distribution systems. Harmonics cause additional power loss/temperature rise;
causing premature failure of cables. Catastrophic failure of power cables leads to great inconvenience to consumers and
loss of system reliability and money. To avoid the overheating of power cables; the additional power loss due to har-
monics should be accurately calculated and properly accommodated by derating the cable. The present method of cal-
culating the power loss in cables in harmonics rich environment is very arduou s. The aim of this paper is to present the
reasonably accurate method for evaluating effects of harmonics on the power loss in XLPE cables. Computational mod-
el is developed in MATLAB for power loss calculation using conventional method. Using this model, calculations are
performed for aluminium and copper conductor XLPE cables of different size and type; for three different types of
harmonics spectrums having total harmonics distortion (THD) of 30.68%, including all odd harmonics components up
to 49th order. Using these results; a mathematical model in the form of simple empirical formula is developed by curve
fitting technique. The results obtained b y various models are presented and compared with error justification.
Keywords: Curve Fitting; Non-sinusoidal Power Lo ss; Per Unit Harmonic Load; Quadratic Polynomial; Sinusoidal
Power Loss
1. Introduction
The increased use of nonlinear loads in all sectors has
resulted in increasingly high level of harmonics, espe-
cially, in the distribution systems. In the recent years, due
to number of technical and commercial reasons, there has
been a remarkable growth in the use of XLPE cables in
underground power distribution systems. Thus, the har-
monics problem and the use of XLPE cables in power
systems are growing simultaneously. Harmonics in dis-
tribution systems causes additional power loss and hence
additional heat/temperature rise. This additional heat
produced because of harmonics is of less significance in
bare conductor overhead lines, but it is very significant in
power cables. This is because power cables are much
more vulnerable to temperature rise as compared to
overhead lines.
Catastrophic failures of XLPE cables cause inconven-
ience to consumers and tremendous loss in terms of sys-
tem reliability, time and money. To avoid the overheat-
ing of XLPE cables; the additional power loss due to
harmonics should be accurately calculated and properly
accommodated by derating the cable. The conventional
method of calculating power loss in cables in harmonics
rich environment is very arduous.
The aim of this paper is to present reasonably accurate
method for evaluating effects of harmonics on the power
loss in XLPE cables. Computational model is developed
in MATLAB for power loss calculation using conven-
tional method. Using this model, calculations are per-
formed for aluminium and copper conductor XLPE ca-
bles of different size and type; for three different types of
harmonics spectrums having total harmonics distortion
(THD) of 30.68%, including all odd harmonics compo-
nents up to 49th order. Using these results; a mathemati-
cal model in the form of simple empirical formula is de-
veloped by iterative curve fitting technique. The results
obtained by both the models are presented and compared
with the proper justificatio n for errors. Practical example
is given to emphasize the proposed approach.
2. Harmonics and XLPE Power Cables Data
2.1. Harmonics Data
The harmonic distortion level in distribution systems in
residential, commercial and industrial areas is above its
tolerable limits as per IEEE std. 519-1992 [1]. However;
the harmonics spectrums for these three types of loads
are not same but they certainly have some characteristic
features. Due to the large percentage of single phase non-
Copyright © 2013 SciRes. EPE
W. Z. GANDHARE, K. D. PATIL
1236
linear loads the percentage of triplen harmonics is much
more in residential load and the higher order harmonics
are absent. Because of large percentage of SMPS loads
the percentage of triplen harmonics is also more in com-
mercial load and at the same time the higher order har-
monics are present. Whereas; industrial load has small
percentage of triplen harmonics with higher order har-
monics as most of the load in this case is three phase
nonlinear load.
Considering above facts, harmonics data for the typi-
cal dominant residential lo ad, dominant commercial load
and dominant industrial load each having THD of
30.68% is used in this paper. All the odd harmonics
components up to order 49th are considered in these
spectrums.
However; it should be noted that, the harmonics spec-
trums are general in nature and no specific load of any
type is dominant in any of these three spectrums. This is
so as to generalize the proposed approach with minimum
errors.
2.2. XLPE Power Cables Data
XLPE cables data for both aluminium and copper cables
used in distribution systems is collected from the product
leaflets of XLPE cable manufacturers in India and abroad.
The study of these product leaflets revealed that, in most
of the cases, the required data for XLPE cables i.e. the
DC resistance at 20°C for aluminium and copper XLPE
cables is strictly specified as per IEC std.60228 [2]. The
same data is used in this study.
3. Computational Model
Let, R20 be the DC resistance of cable conductor per unit
length at 20 0C; then, according to IEC std. 60287-1 [3].
The DC resistance of the cable conductor per unit
length at the permissible maximum operating tempera-
ture (θ) is,


(1)
where,
α20 is the constant, temperature coefficient of resis-
tance for conductor material at 20°C per Kelvin.
As per IEC std. 60502-1 [4], the maximum operating
temperature is 900C for XLPE insulation.
According to IEC std. 60287-1 [3], the AC resistance
of the cable conductor per unit length at the permissible
maximum operating temperature is,
 (2)
where,
Rdc is the DC resistance of the cable conductor per unit
length at the permissible maximum operating tempera-
ture.
ys and yp are respectively skin and proximity effect
factor
Re-writing Equation (2 ),

 



(3)
In Equation (3) both, ys and yp are frequency depend-
ent. Therefore, the ratio (Rac/Rdc) is frequency depend-
ent.
According to [5], the ratio (Rac/Rdc) can be expressed
as,



 










(4)
where,
(5)
where,
f is the frequency (Hz),
In this work all odd harmonic components up to 49th
harmonic order are considered, therefore, the value of the
ratio (Rac/Rdc) is calculated for each frequency compo-
nent using Equations (4 and 5). As Rdc is known from
Equation (1), Rac for each frequency component (i.e. Rac1,
Rac3, Rac5, Rac7, . . . . . , Rac49) can be calculated.
Let, IL be the rated ampacity of cable conductor
(Amp),
In harmonic rich environment [6],


 (6)
Let,
Hh be the percentage harmonic load (pu),
Therefore,
(7)
and,
 (8)
The entire harmonic spectrum for total load current (i.e.
IL) in the phase conductors is,


The entire harmonic spectrum for the current (i.e. IN)
in the neutral (N) conductor under ideally balanced load
condition is,
 
 
Copyright © 2013 SciRes. EPE
W. Z. GANDHARE, K. D. PATIL 1237
In pure sinusoidal conditions (i.e. when, Hh = 0),
power loss in all conductors of the cable is given by,
 
 

 

 
(9)
In non-sinusoid al conditions (i.e. wh en , Hh0), pow er
loss in all conductors of the cable is given by,







 



 


 


(10)
Sheath/screen power loss, armour power loss and di-
electric power loss are called as other losses in XLPE
cable and are generally taken as 5% of the conductor
power loss in both pure sinusoidal and non-sinusoidal
condition; hence, get cancelled in pu power loss calcula-
tions.
At a base value of WS the per unit (pu) power loss in
pure sinusoidal condition (WS-pu) will be given by,




 (11)
At the same base value of WS the per unit (pu) power
loss in non-sinusoidal condition (WNS-pu) will be given
by,


(12)
Computational model in the form of MATLAB pro-
gram is developed to implement this conventional me-
thod.
4. Mathematical Model
Using above computational model, calculations are per-
formed for aluminium and copper conductor XLPE ca-
bles of different size and type; for three different types of
harmonics spectrums having THD of 30.68%. Using
these results; a mathematical model in th e form of simple
empirical formula is developed by iterative curve fitting
technique.
As obtained from the curve fitting exercise, relation-
ship between the percentage harmonic load (x) and per
unit power loss (PL) in XLPE power cables is given by
the empirical formula in equation (13).

 (13)
Where,
a1 and a2 are constants and their values depend upon –
i) Harmonic spectrum
ii) Size and type of cable, and
iii) Conductor material
Values of the a1 and a2 constants for aluminium abd
copper conductor, small, medium and large size cable
types and for three types of harmonic spectrums are cal-
culated.
5. Performance Analysis
5.1. Effect of Harmonics Spectrum
The effect of harmonics spectrum on power loss; respec-
tively calculated using computational and mathematical
model, i.e empirical formula (13) is shown in Figure 1.
As seen from Figure 1, with same THD; there is very
small effect of harmonics spectrum on the power loss in
XLPE power cables and power loss calculation results
using computational and mathematical model are same.
5.2. Effect of Cable Size
The effect of cable size on the power loss for residential
harmonic spectrum is shown in Figure 2. From Figure 2
it is seen that, the effect of harmonics on power loss in
small cable is less and more in large cables. Because;
large cables have higher ampacity. In this case also the
power loss calculation results using both the models are
same and error is negligible.
Figure 1. Effect of harmonic spectrum on power loss.
Copyright © 2013 SciRes. EPE
W. Z. GANDHARE, K. D. PATIL
1238
5.3. Effect of Number of Cores
The effect of number of cores on the power loss for r esi-
dential load is shown in Figure 3. From Figure 3 it is
Figure 2. Effect of cable size on power loss.
Figure 3. Effect of number of cores on power loss.
seen that, the effect of harmonics on power loss in sin-
gle/three core cable is less and is more in three and half
core and four core cable of same size. This is due to the
power loss in neutral conductors in these cables in
non-sinusoidal load condition.
5.4. Effect of Conductor Material
To evaluate the effect of conductor material on power
loss due to harmonics, aluminium and copper cables of
the same size can’t be used; but, cables having same
ampacity need to be used. The results are shown in Fig-
ure 4. From Figure 4 it is seen that, the effect of har-
monics on power loss in aluminium and copper conduc-
tor cables having same ampacity is same.
In each of the four cases above the power loss calcula-
tion results using co mputational and mathematical mod el
are with less than 1% relative percentage error. This
small error is due to truncation and round off errors in
numerical calculations.
6. Illustrative Example
The harmonic analyzer readings of the current through 1
× 50 mm2 copper conductor XLPE cable in industrial
power distri b uti on sy st em are as follows:
h1 h
3 h
5 h
7 h
9 h
11 h
13 h
15 h
17 h19
1 0.17780.30560.22220.0833 0.1556 0.1556 0.04440.10560.0667
h21 h23 h25 h27 h29 h31 h
33 h
35 h
37 h39
0.01110.03720.03720.00300.0233 0.0156 0.0006 0.01000.00830.0003
h41 h43 h45 h47 h49
0.00440.00170 0.00040.0001
Figure 4. Effect of conductor material on power loss.
Copyright © 2013 SciRes. EPE
W. Z. GANDHARE, K. D. PATIL
Copyright © 2013 SciRes. EPE
1239
monics on the power loss in XLPE power cables is de-
veloped.
From the given harmonics spectrum THD is calculated
and is 50.11%. Therefore, the per unit harmonics load for
empirical formulae calculations is (50.11/30.68) = 1.6333.
Power Loss (pu)
Math. Model Result Comp. Model Result
Percentage
Error
= 0.0984739 (1.6333)2 +
0.0000826725 (1.6333) +
1= 1.2628 1.2632 -0.0316
Temperature (℃)
1.2628 x 90 = 113. 652 1.2632x 90 = 113.6 88 -0.0316
The power loss in XLPE power cables significantly
increases with increase in harmonics level. The increase
in power loss with increase in harmonics level follows
rising quadratic relation. Therefore, presence of harmon-
ics in power systems results in severe increase in power
loss and failure rate of XLPE power cables.
The effects of harmonics on the power loss in XLPE
power cables can be very conveniently calculated with
reasonable accuracy using developed empirical formula.
It is interesting to note that, the operating temperature
of the cable (in) can also be very easily calculated
from the pu unit power loss with the same small error. REFERENCES
The per unit power loss fo r 0 to 1.6333 pu variation in
above industrial harmonic load calculated using compu-
tational and mathematical model is shown in Figure 5.
[1] IEEE Recommended Practices and Requirements for
Harmonic Control in Electrical Power Systems, IEEE
Standard 519-1992.
[2] IEC Standard 60228 - Conductors of Insulated Cables,
3rd edition, 2004-11.
7. Conclusions
[3] IEC Standard 60287-1-1 - Electric Cables - Calculation of
the Current Rating, edition 1.2, 2001-11.
The mathematical model to evaluate the effects of har-
[4] IEC Standard 60502-1-1 - Power Cables with Extruded
Insulation and Their Accessories for Rated Voltages from
1 kV up to 30 kV, part-1: Cables for Rated Voltages of 1
kV and 3 kV, 2nd edition, 2004-04.
[5] J. Desmet, et al., “Simulation of Losses in LV Cables
Due to Nonlinear Loads,” Proceedings of IEEE Power
Electronics Specialists Conference,(PESC 2008), 15-19
June 2008, pp. 785-790.
[6] F. L. Tofoli, et al., “Analysis of Losses in Cables and
Transformers under Power Quality Related Issues,” Pro-
ceedings of 19th Annual IEEE Applied Power Electronics
Conference and Exposition, 2004 (APEC '04), Vol. 3,
2004, pp.1521-1526.
Figure 5. Computational and mathematical model results.