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*Corresponding author: E-mail: amadihachy@gmail.com;
British Journal of Applied Science & Technology
17(6): 1-12, 2016, Article no.BJAST.29910
ISSN: 2231-0843, NLM ID: 101664541
SCIENCEDOMAIN international
www.sciencedomain.org
Evaluation of Losses in Distribution Networks of
Selected Industrial Cities in Nigeria Using ETAP
Hachimenum N. Amadi1*
, Fabian I. Izuegbunam1
and Ephraim N. C. Okafor1
1
Department of Electrical and Electronic Engineering, Federal University of Technology,
Owerri, Nigeria.
Authors’ contributions
This work was carried out in collaboration between all authors. Author HNA designed the study,
performed the statistical analysis, wrote the protocol, wrote the first draft of the manuscript and
managed the literature searches. Authors FII and ENCO managed the analyses of the study, literature
searches and improved the final manuscript. All authors read and approved the final manuscript.
Article Information
DOI: 10.9734/BJAST/2016/29910
Editor(s):
(1) Chien-Jen Wang, Department of Electrical Engineering, National University of Tainan, Tainan,
Taiwan.
Reviewers:
(1) A. Ayeshamariam, Khadir Mohideen College, India.
(2) Abubakar Yakubu, Kebbi University of Science & Tech, Aliero, Nigeria.
(3) Rajinder Tiwari, Amity University, Lucknow, India.
Complete Peer review History: http://www.sciencedomain.org/review-history/16740
Received 3
rd
October 2016
Accepted 25th
October 2016
Published 29
th
October 2016
ABSTRACT
Distribution losses contribute to energy shortages and therefore power outages in Nigeria’s
industries. This work evaluated the technical losses in the distribution networks of selected industrial
cities in Nigeria. Power flow simulation of network data collected over the period 2011-2015 from
three distribution companies (DisCos) domiciled in these cities was done by Newton-Raphson (N-R)
technique using the Electrical Transient and Analysis Program (ETAP) software version 12.6.
Results of the power flow simulation showed that between 2011 and 2015 covered by the study, the
cities of Lagos, Kano and Port Harcourt recorded a total power loss of 15.8 MW, 36.2 MW and 6.04
MW respectively. The findings also revealed that overloaded power transformers is part of the
reasons for high losses in the distribution networks of some of the cities. The outcome of the study
provides a guide for system planners and utility companies in providing for prioritization and system
upgrade to ensure improved efficiency of their distribution networks.
Original Research Article
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
2
Keywords: Electricity distribution; distribution losses; distribution networks; energy shortages; power
losses; substations; transformers.
1. INTRODUCTION
The number of power outages in a given locality
per year is an indication of the efficiency of
power supply even as consumer dissatisfaction
with electricity service is often linked to high level
of outages [1-2]. Since the more the number of
power outages, the less efficient the power
system, it follows that given higher system losses
(technical and non-technical), there would be
more power outages indicating the inefficiency of
the system.
The biggest challenge confronting the Nigeria’s
distribution sector presently is the level of
distribution losses namely technical, commercial
and collection losses (Fig. 1). Technical losses
are due to the nature of the components in use in
the network, commercial losses refer to energy
not billed for, and collection losses signify energy
billed but not paid for. When the distribution
companies were privatised as part of the power
sector reform process by the Nigeria
government, the transactions assumed some
particular loss levels. After the asset hand-over,
however, it became clear that the losses were
much higher than had been estimated. In 2014,
~46% of energy was lost through technical
(12%), commercial (6%), and collection losses
(28%) [3].
Over the years, scholars and researchers have
attributed power outages to: Weak grid and
outdated power stations, equipment overloading,
inadequate compensation equipment on the
system, weather and tree related factors,
vandalism, poor maintenance culture, etc.
[1,4,5,6]. No researcher known to this study,
however, has focused on the effects of
distribution losses on electricity supply failures in
the Nigeria industrial sector.
It is imperative therefore to undertake an
assessment of the losses in the nation’s
electricity distribution network in order to
recommend viable and long-lasting solutions to
the perennial problem of system induced power
outages among industries in Nigeria. This forms
the research gap which the outcome of this work
tends to bridge by creating a fresh awareness
among stakeholders in the power sector about
the need for proactive measures towards
minimizing recurrent system induced losses by
ensuring improved efficiency of the country’s
distribution network. The resulting reliable and
adequate electricity supply to the industrial sector
will make the sector more vibrant thereby
growing the country’s gross domestic product
(GDP) and creating more employment
opportunities for the nation’s teeming populace.
2. OVERVIEW OF THE SAMPLED
DISTRIBUTION NETWORKS
2.1 Eko Distribution Network
The Eko distribution network shown in Fig. 2
comprises of the Agbara and Badagry Injection
substations both of which are supplied from the 2
x 45 MVA, 132/33/11 KV transformer
transmission substation at the load centre. The
Agbara Injection substation rated 2 x 15 MVA,
33/11 KV feeds Beecham, Evans, OPIC, and
other 11 KV outgoing feeders while the Badagry
Injection substation rated 15 MVA, 33/11 KV
feeds Unilever, P&G, Nestle and Guinness
industrial feeders.
2.2 Kano Electricity Distribution Network
The Kano Electricity Distribution network shown
in Fig. 3 comprises of the Sabon Gari and
Dakata injection substations. The 30 MVA,
132/33/11 KV transformer transmission
substation at the load centre supplies electricity
to the Sabon Gari 2 x 15 MVA, 33/11 KV
injection substation which in turn feeds Fagge,
Sabon Gari, Abuja 11 KV outgoing feeders
among others. The Dakata 3 x 15 MVA, 33/11
KV Injection substation feeds: Independence,
Brigade, Bompia, Flour Mill and other 11 KV
outgoing feeders. The Murtala outgoing feeder
radiated from a 60 MVA, 33/11 KV injection
substation while Gezawa is supplied directly from
same 30 MVA, 132/33/11 KV substation as the
Sabon Gari injection substation.
2.3 Port Harcourt Distribution Network
The Port Harcourt Electricity Distribution network
shown in Fig. 4 comprises of the Trans-Amadi
and Akanni injection substations. Both the
Akanni and Trans-Amadi injection substations
are supplied from the Port Harcourt Mains
transmission lines via 60 MVA, 132/33/11 KV
transformer transmission substation at the load
centre. The Akanni 2 x 15 MVA, 33/11 KV
Injection substation then feeds: Rumuogba,
Glass Factory, Old Aba Road and Rumurolu
11KV outgoing feeders. The Trans-
MVA, 33/11KV injection substation feeds: Rivoc,
Nda Bros, Water Works and Fimie 11KV
outgoing industrial feeders.
3. METHODOLOGY
Data and diagrams on the sampled distribution
networks were collected from the three electricity
distribution companies located in Nigeria’s three
major industrial cities under review. The
distribution companies are: Eko Electricity
Distribution Company (EKEDP) in Lagos city for
Fig. 1. Level of distribut
Fig. 2. ETAP view of the
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.
3
Injection substation then feeds: Rumuogba,
Glass Factory, Old Aba Road and Rumurolu
-Amadi 2 x 15
n feeds: Rivoc,
Nda Bros, Water Works and Fimie 11KV
Data and diagrams on the sampled distribution
networks were collected from the three electricity
distribution companies located in Nigeria’s three
major industrial cities under review. The
distribution companies are: Eko Electricity
KEDP) in Lagos city for
the Agbara distribution network, Kano Electricity
Distribution Company (KEDCO) in Kano city for
the Sabon Gari distribution network and the Port
Harcourt Electricity Distribution Company
(PHEDCO) in Port Harcourt city for the Port
Harcourt distribution network. In Lagos, seven
industrial feeders supplied from the Agbara
injection substation were considered. The
industrial feeders studied are Beecham, Evans,
OPIC, Unilever, Nestle, P&G and Guinness. In
Kano, nine industrial feeders under the Sabon
Gari Injection substation were investigated.
These are Abuja, Sabon-Gari, Fagge, Murtala,
Flour Mill, Independence, Brigade and Bompia.
In Port Harcourt, eight industrial feeders from two
Fig. 1. Level of distribution losses in Nigeria in 2014 [3]
the Agbara/Badagry injection substations in Lagos
Article no.BJAST.29910
the Agbara distribution network, Kano Electricity
Distribution Company (KEDCO) in Kano city for
the Sabon Gari distribution network and the Port
Harcourt Electricity Distribution Company
(PHEDCO) in Port Harcourt city for the Port
arcourt distribution network. In Lagos, seven
industrial feeders supplied from the Agbara
injection substation were considered. The
industrial feeders studied are Beecham, Evans,
OPIC, Unilever, Nestle, P&G and Guinness. In
der the Sabon-
Gari Injection substation were investigated.
Gari, Fagge, Murtala,
Flour Mill, Independence, Brigade and Bompia.
In Port Harcourt, eight industrial feeders from two
in Lagos
Fig. 3. ETAP view of the
Fig. 4. ETAP view of the Akanni/Trans
injection substations namely Akani and Trans
Amadi injection substations were studied. These
are: Rumuogba, Glass Factory, Old Aba Road
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.
4
the Sabon-Gari/Dakata injection substations in Kano
Akanni/Trans-Amadi injection substations in Port Harcourt
injection substations namely Akani and Trans-
Amadi injection substations were studied. These
Rumuogba, Glass Factory, Old Aba Road
and Rumurolu industrial feeders under Akani
injection substation and Rivoc, Nda
Works and Fimie industrial feeders supplied from
Article no.BJAST.29910
in Kano
in Port Harcourt
and Rumurolu industrial feeders under Akani
injection substation and Rivoc, Nda Bros, Water
Works and Fimie industrial feeders supplied from
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
5
the Trans-Amadi Injection substation. The data
collected include: (i) List of all transformers
connected to the injection substations and their
ratings. (ii) Monthly maximum loading on the
feeders for the period 2011- 2015. (iii) Feeder
route length. (iv) Sizes and ratings of conductors
used for feeders.
These data were subsequently simulated on the
Electrical Transient and Analysis Program
(ETAP) software version 12.6 and the simulation
results used in the computation of the technical
power losses in the respective distribution
networks. The power flow simulation also
evaluated the level of loading of power
transformers installed at the injection substations
under review. This paper chose to perform the
power flow simulation on the ETAP 12.6 software
program owing to its fully graphical electrical
transient and analysis capabilities.
3.1 Mathematical Formulation of Newton-
Raphson Powerflow Equations for
Distribution System
The Newton-Raphson formulates and solves
iteratively the following power flow equation:






∆
∆
Q
P






JJ
JJ
43
21 = 





∆
∆
V
δ
(1)
Where P∆ and Q∆ are bus real power and
reactive power mismatch vectors between
specified value and calculated value,
respectively; V∆ and δ∆ represent bus voltage
magnitude vectors and angle in an incremental
form; and
J1
through J 4
are called Jacobian
matrices.
The Newton-Raphson method has the attribute
of fast convergence and is highly dependent on
the bus voltage initial values. The convergence
criteria for the Newton-Raphson method are
typically set to 0.001 MW and Mvar. A careful
selection of bus voltage initial values is strongly
recommended. Before running load flow using
the Newton-Raphson method, ETAP makes a
few Gauss-Seidel iterations to establish a set of
sound initial values for the bus voltages. The
Newton-Raphson method is often preferred for
use with most systems.
The Newton-Raphson method can be applied to
the power flow studies when the bus voltages are
expressed in polar form. The active and reactive
power at each bus are functions of magnitudes of
phase angles of bus voltages [7]. Thus
),(
1
VfPi
δ= (2a)
|)|,(
2
VfQi
δ= (2b)
For a system of n buses and bus 1 designated as
slack bus, the equations which relate the
changes in active and reactive power to changes
in bus voltage magnitude and angles take the
form [7],
||
||22
V
V
PP
P p
n
p p
i
p
n
p p
i
i
∆
∂
∂
+∆
∂
∂
=∆ ∑∑ ==
δδ
(3a)
∑∑ ==
∆
∂
∂
+∆
∂
∂
=∆
n
p
p
p
i
p
n
p p
i
i V
V
QQ
Q
22
||
||δδ
(3b)
Pi
∆ and Qi
∆ represent the differences between
the specified and the calculated values of Pi
and Q i
.
Replace ||V∆ by
||
||
V
V∆ in Eq. (3), the resulting
equation becomes:
||
||
||
||22 V
V
V
PP
P
p
p
p
n
p
i
p
n
p P
i
i
V
∆
∂
∂
+∆
∂
∂
=∆ ∑∑ ==
δδ
(4a)
||
||
||
||22 V
V
V
V
QQ
Q
p
p
p
n
p p
i
p
n
p p
i
i
∆
∂
∂
+∆
∂
∂
=∆ ∑∑ ==
δδ
(4b)
The set of equations (4) for all the n-1 buses can
be written in the following matrix form,






∆
∆
Q
P
= 





LJ
NH








∆
∆
V
V
δ
(5)
The real and apparent powers at the buses are
expressed as:
)cos(
1
δγδ pipip
n
p
ipii VYVP −−= ∑=
(6a)
)sin(
1
δγδ pipip
n
p
ipii VYVQ −−= ∑=
(6b)
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
6
The incremental values of these powers are as
follows:
)()( calculated
i
specified
ii PPP −=∆ (7a)
)()( calculatedspecified QQQ iii
−=∆
(7b)
The elements of the Jacobian are written as,
When ip ≠
ebfaLH ipipipip
−== (8a)
fbeaJN ipipipip
+=−= (8b)
When ip =
BVQH iiiii i
2
−−= (9a)
GVPN iiiii i
2
+= (9b)
GVPJ iiiii i
2
−= (9c)
BVQL iiiii i
2
−= (9d)
The Newton-Raphson algorithm for power flow
studies [7] is outlined as follows:
1. Assume ||Vi
and δi
at all PQ buses and
δi
at all PV buses. In the absence of any
other information assume ||Vi
at all PQ
buses equal to 1 pu and δi
at all buses
equal to zero.
2. Calculate Pi
and Q i
for all PQ buses
and Pi
for all PV buses (except the slack
bus) using the equations (5)
3. Calculate Pi
∆ and
Q i
∆
for all PQ buses
and Pi
∆ for all PV buses (except the
slack bus) by using the equations (6)
4. Calculate the elements of Jacobian using
Equations. (7) and (8)
5. Solve (4) for δ∆ and
||
||
V
V∆
6. Update the values of voltage magnitudes
and phase angles for all PQ buses and
the values of phase angles for all PV
buses.
7. Calculate Q i
for all PV buses and check
QQQ iii max,min,
<< . If yes, return to Step 2
and start the next iteration. If not, set Q i
equal to Qi min,
or Qi max,
as the case may be
and treat this bus as a PQ bus, return to
Step 2 and start the next iteration.
8. Continue till Pi
∆ and Qi
∆ at all PQ
buses and Pi
∆ at all PV buses are within
prescribed (or assumed) tolerance.
9. Calculate line flows and slack bus powers.
The flow chart for Newton-Raphson
method using polar co-ordinates is given in
Fig. 5.
4. RESULTS AND DISCUSSION
4.1 Power Losses in the Distribution
Networks
Tables 1 - 3 shows the maximum power losses
due to the injection substations of the sampled
distribution networks. During the period 2011-
2015 covered by the study, the Agbara/Badagry
Injection substation in the Agbara distribution
network in the city of Lagos showed a maximum
power loss of 15.8 MW (Table 1). During the
same period, the Sabon Gari/Dakata Injection
substation in Sabon Gari distribution network in
Kano City recorded a maximum power loss of
36.2 MW (Table 2) while the Akanni/Trans-Amadi
Injection substation in the Port Harcourt
distribution network in the Port Harcourt City
showed maximum power loss of 6.04 MW (Table
3). It is obvious from the Tables therefore that the
power losses in each network increased yearly.
This phenomenon is attributable to yearly
increases in load and number of overloaded
transformers and other distribution components
due to lack of regular inspection, preventive
maintenance and absence of infrastructure
upgrade [4-6].
As can be observed from the Tables also, the
highest maximum average power losses during
the 2011-2015 period occurred on Gezewa
feeder in the Kano distribution network, while the
least values were reported on the Rumurolu
feeder in the Port Harcourt distribution network.
The high value of power loss (16.17 MW as
shown in Table 2) on the Gezawa feeder is
attributable to the significant length of the feeder
(405 Km). Recent studies [1,8] have shown that
Fig. 5. Flow chart for load flow studies using
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.
7
attributable to the significant length of the feeder
(405 Km). Recent studies [1,8] have shown that
the longer the distribution feeder lines, the more
the power that gets dissipated due to I
Fig. 5. Flow chart for load flow studies using Newton-Raphson method in polar
co-ordinates [7]
Article no.BJAST.29910
the longer the distribution feeder lines, the more
gets dissipated due to I
2
R losses.
method in polar
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
8
Other factors that could be responsible for the
differences in the power losses in the sampled
distribution networks are increase in load, lack of
good maintenance culture, aging, pattern of
energy use, load density, high rate of illegal
connection to the feeder resulting to overloading
and then capability and configuration of the
distribution system that vary for various system
elements [1,9,10,11]. Figs. 6-8 show the average
power losses in the respective injection
substations during the 2011-2015 period.
Table 1. Maximum power losses in Agbara/Badagry per year
Feeder Maximum power loss (MW) Power loss
(MW)
2011-2015
2011 2012 2013 2014 2015
Unilever 0.36 0.40 0.49 0.65 0.84 2.74
Evans 0.14 0.22 0.35 0.53 0.76 2.0
P&G 0.23 0.36 0.45 0.60 0.82 2.46
Beecham 0.17 0.24 0.37 0.56 0.79 2.13
Nestle 0.12 0.18 0.29 0.51 0.74 1.84
OPIC 0.42 0.47 0.54 0.69 0.88 3.0
Guinness 0.11 0.15 0.27 0.49 0.62 1.64
Total 1.55 2.02 2.76 4.03 5.45 15.8
Table 2. Maximum power loss in Sabon Gari/Dakata per year
Feeder Maximum power loss (MW) Power loss (MW)
2011-20152011 2012 2013 2014 2015
Sabon Gari 0.25 0.52 0.64 0.74 0.83 2.98
Independence 0.23 0.50 0.62 0.68 0.78 2.77
Abuja 0.14 0.25 0.39 0.43 0.56 1.77
Fagge 0.18 0.3 0.44 0.5 0.57 1.99
Gezewa 1.63 2.21 3.22 4.1 5.01 16.17
Brigade 0.29 0.58 0.68 0.85 0.90 3.3
Flour Mill 0.48 0.65 0.84 0.87 1.47 4.32
Bompai 0.1 0.2 0.31 0.39 0.41 1.41
Murtala 0.13 0.22 0.34 0.37 0.43 1.49
Total 3.43 5.43 7.48 8.93 10.96 36.2
Table 3. Maximum power losses in Akanni/Trans-Amadi per year
Feeder Maximum power loss (MW) Power loss (MW)
2011-20152011 2012 2013 2014 2015
Glass Factory 0.14 0.145 0.23 0.30 0.32 1.135
Rumuogba 0.008 0.110 0.112 0.12 0.13 0.48
Rumurolu 0.007 0.105 0.107 0.019 0.05 0.288
Water Works 0.009 0.112 0.115 0.1 0.12 0.456
Nda Bros 0.10 0.116 0.118 0.13 0.15 0.614
Famie 0.11 0.124 0.14 0.15 0.21 0.734
Rivoc 0.15 0.155 0.28 0.37 0.39 1.345
Old Aba Rd 0.13 0.135 0.19 0.26 0.27 0.985
Total 0.66 1.00 1.29 1.45 1.64 6.04
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
9
Fig. 6. Average power losses in Agbara/Badagry for 2011-2015
Fig. 7. Average power losses in Sabon Gari/Dakata for 2011-2015
4.2 Power Transformer Percentage MVA
Loadings in the Distribution
Networks
Figs. 9 -11 show the MVA loadings of some of
the power transformers in the industrial
substations of the samples distribution networks.
As shown in Fig. 9, Transformers T1 and T3 in
the Agbara/Badagry injection substation in the
Agbara distribution network of Lagos City were
loaded to 118% and 104% respectively in 2011
of the rated capacities. Similarly, Transformers
T4, T15, T16 and T27 (Fig. 10) in the Sabon
Gari/Dakata injection substation of Sabon Gari
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
10
electricity distribution network in Kano City were
loaded to 142%, 239.5%, 159.5% and 120.7% of
the rated capacities respectively during the same
period. However, as shown in Fig. 11, the
transformers in the Akanni/Trans-Amadi injection
substation in the Port Harcourt distribution
network were loaded within limits of the rated
capacities during the period covered by the
study. High power losses have been traced to
overloaded power transformers [4-6]. It is
obvious that the relatively low power losses
reported in the Port Harcourt distribution network
is due to controlled loads on the power
transformers.
There is urgent need therefore to reduce the
existing loads and ensure balanced loading on
the overloaded transformers in the Agbara/
Badagry and Sabon Gari / Dakata injection
substations in the Agbara and Sabon Gari
distribution networks in Lagos and Kano cities
respectively so as to minimise power and energy
loss levels and consequently achieve improved
electricity supply reliability in the areas covered
by the affected distribution network substations.
Besides its negative impact on Utility companies
turn-over, high distribution losses are known to
scare potential investors away from investing in
the power sector [1,2,12].
Fig. 8. Average power losses in Akanni/Trans-Amadi for 2011-2015
Fig. 9. MVA loading of power transformers in Agbara/Badagry in 2011
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
11
Fig. 10. MVA loading of power transformers in Sabon Gari/Dakata in 2011
Fig. 11. MVA loading of power transformers in Akanni/Trans-Amadi in 2011
5. CONCLUSION
This work employed the Newton-Raphson Power
Flow technique on the ETAP 12.6 software and
evaluated technical losses in the distribution
networks of the three major industrial Cities in
Nigeria namely Lagos, Kano and Port Harcourt.
Results of the study showed that between 2011
and 2015 covered by the study, the Eko
electricity distribution network in Lagos recorded
a total power loss of 15.8 MW, the Sabon Gari
electricity distribution network in Kano reported
36.2 MW while the Port Harcourt distribution
network reported 6.04 MW. The results of the
simulation further reveal that a significant number
of power transformers in the Agbara/Badagry
and the Sabon Gari/Dakata injection substations
are overloaded well beyond their rated values
thus contributing to high power losses in the host
distribution networks.
This paper recommends that weak electrical
facilities in the distribution network should be
identified and strengthened to make them
function better. Shunt capacitors should also be
installed at appropriate points in the network in
order to improve the system power factor. It is
necessary to ensure reduction in the length of
low tension transmission lines by relocating the
existing distribution substations. Old conductors
and distribution lines/cables should be promptly
disposed of, only conductors and lines of
appropriate sizes should be in use. Lengthy
distribution lines cause high technical losses and
must be avoided. Efforts should be made to
avoid overloading of the feeders by ensuring
balanced loads at all times. Transformers are
Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910
12
responsible for almost half of network losses, it is
advisable therefore to reduce the number of
transformers in use. Using fewer but highly
efficient transformers can make a significant
impact on reduction of technical losses. Besides
serving as a guide for utility companies in
providing for prioritization and system upgrade to
ensure improved efficiency of their distribution
networks, the outcome of this research would
find relevance among policy makers and
researchers especially system planners at the
distribution subsystem of power sectors.
COMPETING INTERESTS
Authors have declared that no competing
interests exist.
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_________________________________________________________________________________
© 2016 Amadi et al.; This is an Open Access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited.
Peer-review history:
The peer review history for this paper can be accessed here:
http://sciencedomain.org/review-history/16740

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Evaluation of losses in distribution networks of selected industrial cities in nigeria using etap

  • 1. _____________________________________________________________________________________________________ *Corresponding author: E-mail: amadihachy@gmail.com; British Journal of Applied Science & Technology 17(6): 1-12, 2016, Article no.BJAST.29910 ISSN: 2231-0843, NLM ID: 101664541 SCIENCEDOMAIN international www.sciencedomain.org Evaluation of Losses in Distribution Networks of Selected Industrial Cities in Nigeria Using ETAP Hachimenum N. Amadi1* , Fabian I. Izuegbunam1 and Ephraim N. C. Okafor1 1 Department of Electrical and Electronic Engineering, Federal University of Technology, Owerri, Nigeria. Authors’ contributions This work was carried out in collaboration between all authors. Author HNA designed the study, performed the statistical analysis, wrote the protocol, wrote the first draft of the manuscript and managed the literature searches. Authors FII and ENCO managed the analyses of the study, literature searches and improved the final manuscript. All authors read and approved the final manuscript. Article Information DOI: 10.9734/BJAST/2016/29910 Editor(s): (1) Chien-Jen Wang, Department of Electrical Engineering, National University of Tainan, Tainan, Taiwan. Reviewers: (1) A. Ayeshamariam, Khadir Mohideen College, India. (2) Abubakar Yakubu, Kebbi University of Science & Tech, Aliero, Nigeria. (3) Rajinder Tiwari, Amity University, Lucknow, India. Complete Peer review History: http://www.sciencedomain.org/review-history/16740 Received 3 rd October 2016 Accepted 25th October 2016 Published 29 th October 2016 ABSTRACT Distribution losses contribute to energy shortages and therefore power outages in Nigeria’s industries. This work evaluated the technical losses in the distribution networks of selected industrial cities in Nigeria. Power flow simulation of network data collected over the period 2011-2015 from three distribution companies (DisCos) domiciled in these cities was done by Newton-Raphson (N-R) technique using the Electrical Transient and Analysis Program (ETAP) software version 12.6. Results of the power flow simulation showed that between 2011 and 2015 covered by the study, the cities of Lagos, Kano and Port Harcourt recorded a total power loss of 15.8 MW, 36.2 MW and 6.04 MW respectively. The findings also revealed that overloaded power transformers is part of the reasons for high losses in the distribution networks of some of the cities. The outcome of the study provides a guide for system planners and utility companies in providing for prioritization and system upgrade to ensure improved efficiency of their distribution networks. Original Research Article
  • 2. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 2 Keywords: Electricity distribution; distribution losses; distribution networks; energy shortages; power losses; substations; transformers. 1. INTRODUCTION The number of power outages in a given locality per year is an indication of the efficiency of power supply even as consumer dissatisfaction with electricity service is often linked to high level of outages [1-2]. Since the more the number of power outages, the less efficient the power system, it follows that given higher system losses (technical and non-technical), there would be more power outages indicating the inefficiency of the system. The biggest challenge confronting the Nigeria’s distribution sector presently is the level of distribution losses namely technical, commercial and collection losses (Fig. 1). Technical losses are due to the nature of the components in use in the network, commercial losses refer to energy not billed for, and collection losses signify energy billed but not paid for. When the distribution companies were privatised as part of the power sector reform process by the Nigeria government, the transactions assumed some particular loss levels. After the asset hand-over, however, it became clear that the losses were much higher than had been estimated. In 2014, ~46% of energy was lost through technical (12%), commercial (6%), and collection losses (28%) [3]. Over the years, scholars and researchers have attributed power outages to: Weak grid and outdated power stations, equipment overloading, inadequate compensation equipment on the system, weather and tree related factors, vandalism, poor maintenance culture, etc. [1,4,5,6]. No researcher known to this study, however, has focused on the effects of distribution losses on electricity supply failures in the Nigeria industrial sector. It is imperative therefore to undertake an assessment of the losses in the nation’s electricity distribution network in order to recommend viable and long-lasting solutions to the perennial problem of system induced power outages among industries in Nigeria. This forms the research gap which the outcome of this work tends to bridge by creating a fresh awareness among stakeholders in the power sector about the need for proactive measures towards minimizing recurrent system induced losses by ensuring improved efficiency of the country’s distribution network. The resulting reliable and adequate electricity supply to the industrial sector will make the sector more vibrant thereby growing the country’s gross domestic product (GDP) and creating more employment opportunities for the nation’s teeming populace. 2. OVERVIEW OF THE SAMPLED DISTRIBUTION NETWORKS 2.1 Eko Distribution Network The Eko distribution network shown in Fig. 2 comprises of the Agbara and Badagry Injection substations both of which are supplied from the 2 x 45 MVA, 132/33/11 KV transformer transmission substation at the load centre. The Agbara Injection substation rated 2 x 15 MVA, 33/11 KV feeds Beecham, Evans, OPIC, and other 11 KV outgoing feeders while the Badagry Injection substation rated 15 MVA, 33/11 KV feeds Unilever, P&G, Nestle and Guinness industrial feeders. 2.2 Kano Electricity Distribution Network The Kano Electricity Distribution network shown in Fig. 3 comprises of the Sabon Gari and Dakata injection substations. The 30 MVA, 132/33/11 KV transformer transmission substation at the load centre supplies electricity to the Sabon Gari 2 x 15 MVA, 33/11 KV injection substation which in turn feeds Fagge, Sabon Gari, Abuja 11 KV outgoing feeders among others. The Dakata 3 x 15 MVA, 33/11 KV Injection substation feeds: Independence, Brigade, Bompia, Flour Mill and other 11 KV outgoing feeders. The Murtala outgoing feeder radiated from a 60 MVA, 33/11 KV injection substation while Gezawa is supplied directly from same 30 MVA, 132/33/11 KV substation as the Sabon Gari injection substation. 2.3 Port Harcourt Distribution Network The Port Harcourt Electricity Distribution network shown in Fig. 4 comprises of the Trans-Amadi and Akanni injection substations. Both the Akanni and Trans-Amadi injection substations are supplied from the Port Harcourt Mains transmission lines via 60 MVA, 132/33/11 KV transformer transmission substation at the load centre. The Akanni 2 x 15 MVA, 33/11 KV
  • 3. Injection substation then feeds: Rumuogba, Glass Factory, Old Aba Road and Rumurolu 11KV outgoing feeders. The Trans- MVA, 33/11KV injection substation feeds: Rivoc, Nda Bros, Water Works and Fimie 11KV outgoing industrial feeders. 3. METHODOLOGY Data and diagrams on the sampled distribution networks were collected from the three electricity distribution companies located in Nigeria’s three major industrial cities under review. The distribution companies are: Eko Electricity Distribution Company (EKEDP) in Lagos city for Fig. 1. Level of distribut Fig. 2. ETAP view of the Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no. 3 Injection substation then feeds: Rumuogba, Glass Factory, Old Aba Road and Rumurolu -Amadi 2 x 15 n feeds: Rivoc, Nda Bros, Water Works and Fimie 11KV Data and diagrams on the sampled distribution networks were collected from the three electricity distribution companies located in Nigeria’s three major industrial cities under review. The distribution companies are: Eko Electricity KEDP) in Lagos city for the Agbara distribution network, Kano Electricity Distribution Company (KEDCO) in Kano city for the Sabon Gari distribution network and the Port Harcourt Electricity Distribution Company (PHEDCO) in Port Harcourt city for the Port Harcourt distribution network. In Lagos, seven industrial feeders supplied from the Agbara injection substation were considered. The industrial feeders studied are Beecham, Evans, OPIC, Unilever, Nestle, P&G and Guinness. In Kano, nine industrial feeders under the Sabon Gari Injection substation were investigated. These are Abuja, Sabon-Gari, Fagge, Murtala, Flour Mill, Independence, Brigade and Bompia. In Port Harcourt, eight industrial feeders from two Fig. 1. Level of distribution losses in Nigeria in 2014 [3] the Agbara/Badagry injection substations in Lagos Article no.BJAST.29910 the Agbara distribution network, Kano Electricity Distribution Company (KEDCO) in Kano city for the Sabon Gari distribution network and the Port Harcourt Electricity Distribution Company (PHEDCO) in Port Harcourt city for the Port arcourt distribution network. In Lagos, seven industrial feeders supplied from the Agbara injection substation were considered. The industrial feeders studied are Beecham, Evans, OPIC, Unilever, Nestle, P&G and Guinness. In der the Sabon- Gari Injection substation were investigated. Gari, Fagge, Murtala, Flour Mill, Independence, Brigade and Bompia. In Port Harcourt, eight industrial feeders from two in Lagos
  • 4. Fig. 3. ETAP view of the Fig. 4. ETAP view of the Akanni/Trans injection substations namely Akani and Trans Amadi injection substations were studied. These are: Rumuogba, Glass Factory, Old Aba Road Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no. 4 the Sabon-Gari/Dakata injection substations in Kano Akanni/Trans-Amadi injection substations in Port Harcourt injection substations namely Akani and Trans- Amadi injection substations were studied. These Rumuogba, Glass Factory, Old Aba Road and Rumurolu industrial feeders under Akani injection substation and Rivoc, Nda Works and Fimie industrial feeders supplied from Article no.BJAST.29910 in Kano in Port Harcourt and Rumurolu industrial feeders under Akani injection substation and Rivoc, Nda Bros, Water Works and Fimie industrial feeders supplied from
  • 5. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 5 the Trans-Amadi Injection substation. The data collected include: (i) List of all transformers connected to the injection substations and their ratings. (ii) Monthly maximum loading on the feeders for the period 2011- 2015. (iii) Feeder route length. (iv) Sizes and ratings of conductors used for feeders. These data were subsequently simulated on the Electrical Transient and Analysis Program (ETAP) software version 12.6 and the simulation results used in the computation of the technical power losses in the respective distribution networks. The power flow simulation also evaluated the level of loading of power transformers installed at the injection substations under review. This paper chose to perform the power flow simulation on the ETAP 12.6 software program owing to its fully graphical electrical transient and analysis capabilities. 3.1 Mathematical Formulation of Newton- Raphson Powerflow Equations for Distribution System The Newton-Raphson formulates and solves iteratively the following power flow equation:       ∆ ∆ Q P       JJ JJ 43 21 =       ∆ ∆ V δ (1) Where P∆ and Q∆ are bus real power and reactive power mismatch vectors between specified value and calculated value, respectively; V∆ and δ∆ represent bus voltage magnitude vectors and angle in an incremental form; and J1 through J 4 are called Jacobian matrices. The Newton-Raphson method has the attribute of fast convergence and is highly dependent on the bus voltage initial values. The convergence criteria for the Newton-Raphson method are typically set to 0.001 MW and Mvar. A careful selection of bus voltage initial values is strongly recommended. Before running load flow using the Newton-Raphson method, ETAP makes a few Gauss-Seidel iterations to establish a set of sound initial values for the bus voltages. The Newton-Raphson method is often preferred for use with most systems. The Newton-Raphson method can be applied to the power flow studies when the bus voltages are expressed in polar form. The active and reactive power at each bus are functions of magnitudes of phase angles of bus voltages [7]. Thus ),( 1 VfPi δ= (2a) |)|,( 2 VfQi δ= (2b) For a system of n buses and bus 1 designated as slack bus, the equations which relate the changes in active and reactive power to changes in bus voltage magnitude and angles take the form [7], || ||22 V V PP P p n p p i p n p p i i ∆ ∂ ∂ +∆ ∂ ∂ =∆ ∑∑ == δδ (3a) ∑∑ == ∆ ∂ ∂ +∆ ∂ ∂ =∆ n p p p i p n p p i i V V QQ Q 22 || ||δδ (3b) Pi ∆ and Qi ∆ represent the differences between the specified and the calculated values of Pi and Q i . Replace ||V∆ by || || V V∆ in Eq. (3), the resulting equation becomes: || || || ||22 V V V PP P p p p n p i p n p P i i V ∆ ∂ ∂ +∆ ∂ ∂ =∆ ∑∑ == δδ (4a) || || || ||22 V V V V QQ Q p p p n p p i p n p p i i ∆ ∂ ∂ +∆ ∂ ∂ =∆ ∑∑ == δδ (4b) The set of equations (4) for all the n-1 buses can be written in the following matrix form,       ∆ ∆ Q P =       LJ NH         ∆ ∆ V V δ (5) The real and apparent powers at the buses are expressed as: )cos( 1 δγδ pipip n p ipii VYVP −−= ∑= (6a) )sin( 1 δγδ pipip n p ipii VYVQ −−= ∑= (6b)
  • 6. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 6 The incremental values of these powers are as follows: )()( calculated i specified ii PPP −=∆ (7a) )()( calculatedspecified QQQ iii −=∆ (7b) The elements of the Jacobian are written as, When ip ≠ ebfaLH ipipipip −== (8a) fbeaJN ipipipip +=−= (8b) When ip = BVQH iiiii i 2 −−= (9a) GVPN iiiii i 2 += (9b) GVPJ iiiii i 2 −= (9c) BVQL iiiii i 2 −= (9d) The Newton-Raphson algorithm for power flow studies [7] is outlined as follows: 1. Assume ||Vi and δi at all PQ buses and δi at all PV buses. In the absence of any other information assume ||Vi at all PQ buses equal to 1 pu and δi at all buses equal to zero. 2. Calculate Pi and Q i for all PQ buses and Pi for all PV buses (except the slack bus) using the equations (5) 3. Calculate Pi ∆ and Q i ∆ for all PQ buses and Pi ∆ for all PV buses (except the slack bus) by using the equations (6) 4. Calculate the elements of Jacobian using Equations. (7) and (8) 5. Solve (4) for δ∆ and || || V V∆ 6. Update the values of voltage magnitudes and phase angles for all PQ buses and the values of phase angles for all PV buses. 7. Calculate Q i for all PV buses and check QQQ iii max,min, << . If yes, return to Step 2 and start the next iteration. If not, set Q i equal to Qi min, or Qi max, as the case may be and treat this bus as a PQ bus, return to Step 2 and start the next iteration. 8. Continue till Pi ∆ and Qi ∆ at all PQ buses and Pi ∆ at all PV buses are within prescribed (or assumed) tolerance. 9. Calculate line flows and slack bus powers. The flow chart for Newton-Raphson method using polar co-ordinates is given in Fig. 5. 4. RESULTS AND DISCUSSION 4.1 Power Losses in the Distribution Networks Tables 1 - 3 shows the maximum power losses due to the injection substations of the sampled distribution networks. During the period 2011- 2015 covered by the study, the Agbara/Badagry Injection substation in the Agbara distribution network in the city of Lagos showed a maximum power loss of 15.8 MW (Table 1). During the same period, the Sabon Gari/Dakata Injection substation in Sabon Gari distribution network in Kano City recorded a maximum power loss of 36.2 MW (Table 2) while the Akanni/Trans-Amadi Injection substation in the Port Harcourt distribution network in the Port Harcourt City showed maximum power loss of 6.04 MW (Table 3). It is obvious from the Tables therefore that the power losses in each network increased yearly. This phenomenon is attributable to yearly increases in load and number of overloaded transformers and other distribution components due to lack of regular inspection, preventive maintenance and absence of infrastructure upgrade [4-6]. As can be observed from the Tables also, the highest maximum average power losses during the 2011-2015 period occurred on Gezewa feeder in the Kano distribution network, while the least values were reported on the Rumurolu feeder in the Port Harcourt distribution network. The high value of power loss (16.17 MW as shown in Table 2) on the Gezawa feeder is
  • 7. attributable to the significant length of the feeder (405 Km). Recent studies [1,8] have shown that Fig. 5. Flow chart for load flow studies using Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no. 7 attributable to the significant length of the feeder (405 Km). Recent studies [1,8] have shown that the longer the distribution feeder lines, the more the power that gets dissipated due to I Fig. 5. Flow chart for load flow studies using Newton-Raphson method in polar co-ordinates [7] Article no.BJAST.29910 the longer the distribution feeder lines, the more gets dissipated due to I 2 R losses. method in polar
  • 8. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 8 Other factors that could be responsible for the differences in the power losses in the sampled distribution networks are increase in load, lack of good maintenance culture, aging, pattern of energy use, load density, high rate of illegal connection to the feeder resulting to overloading and then capability and configuration of the distribution system that vary for various system elements [1,9,10,11]. Figs. 6-8 show the average power losses in the respective injection substations during the 2011-2015 period. Table 1. Maximum power losses in Agbara/Badagry per year Feeder Maximum power loss (MW) Power loss (MW) 2011-2015 2011 2012 2013 2014 2015 Unilever 0.36 0.40 0.49 0.65 0.84 2.74 Evans 0.14 0.22 0.35 0.53 0.76 2.0 P&G 0.23 0.36 0.45 0.60 0.82 2.46 Beecham 0.17 0.24 0.37 0.56 0.79 2.13 Nestle 0.12 0.18 0.29 0.51 0.74 1.84 OPIC 0.42 0.47 0.54 0.69 0.88 3.0 Guinness 0.11 0.15 0.27 0.49 0.62 1.64 Total 1.55 2.02 2.76 4.03 5.45 15.8 Table 2. Maximum power loss in Sabon Gari/Dakata per year Feeder Maximum power loss (MW) Power loss (MW) 2011-20152011 2012 2013 2014 2015 Sabon Gari 0.25 0.52 0.64 0.74 0.83 2.98 Independence 0.23 0.50 0.62 0.68 0.78 2.77 Abuja 0.14 0.25 0.39 0.43 0.56 1.77 Fagge 0.18 0.3 0.44 0.5 0.57 1.99 Gezewa 1.63 2.21 3.22 4.1 5.01 16.17 Brigade 0.29 0.58 0.68 0.85 0.90 3.3 Flour Mill 0.48 0.65 0.84 0.87 1.47 4.32 Bompai 0.1 0.2 0.31 0.39 0.41 1.41 Murtala 0.13 0.22 0.34 0.37 0.43 1.49 Total 3.43 5.43 7.48 8.93 10.96 36.2 Table 3. Maximum power losses in Akanni/Trans-Amadi per year Feeder Maximum power loss (MW) Power loss (MW) 2011-20152011 2012 2013 2014 2015 Glass Factory 0.14 0.145 0.23 0.30 0.32 1.135 Rumuogba 0.008 0.110 0.112 0.12 0.13 0.48 Rumurolu 0.007 0.105 0.107 0.019 0.05 0.288 Water Works 0.009 0.112 0.115 0.1 0.12 0.456 Nda Bros 0.10 0.116 0.118 0.13 0.15 0.614 Famie 0.11 0.124 0.14 0.15 0.21 0.734 Rivoc 0.15 0.155 0.28 0.37 0.39 1.345 Old Aba Rd 0.13 0.135 0.19 0.26 0.27 0.985 Total 0.66 1.00 1.29 1.45 1.64 6.04
  • 9. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 9 Fig. 6. Average power losses in Agbara/Badagry for 2011-2015 Fig. 7. Average power losses in Sabon Gari/Dakata for 2011-2015 4.2 Power Transformer Percentage MVA Loadings in the Distribution Networks Figs. 9 -11 show the MVA loadings of some of the power transformers in the industrial substations of the samples distribution networks. As shown in Fig. 9, Transformers T1 and T3 in the Agbara/Badagry injection substation in the Agbara distribution network of Lagos City were loaded to 118% and 104% respectively in 2011 of the rated capacities. Similarly, Transformers T4, T15, T16 and T27 (Fig. 10) in the Sabon Gari/Dakata injection substation of Sabon Gari
  • 10. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 10 electricity distribution network in Kano City were loaded to 142%, 239.5%, 159.5% and 120.7% of the rated capacities respectively during the same period. However, as shown in Fig. 11, the transformers in the Akanni/Trans-Amadi injection substation in the Port Harcourt distribution network were loaded within limits of the rated capacities during the period covered by the study. High power losses have been traced to overloaded power transformers [4-6]. It is obvious that the relatively low power losses reported in the Port Harcourt distribution network is due to controlled loads on the power transformers. There is urgent need therefore to reduce the existing loads and ensure balanced loading on the overloaded transformers in the Agbara/ Badagry and Sabon Gari / Dakata injection substations in the Agbara and Sabon Gari distribution networks in Lagos and Kano cities respectively so as to minimise power and energy loss levels and consequently achieve improved electricity supply reliability in the areas covered by the affected distribution network substations. Besides its negative impact on Utility companies turn-over, high distribution losses are known to scare potential investors away from investing in the power sector [1,2,12]. Fig. 8. Average power losses in Akanni/Trans-Amadi for 2011-2015 Fig. 9. MVA loading of power transformers in Agbara/Badagry in 2011
  • 11. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 11 Fig. 10. MVA loading of power transformers in Sabon Gari/Dakata in 2011 Fig. 11. MVA loading of power transformers in Akanni/Trans-Amadi in 2011 5. CONCLUSION This work employed the Newton-Raphson Power Flow technique on the ETAP 12.6 software and evaluated technical losses in the distribution networks of the three major industrial Cities in Nigeria namely Lagos, Kano and Port Harcourt. Results of the study showed that between 2011 and 2015 covered by the study, the Eko electricity distribution network in Lagos recorded a total power loss of 15.8 MW, the Sabon Gari electricity distribution network in Kano reported 36.2 MW while the Port Harcourt distribution network reported 6.04 MW. The results of the simulation further reveal that a significant number of power transformers in the Agbara/Badagry and the Sabon Gari/Dakata injection substations are overloaded well beyond their rated values thus contributing to high power losses in the host distribution networks. This paper recommends that weak electrical facilities in the distribution network should be identified and strengthened to make them function better. Shunt capacitors should also be installed at appropriate points in the network in order to improve the system power factor. It is necessary to ensure reduction in the length of low tension transmission lines by relocating the existing distribution substations. Old conductors and distribution lines/cables should be promptly disposed of, only conductors and lines of appropriate sizes should be in use. Lengthy distribution lines cause high technical losses and must be avoided. Efforts should be made to avoid overloading of the feeders by ensuring balanced loads at all times. Transformers are
  • 12. Amadi et al.; BJAST, 17(6): 1-12, 2016; Article no.BJAST.29910 12 responsible for almost half of network losses, it is advisable therefore to reduce the number of transformers in use. Using fewer but highly efficient transformers can make a significant impact on reduction of technical losses. Besides serving as a guide for utility companies in providing for prioritization and system upgrade to ensure improved efficiency of their distribution networks, the outcome of this research would find relevance among policy makers and researchers especially system planners at the distribution subsystem of power sectors. COMPETING INTERESTS Authors have declared that no competing interests exist. REFERENCES 1. Amadi HN, Okafor ENC. The effects of technical and non-technical losses on power outages in Nigeria. International Journal of Scientific and Engineering Research. 2015;6:9. 2. The World Bank. Reducing Technical and Non‐Technical Losses in the Power Sector. Background Paper for the World Bank Group Energy Sector Strategy, Jul; 2009. 3. Nigeria Power Baseline Report. Report Developed by the Advisory Power Team, Office of the Vice President, Federal Government of Nigeria in Conjunction with Power Africa; 2015. 4. Udoh BE. The causes and effect of electric power outages in the North East Zone of Nigeria, using Mubi in Adamawa State as a case study. International Journal of Industrial Electronics and Electrical Engineering. 2014;2:2. 5. Samuel I, Katende J, Ibikunle F. Voltage Collapse and the Nigerian National Grid, EIE’s 2nd Intl’ Conf. Comp., Energy, Net., Robotics and Telecom. eie Con; 2012. 6. Lave L, Apt J, Morgan G. Worst Case Electricity Scenarios: The Benefits & Costs of Prevention. CREATE Symposium. University of South California, Aug; 2005. 7. Gupta BR. Power System Analysis and Design. 6th . ed. New Delhi: S. Chand & Company; 2011. 8. Mufutau WO, Jokojeje RA, Idowu OA, Sodunke MA. Technical power losses determination: Abeokuta, Ogun State, Nigeria Distribution Network as a Case Study. IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE). 2015;10(6):1-10. 9. Kapali D, Gope G. An investigation on the effects of feeder outages and non-linear loads on 11 kV ring distribution network efficiency. PROGRESS Multidisciplinary Research Journal. 2011;1:1. 10. Haque R. Transmission Loss Allocation Using Artificial Neural Networks. MSc. Thesis. University of Saskatchewan, Saskatoon, Saskatchewan; 2006. 11. Sun DIH, Abe S, Shoults RR, Chen MS, Eichenberger P, Farris D. Calculation of energy losses in a distribution system, IEEE transactions on power apparatus and systems. 1980;PAS-99:4. 12. Nguyen TC, Bridle R, Wooders P. A financially sustainable power sector: Developing assessment methodologies. The International Institute for Sustainable Development. Mar; 2014. _________________________________________________________________________________ © 2016 Amadi et al.; This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Peer-review history: The peer review history for this paper can be accessed here: http://sciencedomain.org/review-history/16740