Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
Efficient Power Flow on Direct Current Transmission Lines Using the Load and
Component Sizing Technique
Igbogidi, O. N., *Amadi, H. N.
Department of Electrical Engineering, Rivers State University, Port Harcourt, Nigeria
Corresponding Author
E-Mail Id: hachimenum.amadi@ust.edu.ng
ABSTRACT
Due to losses, hazards and cost implications inherent in the use of alternating current
systems, the benefits surrounding the use of direct current are so large that it is imperative to
explore the technology of direct current, especially on transmission lines. The use of direct
current has become so attractive with its attendant benefits and that is the reason a 132kV
direct current transmission line from Afam power station to Port Harcourt Mains was
proposed. A bipolar direct current link was designed between Afam and Port Harcourt Mains
with full utilization of load and component sizing mathematical approach embedded in
Electrical Transient Analyzer Program (ETAP) 19.0.1 software. Load flow analysis was
conducted on the network after design where buses 1, 2, 3 and 4 maintained total loads of
31.557MW, 31.401MW, 31.341MW and 31.123MW with a total generation of 31.431MW and
a total load demand of 31.123MW, the line still having the capacity to evacuate more energy.
The design has proven to be valid and is sufficiently adequate. Furthermore, it encourages
migration from alternating current mode to direct current mode at some point as no
significant losses are observed.
Keywords: Direct current, bipolar direct current link, Power flow, load and component
sizing technique, power quality
INTRODUCTION
The transmission and distribution of
electricity in the form of direct current
electricity are historically linked to the late
19th century [1], though with less
efficiency because the possibility of
stepping up the already generated low
voltage was not easy. It became very
obvious that alternating current was
accepted after all, less power loss occurred
and generated low voltage could as well be
transformed to higher voltages.
Based on the said advantages, the
generation, transmission and distribution
of electricity have been based on
alternating current technology. All over the
world electricity has been seen as a very
important driver of the economy in all
areas and therefore, the power system has
been developed vastly over the years.
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Nowadays, electricity in large quantities
can always be transmitted to distant areas
i.e. from remote power stations to urban
load centres. The disadvantage of relying
solely on alternating current electricity is
the problem of voltage instability and
voltage regulation constraints. The first
commercial or large size of high voltage
direct current transmission link was of a
monopolar configuration with sea return
connecting the Swedish mainland and the
Island of Gotland with ratings as 20 MW,
200 A and 100 kV. The link came into
being in 1954 [2]
Electricity is vital to socioeconomic and
technological advancements as
acknowledged
by
the
Millennium
Development Goals and the World
Summit on Sustainable Development [3].
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
For a nation to advance technologically,
electricity must be sufficiently available to
satisfy all loads connected to it or planned
to be connected to it. Several commitments
depend on the power systems to drive the
economy for the benefit of mankind
without which the nation will be behind
the time technologically.
Such that depend on electricity to function
may include water, education, charging of
mobile
phones
and
computers,
entertainment,
sanitation,
lighting,
healthcare, communication, etc. [4]. In any
case, electricity can be in the form of
alternating current or direct current. Each
of the systems has a standardized order or
specifications to follow to produce the
most reliable power system. Generally,
high-voltage direct current systems are
preferred over alternating current systems
when long distances are considered [5].
Transmission and distribution lines
connect generation stations to the
consumers. For economic reasons, power
is usually transmitted from generating
stations at high voltages over a long
distance to high-load centres and after that
distributed to various substations at
various locations through distribution lines
[6]. The construction of the various
substations depends largely on available
resources. Based on the attendant
advantages of direct current systems over
alternating current systems, a 10 km high
voltage direct current link from Afam
power station to Port Harcourt mains
transmission station was proposed. The
proposed HVDC line is rated 132kV. The
intention is to design a system that will
allow for an efficient flow of power
irrespective of the fact that generation and
distribution are alternating current
systems.
RELATED WORKS
The operation or implementation of a
direct current 132 kV transmission line
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usually requires the involvement of high
voltage power cables usually installed
underground or suspended on tall or high
transmission towers. Towers designed for
direct current transmission lines are always
taller and smaller in number than the ones
found on alternating current transmission
lines. Direct current systems can be used
over a long distance without intermediate
transformation points. HVDC transmission
lines stand very tall in modern power
transmission systems as efficient and
reliable transfer of bulk power over a long
distance is possible.
Several substations and power components
that are capable to transform and maintain
the different voltage levels are usually
installed between the generation stations
and the power supply users [8]. Electricity
is always generated at low voltages and
not at high voltages. Due to losses inherent
in the transmission of power, it is
comparatively better and more economical
to transmit power at high voltages.
Consumers are supplied with power at low
voltages [7].
It is possible to choose between high
voltage direct current and high voltage
alternating current for transmission of
power. In any case, several reasons and
intentions play major roles under different
conditions in deciding which one to adopt
or to use a hybrid system.
Every high voltage direct current
transmission system has its peculiar
reasons why it is intended. Some of the
reasons are technical which may include:
asynchronous
connection,
increased
system reliability, high controllability,
inadequate short circuit current, small
corona loss and radio interference, small
potential stress, small reactive power need,
fast change of power flow, etc. Economic
reasons for the choice of HVDC are less
investment cost, simplicity and cheap,
reduced losses, stage construction and
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
environment friendly, etc. with little
constraints such as converters being
relatively high in price, high converter
reactive
power
needs,
converters
generation of harmonics by converters, etc.
Specifically speaking, loss levels increase
with distance in a high-voltage AC system
than in a DC system.
High voltage direct current transmission
line design anchors on several factors such
as transmission voltage, sag and tension,
location of the line, conductor type and
size, line supports and cross-arms, span,
configuration of conductor, spacing and
clearance, insulation, etc. Mechanical
strength and electrical properties are
important factors in the design of the
HVDC system when selecting insulators
[9].
The grid or earth mat is placed in the earth
at each terminal for the protection of the
equipment from over voltages and for the
safety of personnel by connecting the
equipment’s earth terminals and the
neutral of the converter transformers to the
earth mat without a known metallic link
between ground electrodes and earth grid.
Comparatively, a high-voltage direct
current system is cheaper than its
corresponding alternating current system
when used over a long distance referred to
as the break-even distance [10].
MATERIALS AND METHOD
Materials
Several data paramount and helpful in the
design of a hitch-free power flow were
made available. The design is a proposal of
a 132kV direct current transmission line
radiating from Afam to Port Harcourt
mains transmission station. All materials
connected to the design completion of an
operatable DC link were considered for the
design proposal.
Method
A trending mathematical formulation
known as the load and component sizing
method was utilized to accomplish the
design of the proposed 132kV direct
current transmission network from Afam
to Port Harcourt mains. A line measuring
about 10km and proposed to be of
Aluminium Conductors Steel Reinforced
(ACSR). Existing equipment capacities
and proposed equipment capacities are all
captured accordingly.
Table 1: Data Considered for the HVDC Line Design [11].
S/No Parameter
Dimensions/UNITS
1
132kV Transmission line route length (Afam to PH) 10km
2
Afam Power Station Transformer T1
150MVA
3
Port Harcourt Mains Transformer T1
60MVA
4
132kV Line Peak Load
80MW
5
Type of Conductor
ACSR
6
Size of Conductor
350mm²
7
Resistivity of Conductor at 20°C
8
132kV Line spacing on 132kV Line
9
PF
10
Base MVA
Source: Transmission Company of Nigeria (TCN).
2.83x
0.8
100
-
Table 1 shows the materials for the proposed Afam/Port Harcourt Mains 132kV direct current
transmission line and is diagrammatically presented in Figure 1.
HBRP Publication Page 1-9 2024. All Rights Reserved
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
Fig. 1: Single Line Diagram of the Proposed Afam/Port Harcourt Mains 132kV Direct
Current Transmission Line [11].
3.3 Proposed Afam/Port Harcourt Mains 132kV Direct Current Transmission Line
According to Igbogidi et al. [11], for a cylindrical conductor with DC flowing round it, the
DC resistance is:
l
(1)
Where,
is conductor resistivity at a given temperature in
is conductor length in m
A is a conductor cross-sectional area in m²
Assuming cross-sectional area, A is
Diameter, d
Also
d
d
r
/m
(2)
(3)
r
(4)
From eqn. 3, the radius can be calculated thus:
r
d
(5)
Per kilometre reactance of one phase can be realized with:
log
r
HBRP Publication Page 1-9 2024. All Rights Reserved
(6)
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
where
is the geometric mean distance between the line conductors
r is considered as the radius of conductors
Line reactance X, is evaluated thus:
(7)
The distributed series impedance is:
=
j
(8)
The equivalent admittance may be realised thus:
j
(9)
The following may be realized from equation (9) as:
(10)
and
j
j
(11)
Where Base MVA and source impedance are already established, then
ource mpedance
ase
(12)
ault
If the line constants for the entire length of line
are established, then transmission
line constants with reference to base MVA in p.u can be realized thus:
(13)
ase
If
is the voltage at the sending end and
current may be taken as:
is the voltage at the receiving end the line
(14)
where R is the resistance of the complete transmission link.
The sending end voltage becomes:
*(
)
+
and the receiving end voltage becomes:
HBRP Publication Page 1-9 2024. All Rights Reserved
(15)
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
*(
)
+
where is the firing angle of rectifier, is
the extinction angle of inverter,
is the
ac side line-to-line rms voltage at the
sending end,
is the ac side line-to-line
(16)
rms voltage at the receiving end,
is the
commutation reactance at the sending end
and
is the commutation reactance at
the receiving end.
Then, the power transferred is thus:
watts
(17)
Transformer full load current may be realized thus:
(18)
A bipolar DC link after modelling was
simulated using Electrical Transient
Analyzer Program (ETAP) to validate the
power flow. This is synonymous with
alternating current environment and is
shown in Figure 2.
Fig. 2: Proposed Afam/Port Harcourt Mains 132kV Direct Current Transmission Line
Modelled in ETAP 19.0.1 Software [11].
HBRP Publication Page 1-9 2024. All Rights Reserved
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
RESULTS AND DISCUSSION
Results
The proposed Afam/Port Harcourt Mains
132kV direct current transmission line was
modelled using the Electrical Transient
Analyzer
Program
(ETAP)
19.0.1
software. The analysis was conducted to
ascertain how seamless power flow could
be and implemented in direct current mode
as it would have been in alternating current
mode without adversely been affected by
load and component placement.
Proposed Afam/Port Harcourt Mains
132kV Direct Current Transmission
Line Power Flow Result Summary
The results realized from the proposed
Afam/Port Harcourt Mains 132kV direct
current transmission line power flow are
contained in Table 2 and Table 3. Figure 3
shows bus loading in MW and Figure 4
shows generation and load demand curve
validation.
Table 2: Summary of Bus Loading.
Bus Total Bus Load (MW)
1
31.557
2
31.401
3
31.341
4
31.123
Fig. 3: Graph Showing Bus Loading.
Table 3: Summary of Generation and Load Demand.
Generation (MW) Static Load (MW)
31.431
31.123
HBRP Publication Page 1-9 2024. All Rights Reserved
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Journal of Research and Advancement in Electrical Engineering
Volume 7 Issue 1
DOI: https://doi.org/10.5281/zenodo.10617869
Fig. 4: Graph Showing Generation and Load Relationship.
CONCLUSION
There is a need to ascertain if load flow is
hitch-free in direct current mode,
especially on high voltage transmission
circuits i.e., the HVDC transmission line
being used for the transmission of high
voltage direct current. This was
domesticated in the Afam/Port Harcourt
Mains 132kV transmission line, a line
measuring about 10km and can evacuate
about 120MW. Most of the data needed for
this research were taken from the
Transmission Company of Nigeria (TCN).
The line was designed based on load and
component sizing principles and embedded
in the Electrical Transient Analyzer
Program (ETAP). After the acquisition of
all the needed data, a trending method
known as load and component sizing
mathematical formulation was used to
design a network known as the Afam/Port
Harcourt
132kV
direct
current
transmission line.
In the design, a bipolar DC link was
considered as its solution was embedded in
ETAP 19.0.1 software. The network was
subjected to a load flow scenario and it
was noted that buses 1, 2, 3 and 4
maintained total loads of 31.557MW,
31.401MW, 31.341MW and 31.123MW
where the total generation is 31.431MW
while load demand is 31.123MW. The
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power flow is seamless and without
friction. Load demand is worth less than
the generation. This depicts a perfect
power flow scenario. Such a system will
operate
without
power
quality
compromise.
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Federal University of Technology
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11. Igbogidi, O. N., Amadi, H. N.,
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Cite as :
Igbogidi, O. N., & Amadi, H. N. (2024).
Efficient Power Flow on Direct Current
Transmission Lines Using the Load and
Component Sizing Technique. Journal of
Research and Advancement in Electrical
Engineering,
7(1),
1–9.
https://doi.org/10.5281/zenodo.10617869
Page 9