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27
© 2024. The A uthor(s). Thi s is an open -acc ess ar ticle d istrib uted unde r the ter ms of the Cre ative Co mmons
Attribution-ShareAlike International License (CC BY-SA 4.0, http://creativecommons.org/licenses/by-sa/4.0/),
which pe rmits u se, distr ibutio n, and rep roduct ion in any me dium, pro vided th at the Ar ticle is proper ly cited .
Corresponding Author: Mykola Romaniuk; e-mail: mykolaromaniuk@ukr.net
1 Department of Electrical Engineering, Lutsk National Technical University, Lutsk, Ukraine; ORCID iD: 0000-
-0002-5944-8665; e-mail: nataliyakomenda@outlook.com
2 Department of Electrical Engineering, Lutsk National Technical University, Lutsk, Ukraine; ORCID iD: 0000-
-0002-9192-2785; e-mail: V.Volynets1973@outlook.com
3 Department of Electrical Engineering, Lutsk National Technical University, Lutsk, Ukraine; ORCID iD: 0000-
-0003-4472-306X; e-mail: iryna_hrytsiuk@hotmail.com
4 Department of Electrical Engineering, Lutsk National Technical University, Lutsk; ORCID iD: 0000-0003-2166-
-4909; e-mail: irina.bandura@hotmail.com
5 Department of Electrical Engineering, Lutsk National Technical University, Lutsk, Ukraine; ORCID iD: 0000-
-0002-1039-1004; e-mail: mykolaromaniuk@ukr.net
POLITYKA ENERGETYCZNA – ENERGY POLICY JOURNAL
2024 Volume 27 Issue 1 27–48
DOI: 10.33223/epj/175239
Nataliya 1, Vladyslav V2, Iryna H3, Irina B4,
Mykola R5
Estimation of the total inuence of methods
forincreasing the line natural load
: Studies aimed at the economically sound increase in the capacity of existing power lines and
improvements in their design are relevant today. In addition to the well-known design methods of
The basis of the methodological approach applied in this study is a qualitative combination of
methods of systematic analysis of ways to increase the capacity of power lines with the analytical
investigation of the prospects for its impact on wave resistance to increase the natural power of
-
28
-
analytical investigation, transmission capacity
Introduction
studies and is already a common reality (Zhang et al. 2023), which leads to a number of pres-
The changes concern all stages of interaction with electricity: production, distribution, and con-
sumption. Most items of Ukraine’s energy strategy until 2030 (Law No. 605… 2017) are aimed
at increasing generating capacity and improving electricity quality, but not much attention is paid
to electricity transmission and distribution, and especially new means of increasing transmission
capacity.
Currently, increasing the capacity transmitted over the network requires large investments.
As electricity consumption increases, grid companies have to renovate existing networks with
-
ally, companies will face the replacement of existing grid pylons with new alternatives designed
for higher loads, or the construction of new transmission lines. The latter can be complicated,
especially when the route of the overhead line (OHL) is located in densely populated areas and
sparsely populated areas of private lands, such as national parks, reserves, and other areas where
construction is prohibited (Deepak Selvakumar et al. 2023). Despite the extensive experience
and research by scientists in this subject area, decision-making in the design of power systems
recommendations and methods. This limits the ability to assess the technical and economic per-
decisions. As practice shows, the market relations that have developed between the subjects of
of transmission lines and the power system in general.
systems and transmission lines are crucial for several reasons. Power systems and transmission
lines are critical infrastructure components. Reliable operation is essential to prevent blackouts,
29
ensure continuous power supply, and maintain public safety. Clear recommendations help in
the designing of systems that meet these reliability requirements. The optimal design of power
systems and transmission lines can result in cost savings, reduced energy losses, and increased
-
evolving challenges and opportunities in the energy sector. Rapid technological advancements,
changing energy demands, and the need for sustainability require continuous research and deve-
this gap by providing a systematic and up-to-date approach for designing power systems and
systems that meet the demands of the modern world.
The main areas in improving the structure of the transmission line should primarily include
increasing the capacity of transmission lines and reducing losses from environmental impact and
utilities (Hasan and Agarwal 2023). However, the most urgent problem is the increase in trans-
for identifying shortcomings in transmission line designs, recent changes to which were made in
the late twentieth century. After all, the proposed solutions can often be aimed at solving a single
problem, rather than solving the problem comprehensively. A striking example is the attempt to
use new types of wires in combination with old support structures, or the use of simple methods
increase throughput can be divided into two most commonly used areas: design (change in com-
position, shape of the wire layout, use of reactive power compensators, lines made of second
generation superconductors) (Bondarenko and Lavrinovich 2007; Xiao et al. 2023); physical
(direct impact on natural power through more optimal solutions from the standpoint of physics,
context of existing energy challenges. As global populations and economies continue to expand,
there is an ever-increasing demand for electricity. To meet this demand, it is essential to enhance
the vulnerability of power grids. Enhancing transmission capacity can improve grid resilience by
The objective of this study is to develop a systematic approach for identifying the most ef-
-
hensive list of methods and techniques used for increasing the transmission capacity of power li-
30
nes. This should encompass both conventional and innovative approaches. Determine how each
1. Materials and methods
The study was conducted in three main stages.
-
line capacity.
The results of researches on the use of isolation in high-voltage wires, constructive changes
in resistance and use of wires with the increased thermal stability and conductivity were
considered.
singled out.
Means of synchronous compensation as a potentially promising means of increasing natural
At the second stage:
A detailed analytical investigation of the method of increasing transmission capacity by in-
troducing a layer of insulation for high-voltage wires was carried out.
In addition to the main properties, for which this method was considered, other quite signi-
process of impact on natural power.
The method of determining the optimal insulation thickness based on the heat balance equ-
ation was considered.
At the third stage:
was performed. To do this, the method of mirror mappings was adapted to calculate the line
voltage, and based on it, a number of simulation programs were built, which allowed calcu-
lating and generating the data necessary for further analysis.
above factors were constructed.
-
31
ting the line impedance was derived, which is considering most of the accepted factors and used
to calculate natural power and compare with the standard version of high-voltage power lines.
layer (presented in the form of a coaxial wire), with the line in the standard for modern design
activities.
2. Results
transmission line gave the following results. Based on equation (1), it is determined that the ef-
tage U in the grid is, conditionally, a constant. Then, according to equation (2), it becomes clear
parameters that make up the impedance: capacitance and inductance of the lines.
However, it was found that the common equation (2) for calculating the wave resistance of
-
ence. Therefore, a number of decisions were made to evaluate the proposed methods and the tran-
sition to equation (3); lines are represented by the ratio of the sum of the resistivity with the
22
2
.. .. 2
.
. ..
2
.. 0 0 ..
3 3 33
36
ph n ph n
nom
n ph n n ph n w
ww w
ph n w w ph n
UU
U
P U I U vC
z z vL
U qv v r U E
= = = = = =
= = πε
(1)
where:
Pn – natural power,
Uph.n. – nominal phase voltage,
In – nominal current,
zw – wave resistance,
Unom. – nominal linear voltage,
L – line inductance,
32
vw – wave conduction,
C – line capacity,
q – charge at the beginning of the line,
ε0 – the value of the electrical constant (8.8541878128·10),
r0 – radius of a single wire.
w
L
Z
C
= (2)
where:
Zw – wave resistance,
L – line inductance,
C – line capacity.
Because the equation of wave resistance, which expresses it as the root of the ratio of the
turn to the record given in (Leenders 2007):
00
00
w
r jx
Zg jb
+
=+ (3)
where:
x0 = ωL0
b0 = ωC0
r0
g0
ned by the expression: .
02
cr av
nom
P
gU
∆
=, where ∆Pcr.av – average annual loss per
crown.
calculate the corona losses:
( )
25
0
0
1350
2.31 1 10
e
k ee k
E
P k n f r E E E lg fr
−
=⋅⋅ ⋅ − ⋅ − ⋅
⋅
⋅ (4)
where:
n – the number of wires in phase,
f –
r0 – radius of a single wire,
33
Ek
Ee
k – weather ratio.
The equivalent voltage is found by the equation:
2
max av
e
EE
E
−
= (5)
Average voltage for split wire:
0
av
av
eq
U
ES
n r ln r
⋅
=
⋅
(6)
Maximum tension:
max y av
E kE⋅=
(7)
where:
( )
11
eq
y
s
r
kn
r
=+ −⋅ ; 1
0
n
n
eq s
r nr r
−
⋅= ⋅ – equivalent radius of a single wire having the
same capacitance as the split phase,
rs – split phase radius,
S – wire section.
The disadvantage of Mayer’s formula is that all the variety of weather conditions is reduced
to two groups of weather: “good” weather (k = 44; Ekk = 31.5;
Ek
for each weather group and then summed according to the duration of the group during the year:
4
1
k ki i
i
PP
=
∑= ⋅ψ
∑ (8)
where:
ψi – relative duration of the weather group,
Pki – average annual power losses of i-the weather group.
The use of ACCC, ASSR, ZTACIR, and Aero-Z (the abbreviations ACCC, ASSR, ZTACIR,
34
the throughput of the line due to their thermal and electrical performance (Selvakumar et al.
-
ties. This wire can improve throughput up to 2.5 times. It was found that the implementation of
Z-shaped wire weaving leads to improved natural cooling of the wire. Of great interest is the use
of insulated wires in high voltage lines. Among the advantages are increased thermal stability
strength, which increases the capacitance and leads to a decrease in impedance. Some studies
strength on the electrode surface is determined by the calculated charge density
0
i
i
E
σ
=ε and for
the distribution limits of dielectric media:
0
1
1
2
i
i
Eσ
= +
εα
(9)
where:
α – parameter related to the dielectric constant of adjacent media: α = (ε2 – ε1)/(ε2 + ε1).
True density σ′ charges on the surface of the core, which is insulated by a dielectric with
relative dielectric constant ε2, more than ε2
is in the air with dielectric constant ε1 = 1. The results of the calculation are shown in Figure 1.
Curve 1 – optimal insulation thickness (3.2 mm) and Curve 2 – 33% less than optimal (2.3 mm)
for shielded wire made of cross-linked polyethylene insulation: (relative dielectric constant)
ε2 = 2.3. Curve 3 – wire with oxide insulation 100 nm thick (relative dielectric constant ε2 = 9:
value of the relative dielectric constant is ε
is the stress distribution on the core surface, Section II (0.04–0.11) is on the insulation surface.
hence, on the capacitance of the line and on its natural power.
-
cessary to determine the impedance, and equation (3) is not able to take into account the changes,
because it is not intended for the calculation of insulated wires. To solve this problem, the study
(Fig. 2). The calculation of the impedance for the coaxial wire was presented in previous work
35
1
2
138
w
d
Z log d
k
= (10)
where:
k – dielectric constant of the insulating layer,
d1, d2 – outer and inner diameter of the coaxial wire.
on the surface of the wire
Note: SDL corresponds to the abbreviation “sum of DL” – the sum of many sections of short length
Fig. 2. Model of coaxial wire
36
-
re the wire is insulated is 14.9% more than for a similar line without insulation. However, for
-
plexity lies in the absence of an equation that would accurately describe the interaction of metal
-
wed shifting the vector of research towards the design features of the supports. To investigate
the impact of changes in the design features of transmission lines, the method of mirror images
the phase, and the splitting step. Modelling is performed and regularities are revealed, according
to which, the line capacity changes depending on the change of the above parameters. The co-
nvergence of phases was found, reducing the number of components and increasing the step of
cleavage. The simulation results for the 330 kV line is shown in Table 1.
1. The simulation results obtained in the program
d0a n iq Qmax iE Emax Ca Cb Cc Co Zv Pn
1 2 3 4 5 6 7 8 9 10 11 12 13
5 40 2 3 1.649 · 10–6 3 27.485 11.295 12.242 11.295 11.611 295.969 3.679 · 105
5 40 3 5 1.309 · 10–6 5 21.816 13.227 14.569 13.227 13.674 251.3 4.333 · 105
5 40 4 7 1.114 · 10–6 7 18.56 14.807 16.532 14.807 15.382 223.406 4.875 · 105
5 40 5 7 9.895 · 10–7 7 16.49 16.207 18.316 16.207 16.91 203.218 5.359 · 105
5 40 6 9 9.027 · 10–7 9 15.043 17.498 20 17.498 18.332 187.453 5.809 · 105
5 45 2 3 1.671 · 10–6 3 27.855 11.433 12.407 11.433 11.758 292.266 3.726 · 105
5 45 3 5 1.337 · 10–6 5 22.285 13.481 14.88 13.481 13.947 246.383 4.42 · 105
5 45 4 7 1.144 · 10–6 7 19.071 15.188 16.987 15.188 15.774 217.852 4.999 · 105
5 45 5 7 1.023 · 10–6 7 17.042 16.671 18.918 16.671 17.42 197.265 5.52 · 105
5 45 6 9 9.378 · 10–7 9 15.629 18.067 20.754 18.067 18.963 181.219 6.009 · 105
5 50 2 3 1.692 · 10–6 3 28.195 11.56 12.558 11.56 11.893 288.946 3.769 · 105
5 50 3 5 1.363 · 10–6 5 22.722 13.716 15.171 13.716 14.201 241.98 4.5 · 105
allowed estimation of the total impact of changes in their design made on the basis of these pa-
As a result of the calculation, values of impedance will be obtained, which can be used to deter-
. .
..
1
nat n conf
nat stand
P
P>.
37
Wire type ZTACIR
0.4 0.4 –
0.4 3 4
Phase layout Triangle Triangle Triangle
Presence of insulation cross-linked
polyethylene (CLP) – –
The number of components in the phase 3 2 1
240 60 120
Wave resistance 323.37 423.06 495.12
Natural power 37.43 28.60 24.44
Compliance with the condition 1.53 1.17 1
-
parameter on the performance of the lines.
3. Discussion
-
-
This is conditioned by the improvement of the following parameters: lower active resistivity of
interfacial distance (implemented due to the insulating layer), the presence of splitting and the
-
thod of synchronous compensation is considered. AC transmission systems are conditioned upon
the lack of investment that has existed in many electricity grids for many years, which is forcing
38
more attention to intensifying the use of existing transmission lines, improving the quality of
electricity transmitted. As a result, there is a sharp increase in interest in both new and conven-
AC Transmission Systems), such as SVC, SVC Light, TCSC. An example of such tasks could
be to increase the capacity of any power line. An attractive solution is to install in the corridor
of the power transmission line additional capacitors included in the series compensation circuit
(Hrechko et al. 2023). The series-connected capacitor reduces the reactance of the power line at
following advantages:
Increase of phase stability: to ensure the transmission of electricity it is necessary to have
increases with increasing transmitted power, and the series-connected capacitor maintains it
within safe limits. In other words, the presence of a capacitor ensures that the phase shift does
not exceed the level at which a dangerous loss of phase stability is possible.
Increase the voltage stability of transmission lines.
Optimal power distribution between both parallel circuits: the absence of series capacitors
-
mission capacity, not allowing any further increase to the power supplied to the system,
despite the fact that the second circuit could receive it. In the presence of series capacitors,
Capacitors connected in series are fully integrated into the power system and use its control,
protection and control mechanisms (Bondarenko et al. 2012). Additionally, they are completely
isolated from the ground. SVC Light technology is the brand name of ABB’s static synchronous
compensator based on insulated gate bipolar transistors (IGBT). This technology, based on the
use of voltage converters (VSC), also provides the necessary means to maintain the required
-voltage direct current (HVDC) transmission line with a counter-parallel circuit in which priority
is given to voltage support using dual SVC Light systems. Of particular importance in this regard
is the fact that the ability to transmit active power using HVDC Light inserts or in certain areas,
or included in the counter-parallel scheme provides both bidirectional transmission of the active
power component and the dynamic reactive power component. This not only maintains the stabi-
lity of the power transmission regime, but also opens up great opportunities to maintain voltage
at the expense of reserve capacity (Gritsyuk et al. 2022).
-
dicate a demand for self-compensating power lines, as the same capacitor banks or motors are
another link that reduces the reliability of the system and their cumbersomeness necessitates ad-
with regard to considering its impact on the natural power of the line. Its complexity is the lack
of an equation that would accurately describe the interaction of metal-insulation and insulation
of J.S.A. Sarmiento and M.C. Tavares (Sarmiento and Tavares 2018) a lot of data on the same
39
phase capacity is provided, but no equations are given by which they could be obtained and esti-
mate the real impact of insulation. However, its presence is an important tool in another method
of increasing natural power and provides an additional margin for thermal stability. Moreover,
The conclusions of these studies indicate that natural factors, such as the intensity of solar
line. However, the disadvantage of the considered approach is that when drawing up impact
-
sure to solar radiation is obtained. Under these conditions, peak values in wind gusts will not
-
As the radius of the wires, the splitting step and the number of components in the phase increase,
line. ?Furthermore, due to the increase in the magnitude of the charge on the wire there is an
increase in the capacity of the line, which leads to a decrease in its impedance and increase the
natural power (Yang 2011).
to a decrease in wire charge and line voltage, but at the same time, decreases electrical capacity,
a) b)
Source: Song et al. 2019
40
simultaneously leads to an increase in the natural power of the line and a decrease in electric
do. According to the scheme, it
a)
b)
c)
Fig. 4. Dependence of the natural power of the line of a) the number of components in phase n and b) on the splitting
step a and c) on the distance between the phases do
na
do
41
of the capacitors (phases A, B, C, and working capacity) and, accordingly, the power of the line
increases. This is conditioned by the decrease in impedance. Furthermore, there is a decrease in
the value of the maximum voltage on the wire and the impedance. This is conditioned by the
increase in the equivalent radius of the wire. Convergence of wires (reduction of distance do)
-
asing the value of capacities (A, B, C, and working capacity) and, accordingly, the power of the
line. This is conditioned by the fact that when the wires come together, the capacitance between
them increases due to the reduction of air gaps, reducing the value of the maximum voltage on
the wire and the impedance (Wang et al. 2019).
The constructed dependences of the calculated characteristics on the magnitude of the split-
ting step a allow distinguishing the following regularities. As the splitting step increases, there
is a slight increase in the value of the maximum voltage on the wire. In addition, with incre-
accordingly, the value of power, which is associated with a decrease in air gap, with increasing
dependences, it can be stated that reducing the maximum value of voltage on the wire and in-
creasing the line power can be done by providing the maximum number of components in the
phase, the maximum value of the splitting step, and the minimum distance between phases. At
the same time, under conditions of actual operation, there are a number of objective limitations
that provide these conditions. In particular, increasing the number of components in the phase
will complicate the design of the phase, which will necessitate an increase in the mechanical
When the phases converge, it is obligatory to consider the possibility of wire collisions,
which is a limiting factor regarding the variation of the value of the splitting step, when the
wires converge in phase. However, the presence of an insulating layer will allow the phases to
converge to much shorter distances than uninsulated, which will completely change the picture
compensating overhead lines (SCOHL) (Fortescue 1918). Comparing traditional OHLs with
controlled self-compensating OHLs, when regulating the phase shift between systems of circuit
voltage vectors in the SCOHL, power is transferred between its circuits, as a result of which,
of capacitive and inductive connections between the circuits of the line, due to which, the mutual
currents and induced EMF from one circuit change the magnitude of the current and voltage of
the adjacent circuit, which is equivalent to the transmission and reception of power (Bence et al.
2022). The main distinguishing features of the calculation of technical and economic indicators
between traditional OHL and SCOHL are as follows. In determining the costs based on the fact
that the charging capacity of the SCOHL is equal to the sum of the charging capacities of two
separately operating circuits (its components) in the case when the angle of displacement of the
0, that is, in the mode of the maximum throughput.
0, and this can be achieved by means of FR in the modes of low loads and idling, which
42
requires the connection of a shunt reactor (SR), the charging power of the SCOHL is much smal-
ler and on average can be determined by equation:
( )
00
0 180
0.55 0.55 2
char char char
SCOHL SCOHL OHL
QQ Q
= = (11)
where:
0
0char
SCOHL
Q 0,
0
180char
SCOHL
Q 0,
char
OHL
Q
– charging power of OHL.
When determining the cost of compensation for electricity losses in the KSPL considers the
possibility of reducing losses on the crown to regulate the parameters of the EP with the help
of FR. The total electricity losses in the SCOHL can be determined by the following equation
(Carslaw and Jaeger 1986):
( )
0
180
100
100
reg
cr load
K
∑
−
∆ = ∆ +∆
(12)
where:
0
180
cr
∆ 0 (maximum),
∆load – loading losses of the electric power in SCOHL,
Kreg
the shear angle between the systems of vectors of circuit voltages when chan-
ging the amount of transmitted power, and reducing the component of losses
per corona compared to traditional OHL (Kreg = 6–10%).
Savings in electricity losses are thus achieved by regulating the phase shift between the cir-
cuits of the SCOHL and thereby, reducing losses on the crown. The cost of SCOHL is assumed
to be equal to 70–80% of the cost of a two-chain traditional OHL. Thus, for SCOHL, the cost is
( )
2 0.7 0.8
trad
SCOHL OHL
KK⋅=⋅−
(13)
where:
trad
OHL
K – the cost of traditional OHL lines.
The savings in investment are also evident due to the reduction in the number of circuits and
the use of a large number of double-chain power supply, and the reduction in investments in the
linear part is complemented by savings on SR, which are much smaller for SCOHL by charging
Э
Э
Э
Э
43
exclusion band for SCOHL is taken to be equal to the sum of twice the width of the single-chain
support and twice its height. It should also be noted that SCOHL create lower levels of electrical
-
pared to the alienation band of traditional OHLs per unit of transmitted power. Therefore, the
considered as one of the perspective methods for the transmission of electrical power, features of
implementation of intersystem communications.
Increasing the natural power or power-handling capacity of a transmission or distribution
line is a critical aspect of electrical engineering. Replacing traditional aluminum conductors with
higher conductivity materials like aluminum-steel composite conductors (ACCC) or aluminum-
with larger cross-sectional area conductors can reduce resistance and increase power-carrying
-
lines. The restriction is limited access to this data due to a variety of reasons, for example, com-
Conclusions
-
ing wire design, applying an insulating layer to the conductor’s surface, altering the design of
resistance to manipulate phase spacing, the number of components within phases, and splitting
-
sation and second-generation superconductors exhibit limited potential in the current stage of
energy development. Moreover, during the evaluation of wave resistance calculations, it became
evident that the existing equation fails to account for insulation presence. The research corro-
44
computation of losses due to corona discharge in the line, which is an issue that warrants detailed
investigation in forthcoming studies.
power of power lines without necessitating substantial alterations to the power transmission
-
mic costs.
evaluating the technical and economic attributes of the proposed projects. This approach has the
potential to substantially reduce expenditures related to further upgrades within the electricity
transmission system. The challenge of rigidity is a common characteristic of energy systems,
the consideration of the insulating layer’s impact and raising questions concerning the redistribu-
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Nataliya , Vladyslav V, Iryna , Irina B, Mykola
Oszacowanie całkowitego wpływu metod zwiększania
obciążenia naturalnego linii
Streszczenie
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