Modeling of Power Supply Systems Equipped with Double Two

Wires and Earth Transmission Lines

Yuri Bulatov

, Andrey Kryukov

2,3 b

, Le Van Thao

, Konstantin Suslov

2,4 d

and Tran Duy Hung

Department of Energy, Bratsk State University, Bratsk, Russia

Department of Power Supply and Electrical Engineering, Irkutsk National Research Technical University, Irkutsk, Russia

Department of Transport Electric Power, Irkutsk State Transport University, Irkutsk, Russia

Department of Energy, Transbaikal State University, Chita, Russia

Military Industrial College, Hanoi, Socialist Republic of Vietnam

Keywords: Power Supply Systems, Coupled Twin and Earth Cables, Modeling.

Abstract: Power supply systems (PSS) of the agro-industrial complex, as well objects located in the areas remote from

the networks of electric power systems, sometimes use electric transmission lines (ETLs) that exploit the

ground as a conducting part. When currents flow in the ground, it causes electrical safety issues. To solve

them, double two wires and earth (TWE) lines can be used. Such lines use special transformers, in which the

voltage vectors of the grounded terminals have an angular shift of 180º. Due to this, there are no currents in

the ground a symmetrical mode. In the context of digitalization of the electric power industry, creating

computer models of such PSSes that adequately simulate stationary modes is of particular relevance. This

paper presents the results of studies aimed at the implementation of computer models of power supply

systems that incorporate double TWE lines. Constructive diagrams of ETLs with double TWE lines are

proposed. Simulation was carried out by means of the Fazonord software package. The simulation results

drew us to the following conclusions: in comparison with a double-circuit ETL, a double TWE line can

significantly reduce the cost of non-ferrous metal; the asymmetrical design of this ETL causes a decrease in

the quality indicators of electricity at its receiving end; in addition, higher power losses are observed; the

double TWE line can be implemented on the basis of two or four single-phase shielded cables.

https://orcid.org/0000-0002-3716-5357

https://orcid.org/0000-0001-6543-1790

https://orcid.org/0000-0003-0484-2857

https://orcid.org/0000-0002-3563-9811

1 INTRODUCTION

In agricultural areas, distribution electrical networks

are of considerable. In order to save non-ferrous

metal, their implementation sometimes implies

construction power lines that use ground as a

conducting part. Such solutions can also be used to

provide electrical energy to objects located in areas

remote from the networks of electric power systems.

A number of works are devoted to solving the

problems of researching power supply systems

equipped with single-wire power lines with earth as

a return wire (Single Wire Earth Return) (SWER).

The article (Helwig and Ahfock, 2013) discusses

the issues of increasing the capacity of these lines. A

solution to a similar problem for rural SWER

networks is presented in (Wolfs, 2005) and (Wolfs et

al., 2007). The paper (Kavi et al., 2016) describes

methods for detecting faults in single-wire

distribution networks. The paper (Brooking et al.,

1992) is devoted to the problems of upgrading SWER

networks. Models for selecting wires in networks with

SWER lines are proposed in (Bakkabulindi et al.,

2013). The results of studies of the influence of

distributed generation on the modes of electrical

networks with SWER lines are given in (Kashem and

Ledwich, 2004) and (Ledwich, 2004).

Bulatov, Y., Kryukov, A., Van Thao, L., Suslov, K. and Hung, T.

Modeling of Power Supply Systems Equipped with Double Two Wires and Earth Transmission Lines.

DOI: 10.5220/0010996500003203

In Proceedings of the 11th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 2022), pages 23-31

ISBN: 978-989-758-572-2; ISSN: 2184-4968

An article (Nkom et al., 2019) discusses the

challenges of using SWER lines in rural Africa. The

article (Nkom et. al., 2018) provides a solution to the

problem of narrow-band modeling of single-wire

power lines. When currents flow in the ground,

electrical safety becomes an issue. To solve them,

dual lines “two wires - ground” (TWE) can be built,

which were first considered in the papers (Andreev,

1952) and (Filshtinsky, 1952). The development of

this idea is given in (Buryanina et al., 2005). These

lines use special transformers in which the voltage

vectors of the grounded terminals have an angular

shift of 180º. Due to this, there are no currents in the

ground in a symmetrical mode.

In the context of the electric power industry

digitalization (Vorotnitsky, 2019), the problems of

creating digital models of PSS with double TWE

lines to ensure adequate simulation of stationary

modes acquire a special relevance.

Such models can

be formed on the basis of developments (Zakaryukin

and Kryukov, 2005) implemented in the Fazonord

software product. These developments are based on

the ideas of building models of elements of electric

power systems (EPS) based on phase coordinates; at

the same time, the main power elements of the EPS,

which include electric transmission line and

transformers, are considered as multi-wire or multi-

winding objects and are presented in the form of

lattice equivalent circuits with a fully connected

topology. Based on this approach, methods and

computer technologies have been implemented, the

distinctive features of which are as follows:

• multi-phase, which consists in the possibility

of modeling multi-phase systems (single-phase,

three-phase, four-phase, six-phase and their various

combinations in one network);

• multi-mode, which allows modeling a wide

range of EPS modes: normal and emergency,

asymmetric, non-sinusoidal, limiting in terms of

static aperiodic stability;

• multitasking, providing the possibility of solving

additional problems relevant for practice: determination

of induced voltages on adjacent transmission lines;

calculation of the intensity of electromagnetic fields

created by traction networks; parametric identification

of transmission lines and transformers according to

measurement data; accounting of active elements of the

EPS; modeling of thermal processes during ice melting.

2 DOUBLE TWE LINE

To justify the use of double TWE lines and to

determine their effectiveness, it is necessary to

develop adequate computer models. Since the

double TWE lines are characterized by an

asymmetric structure, it appears reasonable to build

their models on the basis of phase coordinates.

Below are the results of simulating the modes and

electromagnetic fields (Buyakova et al., 2018) of a

double TWE line with a voltage of 35 kV with

respect to the ground, Fig. 1.

The coordinates of the wires of this line with a

length of 5 km with 95 mm

aluminium conductor

steel reinforced cables are shown in Fig. 2. To assess

energy efficiency, power quality and

electromagnetic safety conditions, the corresponding

indicators were compared with the results of

simulating the modes and electromagnetic fields

(EMF) of a three-phase power trans-mission line

with 95 mm

aluminium conductor steel reinforced

cables, non-standard voltage of 35 kV with respect

to the ground and a line voltage of 60 kV.

UU 3=

UU 33 =

UU 322 =

Figure 1: Schematic diagram of the overhead TWE lines.

SMARTGREENS 2022 - 11th International Conference on Smart Cities and Green ICT Systems

Figure 2: Wires location coordinates.

(a)

(

)

Figure 3: Vector voltage diagrams of the phases of the secondary winding of transformers: (a) – T1, the fifth group of

connections; (b) – T2, the eleventh group of connections.

The lack of current in the ground can be illustrated

using vector diagrams of voltages on the secondary

windings of transformers (Fig. 3). These diagrams were

obtained as a result of determining the mode of the

double TWE line without the grounding of phase C.

The mode calculation was carried out with loads of

4 + j3 MV⋅A per phase at the receiving end. Figure 3

shows that for the groups of transformers 5 and 11, the

voltage vectors of the grounded terminals are in

antiphase. This ensures that there are no ground

currents in symmetrical modes.

The results of determining the PSS modes by the

double TWE line show that on the 10 kV side of the

consumer substation, connected at its receiving end and

at the loads indicated above, the voltage asymmetry

factor in the return sequence is 0.8%, and the total

current flowing into the ground is 0.16 А. Dependences

of losses and asymmetry in the electric transmission

line (ETL)-60 and a double TWE line on the

transmitted active power are shown in Figs. 4 and 5.

They were obtained with a power factor of 0.89. The

analysis of these dependences implies that the double

TWE line is characterized by higher losses in

comparison with the ETL-60 (Fig. 4). At the receiving

end of this ETL, a significantly greater asymmetry is

observed. Figures 6 and 7 show the dependences of the

EMF strengths of the double TWE line on the x

coordinate, which is measured from the center of the

line.

Figure 8 shows three-dimensional diagrams of

the strengths of the electric (a) and magnetic (b)

fields created by the double TWE line.

The simulation results draw us to the following

conclusions:

1. In comparison with the ETL of traditional

design, the TWE line has higher losses and voltage

asymmetry at the receiving end;

2. The strengths of the electric field directly

under the wires of the TWE ETL is 33% higher than

the same indicator for the 60 kV ETL;

3. The maximum amplitude of the magnetic field

of the TWE ETL is twice as high as that one of the

60 kV ETL.

Modeling of Power Supply Systems Equipped with Double Two Wires and Earth Transmission Lines

Figure 4: Dependences of active losses in the line on the transmitted power.

Figure 5: Dependencies of the asymmetry coefficient on the transmitted power.

Figure 6: Dependences of the amplitudes of the electric field strengths at the height of 1.8 m on the x coordinate.

Figure 7: Dependences of the amplitudes of the magnetic field strengths at the height of 1.8 m on the x coordinate.

SMARTGREENS 2022 - 11th International Conference on Smart Cities and Green ICT Systems

(a) (b)

Figure 8: Volumetric diagrams of electric (a) and magnetic (b) field strengths of the double TWE line.

Figure 9: Schematic diagram of the two-cable TWE line connection.

3 THE TWE LINE BUILD WITH

TWO SPECIAL DESIGN

CABLES

In some cases, when forming a PSS, the use of

overhead electric transmission lines is limited. Such

situations are typical for some settlements, sites of

industrial enterprises, as well as for areas with high

wind loads. In addition, the use of cable TWE lines

can be expedient for the transmission of electricity

by submarine cables to facilities located on the

islands of rivers, lakes, and seas.

Implementation of a double TWE cable line may

use the proposed in (Buyakova et al., 2019)

constructive scheme based on two single-core

shielded cables with molecular cross-linked

polyethylene insulation.

In contrast to the widely used designs, cable

shields for this ETL should ensure that the flow of

currents are proportionate to the currents of the

conductors. In addition, they must have the same

insulation class as the conductors. Such cable lines

can be placed in galleries, overpasses and on other

structures of a similar type. The cable line diagram

(Fig. 9) corresponds to Fig. 1; operating currents of

the cable line flow through the shields. The location

coordinates of the conducting parts of a double cable

line are given in Fig 10. The electrical parameters of

the conductors and shields are the same as in the

above-discussed overhead TWE ETL.

The diagram showing the currents distribution

through the wires of overhead and cable lines is given

in Fig. 11. We can observe some differences in the

currents of conductors and shields of the cable TWE

ETL which is associated with its asymmetric design.

Modeling of Power Supply Systems Equipped with Double Two Wires and Earth Transmission Lines

Figure 10: Coordinates of conducting parts.

Vector diagrams characterizing currents and

voltages at the receiving and outgoing ends of the cable

TWE line are shown in Figs. 12 and 13. The input

voltages and currents of cable lines are far from a

symmetrical four-phase system, but the voltages and

load currents on busbars of the 10 kV transformers are

symmetrical with a return sequence voltage asymmetry

coefficient equal to 0.5%.

Figures 14-16 show comparative graphs

characterizing energy efficiency, power quality

indicators for asymmetry and electromagnetic safety of

the considered cable line design in comparison with a

four-wire overhead line.

Compared with the overhead line, the cable TWE

line is characterized by a significantly lower level of

asymmetry (Fig. 15). However, higher magnetic field

strengths are created near the cables. With the same

cross-section of the conducting parts, the active power

losses for overhead lines and cable TWE lines differ

insignificantly (Fig. 14).

Figure 11: Currents in the wires of the overhead line and

cables at the starting ends of the ETL.

Figure 12: Vector diagrams of at the outgoing end of the

cable TWE line.

Figure 13: Vector diagrams of voltages on 10 kV busbars.

SMARTGREENS 2022 - 11th International Conference on Smart Cities and Green ICT Systems

Figure 14: Dependences of losses on the transmitted active power.

Figure 15: Dependences of the return sequence asymmetry coefficient on transmitted power.

Figure 16: Dependences of the amplitudes of the magnetic field strengths at the height of 1.8 m on the x coordinate.

4 THE TWE STRUCTURE BASED

ON FOUR CABLES OF A

STANDARD STRUCTURE

It is possible to consider a scheme of the TWE line

which implementation requires four typical

molecular cross-linked polyethylene cables, Fig. 17.

Its cross-section is shown in Fig. 18.

In simulation, it was assumed that the cable shields

are grounded on one side. At shield currents of 8.2 A,

the total current did not flow through the ground

electrode. Dependences of losses on the transmitted

active power at are shown in Fig. 19 for the following

types of TWE lines: overhead, two-cable, and four-

cable lines. For all types of TWE lines, the losses are

almost the same (Fig. 19). Asymmetry at high

transmitted powers prevails in the double overhead

TWE line. However, at low powers, asymmetry is

greater in the four-cable line, although the asymmetry

coefficient does not exceed 0.5%. The dependences of

the amplitudes of the magnetic field strengths on the x

coordinate are shown in Fig. 21.

Analysis of the simulation results allows us to

conclude that the four-cable TWE line, when

compared to the two-cable one, is characterized by a

higher level of asymmetry and creates a magnetic

field of the same order.

Modeling of Power Supply Systems Equipped with Double Two Wires and Earth Transmission Lines

Figure 17: Schematic diagram of the four-cable TWE line connection.

Figure 18: Coordinates of cable locations.

Figure 19: Dependences of losses on transmitted power.

Figure 20: Dependences of the asymmetry coefficient on transmitted power.

SMARTGREENS 2022 - 11th International Conference on Smart Cities and Green ICT Systems

Figure 21: Dependence of the amplitude of the magnetic field strength on the x coordinate.

5 CONCLUSIONS

We proposed a technique that helps adequately

model and simulate double electric two wires and

earth lines. We considered the original designs of

TWE cable lines that can be implemented when the

use of overhead ETLs is limited. Such situations are

typical for some settlements, sites of industrial

enterprises, as well as for areas with high wind

loads. In addition, the use of cable TWE lines may

be appropriate for the transmission of electricity by

submarine cables to facilities located on the islands

of rivers, lakes, and seas.

ACKNOWLEDGEMENTS

The research was carried out within the state

assignment of Ministry of Science and Higher

Education of the Russian Federation (project code:

FZZS-2020-0039).

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Modeling of Power Supply Systems Equipped with Double Two Wires and Earth Transmission Lines