Digital Models for Power Flow Analysis and Calculation of

Electromagnetic Interference Effects of Long-Distance

Ultrahigh-Voltage Transmission Lines

Andrey Kryukov

1,2 a

, Konstantin Suslov

1,3 b

and Alexandr Kryukov

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 Hydropower and Renewable Energy, National Research University,

“Moscow Power Engineering Institute”, Moscow, Russia

Keywords: Long-Distance Ultrahigh-Voltage Transmission Lines, Comprehensive Modeling in the Phase Frame of

Reference.

Abstract: The goal of the research presented in this article was to develop computer models of long-distance ultra-high

voltage (UHV) power transmission lines to provide comprehensive modeling of power flows and calculating

electromagnetic interference effects on extended steel structures. In developing the models, we employed the

methods based on the use of the phase frame of reference and equivalent lattice circuits with a fully connected

topology. The simulations were carried out for a 1,150 kV UHV transmission line with a length of 900 km,

each phase of which was formed by eight AC-330 wires . Simulations were performed using the software

package Fazonord. Along with power flow calculations and determination of the voltages created by the 1,150

kV long-distance transmission line on the pipeline, we simulated electromagnetic fields, taking into account

the impact exerted by the grounded steel structure. The results of modeling a long-distance 1,150 kV

transmission line with receiving end loads of 300 + j 200 MVA per phase led to the following conclusions: in

the case of a normal power flow with balanced loads at individual points of the structure the levels of induced

voltages did not exceed the allowable limit of 60 V; in the case of two-phase and single-phase short-circuit

power flows the maximum induced voltages also did not exceed the 1,000 V limit set by the regulatory

document. The models presented in the paper can be put into practice when planning the measures to ensure

the electrical safety of technicians working at the pipeline sections located in the areas that are subject to

electromagnetic interference effects of transmission lines. The application scope of the technique developed

covers the cases where a transmission line and a pipeline run in close proximity following a complex trajectory

that includes parallel and oblique segments.

1 INTRODUCTION

The current stage of electric power industry

development is characterized by commissioning of

long-distance ultrahigh-voltage (UHV) DC and AC

transmission lines. An example of such a power

transmission line is the 1,000 kV line, which serves

as a power bridge between the northern and central

regions of the PRC (Li, 2013). The long-distance

UHV transmission line projects that serves as the

backbone of the Northeast Asia power

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

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

https://orcid.org/0000-0003-3272-5738

interconnection are under discussion (Podkovalnikov,

2015). Against the current background of large-scale

use of information technology, the operation of such

power transmission lines calls for digital models that

provide a proper power flow analysis of electric

power systems (EPS) (Bulatov, 2022), in which such

UHV power transmission lines are employed.

The relevance of the task of modeling of long-

distance UHV transmission lines is attested by a large

body of published research on the subject. For

example, article (Wang, 2021) presented the results

Kryukov, A., Suslov, K. and Kryukov, A.

Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage Transmission Lines.

DOI: 10.5220/0011853400003491

In Proceedings of the 12th International Conference on Smar t Cities and Green ICT Systems (SMARTGREENS 2023), pages 40-49

ISBN: 978-989-758-651-4; ISSN: 2184-4968

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

of the study of utility frequency overvoltages and

measures for its suppression in ultra-high voltage

transmission lines. Study (Shao, 2012) dealt with the

analysis of overvoltages arising during single-phase

automatic reclosing in long-distance UHV

transmission lines. The issues of overvoltage

limitation in long-distance 1,000 kV transmission line

were considered in article (Wang, 2018). The problem

of matching the insulation of a half-wavelength ultra-

high voltage transmission line was solved in (Zhang,

2020). In study (Golov, 2020) its authors described an

adjustable sequential compensation installation

proposed by them, which provided an increase in the

transmission capacity of long-distance transmission

lines. Works (Xue, 2011 a, Xue, 2011 b) were devoted

to the study of switching overvoltages in long-distance

UHV transmission lines. Based on the results

obtained, the authors proposed measures to reduce

them. The system of transmitting energy over long

distances from a solar power plant was discussed in

article (Rahul, 2020). Distance protection with a

traveling wave for an UHV line, implemented on the

basis of the wavelet transform, was proposed in (Long,

2018). Article (Dias, 2011) dealt with the issues of

transmitting bulk power over extra-long distances.

Flexible systems for transmitting electricity over long

distances were proposed in (Davydov, 2019)

Theoretical aspects of long-distance power

transmission were discussed in research monographs

(Aleksandrov, 2006, Ryzhov, 2007).

Our analysis of published research reveals that the

tasks of complex modeling of power flows and

determining the electromagnetic fields (EMF) of

long-distance UHV lines and their effects on adjacent

conductive facilities have not been solved to the

extent warranted by the problem. This is due to the

fact that in most cases the single-line approach is used

to model long-distance transmission lines

(Aleksandrov, 2006, Ryzhov, 2007, Zakaryukin,

2005), which makes it difficult to take into account

longitudinal and transverse imbalances in power

systems.

The methods for calculating power system power

flows and computer technologies proposed in

(Zakaryukin, 2005, Zakaryukin, 2020) allow

implementing a proper and comprehensive approach

to the modeling of electric networks with long-

distance transmission lines and ultra-high voltage.

Below we present the results of research aimed at

furthering the development of techniques for

modeling power flows, EMF of long-distance

transmission lines and their electromagnetic

interference effects (EMIE) on extended steel

structures.

2 METHODOLOGY

The study of power flows, EMF and EMIE was

carried out by simulating a transmission line with a

nominal voltage of 1,150 kV and a length of 900 km.

For simulation purposes we used the parameters of

the line "Itat - Barnaul - Ekibastuz - Kokshetau -

Kustanai - Chelyabinsk", built in 1980 - 1988, which

now operates at 500 kV. The design transmission

capacity of this line was 5,500 MW. The line used

split phases made with eight AC-330 wires.

The Fazonord software package (Zakaryukin,

2020) was used as the main tool for carrying out

computer-aided power flow analysis of the long-

distance UHV transmission line. In order to capture

the changes in currents and voltages along the length

of the transmission line, the line model was

partitioned into eleven elements. The first five of

them corresponded to sections that were each 10 km

long. The models of these sections included a

segment corresponding to the above-ground pipeline,

running parallel to the line at a distance of 50 m from

the axis of the transmission line. The diameter of the

pipe was assumed to be 250 mm. Stationary earth

electrodes with a 1 Ohm leakage resistance were

installed along the edges of the structure. In addition,

the distributed grounding of the pipe with a

conductivity of 0.05 S/km was taken into account.

The length of the sixth section was 100 km, and that

of the rest - 150 km. Provision was made for the

transposition of line phases.

To take into account the distributive nature of

parameters of the transmission line and the grounded

pipeline, ladder equivalence circuits of sections

consisting of series-connected multiport devices were

formed (Zakaryukin, 2005, Zakaryukin, 2020,

Kryukov, 2022).

The algorithm for forming a ladder diagram

included the following steps:

1) the maximum length of the short section was

taken equal to a quarter of the thickness of the skin

layer in the ground

μγμπ

=Δ

, (1)

where

– ground conductivity, S/m;

=1; f –

frequency;

Гн/м104

−

⋅π=μ

;

2) the value of the length l was determined so as

to satisfy the condition l2

= L, where n - the number

of sections connected in series; L – the length of the

simulated line;

3) an equivalent lattice circuit (ELC) was

generated for the section with length l;

Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage

Transmission Lines

4) a ladder circuit was formed of 2n ELCs of

sequentially connected sections; the node numbers at

the beginning of the i-th section were taken equal to

the numbers at the end of the i-1 section;

5) intermediate nodes of the generated circuit

were removed and renumbered;

6) steps 4 and 5 of the algorithm were repeated n

times.

The removal of the intermediate node was

performed on the basis of the transformation of a star

polygon into a polygon. It should be noted that the

described procedure led to an increase in the number

of branches of the resulting ELC.

This procedure can be illustrated using the

diagram shown in Fig. 1. In the diagram, we removed

the node numbered 0, to which the ground shunt with

the conductivity

Y =

and N branches with

impedances Z

, Z

, …, Z

were connected.



Figure 1: Transformed section of the circuit.

Branch currents can be found on the basis of their

potentials:

ϕ−ϕ





;

ϕ−ϕ





; …,

ϕ−ϕ





(2)

Then the following relationship can be written for

the potential of the node to be removed:













ϕ−

===ϕ





ZZYY



(3)

from which it follows that



=ϕ



(4)

By introducing the notation



, (5)

for the k-0 branch current, the following expression

can be obtained:













−−

−

−ϕ=

ZYZYZYZYZ

0020

......





(6)

It follows from the above that at each of the nodes

in question a shunt appeared with a conductivity of













−=



ZYZ

. (7)

Furthermore, additional branches were formed

between the nodes, the resistances of which are

defined as follows:

ZYZZYZ

ZYZZYZZYZZYZ

0000

ϕ−ϕ

+ϕ−=

−

−=

−







(8)

From the above it follows that for the resistance

of the branch k-j we can write

jkjk

ZYZZ

(9)

In the transformed circuit there was no node 0.

However, a shunt to ground appeared in each of the

nodes connected to it. The circuit was complemented

by N(N-1)/2 branches, corresponding to the

connections of node 0 to adjacent nodes.

The resulting ladder diagram makes it possible to

properly simulate any long-distance transmission

line, as well as grounded current-carrying parts,

correctly accounting for the distributed nature of

parameters

3 RESULTS OF MODELING

The network schematic is shown in Fig. 2, the spatial

arrangement of wires is shown in Fig. 3, the display

of transformer and transmission line models in the

main window of the software package is shown in

Fig. 4 and 5, the simulation results - in Figs. 6 to 22.

Figure 2: Network schematic: x - distance from the sending

end of the transmission line.

SMARTGREENS 2023 - 12th International Conference on Smart Cities and Green ICT Systems

Figure 3: Coordinates of wires location: a - left phase; b -

middle phase; c - right phase; bold numbers indicate wire

numbers.

At the receiving end of the transmission line, a

balanced load of 300 + j200 MVA per phase was

assumed. The distribution of currents over the wires

at the beginning of the head section of the

transmission line is shown in Fig. 6. In order to ensure

that the voltage deviations are contained within the

permissible limits, it was necessary to install shunt

reactors, the parameters of which are shown in Fig.

7b. A model of the controlled reactive power source

was installed at the receiving end of the long-distance

transmission line, which provided stabilization of

phase voltages at 664 kV.

Figure 4: Models of transformers and autotransformers: a -

3х417 MVA transformer, b - 3х667 MVA autotransformer.

Figure 5: Detail of the visual representation of the

computational model, including the UHV transmission line

and the above-ground pipeline.

Power losses by sections of the transmission line

are shown in Fig. 7a; the losses at sections 1...6 were

summed up to obtain the same length. Fig. 7a shows

that the relationship

()

xPP Δ=Δ has a minimum,

corresponding to the eighth segment with coordinates

x = 300 km at the beginning and x = 450 km at the

end. Specific power losses per kilometer of the

transmission line were in the range of 8.6 to 16.4 kW.

The losses as a percentage of the transmitted active

power were in the range 0.14...0.27%.

Fig. 8 shows the dependencies of asymmetry

coefficients along the reverse (k

) and zero (k

)

sequences on the x-coordinate, from which we can see

that there is insignificant asymmetry at long-distance

transmission line nodal points, which does not exceed

the permissible limits.

Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage

Transmission Lines

Figure 6: Distribution of currents along the wires at the

beginning of the head section of the transmission line: the

bold numbers indicate the numbers of wires according to

Fig. 2.

Figure 7: Power losses along sections of the transmission

line (a) and inductance of shunt reactors (b) reduced to

1,150/√3 kV.

Figure 8: Asymmetry coefficients on the inverse (k

) and

zero (k

) sequences as a function of the x-coordinate.

Fig. 9 shows plots of voltage dependencies of the

1,150 kV transmission line on the x-coordinate

plotted for sections 1-5 that were adjacent to the

pipeline. The above plots show the decrease of

SMARTGREENS 2023 - 12th International Conference on Smart Cities and Green ICT Systems

voltages with the increasing the x-coordinate; at the

same time, the intensity of their decrease, which can

be estimated by the ratio of increments

increases. It should be noted that dependencies

()

are linear in nature. The plots I = I(x)

presented in Fig. 10 show an increase in currents as

the x-coordinate increases. The parameter

corresponding to the intensity of their increase grows

linearly.

Figure 9: Voltages of the 1,150 kV transmission line as a

function of the x-coordinate.

Figure 10: Currents flowing through the wires of UHV

transmission line sections on the source side as a function

of the x coordinate.

An important indicator characterizing the

electromagnetic safety conditions is the levels of

electromagnetic field strengths calculated at a height

of 1.8 m, Fig. 11-13.

Since the long-distance 1,150 kV transmission

line will not run through residential areas, in

compliance with the current standards applicable for

such a line the acceptable level of electric field (EF)

strength is equal to 5 kV/m. The analysis of the

obtained results allowed us to conclude that this level,

in terms of the actual values, was exceeded in

the range of changes in the z-coordinate that spanned

Figure 11: Electric field strength components at a height of

1.8 m as a function of the z-coordinate.

Figure 12: Magnetic field strength components at a height

of 1.8 m as a function of the z-coordinate.

Figure 13: Magnetic field strength components at a height

of 1.8 m as a function of the z- coordinate.

over -42...42 m. The Z axis was perpendicular to the

transmission line axis. The highest values of field

strength were observed directly under the line wires

(Fig. 11), which was to be expected. From Fig. 12, 13

we can see that due to the current flowing through the

Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage

Transmission Lines

pipeline at the point of its location there was an

increase in the magnetic field strength.

The results of determining the electromagnetic

interference effects of the long-distance transmission

line on the pipeline are shown in Fig. 14-17. Fig. 14

presents the dependency of induced voltages (IV) on

the pipeline on the x-coordinate for the balanced load

power flow. It shows that the values of induced

voltages did not exceed the permissible value of 60 V

established by the document (Technische Richtlinien-

71). Fig. 15 shows a plot corresponding to the

dependency of the current flowing through the pipe

on the x-coordinate. This relationship has a

maximum, which corresponds to the value of x = 10

km.

Figure 14: Induced voltages on the pipeline as a function of

the x-coordinate.

Figure 15: Currents flowing through the pipe in the case of

the balanced load power flow as a function of the x-

coordinate.

Fig. 16 shows the dependencies of induced

voltages on the x-coordinate, obtained for unbalanced

power flows, caused by switching off the shunt

reactors. For certainty, we chose the reactors installed

in phase A. We considered the power flows in the

case of shutdowns of the reactors installed at the

points corresponding to the following values of the x-

coordinate: 150, 300, 450, 600, 750 km. The

asymmetry resulting from the shutting down of the

reactors led to an increase in induced voltages. The

greatest increase in IV was observed at the points

located along the edges of the structure. The IV

maximum, exceeding the permissible value of 60 V,

occurred in the power flow with the shutdown of the

shunt reactor installed at the point corresponding to

the x-coordinate of 150 km, Fig. 17.

Figure 16: Induced voltages under unbalanced power flow

caused by reactor shutdown in phase A as a function of the

x coordinate.

Figure 17: Maximum induced voltages in the case with

reactors shut down.

Fig. 18 shows vector diagrams, built by means of

the Fazonord software package, for the power flow of

asymmetrical short circuits occurring at the point x =

50 km, which corresponds to the right end of the

section where the pipeline and the transmission line

SMARTGREENS 2023 - 12th International Conference on Smart Cities and Green ICT Systems

run in close proximity. From the analysis of the above

diagrams, we can conclude that during a two-phase

short circuit fault, the currents flowing through the

phases of the transmission line had a phase shift close

to 180º.

Figure 18: Vector diagrams of long-distance transmission

line currents in short-circuit power flows: a - two-phase

short circuit between phases C-B; b - single-phase short

circuit (phase A).

Figs. 19 to 22 show the results of calculation of

the induced voltages and currents flowing in the pipe

during asymmetrical short circuits in the long-

distance UHV transmission line. In the case of single-

phase short circuits, due to a pronounced

electromagnetic imbalance, the maximum induced

voltages reached 700 V (Fig. 19) but did not exceed

the maximum permissible value of 1,000 V, as

established by the document (Technische Richtlinien-

71). In this power flow, currents exceeding 800 A

were flowing through the pipeline (Fig. 20). The

magnitudes of the induced voltages and especially of

the currents depend on the choice of the faulty phase.

In the case of a single-phase short circuit, the

maximum IV and currents in the pipeline were

observed when phase C was shorted to ground (Fig.

20).

In the two-phase short-circuit power flow, due to

the different direction of currents flowing through the

current-conducting parts of the long-distance

transmission line (Fig. 18), the values of induced

voltages and currents in the pipe are much lower than

in the case of single-phase short circuits (Fig. 21, 22).

Figure 19: Induced voltages for a single-phase short circuit

at the point x = 50 km as a function of the x-coordinate.

Figure 20: Currents flowing in the pipeline as a function of

the x-coordinate in the case of a single-phase short circuit

at the point x = 50 km.

Figure 21: Induced voltages as a function of the x-

coordinate in the case of a two-phase short circuit at the

point x = 50 km.

Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage

Transmission Lines

Figure 22: Currents flowing in the pipeline as a function of

the x-coordinate in the case of a two-phase short circuit at

the point x = 50 km.

4 CONCLUSIONS

We have developed digital models that allow for the

comprehensive modeling of power flows of electric

power systems that have long-distance ultrahigh-

voltage transmission lines as their part. Furthermore,

based on these models it is possible to determine EMF

strengths and induced voltages occurring on the

adjacent above-ground pipeline.

The results of modeling of a long-distance 1,150

kV transmission line with loads at the receiving end

of 300 + j 200 MVA per phase allowed us to draw the

following conclusions:

1. Specific power losses per kilometer of

transmission line ranged from 8.6 to 16.4 kW. The

losses as a percentage of the transmitted active power

were in the range 0.14...0.27%.

2. There was insignificant asymmetry observed at

the nodal points of the long-distance transmission

line, which did not exceed the permissible limits.

3. In the case of a normal power flow with

balanced loads, the induced voltage levels did not

exceed the permissible limit of 60 V.

4. In the case of single-phase short-circuit power

flows, the maximum induced voltages reached 700 V,

but did not exceed the maximum permissible value

set in TRL-71. The maximum IV level occurs when

phase C, whose wires were closest to the pipe, were

shorted. The maximum current flowing in the

pipeline reached 824 A. Because of the opposite

direction of currents flowing through the current-

carrying parts of the long-distance transmission line

during a two-phase short-circuit, the values of

induced voltages and currents in the pipe were much

lower than during a single-phase short circuit. The IV

maximum reached 200 V and occurred when phases

CA were short-circuited. In the above case, currents

of up to 240 A were flowing through the pipe.

Potential applications of the proposed models

cover a rather wide range of tasks. They can provide

the basis for addressing the following issues: analysis

of normal, unbalanced, incomplete-phase, and non-

sinusoidal power flows of electric power systems that

have long-distance transmission lines as their part;

analysis of electromagnetic safety conditions along

the routes of such lines and substations adjoining

them; choice of rational measures to protect

technicians of adjacent structures located in the areas

of electromagnetic interference effects of long-

distance-transmission lines, etc.

The developed numerical models lend themselves

to a rather straightforward modification to account

also for cases where a long-distance transmission line

and an adjacent steel structure run in close proximity

following non-parallel trajectories.

ACKNOWLEDGEMENTS

The research was carried out within the framework of

the state task "Conducting applied scientific research"

on the topic "Development of methods, algorithms

and software for modeling the modes of traction

power supply systems for DC railways and

electromagnetic fields at traction substations for AC

railways".

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Digital Models for Power Flow Analysis and Calculation of Electromagnetic Interference Effects of Long-Distance Ultrahigh-Voltage

Transmission Lines