Influence of Temperature and Transmitted Power on Losses in
Particular Transmission System
LADISLAV RUDOLF1, TOMAS BAROT2*, MILAN BERNAT3, LUBOMIR ZACOK4, MAREK
KUBALCIK5, JAROMIR SVEJDA2
1Department of Technical and Vocational Education, Faculty of Education, University of Ostrava,
Ostrava, Fr. Sramka 3, 709 00 Ostrava, CZECH REPUBLIC
2Department of Mathematics with Didactics, Faculty of Education, University of Ostrava, Ostrava, Fr.
Sramka 3, 709 00 Ostrava, CZECH REPUBLIC
3Physics, Mathematics and Techniques, University of Presov in Presov, 17. Novembra 3724/15,
08001 Presov, SLOVAKIA
4Faculty of Natural Sciences of Matej Bel University in Banska Bystrica, Tajovskeho 40, 974 01
Banska Bystrica, SLOVAKIA
5Department of Process Control, Tomas Bata University in Zlin, Faculty of Applied Informatics, Nad
Stranemi 4511, 760 05 Zlin, CZECH REPUBLIC
Abstract: - Innovations and trends has been significantly increased during modern theory and practical
realizations in the field of energetic. In the Czech Republic, the research of predictions of technical losses on
the transmission system can be considered as novel and important topic. Using software possibilities can be
appropriately utilized in the frame of estimations of the technical losses. While they cannot be eliminated, they
may be minimized. Losses can be measured or calculated using transmission-line parameters. This causality is
considered in the form of the presented and proposed mathematical equations including real measured data of
the atmospheric temperatures achieved on the substations selected in the Moravian-Silesian region. In this
contribution, results of proposed calculations of technical losses based only on line parameters considering the
ambient temperature are being compared in relation to a particular transmission system using prediction
software. Particularly, technical losses caused by a configuration change of a selected part of a transmission
system are considered related to the operation of Dlouhe Strane pumped storage hydro power plant. As can be
conclude, after the resulted comparisons using by the proposed mathematical models in software and the
obtained real measured data, general minimization of the losses is necessary to create the most accurate models
of the states that might occur in the future and to propose required modifications of the given part of the
transmission system. Future bounded research can be focused on the sensors situated on the transmission lines
instead of the substations.
Key-Words: - Transmission System, Technical Losses, Influences of Temperature, Prediction, Software,
Correlation Analysis
Received: March 24, 2021. Revised: January 12, 2022. Accepted: February 21, 2022. Published: March 23, 2022.
1 Introduction
In the research area of the energetic [1]–[3], the
modern approaches and trends has been frequently
occurred with proposals of modifications in favor of
the minimization of external influences as losses or
noises. As near research areas of the solving these
occurred problems, also, the technical cybernetics
[4]–[6] and mathematical modelling of processes
control [7]–[9] has been often considered.
Particularly, in this contribution, the calculation
of predictions using by the software utilities with
following evaluation of losses [10] that occur in the
transmission system located in a certain part of the
Czech Republic [11]. In the paper proposals, the
authors’ own realized software is utilized for
purposes of the calculating the predictions.
The calculation has been performed with the
program which inputs are the measured values
obtained from databases of the transmission grid
control system [12]. The results of the calculation
can be then suitably compared with values of losses
of a second program that calculates the technical
losses based only on the line parameters. It is then
possible to assess the impact of the losses on the
examined transmission system in the area.
The specific area of the transmission system has
been selected in view of the interesting states that
can occur during its operation, especially greater
variations of atmospheric temperatures and
fluctuations of the transmitted power. [13]–[15]
It is an area in which provision of an optimal
power to the Horni Zivotice substation posed
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problems in previous periods. The capacity of the
area has been reinforced by the construction of a
new Kletna substation and by the erection of another
V458 transmission line. An important aspect that
played a role in selecting the examined area has
been the commissioning of a new transmission line
between the Horni Zivotice and Krasikov
substations. This resulted in the creation of a ring
transmission system network boosted by power fed
from the Dlouhe Strane pumped storage hydro
power plant. In terms of the transmission system
operation management the power supplied by this
power plant is variable. The paper also mentions the
states under which this power plant is utilized with
respect to its operation and the atmospheric
temperature. [13]–[15]
Fig 1: Selected Area of Transmission System Used
for Calculations and Analysis [15]
Fig 2: Sample of Measured Atmospheric
Temperature Data in Area Under Investigation [15]
Losses can be measured or calculated using
transmission-line parameters. This causality is
considered in the form of the presented and
proposed mathematical equations including real
measured data of the atmospheric temperatures
achieved on the substations selected in the
Moravian-Silesian region. In this contribution,
results of proposed calculations of technical losses
based only on line parameters taking into account
the ambient temperature are being compared in
relation to a particular transmission system using
prediction software. Particularly, technical losses
caused by a configuration change of a selected part
of a transmission system are considered related to
the operation of Dlouhe Strane pumped storage
hydro power plant. [13]–[15]
2 Particular Transmission Network
The calculations are based on real data and
calculations using a program developed in previous
years [13], [14]. The selected area of the
transmission system is shown in Figure 1 and the
atmospheric temperature data in Figure 2.
2.1 Description of the Selected Network
The selected area of the transmission system
comprises six nodes, five of which are substations
and the sixth the controlled power hydroelectric
power plant. The area network forms a ring, which
consists of six overhead lines, see Table 1 showing
their length. The selected network is also connected
by seven lines to a neighboring transmission system
of Czechia, Slovakia and Poland. The default values
used for the calculations are data measured in the
power dispatching control system (Table 2) and
include node voltages, information on the
transmitted power, reactive power, line current and
temperatures. An important input is the power
contributed into the selected area by the pumped
storage hydro power plant. An emphasis is placed
on selected seasons and atmospheric temperature
changes in the region, which are measured directly
at power utilities. A database has been compiled
based on all parameters of the lines and the
measured data that are used to perform the
calculations with the aid of the program. The
program was developed by the staff of two Ostrava
universities and has been published [13], [14]. The
calculations have been performed due to the need to
verify the accuracy of software calculations and to
clarify changes in the magnitude of losses with
respect to atmospheric temperature movements and
the line transmitted power in the area where network
configuration changes have been made. The changes
included commissioning of a new V458 line,
construction of a new 400 kV Kletne substation and
creation of a V405 line because of splitting the
V459 into two V405 and V459 lines terminated in
the new Kletna substation. The results and
evaluations are set out further in the article.
Table 1: Lengths of Selected Network Lines
400 kV line
Substation 1
Substation 2
Line length
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V457
Dlouhe Strane
Krasikov
59.8 km
V458
Krasikov
Horni
Zivotice
107 km
V459
Horni
Zivotice
Kletne
42.1 km
V402
Krasikov
Prosenice
87.6 km
V403
Prosenice
Nošovice
79.6 km
V405
Nošovice
Kletne
53.5 km
2.2. Measured Values Database Analysis
The measured value database contains the values of
transmitted active and reactive power (P; Q),
technical losses for the given line (P_ztr), voltage
(U), current (I) and temperatures from the power
utilities (T_venk). All values, apart from technical
losses, were measured at the start and end of the
lines of the respective substation. Database data
between August 2017 and February 2018 were used
for processing. The measurement databases also
include seasonal differences according to a given
month and are divided into the summer season - L
and the winter season - Z. The measured values are
then divided into columns, where the respective
measured quantity for the given line is shown in a
separate column. The header of each column
contains an abbreviation for the substation outlet,
the code designation of the line and finally the
symbol of the measured quantity. Take for example
the designation C: KRA4: V402: P, where KRA4
stands for the measurement taken at Krasikov
station. From the line designation of V402 it can be
inferred that it is a 400 kV line, as this designation
starts with the number 4. For the 220 kV line the
designation then starts with the number 2. The last
part consists of a letter. For example, P means active
power values. The sample of the database section is
shown in Table 2.
Fig 3: Transmission Power Network Interactive Map ČEPS [15]
Table 2: Part of Database of Measured Values for v402 Line
Time
C: KRA: 4: V402: P
C: KRA: 4: V402: Q
C: KRA: 4: V402: U
C: KRA: 4: V402: I
C: KRA: T_venk
10.12.2017 24:00:00 Z
-150.36
27.61
418.52
211.16
0
11.12.2017 00:15:00 Z
57.13
19.76
417.29
94.23
0.59
11.12.2017 00:30:00 Z
68.49
20.93
417.38
102.8
0.77
11.12.2017 00:45:00 Z
56.7
20.2
417.16
84.69
0.83
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11.12.2017 01:00:00 Z
94.02
22.11
417.71
143.78
1.09
11.12.2017 01:15:00 Z
99.39
16.79
417.06
151.97
1.14
2.3. Analysis of Calculated Losses of Selected
Transmission System Network
The calculations of the selected network are based
on the real values measured by the sensors that are
part of the energy dispatch control system in the
given power utility. An example of the location of
the sensors in the selected region is shown in Figure
2-3. The values have been selected from certain
periods since 2017. These values serve as a basis for
calculations and analysis of the selected area.
3 Model Statuses for Calculating
Losses of Selected Transmission
System Lines
The program for calculating Joule's losses works on
the following principle: it takes the long-term
measurements and uses it to assemble the predictive
polynomial to calculate the losses in the selected
temperature interval for the specified transmitted
power [13]. The boundary temperatures of the
temperature interval are chosen so that the one
polynomial represents losses at the low temperatures
and the second one loss at the higher temperatures.
The transmitted power values are selected between
0 MW and 100 MW up to the maximum transmitted
power [13], [15]–[18]. The V402 line Joule losses
e.g., at a transmitted power of 500 MW taken from
the line parameters and an assumed power factor of
cosϕ = 0.95 are calculated from the values given in
Table 2 as follows - first we calculate the current
then use it to arrive at the reactive power:
6
3
500 10 760A
3 cos 3 400 10 0.95
P
IU
(1)
3
3 sin
3 400 10 sin(arccos(0.95)) 164Mvar
Q U I
(2)
The Joule’s loses are then:
2
2
26
2
2
2
26
2
10
2
400 354
500 164 10
2
2.57 4.029MW
400
VB
PQ
PR V
(3)
3.1. Analysis and Calculations for V402
Krasikov – Prosenice Line
To calculate Joule's losses using the program, we
select two temperature intervals, one for the winter
and the other for the summer period
ΔT1 between -14°C and 0°C and
ΔT2 between 10°C and 35°C.
Then the resulting prediction polynomials for the
selected temperature ranges are:
52
10.01203 0.00019 1.4 10
T
P P P
(4)
(5)
In Table 3 By program calculated Joule’s loss
results and the losses from the line parameters are
then compared.
Table shows that the program-predicted losses in
dependence on temperature are lower than the losses
calculated by the program without considering the
ambient temperature. These values are more
realistic because they include the influence of the
ambient temperature and the program is based on a
comprehensive database of measured values,
contrary to the losses calculated only from the line
parameters that do not comprise the influence of the
temperature [13], [14], [18]–[21].
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Table 3: Resulting Joule’s Losses of v402 Line of
Selected Part Transmission System Network.
Software calculated losses
Losses from the line
parameters
P
ΔPT1
ΔPT2
I
Q
ΔP
(MW)
(MW)
(MW)
(A)
(Mvar)
(MW)
0
0.012
0.015
0
0
0.013
100
0.176
0.173
152
33
0.174
200
0.629
0.626
304
66
0.655
300
1.371
1.373
456
99
1.459
400
2.402
2.414
608
131
2.583
500
3.722
3.751
760
164
4.029
600
5.331
5.381
912
197
5.795
700
7.229
7.307
1064
230
7.884
800
9.416
9.527
1215
263
10.293
900
11.893
12.041
1367
296
13.024
1000
14.658
14.85
1519
329
16.075
1100
17.713
17.954
1671
362
19.449
1200
21.056
21.352
1823
394
23.143
Figure 3: Technical Loses of V402 Line
Figure 4. Technical Loses of V459 Line
The biggest losses in the year were recorded in
September, when the peak transmitted power was
800 MW, and the lowest one in February with the
transmitted power of up to 600 MW. The graphical
comparison of all three values of losses is shown in
Figure 3 graph.
3.2. Horni Zivotice – Kletne V459 Line
For all subsequent lines, calculations are performed
at the same temperature intervals as for the V402
line.
5 6 2
10.000312 10 5.4 10
T
P P P
(6)
5 6 2
20.00454 6 10 5.9 10
T
P P P
(7)
The difference in predicted losses, considering
the temperature and loss calculated only with
respect to the transmitted power (ΔP - ΔPT1 and ΔP
- ΔPT2) is increasing. At the transmitted power of
1300 MW, the difference is 1.12 MW at low
temperatures and 0.4 MW at high temperatures.
3.3 Dlouhe Strane – Krasikov V457 Line
This line is connected to the Dlouhe Strane pumped
storage hydro power plant with the installed
capacity of 600 MW.
5 6 2
10.00762 5.6 10 8.9 10
T
P P P
(8)
4 6 2
20.01599 4.7 10 7.3 10
T
P P P
(9)
Figure 5: Technical Losses of V457 Line
The V459, together with the V405 line formed
the so-called radial network until the V458 line was
connected. The Dlouhe Strane power plant
transmitted power at higher temperatures ranged
around 300 MW; the maximum of 600 MW was
rarely achieved. Its transmitted power was
influenced by the needs of the transmission system.
Therefore, the higher temperature prediction is more
accurate only up to the transmission power of 300
MW, for higher transmitted power it is distorted
because of the small data rate in the default database
of measured values. At low temperatures, the
prediction is accurate because the peak power
values were much more frequent during this period,
and therefore there were enough data lines to
calculate losses for the transmitted power above 300
MW.
0
5
10
15
20
25
0200 400 600 800 1000 1200 1400
P (MW) - Transmission power
P (MW) - Technical losses
ΔPT1 ΔPT2 ΔP
0
2
4
6
8
10
12
0200 400 600 800 1000 1200 1400
P (MW) - Transmission power
P (MW) - Technical losses
ΔPT1 ΔPT2 ΔP
0
1
2
3
4
5
6
7
0200 400 600 800 1000
P (MW) - Transmission power
P (MW) - Technical losses
ΔPT1 ΔPT2 ΔP
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3.4 Krasikov – Horni Zivotice V458 Line
This is a new line erected in connection with the
construction of a new 400 kV:
5 5 2
10.01769 4 10 1.4 10
T
P P P
(10)
4 5 2
20.19254 9 10 1.6 10
T
P P P
(11)
Figure 6: Technical Losses of V458 Line
The difference in predicted losses, considering
the temperature and loss calculated only for the
transmitted power (ΔP - ΔPT1 and ΔP - ΔPT2), is
again rising. At the transmitted power of 1300 MW
the difference is 1.2 MW at low temperatures and
1.1 MW at high temperatures.
4. Influences on the Dlouhe Strane
Power Plant Operation by Connecting
the New V458 Line
In terms of the transmitted power over the
respective lines, in relation to the technical losses
and the atmospheric temperature the situation
changed in the selected area of the transmission
system after terminating the new V458 line
connecting the Krasikov substation to the Horni
Zivotice substation. Prior to the line termination the
substation formed the end of a radial network that
comprised Nošovice - Kletne - Horni Zivotice
substations. (V405, V459). The V402 and V403
lines experienced a significant drop in technical
losses. The termination of the new V458 line also
changed the direction and size of the transmitted
power by the V405 and V459 lines from the Horni
Zivotice substation to the Nošovice substation. With
the increased power transmission in the area, the
technical losses also increased. The transmitted
power from the Krasikov substation was split into
two directions, along the V402 line and along the
new V458 line. It can be stated that the technical
losses have been divided and their total size has
been reduced. The size of the technical loses is also
notably influenced by the Dlouhe Strane pumped
storage hydro power plant operation. After
connecting the new V458 line, the power plant
started supplying more power to the selected area
[16]–[18].
5. Tightness of Predictive Models
Analyzed by Autocorrelation Analysis
According to the principle of the statistical
significance guarantee included in frame of paired
testing [9], the autocorrelation functions [22] were
utilized. For purposes of influences of the low and
high temperature losses due to the transmission
power, these both types of functions have been
analysed in statistical software PAST Statistics 2.17.
For sessions 3.1-3.4, the regression models in form
of the predictions ΔPT1 and ΔPT2 of aimed variables
were considered and paired compared.
The autocorrelation functions were computed for
each session 3.1-3.4. for both measured approaches
as RΔPT1 and RΔPT2 (Figures 7-10)
Figure 7: Autocorrelation Functions for Considered
Transmission Network in Session 3.1
Figure 8: Autocorrelation Functions for Considered
Transmission Network in Session 3.2
0
5
10
15
20
25
30
0200 400 600 800 1000 1200 1400
P (MW) - Transmission power
P (MW) - Technical losses
ΔPT1 ΔPT2 ΔP
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Figure 9: Autocorrelation Functions for Considered
Transmission Network in Session 3.3
Figure 10: Autocorrelation Functions for
Considered Transmission Network in Session 3.4
On the significance level 0.001, the following
results of the paired comparisons of mathematical
models were obtained using by Wilcoxon test
(Table 4):
Table 4: Resulting Paired Comparisons of
Autocorrelation functions for Mathematical Models
of ΔPT1 and ΔPT2
Network
Paired Comp. RΔPT1 ΔPT1 and RΔPT2 ΔPT2
3.1
z score = 6.846 p<0.001
3.2
z score = 6.791 p<0.001
3.3
z score = 6.843 p<0.001
3.4
z score = 6.901 p<0.001
6. Conclusion
In conclusion we can state that many factors have
changed in the selected area of the transmission
system and those factors significantly influenced the
size of the technical losses. The most important
factors include the new network configuration,
temperature influences, the power transmitted over
the lines and the Dlouhe Strane pumped storage
hydro power plant operation. The technical losses
calculated from the line parameters were compared
and, in the latter case, calculated using a special
program.
The losses calculated by using the program that
takes temperature variations into account were
lower on all lines. We can say that the results
obtained by the program that considers the outdoor
temperature are more realistic because they are
based on the analysis of long-term measurements
performed on the relevant lines and include the
temperature influence. The program can be used for
further analysis of losses in the transmission system
networks and its use will result in correct analyzes
and conclusions.
The computational program used could also find
its use in practice. The analysis of the transmission
system lines’ technical losses is an important
indicator for the economical evaluation of electricity
transmission and also serves to evaluate changes
taking place in certain parts of the system after
construction of new substations and lines. In order
to minimize the losses, it is necessary to create the
most accurate models of the states that might occur
in the future and to propose required modifications
of the given part of the transmission system.
Future bounded research can be focused on the
sensors situated on the transmission lines instead of
the substations.
In additional analysis, the statistically significant
paired differences were being identify across the
observed low and high temperature predictive
models with regards to their thigness. With
statistical guarantee, the tightness of all comparisons
proved the difference behavior for all considered
part of transmission network – as can be assumed
for the various temperature dynamical phenomenon.
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WSEAS TRANSACTIONS on POWER SYSTEMS
10.37394/232016.2022.17.6
Ladislav Rudolf, Tomas Barot,
Milan Bernat, Lubomir Zacok,
Marek Kubalcik, Jaromir Svejda
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WSEAS TRANSACTIONS on POWER SYSTEMS
10.37394/232016.2022.17.6
Ladislav Rudolf, Tomas Barot,
Milan Bernat, Lubomir Zacok,
Marek Kubalcik, Jaromir Svejda
E-ISSN: 2224-350X
61
Volume 17, 2022
