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TOPICAL COLLECTION: INTERNATIONAL CONFERENCE ON THERMOELECTRICS 2018
Development of the Automotive Thermoelectric Generator
Electrical Network
PAVEL SHIRIAEV ,
1,2,3
KONSTANTIN SHISHOV,
1,2
ALEXEY OSIPKOV,
1,2
and LEONID TISHCHENKO
1
1.—Bauman Moscow State Technical University, 2-ya Baumanskaya 5/1, Moscow,
Russian Federation 105005. 2.—Peoples Friendship University of Russia (RUDN University),
6 Miklukho-Maklaya St, Moscow, Russian Federation 117198. 3.—e-mail: shiriaevp@gmail.com
The automotive thermoelectric generator (ATEG) produces electrical power by
converting heat energy of engine exhaust gasses. The transfer of this electrical
energy to a vehicle’s electrical system should be done with minimum losses.
The electrical parameters of thermoelectric modules (TEMs), which are in-
stalled in the ATEG, are changing due to non-stationary ATEG operating
conditions. This fact leads to a mismatch between ATEG resistance and
equivalent electrical load resistance, causing the issue of generating maxi-
mum energy. One potential solution to this problem is a maximum power
point tracking (MPPT) method. MPPT controllers provide harvesting maxi-
mum power from the ATEG. In this way, MPPT application is required for
thermoelectric systems with variable heat flow. However, any MPPT con-
troller has its own conversion losses, which affect overall ATEG system effi-
ciency. These losses depend on MPPT controller working conditions, i.e. TEMs
output voltages and currents. Therefore, the simulation of the electrical circuit
should be done during driving cycles to evaluate the total efficiency of the
entire system. This evaluation helps to estimate the effectiveness of each
element of the electrical network. In this paper, we elaborate our theoretical
and experimental studies of the ATEG electrical network and do compre-
hensive discussion over the design for it.
Key words: Automotive thermoelectric generator, thermoelectric module,
maximum power point tracking, perturb and observe, electrical
losses, efficiency
INTRODUCTION
Carbon dioxide (CO
2
) increase in the atmosphere
is directly proportional to the annual increase in
transport vehicles.
1,2
In addition to the transport
impact on global warming, cars are a source of
various harmful emissions such as nitrogen oxides
(NO
x
), carbon monoxide (CO), sulfur dioxide (SO
2
)
and others, which are dangerous to the environ-
ment.
3
The changes in Europe, the United States,
Japan and other countries on emission standards
not only encourage automakers to search for new
and potential solutions to improve the efficiency of
vehicles,
4
but also compel them to reduce consump-
tion of fuel and harmful substances to decrease
emission. Consequently, the study of the automotive
thermoelectric generator (ATEG) can solve the
environmental and economic problems facing the
automotive industry.
Nowadays, many scientific groups are involved in
the development of automotive thermoelectric gen-
erators, including the research of various types of
ATEG designs.
5,6
In previous articles, we discussed
ATEG designs for various types of vehicles and
investigated different designs of heat exchangers by
considering their influence on the operation of the
(Received July 31, 2018; accepted January 5, 2019)
Journal of ELECTRONIC MATERIALS
https://doi.org/10.1007/s11664-019-06932-1
Ó2019 The Minerals, Metals & Materials Society
internal combustion engine and on the overall
efficiency of the system.
7–9
This paper focuses on
the ATEG electrical network. The electrical circuit
of thermoelectric modules (TEMs) depends on the
ATEG design, i.e. how many sections it has and how
many TEMs are installed.
Our ATEG has a hollow hexahedral prism struc-
ture (Fig. 1). This ATEG is multi-sectional and
consists of five sections. Each section has six
thermoelectric modules, which are pressed between
heat exchangers. We selected different types of
commercially manufactured segmented TEMs. For
experiment we considered bismuth telluride
(Bi
2
Te
3
), germanium telluride (GeTe) and lead
telluride (PbTe). The hot side of the thermoelectric
module (TEM) has been heated to 480°C by the heat
exchanger through vehicle combustion gases. The
cold side of the TEM has been cooled to 50°Cby
circulating water inside the heat exchanger through
the fluid channel. According to the Seebeck effect,
the TEM temperature difference leads to an elec-
tromotive force generation.
In this way, the ATEG converts the thermal
energy of engine exhaust gases and supplies the
vehicle electrical loads. It reduces the amount of
work for an alternator, which requires the energy of
burned fuel for its operation. Therefore, the ATEG
acts as an environment-friendly device and helps to
produce more electrical power for the vehicle, which
leads to fuel economy increase, and consequently
minimizes the harmful emissions of combustion
gases.
The conditions of engine operation change during
the vehicle’s ride. This leads to a change in the heat
flux through the ATEG. The ATEG surface temper-
ature varies with different driving conditions, and
its distribution over the entire surface is not the
same. This was established and studied in our
previous works, where we demonstrated the devel-
oped analytical and numerical models of the
ATEG.
7,10,11
Figure 2shows the temperature dis-
tribution of the ATEG surface, according to our
corresponding model. Consequently, due to the
uneven temperature, it turns out that the TEMs
have different operating conditions. Maximum gen-
erated power of the TEM depends on the match
between equivalent electrical load resistance and its
own internal resistance, which is affected by a
temperature difference. This dependence is shown
in Fig. 3, where the smooth curve is the result of the
approximation of numerous experimental
measurements.
Furthermore, in addition to continuous vehicle
electrical loads, there are many loads that are
switched on depending on the time of day, weather
conditions, driving style, etc. (Fig. 4). They all affect
the total equivalent resistance. Therefore, maxi-
mum power point tracking (MPPT) controllers are
used, which monitor changes in the system and
adjust it, for its most effective work.
The ATEG is a complex system with many
physical phenomena and processes. The models,
which consider the ATEG heat flow, have been
developed by us.
10,12
Within the framework of this
article, we consider the operation of the ATEG
electrical network (Fig. 5). With the help of a
verified mathematical model, we try to predict the
behavior of the electrical network and give recom-
mendations on its electrical part design. The study
of the ATEG power behavior in the non-stationary
conditions, for example in the new European driv-
ing cycle (NEDC), is already carried out.
13–16
But in
these works, the effect of the electrical network is
simplified or not considered. They assume that all
ATEG output energy directly transfers to the vehi-
cle’s battery and electrical systems. In addition,
they do not calculate the influence of electrical
losses. Our research is more detailed at this point.
MATHEMATICAL MODEL
The ATEG electrical network model has been
simulated in MATLAB with Simulink for MPPT
controller operation. The input data for the devel-
oped mathematical model are the parameters of the
TEM, especially the electromotive force and internal
resistance are dependent on the temperature dif-
ference (Fig. 6). By modifying data, the model can
determine the power of the TEM both at a constant
and varying temperature.
Since the model is universal for multi-sectional
generators, it is possible to set the number of
sections and modules on section surfaces. Consid-
ering the circuit type of TEMs and sections, there is
a three-stage simulation at different equivalent
loads (Fig. 7).
Calculation of the ATEG power and electrical
losses of the MPPT controller in the non-stationary
conditions leads to the value of the efficiency of the
selected electrical network design. The electrical
network efficiency is:
gel:net:¼Pload
PATEGmax
ð1Þ
Fig. 1. The ATEG design.
Shiriaev, Shishov, Osipkov, and Tishchenko
where P
load
is the power, which supplies vehicle
electrical load and P
ATEGmax
is the maximum pos-
sible power under current ATEG operation condi-
tions, g
el.net
. is an average efficiency for the whole
driving cycle.
Modeling Circuit Types of TEMs and ATEG
Sections
The TEMs in the ATEG section can be connected
in parallel or series (Fig. 8). The ATEG generates
maximum power when internal resistance of TEMs
equals the vehicle’s load resistance.
17
Since the
Fig. 2. Surface temperature distribution.
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
50
100
150
200
250
300
350
400
Temperature difference, °C
Fig. 3. Effect of temperature on thermoelectric module internal
resistance.
Fig. 4. Examples of vehicle electrical loads.
Fig. 5. Block diagram of the ATEG.
Development of the Automotive Thermoelectric Generator Electrical Network
ATEG can consist of any number of TEMs, the
electrical circuit will increase with each new TEM
in the schema and the power equations will get new
variables. Any new TEM addition changes the total
ATEG internal resistance. As an example, here is
the calculation for the case of two connected
modules.
The output power for TEMs of parallel circuit
type is:
Pparallel ¼ðETEM1rTEM2 þETEM2 rTEM1 Þ2Rload
ðRloadrTEM1 þrTEM1 rTEM2 þRloadrTEM2 Þ2
ð2Þ
where r
TEM1
,r
TEM2
areinternal resistances of TEMs
and E
TEM1
,E
TEM2
are their electromotive forces. In
the case where TEMs have different temperature
conditions, E
TEM1
and E
TEM2
are not equal, just like
r
TEM1
and r
TEM2
.The output power for series con-
nection is:
Pseries ¼ðETEM1 þETEM2Þ2Rload
ðrTEM1 þrTEM2 þRloadÞ2ð3Þ
P
parallel
and P
series
depend on the applied electrical
load resistance R
load
.
Also, the case of a series–parallel circuit type is
considered when some TEMs are connected in series
0
500
5
10
400
15
Power, W
20
T
hot
, °C
300
25
4
3.5
200 3
R
load
2.5
2
1.5
1
100 0.5
0
Fig. 6. Dependence of thermoelectric module power on heating temperature and load resistance.
Fig. 7. Mathematical model algorithm.
Shiriaev, Shishov, Osipkov, and Tishchenko
and others in parallel. Thus, during modeling, the
following examples of characteristic curves are
obtained (Fig. 9). All curves are for six TEMs where
the temperature on the hot side T
hot
= 450°C and
cold side T
cold
=50°C.
The module demonstrated that the series–parallel
connection is not acceptable due to the decrease in
the output power of the ATEG. Regardless of the
ratio of how many modules are connected in parallel
and how many in series, the maximum power of a
series–parallel connection will always be less than a
parallel connection or a series connection. This is
explained by the fact that not all TEMs are in
optimal operating conditions. Despite the series and
parallel circuit types have the same value of max-
imum power, for the parallel connection, the output
currents are high, and the range of equivalent
resistance is small. Such a sharp curve for a parallel
connection, as opposed to a series one, can be
explained by Eqs. 4and 5. If we assume that
E
TEM1
=E
TEM2
=Eand r
TEM1
=r
TEM2
=r, due to
the same temperature difference of 400°C for each
TEM, then Eqs. 2and 3for the two modules
become:
Pparallel ¼4E2Rload
ð2Rload þrÞ2ð4Þ
Pseries ¼4E2Rload
ðRload þ2rÞ2ð5Þ
Since in the denominator of Eq. 4the coefficient of
the higher degree of the polynomial is greater than
in Eq. 5, it follows that the curve for the parallel
connection will be sharper than for the series
connection. With the addition of more TEMs, the
sharpness of the curve will only increase. Conse-
quently, it complicates the selection of the suit-
able R
load
. Thereby, the series connection type of the
TEMs is better due to its wide range of suitable re-
sistance. Also, high currents, which appear when
TEMs are connected in parallel, lead to Joule
heating in wires and the converter, thus further
decreasing the overall system electrical efficiency.
18
Although in this paper the issue of connection
reliability is not considered, it is worth noting that
in the case of a series connection a single TEM
failure leads to a break of the entire electrical
circuit. The developer should bear this in mind
during the design of an ATEG electrical network.
Connection of the TEMs with different tempera-
ture conditions is not desirable. In the temperature-
mismatched condition, the TEMs produce less
power, which is proved in the study of temperature
mismatch effect on TEMs electrically connected in
series and parallel.
18
We know about the existing
temperature gradient on the ATEG heat exchanger
surface, but previous research shows that it can be
assumed that the TEMs within one section is in the
Fig. 8. TEMs circuit type: parallel (a) and series (b).
123456789
10
Rload
0
20
40
60
80
100
120
Power, W
Thot = 450 °C
P = 112.88 W
U = 21.6 V
I = 5.23 A
R = 4.13 Ω
P = 90.3 W
U = 14.4 V
I = 6.27 A
R = 2.3 Ω
P = 112.87 W
U = 3.63 V
I = 31.09 A
R = 0.12 Ω
, Ω
TEMs series circuit type
TEMs parallel circuit type
TEMs series-parallel circuit type
Connection types of TEMs
Fig. 9. Dependence of the ATEG output power on TEMs circuit type.
Development of the Automotive Thermoelectric Generator Electrical Network
same temperature difference. Therefore, within the
single section, the TEMs are connected together in
series. However, the sections connection decreases
maximum ATEG power. The simulation for differ-
ent sections with different temperatures on the hot
side confirms this (Fig. 10). Equivalent electrical
load for this simulation R
load
=6X. It is also
recommended for each section to have its own
MPPT controller.
Modeling the Operation of the MPPT Con-
troller
The model allows one to specify a controller with
different circuit design, different algorithms and
data collection speed from current and voltage
sensors. In this article, we simulate the buck-boost
converter with the perturb and observe (P&O)
algorithm
19
with a modification of the duty cycle
step reduction as the system approaches the max-
imum power point (Fig. 11).
The MPPT controller Simulink model (Fig. 12)
with the help of its solver show changes in the
ATEG power characteristics during the controller’s
operating time. The modified MPPT algorithm is
programmed in Matlab and built into the MPPT
block of the Simulink model. The input data for the
MPPT block are current and voltage at the current
time. Their values are multiplied inside the pro-
gram code, and the power change in comparison to
the previous time step is determined. According to
the work of the P&O algorithm after assessing the
change in power and voltage, a new duty cycle is set.
The duty cycle changes by a step, the value of which
is determined according to the idea of the curve’s
inclination angle (Fig. 11). Further, taking into
account which part of the circuit should be operated,
boost or buck, the corresponding values of the duty
cycle go to the PWM blocks. The PWM blocks
convert the value of the duty cycle into a signal that
controls the transistors: switches them periodically
or turns them off/on. The PWM signal change of the
Simulink model is based on the principles, which
are precisely described in Kazimierczuk’s book in
the chapter of the analysis of the PWM buck-boost
converter.
20
Therefore, with the help of this model, it is
possible to optimize the work of the MPPT controller
by observing algorithm speed, accuracy and the
operation of the circuit electronic components. Sim-
ulated changes in the electrical characteristics of
one TEM are shown in Fig. 13.
Also, the choice of electronic components must
take into account the losses in the circuit they
cause. This directly affects the efficiency of the
ATEG electrical network. Figure 14 shows the
power losses breakdown of the controller main
components.
21
The calculating method for the power loss in the
buck–boost converter
20
is embedded in the
Fig. 10. The connection of ATEG sections with different temperature
conditions.
Fig. 11. Modified P&O algorithm.
Shiriaev, Shishov, Osipkov, and Tishchenko
mathematical model. It considers power losses in
components due to their resistance and due to an
operation frequency, i.e. switching losses. Also, it is
claimed that the converter circuit should always be
lab tested to verify final electrical and thermal
specifications. For acceptable circuit operation, a
proper pc-board layout and judicious component
placements are as critical as choosing the right
components.
21
For each change in the ATEG output character-
istics, i.e. the input characteristics for the MPPT
controller and the load resistance, the power losses
are calculated. In this way, the model allows
determining converter losses during the vehicle
engine operation on time. The MPPT controller
efficiency depends on the difference between the
input voltage-current and output voltage-current.
Figure 15 presents the power output, which vehicle
Fig. 12. MPPT controller Simulink model.
Fig. 13. Oscillogram of the MPPT operation in Simulink.
Development of the Automotive Thermoelectric Generator Electrical Network
consumes, for the case when the MPPT controller is
installed in the electrical network. It is seen how the
electrical losses depend on the load. So according to
the model, the MPPT controller efficiency may vary
from 70% to 97%. The MPPT controller efficiency is:
gMPPT ¼Poutput
Pinput
ð6Þ
where g
MPPT
is the ratio of output power P
output
to
input power P
input
.
Furthermore, during the simulation and experi-
mental test, it is found that the MPPT controller
should have applicability limits. As shown in
Fig. 15, there is the limit when the use of the MPPT
controller is not effective due to its own losses. In
this situation, the connection of the ATEG directly
to the electrical load can increase the electrical
network efficiency. However, the device that
switches between the state of direct connection to
the load and through the converter may also require
energy. In this paper, we do not study this issue, but
we suppose that it should be considered during
electrical network design.
It is important to note that the voltage for the
maximum power point is often not the same as the
battery charging voltage. The output voltage mostly
requires a constant value for the proper battery
charging (for example 12.5–14.5 V).
22
Otherwise, it
leads to battery damage. So, the MPPT system must
be integrated into the DC/DC converter, because its
output voltage is proper for a car battery. However,
during the conversion for the required voltage, there
are losses on the DC/DC converter. The mathemat-
ical model allows taking them into account due to the
calculation procedure described in ‘‘Pulse-Width
Modulated DC–DC Power Converters’’.
20
Therefore,
the total electrical losses depend on two things. The
first is the conversion loss that occurs when the
output voltage is adjusted to the value of the battery
voltage. The second is the loss that appears when
MPPT controller tracks the maximum power point.
Modeling the ATEG Electrical Network
in Non-stationary Operating Conditions
Nowadays, it is believed that the main purpose of
the ATEG is fuel economy.
6
Many research groups
Fig. 14. Controller components electrical losses.
T
hot
= 450 °C
P = 112.88 W
U = 21.62 V
Possible ATEG maximum power, W
Output power without MPPT controller, W
Output power with MPPT controller, W
Applicability limit of MPPT controller
ATEG voltage, V
ATEG current, A
0.4 2 3.6 5.2 6.8 8.4 10 11.6 13.2 14.8 16.4 18 19.6
R
load
Power, W
T
hot
= 450 °C
P = 112.88 W
U = 21.62 V
Possible ATEG maximum power, W
Output power without MPPT controller, W
Output power with MPPT controller, W
Applicability limit of MPPT controller
ATEG voltage, V
ATEG current, A
MPPT controller usage
MPPT controller usage
0
20
40
60
80
100
120
Fig. 15. Output power of the ATEG electrical network with losses.
Shiriaev, Shishov, Osipkov, and Tishchenko
are studying their automotive thermoelectric gen-
erators, not from the position of getting maximum
power in stationary conditions; they tend to test
their systems in non-stationary conditions, i.e. in
those that are closest to the work of the engine in
real driving conditions.
23–28
Such tests are called
driving cycles and this test allows estimation of the
fuel economy. They imitate the car movement—its
speed changes during the distance and a certain
time.
The greatest interest for us is the changes in
temperature on the ATEG surface. They affect the
output power of the TEMs. The prediction of the
surface temperature for the driving cycles is a
difficult task, which involves errors. The collection
of data based on temperature by thermocouples
seems a suitable solution. In this paper, we have
chosen NEDC as an example. So we used collected
temperature data from standard tests and add it to
the mathematical module. Figure 16 shows the
ATEG first section temperature changes during
NEDC, which are obtained experimentally.
Although the changes in engine speed follow the
classic NEDC graph, their irregular behavior is
noticeable, especially after 800 s. Conventional
experiments are carried out while the entire vehicle
is running, i.e. when the car’s wheels are loaded. In
our case we directly regulate the engine, which
makes maintaing constant speed difficult. However,
because the ATEG seems to be a highly inert
system, the speed fluctuation cannot greatly affect
the change in temperature of the ATEG’s surface,
which is why these irregular speed changes are not
critical.
EXPERIMENTAL VERIFICATION AND
RESULTS
We designed a test stand to study the effective-
ness of the ATEG electrical network (Fig. 17). It
consists of the ATEG and the petrol engine VAZ-
21127, which is a source of exhaust gases. The
operation of the engine is regulated by a hydraulic
load device. The supervisory control and data
acquisition system allows adjusting all components
of the test stand and collecting data from them. The
Fig. 16. NEDC for the ATEG.
Fig. 17. The ATEG test stand.
250 270.3 308.6 375.8 438.5 483.2
0
20
40
60
80
100
120
140
160
Power, W
Maximum measured power
Measured power with MPPT controller
Measured power without MPPT controller
Maximum modeled power
Modeled power with MPPT controller
Modeled power without MPPT controller
15 %
Difference between model and experiment
17 %
R
load
Fig. 18. Mathematical model verification.
Development of the Automotive Thermoelectric Generator Electrical Network
ATEG electrical network is imitated by the elec-
tronic load, the battery and the MPPT controller.
We use a buck–boost MPPT converter, due to its
capability of covering all I–Vcharacteristics. Also, it
has a rather high average tracking efficiency at the
low cost of the implementation and at the medium
complexity of the hardware.
29
Since there is no
rapid change in the parameters of ATEG’s electrical
network due to the smooth heating of the ATEG’s
surface, there is no need for a DC–DC converter
with high operating speed. The buck-boost topology
completely copes with its task.
The mathematical model has been verified for
different operating modes. Figure 18 shows the
average values of the experimental data. According
to the results, the difference between the experi-
ment and the model is not more than 20%. This
allows us to assume that the model is applicable for
estimating the electrical characteristics of the
ATEG.
Thereby, knowing the surface temperature dur-
ing NEDC, the output power of the electrical
network in NEDC is plotted (Fig. 19). During
modeling, it is assumed that the battery is not in a
fully charged state, and its required charging
voltage is 12 volts. The curve of the maximum
possible output power, i.e. power without any losses,
is a reference curve. The results are compared to it
for evaluating the efficiency of the ATEG electrical
network g
eff
.
In this way, Table Iis compiled as per the results
of the electrical network simulation. It presents
average powers in NEDC and the electrical network
efficiencies. The results are presented for electrical
networks with the installed vehicle battery. The
simulation confirms that for the cases where the
equivalent load (R
load
=1X) is mismatched with the
ATEG resistance the MPPT usage is necessary and
the controller increases efficiency up to 26%. How-
ever, for the case when the resistances are almost
equal, i.e. the case of the matched electrical load
(R
load
=4X), the efficiency of the schema without
MPPT controller is higher. This is because electrical
power is directly supplied to the load and does not
lose energy on the MPPT converter, which has
electrical losses on its components, as described
earlier. The MPPT converter’s electrical losses
decrease the entire electrical network’s efficiency,
which proves the idea of the MPPT controller
applicability limits.
Based on the current study, the methodology of
the ATEG electrical network design is formed
(Fig. 20). Following these steps, the designer comes
to the choice of such TEM circuits and MPPT
controllers that ensure the highest reduction in fuel
consumption.
Also, according to the conducted research, the
following recommendations are for the ATEG elec-
trical network design:
1. Thermoelectric modules should be connected in
series inside the ATEG sections, due to a wide
range of equivalent load resistances. In the case
of the parallel connection the range of possible
load equivalents is narrowed, thereby narrow-
ing the area of equivalent resistances and
making it difficult to find the matched one.
Also, in a parallel schema high currents lead to
additional losses due to heating of converter and
wires.
2. ATEG sections should not be connected with
each other, because their thermoelectric mod-
ules are in different temperature conditions,
which lead to power losses.
3. There must be a balance between the number of
DC/DC converters and a number of TEMs
connected into an array controlled by one of
them.
18
However, there must be at least one
DC/DC converter per ATEG section.
0 200 400 600 800 1000
Time, s
0
20
40
60
80
100
120
Power, W
Maximum possible output power
Power without MPPT converter (Rload
Power with MPPT converter (Rload
Power without MPPT converter (Rload
Power with MPPT converter (Rload
Fig. 19. Electrical network output powers during NEDC.
Table I. ATEG electrical network efficiency (section fi1) in NEDC
ATEG electrical network type
Average
power (W)
Efficiency,
g
el. net.
The case of mismatched electrical load (R
load
=1X) With MPPT converter 64.33 91.1%
Without MPPT converter 45.97 65.1%
The case of matched electrical load (R
load
=4X) With MPPT converter 68.43 96.9%
Without MPPT converter 68.57 97.1%
Maximum power 70.57
Shiriaev, Shishov, Osipkov, and Tishchenko
4. The DC/DC converter must be equipped with an
MPPT algorithm providing the maximum out-
put power of the ATEG under various engine
operating conditions.
5. Timely disconnection of the MPPT controller
from the electrical network and the ATEG
direct connection to the electrical load leads to
the possibility of obtaining additional efficiency.
CONCLUSIONS
The mathematical model of the ATEG electrical
network is developed. It allows specifying the ATEG
with a different type and number of thermoelectric
modules and simulating the operation of the MPPT
converter. Also, the model calculates the losses
affecting the efficiency of the entire system.
Fig. 20. The ATEG electrical network design methodology.
Development of the Automotive Thermoelectric Generator Electrical Network
The test stand for verifying theoretical research is
designed. The experimental results show the prac-
ticality of theoretical research which encompasses
error more or less 20%. Consequently, we could
state that the mathematical model can be used for
predicting ATEG power characteristics and electri-
cal network losses.
The methodology of ATEG electrical network’s
design is proposed. It shows the way of the prelim-
inary estimation of the electrical network’s effi-
ciency. The recommendations for ATEG developers
are given.
ACKNOWLEDGMENTS
This paper was financially supported by the
Ministry of Education and Science of the Russian
Federation on the program to improve the compet-
itiveness of Peoples’ Friendship University of Rus-
sia (RUDN University) among the world’s leading
research and education centers in the 2016–2020.
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Shiriaev, Shishov, Osipkov, and Tishchenko
