CC BY
3
Civil Aviation High Technologies
Vol. 27, No. 04, 2024
УДК 629.7.064.52
DOI: 10.26467/2079-0619-2024-27-4-50-62
Algorithm for the synthesis of equations of thermal conductivity of lithium-ion accumulator for finite volumes during division
E.A. Punt1
Moscow State Technical University of Civil Aviation, Moscow, Russia
Abstract: The current level of technology development makes it possible to improve the volumes of on-board equipment significantly, the same applies to backup power supply systems, in which the use of lithium-ion batteries is promising, which, if there are significant advantages, have a number of disadvantages that must be taken into account when using them. First of all, this is thermal acceleration, which is caused by internal physico-chemical processes and improper operation. To prevent thermal overclocking, it is proposed to use a digital twin, the basis of which is a mathematical model of thermal processes of a lithium-ion battery, obtained by mathematical prototyping of energy processes. For the numerical implementation of the mathematical prototyping method, it is proposed to use a modified finite volume method with the implementation of the division procedure until the required accuracy of the model is obtained. The presented article discusses the procedure for the formation of thermal conductivity equations when modeling the dynamic distribution of the thermal field in a lithium-ion battery in a three-plane formulation of the problem. This procedure is necessary when implementing the modified finite element method using the method of mathematical prototyping of energy processes, which involves dividing finite volumes to achieve the required calculation accuracy. A special feature of the division procedure is the change in volumes, areas of contact of interacting elements, and the change in elements that are sources of heat. In the simulation cycle, it is necessary to re-form the system of differential equations, taking into account the changes that occurred after the division. For clarity, the article discusses the procedures for dividing volumes into two equal parts according to one of the coordinates, and the Cartesian coordinate system is also considered to obtain a model. The proposed procedure for forming a system of differential equations is implemented in Python, the simulation results have shown the adequacy of the model and the efficiency of the proposed method.
Key words: lithium-ion battery, modified finite volume method, diagnostic method, method of mathematical prototyping of energy processes.
For citation: Punt, E.A. (2024). Algorithm for the synthesis of equations of thermal conductivity of lithium-ion accumulator for finite volumes during division. Civil Aviation High Technologies, vol. 27, no. 4, pp. 50-62. DOI: 10.26467/2079-0619-2024-27-450-62
Алгоритм синтеза уравнений теплопроводности литийионного аккумулятора для конечных объемов при делении
Е.А. Пунт1
1 Московский государственный технический университет гражданской авиации,
г. Москва, Россия
Аннотация: Современный уровень развития техники и технологий позволяет существенно улучшить возможности бортового оборудования, это же касается и систем резервного электропитания, в которых перспективным представляется применение литийионных аккумуляторных батарей, которые при наличии существенных преимуществ обладают рядом недостатков, которые необходимо учитывать при их использовании. В первую очередь это тепловой разгон, обусловленный внутренними физико-химическими процессами и неправильной эксплуатацией. Для предотвращения теплового разгона предлагается использовать цифровой двойник, основой которого является математическая модель тепловых процессов литийионного аккумулятора, полученная методом математического прототипирования энергетических процессов. Для численной реализации метода математического прототипирования предложено использовать модифицированный метод конечных объемов с реализацией процедуры деления до получения требуемой точности модели. В представленной статье рассматривается процедура формирования уравнений теплопроводности при
Vol. 27, No. 04, 2024
Civil Aviation High Technologies
моделировании динамического распределения теплового поля в литийионном аккумуляторе в трехмерной постановке задачи. Эта процедура необходима при реализации модифицированного метода конечных элементов с помощью метода математического прототипирования энергетических процессов, который предполагает деление конечных объемов для достижения требуемой точности расчетов. Особенностью процедуры деления является изменение объемов, площадей соприкосновения взаимодействующих элементов, изменение элементов, которые являются источниками тепла. В цикле моделирования необходимо заново формировать систему дифференциальных уравнений с учетом тех изменений, которые произошли после деления. Для наглядности в статье рассматриваются процедуры деления объемов на две равные части по одной из координат, также для получения модели рассматривается декартова система координат. Предложенная процедура формирования системы дифференциальных уравнений реализована в среде Python, результаты моделирования показали адекватность модели и работоспособность предлагаемого метода.
Ключевые слова: литийионный аккумулятор, модифицированный метод конечных объемов, метод диагностики, метод математического прототипирования энергетических процессов.
Для цитирования: Пунт Е.А. Алгоритм синтеза уравнений теплопроводности литийионного аккумулятора для конечных объемов при делении // Научный Вестник МГТУ ГА. 2024. Т. 27, № 4. С. 50-62. DOI: 10.26467/2079-06192024-27-4-50-62
Introduction
The current stage of aircraft electrical engineering development is new chemical current sources - lithium-ion batteries and hydrogen fuel elements [1, 2], semiconductor, conductor and magnetic devices implementation. The given technologies make it possible to both significantly improve the volumes of on-board equipment and create new aircraft, in which the electromechanical engine is the basic element, empowered by chemical current sources [2, 3]. The same applies to backup power supply systems, in which the use of lithium-ion batteries is promising, which, if there are significant advantages among other battery types in terms of specific energy [4, 5], have a dramatic disadvantage - they are exposed to thermal acceleration in certain external conditions and while being recharged. Besides that, lithium-ion batteries (LIB) operation temperature increase significantly reduces its capacity, which affects its operation features.
There is a number of publications [6-9] on LIB thermal operation modes, in which diverse approaches of the given phenomenon prevention - by using new materials, technologies, operation rules, etc. [10-12] - are presented. It is important to reveal the reasons of emergency in advance, for instance, by forecasting the thermal limit values within the batteries [13-16] in terms of operation.
It is proposed to use a modified finite volume method, in which the thermal conductivity equa-
tion synthesis is the particular issue based on mathematical prototyping of energy processes [17-19] for forecasting the reaching of LIB thermal limit, as the regular capacity division procedure involves forming a new differential equations system for new finite capacities set.
It is assumed to use the presented thermal condition diagnosis and forecasting approach for lithium-ion current sources of on-board power systems as a thermal process digital twin [20-23], integrated into promising aircraft power system [24, 25] smart current distribution schemes.
Research methods and methodology
Mathematical prototyping of energy processes method [18-20] is the basic one for LIB thermal condition diagnosis and forecasting, which a mathematical model, meeting the basic conservation and thermodynamic laws and analytic expressions for thermal scalar field distribution can be obtained with, allowing then to forecast thermal changes taking into consideration the known influencing factors.
The following general form of mathematical prototyping of energy processes equations presentation [19] should be used for thermody-namical problems:
Civil Aviation High Technologies
Vol. 27, No. 04, 2024
dW = dU - T*dS,
dS = X
11 T _
mU mU
u=XU+ X ф>,
i=1 i=mrr+1
d0t = -X X°kdxk, i = mU+1,mu,
k=1
dxk = X^b ÔAXr + Г dxk
dt r=i ' dt V dt Jext V dt ;ext
dXk T' . — I , k = 1,mr,
dU ôQi
dx,
-X Xi-k-TT' i = 1,mu,
dt dt k=1 dt
¿a = x -X Qер)
dt dt
Г mt f 1
j=i+1
dt
••'Ax
X к
ÖQT) , Г ôQr
ôQr
dt
r=1 dt л л
dt
dt
i = 1-mU,
X X Xl,k+ X Xl,k
AF.
Ax,r
V k=1 \ l=1
T
l=mU +1
Г mx mU
öAx,
i=1
Ti
i
J
mu
dt
-- r = 1-mAx-
\ л
X ßi,r^T X X Xl.k+ X Xlk
vk=1 v
l=1
l=mu+1
k,r
J
- r = 1-mAx-
T T
AFQj=T ~ Y-j = 1-j -1- i = 2-mu-
i 1
XAx mU l-1 mAx _
0Axr _ X X aQlg AF + XaAx,qAF r = 1 zL Z-t UAx,rZJ1 Q,g UAx,rnl Ax,q ' ' 1>
dt
m
Ax
l=2 g=1 eP) mu l-1
q=1
i1
dt
XXaQj AFq + XaQjAF^ 1 = 1,i -1, i = 2-mu-
l=2 g=1
q=1
(1)
where Ui - energetic degrees of freedom (EDF) inner energies, which are the system condition coordinates;
xk - other condition coordinates (condition
coordinates vector plane);
Qt - the i-th quantity of thermal component
of the EDF system obtained; bkr - topology matrix components, commonly obtained from conservation laws;
(Ql*ix,, (¿Qi/d< ¿'KM)t -
external thermal streams in and out of EDF system and their occasional components;
(dxkjdt )) - external streams in and out of
other condition coordinates system(s) and
their occasional components;
Qj) - thermal volumes between the EDF
(destination from the smaller values to the bigger ones is considered to be the positive direction of every thermal between the EDFs);
Axr - other processes coordinates besides
thermal shift between the EDFs;
QrHeK) - uncompensated thermals, arisen
during physical and chemical processes (irreversible work shifting into thermal); Pir > 0 - uncompensated thermal propor-
U
tions by EDFs, meeting X ßir =1 condition;
i=1
Vol. 27, No. 04, 2024
Civil Aviation High Technologies
Tt > 0 - the EDF temperatures; X.k - thermodynamic potentials of essential EDFs interaction by xk condition coordinates;
AFQij - dynamic powers, thermal shift between EDFs driving processes; AFAxr - dynamic powers, driving the other
processes;
T* - the reference temperature, which the W
system free energy is set through;
AaQj, AaAq, AAfxf , AA^ - positive dis-
sipative matrix components; S - system enthropy; U - total system inner energy; - EDFs interaction energies.
Setting the problem
The equilibrium thermodynamic system, in which all the components (finite capacities) are of constant thermal capacity and conductivity, thermolysis coefficients between the adjacent elements are also the constant ones, all the capacities are set by inequation systems and planes, parallel to the Cartesian coordinate system planes, is the subject of the given research.
The battery having a single electrode, both positive and a negative one (fig. 1), with an electrolyte in between, is then the object. Component densities and ohmic resistances are all constant ones. There are the extra areas (finite capacities) between the battery, imitating the area environment, which the inner boundary the temperature is constant on.
The general matrix differential equation of a variable plane based on mathematical prototyping of energy processes method is made for temperature distribution calculation in the battery researched:
CpV dT=AT+TJ+Q,
(2)
where C - thermal conductivity matrix of the researched objects; p - matrix of capacity densities;
T = (T],..., Tn)r - column vector of every capacity temperature;
n - capacity quantity, which all the researched space is divided into, this quantity increases after the division, which all the matrixes of equation (2) changing; A - matrix for thermal conductivity, thermal transfer and thermolysis surface areas; T01 - matrix for conductivity thermal transfer with the environment; T0 - environment temperature; Q - inner thermal source due to currents in electrodes and an electrolyte.
With K = CpV
K dTT=AT+T01T0+Q
(3)
Fig. 1. Spatial model of the battery
is obtained.
It is necessary to divide subsequently the capacities, calculate all capacity temperature dynamics change and form thermal dynamic sca-lars analytic functions for the given geometry of the researched space in accordance with modified finite capacities method procedure.
Mathematical model equation synthesis algorithm
The quantity of equations in the model (all the matrix planes) and all the matrixes K, A,T01,Q themselves in equation (3) both change while implementing the given method, which is its fundamental problem. Changes in all
Civil Aviation High Technologies
Vol. 27, No. 04, 2024
Начало - Start;
Задание геометрии, свойств веществ и справочных данных - Setting the geometry, substance features and reference data;
Первичное разбиение области расчета - Primary calculation area division;
Каждый элемент - отдельный объем - Every single element is a particular capability;
Деление всех объемов пополам -All the capabilities division in half;
Новые свойства объекта - New object features;
Расчет новых координат - New coordinates calculation;
Расчет новых границ - New boundaries calculation;
Расчет нового объема - New capability calculation;
Расчет токов - Currents calculation;
Расчет сопротивлений - Resistances calculation;
Новые свойства взаимодействия объекта - New object interaction features;
Расчет площадей соприкосновения объектов - Object contiguity squares calculation;
Расчет новых матриц в уравнениях ММПЭП - New matrixes
in in the modified finite volume method calculation;
Конец - Finish
Fig. 2. The algorithm for the synthesis of thermal conductivity equations in the division of elements
in the modified finite volume method
volume geometrical parameters are the first ground for it.
There is the algorithm of equation (3) forming and matrixes recalculation in Figure 2. Equation (3) is then presented as differential figure integration equation with Eyler's method.
Ti=Ti_1 + K1 {AT-1 + To1To+Q)At. (4)
Recalculation procedures are divided into two steps: forming the new object features after
division and new system features, responsible for object interaction (thermal transfer in the given case), which is the algorithm peculiarity.
New object essential feature determination procedure is quite simplified due to use of object-focused programming technology: all substance features (thermal conductivity, thermal capacity, density, specific ohmic resistance, current densities at all the coordinates), along with integral features (mass, volume, ohmic resistance, mass centre coordinates) calculation
Vol. 27, No. 04, 2024
Civil Aviation High Technologies
Fig. 3. Possible combinations of the intersection of the faces of two volumes along the X-axis that are in the same plane
methods are inherited from parental objects after division. Only boundary space coordinates are redetermined depending on division concept. Volume division in half at all the Cartesian coordinates is observed in the given paper - that is the new object boundary coordinate determination procedure is simplified due to without violating the general principle of mathematical model forming. These features are used for K and Q matrixes determination.
The procedure of new object interaction features determination, which is to be run again for all the system objects after the division, should be observed particularly. These features are necessary for thermal transfer parameter determination, primarily depending on their contiguity surface area.
Besides the new interacting couples multitude it is necessary to determine thermal transfer coefficients (during object interaction from different substances) or thermal conductivity coefficients (for the same substances in the object couple). These features are used for A and T01 matrixes forming.
It is necessary to observe all the couples of the system object multitude, which is the procedure peculiriality, then there are 6 interaction variants for all the coordiantes (x, y, z) of all the volumes couples in case the object faces are in the same plane:
variants 1 and 2 - the second object boundary surface area is within the first object surface area (fig. 3, A, E) or the first object boundary
Civil Aviation High Technologies
Vol. 27, No. 04, 2024
surface area is within the second object surface area;
variants 3 and 4 - surface areas do not overlap (fig. 3, B, /);
variants 5 and 6 - surface area overlapping, during which every couple object surface areas overlap only partly (fig. 3, ff, E).
Research results
The presented synthesis algorithm is implemented in Python environment with object-focused technology use. The following procedures are implemented in program complex:
- the initial material features reference data setting;
- forming a fundamental "volume" unit, which is a predecessor of all the new units;
- forming a unit collection, inherited from the fundamental one and their interaction parameter determination;
- object division (in half with a plane) at all the Cartesian coordinates;
- geometrical parameters and K, A, T01 and Q matrixes calculation;
- support procedures.
Numerical experiments demonstrated that the given method allows to determine temperature field and obtain thermal scalar field analytical functions quite accurately even having done a small amount of divisions and, consequently, having obtained a small amount of object which the researched space is divided into.
There is the initial battery geometry in Figure 4:
- X(0; 0,02); Y(0; 0,02); Z(0; 0,02) - volume for modelling the electrode 1;
- X(0,02; 0,04); Y(0; 0,02); Z(0; 0,02) - volume for modelling an electrolyte;
- X(0,04; 0,06); Y(0; 0,02); Z(0; 0,02) - volume for modelling the electrode 2;
and extra air volumes:
- X(-0,06; 0); Y(0; 0,02); Z(0; 0,02) - volume for modelling air boundary with electrode 1 (by X axis);
Vol. 27, No. 04, 2024
Civil Aviation High Technologies
Fig. 5. Temperature distribution inside the volume X = (-0,06; 0); Y = (0; 0,02); Z = (0; 0,02) when dividing by coordinate X (Усредненная координата Х - Mean X coordinate)
- X(0,06; 0,12); Y(0; 0,02); Z(0; 0,02) - volume for modelling air boundary with electrode 2 (by X axis);
- X(-0,06; 0,12); Y(0; 0,02); Z(0,02; 0,04) -volume for modelling the above air boundary with the battery (by Z axis);
- X(-0,06; 0,12); Y(0; 0,02); Z(-0,04; 0) -volume for modelling the below air boundary with the battery (by Z axis);
- X(-0,06; 0,12); Y(0,04; 0,02); Z(0; 0,02) -volume for modelling the front air boundary with the battery (by Y axis);
- X(-0,06; 0,12); Y(-0,04; 0); Z(0; 0,02) -volume for modelling the back air boundary with the battery (by Y axis).
Temperature field was calculated with the modified finite volumes method for the initial scheme (fig. 4). Temperature field was calculated for air volumes. The results are presented in Figures 5-7.
Judging by graphs in Figures 5-7 obtained, area above the electrolyte is the most heated one, which matches the experiment results. The data obtained may be used for forming the analytical expression, which lithium-ion battery pre-failure stages diagnosis method will be based on.
Conclusion
1. Automatical thermal conduction equation synthesis algorithm is obtained through modified finite volume method, involving space division during calculation, with, consequently, equation synthesis at every iteration required.
2. The algorithm is implemented in the Python object-focused program environment for lithium-ion battery fundamental prismatic geometry, graphs of temperature dependence on space coordinates, analysis of which has demonstrated the appropriate resemblance with genuine physical processes, are obtained.
3. The equation synthesis algorithm presented is developed considering the assumption about all the volumes presented as rectangular parallelepipeds, which faces are parallel to the basic Cartesian coordinates planes. It is necessary to revise some of the algorithm procedures for any other division shape.
4. The direct forming of electrotechnical aircraft equipment temperature scalar field analytical dynamic models is the development of the algorithm presented.
Civil Aviation High Technologies
Vol. 27, No. 04, 2024
Fig. 6. Temperature distribution inside the volume Х = (-0,06; 0,12); Y = (0,00; 0,02); Z = (0,02; 0,04) when dividing by coordinate X (Усредненная координата Х - Mean X coordinate)
Fig. 7. Temperature distribution inside the volume Х = (-0,06; 0,12); Y = (0,02; 0,04); Z = (-0,02; 0,04) when dividing by coordinate X (Усредненная координата Х - Mean X coordinate)
References
1. Schefer, H., Mallwitz, R., Fauth, L.
(2020). Discussion on electric power supply systems for all electric aircraft. IEEE Access,
vol. 8, pp. 84188-84216. DOI: 10.1109/ ACCESS.2020.2991804 (accessed: 13.01.2024).
2. Kudryakov, S.A., Bunas, K.V. (2019). Analysis of the state and trends in the development of aviation power supply systems. Molodoy uchenyy, no. 40 (278), pp. 19-21. (in Russian)
3. Arzamastseva, V.A., Sagitov, D.I.
(2024). Trends and prospects for the development of aviation electrical equipment. Dostizheniya nauki i obrazovaniya, no. 2 (93), pp. 4-6. (in Russian)
4. Khalyutin, S.P., Davidov, A.O. (2019). Aircraft electrical power systems specific properties evaluation. Elektropitaniye, no. 2, pp. 43-54. (in Russian)
5. Sokolov, O.A., Melikhov, I.P. (2023). Application of aviation batteries. Alleya nauki, vol. 1, no. 10 (85). pp. 209-219. (in Russian)
6. Shesterikova, D.S., Obrokova, E.I., Grigoreva, M.D. (2021). Trends in the development of electric-powered aircraftt. XXV Tupolev-skiye chteniya (shkola molodykh uchenykh): sbornik trudov Mezhdunarodnoy molodezhnoy nauchnoy konferentsii, posvyashchennyy 60-letiyu so dnya osushchestvleniya Pervogo poleta che-loveka v kosmicheskoye prostranstvo i 90-letiyu Kazanskogo issledovatelskogo universiteta im. A.N. Tupoleva - KAI. Kazan: Izdatelstvo IP Sagiyeva A.R., pp. 384-390. (in Russian)
7. Zhang, H., Fotouhi, A., Auger, D.J., Lowe, M. (2024). Battery temperature prediction using an adaptive neuro-fuzzy inference system. Batteries, vol. 10, no. 3, ID: 85. DOI: 10.3390/ batteries10030085 (accessed: 13.01.2024).
8. Aiello, L., Ruchti, P., Vitzthum, S., Coren, F. (2024). Influence of pressure, temperature and discharge rate on the electrical performances of a commercial pouch li-ion battery. Batteries, vol. 10, no. 3, ID: 72. DOI: 10.3390/ batteries10030072 (accessed: 13.01.2024).
9. Li, W., Xie, Y., Li, W., Wang, Y., Dan, D., Qian, Y., Zhang, Y. (2024). A novel quick temperature prediction algorithm for battery thermal management systems based on a flat heat pipe. Batteries, vol. 10, no. 1, ID: 19. DOI: 10.3390/batteries10010019 (accessed: 13.01.2024).
10. Kafadarova, N., Sotirov, S., Herbst, F., Stoynova, A., Rizanov, S. (2023). A system for determining the surface temperature of cylindrical lithium-ion batteries using a thermal imaging camera. Batteries, vol. 9, no. 10, ID: 519. DOI: 10.3390/batteries9100519 (accessed: 13.01.2024).
11. Wang, X., Zhang, Y., Deng, Y., Yuan, Y., Zhang, F., Lv, S., Zhu, Y., Ni, H.
(2023). Effects of different charging currents and temperatures on the voltage plateau behavior of li-ion batteries. Batteries, vol. 9, no. 1, ID: 42. DOI: 10.3390/batteries9010042 (accessed: 13.01.2024).
12. Spitthoff, L., Burheim, O.S., Shearing, P.R. (2021). Temperature, ageing and thermal management of lithium-ion batteries. Energies, vol. 14, no. 5, ID: 1248. DOI: 10.3390/en140 51248 (accessed: 13.01.2024).
13. Kong, D., Gongquan, W., Ping, P., Wen, J. (2021). Numerical investigation of thermal runaway behavior of lithium-ion batteries with different battery materials and heating conditions. Applied Thermal Engineering, vol. 189, ID: 116661. DOI: 10.1016/j.applthermaleng. 2021.116661 (accessed: 13.01.2024).
14. Smelkov, G.I., Pehotikov, V.A., Bokov, G.V., Nazarov, A.A. (2022). Fire safety problems of the thermal acceleration mode in lithium storage batteries. Fire safety, no. 4 (109), pp. 73-79. DOI: 10.37657/vniipo.pb.2022.109. 4.008 (in Russian)
15. Kharlamenkov, A.S. (2022). The fire hazard of the use of lithium-ion batteries in Russia. Fire and Explosion Safety, vol. 31, no. 3, pp. 96-102. (in Russian)
16. Keller, M.V., Savenko, A.E. (2023). Assessment, monitoring and safety during thermal heating for lithium-ion batteries. Bulletin of Kerch State Marine Technological University. Series: Marine Technology, no. 1, pp. 23-31. (in Russian)
17. Punt, E.A., Khalyutin, S.P., Tro-shin, M.O., Starostin, I.E. (2023). Modified finite volume method study for numerical calculation of lithium battery temperature. 2023 IEEE 24th International Conference of Young Professionals in Electron Devices and Materials (EDM), pp. 1230-1234. DOI: 10.1109/EDM583 54.2023.10225111
18. Khalyutin, S.P., Starostin, I.E., Agafonkina, I.V. (2023). Generalized method of mathematical prototyping of energy processes for digital Twins development. Energies, vol. 16, no. 4, ID: 1933. DOI: 10.3390/en16041933 (accessed: 13.01.2024).
19. Starostin, I.E., Khalyutin, S.P., Parievskiy, V.V. (2022). Types and forms of
representation of the basic equations of the method of mathematical prototyping of energy processes. Elektropitaniye, no. 4, pp. 4-14. (in Russian)
20. Starostin, I.E., Khalyutin, S.P. (2023). Obtaining analytical solutions to equations of the method of mathematical prototyping of energy processes using neural networks. In: XVI Vse-rossiyskaya multikonferentsiya po problemam upravleniya (MKPU-2023): Materialy multikon-ferentsii. V 4-kh tomakh. Tom 3. Volgograd: Volgogradskiy gosudarstvennyy tekhnicheskiy universitet, pp. 80-82. (in Russian)
21. Brucherseifer, E., Fay, A. (2021). Digital Twins. at - Automatisierungstechnik, vol. 69, no. 12, pp. 1023-1025. DOI: 10.1515/auto-2021-0155
22. Fimushin, A.S., Slavinsky, A.S., Kapustin, A.V. (2023). Digital technologies in the control and forecasting of the technical condition of aviation equipment. In: Aktualnyye problemy i perspektivy razvitiya grazhdanskoy aviatsii: sbornik trudov XII Mezhdunarodnoy nauchno-prakticheskoy konferentsii, posvya-shchennoy prazdnovaniyu 100-letiya otechest-vennoy grazhdanskoy aviatsii. Irkutsk: MGTU GA, pp. 170-175. (in Russian)
23. Punt, E.A., Khalyutin, S.P. (2021). Formation of thermal portraits of electrical devices based on the finite element method. 2021 IEEE 22nd International Conference of Young Professionals in Electron Devices and Materials (EDM). Russia, Souzga, the Altai Republic, pp. 310-314. DOI: 10.1109/EDM 52169.2021. 9507697
24. Khalyutin, S.P. (2020). Aircraft electrical power distribution system - equipment diagnostics and prognostics center. Elektropitaniye, no. 2, pp. 4-14. (in Russian)
25. Pyastolov, A.V., Sagitov, D.I. (2023). Analysis of aircraft equipment control systems. Izvestiya Tulskogo Gosudarstvennogo Universi-teta. Tekhnicheskiye Nauki, no. 11, pp. 697-703. DOI: 10.24412/2071-6168-2023-11-697-698 (in Russian)
Список литературы
1. Schefer H., Mallwitz R., Fauth L. Discussion on electric power supply systems for all electric aircraft [Электронный ресурс] // IEEE Access. 2020. Vol. 8. Pp. 84188-84216. DOI: 10.1109/ACCESS.2020.2991804 (дата обращения: 13.01.2024).
2. Кудряков С.А., Бунас К.В. Анализ состояния и тенденции развития авиационных систем электроснабжения // Молодой ученый. 2019. № 40 (278). С. 19-21.
3. Арзамасцева В.А., Сагитов Д.И. Тенденции и перспективы развития авиационного электрооборудования // Достижения науки и образования. 2024. № 2 (93). С. 4-6.
4. Халютин С.П., Давидов А.О. Оценка удельных свойств энергосистем самолетов на электрической тяге // Электропитание. 2019. № 2. С. 43-54.
5. Соколов О.А., Мелихов И.П. Применение авиационных аккумуляторных батарей // Аллея науки. 2023. Т. 1, № 10 (85). С. 209-219.
6. Шестерикова Д.С., Оброкова Е.И., Григорьева М.Д. Тенденции развития летательных аппаратов на электрической тяге // XXV Туполевские чтения (школа молодых ученых): сборник трудов Международной молодежной научной конференции, посвященной 60-летию со дня осуществления первого полета человека в космическое пространство и 90-летию Казанского национального исследовательского технического университета им. А.Н. Туполева - КАИ, Казань, 10-11 ноября 2021 года. Казань: Изд-во ИП Сагиева А.Р., 2021. С. 384-390.
7. Zhang H. Battery temperature prediction using an adaptive neuro-fuzzy inference system / H. Zhang, A. Fotouhi, D.J. Auger, M. Lower [Электронный ресурс] // Batteries. 2024. Vol. 10, no. 3. ID: 85. DOI: 10.3390/bat teries10030085 (дата обращения: 13.01.2024).
8. Aiello L. Influence of pressure, temperature and discharge rate on the electrical performances of a commercial pouch li-ion battery / L. Aiello, P. Ruchti, S. Vitzhum, F. Coren [Электронный ресурс] // Batteries. 2024.
Vol. 10, no. 3. ID: 72 DOI: 10.3390/batte ries10030072 (дата обращения: 13.01.2024).
9. Li W. A Novel quick temperature prediction algorithm for battery thermal management systems based on a flat heat pipe / W. Li, Y. Xie, W. Li, Y. Wang, D. Dan, Y. Qian, Y. Zhang [Электронный ресурс] // Batteries. 2024. Vol. 10, no. 1. ID: 19. DOI: 10.3390/bat teries10010019 (дата обращения: 13.01.2024).
10. Kafadarova N. A system for determining the surface temperature of cylindrical lithium-ion batteries using a thermal imaging / N. Kafadarova, S. Sotirov, F. Herbst, A. Stoyno-va, S. Rizanov [Электронный ресурс] // Batteries. 2023. Vol. 9, no. 10. ID: 519. DOI: 10.3390/batteries9100519 (дата обращения: 13.01.2024).
11. Wang X. Effects of different charging currents and temperatures on the voltage plateau behavior of li-ion batteries / X. Wang, Y. Zhang, Y. Deng, Y. Yuan, F. Zhang, S. Lv, Y. Zhu, H. Ni [Электронный ресурс] // Batteries. 2023. Vol. 9, no. 1. ID: 42. DOI: 10.3390/batte ries9010042 (дата обращения: 13.01.2024).
12. Spitthoff L., Burheim O.S., Shearing P.R. Temperature, ageing and thermal management of lithium-ion batteries [Электронный ресурс] // Energies. 2021. Vol. 14, no. 5. ID: 1248. DOI: 10.3390/en14051248 (дата обращения: 13.01.2024).
13. Kong D. Numerical investigation of thermal runaway behavior of lithium-ion batteries with different battery materials and heating conditions / D. Kong, W. Gongquan, P. Ping, J. Wen [Электронный ресурс] // Applied Thermal Engineering. 2021. Vol. 189. ID: 116661. DOI: 10.1016/j.applthermaleng.2021.116661 (дата обращения: 13.01.2024).
14. Смелков Г.И. Проблемы пожарной безопасности режима теплового разгона в литиевых аккумуляторных батареях / Г.И. Смелков, В.А. Пехотиков, Г.В. Боков, А.А. Назаров // Пожарная безопасность. 2022. № 4 (109). С. 73-79. DOI: 10.37657/vniipo.pb. 2022.109.4.008
15. Харламенков А.С. Пожарная опасность применения литий-ионных аккумуляторов в России // Пожаровзрывобезопасность. 2022. Т. 31, № 3. С. 96-102.
16. Келлер М.В., Савенко А.Е. Оценка, наблюдение и обеспечение безопасности при термическом нагреве для литий-ионных аккумуляторов // Вестник Керченского государственного морского технологического университета. Серия: Морские технологии. 2023. № 1. С. 23-31.
17. Punt E.A. Modified finite volume method study for numerical calculation of lithium battery temperature / E.A. Punt, S.P. Khalyutin, M.O. Troshin, I.E. Starostin // 2023 IEEE 24th International Conference of Young Professionals in Electron Devices and Materials (EDM). 2023. pp. 1230-1234. DOI: 10.1109/ EDM58354.2023.10225111
18. Khalyutin S.P., Starostin I.E., Aga-fonkina I.V. Generalized method of mathematical prototyping of energy processes for digital Twins development [Электронный ресурс] // Energies. 2023. Vol. 16, no. 4. ID: 1933. DOI: 10.3390/en16041933 (дата обращения: 13.01.2024).
19. Старостин И.Е., Халютин С.П., Па-риевский В.В. Виды и формы представления основных уравнений метода математического прототипирования энергетических процессов // Электропитание. 2022. № 4. С. 4-14.
20. Старостин И.Е., Халютин С.П. Виды и формы представления основных уравнений метода математического прототипиро-вания энергетических процессов // XVI Всероссийская мультиконференция по проблемам управления (МКПУ-2023): материалы мультиконференции. В 4-х тт. Т. 3. Волгоград, 11-15 сентября 2023 года. Волгоград: Волгоградский государственный технический университет, 2023. С. 80-82.
21. Brucherseifer E., Fay A. Digital Twins // Automatisierungstechnik. 2021. Vol. 69, no. 12. Pp. 1023-1025. DOI: 10.1515/ auto-2021-0155
22. Фимушин А.С., Славинский А.С., Капустин А.В. Цифровые технологии в вопросах контроля и прогнозирования технического состояния авиационной техники // Актуальные проблемы и перспективы развития гражданской авиации: сборник трудов XII Международной научно-практической конференции, посвященной празднованию
100-летия отечественной гражданской авиации. Иркутск, 12-13 октября 2023 года. Иркутск: МГТУ ГА, 2023. С. 170-175.
23. Punt E.A., Khalyutin S.P. Formation of thermal portraits of electrical devices based on the finite element method // 2021 IEEE 22nd International Conference of Young Professionals in Electron Devices and Materials (EDM). Russia, Souzga, the Altai Republic, 2021. Pp. 310-314. DOI: 10.1109/EDM52169.2021.9507697
24. Халютин С.П. Система распределения электроэнергии воздушных судов - центр диагностирования и прогнозирования состояния авиационного электрооборудования // Электропитание. 2020. № 2. С. 4-14.
25. Пястолов А.П., Сагитов Д.И. Анализ систем контроля авиационного оборудования // Известия Тульского государственного университета. Технические науки. 2023. № 11. С. 697-703. DOI: 10.24412/2071-61682023-11-697-698
Information about the autor
Elena A. Punt, Postgraduate student of the Electrical Engineering and Aviation Electrical Equipment Chair, Moscow State Technical University of Civil Aviation, [email protected].
Сведения об авторе
Пунт Елена Александровна, аспирант кафедры электротехники и авиационного электрооборудования МГТУ ГА, [email protected].
Поступила в редакцию 11.04.2024
Одобрена после рецензирования 03.06.2024 Принята в печать 25.07.2024
Received 11.04.2024
Approved after reviewing 03.06.2024 Accepted for publication 25.07.2024
