Scientists have created a complete model of a battery, detailed down to the level of individual atoms. Identification of the mathematical model of the traction battery of a hybrid car Mathematical models of lead-acid battery discharge

In the first chapter of the dissertation work, known methods for approximating AB discharge curves at constant current values were considered. These methods are static, i.e. do not take into account the change in the battery discharge mode that constantly occurs on an electric vehicle. When modeling unsteady battery loading, it is necessary to take into account the dependence of the maximum battery capacity on the discharge current. For this, the Peukert equation (2) is most suitable.

In Fig.3. A simplified algorithm is presented that allows you to determine the voltage on the battery at each calculation step in a simulation model of the movement of an electric vehicle.

This approach to calculating a non-stationary battery discharge can also be extended to describe the non-stationary charge that occurs during regenerative braking.

The ultimate goal of developing an electric vehicle model is to determine its performance indicators and battery characteristics in a given driving mode. The following were taken as the main parameters:

mileage (power reserve);
energy consumption when moving;
energy consumption per unit of path and load capacity;
specific energy delivered by the battery.

The initial data for the calculation are:

parameters of the battery and (or) energy storage device: family of temporary discharge and charging characteristics for current values in the operating range at a constant temperature, weight of the battery module and additional equipment, number of installed modules, etc.;
electric motor parameters: rated current and voltage, resistance of the armature circuit and field winding, design data, no-load characteristics, etc.;
parameters of the base vehicle: total weight, gear ratios of the gearbox and final drive, transmission efficiency, moment of inertia and rolling radius of the wheels, air resistance coefficient, streamlined surface area, rolling resistance coefficient, load capacity, etc.;
driving mode parameters.

In the third chapter dissertation work, an analysis of experiments and model data was carried out using the developed simulation model and the problem of choosing AB parameters was solved.

When modeling the movement of EVs in the SAE j 227 C cycle, results were obtained with the data structure presented in Table 2.

The results of factor analysis (Table 3) showed that already three factors determine 97% of the information, which makes it possible to significantly reduce the number of latent factors and, accordingly, the dimension of the simulation model.

Results of calculation of the main performance indicators of EVs during acceleration.


1	2	3	4	5	6	7	8	9	10	11	12
1,00	129,93	25,21	250,00	7,2	19,49	120,11	3,00	280,92	0,46	4487,4	0,02
2,00	129,80	41,11	250,00	7,2	19,58	121,19	6,23	583,47	1,81	12873,1	0,32

38,00	116,73	116,30	111,73	3,4	26,36	23,40	47,53	4449,17	393,5	828817,1	-

The results of factor analysis (Table 3) showed that already three factors provide 97% of the information, which makes it possible to significantly reduce the number of latent factors and, accordingly, the dimension of the simulation model.

To clarify the analytical representation of the discharge characteristics of the battery 6EM-145, from which an electric vehicle battery is formed with a total mass of 3.5 tons and a battery weight of 700 kg, in order to study the possibility of short-term recharging of the battery during a work shift and, as a result, increasing mileage, an experiment was conducted to test the 6EM-145 battery according to a special program. The experiment was carried out for 2 months using 2 6EM-145 batteries.

Information content of abstract factors

	^ Eigenvalue	Percentage of Variance	Accumulated eigenvalues	Accumulated variance percentage
1	8,689550	78,99591	8,68955	78,9959
2	1,173346	10,66678	9,86290	89,6627
3	0,832481	7,56801	10,69538	97,2307
4	0,235172	2,13793	10,93055	99,3686

The tests were carried out according to the following method:

Charge with two-stage current 23A and 11.5A (recommended by the battery manufacturer)
Control discharge (according to the manufacturer’s recommendation) with a current of 145A to a minimum voltage value of 9V.
Charge up to 20%, 50% and 80% charge levels with currents of 23.45 and 95A.
Discharge current 145A to a minimum voltage value of 9V.

The measured and calculated quantities were: removed capacity, charging capacity, degree of charge, efficiency coefficients of capacity and energy, etc.

The results of multiple regression for almost all dependent variables showed statistically significant results (the correlation coefficient was equal to R=0.9989, a F-attitude F(2.6)=1392.8). As a result, the possibility of legitimate use of linear models is shown.

The first acceleration stage is calculated at the magnetic flux value F= F max= 0.0072 Wb and maintaining the armature current at a constant level I i = I r1 = 250 A. This stage begins at time t= 0 and ends when the duty cycle reaches 1. Constant values for this acceleration stage: excitation current I in = a∙F max 3 + b∙F max 2 + c∙F max=10.68 A and voltage on the excitation winding U in = I∙R ov

In accordance with the principle of two-zone regulation, an increase in the rotation speed of the electric motor shaft at full voltage can be achieved by weakening the magnetic field. This is implemented in an electronic current regulator that controls an independent field winding. The second stage of acceleration begins at the time corresponding to  =1 and ends when the electric vehicle reaches a given speed. Initial values V, n, U d etc. are the results of calculating the last acceleration step at full flow, when  =1.

Multiple Regression Results

	Statistics	Standard error	^ Score Regression parameters	Standard error	Statistical teak Student per confidence interval	level of error in accepting the significance of a regression parameter
Free member			-0,267327	1,944346	-0,13749	0,895142
A	0,005475	0,019047	0,006819	0,023722	0,28744	0,783445
V3	0,999526	0,019047	1,233841	0,023513	52,47575	0,000000

Electric vehicle braking can be mechanical or regenerative. The last stage of movement in the cycle begins at the time t= t a + t cr + t co and ends when t= t a + t cr + t co + t b. Braking in the SAE j 227 C cycle occurs with constant deceleration, which can be defined as: a= V select /(3.6∙ t b) m/s 2 , where V select - speed at the end of the run, km/h

The simulation experiments carried out in the dissertation work to assess the characteristics of the movement of electric vehicles showed that a conditionally non-stationary random process of characteristics is well approximated by a process with an autocovariance function of the form:

Where r 1 (t) And r 2 (t) respectively equal:

(9)

Analytical expressions are obtained to describe the conditionally non-stationary process. Let the column vector S=(S 0 , S -1 , ... , S -m ) T determines the values of movement characteristics ( t) in moments St=t 0 ,t -1 ,…,t - m  , (t 0 >t -1 >.. >t -m ). Then the mathematical expectation is:

Where D  (t) = (r(t-t 0 ), r(t-t -1 ), ... , r(t-t -m ) row vector of covariances;

D  =||cov( (t i ),  (t j ))||=||r(t i -t)||, i,j=0..-m - covariance matrix of the process history at moments t i , t j ; r(t) - autocorrelation function of stationary mode of movement.

Stochastic approximation algorithms were chosen as algorithms for controlling EV motion modes in the dissertation. Let ^X vector variable in R N, for which the following conditions are met:

1. Each combination of controlled parameters X corresponds to a random variable Y characteristics of movement with mathematical expectation M Y(X).

2. M Y(X) has a single maximum, and second partial derivatives  2 M Y/x i x j are limited over the entire range of changes in control modes.

3. Sequences ( a k) And ( c k) satisfy the conditions:

, b)

, V)

, G)

(12)

4. The recurrent sequence of random control modes is determined based on the transition according to the sign of the increment: .

5. Vector  Y k changes in movement characteristics are determined based on the implementation of random values of the current modes X k in accordance with one of the plans P 1 , P 2 or P 3:

P 1 =[X k, X k +c k E 1 , . . . , X k +c k E i , . . . , X k +c k E N ] T - central plan;

P 2 =[X k +c k E 1 , X k-c k E 1 , . . . X k +c k E N, X k-c k E N ] T - symmetrical plan;

P 3 =[X k, X k +c k E 1 , X k-c k E 1 , . . . X k +c k E N, X k-c k E N ] T .- plan with a central point, where .

6. Dispersion of the assessment of movement characteristics  k 2 for each combination of modes X k is limited  k 2  2
The research carried out in the dissertation showed that when the above conditions are met, the sequence of selected control modes X k converges to optimal values with probability 1.

As a result of the formalization, the functioning algorithm of the controlled simulation model of EV movement is the following sequence of actions:

1. Initial setup of the model and selection of initial modes of movement X 0 , k=0.

2. For a given combination of modes X k in its local neighborhood in accordance with one of the plans P i (i=1,2,3) sample trajectories of movement characteristics are generated ( Xk,l ( t|s k)) l=1 L duration T each from a common initial state s k .

3. Average integral estimates of characteristics are calculated for all l=1 …L with a general initial state s k :

6. Set the initial state s k +1 of the next control interval, equal to the final state of one of the processes of the previous step.

7. In accordance with the selected stopping criterion, the transition is made to step 2, or to the end of the simulation.

In the fourth chapter The developed methods and models were tested.

When choosing the size of a battery installed on an electric vehicle, the concept of transport work is used to optimize the relationship between the load capacity and mileage of the electric vehicle. A=G E ∙L t∙km, where G E– load capacity of the EM, t; L– EV power reserve (mileage). Load capacity of EV G E =G 0 - m b / 1000 t, where G 0 =G A – m– chassis load capacity, determined by the load capacity of the base vehicle G A taking into account mass  m, released when replacing the internal combustion engine with an electric drive system, t; m b – mass of the energy source, kg. Mileage value L electric vehicle is generally calculated using the formula known in the literature
km, where E m- specific energy of the current source, Wh/kg;  - specific energy consumption when driving, Wh/km. As a result, for transport work the following is true:

t∙km,

(15)

where: coefficient
km/kg.

Based on the developed simulation model, the movement of an electric vehicle based on the GAZ 2705 "GAZelle" car with a carrying capacity was calculated G 0 =1700 kg. The calculation was carried out for sources assembled from 10 series-connected OPTIMA D 1000 S battery blocks. The number of parallel-connected batteries in each block varied from 1 to 8. Thus, in increments of 20 kg, the mass of the energy source changed in the theoretically possible range from 0 to G A .

Calculations were carried out for movement in a cycle S AE j 227 C and for movement at constant speed. In Fig.4. The theoretical and simulation-based dependence of transport work on the mass of the battery is shown.

According to the calculation results, the maximum transport work is achieved with a battery weight slightly greater than half the load capacity. This is explained by an increase in specific energy E m current source with increasing its capacity.

Cycle S AE j 227 C is one of the most intense test cycles; non-stop driving mode, on the contrary, is one of the easiest. Based on this, it can be assumed that the graphs corresponding to intermediate driving modes will be located in the area limited by the corresponding curves, and the maximum transport work when operating on the OPTIMA D1000S battery lies in the range from 920 to 926 kg.

In custody The main results of the work are presented.

Application contains documents on the use of the results of the work.
^

Main conclusions and results of the work

A classification of batteries and an analysis of known methods for calculating the characteristics of batteries have been carried out. An assessment is made of the possibility of their use in modeling non-stationary battery charge and discharge.
Based on the research carried out in the dissertation, the use of a decomposition approach was proposed to model unsteady battery loading under various modes and conditions of EV movement, which allows the integration of hybrid analytical-simulation models, including models of the mechanical part, control systems, motion modes and others.
The work poses and solves the problem of formalizing the principles of constructing an EV simulation model using a process description of objects and system components, which makes it possible to simulate non-stationary modes of EV motion and their impact on the non-stationary characteristics of AB loading.
A factor analysis of overclocking characteristics was carried out, which showed that three factors already explain 97% of the information. This made it possible to significantly reduce the number of latent factors in the model and thereby the dimension of the simulation model.
A methodology for conducting an experiment for a comparative analysis of the discharge characteristics of rechargeable batteries has been developed and experiments have been carried out. The experimental data obtained showed that the use of linear models is legitimate for almost all dependent variables.
The simulation experiments carried out to assess the characteristics of the movement of EVs showed that the non-stationary random process of characteristics is well approximated by a process with a hyperexponential autocovariance function. Analytical expressions are obtained to describe the characteristics of a conditionally non-stationary process.
To solve optimization problems on a simulation model, stochastic approximation algorithms were chosen as control algorithms, which provide high convergence speed under conditions of large dispersions of motion characteristics.
A software modeling complex has been developed, which has been implemented for practical use in a number of enterprises, and is also used in the educational process at MADI (GTU).

Publications on the topic of the dissertation work

The research results were published in 6 publications.

Ioanesyan A.V. Methods for calculating the characteristics of rechargeable batteries for electric vehicles / E.I. Surin, A.V. Ioanesyan // Materials of the scientific-methodological and scientific research conference of MADI (GTU). –M., 2003. – P.29-36.
Ioanesyan A.V. Methods for determining the end of discharge and charge of a battery on an electric vehicle / Ioanesyan A.V. // Electrical engineering and electrical equipment of transport. – M.: 2006, No. 6 - pp. 34-37.
Ioanesyan A.V. Basic parameters of batteries for electric vehicles / A.V. Ioanesyan // Methods and models of applied informatics: interuniversity collection. scientific tr. MADI (GTU). – M., 2009. – P.121-127.
Ioanesyan A.V. Model of the mechanical part of an electric vehicle / A.V. Ioanesyan // Methods and models of applied informatics: interuniversity collection. scientific tr. MADI (GTU). – M., 2009. – P.94-99.
Ioanesyan A.V. Generalized simulation model of electric vehicle movement / A.V. Ioanesyan // Principles of construction and features of the use of mechatronic systems: collection. scientific tr. MADI (GTU). – M., 2009. – P.4-9.
Ioanesyan A.V. Models of non-stationary processes of electric vehicle movement / A.V. Ioanesyan // Principles of construction and features of the use of mechatronic systems: collection. scientific tr. MADI (GTU). – M., 2009. – P.10-18.

When it comes to developing new high-tech and miniature devices, batteries are the biggest bottleneck. Currently, this is especially felt in the field of production and operation of electric cars, in backup energy storage devices for energy networks and, of course, in consumer miniature electronics. In order to meet modern requirements, energy storage devices, the development of which has certainly not kept pace with the development of all other technologies, must provide more stored energy over a large number of charge-discharge cycles, have a high energy storage density and provide high dynamic characteristics.

Creating and testing new batteries of various types is a difficult process that takes a long time, which makes it very expensive. Therefore, for electrochemical scientists, the ability to perform detailed simulations before embarking on practical experiments would be a real boon. But until recently, no one had been able to create a mathematical model of a battery, detailed down to the level of individual atoms, due to the complexity of such a model and due to the limitations of existing mathematical modeling tools.

But that has now changed, thanks to the work of two German researchers, Wolf Dapp from the Institute for Advanced Simulation and Martin Muser from the University of Saarlandes. These scientists created a complete mathematical model of the battery and made its calculations down to the level of individual atoms. It should be noted that according to the simulation results, the properties of the “mathematical battery” largely coincide with the properties of real batteries with which we are all accustomed to dealing.

In recent years, computer scientists have repeatedly created battery models, but all of these models operated at a much larger scale than the level of individual atoms and relied on data and parameters whose values were obtained experimentally, such as ionic and electron conductivity, propagation coefficients, current density, electrochemical potentials, etc.

Such models have one serious drawback - they work extremely inaccurately or do not work at all when it comes to new materials and their combinations, the properties of which have not been fully studied or not studied at all. And, in order to fully calculate the behavior of a battery made from new materials as a whole, electrochemists must conduct simulations at the level of individual molecules, ions and atoms.

In order to simulate the battery as a whole, the computer model must calculate any changes in energy, chemical and electrochemical potentials at each computational step. This is exactly what Depp and Musru managed to achieve. In their model, electrical energy is a variable whose value is determined by the interactions of atoms and the bonds between atoms and ions at each stage of the calculation.

Naturally, the researchers had to make concessions to reality. The mathematical complexity of a battery is a far cry from the battery you can get out of your cell phone. The mathematical model of the “nanobattery” consists of only 358 atoms, of which 118 atoms are the material of the electrodes, cathode and anode. According to the initial conditions, the cathode is covered with a layer of 20 atoms of the electrolyte substance, and in the electrolyte itself there are only 39 positively charged ions.

But, despite such apparent simplicity, this mathematical model requires considerable computing power for its calculations. Naturally, all modeling is carried out on a scale of discrete units, steps, and a full cycle of calculations requires a minimum of 10 million steps, at each of which a series of extremely complex mathematical calculations is performed.

The researchers report that the model they created is just proof of the principles they used and that there are several ways to improve the model. In the future, they are going to complicate the model they created by presenting an electrolyte solution as a set of particles with a stationary electric charge. This, along with an increase in the number of atoms in the model, will require the power of not the weakest supercomputer to calculate the model, but it is worth it, because such research can lead to the creation of new energy sources that will revolutionize the field of portable electronics.

Military special sciences Aeroballistic method of increasing the ballistic efficiency of the guided aviation bombs. Key words: distance of flight, guided aviation bomb, additional airfoil. Fomicheva Olga Anatolievna, candidate [email protected] , Russia, Tula, Tula State University of technical science, docent, UDC 621.354.341 MATHEMATICAL MODEL OF OPERATION OF A BATTERY HEATING SYSTEM USING A CHEMICAL HEATING ELEMENT E.I. Lagutina The article presents a mathematical model of the process of maintaining a battery in an optimal thermal state in conditions of low ambient temperatures through the use of a chemical heating element. Key words: thermostating, convective heat transfer, battery, chemical heating element, mathematical model. At this stage of development of weapons and military equipment, it is difficult to imagine the successful conduct of combat operations with minimal personal losses without a unified command and control system. Taking into account the ever-increasing dynamism of combat operations, the basis of the troop control system at the tactical command and control level is radio equipment. This role of radio equipment in the control system, in turn, forces special attention to be paid to the power supply of radio equipment - the battery, as the basis for their uninterrupted operation. Taking into account the climatic characteristics of our country (the presence of a large percentage of territories with a predominantly cold climate, the ability to successfully conduct combat operations in some operational areas of the Far East only in the winter months), maintaining the optimal thermal operating conditions of the battery in conditions of low ambient temperatures is one of the most important tasks . It is the resource-saving operating conditions of the batteries that largely determine the stable functioning of the communication system, and, consequently, the successful completion of combat missions. 105 News of Tula State University. Technical science. 2016. Issue. 4 At the moment, quite a lot of thermostatting devices have been developed. But the common disadvantages for them are mainly the relatively high energy consumption (and they are powered from the battery itself) and the need for human participation in controlling the thermostatting process. Taking into account the above disadvantages, in the thermostatting device being developed, in combination with a heat-insulating body, it is proposed to use a chemical heating element based on supersaturated sodium acetate trihydrate NaCH3COO 3H2O with an equilibrium phase transition temperature Тf = 331 K and latent heat of phase transition rt = 260 kJ/kg, which is stable under supercooling conditions with the introduction of small additives and can be supercooled, according to data, up to T = 263 K. A patent search has shown the presence of a very small number of patents describing thermal phase change accumulators (PTACs) using supercooled liquids as heat storage materials (TAM). This indicates the practical absence in this area of proven technical solutions that would allow implementing a controlled process of releasing previously accumulated heat. Considering also that the specific heat of the phase transition of the selected TAM is quite high, and at the same time it is capable of supercooling to very low temperatures, then there is a need to conduct an independent computational study of this substance in order to identify its practical applicability. The basis for constructing a mathematical model of TAFP is the Stefan problem, which is a problem about the temperature distribution in a body in the presence of a phase transition, as well as about the location of the phases and the speed of movement of their interface. For simplicity, we will consider a plane problem (when the phase transition surface is a plane). From a classical point of view, it is a problem of mathematical physics and comes down to solving the following equations: 2 dT1 2 d T1 = a1. for 0< x < ξ, 2 dτ dx 2 dT2 2 d T2 = a2 . для ξ < x < ∞, dτ dx 2 с дополнительными условиями T1 = C1 = const < Tф при x = 0, T2 = C = const > Tf and the conditions of phase transition 106 at τ = 0, (1) (2) (3) (4) News of Tula State University. Technical science. 2016. Issue. 4 2. In the reversible processes of phase transition TAM melting crystallization at τ = 0 the phase boundaries are formed, the temperature field of TAM in the growing phase is linear, and the temperature of the disappearing phase is equal to the temperature of the phase transition. 3. There is no thermal conductivity of TAM in the longitudinal direction. 4. The TAM phase transformation process is assumed to be one-dimensional. In this case, the phase boundaries are unchanged in shape and at each moment of time they represent cylindrical surfaces located concentrically with respect to the walls of the body of the chemical heating element. 5. Heat losses to the environment from the TAFP during its discharge and heating of the radio station parts adjacent to the battery housing are not taken into account. 6. Transfer coefficients (heat transfer, heat transfer, thermal conductivity) and specific heat capacities are constant and do not depend on temperature. The process of convective heat exchange between the TAM and the walls of the body of the chemical heating element is described by the equation q times (τ) = ak ⋅ Fк (Ttam (τ) − Tк (τ)), (11) where q times (τ) is the thermal power given to the body of the chemical heating element , W; ak is the heat transfer coefficient from the TAM to the body of the chemical heating element, W/(m2·K); Fк – area of contact between the TAM and the inner wall of the body of the chemical heating element, m2; Ttam(τ) – temperature of the heat-accumulating material, K; Tk(τ) is the temperature of the body wall of the chemical heating element, K. At τ>0 the following equations are valid: Tf − T there (τ) q times (τ) = λtv ⋅ ⋅ Fк, (12) t z (τ) dz ( τ) q times (τ) = ρ tv ⋅ r ⋅ ⋅ Fк, (13) t r d (τ) where λtv t is the thermal conductivity coefficient of TAM in the solid phase, W/(m K); z(τ) – thickness of the crystallized TAM layer at time τ, m; 3 ρ tv t – TAM density in the solid phase, kg/m. The accepted assumption about describing the thermal state of the body of a chemical heating element by its average temperature makes it possible not to calculate local velocity fields and heat transfer coefficients at various points. Then for τ>0 the following equation is valid: q times (τ) = a t ⋅ Ft (Ttam (τ) − Tk (τ)), (14) 108 Military special sciences where at is the heat transfer coefficient from the storage material to the heat exchange surface , W/(m2·K); Ft – heat exchange surface area, m2; Considering that the heat supplied to the body of the chemical heating element goes to increase its internal energy and to heat loss into the battery body, at τ>0 the following equation takes place: dT (τ) q times (τ) = Sk ⋅ k + av ⋅ Fв ( Tv (τ) − T0), (15) dτ where Sk is the total heat capacity of the body of the chemical heating element in contact with the battery body, J/K; ав is the heat transfer coefficient from the walls of the chemical heating element to the surface of the battery, W/(m2·K); Fв – surface area of the body of the chemical heating element in contact with the battery body, m2; T0 – initial temperature of the battery, K. The last equation describing the process of functioning of the TAFP system - battery housing at τ>0 is the balance equation: q times (τ) = av ⋅ Sk ⋅ (Tk (τ) − Tv (τ)). (16) The system of equations (11 – 16) is a mathematical model of the functioning of the heating system of the battery housing during the period of discharging the TAFP. The unknown functions in it are qraz(τ), z(τ), Tk(τ), TV(τ), Ttam(τ). Since the number of unknown functions is equal to the number of equations, this system is closed. To solve it in the case under consideration, we formulate the necessary initial and boundary conditions: q times (0) = 0   0 ≤ z (τ) ≤ δ ; z (0) = 0  t (17)  Tk (0) ≈ Tf  TB (0) = Tb (0) = Tthere (0) = T0 where δ t – thickness of the battery case, m; TB – battery temperature at time τ, K. By algebraic transformations of equations (11 – 17) we obtain a system consisting of two differential equations: E − D ⋅ Tк (τ) dz (τ) (18) = , dτ N ⋅ ( W + B ⋅ z (τ)) dTк (τ) E − D ⋅ Tк (τ) = − I ⋅ Tк (τ) + M , (19) dτ Z + Y ⋅ z (τ) where B, W, D , E, I, M, N, Z, Y – some constants calculated using formulas (20 – 28): B = ав ⋅ ат ⋅ Fв ⋅ Fц, (20) 109 Proceedings of Tula State University. Technical science. 2016. Issue. 4 W = (a t ⋅ Fk + av ⋅ Fv) ⋅ λtv t ⋅ Fk, D = B ⋅ λtv t ⋅ Fk, E = D ⋅ Tf, a ⋅F I= B B, SB M = I ⋅ T0 , (21 ) (22) (23) (24) (25) (26) N = ρ tv t ⋅ rr ⋅ Fк, Z = W ⋅ SB, (27) Y = B ⋅ SB. (28) 2 where aB is the thermal diffusivity coefficient of the battery, m/s, FB is the surface area of the battery in contact with the chemical heating element, m2; SB – battery heat capacity, J/K. By analyzing a system of differential equations, we can conclude that they are nonlinear. To solve this system with initial and boundary conditions, it is advisable to use numerical methods, for example, the fourth-order Runge-Kutta method, implemented using the Mathcad computer program for Windows. References 1. Study of the possibility of using supercooled liquids as heat-storing materials in phase-transition heat accumulators installed on mobile vehicles for pre-heating of their engines in winter: research report (final) / Military. engineer-techn. University; hands V.V. Shulgin; resp. performer: A.G. Melentyev. St. Petersburg, 2000. 26 p. No. 40049-L. Inv. No. 561756-OF. 2. Bulychev V.V., Chelnokov V.S., Slastilova S.V. Heat storage devices with phase transition based on Al-Si alloys // News of higher educational institutions. Ferrous metallurgy. No. 7. 1996. P. 64-67. 3. Study of the possibility of using supercooled liquids as heat-storing materials in phase-transition heat accumulators installed on mobile vehicles for pre-heating of their engines in winter: research report (interim at stage No. 3) / Military. technical engineer University; hands V.V. Shulgin; resp. performer: A.G. Melentyev. St. Petersburg, 2000. 28 p. No. 40049-L. Inv. No. 561554-OF. 4. Patankar S.V., Spaulding D.B. Heat and mass transfer in boundary layers / ed. acad. Academy of Sciences of the BSSR A.V. Lykova. M.: Energy, 1971. 127 p. 5. Mathcad 6.0 PLUS. Financial, engineering and scientific calculations in the Windows 95 environment / translation from English. M.: Information and Publishing House "Filin", 1996. 712 p. 110 Military special sciences Lagutina Elizaveta Igorevna, associate professor of the department of radio, radio relay, tropospheric, satellite and wire communications, [email protected], Russia, Ryazan, Ryazan Higher Airborne Command School MATHEMATICAL MODEL OF FUNCTIONING SYSTEM WARMING UP THE BATTERY WITH USING A CHEMICAL HEATING ELEMENT E.I. Lagutina In the article, the mathematical model of the process of maintaining the battery in optimum thermal condition at low ambient temperatures using a chemical heating element. Key words: temperature control, convective heat transfer, battery, chemical heating element, mathematical model. Lagutina Elizaveta Igorevna, adjunct of the department of radio, radio relay, tropospheric, satellite and wire line communication, [email protected], Russia, Ryazan, Ryazan higher airborne command school UDC 62-8 COMPARATIVE ANALYSIS OF MATHEMATICAL MODELS OF GAS DYNAMIC PROCESSES IN A FLOW VOLUME A.B. Nikanorov In this work, a comparative analysis was carried out to determine the area of expedient application of mathematical models of gas-dynamic processes in flow-through volumes, obtained on the basis of the laws of conservation of mass, energy and momentum obtained for the average integral parameters of the medium. Key words: air-dynamic steering drive, conservation law, mathematical model, power system, flow volume. The work considered an approach to constructing models of gas-dynamic processes based on the basic conservation laws for thermodynamic functions and parameters averaged integral over the volume and surface. A mathematical model for gas-dynamic processes in a flow volume is obtained. This article discusses models of the following level of idealization: 1. Model of quasi-static processes in a flow volume for average integral thermodynamic functions and parameters. Let us consider the process occurring in the volume w0 (Fig. 1), while assuming it to be quasi-static, that is, assuming that the speed of gas movement in the volume, as well as the speed of the mechanical process of deformation of the control surface, is negligible compared to the speeds of medium transfer through the control surface of the volume . 111

In recent years, so-called “smart” batteries, or in other words Smart batteries, have gained popularity. Batteries of this group are equipped with a microprocessor that is capable of not only exchanging data with the charger, but also regulating the operation of the batteries and informing the user about the degree of their performance. Batteries equipped with a specialized intelligent control system are widely used in a wide variety of technical electrical equipment, including electric vehicles. It is noteworthy that the group of smart batteries consists mainly of lithium-containing batteries, although sealed or ventilated lead-acid and nickel-cadmium batteries are also found among them.

Smart batteries are at least 25% more expensive than regular batteries. However, smart batteries differ not only in price, as most people assume, but also in the features of the control device included with them. The latter guarantees the identification of the type of batteries with the charger, monitors the temperature, voltage, current, and state of charge of the batteries. A significant portion of lithium-ion battery modules have a built-in monitoring and control system ( BMS), which is responsible for the condition of the batteries and manages them in such a way as to maximize the performance of the batteries under various conditions.

Let's take a closer look at what a battery with a BMS is. Smart batteries are batteries equipped with a special chip in which permanent and temporary data are programmed. Permanent data is programmed at the factory and cannot be changed: data regarding the BMS production series, its marking, compatibility with the type of battery, voltage, maximum and minimum voltage limits, temperature limits. Temporary data is data that is subject to periodic updating. These primarily include operational requirements and user data. As a rule, it is possible to connect the control and balancing system to a computer or controller in order to monitor the condition of the batteries and control their parameters. Some BMS models can be configured for different types of batteries (voltage levels, current values, capacity).

Battery management system (BMS) is an electronic system that controls the charge/discharge process of a battery, is responsible for the safety of its operation, monitors the condition of the battery, and evaluates secondary performance data.

BMS (Battery Management System)– this is an electronic board that is placed on the battery in order to control the process of its charge/discharge, monitor the condition of the battery and its elements, control the temperature, the number of charge/discharge cycles, and protect the components of the battery. The control and balancing system provides individual control of the voltage and resistance of each battery element, distributes currents between the components of the battery during the charging process, controls the discharge current, determines the loss of capacity from imbalance, and guarantees safe connection/disconnection of the load.

Based on the received data, the BMS performs cell charge balancing, protects the battery from short circuit, overcurrent, overcharge, overdischarge (high and excessively low voltage of each cell), overheating and hypothermia. The BMS functionality allows not only to improve the operation of batteries, but also to maximize their service life. When a critical condition of the battery is detected, the Battery Management System reacts accordingly by issuing a ban on the use of the battery in the electrical system - turning it off. Some BMS models provide the ability to maintain a register (record data) about the operation of the battery and then transfer it to a computer.

Lithium iron phosphate batteries (known as LiFePO4), which are significantly superior to other lithium-ion battery technologies in terms of safety, stability and performance, also come with BMS control circuits. The fact is that lithium iron phosphate batteries are sensitive to overcharging, as well as discharging below a certain voltage. In order to reduce the risk of damage to individual battery cells and failure of the battery as a whole, all LiFePO4 batteries are equipped with a special electronic balancing circuit - a battery management system (BMS).

The voltage on each of the cells combined into a lithium iron phosphate battery must be within certain limits and be equal to each other. The situation is such that ideally equal capacity of all cells that make up a single battery is a rather rare occurrence. Even a small difference of a couple of fractions of ampere-hours can provoke a further difference in the voltage level during the charging/discharging process. The difference in the charge/discharge level of the cells of a single LiFePO4 battery is quite dangerous, as it can destroy the battery.

When cells are connected in parallel, the voltage on each of them will be approximately equal: more charged elements will be able to pull out less charged ones. With a series connection, uniform distribution of charge between the cells does not occur, as a result of which some elements remain undercharged, while others are recharged. And even if the total voltage at the end of the charging process is close to ideal, due to even a slight overcharge of some cells in the battery, irreversible destructive processes will occur. During operation, the battery will not provide the required capacity, and due to uneven charge distribution, it will quickly become unusable. Cells with the lowest charge level will become a kind of “weak point” of the battery: they will quickly succumb to discharge, while battery cells with a larger capacity will only undergo a partial discharge cycle.

The balancing method allows you to avoid negative destructive processes in the battery. The BMS cell control and balancing system ensures that all cells receive equal voltage at the end of charging. When the charging process approaches the end, the BMS performs balancing by shunting the charged cells or transfers the energy of elements with a higher voltage to elements with a lower voltage. Unlike active balancing, with passive balancing, cells that have almost completely recharged their charge receive less current or are excluded from the charging process until all battery cells have the same voltage level. The Battery Management System (BMS) provides balancing, temperature control and other functions to maximize battery life.

Typically, stores sell ready-made prefabricated batteries with a BMS, but some stores and companies still provide the opportunity to purchase battery components separately. The Elektra company is one of them. Electra is the first company in Ukraine that decided to supply and create a market for battery cells for self-assembly and design of lithium iron phosphate batteries (LiFePO4) in our country. The main advantage of self-assembly of batteries from individual cells is the possibility of obtaining a prefabricated battery kit that is as close as possible to the user’s needs in terms of operating parameters and capacity. When purchasing components for assembling a LiFePO4 battery, it is important to pay attention not only to the compliance of the battery cells with each other, but also to look at the BMS parameters: voltage, discharge current, number of cells for which it is designed. The operation of a lithium iron phosphate battery also requires the use of only a charger that matches its type. Its voltage should be equal to the total voltage of the battery.

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The main purposes of using BMS (BatteryManagementSystem) as a battery regulator:

Protection of battery cells and the entire battery from damage;

Increased battery life;

Maintaining the battery in a condition in which it will be possible to perform all the tasks assigned to it to the maximum extent possible.

FunctionsBMS (Battery Management System)

1. Monitoring the condition of the battery cells in terms of:

- voltage: total voltage, individual cell voltage, minimum and maximum cell voltage;

- temperatures: average temperature, electrolyte temperature, outlet temperature, temperature of individual battery cells, boards BMS(the electronic board is usually equipped with both internal temperature sensors that monitor the temperature of the control device itself, and external ones that are used to monitor the temperature of specific battery elements);

- charge and depth of discharge;

- charge/discharge currents;

- serviceability

The cell control and balancing system can store in memory such indicators as the number of charge/discharge cycles, maximum and minimum cell voltage, maximum and minimum charge and discharge current values. It is this data that allows you to determine the health status of the battery.

Improper charging is one of the most common causes of battery failure, so charge control is one of the main functions of the BMS microcontroller.

2. Intellectual computing. Based on the above points, BMS makes an assessment:

Maximum permissible charge current;

Maximum permissible discharge current;

The amount of energy supplied due to charging, or lost during discharge;

Internal cell resistance;

The total operating time of the battery during operation (total number of operating cycles).

3. Connected. The BMS can supply the above data to external control devices through wired or wireless communication.

4. Protective. The BMS protects the battery by preventing it from exceeding its safe operating limits. BMS guarantees the safety of connecting/disconnecting the load, flexible load control, protects the battery from:

Overcurrent;

Overvoltage (during charging);

Voltage drops below the permissible level (during discharge);

Overheating;

Hypothermia;

Current leaks.

BMS can prevent a process dangerous to the battery by directly influencing it or by sending an appropriate signal about the impossibility of subsequent use of the battery to the control device (controller). The intelligent monitoring system (BMS) disconnects the battery from the load or charger when at least one of the operating parameters goes beyond the permissible range.

5. Balancing. Balancing is a method of distributing charge evenly among all cells of a battery, thereby maximizing the life of the battery.

BMS prevents excessive overcharging, undercharging and uneven discharge of individual battery cells:

By “shuffling” energy from the most charged cells to the less charged ones (active balancing);

By reducing the current flow to a nearly fully charged cell to a sufficiently low level while the less charged battery cells continue to receive normal charging current (bypass principle),

Providing modular charging process;

By regulating the output currents of the battery cells connected to an electrical device.

In order to protect the BMS board from the negative effects of moisture and dust, it is coated with a special epoxy sealant.

Batteries do not always have only one control and balancing system. Sometimes, instead of one BMS board connected via output wires to the battery and controller, several interconnected control electronic boards are used, each of which controls a certain number of cells and supplies output data to a single controller.

From a practical standpoint, BMSs can perform much more than just battery management. Sometimes this electronic system can take part in monitoring the operating mode parameters of an electric vehicle, and carry out appropriate actions to control its electrical power. If the battery is involved in the energy recovery system when braking an electric vehicle, then the BMS can also regulate the battery recharging process during deceleration and descent.