Battery modeling for battery management systems. Lithium iron phosphate battery charging mode simulation. Effect of capacity variation

Relevance of the topic. Power supply systems (PSS) are integral parts of spacecraft (SV), determine their energy supply and significantly influence their operating efficiency.

The specificity of the operation of solar power systems of spacecraft is cyclicality, high inertia, a strict time limit for receiving energy from solar panels, as well as the most rational distribution of the received energy between consumers. Due to the long stay of spacecraft in orbit, the number of cycles of operation of power supply systems can reach tens of thousands, as a result of which nickel-hydrogen rechargeable batteries (HBAB), which have the largest number of charge/discharge cycles and a long service life, are increasingly used in these systems. life cycle. However, nickel-hydrogen batteries have a number of specific and characteristic parameters only for them.

Due to the above specifics the most important stage when developing power supply systems for spacecraft, it is necessary to conduct ground tests on specialized automated bench complexes, and one of the most important, labor-intensive and complex work in building power supply systems is the development of subsystems responsible for working with batteries, that is, charger-discharge devices.

In practice, methods for testing charger-discharge devices without batteries are usually used, based on the use various devices, simulating their individual elements and modes. Existing developments in the field of simulating the operation of nickel-hydrogen batteries are based on manual change parameters, are distinguished by the complexity of their design and the lack of unification even for batteries of the same type. In this regard, there is a need to create an automated test bench that simulates the behavior of nickel-hydrogen batteries under various conditions, which, in turn, requires the development of an appropriate mathematical model.

Thus, the relevance of the topic of the dissertation research is dictated by the need to develop mathematical tools for modeling complex electrochemical processes occurring in nickel-hydrogen batteries onboard power supply systems of spacecraft, which are the functional core of specialized machine simulators that ensure high-quality and safe ground tests and experiments within the framework of automated testing complexes.

The topic of the dissertation work corresponds to the scientific direction of the State Educational Institution of Higher Professional Education "Voronezh State Technical University" "Computer systems and hardware and software electrical systems."

The goal of the work is to develop a formalized description of the processes occurring in nickel-hydrogen batteries as a basis for constructing mathematical models that simulate the dynamics of changes in parameters that determine the operating modes of the test object, within the framework of an automated software and hardware test complex for on-board power supply systems.

Based on this goal, the following main tasks were set and solved:

Conducting an analysis of the main approaches to modeling batteries and analyzing the factors affecting their operation;

Conducting an analysis of statistical information characterizing the operating modes of nickel-hydrogen batteries as part of the power supply system based on orbital telemetry data from the international space station; development of recommendations for its practical application;

Carrying out an analysis of electrochemical processes occurring in nickel-hydrogen batteries, developing their formalized description and a comprehensive model in charge, discharge and self-discharge modes;

Development of the structure and means of implementing an automated test complex for power supply systems of autonomous objects based on the developed models of nickel-hydrogen batteries.

Research methods. To solve the problems, methods of system analysis, the provisions of the theoretical foundations of electrical engineering, the theoretical foundations of electrochemistry, the theory of automatic control, elements of the mathematical apparatus for the numerical solution of partial differential equations, and elements of graph theory were used.

The scientific novelty of the dissertation work is as follows:

A method for constructing the discharge characteristics of nickel-hydrogen batteries when changing the initial data according to the available measured experimental and orbital data is proposed, characterized by an error not exceeding 5%;

A comprehensive model of electrochemical and physical processes in a nickel-hydrogen battery has been developed, which takes into account the phenomenon of self-discharge;

A nonlinear dynamic mathematical model of a nickel-hydrogen battery has been developed, including electrical and non-electrical quantities and showing the hysteretic behavior of the battery potential during charge/discharge, characterized by its implementation in terms of longitudinal and transverse variables in numerical form;

A method for modeling complex electrical devices is proposed, characterized by reducing control equations to a matrix form discretized in time;

The structure of an automated software and hardware simulator of battery signals has been developed, characterized by simplified hardware, flexibility in changing the parameters of the simulators, as well as unification for the same type of batteries;

Tools have been developed to ensure automated operation of the testing complex, as well as processing of test results.

Practical significance of the work. The results obtained in the work can be used as the basis for engineering methods for calculating transient processes in power supply systems of autonomous objects using nickel-hydrogen batteries. The developed complex mathematical model makes it possible to determine various characteristics nickel-hydrogen batteries without experimentation and testing of actual batteries. The proposed model can be used as part of an automated bench software and hardware system for testing power supply systems of autonomous objects (such as spacecraft, hybrid cars, autonomous wind power systems, etc.) together with a nickel-hydrogen battery signal simulator.

Implementation and implementation of work results.

The main provisions of the dissertation work were introduced into the developments of NPO Electrotechnical Holding LLC "Energia" in the form of software components within the framework of an automated software and hardware bench complex for testing spacecraft power supply systems.

Approbation of work. The main provisions of the dissertation work were discussed and approved at scientific seminars of the Department of Management and Informatics in technical systems Academy of VSTU (2002 - 2006); at conferences of VSTU faculty (2001 -2004); at the international school-conference “High Energy Saving Technologies” (Voronezh, 2005); at the All-Russian student scientific and technical conference “Applied problems of electromechanics, energy, electronics.” (Voronezh, 2006).

Publications. The results of the research were published in 6 printed works, including 1 publication recommended by the Higher Attestation Commission of the Russian Federation. In the works published in co-authorship and given at the end of the abstract, the applicant personally owns: - a study of the metrological characteristics of the complex testing stand for the ISS SES was carried out; - a study of various mathematical models of rechargeable batteries was carried out; - a unified structure of test benches has been developed, as well as an algorithm for the operation of the software.

Structure and scope of work. The dissertation consists of an introduction, four chapters, a conclusion, a bibliography of 89 titles and appendices. The main part of the work contains 165 pages, 70 figures and 7 tables.

1. The developed structure and operating algorithm of the software make it possible to fully implement various types testing a wide range of radio-electronic equipment products, which is ensured by a unified ideology for constructing software divided by functional characteristics;

2. The proposed algorithm for calibrating the measuring channels can significantly increase the accuracy of measurements during tests, and, taking into account that the need for calibration arises only at the stage of manufacturing and setting up the test bench, then directly during testing the speed of the information-measuring system as a whole increases;

3. The developed algorithm for digital filtering of measurement results can significantly reduce the influence of industrial dynamic noise affecting test equipment during testing;

4. The developed block diagram of the battery signal simulator provides a significant increase in the quality of tests by simplifying the hardware responsible for setting the simulator modes, providing flexibility in changing the parameters of the simulators, as well as unifying the simulator, at least for the same type of batteries;

5. Preliminary preparation The test program allows you to automate the testing process, and the use of a mathematical model of a nickel-hydrogen battery can significantly reduce the labor intensity of the preparatory testing stage.

Conclusion

The research carried out within the framework of the dissertation work in the field of modeling the processes of charge, discharge and self-discharge of a nickel-hydrogen battery as part of the power supply systems of autonomous objects allowed us to obtain the following results:

1. Based on the analysis of the main approaches to modeling various types batteries, as well as their equivalent circuits, the main tasks aimed at improving the quality of testing of spacecraft power supply systems have been identified.

2. A comprehensive model has been developed that describes the electrochemical and physical processes in a nickel-hydrogen battery, taking into account the phenomenon of self-discharge.

3. A nonlinear dynamic mathematical model of a nickel-hydrogen battery has been developed, including electrical and non-electrical quantities and showing the hysteretic behavior of the battery potential during charge/discharge, implemented in terms of longitudinal and transverse variables in numerical form.

4. A model is proposed for analyzing the discharge characteristics of a nickel-hydrogen battery when changing the initial data according to the available measured experimental and orbital data using a combined bias.

5. A method for modeling complex electrical devices is proposed, based on reducing control equations to a matrix form discretized in time.

6. The structure of an automated software and hardware complex that simulates battery signals has been developed, which has simplified hardware, flexibility in changing the parameters of the simulators, as well as unification for the same type of batteries

7. Tools are proposed that provide an automated mode of operation of the testing complex, as well as processing of test results.

2. Astakhov Yu.N., Venikov V.A., Ter-Ghazaryan A.G. Energy storage devices in electrical systems. M.: Higher School, 1989. 160 p.

3. Babkov O.I. Main problems of space power engineering / O.I. Babkov, N.Ya. Pinigin, E.E. Romanovsky, B.E. Chertok // Industry of Russia. -1999. -No. 9. -s. 7-22.

4. Signal simulator block, 33Y.2574.003 TU, Korolev, Moscow region, RSC Energia, 1987.

5. Varenbud JI.P, Livshin G.D., Tishchenko A.K. Development of the structure and hardware of an information and control complex for testing spacecraft power supply systems / Energy: Scientific and practical. Vestn. 1999. - No. 4 - pp. 36-54.

6. Varenbud JI.P, Ledyaykin V.V., Sazanov A.B. Development of an algorithm for testing SES using an automated hardware and software complex. // Energy: Scientific and practical. Vestn. -2001.-No. 1 p. 16-28

7. Vedeneev G.M. Ways to improve autonomous power supply systems / Vedeneev G.M., Orlov I.N., Tokarev A.B., Chechin A.V.//C6. scientific works No. 143. M.: Moscow. Energy int. 1987. -p. 7.

8. German-Galkin S. G. Computer modelling semiconductor systems in MATLAB 6.0: Tutorial. St. Petersburg: CORONA print, 2001.9." German-Galkin S. G. Linear electrical circuits. Laboratory works. SPb.: Teacher and student, CORONA print, 2002.

9. German-Galkin S. G. Spectral analysis of processes of power semiconductor converters in the MATLAB package (R 13) // Scientific and practical journal "Exponenta Pro. Mathematics in applications", 2003, No. 2. P. 80 82.

10. Dynamic modeling and testing of technical systems / Ed. I.D. Kochubievsky. M.: Energy, 1978. -303 p.

11. Duplin N.I., Podvalny S.JL, Savenkov V.V., Tishchenko A.K. Analysis of the stability of branched DC power supply systems // Control systems and information technologies: Coll. scientific works -Voronezh, VSTU. 2000. -s. 40-49.

12. Dyakonov V. Simulink 4. Special reference book. St. Petersburg 2002

13. Zlakomanov V.V., Yakovlev B.S. Interaction of dynamic systems with energy sources. M.: Energy, 1980. - p. 144.

14. Signal simulator block, 33Y.2574.003 TU, Korolev, Moscow region, RSC Energia, 1987.

15. Lelekov A.T. Modeling of thermophysical characteristics of a nickel-hydrogen battery. // Bulletin of Sib.gos. aerospace univ.: Sat. scientific Proceedings / ed. prof. G.P. Belyakova; Sib. state aerospace unt. Krasnoyarsk, 2004. Issue. 4. - page 128

16. Klinachev N.V. Fundamentals of modeling systems or 7 domains of Ohm’s and Kirchhoff’s laws: Selected fragments. Chelyabinsk, 2000-2005.

17. Savenkov V.V. Modeling, development and experimental research of electrical power systems for autonomous objects. Diss. Ph.D., VSTU, Voronezh, 2002.

18. Sazanov A.B. Mathematical modeling of operating modes of rechargeable batteries.// Scientific and technical journal “Mechanical Engineering”, No. 2, Moscow, 2007, “Virage Center”, pp. 27-30.

19. Sazanov A.B., Litvinenko A.M. Automation of acceptance tests of electronic units of radio-electronic equipment products.// Scientific and technical journal “Electrical complexes and control systems”, No. 2, Voronezh, 2006, “Kvarta” pp. 51-56.

20. Sazanov A.B., Litvinenko A.M. Self-discharge model of a nickel-hydrogen battery. // Bulletin of VSTU, series “Energy”, Issue 6, 2007/ Voronezh, state. those. university. Voronezh, 2007.

21. Semykin A.V., Kazarinov I.A., Nickel-hydrogen rechargeable electrochemical systems. // Electrochemical energy. Saratov State University, Saratov 2004, T. 4, No. 1 pp. 3-28, No. 2 pp. 63-83, No. 3 pp. 113-147.

22. Tenkovtsev V.V., Tsenter B.I., Fundamentals of the theory and operation of sealed nickel-cadmium batteries. L.: Energoatomizdat. Leningr. Dept., 1985.

23. Tishchenko A.K., Gankevich P.T., Livshin G.D., Unified power supply system for spacecraft // Voronezh. Energy: Scientific and practical. messenger 1999.-No. 3. -p. 34-51.

24. Tishchenko A.K., Gankevich P.T., Savenkov V.V. Features of the design of unified high-voltage power supply systems for spacecraft // Voronezh. Energy: Scientific and practical. messenger -1999 -№1-2 pp. 6-17

25. Center B.I., Lyzlov N.Yu. Metal-hydrogen electrochemical systems. Theory and practice. L.: Chemistry, 1989, 282 p.

26. Chernykh I.V. Modeling of electrical devices in MATLAB, SimPowerSystems and Simulink. 1st edition, 2007

27. Shannon R. Simulation modeling of art and science systems: Transl. from English M.: Mir, 1978. 418 p.

28. Power supply of aircraft / ed. N.T. Korobina. -M.: Mechanical Engineering, 1975. -p. 382.

29. Appelbaum, J and Weiss, R., "Estimation of Battery Charge in Photovoltaic Systems", 16th IEEE Photovoltaic Specialists Conference, pp. 513-518, 1982

30. Baudry, P. et al, "Electro-thermal modeling of polymer lithium batteries for starting period and pulse power", Journal of Power Sources, Vol 54, pp. 393-396, 1995

31. Bernardi D., E. Pawlikowski, J. Newman, A general energy balance for battery systems, J. Electrochem. Soc. 132 (1) (1985) 5-12.

32. Bratsch S. G., J. Phys. Chem. Ref. Data, 18.1 (1989).

33. Brenan, K. E., Campbell, S. L., and Petzold, L. R., Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, North-Holland, New York (1989).

34. Bumby, J. R., P. H. Clarke, and I. Forster, U of Durham UK, “Computer modeling of the automotive energy requirements for internal combustion engine and battery electric-powered vehicle,” IEE Proceedings, Vol 132, Pt. A, No. 5, Sept 1985, pp. 265-279

35. Chapman, P. and M. Aston, “A generic battery model for electric and hybrid vehicle simulation performance prediction,” Electric and Hybrid Vehicles, SP-2, Int. J. Veh. Design, 1982, pp. 82-95

36. Cohen, F. and Dalton, P. J. "International Space Station Nickel-Hydrogen Battery Start-Up and Initial Performance." Proceedings of the 36th Intersociety Energy Conversion Engineering Conference, Savannah, GA, July 29-August 2, 2001.

37. Conway, W. E. and Bourgault, P. L., Can J. Chem., 37, 292 (1959).

38. Dalton, P., Cohen, F., "Battery Reinitialization of the Photovoltaic Module of the International Space Station," paper no.20033, Proceedings of the 37th Intersociety Energy Conversion Engineering Conference, Washington DC, July 28-August 2, 2002.

39. Dalton, P., Cohen, F., "International Space Station Nickel-Hydrogen Battery On-Orbit Performance," paper no.20091, Proceedings of the 37th Intersociety Energy Conversion Engineering Conference, Washington DC, July 28-August 2, 2002.

40. Dalton P., Cohen F., Update on international space station nickel-hydrogen battery on-orbit performance, in: Proceedings of AIAA 2003, Paper #12066, 2003.

41. De Vidts P., Delgado J., and White R. E., J. Electrochem. Soc., 143, 3223 (1996).

42. De Vidts P., Delgado J., Wu W., See D., Kosanovich K., and White R. E., J. Electrochem. Soc., 145.3874 (1998).

43. Dobner, Donald J. and Edward J. Woods, GM Research Laboratories, "An Electric Vehicle Dynamic Simulation", 1982, pp. 103-115

44. Dougal R.A., Brice C.W., Pettus R.O., Cokkinides G., Meliopoulos A.P.S.,

45. Virtual prototyping of PCIM systems—the virtual test bed, in: Proceedings of PCIM/HFPC "98 Conference, Santa Clara, CA, November 1998, pp. 226234.

46. ​​Dunlop J.D., Rao G.M., Yi T.Y., NASA Handbook for Nickel-Hydrogen Batteries, NASA Reference Pub. 1314, September 1993.

47. Dunlop J.D., Giner J., Van Ommering G., Stockel J.F., Nickel Hydrogen Cell, U.S. Patent 3867299, 1975.

48. Facinelli, W. A., "Modeling and Simulation of Lead-Acid Batteries for Photocoltaic Systems", 1983 18th Intersociety Energy Conversion Engineering Conference IECEC, Volume 4, 1983

49. Halpert G., J. Power Sources, 12,177 (1984).

50. Hojnicki, J.S., Kerslake, T.W., 1993, "Space Station Freedom Electrical Performance Model," paper no. 93128, Proceedings of the 28th Intersociety Energy Conversion Engineering Conference, Atlanta, Georgia, August 8-13, 1993.

51. Gear C.W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.

Introduction.

Lithium-ion batteries are the de facto standard in the field of power supplies for electric vehicles, uninterruptible power systems, mobile devices and gadgets. Another example of the use of lithium-ion batteries is storage for renewable energy sources (mainly solar panels and wind generators). Thus, in 2011, a storage device based on lithium-ion batteries with a total capacity of 36 MWh was installed in China, capable of delivering 6 MW to the network electrical power within 6 hours. An example on the opposite scale is lithium-ion batteries for implantable pacemakers, whose load current is on the order of 10 μA. The very capacity range of a single commercially produced lithium-ion cell has long crossed the 500 Ah mark.

The use of lithium-ion batteries requires compliance with the discharge and charging parameters of the battery, otherwise irreversible degradation of capacity, failure and even fire of the battery due to self-heating may occur. Therefore, lithium-ion batteries are always used together with a monitoring and control system - MCS or BMS (battery management system). The battery management system performs protective functions by monitoring temperature, charge-discharge current and voltage, thus preventing over-discharge, overcharging and overheating. BMS also monitors the battery condition by assessing the state of charge (State of Charge, SOC) and state of health (State of Health, SOH). An intelligent BMS is essential in virtually any lithium-ion battery application, providing information on how long the device will last before needing to be recharged (SOC value) and when the battery should be replaced due to loss of capacity (SOH value).

In this work, we focus on models for SOC and SOH state estimation suitable for real-time implementation in battery management systems. Unfortunately, in the Russian-language scientific literature there are practically no publications that consider such issues specifically for lithium-ion batteries. Therefore, in this article we will try to fill this gap.

1. Preliminary information.

1.1. Lithium-ion battery - a basic description.

The processes of discharging and charging a lithium-ion battery can be schematically represented in Figure 1.

Figure 1. Elementary representation of the processes in a lithium-ion battery.

The battery consists of a carbon anode and a metal oxide cathode that also contains lithium (for example, LiMn2O4). Positive lithium ions Li+ migrate between the anode and cathode through the organic electrolyte. The important point is that lithium never appears in a free metallic state - only the exchange of its ions occurs between the cathode and anode. Therefore, such batteries are called “lithium-ion”

When a lithium-ion battery is charged, lithium is deintercalated (removed) from the lithium-containing cathode and lithium ions are intercalated (introduced) into the carbon material of the anode. When the battery is discharged, the processes occur in the opposite direction: the negative charge is transferred by the flow of electrons from the cathode to the anode, and lithium ions move in the opposite direction - from the anode to the cathode.

More detailed description We will consider processes when modeling a battery at the electrochemical level.

1.2. System level description of the battery.

From a circuit point of view, the battery appears to be a two-terminal network. In this work, we will use its description in the form of a black box, as a system with one input (current in the circuit) and voltage at the battery terminals.

Open circuit voltage (OCV) is the voltage at the battery terminals when there is no current drawn.

The most important parameter is battery capacity, defined as the maximum amount of electrical energy (in Ah) that the battery supplies to the load from the moment it is fully charged to the state of discharge, which does not lead to premature degradation of the battery.

As stated earlier, the main functions of a smart BMS are SOC and SOH assessment.

Battery state of charge (SOC) is an indicator characterizing the state of charge of the battery: 100% – fully charged, 0% – fully discharged. The equivalent indicator depth of discharge (DoD) is . Usually SOC is measured as a percentage, but in this work we will assume that . Formally, SOC is expressed as , where is the current charge in the battery.

Battery state of health (SOH) is a qualitative indicator characterizing the current degree of degradation of the battery capacity. The result of the SOH assessment is not a numerical value, but an answer to the question: “Does the battery need to be replaced in this moment?. Currently, there is no standard regulating on the basis of which battery parameters SOH should be calculated. Various manufacturers BMSs use various metrics for this, such as comparing the original and actual battery capacity or internal resistance.

2. Models for determining the state of charge.

Determining the state of charge of the SOC is the task of observing the latent states of the system from the available process model and the measured output response from the input stimulus. Models intended for use as part of battery management systems to determine SOC can be classified into two broad groups:

Empirical models that replicate battery behavior from a black box perspective;

Physical models simulating internal electrochemical processes in a battery.

2.1 Empirical models.

The class of empirical models includes a number of different approaches, general features are a significant simplified simulation of the physical processes in the battery. Empirical models are a standard in the implementation of BMS, since they are, on the one hand, sufficiently simple for implementation, and on the other hand, have acceptable accuracy for estimating SOC , . A quantitative comparison of 28 different empirical models is contained in the paper.

The main type of empirical models is substitution schemes.

The starting premise for the empirical modeling is the observation that battery dynamics can be divided into two parts:

Slow dynamics due to battery charging and discharging

Fast dynamics associated with the internal impedance of the battery: the active resistance of the electrolyte and electrodes, as well as with electrochemical capacitances.

The processes of aging and capacity degradation are modeled as nonstationarity of system parameters.

In fact, slow dynamics comes down to modeling the effect of SOC on the electrical characteristics of the battery. It has been noted that the open circuit voltage (OCV) is a fairly clear function of the state of charge (SOC or DoD):

and is slightly susceptible to temperature variations (except in areas where the battery is almost fully charged or discharged), and also changes slightly when the battery ages (if we consider when the battery is charged to its current level, taking into account capacity degradation).

Typical curves for lithium-ion batteries with different chemistries are shown in Figure 2.

Figure 2. Typical open circuit voltage versus state of charge.

Dependency approximation can be performed different ways, including piecewise linear or polynomial. One of the classic versions of approximation (1) is the Shepherd equation (Shepherd model), a modification of which for a lithium-ion battery has the form:

where the coefficients are calculated based on the characteristic points of the battery discharge curve, which is usually given in technical documentation, a is the total charge passed from or into the battery during the time: .

In the work, for example, the following expression is used for approximation:

Various parameterization options are systematically reviewed in the work.

To obtain a complete battery model, equation (2) can also be supplemented with terms that depend on the battery current, for example, as is implemented in the Simulink system in the Battery block from SimPowerSystem (, ).

2.1.2 Internal battery impedance.

The second part of the empirical model is a description of the internal impedance, which is responsible for the current-voltage characteristics and fast dynamics.

The simplest modeling option is an active resistance connected in series with an adjustable EMF source (Figure 3). This equivalent circuit simulates the internal resistance of the battery created by the materials of the electrodes and electrolyte, across which an ohmic voltage drop and heat generation are observed.

Figure 3. Elementary battery replacement circuit.

To simulate transient processes in a battery, this is simplest scheme substitution must be supplemented with reactive elements. Thus, a complex resistance with impedance is connected in series with .

Typically, the following electrochemical phenomena are distinguished that significantly affect the dynamics of electrical transient processes (,):

Classic double electrical layer in electrode-electrolyte contact (Double-Layer)

Formation of a passive film (solid-electrolyte interface, SEI) on electrodes.

As a result of these factors, electrochemical distributed capacitors appear inside the lithium-ion battery. The study of battery impedance is carried out using electrochemical impedance spectroscopy (EIS) -.

A fairly large number of equivalent circuits have been proposed - ranging from simple ones containing several reactive elements, to detailed modeling of electrochemical phenomena using a large number of RC circuits, and even nonlinear elements.

An almost well-proven version (Figure 4) of an equivalent circuit is based on a series connection of an active internal resistance and two RC circuits that simulate polarization processes with the formation of volumetric capacitances:

Electrochemical double layer capacitance, the effect of which is observed at higher frequencies,

Capacitance associated with lithium intercalation and mass transfer, dominant at low frequencies.

Figure 4. Equivalent circuit for a second-order dynamic battery model.

Thus, the second-order dynamic model in state space presented in Figure 4 is written as:

where , and the parameters are selected based on experimental data taken from a specific type of battery.

In reality, battery impedance is a function of temperature and SOC, and over the long term also changes as the battery ages.

Internal active resistance decreases with increasing temperature, but within the range of 25-40°C, it remains fairly stable. Experiments conducted with polymer lithium-ion batteries have shown that the equivalent circuit parameters remain constant at SOC greater than 20%. At lower SOC values, there is an exponential increase in resistances and an exponential decrease in capacitances.

2.1.3 Modeling the state of charge.

Since the SOC value changes during the charging and discharging of the battery, it is natural to consider SOC as another state of the system, adding a fragment to simulate it in the equivalent circuit.

The complete equivalent circuit is shown in Figure 5. An isolated circuit with a source-controlled current is added to the circuit, providing a current through and equal to the current in the battery circuit. In this way, the capacity is discharged and charged, simulating the battery capacity. The voltage across the capacitance is numerically equal to SOC, . The capacitance value is determined as follows:

where is the total capacity of the battery in Ah, is the correction factor to take into account the dependence of the battery capacity on temperature, is the correction factor for modeling the aging process ( is the number of charge-discharge cycles).

Figure 5. Complete equivalent circuit for a second-order dynamic model.

The resistance models the self-discharge of the battery.

Taking into account the introduced fragment of the circuit, the battery model in state space is supplemented with another equation for the variable:

The actual task of determining SOC comes down to synthesizing an observer for model (3)-(4).

2.2 Physical models.

Some researchers propose using physical models to predict SOC and SOH. This class of models is based on the use of equations that describe electrochemical processes in the battery.
The main advantage of this approach is quite obvious - high modeling accuracy is achieved through the transition from the empirical to the physical level of the model description. The disadvantages are the high computational complexity of the model and the large number of parameters that must be identified from experimental data. Despite this, physical models are of sufficient interest for future generations of battery management systems.

Two classes of physical models are presented in the literature:

Single particle model -,

One-dimensional spatial model (1D-spatial model).

The single-particle model is based on the assumption that each of the electrodes of a lithium-ion cell can be considered a single spherical particle of sufficiently large radius (so that its surface area matches the area of ​​the porous cathode or anode of the battery). Changes in concentration and potential in the electrolyte are ignored, as are temperature effects.

The one-dimensional spatial model is further development single-particle model, in which each of the electrodes is modeled as a set of intersecting spheres with centers on the same line. This approach makes it possible to more accurately describe the process of intercalation (diffusion) of lithium ions into porous battery electrodes.

Note that even such approximate physical models of lithium-ion batteries are based on partial differential equations and the synthesis of observers for such objects is a separate non-trivial task.

2.2.1 Single-particle model.

The single-particle model is based on the simulation of the following phenomena in the battery: diffusion of lithium ions into the electrodes and electrochemical kinetics of ion flow. Processes in the electrolyte (liquid phase) are presented in the form of constant conductivity and are not actually modeled. The schematic structure of the battery in the single-particle model is shown in Figure 6. Next, we briefly reproduce the main components of the model. All equations are assumed to equally satisfy both the reaction conditions at the anode and equally at the cathode (with appropriate parameters).

Figure 6. Schematic representation of a battery in a single-particle model.

Lithium intercalation into electrodes is modeled as diffusion described by Fick's law:

where is the concentration of lithium ions in the electrodes (solid phase), and is the diffusion coefficient.

This equation can be rewritten in spherical coordinates

with boundary conditions

Molar diffusion fluxes can be expressed as the current density through the electrode surface:

where is Faraday’s constant and is the effective surface area of ​​each electrode.

To assess the state of charge of the battery, it is convenient to move from local concentrations to those averaged over the entire volume of the electrodes -:

Direct calculations show that the time derivative is found as

where is the proportionality coefficient, is the battery current.

Electrochemical kinetics is modeled using the Butler-Volmer equation for the molar flux of lithium ions:

in which overvoltages can be expressed as follows

where are the potentials of the positive and negative electrodes, is a function of the concentration of lithium ions on the surface of the electrodes, is the resistance of the electrolyte (liquid phase) and the passive film on the electrode, is the universal gas constant, is the battery temperature.

Equation (7) can be solved for overvoltage by considering that the fluxes are expressed in terms of battery current using (5):

where are constants expressing the exchange current density.

Note that the voltage at the battery contacts is equal to the potential difference , and the potentials can be expressed through (8) using substitution (9). From here we get the required

Equations (6) and (10) constitute an electrochemical single-particle model of a lithium-ion battery.

2.2.2 Relationship between the single-particle model and the equivalent circuit.

The concentrations for the positive and negative electrodes are related to each other from equation (6): with an increase in , the concentration decreases proportionally, and vice versa. Obviously, the state of charge is proportional to the concentration. Then we can introduce the quantity into consideration as the state of the system, and the concentrations and will linearly depend on: , .

From here we can write the following equation for in the single-particle model

where is some positive constant.

The term in (10), based on the introduced state, on which and linearly depend on the concentration, can be represented as a certain function. The work proposes the following approximation for:

The remaining part of (10) is a function of the current, for which the following parameterization is proposed:

where are constant coefficients identified from experimental data.

The state space model is finally obtained in the form:

(12)

Comparing (4) and (11), it is quite obvious that the charge state equation in the single-particle model (11) is completely similar to the representation by equivalent circuit (4), while the self-discharge of the battery is not modeled. From the equation in (12) it follows that the function corresponds to the function for the open circuit voltage in the equivalent circuit. But at the same time, in the single-particle model there is an additional nonlinear element with a voltage drop, connected in series with the internal active resistance. Unlike the empirical equivalent circuit representation, the electrochemical capacitance of the electrical double layer is not modeled in the single-particle model.

The electrochemical single-particle model itself can be represented as an equivalent circuit shown in Figure 7.

Figure 7. Equivalent equivalent circuit for the single-particle model.

Conclusion.

This paper provides an overview of two types of lithium-ion battery models for battery management systems. The equivalent circuit-based empirical model is shown to be the most common in the literature, simple to implement, and flexible in scaling for simulating special phenomena in a battery. The model parameters are non-stationary, subject to both the aging process of the battery and variations from the state of charge and temperature. Based on an analysis of recent publications, it was concluded that a promising direction for improving models for a new generation of battery management systems is physical models that quantitatively describe electrochemical phenomena in the battery. It is shown that a single-particle electrochemical model can be represented in the form of an equivalent circuit that is similar to the empirical model.

1. Ramadesigan V. et al. Modeling and simulation of lithium-ion batteries from a systems engineering perspective //Journal of The Electrochemical Society. – 2012. – T. 159. – No. 3. – C. R31-R45
2. Garage A. The world's largest battery is manufactured in China [ Electronic resource] / A. Garanzha – Access mode: http://www.liotech.ru/sectornews_207_503 – Cap. from the screen.
3. Axcom Battery Technology GmbH, CNFJ-500 2V/500Ah product specification [Electronic resource] – Access mode: http://www.axcom-battery-technology.de/uploads/media/Lead_Crystal_Battery_CY2-500.pdf – Cap. from the screen
4. Pistoia G. (ed.). Lithium-Ion Batteries: Advances and Applications. – Newnes, 2013. – 634 p.
5. Lithium Ion Rechargeable Batteries: Technical Handbook, Sony Corporation [Electronic resource] – Access mode: http://www.sony.com.cn/products/ed/battery/download.pdf – Cap. from the screen.
6. Alignment of parameters of battery sections ensures Extra time operation and increases the service life of batteries [Electronic resource] – Access mode: http://www.scanti.ru/bulleten.php?v=211&p=44 – Cap. from the screen
7. Rahimi-Eichi H., Ojha U., Baronti F., Chow M. Battery Management System: An Overview of Its Application in the Smart Grid and Electric Vehicles // Industrial Electronics Magazine, IEEE - June 2013. - vol.7, no .2, — pp.4-16
8. Chen M., Rincon-Mora G. A. Accurate electrical battery model capable of predicting runtime and IV performance //Energy conversion, ieee transactions on. - 2006. - T. 21. - No. 2. - pp. 504-511.
9. V. Pop, H.J. Bergveld, D. Danilov, P.P.L. Regtien, P.H.L. Notten, Battery Management Systems: Accurate State-of-Charge Indication for Battery-Powered Applications. ISBN: 978-1-4020-6944-4, In: Philips Research Book Series, vol. 9, Springer, 2008. pp. 24?37.
10. Melentjev S., Lebedev D. Overview of Simplified Mathematical Models of Batteries. // 13th International Symposium “Topical problems of education in the field of electrical and power engineering”. — Doctoral school of energy and geotechnology: Parnu, Estonia, January 14-19, 2013. — pp. 231-235
11. Tremblay O., Dessaint L. A. Experimental validation of a battery dynamic model for EV applications // World Electric Vehicle Journal. - 2009. - T. 3. - No. 1. - pp. 1-10.
12. Bochenin V.A., Zaichenko T.N. Research and development of a Li-Ion battery model // Scientific session TUSUR-2012: Materials of the All-Russian scientific and technical conference of students, graduate students and young scientists, Tomsk, May 16–18, 2012 - Tomsk: V-Spektr, 2012 - Volume 2. – from 174-177.
13. Weng C., Sun J., Peng H. An Open-Circuit-Voltage Model of Lithium-Ion Batteries for Effective Incremental Capacity Analysis //ASME 2013 Dynamic Systems and Control Conference. – American Society of Mechanical Engineers, 2013. DSCC2013-3979 – pp. 1-8.
14. Tang X. et al. Li-ion battery parameter estimation for state of charge //American Control Conference (ACC), 2011. – IEEE, 2011. – pp. 941-946.
15. Zhao J. et al. Kinetic investigation of LiCOO2 by electrochemical impedance spectroscopy (EIS) //International Journal of Electrochemical Science. – 2010. – T. 5. – No. 4. – pp. 478-488.
16. Jiang Y. et al. Modeling charge polarization voltage for large lithium-ion batteries in electric vehicles // Journal of Industrial Engineering & Management. – 2013. – T. 6. – No. 2. – pp. 686-697.
17. Rahmoun A., Biechl H. Modeling of Li-ion batteries using equivalent circuit diagrams //PRZEGLAD ELEKTROTECHNICZNY. – 2012. – T. 88. – No. 7 B. – pp. 152-156.
18. He H., Xiong R., Fan J. Evaluation of lithium-ion battery equivalent circuit models for state of charge estimation by an experimental approach //energies. – 2011. – T. 4. – No. 4. – pp. 582-598.
19. Wang C., Appleby A. J., Little F. E. Electrochemical impedance study of initial lithium ion intercalation into graphite powders //Electrochimica acta. – 2001. – T. 46. – No. 12. – S. 1793-1813.
20. Lee J., Nam O., Cho B. H. Li-ion battery SOC estimation method based on the reduced order extended Kalman filtering // Journal of Power Sources. – 2007. – T. 174. – No. 1. – pp. 9-15.
21. Johnson V. H., Pesaran A. A., Sack T. Temperature-dependent battery models for high-power lithium-ion batteries. – City of Golden: National Renewable Energy Laboratory, 2001.
22. Hu X., Li S., Peng H. A comparative study of equivalent circuit models for Li-ion batteries // Journal of Power Sources. – 2012. – T. 198. – P. 359-367.
23. Santhanagopalan S., White R. E. Online estimation of the state of charge of a lithium ion cell // Journal of Power Sources. – 2006. – T. 161. – No. 2. – pp. 1346-1355.
24. Rahimian S. K., Rayman S., White R. E. Comparison of single particle and equivalent circuit analog models for a lithium-ion cell // Journal of Power Sources. – 2011. – T. 196. – No. 20. – pp. 8450-8462.
25. Bartlett A. et al. Model-based state of charge estimation and observability analysis of a composite electrode lithium-ion battery //Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on. – IEEE, 2013. – pp. 7791-7796.
26. Moura S. J., Chaturvedi N. A., Krstic M. Adaptive Partial Differential Equation Observer for Battery State-of-Charge/State-of-Health Estimation Via an Electrochemical Model // Journal of Dynamic Systems, Measurement, and Control. – 2014. – T. 136. – No. 1. – S. 011015.
27. Klein R. et al. State estimation of a reduced electrochemical model of a lithium-ion battery //American Control Conference (ACC), 2010. – IEEE, 2010. – pp. 6618-6623.
28. Fang H. et al. Adaptive estimation of state of charge for lithium-ion batteries //American Control Conference (ACC), 2013. – IEEE, 2013. – pp. 3485-3491.

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IOANESYAN ALEXEY VILYAMOVICH

MODELING OF NON-STATIONARY OPERATING MODES OF AN ELECTRIC VEHICLE BATTERY

Specialty 05.09.03 - Electrical complexes and systems

Dissertations for an academic degree

Candidate of Technical Sciences

Moscow - 2009

The work was carried out at the Department of Electrical Engineering and Electrical Equipment at the Moscow Automobile and Highway Institute (State Technical University)

Leading organization: Federal State Unitary Enterprise Research and Experimental Institute of Automotive Electronics and Electrical Equipment (FSUE NIIAE), Moscow.

The defense will take place on November 24, 2009 at 10:00 am at a meeting of the dissertation council D.212.126.05 at the Moscow Automobile and Highway Institute (State Technical University) at the address:

125329 GSP A-47, Moscow, Leningradsky pr., 64.

The dissertation can be found in the library of MADI (GTU)

Scientific Secretary

Dissertation Council,

Candidate of Technical Sciences, Associate Professor Mikhailova N.V.

general description of work

Relevance of the problem

Currently largest producers cars (General Motors, Ford, Daimler-Chrysler, Toyota, Honda, Nissan, Mazda, etc.) are intensively working on the design and production of electric vehicles. In terms of characteristics such as range and load capacity, some modern models of electric vehicles are very close to traditional cars, but their main disadvantage is their high cost.

The characteristics of an electric vehicle and its cost are largely determined by the parameters of the power plant used and, in particular, the battery. To optimize the parameters of a power plant, calculate the characteristics of an electric vehicle and determine its efficiency in comparison with a traditional car, the main tools are mathematical and simulation modeling.

The most difficult task when building a model of an electric vehicle is simulating the operation of the battery during its non-stationary discharge and charging on an electric vehicle. Calculated determination and analysis of battery parameters is also required in the battery control system on an electric vehicle, which ensures optimal operating conditions, increases service life, prevents overcharging and excessive discharge, ensures operational safety and informs the driver about the state of charge and other parameters of the battery.

The dissertation is devoted to the development of models for the movement of an electric vehicle and the study of non-stationary operating modes of the battery of an electric vehicle, which seems to be very relevant at the present time.

Purpose and main objectives of the study

In accordance with the goal set in the dissertation, the following tasks are solved:

• 
  analysis and systematization of methods and models for calculating AB characteristics;
• 
  formalization of methods for processing and analyzing statistical data and simulation experiments to analyze discharge characteristics;
• 
  development of a simulation model of unsteady motion of an electric vehicle;
• 
  development of a methodology for integrating heterogeneous EV components;
• 
  
• 
  formulation and solution of optimization problems using a simulation model.

Research methods

Scientific novelty

• 
  aggregated process representation of the simulation model of non-stationary movement of electric vehicles;
• 
  models of non-stationary random processes of the dynamics of EV movement and battery charge/discharge;
• 
  models for classifying vehicle types and problems of selecting types for given characteristics of EV movement;
• 
  software implementation EM simulation model;
• 
  optimization algorithms based on an EV simulation model.

Practical value and implementation of work results

Approbation of work

• 
  at republican and interregional scientific and technical conferences, symposia and seminars (2003-2009);
• 
  at a meeting of the Department of Electrical Engineering and Electrical Equipment of MADI (STU).

In the introduction the relevance of the work is substantiated, the goal is determined and the main objectives of the research are set.

In the first chapter dissertation, modern ABs are classified and their main characteristics are determined. A systematization of known methods for calculating AB characteristics has been carried out and the possibility of their use in modeling unsteady loading has been assessed.

The characteristics of EVs are mainly determined by the performance of onboard electrical energy sources. Lead-acid (PbAcid), nickel-cadmium (Ni-Cd), nickel-metal hydride (Ni-MH) batteries and lithium-based batteries (Li-Ion, Li-Metal, Li-Polymer) are the most widely used in EV power plants. )

Analyzing the characteristics of various types of batteries declared by manufacturers, two groups can be distinguished: high-energy (traction) batteries used in “pure” electric vehicles and high-power (pulse) batteries.

The specific energy of batteries of the first group reaches 35 Wh/kg for lead-acid batteries; nickel-cadmium – 45 Wh/kg. These batteries are inexpensive, but their use significantly reduces performance characteristics and limits the scope of EV use.

Nickel-metal hydride batteries are promising E m=80 Wh/kg, P m=200 W/kg, lithium-ion batteries E m=140 Wh/kg, P m=420 W/kg and their version with polymer electrolyte (Li-Polymer) E m=205 Wh/kg, P m=420 W/kg. The specific energy values ​​are given for a 3-hour discharge mode, and the power values ​​correspond to a pulse lasting 30 s at 80% charge level.

The given specific characteristics of batteries are not enough to compare the efficiency of their use on EVs, therefore the main objective of the dissertation is to model the unsteady loading of batteries on EVs, for which a “black box” model is proposed using classical methods of experiment planning.

Based on the studied parameters (input and output), the following groups of methods can be distinguished:

• 
  methods for describing a family of discharge curves - dependence U=f( I, t) at a given constant temperature value ( T=const);
• 
  calculation of the maximum discharge time (battery capacity) depending on the discharge current;
• 
  methods for simplified calculation of non-stationary battery discharge, i.e. discharge with time-varying discharge current or power consumption [ t m=f( I), I=var or t m=f(P) P=var];
• 
  determining the moment of the end of the battery discharge at a given current, which is used not only in modeling EVs, but also in the battery control system directly on board the EV;
• 
  complex methods that determine dependencies U=f( I, t, T) And t m=f( I).

The most famous is the method of analytical description of the discharge characteristics of batteries, proposed by Shepherd. This method allows us to describe the dependence U= f( I,t) as:

The main disadvantage of the method is that the coefficients are selected for a certain range of discharge currents and when going beyond this range, the approximation error increases significantly.

One of the simplest and most accurate ways to evaluate the characteristics of a battery when it is loaded with a time-varying current is the Hoxie method. The method is based on the Peukert relation, which determines the dependence of the maximum battery capacity (discharge time) on the discharge current

Where I 1 ,I 2 …I z– current values ​​in sections of the discharge graph I=f( t); t 1 ,t 2 ... t z- discharge time with corresponding currents I 1 ,I 2 …I z .

In this model, the current graph I=f( t) represents a piecewise constant function divided into z sections. Peukert coefficients are determined for the operating range of currents. To solve the Hoxie equation, a search algorithm is used to determine t m provided that the right side of the equation is equal to one.

Applying this method to calculate an electric vehicle, setting as the initial schedule I=f( t) change in battery current during a driving cycle, you can calculate the maximum number of cycles that an electric vehicle will complete before the battery is completely discharged N ts =t m /t ts, Where t ts– duration of one cycle.

In this work, on the basis of a simulation experiment, the accuracy of several methods for simplified calculation of unsteady battery loading during EV movement in the SAE j 227C cycle was assessed (Table 1). An EV with an OPTIMA YellowTop D 1000 S battery was considered (10 series-connected batteries with a total weight of 195 kg were installed on the EV).

The results of calculating the movement of an electric vehicle

Based on the research carried out in the dissertation to simulate unsteady loading of the battery at various modes and conditions of EV movement, it is proposed to use hybrid analytical-simulation models based on a decomposition approach, which is based on the following axioms of the theory of complex systems: Hierarchy: if  0 is a subsystem of the system  and (...) is a measure of complexity, then ( 0) (), i.e. a subsystem cannot be more complex than the system as a whole. Parallel connection: if = 1  2 ….. k , i.e.  is a parallel connection of subsystems , then
. Serial connection: if = 1 + 2 +…+ k, i.e.  is a serial connection of subsystems  i , then () ( 1)+( 2)+... ( k). Connection with feedback(OS): if there is an OS operation  from subsystem  2 to subsystem  1, then ()( 1)+( 2)+( 2  1). The listed properties of a complex system allow for the possibility of reducing its apparent complexity by combining individual variables into subsystems. With this decomposition, the goal is to simplify the analysis of the system, considering it as a loosely coupled set of interacting subsystems.

In the second chapter the task of formalizing the principles of constructing an EM simulation model is posed and solved. Functioning is understood as the process of changing its state over time. Modeling of the process as a whole should include a model of the road surface, models of the interaction of the wheel with the road surface, models of the machine itself, transmission and others, all of which are interconnected and nested one within the other (Fig. 2.).

It is assumed that system- there are many parameters
(humidity, rotation angle, etc.). Each parameter q i takes on a set of numeric values ​​( q i). Let's define with condition process as a whole, as s j =, where q i j ( q i). Process Z there is a four: Z=S, T, F,  >, Where S- state space; T- many times of state change; F- phase characteristic of the process, defined as the transformation of state over time F:T S,  - linear order relation on T.

The time interval for modeling the movement of EVs is [ t N, t K ], where
,
. Assuming that the EM behaves fairly uniformly in individual areas, it is possible to decompose the entire process into subprocesses. Subprocess there is a subset of the process Z on the time interval [ t i ; t j]. The concept of a subprocess allows us to consider a process as a sequence of subprocesses. To ensure the correctness of descriptions of the functioning of both the system as a whole and its components, a number of operations on processes are introduced.

Process Z 1 =S 1, T 1 , F 1 ,  1 > represents the convolution of the process Z, if it is obtained as a result of the following transformations: a) a complete partition of the process definition interval has been performed Z into n subintervals [ j ,  j+1 ], where j=1..n, and  1 = t N,  n+1 = t TO . Then we get the process split Z for n subprocesses Z j(j=1..n); b) match each subprocess Z j one state value from many S 1 and one time value  j from the interval [ j ,  j+1 ]. The unfolding operation is the inverse of the convolution operation: the process Z is a development of the process Z 1 . Process Z 1 is the process projection Z to coordinate space
(designation
), If Q 1 Q.

Let the processes be given Z 1 =, T 1 , F 1 ,  1 > and Z 2 =, T 2 , F 2 ,  2 >. Process Z=, T, F, > is a union of processes Z 1 and Z 2 (designation Z=Z 1 Z 2), if: S Q is the union of spaces and
.

The introduced operations make it possible to create a formalized description of both individual component processes (road profile, dynamic change in traffic characteristics, etc.) and the interaction of components of the entire system.

The EV motion model includes the components shown below.

Mechanical model

The force of resistance to movement creates a moment of resistance on the EM wheel, which, taking into account the transmission gear ratios, is brought to the electric motor shaft, taking into account the transmission efficiency.

Thus, the moment of resistance to movement on the electric motor shaft
Where r k – wheel rolling radius, m; i tr – transmission gear ratio; tr – transmission efficiency.

In addition, the model of the mechanical part must take into account the movement of the electric vehicle along a section of the road with a slope (ascent or descent) and the resistance to movement due to unevenness of the road. When modeling the movement of EVs on descents, the recuperation of braking energy should be taken into account.

Electric motor model

The torque on the electric motor shaft is determined based on:

(5)

In the simulation model of the electric motor, the total power losses are calculated at each step, based on the design parameters of the DC motor and the idle characteristics obtained during testing E = f(I c) at a constant speed of the electric motor shaft.

Despite the tendency to use asynchronous motors or contactless permanent magnet motors on EVs as traction electric motors, consideration of DFC remains the most convenient and quite sufficient when solving problems of EV simulation to obtain a picture of AB loading.

Control system model

Motor voltage regulation U D can be done using a thyristor control device using the pulse-width control method; while the duty cycle   varies from 0 to 1:

(6)

Model of driving modes

Based on experimental motion graphs, a technique for forming a motion mode has been developed by randomly selecting cycles and forming a random sequence of them. Thus, disorderly urban traffic was simulated.

The driving modes obtained on the basis of experimental data differ significantly from the driving modes in the SAE j 227 C cycle; in particular, when calculating for real driving modes, a lower specific energy consumption (260 Wh/km) was obtained than for driving in the cycle ( 390 Wh/km).

Battery model

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.

• 
  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.

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 for testing the 6EM-145 battery special program. The experiment was carried out for 2 months using 2 6EM-145 batteries.

Information content of abstract factors

1. 
   Charge with two-stage current 23A and 11.5A (recommended by the battery manufacturer)
2. 
   Control discharge (according to the manufacturer’s recommendation) with a current of 145A to a minimum voltage value of 9V.
3. 
   Charge up to 20%, 50% and 80% charge levels with currents of 23.45 and 95A.
4. 
   Discharge current 145A to a minimum voltage value of 9V.

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 field 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

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:

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 stationary mode 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:

A) , b) , V) , G) .

(12)

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 models and choice of initial travel modes 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– lifting 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:

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, 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

1. 
   A classification of batteries and an analysis of known methods for calculating the characteristics of batteries were carried out. An assessment is made of the possibility of their use in modeling non-stationary battery charge and discharge.
2. 
   Based on the research carried out in the dissertation, the use of a decomposition approach was proposed to model unsteady loading of the battery under various modes and driving conditions of the vehicle, which allows integrating hybrid analytical and simulation models, including models of the mechanical part, control systems, driving modes and others.
3. 
   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.
4. 
   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.
5. 
   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.
6. 
   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.
7. 
   To solve optimization problems on a simulation model, stochastic approximation algorithms were selected as control algorithms, which provide high speed convergence in conditions of large dispersions of motion characteristics.
8. 
   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

1. 
   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.
2. 
   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.
3. 
   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.
4. 
   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.
5. 
   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.
6. 
   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. A mathematical battery is a far cry from the complexity of the battery you can get out of your mobile 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.