Battery Model for Embedded Systems

1. Battery Model for Embedded Systems Venkat Rao, EE Department, IIT Delhi. Gaurav Singhal, CSE Department, IIT Delhi. Anshul Kumar, CSE Department, IIT Delhi. Nicolas Navet, LORIA, France. Work Done at :

2. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

3. Introduction Mobile Embedded Systems Design : • Battery lifetime is major constraint. • Slow growth in energy densities not keeping up with increase in power consumption. • Estimation of battery lifetime important to choose between alternative architecture and implementations.

4. Traditional approaches to energy optimization • Dynamic Voltage Scaling (DVS): busy system => increase frequency idle system => decrease frequency • The algorithms on DVS considers battery as an ideal power source, i.e. energy delivered by the battery is constant under varying conditions of voltages and currents. Battery is a Non ideal Source of energy!!

5. Battery lifetime and the total energy delivered by it depends heavily on discharge profile. • Need for accurate battery model which takes into account the battery non-linearities. A Typical Discharge Profile (Li/MnO2 Cells)

6. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

7. Electron Flow _ Load + Cathode Positive Ions Anode Electrolyte Battery Basics • Battery characterized by Voc and Vcut. • Electric current obtained by electrochemical reactions occurring at electrode-electrolyte interface. • Battery lifetime governed by active species concentration at electrode-electrolyte interface. • Phenomenon governing battery lifetime: • “Rate Capacity Effect” • “Recovery Effect”

8. Rate Capacity Effect • Total charge delivered by the battery goes down with the increase in load current. • Concentration of active species at interface falls rapidly with increasing load current. • Battery seems discharged when the concentration at interface becomes zero. Rate Capacity Effect

9. Intermittent Discharge Cell Voltage Continuous discharge Elapsed time of discharge Recovery Effect • Battery recovers capacity if given idle slots in between discharges. • Diffusion process compensates for the low concentration near the electrode. • Battery can support further discharge. Recovery Effect

10. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

11. Battery Model

12. Kinetic Battery Model • Simplest PDE model to explain both recovery and rate capacity. • Available and Bound charge wells • Dynamic transfer of charges governed by a rate constant and difference in heights.

13. Stochastic model- Dey, Lahiri et al. • Fast and reasonably accurate. • Markovian chain with each representing battery state of charge. • Transitions associated with state dependent probabilities, model discharge and recovery.

14. Diffusion Model- Rakhmatov, Vrudula et al. Active Species Electrolyte Electrode Before Recovery Charged State Discharged State After Recovery • Complex PDE model. • Mathematically very sound but computationally expensive. • Cannot be used in real time dynamic scheduling.

15. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

16. While working on power profiling we conducted a few experiments on battery discharge and simulated for these models. • FOUND !! That the results could not be accurately explained by any of the previous models. • We developed our own Battery Model, that could better predict the experimental results.

17. Power Supply A Voltmeter V Rc npn SL100 Vin Function Generator Ground Circuit Diagram Ammeter Experiment 1. Vin :: Square waves with varying frequencies. Battery Batteries used: 1.2 Volts AAA Ni-MH

18. Results for Experiment 1

19. Observation unexpected because duty cycle for all is 50%, i.e same recovery expected.

20. OFF ON OFF ON OFF ON OFF ON Experiment 2 To explore further battery recovery phenomenon. Variation in OFF time with constant ON time by adjusting Duty Cycle and Frequency

21. Results for Experiment 2.

22. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

23. Stochastic Modified KiBaM • Simple and accurate stochastic model derived from the KiBaM. • Models recovery and rate capacity. • Able to predict variation due lengths of idle slots. Intuitive Picture

24. j i ‘t’ is the length of the current idle slot • 3-Dimensional Stochastic Process to model recovery and rate capacity. • (i,j,t) is the tuple which describes the present state of the system.

25. Determining parameters ‘i’ and ‘j’ ‘i+j’(total charge in the battery) ‘i’ (available charge)

26. Transitions Probability to recover in an idle slot Probability of no recovery in an idle slot Probability of q1 charge being drawn

27. Transition Equations While current I is being drawn Idle slot after time t

28. Determining p(t) and Q • The average recovery per idle slot serves as a characteristic for the particular battery (as derived from Experiment set 2). • The differential p(t) of the curve gives the probability to recover with time during an idle slot. • The quanta (Q) of charge battery recovers depends on the current state of the battery i.e. height difference and the granularity of time. • The quanta (Q) of recovery is calculated so as the charge recovered for an infinitely long idle slot is equal to total charge that needs to be transferred between the two wells before there heights are equalized.

29. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

30. Simulation • A C simulation of our model was on a P4 Desktop with 256MB RAM using the parameters calculated as explained before for Panansonic Ni-MH AAA battery. • We ran our simulations on different charge profiles and compared them with experimental results. • The simulation was run several times on each profile and results were averaged to approximate battery lifetime and charge delivered by the battery. • Simulation results suggest that the model was quite accurate in predicting the battery life and charge drawn for the battery with a maximum error of 2.65% .

31. Simulation Results

32. Simulation Results contd..

34. Introduction • Battery Basics • Rate Capacity Effect • Recovery Effect • Related Work : Review of relevant models • Experiments • Our Model. • Simulation and Results • Future Work

35. Future Work • In future we would like to conduct experiments on different battery technologies, to have a better picture of the behavior of battery in general. • We are doing our major project on “Integrated Power Management for Embedded Systems”, which utilizes this battery model for Real time scheduling whose aim is to maximize battery life (as opposed to traditional DVS algorithms, which aim to reduce energy consumption).

36. References • D. Panigrahi, C. Chiasserini, S. Dey, R. Rao, A. Raghunathan, and K. Lahiri. “Battery Life Estimation of Mobile Embedded Systems”.In Proceedings of International Conference on VLSI Design.January 2001. • V. Rao, G. Singhal, and A. Kumar. “Real Time Dynamic Voltage Scaling for Embedded Systems”. In Proceedings of International Conference on VLSI Design, January 2004. • P. Rong and M. Pedram. “Battery Aware Power Management Based on Markovian Decision Processes.” Proceedings of the IEEE/ACM International Conference on Computer aided design, 2002. • S.Vrudhula and D.Rakhmatov. “Energy Management for Battery Powered Embedded Systems.” ACM Transactions on Embedded Computing Systems, August 2003. • D. Linden. “Handbook of Batteries and Fuel Cells.”1984. • T. L. Martin. “Balancing Batteries, Power, and Performance: System Issues in CPU Speed-Setting for Mobile Computing.” PhD thesis, Carnegie Mellon University, Pittsburgh, Pennsylvania, 1999.

37. THANK YOU