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.
Introduction

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

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

7. 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”
Positive
Ions
Load _ +
Electron Flow
Anode
Cathode
Electrolyte
1. Wait

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.
Factors that may affect the battery performance include:
When a battery stands idle after a discharge, certain chemical and physical changes take place which can result in voltage recovery. So, the voltage will rise after a rest period, giving a saw-tooth-shaped discharge.
Shelf Life: even during storage, the battery is still discharge itself. Depending on the storage temp and humidity, the short shelf life can be a problem on long-term discharges.
Around room temp, alkaline lose about 3% capacity per year, however zinc-carbon can lose up to 15% of the capacity
Rate Capacity Effect

9. 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.
Elapsed time of discharge
Cell Voltage
Intermittent Discharge
Continuous discharge
Factors that may affect the battery performance include:
When a battery stands idle after a discharge, certain chemical and physical changes take place which can result in voltage recovery. So, the voltage will rise after a rest period, giving a saw-tooth-shaped discharge.
Shelf Life: even during storage, the battery is still discharge itself. Depending on the storage temp and humidity, the short shelf life can be a problem on long-term discharges.
Around room temp, alkaline lose about 3% capacity per year, however zinc-carbon can lose up to 15% of the capacity
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. (higher forms of KiBaM)
Battery Model
Advantages
Disadvantages
PDE
(higher forms of KiBaM)
Accurate
Slow, involves a large number of parameters
Circuit
Use capacitor and resistors to represent battery
Not accurate, elements change value depending conditions
Stochastic
Relatively accurate and fast.
Still in the process of development.
Based solely on the electro-chemistry.
Sometime rely on empirically established
2. PDE: finite element models, divide each cell into a number of finite elements interacting with each other, models current flow and potential distribution in the cell. Quite complex and slow while accurate, not suitable for mobile OS. 3.
4. Stochastic is a promising modeling method. Represent the battery behavior as
A discrete time transient stochastic process, that tracks the the cell state of the charge.

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.
Electrode
Electrolyte
Active Species
Charged State
Before Recovery
After Recovery
Discharged State
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. Circuit Diagram Experiment 1. Batteries used:
Function Generator
Voltmeter
npn SL100
Power Supply
Ground A V
Vin
Ammeter
Experiment 1.
Vin :: Square waves with varying frequencies.
Battery
Batteries used:
1.2 Volts AAA Ni-MH

18. Results for Experiment 1

19. Frequency mA.min delivered
Continuous(∞)
62000
1000hz
66000
1Hz
69500
0.2Hz
81000
Observation unexpected because duty cycle for all is 50%, i.e same recovery expected.

20. Experiment 2 To explore further battery recovery phenomenon.
OFF
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. 3-Dimensional Stochastic Process to model recovery and rate capacity.
‘t’ is the length of the current idle slot j i
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 Idle slot after time t
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