battery model for embedded systems venkat rao, ee department, iit delhi. gaurav singhal, cse...
TRANSCRIPT
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 :
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
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
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!!
• Need for accurate battery model which takes
into account the battery non-linearities.
A Typical Discharge Profile
(Li/MnO2 Cells)
• Battery lifetime and the total energy delivered by it
depends heavily on discharge profile.
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
Positive Ions
Load_ +
Electron Flow
Anode
Cathode
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:
1. “Rate Capacity Effect”
2. “Recovery Effect”
Rate Capacity Effect
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.
Recovery Effect
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
Cel
l V
olt
age Intermittent Discharge
Continuous discharge
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
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.
Battery Model
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.
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.
Diffusion Model- Rakhmatov, Vrudula et al.
• Complex PDE model.
• Mathematically very sound but computationally expensive.
• Cannot be used in real time dynamic scheduling.
Charged State
Discharged StateAfter Recovery
Before Recovery
Electrode Electrolyte Active Species
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
• 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.
Circuit Diagram
Experiment 1.
Vin :: Square waves with
varying frequencies.
Batteries used:
1.2 Volts AAA Ni-MH
Battery
Ammeter
Rc
Function Generator
Voltmeter
npn SL100
Power Supply
Ground
A
V
Vin
Results for Experiment 1
Discharge at 1000mA at Different Frequency
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 50 100 150 200
Time (in mins)
Volta
ge (i
n Vo
lts) Continuous
0.2Hz
1Hz
1000Hz
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.
Experiment 2
Variation in OFF time with constant ON time by adjusting Duty Cycle and Frequency
To explore further battery recovery phenomenon.
ON OFF
ON OFF
ON OFF
ON OFF
Results for Experiment 2.
Experimental Recovery Vs length of idle slot
0
100
200
300
400
500
0 1 2 3 4 5
Length of idle slot (in seconds)
mA
h d
eli
vere
d a
bo
ve
rate
d.
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
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
• 3-Dimensional Stochastic Process to model recovery and rate capacity.
j i ‘t’ is the length of the current idle slot
• (i,j,t) is the tuple which describes the present state of the system.
‘i+j’ (total charge in the battery)
‘i’ (available charge)
Determining parameters ‘i’ and ‘j’
TransitionsProbability of no recovery in an idle slot
Probability to recover in an idle slot
Probability of q1 charge being drawn
Transition Equations
Idle slot after time t
While current I is being drawn
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.
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
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% .
Simulation Results
Simulation Results contd..
• Introduction• Battery Basics
1. Rate Capacity Effect 2. Recovery Effect
• Related Work : Review of relevant models• Experiments• Our Model.• Simulation and Results• Future Work
Future Work
• 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).
• In future we would like to conduct experiments on different battery technologies, to have a better picture of the behavior of battery in general.
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.
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