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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 :

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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

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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 !!

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Need for accurate battery model which takes into account the battery non-linearities. A Typical Discharge Profile (Li/MnO 2 Cells) Battery lifetime and the total energy delivered by it depends heavily on discharge profile.

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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Positive Ions Load_ + Electron Flow AnodeAnode CathodeCathode Electrolyte Battery Basics Battery characterized by V oc and V cut. 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

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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.

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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

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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

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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.

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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.

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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 State After Recovery Before Recovery Electrode Electrolyte Active Species

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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.

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

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Results for Experiment 1

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FrequencymA.min delivered Continuous()62000 1000hz66000 1Hz69500 0.2Hz81000 Observation unexpected because duty cycle for all is 50%, i.e same recovery expected.

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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

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Results for Experiment 2.

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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

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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.

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i+j (total charge in the battery) i (available charge) Determining parameters i and j

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Transitions Probability of no recovery in an idle slot Probability to recover in an idle slot Probability of q 1 charge being drawn

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

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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.

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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%.

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Simulation Results

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Simulation Results contd..

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Introduction Battery Basics 1. Rate Capacity Effect 2. Recovery Effect Related Work : Review of relevant models Experiments Our Model. Simulation and Results Future Work

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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.

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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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THANK YOU

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