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

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**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

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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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**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.

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**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

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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

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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. 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

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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 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

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

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**(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.

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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.**

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.

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Introduction Battery Basics Rate Capacity Effect 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. 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

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**Results for Experiment 1**

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**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.

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**Experiment 2 To explore further battery recovery phenomenon.**

OFF Variation in OFF time with constant ON time by adjusting Duty Cycle and Frequency

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**Results for Experiment 2.**

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Introduction Battery Basics Rate Capacity Effect 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.**

‘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.

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**Determining parameters ‘i’ and ‘j’**

‘i+j’ (total charge in the battery) ‘i’ (available charge)

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**Transitions Probability to recover in an idle slot**

Probability of no recovery in an idle slot Probability of q1 charge being drawn

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**Transition Equations Idle slot after time t**

While current I is being drawn Idle slot after time t

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

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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).

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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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البحث الثامن بحث منفرد منشور فى مؤتمر دولى متخصص ( منشور التحكيم علي البحث الكامل ) Adel A. Elbaset 14 th International Middle East Power Systems Conference.

البحث الثامن بحث منفرد منشور فى مؤتمر دولى متخصص ( منشور التحكيم علي البحث الكامل ) Adel A. Elbaset 14 th International Middle East Power Systems Conference.

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