P u b l i s h e d b y t h e I E E E C o m p u t e r S o c i e t y
Battery Modeling for Energy-AwareSystem Design
Many features of modern portable elec-tronic devices—such as high-speedprocessors, colorful displays, opti-cal/magnetic storage drives, and wire-less network interfaces—carry a sig-
nificant energy cost. However, advances in batterytechnology have not kept pace with rapidly grow-ing energy demands.1,2
Most laptops, handheld PCs, and cell phones userechargeable electrochemical batteries—typically,lithium-ion batteries—as their portable energysource. These batteries take anywhere from 1.5 to4 hours to fully charge, but they can run on thischarge for only a few hours or, in the case of somenewer pocket PCs, up to about 14 hours.
The battery has thus emerged as a key parame-ter to control in the energy management of porta-bles.3-8 To meet the stringent power budget of thesedevices, researchers have explored various archi-tectural, hardware, software, and system-level opti-mizations to minimize the energy consumed peruseful computation.
Maximizing the number of useful computationsis effectively a problem of maximizing battery life-time subject to system performance constraints.Given a load applied to a battery over a certainperiod, information about when the battery fails aswell as its state of charge, or remaining capacity, atany time can be used to trade off system perfor-mance for battery lifetime at both the design stageand runtime, possibly with the user’s active partic-ipation. For example, an energy-aware picturephone could let a user trade off image quality with
talk time and the number of photos the phone couldtake using the remaining battery capacity.
Incorporating battery-state information into alifetime optimization strategy requires a mathe-matical model that captures battery nonlinearities.Accurate low-level models9-11 based on the differ-ential equations that describe the complex phe-nomena occurring in an electrochemical cell havebeen around for about a decade, but solving theseequations can take days. In recent years, however,researchers have developed high-level battery mod-els4,5,7,12-15 that reduce simulation time while pre-dicting relevant variables with acceptable accuracy.
BATTERY DISCHARGE BEHAVIORBecause the energy drawn from a battery is not
always equivalent to the energy consumed in devicecircuits, understanding discharge behavior is essen-tial for optimal system design.
Batteries consist of cells arranged in series, par-allel, or a combination of both. Two electrodes—ananode and a cathode, separated by an electrolyte—constitute each cell’s active material. When the cellis connected to a load, a reduction-oxidation reac-tion transfers electrons from the anode to the cath-ode. This transfer converts the chemical energystored in the active material to electrical energy,which flows as a current in the external circuit.16
As the battery discharges, its voltage drops; whenthis voltage falls below a certain cutoff, the batterydisconnects from the load.
We define capacity in terms of charge units ratherthan energy.17 Full charge capacity is the remaining
Computationally feasible mathematical models are now available that cap-ture battery discharge characteristics in sufficient detail to let designersdevelop an optimization strategy that extracts maximum charge.
capacity of a fully charged battery at the beginningof a discharge cycle, and full design capacity is theremaining capacity of a newly manufactured bat-tery. Further, theoretical capacity is the maximumamount of charge that can be extracted from a bat-tery based on the amount of active material it con-tains, standard capacity is the amount of chargethat can be extracted from a battery when dis-charged under standard load and temperature con-ditions, and actual capacity is the amount of chargea battery delivers under given load and tempera-ture conditions.3
Like other electrochemical systems, the laws ofthermodynamics, electrode kinetics, and transportphenomena determine the complex set of equationsthat govern battery behavior.18 Thus, as Figure 119
shows, battery discharge behavior is sensitive tonumerous factors including the discharge rate, tem-perature, and the number of charge-recharge cycles.Consequently, battery discharge behavior deviatessignificantly from the behavior of an ideal energysource.
Rate-dependent capacity Battery capacity decreases as the discharge rate
increases. To illustrate this phenomenon, Figure 2shows a simplified symmetric electrochemical cellin which similar processes occur at both electrodes.
In a fully charged cell (Figure 2a), the electrodesurface contains the maximum concentration ofactive species. When the cell is connected to a load,a current flows through the external circuit; activespecies are consumed at the electrode surface andreplenished by diffusion from the bulk of the elec-trolyte. However, this diffusion process cannot keepup with the reaction process, and a concentrationgradient builds up across the electrolyte (Figure 2b).
A higher load current results in a higher concen-tration gradient9 and thus a lower concentration ofactive species at the electrode surface. When thisconcentration falls below a certain threshold, whichcorresponds to the voltage cutoff, the electro-chemical reaction can no longer be sustained at theelectrode surface. At this point, the charge that wasunavailable at the electrode surface due to the gra-dient remains unusable (Figure 2d) and is respon-sible for the reduction in capacity.
However, the unused charge is not physically“lost,” but simply unavailable due to the lag betweenreaction and diffusion rates. Decreasing the dis-charge rate effectively reduces this lag as well as theconcentration gradient. If the battery’s load goes tozero, the concentration gradient flattens out after asufficiently long time, reaching equilibrium again(Figure 2c). The concentration of active species nearthe electrode surface following this rest period makessome unused charge available for extraction.
System designers can exploit this charge recov-ery effect to control the discharge rate to maximizebattery lifetime under performance constraints.However, at sufficiently low discharge rates, thebattery will behave like an ideal energy source. Forexample, in Figure 1a, battery capacity will not sig-nificantly differ from that of the 180-mAh curvefor constant currents below 900 mA.
Temperature effectTemperature also strongly affects battery dis-
charge behavior. Below room temperature (around25°C), chemical activity in the cell decreases andinternal resistance increases, reducing full chargecapacity and increasing the slope of the dischargecurve. At much higher temperatures, a decrease ininternal resistance increases the full charge capac-ity and voltage. However, the higher rate of chem-ical activity, or self-discharge, can reduce the actualcapacity delivered.16 Unlike the discharge rate, tem-
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Charge conditions: Constant voltage/constant current—4.2 V, 900 mA (maximum), 45 mA cutoff at 20°C.Discharge conditions: Constant current—900 mA,2.75 V cutoff at various temperatures.
perature is not an easily controllable variable inenergy-aware system design.
Capacity fadingBecause of their high energy density and capac-
ity, lithium-ion batteries are the popular choice formany portable applications. However, these bat-teries lose a portion of their capacity with each dis-charge-charge cycle. This capacity fading resultsfrom unwanted side reactions including electrolytedecomposition, active material dissolution, andpassive film formation.16 These irreversible reac-tions increase cell internal resistance, ultimatelycausing battery failure.
To deal with this problem, system users canattempt to control the depth of discharge beforerecharging. Typically, a battery subjected to shallowdischarges—that is, voltage is still relatively highwhen recharging occurs—will be good for morecycles than a battery subjected to deep discharges—for example, until the cutoff voltage is reached.
BATTERY MODELSResearchers have developed numerous compu-
tationally feasible mathematical models that cap-ture battery behavior in sufficient detail. Physicalmodels provide a detailed description of the phys-ical processes occurring in the battery. Empiricalmodels consist of ad hoc equations describing bat-tery behavior with parameters fitted to matchexperimental data. Abstract models represent a bat-tery as electrical circuits, discrete-time equivalents,stochastic process models, and so on. Mixed mod-els offer a simplified view of the physical processeswith empirically fitted parameters.
Models in each category can be evaluatedaccording to four basic criteria:
• Accuracy. How closely do the predicted valuesof the battery variables of interest—lifetime,voltage, and so on—match experimental data?Can the model handle a general case of time-varying loads? Does it account for the tem-perature effect and capacity fading?
• Computational complexity. How long do thesimulations take?
• Configuration effort. How many parameterscan the model estimate? Does the model requirein-depth knowledge of battery chemistry?
• Analytical insight. Do the equations describ-ing the model provide some qualitative under-standing of battery behavior? Is such insightuseful in exploring ways to trade off lifetimeand performance?
Table 1 summarizes a number of representative bat-tery models with respect to these criteria anddescribes some of their applications.
Physical modelsPhysical models are the most accurate and have
great utility for battery designers as a tool to opti-mize a battery’s physical parameters. However, theyare also the slowest to produce predictions and thehardest to configure, providing limited analyticalinsight for system designers.
Marc Doyle, Thomas F. Fuller, and JohnNewman9,10 developed an isothermal electrochem-ical model that describes the charge and dischargeof a lithium (anode)/polymer (electrolyte)/insertion(cathode) cell for a single cycle. This model uses con-centrated solution theory to derive a set of differ-ential equations that, when solved, provide cellpotential values as a function of time.18
Dualfoil20 is a Fortran program that uses thismodel to simulate lithium-ion batteries. The pro-gram reads the load profile as a sequence of con-stant current steps, and the battery lifetime isobtained from the output by reading off the time atwhich the cell potential drops below the cutoff volt-age. Researchers have used Dualfoil to evaluateother battery models, and have extended thelithium/polymer/insertion cell model to includeadditional factors such as energy balance andcapacity fading.11
Nevertheless, simulating a given lithium-ion bat-tery can require specifying more than 50 parame-ters based on knowledge of the structure, chemicalcomposition, capacity, temperature, and othercharacteristics. In addition, solving the model’sinterdependent partial differential equationsrequires using complex numerical techniques. Asa result, simulating each load profile can take sev-eral hours or even days.
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(a) Charged state
W
(c) After recovery
(b) Before recovery
x = 0
(d) Discharged state
Electrode Electrolyte Electroactive species
Figure 2. Batteryoperation. In a symmetric electrochemicalcell, similarprocesses occur atboth electrodes: (a)fully charged state,(b) before recovery,(c) after recovery,and (d) dischargedstate.
Physical Lithium- Yes Yes; support Very high High Very high (> 50 Low polymer- for Arrhenius parameters) insertion temperature cell (Doyle et al.) dependence and
cycle aging added by Rong and Pedram
Empirical Peukert’s Yes; needs No Medium (14% Low Low (2 Low law recalibration average error parameters)
for each for constant load,temperature 8% average error
for interrupted and variable loads)
Battery Yes; needs No Medium Low Low (2 Low Design of efficiency recalibration parameters) interleaved dual-(Pedram for each battery powerand Wu) temperature supply; load
splitting for maximum lifetime of multibattery systems
Weibull fit Yes No Medium Low Low (3 Low (Syracuse parameters) and Clark) Abstract Electrical- Yes Yes Medium (12% Medium Medium (> 15 Mediumcircuit error predicting parameters) (Gold) cell voltage and
Electrical- Yes No Medium Medium High (> 30 Medium Thermostatic chargecircuit parameters) method: high (Bergveld et al.) charging efficiency Discrete-time Yes No Medium (1% Medium Medium (>15 Medium Dynamic Power (Benini et al.) compared to parameters) Management;
Stochastic No No High (1%) Low Low (2 Medium Shaping load (Chiasserini parameters) (stochastic pattern to exploit and Rao) model of load charge recovery
pattern assumed) Mixed Analytical No No High (5%) Medium Low (2 High Task scheduling high-level parameters) by sequencing and (Rakhmatov V/f scaling; analysis et al.) of discharge
methods for multibattery systems
Analytical Yes Yes High (3.5%) Medium Medium (> 15 Highhigh-level parameters) (Rong and Pedram)
Empirical modelsEmpirical models are the easiest to configure, and
they quickly produce predictions, but they generallyare the least accurate. Although they work well incertain special cases, the constants used have nophysical significance, which seriously limits theiranalytical insight.
Peukert’s law. Some models attempt to capturenonideal discharge behavior using relatively sim-ple equations in which the parameters matchempirical data. While an ideal battery with capac-ity C discharged at a constant current would beexpected to have a lifetime L given by C = LI,Peukert’s law16 expresses this as a power law rela-tionship, C = LIα. The exponent provides a simpleway to account for rate dependence. However, theα values for different temperatures must beobtained empirically, and the fit is not always accurate.21
Though easy to configure and use, Peukert’s lawdoes not account for time-varying loads. Most bat-teries in portable devices experience widely vary-ing loads—for example, a pocket PC user may runa movie player application followed by a notes edi-tor, which yields a profile with two very differentloads for the battery.
Battery efficiency model. Massoud Pedram andQing Wu5 model battery efficiency—the ratio ofactual capacity to theoretical capacity—as a linear-quadratic function of the load current. They derivebounds on the actual power consumed for differ-ent current distributions with the same averagecurrent and show that these bounds depend on thecurrent’s maximum and minimum values. Amongall distributions with the same mean, a constantcurrent (least variance) would give the longest battery lifetime, and a uniformly distributed cur-rent (highest variance) would give the shortest.
This model accounts for rate dependence and canhandle variable loads. Researchers have used it,with slight modifications, to maximize the lifetimeof multibattery systems,6 to minimize the discharge-delay product in an interleaved dual-battery sys-tem design,22 and in static task scheduling forreal-time embedded systems.23
Weibull fit model. K.C. Syracuse and W.D.K.Clark13 used statistical methods to model the dis-charge behavior of lithium-oxyhalide cells. For afixed load and temperature, they noted batteryvoltage values at various stages of discharge. Theythen fit a Weibull model with three coefficients tothese values to express voltage as a function ofdelivered capacity, or charge lost. Syracuse andClark estimated the coefficients for different
load/temperature combinations similarly,and modeled the coefficients’ variation as aquadratic surface. They used a similarmethod to predict battery lifetime as a func-tion of load and temperature.
Abstract modelsInstead of modeling discharge behavior
either by describing the electrochemicalprocesses in the cell or by empirical approx-imation, abstract models attempt to provide anequivalent representation of a battery. Althoughthe number of parameters is not large, such mod-els also employ lookup tables that require consid-erable effort to configure. In addition, despiteacceptable accuracy and computational complex-ity, these models have limited utility for automateddesign space exploration because they lack analyt-ical expressions for many variables of interest.
Electrical-circuit and discrete-time models are par-ticularly useful when compatible models of othersystem components—circuit models or VHSICHardware Description Language (VHDL) models—are available to simulate the entire system in a sin-gle continuous-time or discrete-time environment.
Electrical-circuit models. Steven C. Hageman24 andSean Gold12 have each proposed PSpice circuitsconsisting of linear passive elements, voltagesources, and lookup tables to model nickel-metal-hydride and lithium-ion batteries, respectively.Henk Jan Bergveld, Wanda S. Kruijt, and PeterH.L. Notten14 likewise devised an electrical-circuitmodel of a nickel-cadmium battery by grouping the mathematical equations describing the batteryprocesses.
In Gold’s approach, capacity fading is modeledby a capacitor CCAP whose capacitance decreaseslinearly with the number of cycles. The load cur-rent I minus a rate-dependence offset flows throughthis capacitance. The voltage across CCAP repre-sents the ratio of delivered capacity to full chargecapacity. This normalized state of charge is thenconverted via a lookup table into a voltage VCOMP.
The temperature effect is modeled as a resistor-capacitor circuit with two temperature-dependentsources, VAMBIENT ∝ T and ERISE ∝ I2Rcell, where Tis the ambient temperature and Rcell is cell internalresistance. The main loop computes the cell volt-age by superposing the effect of the state of charge,temperature, and cell internal resistance.
Electrical-circuit models are inherently continu-ous-time and, while their simulation times are fasterthan those of physical models, they are still time-consuming. For example, while the number of circuit
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Abstract modelsattempt to provide
an equivalent representation
of a battery.
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parameters in Gold’s model is not large, configuringthe lookup tables requires substantial effort.
Discrete-time model. Using VHDL, Luca Benini andcolleagues15 approximated the continuous-timemodel shown in Figure 3 to a discrete-time model.Their approach incorporates battery voltage de-pendence on first-order effects—charge state, dis-charge rate, and discharge frequency—and thesecond-order effects of temperature and internalresistance. A lookup table models DC-DC con-verter characteristics. For constant and time-vary-ing loads, this model predicts lifetime values fordifferent battery types that are similar to thoseof the continuous-time model on which it wasbased. Researchers have used the discrete-timemodel to compare different Dynamic PowerManagement15,25 and multibattery discharge tech-niques.26
Stochastic model. Carla-Fabiana Chiasserini andRamesh R. Rao7 developed a battery model, shownin Figure 4, that represents charge recovery as adecreasing exponential function of the state ofcharge and discharged capacity. Assuming eachcell’s load to be a pulsed discharge, this model rep-
resents discharge and recovery as a transient sto-chastic process.
Each discharge demand of i units causes a tran-sition to i states lower, while rest periods cause statetransitions to successively higher states. Capacitygain is expressed as G = Acu/N, where Acu repre-sents the average number of charge units and N isthe nominal capacity—the charge extractable by aconstant load. Using the Dualfoil simulator, theresearchers obtained curves for G as a function ofthe discharge rate for different values of load cur-rent density and fitted two of the model parame-ters to match these curves.
This model is useful for representing pulsed dis-charge, as it can obtain capacity gain for differenttypes of stochastic loads analytically without sim-ulation; Chiasserini and Rao reported several ana-lytical results related to distributing the loadbetween two cells of a battery package. However,because it concentrates only on charge recovery,their model does not account for other battery non-linearities. Debashis Panigrahi and colleagues27
added a lookup table to incorporate rate depen-dence, resulting in an abstract model that is both
+–
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Figure 3. Continuous-time model used byBenini et al. in theirdiscrete-timeapproximation. Themodel incorporatesbattery voltagedependence on (a)first-order effectsand (b) second-ordereffects.
r1(f )
0 1
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q1q2Σqi
i = 2
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Figure 4. Stochasticcell model. Given acell state of charge0, 1, ..., N, eachdischarge demandof i units causes atransition to i stateslower, while restperiods cause state transitions to successivelyhigher states.
fast and capable of producing predictions closelymatching Dualfoil predictions.
Mixed modelsSome models combine a high-level representa-
tion of a battery for which experimental data deter-mines the parameters with analytical expressionsbased on physical laws. For example, Daler N.Rakhmatov and Sarma Vrudhula4 developed ahigh-level analytical model that characterizes a bat-tery using two constants, α and β, derived from thelifetime values for a series of constant load tests.The α parameter is a measure of the battery’s the-oretical capacity, while β models the rate at whichthe active charge carriers are replenished at the electrode surface.
Starting with Faraday’s law for electrochemicalreaction and Fick’s laws28 for concentration behav-ior during one-dimensional diffusion in an electro-chemical cell, these researchers obtained thefollowing expression relating the load i, battery life-time L, and battery parameters:
The first term represents the charge the load con-sumed over the period [0, L), while the second termrepresents the charge that was “unavailable” at theelectrode surface at the time of failure L. Theunavailable charge models the effect of the con-centration gradient that builds up as the flow ofactive species through the electrolyte falls behindthe rate at which they discharge at the electrodesurface.
Battery lifetime predictions using this modelclosely match both Dualfoil simulation results andexperimental measurements.29,30 The simulationtime is moderate, and the authors point out that itis possible to trade off accuracy with speed byreducing the number of terms in the summationand approximating the continuous-time load wave-form i(t) to an N-step staircase (in the extreme caseof a constant load approximation, N = 1). How-ever, the model does not account for the effect oftemperature and capacity fading on the dischargecharacteristics. Compared to the stochastic model,it has higher computational complexity butrequires less configuration effort and offers moreanalytical insight.
Peng Rong and Pedram17 recently proposed a high-level battery model to estimate remaining capacitythat considers both the temperature effect and capac-ity fading with successive cycles but assumes a con-
stant current load. They derived an expressionfor cell terminal voltage as a function of timeand, using the Arrhenius dependence on tem-perature of cell kinetics and transport phe-nomena, obtained an expression for the bulkproperties of the active material as a functionof the temperature. They also derived anexpression for film thickness as a function ofthe temperature, discharge rate, and numberof cycles. Using these quantities, they definestate of charge as remaining capacity/fullcharge capacity and state of health as fullcharge capacity/full design capacity.
These capacity ratios match well withDualfoil simulations, and the model effec-tively captures the effect of temperature and cycleaging on the battery state of charge. However, theexpressions for remaining capacity are moreinvolved than those in Rakhmatov and Vrudhula’smodel, requiring configuration of more than 15different parameters to set up the equivalent bat-tery. In addition, the constant-load assumption lim-its the model’s application for optimizing portablesystems with highly variable loads.
APPLICATIONS Using one of these models to understand battery
behavior can help system designers devise optimalbattery management algorithms and policies.Examples of such management include shaping thedischarge current profile under performance con-straints, developing optimal charging procedures,and customizing batteries for a given applicationunder volume and weight constraints.
Battery-aware power supply designThe digital circuits in most modern electronic
devices are designed using complementary metaloxide semiconductor logic. The supply voltage Vdd
and the threshold voltage Vth characteristic ofCMOS transistors affect the power consumed dur-ing switching in these circuits.
To minimize the product of battery discharge anddelay, Wu, Qinru Qiu, and Pedram22 use the batteryefficiency model5 to compute the optimal Vdd. They define battery discharge as the ratio betweenthe actual energy drawn from the battery and thetotal energy stored in a new battery. For CMOScircuits, the delay is proportional to Vdd/(Vdd −Vth)α, where 1 ≤ α ≤ 2.
These researchers also propose an interleavedpower supply system, shown in Figure 5, to dis-charge a pair of batteries with different current-capacity characteristics. For a total energy
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Using a model to understand
battery behavior can help systemdesigners deviseoptimal battery managementalgorithms
and policies.
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constraint, they find the distribution of active mate-rial weight between the two batteries that maxi-mizes system lifetime and then compare the loadvalue to a threshold to choose the more efficientbattery. Hspice simulations using random currentdistributions show that a dual-battery system offersa 25 percent improvement in power supply over asingle optimal battery.22
Static task scheduling for real-time embedded systems
Drawing on previous work,5,8 Jiong Luo andNiraj K. Jha23 proposed a battery-aware schedulingalgorithm for real-time embedded systems that sup-port variable voltages. The algorithm seeks toreduce the mean value of the discharge current andshape the discharge profile to maximize battery life-time. The actual power drawn from the battery isthe cost function to be minimized.
After obtaining an initial feasible schedule witha list-scheduling algorithm, Luo and Jha used aglobal shifting transformation to reduce peakpower consumption. They then applied local trans-formations involving iteratively sequencing andshifting tasks, starting at points along the hyper-period with highest power consumption, to reducethe cost function. Next, they performed voltage-clock scaling for processing elements that supportvariable voltages by distributing the total availableslack time among all the tasks. They chose speedand voltage reduction ratios for each task to mini-mize total energy consumption.
Rakhmatov, Vrudhula, and Chaitali Chakra-barti21,31 used an analytical model of a battery todevelop a cost function σ(t) of a battery as a func-tion of the time-varying load i(t). The cost functionis the sum of the actual charge lost to the load l(t)and the temporarily unavailable charge u(t). Thetask-scheduling problem involved assigning starttimes tk and voltage-frequency combinations Vk
and φk for each of a set of N tasks to minimize thecost function of the chosen schedule, subject to thefollowing constraints:
• the scheduling maintains task dependencies,• the time by which all tasks complete does not
exceed a deadline B, and• the battery does not fail before completing all
tasks.
Minimizing the charge lost to the load—or effec-tively, the energy consumed—after completing alltasks was the objective of several early approachesto task scheduling, but the authors point out thatthe charge lost is actually a lower bound on σ.Given the difficulty of deriving an exact solutionto the task-scheduling problem, they proposedheuristics for the general case starting from initialsolutions corresponding to the minimum-charge,lowest-power, or highest-power load profile. Theseheuristics are based on the provable properties ofthe cost function. The researchers subsequentlyimproved the load profile by inserting rest periods,voltage up/down scaling, and task sequencing.
Load-profile shaping for multibattery systems
More portable devices such as laptops employmultiple batteries. Because researchers have foundthe traditional method of discharging batteries insequence to be suboptimal, there is increasing inter-est in developing new discharge methods at boththe experimental and analytical level.
Experimental work. Benini and colleagues26 used adiscrete-time model15 to simulate three differenttechniques:
• sequentially discharging each battery until itfails;
• static switching—discharging each battery fora fixed duration and in round-robin schedule;and
• dynamic switching—scheduling the healthiestbattery for discharge at any instant dynami-cally while the other batteries rest.
For comparison, the authors also simulated amonolithic equivalent of the multibattery system.They generally found the lifetimes to follow therelation monolithic ≥ dynamic switching ≥ staticswitching ≥ sequential discharge. They alsoobserved that, as frequency increased in the staticswitching case, the resulting lifetime approachedthat of the monolithic battery.
Another effort led by Benini6 incorporates fastswitching between batteries to achieve a “virtualparallel” discharging of multiple batteries. Model-ing rate dependence using an approach similar tothat of Pedram and Wu,5 the researchers performednonlinear optimization to split the load currentover a set of multiple batteries to maximize systemlifetime. Their proportional current-allocationscheme was a moderate improvement compared toequally dividing the load among all batteries.
BatteryA
BatteryB
DC/DCconverter
VLSIcircuit
Currentcomparator Ith
Figure 5. Interleavedpower supplysystem. A dual-battery systemoffers a 25 percentimprovement inpower supply over a single optimal battery.
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Davide Bruni and colleagues32 implemented thevirtual parallel scheme along with one in whichmultiple batteries are connected in series and thecombined voltage down-converted and demon-strated good improvement in system lifetime forhigh current loads.
Analytical work. Chiasserini and Rao7 appliedresults from load balancing in computer systemsto distributing the load between two cells of a bat-tery package. They first considered a delay-freeapproach that provides charge units to the loadas soon as they are required, then a delayedapproach that introduces some delay so that thedischarge profile can be shaped to maximize bat-tery lifetime. They used a stochastic cell model toanalytically show that a best of two approach isbetter than the round-robin and random schedul-ing approaches. The delayed approach is similarto dynamic switching26 but buffers requests if nocell is active. The goal is to let each cell recover asmuch charge as required to maximize the chargeit delivers.
The charge delivered using the delayed approachhypothetically equals the battery’s theoreticalcapacity, at the cost of delay. However, assumingan infinite buffer to hold the load’s requests forcharge units is unrealistic for most portable appli-cations. Also, many applications, such as the dis-play, cause a constant drain on the battery; suchbackground discharge can be significant and yetcannot be modeled stochastically.
We used a high-level battery model4 to obtain anupper bound on the lifetime of a multibattery sys-tem for a given load.33 This study showed that thelifetime of multiple batteries discharged
• sequentially is no greater than that of an equiv-alent monolithic battery discharged by thesame load;
• simultaneously (in parallel) is equal to that ofan equivalent monolithic battery dischargedby the same load; and
• by switching at a fixed frequency approachesthat of an equivalent monolithic battery athigh frequencies, when both are discharged bythe same constant load.
Our results also demonstrate that parallel dischargeperforms as well as a monolithic battery, whileswitching techniques achieve this performance onlyasymptotically. As technology supporting simulta-neous discharge of multiple batteries is available,34
we conclude that parallel discharge is preferable tomore complex switching techniques.
Battery-aware Dynamic Power Management
DPM policies attempt to minimize a sys-tem’s average power consumption by shift-ing to low-power modes such as standby,sleep, and off if the system remains idle aftera certain time-out period. These periods arebased on the overhead due to mode transi-tions and the energy savings resulting fromthe transition. However, DPM policies do notconsider the battery’s state of charge in deter-mining when to change modes.
Benini and colleagues25 proposed closed-loop DPM policies that exploit battery-stateinformation from a discrete-time battery model15
to change the system state. They implemented asimple scheme to switch between a “fine” and alower-power “raw” play mode on an MP3 player,based on whether the battery voltage was above orbelow a certain threshold. The researchers showedsignificant improvements in lifetime with a smallperformance penalty.
T he accurate mathematical modeling of batter-ies is now a mature field, and researchers haveapplied such models fairly successfully in
optimizing system behavior to achieve maximum lifetime. Because many of these models are inde-pendent of the battery chemistry, they shouldremain relevant as technology advances. The taskschedulers of portable device operating systems ulti-mately must incorporate algorithms that dynami-cally adapt system behavior based on the battery’sstate of charge. Implementation efforts are alreadyunder way—for example, the advanced configura-tion and power interface specification implementedin most modern laptops offers power-savingoptions.
Research in battery-aware optimization is nowmoving from stand-alone devices to networks ofwireless devices—specifically, ad hoc and distrib-uted-sensor networks. The collaborative nature ofthese networks provides ample ground for usingbattery-state information to improve the nodes’efficiency. Battery life is especially important insuch networks because they are often deployed inpotentially hazardous or unreachable conditionsto sense data for reconnaissance, environmental-monitoring, or health-monitoring purposes.Developing efficient routing protocols, medium-access protocols, and discharge-shaping techniquesto maximize battery life are active areas of researchin this field. �
Research in battery-aware optimization is
now moving fromstand-alone
devices to ad hocand distributed- sensor networks.
86 Computer
AcknowledgmentThis work was carried out at the National
Science Foundation’s State/Industry/UniversityCooperative Research Centers’ Center for LowPower Electronics, which is supported by the NSFunder grant EEC-9523338, the Department ofCommerce of the State of Arizona, and an indus-trial consortium.
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Ravishankar Rao is a graduate student in the Elec-trical and Computer Engineering Department atthe University of Arizona, Tucson. His researchinterests include energy management for portablebattery-powered systems. Rao received a BE inelectronics and communication engineering fromRegional Engineering College, Surathkal, India.He is a student member of the IEEE. Contact himat [email protected].
Sarma Vrudhula is a professor in the Electrical andComputer Engineering Department at the Univer-sity of Arizona, Tucson, and director of the NSFCenter for Low Power Electronics. His researchinterests are in design automation and VLSI com-puter-aided design. Vrudhula received a PhD inelectrical engineering from the University of South-ern California. He is a senior member of the IEEE.Contact him at [email protected].
Daler N. Rakhmatov is an assistant professor inthe Department of Electrical and Computer Engi-neering at the University of Victoria, BritishColumbia, Canada. His research interests includemodeling and optimization of embedded systems,with an emphasis on hardware-software supportfor energy-efficient reconfigurable computing.Rakhmatov received a PhD in electrical and com-puter engineering from the University of Arizona,Tucson. He is a member of the IEEE. Contact himat [email protected].
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