Improving Battery-Efficiency of Embedded Devices

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

Improving Battery-Efficiency of Embedded Devices by Favorably Discharging only towards End-of-life Thomas Menzel, Daniel Willkomm, and Adam Wolisz Telecommunication Networks Group, TU Berlin, Einsteinufer 25, 10587 Berlin, Germany {menzel|willkomm|wolisz}@tkn.tu-berlin.de

Abstract. Energy efficiency has always been a major issue for batterypowered mobile or embedded devices such as smart-phones or wireless sensor nodes. Interestingly enough the amount of energy which can be drawn out of a given battery does not only depend on the parameters of this battery, but also on the operational modus of its discharge. As the communication is known to have a significant share in the energy consumption of cooperating objects, this phenomenon should influence the way such communication is to be designed. In fact, after some studies have provided patterns of “favorable” battery usage, the question appears if such patterns should be necessarily enforced into cooperating objects communication scenarios. Using an accurate, well-accepted battery simulator we demonstrate that — surprisingly enough — in order to use the battery capacity in “almost the best” way, it is enough to enforce a “favorable” discharge modus shortly before complete battery depletion. The modus of battery operation during the majority of its lifetime seems, in contrast, to have only a marginal influence.

1

Introduction

Electrochemical primary batteries are still the main means to power most of the embedded systems considered in the usual cooperating objects scenarios (e.g. sensor networks communicating with mobile robots and smart phones). Traditionally, the research on energy efficiency has been focused on the reduction of energy being drawn from batteries per hour of operation to achieve a given task (we do not address here research in improving the battery construction — but only the usage of available batteries). It has however been observed, that not only the amount of the drawn energy, but also the timing of discharge has an impact on battery lifetime [3]. We see “battery efficieny” as an extension to “energy efficieny” covering such nonlinearities. Mainly two of these nonlinearities are considered: Firstly, the rate-capacity effect [7] states that more capacity can be drained out of a battery at lower currents. Secondly, the recovery effect [7] lets a battery to regain some of its apparently lost capacity when pulsing the discharge. We therefore state, in the most general sense, high constant discharge

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

as “non-battery-friendly” while we consider both, low constant and high pulsed discharge as “battery-friendly”. Since these nonlinearities are found to considerably affect the obtainable battery capacity (see e.g. [3]), there is an obvious temptation to consider the “battery friendly” mode of discharge as a guideline for designing the algorithms and protocols in sensor networks and other cooperating object scenarios (e.g. [2,13,15]). In this paper we address the fundamental question of: “How restrictive are such guidelines?” As the main contribution of this paper we demonstrate that in order to use the battery capacity in “almost the best” way, it is enough to enforce a “battery-friendly” discharge modus only shortly before complete battery depletion. The modus of battery operation during the majority of its lifetime seems, in contrast, to have only a marginal influence. The remaining paper is organized as follows: In Section 2, we discuss some concepts related to the process of battery discharge, the previous work on improving the discharge process, and formulate our research hypothesis. In Section 3 we describe our system model. In Section 4, we explain our simulation setup and methodology and then present our results. Finally, in Section 5, we conclude the paper and outline our ongoing and further research.

2

Basic Notions, Previous Work, and Research Hypothesis

Historically, while discussing the battery-based system lifetime, the case of constant discharge has usually been considered. In context of sensor networks it has early become obvious, that the operation times under such scenarios are not sufficient. Lifetimes in the range of weeks rather than the desired years are obtained. Running devices intermittently (switching them off when they can be considered dispensable) has become an elementary power-saving technique. The rate capacity effect (an increased capacity for lower currents) can be considered to be known for as long as electrochemical batteries exist. As early as 1990 it has been also observed that the total amount of energy drawn from a battery does not remain constant under different pulsed operation conditions [8]. In fact, it has been demonstrated that pulsed discharge patterns cause the so called recovery effect (the total capacity of a battery increases in pulsed discharge mode). With these findings, the aspect of battery efficieny became under closer investigation in numerous studies. In [2, 3, 13], discharge breaks (rest periods) are inserted into wireless sensor nodes’ or other communication devices’ operation cycles in order to gain from the recovery effect. All these works quote or even perform themselves real experiments justifying their approach. However, the large performance gains in the latter two works are only obtained using not quantitatively validated stochastic battery models. While this does not compromise the qualitative insight obtained from these works’ modeling approach, it relativizes the quantitative conclusions. In [15], the rate capacity effect is utilized to balance the lifetimes of individual nodes in a wireless sensor network by designing a battery-aware deployment

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

scheme. A comparison between FSK and PPM modulation based on the same effect is performed in [14]. In [9], the authors first discuss the extent of both, rate capacity and recovery effect in general. Afterwards, they evaluate the impact of several modifications of the pulsing characteristics (e.g. pulse width and pulse height). To get an idea of the achievable gains through battery-friendly discharge, we provide some exemplary numbers on quantitative capacity gains achieved by the two effects in the above mentioned studies: In [2]’s experimental section, a wireless sensor node is powered by two off-the-shelf nickle metal hydride batteries. A capacity gain of 22 % is obtained by enforcing regular sleep periods in the range of seconds. In [9], the discharge of a lithium polymer cell is simulated using an accurate battery model. The current rates are chosen from a region resulting in depletion within a few hours. A capacity increase of 56 % is obtained by reducing the current rate to 25 %. Pulse discharging with a duty cycle of 25 % also increased the capacity, but — depending on the actual pulse duration — to a lesser extent. In [2] and [3]’s modeling section, capacity gains of up to 100 % and 1000 % are derived using not quantitatively validated stochastic battery models. A very high constant discharge current is assumed in [3], which results in only 10 % of the theoretical cell capacity being obtained. Pulse discharging with sufficiently large rest periods enables to draw the full theoretical capacity from the cell, which corresponds to a gain of 1000 %. Therefore — notwithstanding these actual numbers — it is difficult to quantitatively summarize the potential of these effects, since it is always possible to construct an arbitrarily bad non-battery-friendly discharge scenario. However, with these and other studies it is shown at least qualitatively, that high constant discharge can be less battery-friendly than discharging at a low rate or in a pulsed mode (with properly chosen pulse width and height). The metric used in all the above studies is battery capacity or effective battery lifetime which is calculated by integrating the consumed power over the obtained battery lifetime. This metric is very conclusive from an application perspective. However, being only geared to this metric without keeping in mind the underlying effects which actually induce the observable battery depletion might result in overseeing important aspects of the complete picture, namely, the precise definition of a discharged battery: The voltage of a cell when no load is applied, is the open-circuit voltage, while the operating voltage is the voltage one sees when a current is drawn from the cell. The overpotential (also: overvoltage or polarization) is the difference between those two voltages. It reflects the electrochemical and physical processes inside the battery and is therefore not constant over time. In particular, it does not linearly depend on the intensity of the current running through the cell. When charging, the operating voltage is higher, when discharging it is lower than the open-circuit voltage. Besides the less relevant types of overpotential (adsorption, crystallization and reaction) there are activation (or chargetransfer) polarization and concentration polarization which contribute most to the observable voltage differences [6, 12]. Activation polarization occurs due to

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

limitations of the chemical reactions and the needed charge-transition between the electrolyte and the electrode surface, while concentration polarization arises from concentration differences of the active species in the electrolyte. Often, the ohmic loss due to the cell’s internal resistance is also referred to as ohmic polarization, which itself is — contrary to the overvoltage definition stated above — obviously linearly dependent on the current. The slope and shape of the this voltage curve over withdrawn energy depend on battery chemistry and construction. It always decreases with the increasing depletion. A cell is always considered depleted when the cutoff voltage (mostly defined by application, but sometimes also by cell type) is reached. However, remember that there is a difference between the operating voltage (voltage under load) and the open-circuit voltage. The difference between the two is the overpotential as explained above. The size of the overpotential depends on the current but also increases with the duration of the current pulse being drawn. Thus, with increasing depletion (and thus decreasing open circuit voltage) there is a rising probability that the cutoff voltage is reached. An operating voltage falling below the cutoff voltage defines battery depletion. In such cases, a slightly shorter or smaller discharge pulse might have prevented this frontier crossing and could have enabled recovery back to open circuit voltage which would have resulted in a longer battery life. This risk is especially increased for battery types with flat discharge curves when they are operated close to cutoffvoltage. A battery-friendly discharge mode (e.g. a specific protocol modification) can therefore indeed delay the falling of the operating voltage below the cutoff voltage. Friendly and non-friendly mode of discharge thus mainly differ in the amount of capacity which they leave unused in the battery. Only when the open circuit voltage reaches the cutoff voltage, the battery is irrecoverably depleted. Hence, overpotential can be seen as the actual reason behind the rate-capacity and the recovery-effect. Our hypothesis is the following: Despite the impact of the rate capacity effect and the recovery effect on the operating voltage of a battery, a “just in time” change from non-friendly to friendly mode of discharge will always enable to draw this otherwise lost capacity from the cell. As long as the operating voltage remains above the cutoff voltage, there is no need to act battery-friendly.

3

System Model

Neglecting the actual application in mind, we consider generic electrochemical batteries suited to power state-of-the-art embedded devices. Without excluding primary (non-rechargeable) batteries (e.g. Alkaline) we are focusing on secondary (rechargeable) cells — particularly lithium-ion (li-ion) cells. Those are cells with high energy density and low self-discharge and therefore well suited for the envisioned area of usage.

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

3.1

Battery Model

Various battery modeling approaches have been developed in the past. They differ in accuracy, computational complexity, and the possibilities of parametrization. Choosing the appropriate approach heavily depends not only on the actual motivation to perform the battery modeling, but also on the available computational resources and factual knowledge about the specific cell. We are using the electrochemical model of Doyle, Fuller and Newman [5]. The main advantage of this model is its high accuracy, which e.g. is shown in [1] by applying a similar battery and — among others — similar current range like we will use in this study. The model is well appreciated in the research community (e.g. [4], [11], [7]). The major drawbacks of this battery model are a) its high demand for processing power and b) very accurate knowledge about the investigated cell (the model needs setting of about 50 parameters). However, in the presented work, we do not depend on realtime simulation results and do not need to restrict ourselves to resource-constrained computers. Furthermore, we are not interested in the performance of a specific cell, but in the general impact of the rate capacity and the recovery effect which are assumed to be (qualitatively) similar with all cells. For comparison reasons we adopt the parametrization of [9] as much as possible. However, since not all relevant battery parameters are given, we cannot perfectly replicate the cell. With Dualfoil [10], a simulation implementation of this model is available in the Fortran programming language which we are using in this study. 3.2

Load Model

When a load is applied to a battery, the appearing current / voltage working point results on the mutual interaction between the two systems. Thus, when discussing battery properties like we do in this work, we also have to decide on how to model the load applied to the battery under investigation. Starting with the open-circuit voltage, the load model determines the current which is drawn from the battery which again determines the resulting voltage drop in the battery model. Several types of load models for this purpose do exist. For a specific application, it is always most accurate to precisely model the current-voltage characteristic of the actual physical load or device. However, when aiming for a more general evaluation of battery behavior, a general load model is to be considered. Such models are the constant current, the constant voltage, the constant power and the constant resistance model. We assume a time-discrete simulation. Thus, in all but the first cases, the simulation environment has to adequately adjust the current running through the cell in order to keep the voltage, power or resistance constant during the specific time step. Note that this time step can be arbitrarily small in order to model complex discharge patterns. The constant resistance case is in general the one closest to real devices, but it is difficult to compare the amount of withdrawn energy obtained by different experiments, since for each point in time, voltage and current need to be recorded. In order to

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

obtain comparable results to other simulation based works, we assume constant power discharge. This load model is often chosen because energy values can easily be obtained by multiplying by runtime. However, it will be hard to hold this assumption in a potential future experimental validation.

4 4.1

Evaluation Performance Metrics

Comparing results of individual experiments is an important, but non-trivial task. Battery voltage decreases with increasing depletion and as explained above, the end of life is reached when the cell’s operating voltage drops below the cutoff voltage. This threshold is either the minimum voltage needed to run certain circuitry or defined by battery chemistry. In order to analyze the differences between the discharge modes under investigation, we want to visualize the different voltage curves leading to different battery lifetimes. The energy drawn from a cell is measured in watt hours (Wh). The total amount of energy which is obtained until depletion is referred to as the cell’s capacity. It is also measured in (Wh) and is the metric mainly used in this paper. Energy and capacity are often considered in relation to the cell’s mass or — assuming a layered, flat construction — it’s area. They are then called “specific” energy and capacity and are measured in watt hours per kilogram (Wh/kg) or watt hours per square meter (Wh/m2 ). 4.2

Simulation Scenario

With our simulation scenario we follow [9], since in this work both, rate capacity and recovery effect is analyzed with the same battery model we use with the Dualfoil simulator. Furthermore, we use the same high and low power rates and the same duty cycle. Dualfoil’s output is always in relation to battery area. Therefore, in order to be directly comparable to [9] who relate parameters and results to kilogram, we assume a weight of 0.62 kg/m2 . The first approach to increase battery efficiency we investigate is the rate capacity effect. According to this effect, a lower discharge rate will be more batteryefficient in terms of obtained capacity. Following [9], we apply the rates 300 W/kg (“high constant” power discharge) and 75 W/kg (“low constant” power discharge) in our simulation. We consider the high rate as non-battery-friendly and the low rate as battery-friendly. Afterward, our actual approach comes into place. We start to discharge the battery non-battery-friendly, but only until 95 % of the previously determined depletion in terms of capacity. We then switch to battery-friendly discharge until full depletion and determine the total obtained capacity. The second effect we want to discuss is the recovery effect. As counterpart to the high constant power mode we are this time evaluating the obtainable capacity at pulsed discharge using the same power amplitude. Like in the case of the

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

rate capacity effect, we are expecting a higher obtained capacity, which allows to classify the two discharge modes as non-battery-friendly and battery-friendly. Afterward, we will also apply (non-battery-friendly) high constant power discharge until 95 % depletion and then switch to (battery-friendly) high pulsed power discharge. 4.3

Simulation Results

Plotting the voltage curve over withdrawn energy helps to understand how different discharge characteristics lead to different capacities. High constant vs. low constant power discharge 4.5

A: High constant power B1: Low constant power 95% A, then B1

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Specific energy drawn from cell [Wh/kg] Fig. 1. By switching from high constant to low constant discharge at 95 % depletion, 80 % of the difference in withdrawable energy can be regained.

Figure 1 shows the voltage curves of high constant and low constant power discharge of a Li-ion battery over withdrawn specific energy. Note that the higher power results in higher (ohmic) polarization and therefore lower operating voltage. As a third curve, the combination of the two discharge modes is shown. The battery is first discharged using the unfavorable high constant power mode. When 95 % are withdrawn, we switch to the low constant power discharge mode until end of life. The cutoff voltage of 2 V is reached after 125.5 Wh/kg in case of high constant mode of discharge. Applying low constant discharge results in 140 Wh/kg capacity. Low constant outperforms high constant discharge by about 12 % which qualifies the two modes to be be perceived as favorable and non-favorable or

In Proc. of the CONET 2011 workshop in conjunction with CPSWeek 2011, Chicago, USA, apr 2011.

battery-friendly and non-battery-friendly mode of discharge. The vertical difference of the two curves is due to the different heights of overvoltage. Applying the combined discharge of our approach, one can clearly see the reduction of overvoltage when the mode is switched from high constant to low constant power. A capacity of 138.3 Wh/kg is reached. Thus, by switching from non-battery-friendly to battery-friendly mode at 95 % depletion, 80 % of the energy difference can be regained.

High constant vs. high pulsed power discharge 4.5

A: High constant power B2: High pulsed power 95% A, then B2

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Specific energy drawn from cell [Wh/kg] Fig. 2. By switching from high constant power to high pulsed power discharge at 95 % depletion, 90 % of the difference in obtained capacity can be regained.

Like the power rate reduction in order to exploit the rate capacity effect which is shown above, we are now using pulsed instead of constant discharge to gain from the recovery effect. Following [9], we pulse discharge the cell at a 25 % duty cycle using the same power amplitude as in the constant discharge experiment (300 W/kg). Thus, the average power consumption stays the same. A cycling period of 1 s is chosen, thus a 0.25 s pulse is followed by a rest of 0.75 s. As shown in Figure 2 (high pulsed power ), a capacity of 136.0 Wh/kg is obtained. Note that the referring voltage curve appears widened. This is due to the high pulse rate of 1 s. Each cycle causes the battery voltage to alternate between the open circuit voltage and the operating voltage under load. High constant power discharge in Figure 2 is the same that in Figure 1 (300 W/kg). Thus, here with 136 Wh/kg, (battery-friendly) high pulsed discharge results in about 8.4 % higher capacity than (non-battery-friendly) high constant discharge.

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We now apply the same approach as before. The cell is discharged in high constant power mode until 95 % depletion and then we switch to high pulsed discharge. We obtain a capacity of 134.8 Wh/kg. Again, a big portion of the capacity difference can be regained (9.3 Wh/kg of 10.5 Wh/kg corresponds to 89 %).

Ragone Plot: Capacity over Power

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Fig. 3. When working with batteries, battery-friendly (B1, B2)) and non-batteryfriendly (A) discharge represent two mutually exclusive operating regions in the capacity-power tradeoff in the upper left and in the lower right of the Ragone plot. This work’s approach to generally allow non-battery-friendly discharge and only switch to battery-friendly discharge shortly before battery depletion enables to break this tradeoff. The upper right region representing high capacity at high power discharge becomes now accessible.

A Ragone plot displays specific capacity over specific power. It is therefore often used to illustrate the classical trade-off in battery-design and chemistry between those two measures. But it can also be used to analyze the same tradeoff in a specific cell. We use Figure 3 to summarize in a single figure the two approaches discussed above. High constant discharge results in a point in the lower right representing the low capacity which is obtainable at high power discharge. Low constant and high pulsed discharge result in points in the upper left. Thus, in comparison to the high constant case, a high specific capacity is obtained, but only by either directly reducing the average power or indirectly by pulsing. Capacity and power therefore constitute the mentioned trade-off. However, by applying the approach

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suggested in this work we can escape this trade-off. The upper right region (high capacity albeit high power) can be reached by allowing non-battery-friendly discharge and only switching to battery-friendly mode shortly before battery depletion.

5

Conclusions

We simulated non-battery-friendly discharge until 95 % of depletion and only then switched to a battery-friendly mode using an accurate, well-accepted battery simulator. Using this approach, we could regain 80 - 89 % of the difference between the purely non-friendly case and the purely friendly cases. There are two possible ways to interpret this result. Firstly literally: One could define the — in this work arbitrarily chosen — limit of 95 % depletion more generally and then really design and evaluate discharge regimes (e.g. protocols) which start to discharge in a battery-friendly manner only beyond this depletion limit. However, this is not our main intention. Instead, we rather see this work as a general call to bring the — unquestionable existing — battery nonlinearities from the often seen rather qualitative to a more application-oriented, validated quantitative discussion. The influence of the rate capacity effect as well as the recovery effect on the available capacity of a battery depend on the used power rates: The obtainable capacity difference between non-friendly and friendly discharge is higher for higher power rates (obviously the power rates have to be considered in relation to the battery size). This is why in most studies advocating battery-friendly discharge approaches relatively high power rates are used. To be able to compare our results to such studies we also used such high power rates. We showed, that at such rates the allegedly losses of capacity due to unfavorable discharge are reversible. For the small power rates occurring in typical wireless sensor network (WSN) scenarios this has to be case all the more. With this paper we want to trigger a quantitative discussion of the influence of battery-nonlinearities on the usable battery capacity based on realistic power rates in typical WSN applications. We strongly believe that if a significant influence can be shown for such scenarios, the results presented in this paper can be applied. As a first step we therefore plan to validate the applicability of the presented work to WSN scenarios by changing the generic set of parameters for the Dualfoil model used in this paper to specific parametrizations reflecting WSN scenarios. Furthermore, we are currently conducting experimental measurements with real batteries in order to validate the simulation results of this paper and the used simulation environment for future investigations of WSN scenarios.

References 1. Arora, P., Doyle, M., Gozdz, A.S., White, R.E., Newman, J.: Comparison between computer simulations and experimental data for high-rate discharges of plastic lithium-ion batteries. Journal of Power Sources 88(2), 219

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2.

3.

4.

5.

6. 7.

8.

9. 10. 11.

12. 13.

14.

15.

– 231 (2000), http://www.sciencedirect.com/science/article/B6TH1-40B85BD7/2/e1d75f2dd3f910090f32c6037d8c5536 Chau, C.K., Qin, F., Sayed, S., Wahab, M., Yang, Y.: Harnessing battery recovery effect in wireless sensor networks: Experiments and analysis. Selected Areas in Communications, IEEE Journal on 28(7), 1222 –1232 (sep 2010) Chiasserini, C.F., Rao, R.R.: Pulsed battery discharge in communication devices. In: Proceedings of the 5th annual ACM/IEEE international conference on Mobile computing and networking. pp. 88–95. MobiCom ’99, ACM, New York, NY, USA (1999), http://doi.acm.org/10.1145/313451.313488 Chiasserini, C., Rao, R.: Energy efficient battery management. INFOCOM 2000. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE 2, 396–403 vol.2 (2000) Doyle, M., Fuller, T.F., Newman, J.: Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of The Electrochemical Society 140(6), 1526–1533 (1993), http://link.aip.org/link/?JES/140/1526/1 Hamann, C.H., Hamnett, A., Vielstich, W.: Electrochemistry. Wiley-VCH, 2 edn. (2007) Jongerden, M.R., Haverkort, B.R.H.M.: Battery modeling. Technical Report TRCTIT-08-01, Centre for Telematics and Information Technology University of Twente, Enschede (January 2008) LaFollette, R.M., Bennion, D.N.: Design fundamentals of high power density, pulsed discharge, lead-acid batteries. Journal of The Electrochemical Society 137(12), 3701–3707 (1990), http://link.aip.org/link/?JES/137/3701/1 Martin, T.L., Siewiorek, D.P.: Nonideal battery properties and their impact on software design for wearable computers. IEEE Trans. Comput. 52(8), 979–984 (2003) Newman, J.: Fortran programs for the simulation of electrochemical systems (02 2008), http://www.cchem.berkeley.edu/jsngrp/fortran.html Rakhmatov, D., Vrudhula, S., Wallach, D.: A model for battery lifetime analysis for organizing applications on a pocket computer. Very Large Scale Integration (VLSI) Systems, IEEE Transactions on 11(6), 1019 – 1030 (dec 2003) Reddy, T.B., Linden, D. (eds.): Linden’s Handbook of Batteries. McGraw-Hill, 4 edn. (2010) Sausen, P., Spohn, M., Salvadori, F., de Campos, M., Perkusich, A.: Applying dynamic power management with mode switching in wireless sensor networks. In: Industrial Electronics, 2008. IECON 2008. 34th Annual Conference of IEEE. pp. 1713 –1717 (nov 2008) Tang, Q., Yang, L., Giannakis, G., Qin, T.: Battery power efficiency of ppm and fsk in wireless sensor networks. Wireless Communications, IEEE Transactions on 6(4), 1308 –1319 (april 2007) Zhang, J., Ci, S., Sharif, H., Alahmad, M.: Lifetime optimization for wireless sensor networks using the nonlinear battery current effect. In: Communications, 2009. ICC ’09. IEEE International Conference on. pp. 1 –6 (jun 2009)