ON-LINE MONITORING OF BATTERY STATE

IN WIRELESS SENSOR NETWORKS

Using Two Battery Models in WSN Constraints

Anania Aron

, Gabriel Girban

and Mircea Popa

Department of Mathematics, Politehnica University of Timisoara, Timisoara, Romania

Faculty of Automation and Computer Science, Politehnica University of Timisoara, Timisoara, Romania

Keywords:

WSN, Battery, Monitoring, Energy, Mathematical Models.

Abstract:

This paper addresses the class of wireless sensor networks where the nodes are using batteries as power

sources. It describes the adaptation of an existing analytical battery model to ﬁt the constraints of the wireless

sensors in terms of available resources, the algorithm complexity being reduced to O(n) in case of constant

loads. The analytical battery model obtained is used together with another existing battery model to pro-

vide real time information about the remaining capacity of the battery, based on the electric current draw and

elapsed time. The current consumption is estimated using application speciﬁc power proﬁles, thus the mon-

itoring solution proposed does not imply additional hardware on a mote and can be used on each node of a

WSN during network employment as a real time decision support.

1 INTRODUCTION

The purpose of wireless sensor networks (WSN) is

acquiring and processing the information about natu-

ral or technological systems and transmission of the

obtained data toward a collecting center. These net-

works are characterized by a high density of intelli-

gent and autonomous sensor nodes and an efﬁcient

use of available resources is required. A signiﬁcant

factor inﬂuencing the design of wireless sensor net-

works is the energy consumption at the network node

level, which determines the remaining battery capac-

ity and implicit the time in which that node can be

operated. Thus, the energy efﬁciency is a goal in

both, hardware design and software that implements

the communication protocols and the strategies used

to prolong the network lifetime. Although research

in this area is heavily focused on energy efﬁciency,

paradoxically, the interest in monitoring the state of

the battery is very low, even if a network manage-

ment that takes into account the energy consumption

and the energy available at a node level can lead to

signiﬁcant network improvements. As an example,

if the battery properties are taken into account in se-

lecting the level of transmission power, the amount of

data transmitted by a node can be improvedwith more

than 50% (Park et al., 2005).

In this context, the paper presents a work around

the equations of an analytical battery model in order

to obtain a form which is proper to be implemented in

a real-time monitoring software that runs on wireless

sensors. The battery model obtained is interfaced with

an energy consumption monitoring software that esti-

mates the charge drawn from battery and provide this

information using two parameters, the current draw

previously determined for the operations performed

and the related time interval.

The section 2 gives an overview of the solutions

used in wireless sensor networks for current draw

monitoring at a node level, while some of the batter-

ies properties are highlighted in section 3. An exist-

ing battery analytical model for constant loads is pro-

cessed until it is reduced to a shorter form which is

than approximated with several expressions that are

proper for real-time computations. The expressions

obtained are than compared with the one proposed in

the referenced paper, better results being obtained for

longer time intervals. Finally, a second battery model

is brieﬂy described, this being used to model the be-

havior of variable loads as it is taking into account the

rate capacity and recovery effects. The section 4 con-

cludes the paper and introduces the further work in

ﬁnding solutions that avoid the drawbacks of the used

battery models in terms of computational effort.

Aron A., Girban G. and Popa M..

ON-LINE MONITORING OF BATTERY STATE IN WIRELESS SENSOR NETWORKS - Using Two Battery Models in WSN Constraints.

DOI: 10.5220/0003835500910094

In Proceedings of the 1st International Conference on Sensor Networks (SENSORNETS-2012), pages 91-94

ISBN: 978-989-8565-01-3

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

2 WSN ENERGY CONSUMPTION

MONITORING

Even if the optimization of the energy consumption is

a key element in designing the wireless networks, us-

ing a current draw monitoring system during network

employment is not an usual thing in WSN. The en-

ergy consumption is optimized through development

of energy efﬁcient strategies and protocols which are

not aware of the amount of charge available in battery

at a certain time.

A 2007 survey (Sohraby et al., 2007) gather the

main research topics in WSN into a list which is

sorted based on the number of scientiﬁc articles re-

lated to a subject. The network monitoring, in gen-

eral, is only on position 21 with 2.12% from all pa-

pers. The lack of interest in monitoring the energy

consumption and available charge in nodes batter-

ies, if the beneﬁts described by (Park et al., 2005)

are taken into account, can be explained by the ab-

sence o a solution offering a reasonable trade-off be-

tween these beneﬁts and resources implied, as an ac-

curate monitoring solution implies hardware compo-

nents which means additional energy consumption.

There are two types of monitoring solutions in

WSN, off-line monitoring performed in the lab using

testbeds or simulators, and on-line monitoring per-

formed during network employment.

Related to the topic of on-line monitoring, only

a few solutions can be found in literature. As hard-

ware solutions, the JAWS platform (Beutel, 2006) and

SPOT (Jiang et al., 2007) system can be found but

they require additional costs and energy consumption.

There are three software solutions identiﬁed for on-

line monitoring of sensor nodes: Levels (Lachenmann

et al., 2007), another solution based on a theoretical

model calibrated with accurate measurements (Kell-

ner et al., 2008) and a solution based on power proﬁles

deﬁned according to the states of the microcontroller

and transceiver (Dunkels et al., 2007).

The monitoring system for power consumption

used in this paper is a software one and provides the

consumption information using two parameters: the

estimated current draw and the related time. Thus the

battery model to be used should be able to provide

information about charge available based on the two

input parameters.

3 BATTERY MODELS

An accurate battery model should be able to cover the

following behavior (Rao et al., 2003): charge diminu-

tion over time - self discharge; rate capacity effect -

at high discharge rates the effective capacity of the

battery will be lower than the nominal capacity; re-

laxation effect - at very small discharge rates, the bat-

teries can partially recover their capacity; temperature

inﬂuence and the capacity fading in case of recharge-

able batteries.

There are several types of battery models devel-

oped. The linear models are elementary and none of

the previous properties are taken into account. The

initial battery capacity is decreased with the charge

drawn until it reaches a cut

off value when the bat-

tery is considered fully discharged. These models

require a minimum computational effort but are the

worst from accuracy point of view. The electric cir-

cuit models are using equivalent electric schemes that

describe the batteries behavior while the stochastic

battery models are based on simulations. Electro-

chemical models are the most accurate, describing the

battery properties through reduction-oxidation chem-

ical reactions. They are used as a reference in valida-

tion of other models but due to their complexity and

required computational effort can not be used in on-

line monitoring systems. These models are solved us-

ing numeric integration and have solutions very close

to the real system behavior.

Analytical models are usually derived from elec-

trochemical models and therefore quite accurate but

not so computational intensive. Such a model is pro-

posed in (Rakhmatov and Vrudhula, 2001) where the

authors are taking into account the ions diffusion in

the electrolyte, or the Kinetic Battery Model from

(Rao et al., 2007). These two models are used as ref-

erence in this paper as they are representative for the

class of analytical models.

3.1 Battery Model for Constant Loads

The battery mathematical model presented in

(Rakhmatov and Vrudhula, 2001) is used for the case

of constant loads as it is less computational intensive

than its approach for variable loads. The model is

based on the principle of diffusion and is described

by the following equations and boundary conditions:

−J(x,t) = D

∂C(x, t)

∂x

∂C(x, t)

∂t

= D

∂

C(x, t)

∂x

i(t)

νFA

= D

∂C(x, t)

∂x



x=0

0 = D

∂C(x, t)

∂x



x=w

where

SENSORNETS 2012 - International Conference on Sensor Networks

- C(x,t) is the concentration of species at time t ∈

[0, L] at distance x ∈ [0, w]

- C

∗

= C(x, 0), ∀x is the initial concentration

- J(x, t) is the ﬂux of species at time t at the distance

- D is the diffusion coefﬁcient

- i(t) is the current

- F = 96485, 31C mol

−1

is the Faraday’s constant

- A is the area of the electrode.

Starting from the relation for C(0, t) obtained in

(Rakhmatov and Vrudhula, 2001) we have:

C(0, t) = C

∗

−

2iw

√

νFA

√

πD

−

4iw

νFAD

√

∞

∑

m=1



−m

√

π+

√

−

√

πm·erf



√



(1)

where erf(y) is the error function that, for y ≪ 1 may

be written in the following form:

erf(y) =

√

−y

∞

∑

n=0

(2y)

2n+1

(2n+ 1)!!

We take the ﬁrst 3 terms from its power series and

after calculating the sum expression with 1000 terms,

the equation (1) becomes:

C(0, t) = C

∗

−

2iw

√

νFA

√

πD

−

4iw

νFAD

√

3(Dt)

[300(Dt)

−15150

√

π(Dt)

+ 100150050(Dt)

−1025166665(Dt)

+ 8874428471430(Dt)

+ 46471109244533332Dtw

+ 767939313947393539400w

]

(2)

The advantage of this form is derived from the type

of arithmetic operators used, the most complex being

the square root. Instead of the big values that requires

operations on 64 bits, it is easier to be implemented

in the software running on a wireless sensor than the

original form used in the referenced paper, where the

function erf(y) is approximated to the following ex-

ponential form:

erf(y) ≈ 1−

−y

√



y−

√

+π



In Fig. 1, we compare our results with the ones

obtained using the (Rakhmatov and Vrudhula, 2001)

approximation. On the horizontal axes we have the

time in seconds while on the vertical axes the differ-

ence between real C, given by 1, and the values of C

obtained through erf(y) function approximations. It

can be observed that for small time intervals, the ap-

proximation we proposed behave worst than the one

from referenced paper but it performs much better for

longer time intervals, where it is quite the same as the

real solution.

The drawback of this model in case of our ap-

proach is related to the limitations of the Micaz mote

we are using. The mote is based on a 8 bit micro-

controller (ATmega128L) which has no instructions

deﬁned for ﬂoating point operations or 64bit data,

therefore all computations are slow as they are han-

dled through library functions.

100

150

200

250

300

0.002

0.004

0.006

0.008

Figure 1: The difference between the proposed approxima-

tion (dashed), the referenced solution approximation (con-

tinuous) and the real solution.

3.2 Battery Model for Variable Loads

Taking into account that results obtained in the previ-

ous subsection can be used only when there are con-

stant loads longer than a certain time interval, we fo-

cused also on a battery model capable to take into ac-

count the rate capacity and relaxation effects. It is

the modiﬁed Kinetic Battery Model from (Rao et al.,

2007), from which we removed the probability ap-

proach. The model used can be summarized as:

bool chrg_clc(int32_t cons,uint32_t t){

uint32_t n; double I_n;

I_n=1.0*cons;

n=t/CHRG_TIME_UNIT;

while(n--){

if (i<I_n) return FALSE;

if(I_n<J&&h_1>=h_2){

i-=I_n*c_ct;j-=I_n*(1.0-c_ct);}

else{

j-=J; i=i-I_n+J;

h_1=i/c_ct; h_2=j/(1.0-c_ct);

J=k_ct*(h_2-h_1)*h_2;}

}

return TRUE;}

ON-LINE MONITORING OF BATTERY STATE IN WIRELESS SENSOR NETWORKS - Using Two Battery Models in

WSN Constraints

where the current draw is denoted by I n and the al-

gorithm is processed as long as the h 2 > h 1. The

parameters c

ct and k ct are battery speciﬁc and are

linked with the rate capacity and recovery effects. Af-

ter each change in the load, the time elapsed from the

previous change is computed and the Kinetic Battery

Model is triggered with the load given as current draw

and the time interval transformed in time units (I

n).

Even if the algorithm described is very short, it re-

quires additional 20 bytes of RAM memory and more

than 2 Kilobyte of ROM on a Micaz mote. Unlike the

previous model, the ﬂoating point data can be sub-

stituted with integer operations but the computational

time is also affected by the existence of a loop.

4 CONCLUSIONS

This paper analyze the usage of two battery models

for monitoring the state of charge at a node level in a

wireless sensor network. It describes the adaptation of

an existing analytical model derived from a realistic

battery model, this adaptation being required to ﬁt the

constraints of the wireless sensors in terms of avail-

able resources. The algorithm complexity was re-

duced to O(n) in case of constant loads as only classic

arithmetic operators are used, and no loops are neces-

sary. The biggest computational effort is required to

process the square root function and to obtain the or-

der power of 10 for numbers represented on more than

one byte. On the other hand, when there are variable

loads, the Kinetic battery model used will not require

more complicated operations than multiplications on

larger data types but some loops should be performed,

depending on the load value and the related time.

The monitoring solution used in conjunction with

these battery models can be implemented on each

node of a WSN during network employment as a deci-

sion support. The drawbacks of the proposed methods

are linked with the related computational effort which

is signiﬁcant if we take into account that only sim-

pliﬁed and not quite accurate versions of referenced

battery models were used.

Further work consist in modeling the battery

through interpolation tables based on the electro-

chemical model solution given as an intersection of

two surfaces through Hamilton-Poisson Geometry.

ACKNOWLEDGEMENTS

This paper was supported by the project ”Develop-

ment and support of multidisciplinary postdoctoral pr-

ogrammes in major technical areas of national strat-

egy of Research - Development - Innovation” 4D-

POSTDOC, contract no. POSDRU/89/1.5/S/52603,

project co-funded by the European Social Fund

through Sectoral Operational Programme Human Re-

sources Development 2007-2013.

This work was partially supported by the strate-

gic grant POSDRU/88/1.5/S/50783, Project ID50783

(2009), co–ﬁnanced by the European Social Fund -

Investing in People, within the Sectoral Operational

Programme Human Resources Development 2007 -

2013.

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