Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 627963 11 pageshttpdxdoiorg1011552013627963
Research ArticleEfficiency-Aware Maximizing Energy Utilization for SensorNodes Using Photovoltaic-Supercapacitor Energy Systems
Zheng Liu1 Xinyu Yang1 Shusen Yang2 and Julie McCann2
1 Computer Science and Technology Department School of Electronics amp Information EngineeringXirsquoan Jiaotong University Xirsquoan 710049 China
2Department of Computing Imperial College London London SW7 2AZ UK
Correspondence should be addressed to Xinyu Yang yxyphdmailxjtueducn
Received 4 December 2012 Revised 25 March 2013 Accepted 27 March 2013
Academic Editor George P Efthymoglou
Copyright copy 2013 Zheng Liu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Recently photovoltaic-supercapacitor-based energy systems have become more and more popular in the design of energyharvesting wireless sensor networks (EH-WSNs) as an alternative to battery power Existing research on this area mainly focuseson hardware design and the improvement of the charging efficiency However energy is wasted not only by the inefficientcharging process but also the inefficient discharging process and energy leakage Therefore to maximize node lifetime andenergy utilization all the previous energy loss should be considered In this paper we develop realistic hardware models of thecomplete photovoltaic-supercapacitor energy systems and propose the efficiency-aware a systematic duty cycling framework tomaximize energy utilization We formalize the maximization problem as a nonlinear optimization problem and develop twoefficient algorithms for its optimal solutions The performance of our approaches is evaluated via extensive numeric simulationsand the results show that our efficiency-aware framework can respectively achieve 60 and 56 more active time (ie energyutilization) than the fixed duty cycle scheme and leakage-aware a state-of-the-art scheme for photovoltaic-supercapacitor energysystems
1 Introduction
Harvesting energy from the environment provides a promis-ing solution to address the issues arising from energy scarcityin wireless sensor networks (WSNs) [1ndash4] More and moreresearchers choose photovoltaic-supercapacitor hardwaresystems to design the sensor nodes that utilize energy-harves-ting WSNs (EN-WSNs) The main reason is that solar energyis readily available and supercapacitors have larger charging-discharging efficiencies and much longer recharging cycles(thousands times or more) than batteries More importantlythe residual energy of supercapacitors is easy to meter onlinewith high accuracy which can support power managementalgorithms and emergent energy-aware network protocols[5ndash9]
The key issue of sensor nodes with photovoltaic-super-capacitor energy systems is how to maximize the utility ofthe harvested energy Due to the time-varying nature of solar
energy and the highly nonlinear output versus voltage char-acteristics of supercapacitor it is challenging to model thethe whole energy system as well as to maximize its efficiencyThere are several efforts [3 10ndash14] aiming to improve theefficiency of energy systems A quick-charge circuit to switchbetween parallel and series connection of photovoltaic (PV)cells is used in [3] to shorten the supercapacitor chargingtime The well-known MPPT techniques [2 3 10ndash12] haveobtained the maximum output power by adjusting the oper-ating point of the solar panels dynamically Reference [13]points out that the charging efficiency of MPPTs has a strongrelationshipwith themismatch between themaximumpowerpoint voltage of the solar panels (119881mpp) and the supercapac-itor voltage (119881cap) and achieves high charging efficiency byselecting supercapacitors with appropriate capacities How-ever they assume that the supercapacitor does not dischargein day time and their optimal solution is for a fixed solarirradiance model only Leakage-aware [4] is the first indepth
2 International Journal of Distributed Sensor Networks
Inputregulator
Outputregulator
MicaZ
PV array
119866
119875119868
120578in 120578out
119875load
119881cap
119875le
akag
e
Supercapacitor
Figure 1 Energy translation of a photovoltaic-supercapacitorenergy system
work that focuses on reducing the leakage of supercapacitorsby dynamically adjusting the duty cycle However it does notconsider the charging and discharging efficiency (chargingefficiency discharging efficiency and charging-dischargingefficiency are the energy conversion efficiencies of inputregulator output regulator and energy storages (batteries orsupercapacitors)) caused by the state of the supercapacitorand it is quite difficult to find a suitable adjustment step lengthwhen the daily solar irradiation changes frequently Besidesit needs to wake up the node frequently and can only assignduty cycles for a small duration in each calculation (tens ofseconds compared with tens of minutes of our efficiency-aware framework)
The energy transfer model of a representative photovol-taic-supercapacitor energy system can be simply illustratedby Figure 1 The power (the power harvested by a solar panelis highly depending on solar irradiance and the states of thesolar panel Here it represents the harvesting power on themaximumpower point of a solar panel) (119875
119868) harvested by the
solar panel (PV Array) is transferred into the supercapacitorthrough the input regulatorwith the efficiency 120578in and energyin the supercapacitor can be used by the node (eg Micaz)through the output regulator with the efficiency 120578out as wellas being leaked away with the power 119875leakage According to [411ndash13] 120578in 120578out and 119875leakage highly depend on the voltage ofthe supercapacitor (119881cap)Through a number of experimentswe also find that these variables can be expressed by functionsof 119881cap through theoretical analysis or model fitting As 119875
119868
can be predicted by prediction algorithms such as EWMA[15] and WCMA-PDR [16] 119881cap can be controlled to thestates beneficial to energy harvesting by adjusting the power(119875load) consumed by the node using duty cycle schedulingschemes
In this context this paper proposes efficiency-aware arealistic and complete way tomaximize the energy utilizationefficiency of photovoltaic-supercapacitor energy systemsEfficiency-aware is a three-layer design as shown in Figure 2All themodels in hardware layer are based on actualmeasure-ments or empirical formulas and the duty cycle controlleruses energy control algorithms to suggest optimal duty cycleto the adaptation layer The major contributions of our workare as follows
Adaptationlayer Sensing Communication
Duty cyclecontrollerControl layer
Energyinformation
Solar panelmodel
Efficiencymodel
LeakagemodelHardware
layer Residual energymodel
Solarpredictor
Suggestedduty cycle
QoS
middot middot middot
Figure 2 Overview of efficiency-aware
(i) Modeling all the power models of a commonly usedphotovoltaic-supercapacitor energy systems describ-ing the results and using them to develop energy-harvesting-aware algorithms and systems
(ii) Proposing a framework that can be used in photovol-taic-supercapacitor energy systems with predictablesolar energy to maximize energy utilization in suchsystems
(iii) Formulating the utility maximization problem as anoptimization problem that produces duty cycle sched-ules and proposing algorithms to solve this opti-mization We also make an extensive comparativeperformance analysis of leakage-aware fixed dutycycle scheme and our method
The rest of this paper is organized as follows An overviewof the efficiency-aware design architecture is presented inSection 2 In Section 3 we present power models of individ-ual hardware components of the photovoltaic-supercapacitorenergy systems The formalization of the optimization prob-lem and algorithms to solve the problem are presented inSection 4 Numeric results are presented in Section 5 Finallywe conclude the paper in Section 6
2 Overview of Efficiency-Aware Framework
The efficiency-aware framework for the photovoltaic-super-capacitor energy systems is a three-layer architecture asshown in Figure 2
The hardware layer provides offline hardware models andpredicted solar energy to the control layer The offline hard-waremodels include a solar panelmodel efficiency (ie char-ging and discharging) models a residual energy model anda leakage model
Continuous time is divided into discrete slots in ourdesign (as shown in Figure 3) At the beginning of every pre-diction interval the control layer computes the optimal dutycycles for those slots based on the information provided by
International Journal of Distributed Sensor Networks 3
Prediction interval 119871middotΔ119879
1 2 119870
1198711 2
Δ119879
Δ119905
Figure 3 Harvested energy prediction interval
the hardware layer predicted solar power and QoS require-ments
The adaptation layer changes its schedules (eg sensingand communication) according to the duty cycle determinedby the control layer
3 Power Models
In general a photovoltaic-supercapacitor energy systemincludes a solar panel an input regulator (except direct con-nection) a supercapacitor and an output regulator In orderto provide a systematic understanding of the photovoltaic-supercapacitor energy system it is necessary to know thecharacteristics of each individual component To this end wepresent the solar model charging efficiency model for theinput regulator discharging efficiency model for the outputregulator the residual energy model and the leakage modelfor the supercapacitor In addition a simple duty cycle modelis given in this section
31 Solar Panel Model Previous work [12] presents an accu-rate simulationmodel of solar panels By neglecting the shuntresistance and considering that the series resistor is largeenough the I-V characteristic of solar panels can be given bythe following equation [12 17]
119868panel = 119868119892 minus 119868119900 (119890119902sdot119881panel119860sdot119870sdot119879 minus 1) (1)
where 119868119892is the generated current 119902 is the electron charge 119868
119900
is diode saturation current 119860 is an ideality factor 119870 is theBoltzmannrsquos constant and 119879 is the solar panel temperature indegree Kelvin
119868119900and 119868119892depend on solar irradiance and temperature as
119892STC are the diode saturation current andthe generated current in Standard Test Condition (STC) 119879refis the reference temperature 119864gap is the energy gap 119861 is theideality constant119870
119868is the temperature coefficient119866STC is the
solar irradiance in STC typically 1000Wm2 120578 is the energy
conversion efficiency of the solar panel and 119878 is the area ofthe solar panels 119868
119892STC can be considered equal to the short-circuit current in STC and 119868
Since the charging-discharging efficiency of supercapaci-tors is close to 100 in practice we assume that it equals 100in our model In direct connection119881panel equals119881cap and thecharging current equals 119868panel So 120578in is
120578in =119881cap sdot 119868panel
119875119868
(6)
where 119868panel can be determined by combining (1) (2) (3) and(4) as 119875
119868 119879 and 119881panel have been determined
33 Residual Energy Model The residual energy of superca-pacitors can be given by
119864cap =1
21198621198812
cap (7)
34 Discharging Efficiency Model As the voltage range ofsupercapacitors is wide and the operating voltage of sensornodes may be very different from 119881cap (eg 0ndash27V forsupercapacitors compared with 27ndash33 V for MicaZ) it isessential to adopt an output regulator between themTheDC-DC converter discharging efficiency (120578out) is determined byinput voltage output voltage (119881out) and output current (119868out)
We assume that the node operates in two states onlyactive (MCU active and radio on for MicaZ) and sleep statesIn sleep state the current is tens of 120583A and can be ignoredIn the active state the current as measured is about 223mAand 119881out is a fixed voltage (eg 3 V) So 120578out is
120578out = 119891out (119881cap) (9)
35 Duty Cycle Model Duty cycle (D) can be represented as
119863 =119905active
119905active + 119905sleep (10)
4 International Journal of Distributed Sensor Networks
where 119905active is the node active duration and 119905sleep is the nodesleep durationTherefore the average power consumedby thenode (119875avg) is
where 119875active and 119875sleep are the power consumptions of theactive and sleep states respectively Since119875sleep is small (abouttens of 120583W compared with tens of mW of 119875active) 119875avg can beapproximately represented as
119875avg = 119863 sdot 119875active (12)
36 Leakage Model The leakage power of a supercapacitor119875leakage is mainly determined by 119881cap and it can be approxi-mately represented as
119875leakage = 119891119897 (119881cap) (13)
4 Duty Cycling Scheme Design
The duty cycle controller uses energy information (themodels mentioned previously) and predicted solar energyto allocate duty cycles for several future slots resulting in amaximum sum of duty cycles of those time slots
41 Problem Formulation As shown in Figure 3 119871 sdot Δ119879 is thepredicted interval consisting of 119871 successive time slots withthe durationΔ119879We can choose a smallΔ119879 (eg 30minutes)during which the solar irradiance changes slightly Hence wecan assume that the solar power keeps constant during a slotand use 119875119894
119868to represent the solar power in the 119894th slot Let
119863119894 be the duty cycle in slot 119894 Then the residual energy of the
Since it is difficult to know 120578in(119905) 120578out(119905) and 119875leakage(119905)due to the changing 119881cap we divide Δ119879 into 119870 smallertime slots (s-slot) with a duration Δ119905 Δ119905 must be smallenough (eg 30 seconds) so the supercapacitor voltage canbe considered almost constant over this duration Let 119896 be thes-slot index and let the tuple (119894 119896) represent the beginning ofthe s-slot 119896 in slot 119894 Then (14) can be replaced by (15)
119864119894119896+1
cap = 119864119894119896
cap + 119875119894
119868sdot 120578119894119896
in sdot Δ119905
minus 119875119894
avg sdotΔ119905
120578119894119896
outminus 119875119894119896
leakage sdot Δ119905
119864119894+11
cap = 119864119894119870+1
cap
(15)
According to (5) (7) (9) (12) (13) and (15) we have
1
2119862(119881119894119896+1
cap )2
=1
2119862(119881119894119896
cap)2
+ 119875119894
119868sdot 119891in (119875
119894
119868 119881119894119896
cap 119879 119881panel) sdot Δ119905
minus 119863119894sdot 119875active sdot
Δ119905
119891out (119881119894119896
cap)minus 119891119897(119881119894119896
cap) sdot Δ119905
(16)
119881119894+11
cap = 119881119894119870+1
cap (17)
Reference [1] presents a performance model in terms ofsystem utility to the user To maximize the system perfor-mance and save energy we have
119863min le 119863119894le 119863max (18)
where119863min is the application that definedminimal duty cyclerequirement and 119863max is the maximum duty cycle Anyassigned duty cycle that is larger than 119863max cannot improvethe system performance further and will lead to more energyconsumption
In order to ensure the survival time of the node (work at119863min until death) there should be some energy 119864 left in thesupercapacitor at the end of every prediction interval Mean-while the supercapacitor voltage should be higher than thestartup voltage (119881startup) of the DC-DC converter and smallerthan the maximum operating voltage of the supercapacitor(119881max) So we have
119881119871119870+1
cap ge 119881 (19)
119881startup le 119881119894119896
cap le 119881max (20)
Then we formalize the cumulated duty cycle maximiza-tion problem as follows
max 119911 = 119864119871119870+1cap minus 11986411
cap +119871
sum
119894=1
119863119894sdot 119875active sdot Δ119879
st (17)ndash(21)
(21)
where 119911 is the total available energy in the prediction interval119871 sdot Δ119879 It equals the sum of the energy growth of thesupercapacitor and energy consumption of the node If119864119871119870+1capand 11986411cap both equal 119864 then the system achieves energyneutral operation (ENO) [18] and (21) can be rewritten asfollows
max 119911 =119871
sum
119894=1
119863119894
st (17)ndash(21)
(22)
For a link the previous optimization problems can beextended as data rate utility optimization problems As shownin Figure 4 we assume that ArarrBrarr Sink is a fixed routing ina data collection sensor network Node A and node B collect
International Journal of Distributed Sensor Networks 5
(1) 119863total(119895 119894) larr 0 119860(119895 119894) larr minusinfin119861(119895 119894) larr 0119863 larr minusinfinforall119894 lt 119871 forall119895 le (119881max minus 119881startup) Δ119881(2) for 119894 larr 1 to 119871 do(3) for 119895
1larr 0 to (119881max minus 119881startupΔ119881) do
(4) 119881119894+1
cap larr 119881startup + 1198951 sdot Δ119881(5) for 119895
2larr 0 to 119881max minus 119881startupΔ119881 do
st (119890119903119909+ 119890119905119909) sdot 119903A (119894) + 119890119905119909 sdot 119903B (119894) le 119863
119894
B sdot 119875active (24)
119890119905119909sdot 119903A (119894) le 119863
119894
A sdot 119875active
AB constraints (17)ndash(21) (25)
where 119903A(119894) and 119903B(119894) are the data rates of node A and node Bin slot i 119890
119903119909and 119890119905119909are the energetic costs to receive and to
transmit one bit of data
42 Duty Cycle Assignment According to (16) and (17) thedetermination of 119863119894 is an iterative process and 119863119894 cannot beexpressed as linear combination of duty cycles under otherslots So the maximization problems previously mentionedcan neither be solved by convex optimization nor standardlinear programming However for quantized energy storagethe problem can be solved by a dynamic programmingroutine algorithm (see Algorithm 1)
In Algorithm 1 the supercapacitor voltage is quantizedfrom 119881startup to 119881max with the step Δ119881 For every loop online 2 the algorithm calculates themaximum cumulated dutycycle (119863total) for every quantized supercapacitor voltage inslot 119894 + 1 and stores the serial number 119895
2as well as the duty
(1) 1198631larr 119863max
(2) while1198631gt 119863min do
(3) for 119896 larr 1 to 119870 do(4) Calculate 119881119894119896+1cap using (16)(5) end for(6) if 10038161003816100381610038161003816119881
119894119870+1
cap minus 119881119894+1
cap10038161003816100381610038161003816lt 120575 then
(7) 119863 larr 1198631
(8) break(9) 119863
1larr 1198631minus Δ119863
(10) end if(11) end while
Algorithm 2 Duty cycle computation algorithm
cycle 119863 corresponding to the maximum cumulated dutycycle in two arrays A and B Going ldquobackwardsrdquo Algorithm 1determines a vector 1198631 1198632 119863119871 that maximizes thecumulated duty cycle and the vector is the optimal energyallocation The running time of Algorithm 1 is 119874(119871 sdot [(119881max minus
119881startup)Δ119881]2)
Since 120578in 120578out and 119875leakage (line 7 in Algorithm 1) varywith 119881cap it is hard to calculate these values if the slot time(Δ119879) is very large (eg tens of minutes) In fact Δ119879 in mostof the solar prediction algorithms is set to be tens of minutesSo we further divide every slot into119870 small slotsThen119863 (inline 7) can be calculated as shown in Algorithm 2
In Algorithm 2 1198631is quantized from 119863min to 119863max with
the step Δ119863 The algorithm starts with 1198631larr 119863max and
calculates 119881119894119870+1cap for every loop on line 1 If there are someduty cycles which can make the supercapacitor voltages atthe end of the slot (119881119894119870+1cap ) and 119881119894+1cap equal the algorithm willfind the maximum duty cycle and assign it to 119863 120575 is a smallthreshold compared to 119881119894+1cap (eg 001 V)
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
2 International Journal of Distributed Sensor Networks
Inputregulator
Outputregulator
MicaZ
PV array
119866
119875119868
120578in 120578out
119875load
119881cap
119875le
akag
e
Supercapacitor
Figure 1 Energy translation of a photovoltaic-supercapacitorenergy system
work that focuses on reducing the leakage of supercapacitorsby dynamically adjusting the duty cycle However it does notconsider the charging and discharging efficiency (chargingefficiency discharging efficiency and charging-dischargingefficiency are the energy conversion efficiencies of inputregulator output regulator and energy storages (batteries orsupercapacitors)) caused by the state of the supercapacitorand it is quite difficult to find a suitable adjustment step lengthwhen the daily solar irradiation changes frequently Besidesit needs to wake up the node frequently and can only assignduty cycles for a small duration in each calculation (tens ofseconds compared with tens of minutes of our efficiency-aware framework)
The energy transfer model of a representative photovol-taic-supercapacitor energy system can be simply illustratedby Figure 1 The power (the power harvested by a solar panelis highly depending on solar irradiance and the states of thesolar panel Here it represents the harvesting power on themaximumpower point of a solar panel) (119875
119868) harvested by the
solar panel (PV Array) is transferred into the supercapacitorthrough the input regulatorwith the efficiency 120578in and energyin the supercapacitor can be used by the node (eg Micaz)through the output regulator with the efficiency 120578out as wellas being leaked away with the power 119875leakage According to [411ndash13] 120578in 120578out and 119875leakage highly depend on the voltage ofthe supercapacitor (119881cap)Through a number of experimentswe also find that these variables can be expressed by functionsof 119881cap through theoretical analysis or model fitting As 119875
119868
can be predicted by prediction algorithms such as EWMA[15] and WCMA-PDR [16] 119881cap can be controlled to thestates beneficial to energy harvesting by adjusting the power(119875load) consumed by the node using duty cycle schedulingschemes
In this context this paper proposes efficiency-aware arealistic and complete way tomaximize the energy utilizationefficiency of photovoltaic-supercapacitor energy systemsEfficiency-aware is a three-layer design as shown in Figure 2All themodels in hardware layer are based on actualmeasure-ments or empirical formulas and the duty cycle controlleruses energy control algorithms to suggest optimal duty cycleto the adaptation layer The major contributions of our workare as follows
Adaptationlayer Sensing Communication
Duty cyclecontrollerControl layer
Energyinformation
Solar panelmodel
Efficiencymodel
LeakagemodelHardware
layer Residual energymodel
Solarpredictor
Suggestedduty cycle
QoS
middot middot middot
Figure 2 Overview of efficiency-aware
(i) Modeling all the power models of a commonly usedphotovoltaic-supercapacitor energy systems describ-ing the results and using them to develop energy-harvesting-aware algorithms and systems
(ii) Proposing a framework that can be used in photovol-taic-supercapacitor energy systems with predictablesolar energy to maximize energy utilization in suchsystems
(iii) Formulating the utility maximization problem as anoptimization problem that produces duty cycle sched-ules and proposing algorithms to solve this opti-mization We also make an extensive comparativeperformance analysis of leakage-aware fixed dutycycle scheme and our method
The rest of this paper is organized as follows An overviewof the efficiency-aware design architecture is presented inSection 2 In Section 3 we present power models of individ-ual hardware components of the photovoltaic-supercapacitorenergy systems The formalization of the optimization prob-lem and algorithms to solve the problem are presented inSection 4 Numeric results are presented in Section 5 Finallywe conclude the paper in Section 6
2 Overview of Efficiency-Aware Framework
The efficiency-aware framework for the photovoltaic-super-capacitor energy systems is a three-layer architecture asshown in Figure 2
The hardware layer provides offline hardware models andpredicted solar energy to the control layer The offline hard-waremodels include a solar panelmodel efficiency (ie char-ging and discharging) models a residual energy model anda leakage model
Continuous time is divided into discrete slots in ourdesign (as shown in Figure 3) At the beginning of every pre-diction interval the control layer computes the optimal dutycycles for those slots based on the information provided by
International Journal of Distributed Sensor Networks 3
Prediction interval 119871middotΔ119879
1 2 119870
1198711 2
Δ119879
Δ119905
Figure 3 Harvested energy prediction interval
the hardware layer predicted solar power and QoS require-ments
The adaptation layer changes its schedules (eg sensingand communication) according to the duty cycle determinedby the control layer
3 Power Models
In general a photovoltaic-supercapacitor energy systemincludes a solar panel an input regulator (except direct con-nection) a supercapacitor and an output regulator In orderto provide a systematic understanding of the photovoltaic-supercapacitor energy system it is necessary to know thecharacteristics of each individual component To this end wepresent the solar model charging efficiency model for theinput regulator discharging efficiency model for the outputregulator the residual energy model and the leakage modelfor the supercapacitor In addition a simple duty cycle modelis given in this section
31 Solar Panel Model Previous work [12] presents an accu-rate simulationmodel of solar panels By neglecting the shuntresistance and considering that the series resistor is largeenough the I-V characteristic of solar panels can be given bythe following equation [12 17]
119868panel = 119868119892 minus 119868119900 (119890119902sdot119881panel119860sdot119870sdot119879 minus 1) (1)
where 119868119892is the generated current 119902 is the electron charge 119868
119900
is diode saturation current 119860 is an ideality factor 119870 is theBoltzmannrsquos constant and 119879 is the solar panel temperature indegree Kelvin
119868119900and 119868119892depend on solar irradiance and temperature as
119892STC are the diode saturation current andthe generated current in Standard Test Condition (STC) 119879refis the reference temperature 119864gap is the energy gap 119861 is theideality constant119870
119868is the temperature coefficient119866STC is the
solar irradiance in STC typically 1000Wm2 120578 is the energy
conversion efficiency of the solar panel and 119878 is the area ofthe solar panels 119868
119892STC can be considered equal to the short-circuit current in STC and 119868
Since the charging-discharging efficiency of supercapaci-tors is close to 100 in practice we assume that it equals 100in our model In direct connection119881panel equals119881cap and thecharging current equals 119868panel So 120578in is
120578in =119881cap sdot 119868panel
119875119868
(6)
where 119868panel can be determined by combining (1) (2) (3) and(4) as 119875
119868 119879 and 119881panel have been determined
33 Residual Energy Model The residual energy of superca-pacitors can be given by
119864cap =1
21198621198812
cap (7)
34 Discharging Efficiency Model As the voltage range ofsupercapacitors is wide and the operating voltage of sensornodes may be very different from 119881cap (eg 0ndash27V forsupercapacitors compared with 27ndash33 V for MicaZ) it isessential to adopt an output regulator between themTheDC-DC converter discharging efficiency (120578out) is determined byinput voltage output voltage (119881out) and output current (119868out)
We assume that the node operates in two states onlyactive (MCU active and radio on for MicaZ) and sleep statesIn sleep state the current is tens of 120583A and can be ignoredIn the active state the current as measured is about 223mAand 119881out is a fixed voltage (eg 3 V) So 120578out is
120578out = 119891out (119881cap) (9)
35 Duty Cycle Model Duty cycle (D) can be represented as
119863 =119905active
119905active + 119905sleep (10)
4 International Journal of Distributed Sensor Networks
where 119905active is the node active duration and 119905sleep is the nodesleep durationTherefore the average power consumedby thenode (119875avg) is
where 119875active and 119875sleep are the power consumptions of theactive and sleep states respectively Since119875sleep is small (abouttens of 120583W compared with tens of mW of 119875active) 119875avg can beapproximately represented as
119875avg = 119863 sdot 119875active (12)
36 Leakage Model The leakage power of a supercapacitor119875leakage is mainly determined by 119881cap and it can be approxi-mately represented as
119875leakage = 119891119897 (119881cap) (13)
4 Duty Cycling Scheme Design
The duty cycle controller uses energy information (themodels mentioned previously) and predicted solar energyto allocate duty cycles for several future slots resulting in amaximum sum of duty cycles of those time slots
41 Problem Formulation As shown in Figure 3 119871 sdot Δ119879 is thepredicted interval consisting of 119871 successive time slots withthe durationΔ119879We can choose a smallΔ119879 (eg 30minutes)during which the solar irradiance changes slightly Hence wecan assume that the solar power keeps constant during a slotand use 119875119894
119868to represent the solar power in the 119894th slot Let
119863119894 be the duty cycle in slot 119894 Then the residual energy of the
Since it is difficult to know 120578in(119905) 120578out(119905) and 119875leakage(119905)due to the changing 119881cap we divide Δ119879 into 119870 smallertime slots (s-slot) with a duration Δ119905 Δ119905 must be smallenough (eg 30 seconds) so the supercapacitor voltage canbe considered almost constant over this duration Let 119896 be thes-slot index and let the tuple (119894 119896) represent the beginning ofthe s-slot 119896 in slot 119894 Then (14) can be replaced by (15)
119864119894119896+1
cap = 119864119894119896
cap + 119875119894
119868sdot 120578119894119896
in sdot Δ119905
minus 119875119894
avg sdotΔ119905
120578119894119896
outminus 119875119894119896
leakage sdot Δ119905
119864119894+11
cap = 119864119894119870+1
cap
(15)
According to (5) (7) (9) (12) (13) and (15) we have
1
2119862(119881119894119896+1
cap )2
=1
2119862(119881119894119896
cap)2
+ 119875119894
119868sdot 119891in (119875
119894
119868 119881119894119896
cap 119879 119881panel) sdot Δ119905
minus 119863119894sdot 119875active sdot
Δ119905
119891out (119881119894119896
cap)minus 119891119897(119881119894119896
cap) sdot Δ119905
(16)
119881119894+11
cap = 119881119894119870+1
cap (17)
Reference [1] presents a performance model in terms ofsystem utility to the user To maximize the system perfor-mance and save energy we have
119863min le 119863119894le 119863max (18)
where119863min is the application that definedminimal duty cyclerequirement and 119863max is the maximum duty cycle Anyassigned duty cycle that is larger than 119863max cannot improvethe system performance further and will lead to more energyconsumption
In order to ensure the survival time of the node (work at119863min until death) there should be some energy 119864 left in thesupercapacitor at the end of every prediction interval Mean-while the supercapacitor voltage should be higher than thestartup voltage (119881startup) of the DC-DC converter and smallerthan the maximum operating voltage of the supercapacitor(119881max) So we have
119881119871119870+1
cap ge 119881 (19)
119881startup le 119881119894119896
cap le 119881max (20)
Then we formalize the cumulated duty cycle maximiza-tion problem as follows
max 119911 = 119864119871119870+1cap minus 11986411
cap +119871
sum
119894=1
119863119894sdot 119875active sdot Δ119879
st (17)ndash(21)
(21)
where 119911 is the total available energy in the prediction interval119871 sdot Δ119879 It equals the sum of the energy growth of thesupercapacitor and energy consumption of the node If119864119871119870+1capand 11986411cap both equal 119864 then the system achieves energyneutral operation (ENO) [18] and (21) can be rewritten asfollows
max 119911 =119871
sum
119894=1
119863119894
st (17)ndash(21)
(22)
For a link the previous optimization problems can beextended as data rate utility optimization problems As shownin Figure 4 we assume that ArarrBrarr Sink is a fixed routing ina data collection sensor network Node A and node B collect
International Journal of Distributed Sensor Networks 5
(1) 119863total(119895 119894) larr 0 119860(119895 119894) larr minusinfin119861(119895 119894) larr 0119863 larr minusinfinforall119894 lt 119871 forall119895 le (119881max minus 119881startup) Δ119881(2) for 119894 larr 1 to 119871 do(3) for 119895
1larr 0 to (119881max minus 119881startupΔ119881) do
(4) 119881119894+1
cap larr 119881startup + 1198951 sdot Δ119881(5) for 119895
2larr 0 to 119881max minus 119881startupΔ119881 do
st (119890119903119909+ 119890119905119909) sdot 119903A (119894) + 119890119905119909 sdot 119903B (119894) le 119863
119894
B sdot 119875active (24)
119890119905119909sdot 119903A (119894) le 119863
119894
A sdot 119875active
AB constraints (17)ndash(21) (25)
where 119903A(119894) and 119903B(119894) are the data rates of node A and node Bin slot i 119890
119903119909and 119890119905119909are the energetic costs to receive and to
transmit one bit of data
42 Duty Cycle Assignment According to (16) and (17) thedetermination of 119863119894 is an iterative process and 119863119894 cannot beexpressed as linear combination of duty cycles under otherslots So the maximization problems previously mentionedcan neither be solved by convex optimization nor standardlinear programming However for quantized energy storagethe problem can be solved by a dynamic programmingroutine algorithm (see Algorithm 1)
In Algorithm 1 the supercapacitor voltage is quantizedfrom 119881startup to 119881max with the step Δ119881 For every loop online 2 the algorithm calculates themaximum cumulated dutycycle (119863total) for every quantized supercapacitor voltage inslot 119894 + 1 and stores the serial number 119895
2as well as the duty
(1) 1198631larr 119863max
(2) while1198631gt 119863min do
(3) for 119896 larr 1 to 119870 do(4) Calculate 119881119894119896+1cap using (16)(5) end for(6) if 10038161003816100381610038161003816119881
119894119870+1
cap minus 119881119894+1
cap10038161003816100381610038161003816lt 120575 then
(7) 119863 larr 1198631
(8) break(9) 119863
1larr 1198631minus Δ119863
(10) end if(11) end while
Algorithm 2 Duty cycle computation algorithm
cycle 119863 corresponding to the maximum cumulated dutycycle in two arrays A and B Going ldquobackwardsrdquo Algorithm 1determines a vector 1198631 1198632 119863119871 that maximizes thecumulated duty cycle and the vector is the optimal energyallocation The running time of Algorithm 1 is 119874(119871 sdot [(119881max minus
119881startup)Δ119881]2)
Since 120578in 120578out and 119875leakage (line 7 in Algorithm 1) varywith 119881cap it is hard to calculate these values if the slot time(Δ119879) is very large (eg tens of minutes) In fact Δ119879 in mostof the solar prediction algorithms is set to be tens of minutesSo we further divide every slot into119870 small slotsThen119863 (inline 7) can be calculated as shown in Algorithm 2
In Algorithm 2 1198631is quantized from 119863min to 119863max with
the step Δ119863 The algorithm starts with 1198631larr 119863max and
calculates 119881119894119870+1cap for every loop on line 1 If there are someduty cycles which can make the supercapacitor voltages atthe end of the slot (119881119894119870+1cap ) and 119881119894+1cap equal the algorithm willfind the maximum duty cycle and assign it to 119863 120575 is a smallthreshold compared to 119881119894+1cap (eg 001 V)
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
International Journal of Distributed Sensor Networks 3
Prediction interval 119871middotΔ119879
1 2 119870
1198711 2
Δ119879
Δ119905
Figure 3 Harvested energy prediction interval
the hardware layer predicted solar power and QoS require-ments
The adaptation layer changes its schedules (eg sensingand communication) according to the duty cycle determinedby the control layer
3 Power Models
In general a photovoltaic-supercapacitor energy systemincludes a solar panel an input regulator (except direct con-nection) a supercapacitor and an output regulator In orderto provide a systematic understanding of the photovoltaic-supercapacitor energy system it is necessary to know thecharacteristics of each individual component To this end wepresent the solar model charging efficiency model for theinput regulator discharging efficiency model for the outputregulator the residual energy model and the leakage modelfor the supercapacitor In addition a simple duty cycle modelis given in this section
31 Solar Panel Model Previous work [12] presents an accu-rate simulationmodel of solar panels By neglecting the shuntresistance and considering that the series resistor is largeenough the I-V characteristic of solar panels can be given bythe following equation [12 17]
119868panel = 119868119892 minus 119868119900 (119890119902sdot119881panel119860sdot119870sdot119879 minus 1) (1)
where 119868119892is the generated current 119902 is the electron charge 119868
119900
is diode saturation current 119860 is an ideality factor 119870 is theBoltzmannrsquos constant and 119879 is the solar panel temperature indegree Kelvin
119868119900and 119868119892depend on solar irradiance and temperature as
119892STC are the diode saturation current andthe generated current in Standard Test Condition (STC) 119879refis the reference temperature 119864gap is the energy gap 119861 is theideality constant119870
119868is the temperature coefficient119866STC is the
solar irradiance in STC typically 1000Wm2 120578 is the energy
conversion efficiency of the solar panel and 119878 is the area ofthe solar panels 119868
119892STC can be considered equal to the short-circuit current in STC and 119868
Since the charging-discharging efficiency of supercapaci-tors is close to 100 in practice we assume that it equals 100in our model In direct connection119881panel equals119881cap and thecharging current equals 119868panel So 120578in is
120578in =119881cap sdot 119868panel
119875119868
(6)
where 119868panel can be determined by combining (1) (2) (3) and(4) as 119875
119868 119879 and 119881panel have been determined
33 Residual Energy Model The residual energy of superca-pacitors can be given by
119864cap =1
21198621198812
cap (7)
34 Discharging Efficiency Model As the voltage range ofsupercapacitors is wide and the operating voltage of sensornodes may be very different from 119881cap (eg 0ndash27V forsupercapacitors compared with 27ndash33 V for MicaZ) it isessential to adopt an output regulator between themTheDC-DC converter discharging efficiency (120578out) is determined byinput voltage output voltage (119881out) and output current (119868out)
We assume that the node operates in two states onlyactive (MCU active and radio on for MicaZ) and sleep statesIn sleep state the current is tens of 120583A and can be ignoredIn the active state the current as measured is about 223mAand 119881out is a fixed voltage (eg 3 V) So 120578out is
120578out = 119891out (119881cap) (9)
35 Duty Cycle Model Duty cycle (D) can be represented as
119863 =119905active
119905active + 119905sleep (10)
4 International Journal of Distributed Sensor Networks
where 119905active is the node active duration and 119905sleep is the nodesleep durationTherefore the average power consumedby thenode (119875avg) is
where 119875active and 119875sleep are the power consumptions of theactive and sleep states respectively Since119875sleep is small (abouttens of 120583W compared with tens of mW of 119875active) 119875avg can beapproximately represented as
119875avg = 119863 sdot 119875active (12)
36 Leakage Model The leakage power of a supercapacitor119875leakage is mainly determined by 119881cap and it can be approxi-mately represented as
119875leakage = 119891119897 (119881cap) (13)
4 Duty Cycling Scheme Design
The duty cycle controller uses energy information (themodels mentioned previously) and predicted solar energyto allocate duty cycles for several future slots resulting in amaximum sum of duty cycles of those time slots
41 Problem Formulation As shown in Figure 3 119871 sdot Δ119879 is thepredicted interval consisting of 119871 successive time slots withthe durationΔ119879We can choose a smallΔ119879 (eg 30minutes)during which the solar irradiance changes slightly Hence wecan assume that the solar power keeps constant during a slotand use 119875119894
119868to represent the solar power in the 119894th slot Let
119863119894 be the duty cycle in slot 119894 Then the residual energy of the
Since it is difficult to know 120578in(119905) 120578out(119905) and 119875leakage(119905)due to the changing 119881cap we divide Δ119879 into 119870 smallertime slots (s-slot) with a duration Δ119905 Δ119905 must be smallenough (eg 30 seconds) so the supercapacitor voltage canbe considered almost constant over this duration Let 119896 be thes-slot index and let the tuple (119894 119896) represent the beginning ofthe s-slot 119896 in slot 119894 Then (14) can be replaced by (15)
119864119894119896+1
cap = 119864119894119896
cap + 119875119894
119868sdot 120578119894119896
in sdot Δ119905
minus 119875119894
avg sdotΔ119905
120578119894119896
outminus 119875119894119896
leakage sdot Δ119905
119864119894+11
cap = 119864119894119870+1
cap
(15)
According to (5) (7) (9) (12) (13) and (15) we have
1
2119862(119881119894119896+1
cap )2
=1
2119862(119881119894119896
cap)2
+ 119875119894
119868sdot 119891in (119875
119894
119868 119881119894119896
cap 119879 119881panel) sdot Δ119905
minus 119863119894sdot 119875active sdot
Δ119905
119891out (119881119894119896
cap)minus 119891119897(119881119894119896
cap) sdot Δ119905
(16)
119881119894+11
cap = 119881119894119870+1
cap (17)
Reference [1] presents a performance model in terms ofsystem utility to the user To maximize the system perfor-mance and save energy we have
119863min le 119863119894le 119863max (18)
where119863min is the application that definedminimal duty cyclerequirement and 119863max is the maximum duty cycle Anyassigned duty cycle that is larger than 119863max cannot improvethe system performance further and will lead to more energyconsumption
In order to ensure the survival time of the node (work at119863min until death) there should be some energy 119864 left in thesupercapacitor at the end of every prediction interval Mean-while the supercapacitor voltage should be higher than thestartup voltage (119881startup) of the DC-DC converter and smallerthan the maximum operating voltage of the supercapacitor(119881max) So we have
119881119871119870+1
cap ge 119881 (19)
119881startup le 119881119894119896
cap le 119881max (20)
Then we formalize the cumulated duty cycle maximiza-tion problem as follows
max 119911 = 119864119871119870+1cap minus 11986411
cap +119871
sum
119894=1
119863119894sdot 119875active sdot Δ119879
st (17)ndash(21)
(21)
where 119911 is the total available energy in the prediction interval119871 sdot Δ119879 It equals the sum of the energy growth of thesupercapacitor and energy consumption of the node If119864119871119870+1capand 11986411cap both equal 119864 then the system achieves energyneutral operation (ENO) [18] and (21) can be rewritten asfollows
max 119911 =119871
sum
119894=1
119863119894
st (17)ndash(21)
(22)
For a link the previous optimization problems can beextended as data rate utility optimization problems As shownin Figure 4 we assume that ArarrBrarr Sink is a fixed routing ina data collection sensor network Node A and node B collect
International Journal of Distributed Sensor Networks 5
(1) 119863total(119895 119894) larr 0 119860(119895 119894) larr minusinfin119861(119895 119894) larr 0119863 larr minusinfinforall119894 lt 119871 forall119895 le (119881max minus 119881startup) Δ119881(2) for 119894 larr 1 to 119871 do(3) for 119895
1larr 0 to (119881max minus 119881startupΔ119881) do
(4) 119881119894+1
cap larr 119881startup + 1198951 sdot Δ119881(5) for 119895
2larr 0 to 119881max minus 119881startupΔ119881 do
st (119890119903119909+ 119890119905119909) sdot 119903A (119894) + 119890119905119909 sdot 119903B (119894) le 119863
119894
B sdot 119875active (24)
119890119905119909sdot 119903A (119894) le 119863
119894
A sdot 119875active
AB constraints (17)ndash(21) (25)
where 119903A(119894) and 119903B(119894) are the data rates of node A and node Bin slot i 119890
119903119909and 119890119905119909are the energetic costs to receive and to
transmit one bit of data
42 Duty Cycle Assignment According to (16) and (17) thedetermination of 119863119894 is an iterative process and 119863119894 cannot beexpressed as linear combination of duty cycles under otherslots So the maximization problems previously mentionedcan neither be solved by convex optimization nor standardlinear programming However for quantized energy storagethe problem can be solved by a dynamic programmingroutine algorithm (see Algorithm 1)
In Algorithm 1 the supercapacitor voltage is quantizedfrom 119881startup to 119881max with the step Δ119881 For every loop online 2 the algorithm calculates themaximum cumulated dutycycle (119863total) for every quantized supercapacitor voltage inslot 119894 + 1 and stores the serial number 119895
2as well as the duty
(1) 1198631larr 119863max
(2) while1198631gt 119863min do
(3) for 119896 larr 1 to 119870 do(4) Calculate 119881119894119896+1cap using (16)(5) end for(6) if 10038161003816100381610038161003816119881
119894119870+1
cap minus 119881119894+1
cap10038161003816100381610038161003816lt 120575 then
(7) 119863 larr 1198631
(8) break(9) 119863
1larr 1198631minus Δ119863
(10) end if(11) end while
Algorithm 2 Duty cycle computation algorithm
cycle 119863 corresponding to the maximum cumulated dutycycle in two arrays A and B Going ldquobackwardsrdquo Algorithm 1determines a vector 1198631 1198632 119863119871 that maximizes thecumulated duty cycle and the vector is the optimal energyallocation The running time of Algorithm 1 is 119874(119871 sdot [(119881max minus
119881startup)Δ119881]2)
Since 120578in 120578out and 119875leakage (line 7 in Algorithm 1) varywith 119881cap it is hard to calculate these values if the slot time(Δ119879) is very large (eg tens of minutes) In fact Δ119879 in mostof the solar prediction algorithms is set to be tens of minutesSo we further divide every slot into119870 small slotsThen119863 (inline 7) can be calculated as shown in Algorithm 2
In Algorithm 2 1198631is quantized from 119863min to 119863max with
the step Δ119863 The algorithm starts with 1198631larr 119863max and
calculates 119881119894119870+1cap for every loop on line 1 If there are someduty cycles which can make the supercapacitor voltages atthe end of the slot (119881119894119870+1cap ) and 119881119894+1cap equal the algorithm willfind the maximum duty cycle and assign it to 119863 120575 is a smallthreshold compared to 119881119894+1cap (eg 001 V)
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
where 119875active and 119875sleep are the power consumptions of theactive and sleep states respectively Since119875sleep is small (abouttens of 120583W compared with tens of mW of 119875active) 119875avg can beapproximately represented as
119875avg = 119863 sdot 119875active (12)
36 Leakage Model The leakage power of a supercapacitor119875leakage is mainly determined by 119881cap and it can be approxi-mately represented as
119875leakage = 119891119897 (119881cap) (13)
4 Duty Cycling Scheme Design
The duty cycle controller uses energy information (themodels mentioned previously) and predicted solar energyto allocate duty cycles for several future slots resulting in amaximum sum of duty cycles of those time slots
41 Problem Formulation As shown in Figure 3 119871 sdot Δ119879 is thepredicted interval consisting of 119871 successive time slots withthe durationΔ119879We can choose a smallΔ119879 (eg 30minutes)during which the solar irradiance changes slightly Hence wecan assume that the solar power keeps constant during a slotand use 119875119894
119868to represent the solar power in the 119894th slot Let
119863119894 be the duty cycle in slot 119894 Then the residual energy of the
Since it is difficult to know 120578in(119905) 120578out(119905) and 119875leakage(119905)due to the changing 119881cap we divide Δ119879 into 119870 smallertime slots (s-slot) with a duration Δ119905 Δ119905 must be smallenough (eg 30 seconds) so the supercapacitor voltage canbe considered almost constant over this duration Let 119896 be thes-slot index and let the tuple (119894 119896) represent the beginning ofthe s-slot 119896 in slot 119894 Then (14) can be replaced by (15)
119864119894119896+1
cap = 119864119894119896
cap + 119875119894
119868sdot 120578119894119896
in sdot Δ119905
minus 119875119894
avg sdotΔ119905
120578119894119896
outminus 119875119894119896
leakage sdot Δ119905
119864119894+11
cap = 119864119894119870+1
cap
(15)
According to (5) (7) (9) (12) (13) and (15) we have
1
2119862(119881119894119896+1
cap )2
=1
2119862(119881119894119896
cap)2
+ 119875119894
119868sdot 119891in (119875
119894
119868 119881119894119896
cap 119879 119881panel) sdot Δ119905
minus 119863119894sdot 119875active sdot
Δ119905
119891out (119881119894119896
cap)minus 119891119897(119881119894119896
cap) sdot Δ119905
(16)
119881119894+11
cap = 119881119894119870+1
cap (17)
Reference [1] presents a performance model in terms ofsystem utility to the user To maximize the system perfor-mance and save energy we have
119863min le 119863119894le 119863max (18)
where119863min is the application that definedminimal duty cyclerequirement and 119863max is the maximum duty cycle Anyassigned duty cycle that is larger than 119863max cannot improvethe system performance further and will lead to more energyconsumption
In order to ensure the survival time of the node (work at119863min until death) there should be some energy 119864 left in thesupercapacitor at the end of every prediction interval Mean-while the supercapacitor voltage should be higher than thestartup voltage (119881startup) of the DC-DC converter and smallerthan the maximum operating voltage of the supercapacitor(119881max) So we have
119881119871119870+1
cap ge 119881 (19)
119881startup le 119881119894119896
cap le 119881max (20)
Then we formalize the cumulated duty cycle maximiza-tion problem as follows
max 119911 = 119864119871119870+1cap minus 11986411
cap +119871
sum
119894=1
119863119894sdot 119875active sdot Δ119879
st (17)ndash(21)
(21)
where 119911 is the total available energy in the prediction interval119871 sdot Δ119879 It equals the sum of the energy growth of thesupercapacitor and energy consumption of the node If119864119871119870+1capand 11986411cap both equal 119864 then the system achieves energyneutral operation (ENO) [18] and (21) can be rewritten asfollows
max 119911 =119871
sum
119894=1
119863119894
st (17)ndash(21)
(22)
For a link the previous optimization problems can beextended as data rate utility optimization problems As shownin Figure 4 we assume that ArarrBrarr Sink is a fixed routing ina data collection sensor network Node A and node B collect
International Journal of Distributed Sensor Networks 5
(1) 119863total(119895 119894) larr 0 119860(119895 119894) larr minusinfin119861(119895 119894) larr 0119863 larr minusinfinforall119894 lt 119871 forall119895 le (119881max minus 119881startup) Δ119881(2) for 119894 larr 1 to 119871 do(3) for 119895
1larr 0 to (119881max minus 119881startupΔ119881) do
(4) 119881119894+1
cap larr 119881startup + 1198951 sdot Δ119881(5) for 119895
2larr 0 to 119881max minus 119881startupΔ119881 do
st (119890119903119909+ 119890119905119909) sdot 119903A (119894) + 119890119905119909 sdot 119903B (119894) le 119863
119894
B sdot 119875active (24)
119890119905119909sdot 119903A (119894) le 119863
119894
A sdot 119875active
AB constraints (17)ndash(21) (25)
where 119903A(119894) and 119903B(119894) are the data rates of node A and node Bin slot i 119890
119903119909and 119890119905119909are the energetic costs to receive and to
transmit one bit of data
42 Duty Cycle Assignment According to (16) and (17) thedetermination of 119863119894 is an iterative process and 119863119894 cannot beexpressed as linear combination of duty cycles under otherslots So the maximization problems previously mentionedcan neither be solved by convex optimization nor standardlinear programming However for quantized energy storagethe problem can be solved by a dynamic programmingroutine algorithm (see Algorithm 1)
In Algorithm 1 the supercapacitor voltage is quantizedfrom 119881startup to 119881max with the step Δ119881 For every loop online 2 the algorithm calculates themaximum cumulated dutycycle (119863total) for every quantized supercapacitor voltage inslot 119894 + 1 and stores the serial number 119895
2as well as the duty
(1) 1198631larr 119863max
(2) while1198631gt 119863min do
(3) for 119896 larr 1 to 119870 do(4) Calculate 119881119894119896+1cap using (16)(5) end for(6) if 10038161003816100381610038161003816119881
119894119870+1
cap minus 119881119894+1
cap10038161003816100381610038161003816lt 120575 then
(7) 119863 larr 1198631
(8) break(9) 119863
1larr 1198631minus Δ119863
(10) end if(11) end while
Algorithm 2 Duty cycle computation algorithm
cycle 119863 corresponding to the maximum cumulated dutycycle in two arrays A and B Going ldquobackwardsrdquo Algorithm 1determines a vector 1198631 1198632 119863119871 that maximizes thecumulated duty cycle and the vector is the optimal energyallocation The running time of Algorithm 1 is 119874(119871 sdot [(119881max minus
119881startup)Δ119881]2)
Since 120578in 120578out and 119875leakage (line 7 in Algorithm 1) varywith 119881cap it is hard to calculate these values if the slot time(Δ119879) is very large (eg tens of minutes) In fact Δ119879 in mostof the solar prediction algorithms is set to be tens of minutesSo we further divide every slot into119870 small slotsThen119863 (inline 7) can be calculated as shown in Algorithm 2
In Algorithm 2 1198631is quantized from 119863min to 119863max with
the step Δ119863 The algorithm starts with 1198631larr 119863max and
calculates 119881119894119870+1cap for every loop on line 1 If there are someduty cycles which can make the supercapacitor voltages atthe end of the slot (119881119894119870+1cap ) and 119881119894+1cap equal the algorithm willfind the maximum duty cycle and assign it to 119863 120575 is a smallthreshold compared to 119881119894+1cap (eg 001 V)
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
st (119890119903119909+ 119890119905119909) sdot 119903A (119894) + 119890119905119909 sdot 119903B (119894) le 119863
119894
B sdot 119875active (24)
119890119905119909sdot 119903A (119894) le 119863
119894
A sdot 119875active
AB constraints (17)ndash(21) (25)
where 119903A(119894) and 119903B(119894) are the data rates of node A and node Bin slot i 119890
119903119909and 119890119905119909are the energetic costs to receive and to
transmit one bit of data
42 Duty Cycle Assignment According to (16) and (17) thedetermination of 119863119894 is an iterative process and 119863119894 cannot beexpressed as linear combination of duty cycles under otherslots So the maximization problems previously mentionedcan neither be solved by convex optimization nor standardlinear programming However for quantized energy storagethe problem can be solved by a dynamic programmingroutine algorithm (see Algorithm 1)
In Algorithm 1 the supercapacitor voltage is quantizedfrom 119881startup to 119881max with the step Δ119881 For every loop online 2 the algorithm calculates themaximum cumulated dutycycle (119863total) for every quantized supercapacitor voltage inslot 119894 + 1 and stores the serial number 119895
2as well as the duty
(1) 1198631larr 119863max
(2) while1198631gt 119863min do
(3) for 119896 larr 1 to 119870 do(4) Calculate 119881119894119896+1cap using (16)(5) end for(6) if 10038161003816100381610038161003816119881
119894119870+1
cap minus 119881119894+1
cap10038161003816100381610038161003816lt 120575 then
(7) 119863 larr 1198631
(8) break(9) 119863
1larr 1198631minus Δ119863
(10) end if(11) end while
Algorithm 2 Duty cycle computation algorithm
cycle 119863 corresponding to the maximum cumulated dutycycle in two arrays A and B Going ldquobackwardsrdquo Algorithm 1determines a vector 1198631 1198632 119863119871 that maximizes thecumulated duty cycle and the vector is the optimal energyallocation The running time of Algorithm 1 is 119874(119871 sdot [(119881max minus
119881startup)Δ119881]2)
Since 120578in 120578out and 119875leakage (line 7 in Algorithm 1) varywith 119881cap it is hard to calculate these values if the slot time(Δ119879) is very large (eg tens of minutes) In fact Δ119879 in mostof the solar prediction algorithms is set to be tens of minutesSo we further divide every slot into119870 small slotsThen119863 (inline 7) can be calculated as shown in Algorithm 2
In Algorithm 2 1198631is quantized from 119863min to 119863max with
the step Δ119863 The algorithm starts with 1198631larr 119863max and
calculates 119881119894119870+1cap for every loop on line 1 If there are someduty cycles which can make the supercapacitor voltages atthe end of the slot (119881119894119870+1cap ) and 119881119894+1cap equal the algorithm willfind the maximum duty cycle and assign it to 119863 120575 is a smallthreshold compared to 119881119894+1cap (eg 001 V)
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
6 International Journal of Distributed Sensor Networks
In order to solve the cumulated duty cycle maximiza-tion problem we developed Algorithms 1 and 2 With thesupercapacitor voltage being quantized from 119881startup to 119881maxthe constraint (20) is satisfied The constraint (18) can beobtained in Algorithm 2 We denote that the cumulated dutycycle is maximized when inequality (19) is equality (Supposethat 1198631
1 119863
119871
1 is the optimum duty cycle vector of 119881 +
119895 sdot Δ119881 and 1198631 119863119871 is the optimum duty cycle vectorof 119881 then 1198631
1 119863
119871minus1
1 119863119871
2 can be a feasible vector of 119881
It is quite obvious that 1198631198712is larger than 119863119871
1 So sum119871
119894=1119863119894ge
sum119871minus1
119894=1119863119894+ 119863119871
2ge sum119871
119894=1119863119894
1) Then the cumulated duty cycle
maximization problem can be solved by Algorithm 1 with itsline 7 being replaced by Algorithm 2 Algorithm 2 runs in119874(119870 sdot (119863max minus119863min)Δ119863) Thus to solve the cumulated dutycycle maximization problem it runs119874(119870 sdot 119871 sdot (119863max minus119863min) sdot
(119881max minus 119881startup)2(Δ119863 sdot Δ119881
2)) time
For quantized energy values and duty cycles the data rateutility maximization problem can be solved by an extensionof Algorithms 1 and 2 Over all 119903A(119894) 119903B(119894) that satisfyconstraints of (24) and (25) the maximum utility can bedetermined as followsℎ (119881A (119894 + 1) 119881B (119894 + 1) 119894 + 1)
Vectors 119903A(1) 119903A(119871) and 119903B(1) 119903B(119871) that maxi-mize ℎ(119881A(119871 + 1) 119881B(119871 + 1) 119871 + 1) are the optimal and it hasthe complexity119874(119870sdot119871sdot(119863maxminus119863min) sdot(119881maxminus119881startup)
4(Δ119863sdot
Δ1198814)) to solve this problem Solving this problem directly
may be computationally expensive for nodes with limitedcapabilities Instead the nodes can determine their dutycycles (eg 119863119894A and 119863119894B) independently using Algorithms 1and 2 and then for each slot i under constraints (24) and(25) the nodes can adjust their rates to obtain a solution tomax[119880(119903A(119894)) + 119880(119903B(119894))] For example if we use log(sdot) asthe function of data rate utility the subproblem solution is119903A = min[119863119894A sdot 119875active119890119905119909 119863
119894
B sdot 119875active(2 lowast (119890119905119909 + 119890119903119909))] and119903B = 119863
119894
B sdot 119875active119890119905119909 minus 119903A
5 Numerical Results
This section provides numerical results that demonstratethe high performance of efficiency-aware Models based onactual measurements described in Section 3 are used asinputs to the algorithms described in Section 4
Figure 5 shows the 119868-119881 measurements and simulationsof a 110 times 70mm2 solar panel under different temperaturesand solar irradiance Figure 6 shows 119875-119881measurements andsimulations of the same solar panel under the same condi-tions As shown the error between numerical simulation andmeasurement results is less than 6 when 119881panel is smallerthan the max power point voltage Although the error willincrease with the increase of temperature and solar irradiancewhen 119881panel is larger than the max power point voltage thiscan be avoided by choosing a suitable solar panel In factto achieve higher charging efficiency it is better to choose a
432100
10
20
30
40
50
119868pa
nel
(mA
)
119881panel (V)
MeasuredSimulated
223 Wm2 55∘C
79 Wm2 35∘C48 Wm2 32∘C
173Wm2 40∘C
113Wm2 37∘C
16Wm2 30∘C
Figure 5 Measurements and simulations of solar panel outputcurrent
0 1 2 3 40
20
40
60
80
100119875
pane
l(m
W)
119881panel (V)
MeasuredSimulated
Figure 6 Measurements and simulations of solar panel outputpower
solar panel with its max power point voltage under sufficientsolar radiation (eg at noon in a sunny day) being close tothe maximum operating voltage of the supercapacitor andtherefore119881panel can rarely be larger than themax power pointvoltage
Previous works [12 19] provide energy models of switch-ing converters and MPPT circuits For simplicity we modelthe MPPT circuit in [12] using piecewise linear approxi-mation based on real data measurements However it isworth noting that our efficiency-aware framework is notrestricted to a specific model or a charging circle becauseour approach does not depend on the characteristics of theanalysis model The modeling results are shown in Figure 7As shown the charging efficiency of the MPPT circuitincreases with the increasing of the supercapacitor voltagewhen the supercapacitor voltage is smaller than 18 V anddecreases slowly as the voltage goes larger than 18 V The
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
International Journal of Distributed Sensor Networks 7
0 05 1 15 2 25 30
20
40
60
80
100
Supercapacitor voltage (V)
223 Wm2 55∘C 79 Wm2 35∘C48 Wm2 32∘C173Wm2 40∘C
113Wm2 37∘C Simulated
MPP
T in
put e
ffici
ency
()
Figure 7 Measurements and a simulation of a MPPT circuitcharging efficiency
1 15 2 2540
50
60
70
80
90
100
Supercapacitor voltage (V)
Disc
harg
ing
effici
ency
()
SimulatedNCP1402LTC3401
Figure 8 Discharging efficiency of NCP1402 and LTC3401
variation trend of the efficiency is similar to the results of [11]Moreover our model is also quite accurate (the relative erroris no more than 5 when the irradiance is low)
Figure 8 shows discharging efficiencies of two commonlyused DC-DC converter chips (NCP1402 [22] and LTC3401[21]) and Figure 9 shows the leakage of a 10 F and a 100 Fsupercapacitors We also model the efficiencies of those twochips and the leakage of a 100 F supercapacitor based onthe measurements As shown the discharging efficienciesand the leakage both increase with the increasing of thesupercapacitor voltage and the models are also of highaccuracies (the relative error is no more than 2)
Figure 10 shows the solar profile of three common winterdays in Ashland [20] The solar radiation is collected once
1 15 2 25 30
5
10
15
20
25
Supercapacitor voltage (V)
Leak
age p
ower
(mW
)
10F100FSimulation of 100F
Figure 9 Leakage of a 100 F and a 10 F supercapacitor
0 20 40 600
50
100
150
200
Time (hour)
Sola
r pow
er (m
W)
Figure 10 Solar profile of 3 days
0 02 04 06 08 10
5
10
15
Duty cycle
Cum
ulat
ed ac
tive t
ime (
hour
)
12
34
Figure 11 Cumulated active time of the fixed duty cycle scheme
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
8 International Journal of Distributed Sensor Networks
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 12 Simulation results under condition 1
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 13 Simulation results under condition 2
every 5 minutes and has been converted into the power thatcan be harvested by the solar panel
We evaluated two sets of data under four conditionsMPPT NCP1402 and a 100 F supercapacitor were used incondition 1 direct connectionNCP1402 and a 100 F superca-pacitor were used in condition 2MPPT LTC3401 and a 100 Fsupercapacitor were used in condition 3 and direct connec-tion LTC3401 and a 100 F supercapacitor were used in con-dition 4 In all the four conditions 119881startup = 1 V 119863min = 1119863max = 100 and we ignored the influence of temperatureand the prediction error of the solar radiationΔ119881Δ119863 and 120575are 002V 1 and 001 VThe prediction interval was set to beone dayΔ119879 andΔ119905were 30minutes and 30 seconds Figure 11shows cumulated active time of the fixed duty cycle scheme
under these four conditions As shown the cumulated activetime increases with increasing duty cycle and decreases aftersome duty cycle The reason is that energy surplus is largewhen the duty cycle is low and high duty cycle leads to lowworking voltage and inefficiency Figures 12 13 14 and 15show the supercapacitor voltage and cumulated active timeof efficiency-aware leakage-aware and the fixed duty cyclescheme over 72 hours under these four conditions The fixedduty cycles were set to 076 045 08 and 051 where thefixed duty cycle scheme can achieve themax cumulated activetime Table 1 shows the numerical results The results revealthat our algorithms can achieve 56 more cumulated timethan leakage-aware and 60more cumulated time than fixedduty cycle scheme In Figures 12(a) 13(a) 14(a) and 15(a) the
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
International Journal of Distributed Sensor Networks 9
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 14 Simulation results under condition 3
0 20 40 60
0
05
1
15
2
25
3
Time (hour)
Capa
cito
r vol
tage
(V)
Leakage-awareFixed duty cycleEfficiency-aware
(a) Supercapacitor voltage
0 20 40 600
5
10
15
20
Time (hour)
Cum
ulat
ed ac
tive t
ime (
hour
)
Leakage-awareFixed duty cycleEfficiency-aware
(b) Cumulated active time
Figure 15 Simulation results under condition 4
supercapacitor voltages of our algorithms at 24th 48th and72nd hour are 15 V compared with 125V of leakage-awareand 1V with fixed duty cycle scheme It illustrates that ouralgorithms perform better in terms of sustainable operation(eg nodes never run out of energy in their supercapacitors)It worth noting that leakage-aware uses leakage as the onlyfactor in determining nodesrsquo life while a practical one shouldconsider the minimum requirements of the application aswell as leakage
Figure 16 shows the results for the data rate determinationproblems under condition 1 The solar profile of the first daywas used as the energy input for both nodes A and B andlog(sdot) was used as the utility function of data rate (119880(sdot)) Weassumed that both 119890
119905119909and 119890119903119909are 50 nJbit
6 Conclusion
In this paper we study how to optimize the energy efficiencyof photovoltaic-supercapacitor systems for sustainable nodeoperations in solar-powered wireless sensor networks Basedon realistic power model of every hardware componentwe present energy-aware the first duty cycling frameworkthat maximizes the energy utilization efficiency of the wholephotovoltaic-supercapacitor system We consider all possi-ble energy losses in the energy conversion process (charg-ing discharging and leakage) and model all the powermodels of a commonly used photovoltaic-supercapacitorenergy systems We have proposed a general duty cyclingoptimization problem and associated efficient algorithms
10 International Journal of Distributed Sensor Networks
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
to solve the problem Numerical results show that ourapproach performs better than fixed duty cycling schemesand leakage-aware [4] a state-of-art duty cycling scheme forphotovoltaic-supercapacitor systems As efficiency-aware ismodel-independent it can be used in most of photovoltaic-supercapacitor energy systems with predictable harvestingenergy for local power management or to meet other QoSrequirements in wireless sensor networks
References
[1] A Kansal J Hsu M Srivastava and V Raqhunathan ldquoHar-vesting aware power management for sensor networksrdquo inProceedings of the 2006 43rd ACMIEEE Design AutomationConference pp 651ndash656 September 2006
[2] C Park and P H Chou ldquoAmbiMax autonomous energyharvesting platform for multi-supply wireless sensor nodesrdquo inProceedings of the 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications andNetworks (SECON rsquo06)vol 1 pp 168ndash177 September 2006
[3] W S Wang T OrsquoDonnell N Wang M Hayes B OrsquoFlynn andC OrsquoMathuna ldquoDesign considerations of sub-mw indoor lightenergy harvesting for wireless sensor systemsrdquoACM Journal onEmerging Technologies in Computing Systems vol 66 no 2 pp1ndash6 2008
[4] T Zhu Z Zhong Y Gu T He and Z L Zhang ldquoLeakage-aware energy synchronization for wireless sensor networksrdquo inProceedings of the 7th ACM International Conference on Mobile
Systems Applications and Services (MobiSys rsquo09) pp 319ndash332ACM Krakow Poland June 2009
[5] G W Challen J Waterman and M Welsh ldquoPoster abstractintegrated distributed energy awareness for wireless sensor net-worksrdquo in Proceedings of the 7th ACM Conference on EmbeddedNetworked Sensor Systems (SenSys rsquo09) pp 381ndash382 ACMBerkeley Calif USA November 2009
[6] K-W Fan Z Zheng and P Sinha ldquoSteady and fair rate alloca-tion for rechargeable sensors in perpetual sensor networksrdquo inProceedings of the 6th ACM Conference on Embedded NetworkSensor Systems (SenSys rsquo08) pp 239ndash252 ACM Raleigh NCUSA November 2008
[7] M Gorlatova A Wallwater and G Zussman ldquoNetworkinglow-power energy harvesting devices measurements and algo-rithmsrdquo in Proceedings of the IEEE International Conferenceon Computer Communications (INFOCOM rsquo11) pp 1602ndash1610April 2011
[8] L Huang and M J Neely ldquoUtility optimal scheduling inenergy harvesting networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) p 21 ACM Paris France May 2011
[9] I C Paschalidis and RWu ldquoRobust maximum lifetime routingand energy allocation in wireless sensor networksrdquo vol 2012Article ID 523787 14 pages 2012
[10] C Alippi and C Galperti ldquoAn adaptive system for opimalsolar energy harvesting in wireless sensor network nodesrdquo IEEETransactions on Circuits and Systems I vol 55 no 6 pp 1742ndash1750 2008
[11] D Brunelli L Benini CMoser and LThiele ldquoAn efficient solarenergy harvester for wireless sensor nodesrdquo in Proceedings of theDesign Automation and Test in Europe Conference (DATE rsquo08)pp 104ndash109 Munich Germany March 2008
[12] D Dondi A Bertacchini D Brunelli L Larcher and L BeninildquoModeling and optimization of a solar energy harvester systemfor self-powered wireless sensor networksrdquo IEEE Transactionson Industrial Electronics vol 55 no 7 pp 2759ndash2766 2008
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
International Journal of Distributed Sensor Networks 11
[13] Y Kim N Chang Y Wang andM Pedram ldquoMaximum powertransfer tracking for a photovoltaic-supercapacitor energy sys-temrdquo in Proceedings of the 16th ACMIEEE International Sym-posium on Low-Power Electronics and Design (ISLPED rsquo10) pp307ndash312 August 2010
[14] V Raghunathan A Kansal J Hsu J Friedman and MSrivastava ldquoDesign considerations for solar energy harvestingwireless embedded systemsrdquo in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks(IPSN rsquo05) pp 457ndash462 April 2005
[15] D R Cox ldquoPrediction by exponentiallyweightedmoving avera-ges and related methodsrdquo Journal of the Royal Statistical SocietyB vol 23 no 2 pp 414ndash422 1961
[16] C Bergonzini D Brunelli and L Benini ldquoComparison ofenergy intake prediction algorithms for systems powered byphotovoltaic harvestersrdquoMicroelectronics Journal vol 41 no 11pp 766ndash777 2010
[17] K S P Kiranmai and M Veerachary ldquoMaximum power pointtracking a PSPICE circuit simulator approachrdquo in Proceedingsof the 6th International Conference on Power Electronics andDrive Systems (PEDS rsquo05) vol 2 pp 1072ndash1077 December 2005
[18] A Kansal J Hsu S Zahedi and M B Srivastava ldquoPowermanagement in energy harvesting sensor networksrdquo ACMTransactions on Embedded Computing Systems vol 6 no 4article 32 2007
[19] Y Choi N Chang and T Kim ldquoDC-DC converter-awarepower management for low-power embedded systemsrdquo IEEETransactions on Computer-Aided Design of Integrated Circuitsand Systems vol 26 no 8 pp 1367ndash1381 2007
[20] University of Oregon Solar Radiation Monitoring LaboratoryldquoSolar datardquo httpsolardatuoregoneduSelectArchivalhtml
