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Montecucco, A., and Knox, A. (2015) Maximum power point tracking converter based on the open-circuit voltage method for thermoelectric generators. IEEE Transactions on Power Electronics, 30 (2). pp. 828-839. ISSN 0885-8993 Copyright 2014 The Authors http://eprints.gla.ac.uk/92833 Deposited on: 13 November 2014

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828 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 30, NO. 2, FEBRUARY 2015

Maximum Power Point Tracking Converter Basedon the Open-Circuit Voltage Method for

Thermoelectric GeneratorsAndrea Montecucco, Student Member, IEEE, and Andrew R. Knox, Senior Member, IEEE

AbstractThermoelectric generators (TEGs) convert heat en-ergy into electricity in a quantity dependent on the temperaturedifference across them and the electrical load applied. It is criticalto track the optimum electrical operating point through the useof power electronic converters controlled by a maximum powerpoint tracking (MPPT) algorithm. The MPPT method based onthe open-circuit voltage is arguably the most suitable for the linearelectrical characteristic of TEGs. This paper presents an innova-tive way to perform the open-circuit voltage measure during thepseudonormal operation of the interfacing power electronic con-verter. The proposed MPPT technique is supported by theoreticalanalysis and used to control a synchronous BuckBoost converter.The prototype MPPT converter is controlled by an inexpensive mi-crocontroller, and a lead-acid battery is used to accumulate theharvested energy. Experimental results using commercial TEGdevices prove that the converter accurately tracks the maximumpower point during thermal transients. Precise measurements inthe steady state show that the converter finds the maximum powerpoint with a tracking efficiency of 99.85%.

Index TermsBuck-Boost, converter, dcdc, maximum powerpoint tracking (MPPT), synchronous, thermoelectric (TE), ther-moelectric generator (TEG).

I. INTRODUCTION

THERMOELECTRIC generators (TEGs) are physicallyand electrically robust semiconductor devices able to con-vert thermal energy into electrical energy, provided that a tem-perature gradient is maintained across them, exploiting theSeebeck effect [1]. In the steady state, they can be modeled by adc voltage source in series with an internal resistance, thereforefor the theorem of maximum power (MP) transfer if the loadmatches the internal resistance then MP is produced. A descrip-tion of the structure and functioning of a typical thermoelectric(TE) device is presented in Section II-A.

Due to relatively high cost and low efficiencyaround 5%the use of TEGs has been in the past restricted to specializedmedical, military, remote, and space applications [2]. However,

Manuscript received 16 Dec. 2013; revised 4 Feb. 2014; accepted 10 Mar.2014. Date of publication March 21, 2014; date of current version October7, 2014. This work was supported by the Engineering and Physical SciencesResearch Council under Grant EP/K022156/1 (RCUK). Recommended for pub-lication by Associate Editor M. Vitelli.

The authors are with the School of Engineering, University of Glasgow,Glasgow G12 8LT, U.K. (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2014.2313294

in recent years, an increasing environmental issues and energycost have motivated research into alternative commercial meth-ods of generating electrical power. TEs is one of several thathas emerged as a viable source of electricity [3]. Moreover,the efficiency of TEGs is improving [4], [5] and the devicecost is decreasing. Consequently, TEGs can now be success-fully employed to harvest the heat energy rejected by otherprocesses (automotive [6], [7], stove [8][11], geothermal [12],or power stations [13], [14]), to power sensors [15][18] or toincrease the system efficiency in symbiotic applications [20].Mass-produced energy scavenging applications such as exhaustgas systems are likely to lead to a further reduction of TE devicecost [21]. In applications of waste heat harvesting, the inputthermal power is essentially free; therefore the low conversionefficiency is not a serious drawback per se, but it is important tomaximize the power obtained from the device utilized in orderto minimize the cost per Watt produced.

The magnitude of the TEGs open-circuit voltage is directlyproportional to the temperature difference, and like with solarcells a convenient number of TEGs can be connected in series orparallel in order to achieve desired levels of voltage and current.Power electronic converters are very often used to interfaceTEGs to the required load. The choice of converter typologydepends on the output and input voltages; as an example, forconnection to dc microgrids a high step-up gain converter isrequired [22], while for connection to a 12-V car battery a Buckor BuckBoost type can be used. This work uses a synchronousBuck-Boost to guarantee a wide input voltage range and con-sequently harvest power from the TEGs over a wide range ofoperating temperatures.

TEGs are often employed in dynamic environments withtime-varying temperature differences, e.g., cars exhaust gassystems [19], [23], therefore it is of great importance to quicklyand precisely adjust the best electrical operating point in order toalways maximize the harvested power. It is necessary to controlthe power electronic converters with a maximum power pointtracking (MPPT) algorithm that matches the virtual load seenby the TEG to its actual internal resistance by changing the dutycycle of the converter. Ideally, each TEG should be indepen-dently electronically controlled but this would greatly increasethe number of MPPT power electronic converters needed andadversely affect the cost of implementing the system. As a con-sequence, TEGs are often electrically interconnected in seriesand/or parallel to form arrays [24]. This leads to the formationof what is called a distributed MPPT (DMPPT) subsystem inwhich each TEG arrays electrical operating point is controlled

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MONTECUCCO AND KNOX: MAXIMUM POWER POINT TRACKING CONVERTER BASED ON THE OPEN-CIRCUIT VOLTAGE METHOD 829

Fig. 1. Blocks diagram illustrating the fundamental structure of the proposedsystem.

independently in a similar way as for photovoltaics (PV) sys-tems [25]. An additional centralized MPPT function could berequired if an inverter is employed for grid connection, thusforming an hybrid MPPT system [26].

In the literature, the most used MPPT algorithms for TEGsare the Perturb & Observe (P&O) [27][29] and the incrementalconductance (INC) [30]. These MPPT algorithms have origi-nally been developed for PV systems, in which the relationshipbetween voltage and current is logarithmic. On the contrary, inTEGs, the electrical characteristic is linear:

VMP =VOC2

and IMP =ISC2

(1)

where VMP and IMP are the voltage and current at the maximumpower point, VOC is the open-circuit voltage and ISC is the short-circuit current. MPPT algorithms that use this relationship eithermeasure the open-circuit voltage [17], [31], [32] or the short-circuit current [22]; they provide a number of advantages overthe aforementioned methods:

1) measurement of only one parameter (voltage or current);2) lower numerical computational requirements;3) no steady-state oscillation (P&O) or error (INC).These methods have the disadvantage that no energy flows

from the TEG to the converter during the sampling time becausethe converter must be disconnected from the TEG to allow forthe measurement of VOC or ISC . In the literature, Laird et al. [33]compared P%O, INC, and fractional ISC .

This paper proposes an innovative open-circuit voltage mea-surement technique, described and analyzed in Section III, thatcan be undertaken during the normal switching of the converter,with a minimal reduction in collection efficiency.

Fig. 1 shows the block diagram of the proposed system, wherethe TEG array is connected to the input of a synchronous nonin-verting BuckBoost converter, which is described in Section IV.A microcontroller implements the MPPT algorithm controllingthe transfer of energy from the TEGs and driving the converterMOSFET switches through gate drivers. The load is representedby a battery.

The proposed MPPT prototype converter is tested with realTEGs, both in steady state and under thermal transients; theexperimental results are presented in Section V, before drawingthe conclusions.

II. TE POWER GENERATING SYSTEMThis Section first describes the structure and functioning of

a typical TE device; second, it presents the test rig used in the

Fig. 2. Mechanical drawing illustrating the components of a TE device andthe physical phenomena happening during power generation.

experiments and finally the performance of the TEGs used inthe experiments is analyzed.

A. TE Power Generating DeviceA TE device is composed of n- and p-doped semiconductor

pellets electrically connected in series and thermally in parallel.In the power generation mode, every pellet produces a voltagedifferential when a temperature gradient T is established at itssides, thanks to the Seebeck effect [1]; the voltage magnitude islinearly dependent on T and the Seebeck coefficient , whichis a property of the material used and varies with temperature.As shown in Fig. 2, each voltage adds up thanks to the seriesconnection and when a load is connected to the TEGs terminals,current flows through the device, because both electrons andholes are moved from the hot to the cold side by the flow of heat.This current flow produces heat by Joule heating and pumpsadditional heat from the hot to the cold side because of the Peltiereffect, which is considered a parasitic effect in power generation;in fact it effectively increases the thermal conductivity of thedevice. A high load current amplifies the Peltier effect, whichincreases the effective thermal conductivity of the device whichin turns decreases the temperature difference T [34].

In the steady state, a TEG can effectively be modeled by avoltage source VOC in series with an internal resistance Rint[35], [36], which slightly varies with the average temperature ofthe TEG, affecting the slope of the VI curve.

The cross-sectional area of the pellets greatly influences theinternal resistance and the currentvoltage rating of the device.A module with wide pellets can fit a small number of pellets,therefore it will have relatively small output voltage and in-ternal resistance, but high output current [37]. As an example,Table I shows how the size and number of pellets influencesthe currentvoltage ratings in two TEGs offered by EuropeanThermodynamics Ltd.

The most commonly used material is Bismuth Telluride(Bi2Te3), however other materials like Silicides, Skutterudites,Oxysulphides, TiS, NiCrS, and Cobalt oxides are being de-veloped for automotive applications over a range of tempera-tures [38][41]. These materials have a variety of issues (e.g.,


TABLE ICOMPARISON OF SOME GEOMETRICAL AND ELECTRICALPARAMETERS BETWEEN TWO TEG DEVICES OFFERED BY

EUROPEAN THERMODYNAMICS LTD

Fig. 3. Schematic of the mechanical test rig used in the experiments.

they are difficult to form electrical connections to, they arechemically reactive at high temperatures and expensive to man-ufacture) which still have to be overcome before their large-scalecommercial deployment is viable.

B. Mechanical Test RigThe test rig used in this work is designed to test TEG perfor-

mance providing accurate repeatable measurements. A completedescription of the system can be found in [42]. This test appa-ratus is able to independently control the mechanical load andthe temperature difference across each of the four TEG channelsthat can be used at the same time. Fig. 3 illustrates the schematicof one channel. The TEG device is sandwiched between a hotblock and a cold block. The former contains a high-temperaturehigh-power heater powered by a dc power supply, while thelatter is water-cooled by a chiller unit. The output of the TEGcan be connected to an electronic load or to any other desiredload. A load cell measures the mechanical pressure over theTEG and thermocouple sensors are fitted through the copperblocks touching the TEGs hot and cold faces, in order to obtainprecise temperature measurements. Agilent VEE Pro is a graph-ical programming tool for automated control of the laboratoryequipment. A VEE Pro program operates all the instrumentsand precisely controls the temperature difference across the TEdevices to the desired value. Using such equipment, it is pos-sible to do an accurate electrical characterization of the TEGunder test, sweeping the load at different values, all at the sametemperature difference.

C. TEGs Electrical CharacteristicIn the experiments presented in Section V of this paper, three

TEG devices from European Thermodynamics Ltd. (product

Fig. 4. Experimental electrical characterization for the TEG module # 2.The gray dots in the curves represent experimental data points. T =100 C, 150 C, 200 C, clamped at 2 kN/1.25 MPa.

code GM250-127-14-10) have been used. Each one was charac-terized separately at three different temperature gradients T :100 C, 150 C, and 200 C. Every test was performed imposing1.25MPa of mechanical pressure onto each TEG, which corre-sponds to 209 kg on a surface of 40 40mm2 . Fig. 4 plots theoutput voltage and power versus current for one of the TEGs(TEG#2).

Table II lists the performance data of the three TEGs. Themaximum deviation in performance between the three devicesstands at less than 5% for power production; this differencemay be due to manufacturing tolerances, contact resistance mis-match, or measurement accuracy. However, this performancevariation will not influence the MPPT converter evaluation, asit will be explained shortly. These data are used to formulate amathematical characterization using a similar technique to thatexplained in [43]. Voltage and power are calculated as a functionof the current load and temperature difference.

In the steady state, it can be written that

Vload = VOC RintIload . (2)The open-circuit voltage is proportional to the Seebeck coeffi-cient (VOC = T ), which varies depending on the Thomsoncoefficient [44]. A 2nd-order polynomial fitting technique hasbeen used to model the variation of VOC and Rint with T .Using a similar technique to [43], (2) can now be written as

Vload = (aT 2 + bT + c) (dT 2 + eT + f)Iload(3)

where a, b, c, d, e, and f are constant coefficients, different foreach TEG, obtained from the experimental data. Even if theperformance variation for the three devices used is up to 5%,the actual expected performance is calculated for each TEGindividually.

Using (3), it is possible to replicate the electrical character-istics of the TEGs used, after obtaining the necessary param-eters from the experimental data. Fig. 5 shows the resulting


TABLE IIPERFORMANCE PARAMETERS FOR THE THREE TE MODULES USED IN THE EXPERIMENT

Fig. 5. Mathematical electrical characterization for the TEG module # 2.

mathematical electrical characterization for TEG# 2. As itcan also be appreciated from a comparison with Fig. 4, theaverage deviation between the mathematically derived valuesand the experimental data is always less than 1.5%. This meansthat it is now possible to independently predict the output fromeach of the three TEGs at any temperature difference with highconfidence, even when they are at different thermal operatingpoints. This formulation is used to compare the performance ofthe MPPT converter in Section V.

III. MPPT METHOD

It was explained in Section I that the method usually called(fractional) open-circuit voltage consists in measuring theTEGs open-circuit voltage and then setting the at-load operat-ing voltage at half of VOC . This method normally requires theconverter to be disconnected for a certain duration to allow forthe converters input capacitors to be charged up to VOC [33];during such time no power is harvested. In order to meet theRMS input current requirements, input capacitors might be inthe order of tens of microfarad, which means that they mayneed hundreds of microsecond to charge up to VOC , dependingon Rint . Sometimes, an additional series switch is needed todisconnect the TEGs from the converter [17], [32]. This switchmight need a high-side gate driver with continuous conductiontime for long periods. This switch introduces additional I2Rlosses when it is closed, and its use interrupts the normal oper-ation of the converter, thus creating a transient event every timethe VOC measurement is taken. The method that we have alreadypresented at ECCE12 [45] reduces these drawbacks. Following

Fig. 6. Schematic drawing of the components required for the proposed MPPTtechnique.

is a description of this method and a theoretical analysis of itsperformance.

A. Open-circuit Voltage MPPT MethodThis section describes an innovative technique to measure

the open-circuit voltage of a TEG, which can be used withany converter topology derived from the Buck or Buck-Boosthaving a switch at its input. The basic circuit schematic, whichhighlights the necessary components required, is provided inFig. 6. A TEG is connected to the input of a Buck or BuckBoost derived converter. The converters input capacitors Cinare connected to ground through the switch Mcap . The high-side switch M1 represents the input switch of a Buck or BuckBoost converter, while the remaining converters componentsare generically represented by the following box connected tothe output capacitors Cout .

To aid explanation of how the voltage measurement isachieved, a timing diagram for the operation of the aforemen-tioned switches is provided in Fig. 7. In the next description, tonand to are the high and low states of pulse width modulation(PWM1), respectively. Under normal operation, Mcap is closedand Cin contributes to the pulsating input current required bythe converter during ton . When the open-circuit voltage mea-surement is required, Mcap gets opened. The bottom part ofFig. 7 provides a zoomed-in view of what happens in this sit-uation. During to , M1 is open and the TEG is momentarilydisconnected from the converter. The current cannot flow intoCin , hence the potential at the TEGs terminals rises to the open-circuit voltage VOC , typically within tens of nanoseconds [27].The microcontroller is timed to measure VTEG during to whilethe converter is still operating in a pseudonormal state: as it willbe analyzed in the next section, both the TEG and Cin are stillproviding power to the converter during ton . The open-circuitmeasurement process is repeated every Tmeas , which is a design


Fig. 7. Timing diagram explaining how the open-circuit voltage measurementis achieved. The bottom part of the image provides a zoomed-in view of themeasurement operation, which takes place every Tmeas .

parameter that depends on the thermal time constant of the TEGsystem used. It is usually chosen based on experience and it istypically between 0.1 and 1 s. In between VOC measurements,a digital control loop keeps on adjusting the converters dutycycle to maintain VTEG at half of VOC .

This VOC measurement technique is considerably faster thandisconnecting the converter (by keeping PWM1 low) until Cinreaches VOC . Also, it is more accurate because when the TEG iskept at open circuit the Peltier effect is null, therefore the tem-perature difference increases slightly, and with it VOC , leadingto a wrong VOC value [46]; this means that the converter wouldchoose a slightly higher operating voltage. On the contrary, suchproblem does not occur using the proposed MPPT method be-cause the TEG is left at the open circuit for less than a switchingperiod.

B. Theoretical Analysis of MPPT EfficiencyThis section presents a theoretical analysis to quantify the

losses introduced by the additional switch Mcap in series withCin , and by the VOC measurement technique used. In order todo so, it is necessary to calculate the RMS current IC i n R M S flow-ing into the input capacitors and to understand the convertersbehavior in response to the measurement technique.

Without loss of accuracy, we can consider either a Buck orBuckBoost converter for what concerns the input capacitorsRMS current calculations.

Fig. 8. Plots of the currents in a Buck or Buck-Boost derived converter withoutMcap (values are generic): in the inductor (IL blue, and ILAV G orange); in theswitch (IS red) and average input current (Iin light blue); in the input capacitor(IC in green).

The input capacitors are important because they store addi-tional energy from the input source when the switch M1 is openduring the off-time to of the switching period Tsw , and provideit to the load when M1 closes. The input current is pulsating,and the amount of current that the input source can provide islimited by its series resistance, which is usually fairly high (onehalf to several ohms) in TEGs.

Referring to the plots in Fig. 8, the current IS (in red) flowsin the converters switch only during the on-time ton of theswitching period Tsw , while it stays at zero for the rest of Tsw .During to , the input source charges Cin , which effectivelyfilters an ac current. The input current Iin (in light blue) can bewritten as IS + IC in or as the average of IS over Tsw .

Let us assume that the MPPT converter is setting the cor-rect MP point at the TEGs output, so that the average inputcapacitors voltage is VMP = VOC/2. Considering a small volt-age ripple on Cin [47], during to , Cin is charged by the cur-rent IC in , o f f = VOC/2R, in which R = Rint + ESR, sum of theTEGs internal resistance and the equivalent series resistance(ESR) of the input capacitors. We can calculate the RMS ofIC in , o f f as

I2C in , o f f R M S= DI2in =

DV 2OC4R2

(4)

where D is the duty cycle of the converter and D = (1D).For the trapezoidal segment of iC in (t) during ton , the RMS

current into Cin is

I2C in , o n R M S=

D

3

[(Iin ILm in )2 + (Iin ILm a x )2 +

+ (Iin ILm in ) (Iin ILm a x )]. (5)

For both Buck and BuckBoost converters IL = Iin/D; there-fore, we can write that Iin IL = Iin(1 1/D) = DIin/D.Also, ILm in = IL IL/2 and ILm a x = IL + IL/2. Using


these relationships in (5) and knowing that for both Buck andBuckBoost converters IL = Vo u t D

fsw L

, we obtain

I2C in , o n R M S= D2

[I2inD

+DV 2out

12f 2swL2

](6)

where iC in (t) is a periodic waveform composed of two orthog-onal piecewise segments [48], therefore its RMS value can beobtained from (4) and (6):

IC in R M S =

D

[I2inD

+DDV 2out12f 2swL2

]. (7)

The power dissipated on the low-side switch Mcap in series withthe input capacitors is

PM c a p = ronI2C i n R M S

(8)where ron is the on-resistance of the switch used. Section IV-Bprovides the losses value for the converter used. The switchingand body diode losses of Mcap are almost irrelevant becausethey occur for a few microsecond every Tmeas .

Referring to Figs. 6 and 8, let us now consider what happenswhen Mcap is switched open. In this case, the TEGs can supplypower to the converter only during ton , because during toM1 is open and current cannot flow into Cin , hence the TEGsgo to the open circuit. During ton , the internal resistance Rintlimits the quantity of current that can flow from the TEGs, andthe body diode of Mcap is forced into conduction so that Cinsupplements the additional current required by the converter andslightly discharge.

After each PWM period Tsw , the voltage across Cin de-creases because when Mcap is open the input capacitor can-not be charged as it would normally happen during to . Pro-vided that Mcap is left open for just a few cycles, the capac-itance of Cin is usually enough to guarantee that vin(t) doesnot decrease significantly; the following calculations are usefulto estimate how much the voltage on the capacitor sags dur-ing the VOC measurement. The initial energy stored in Cin isEC in 0 = CinV

2C in 0/2. To derive the worst-case scenario, let us

consider that ILm in Iin 0 and let us calculate the energyremoved from Cin during the ton of one switching cycle:

E1P W M = to n

0vC i n (t)iC i n (t) dt

= to n

0

(ILm in Iin + IL

t

ton

)Vin dt

= VinDTsw (1D)IL = PinDTsw (9)where we considered vin(t) constant at Vin . This slightly over-estimates the calculation of the voltage drop because after everyTsw vin(t) decreases.

The final energy stored in Cin is

EC in f = EC in 0 nPWME1P W M =12CinV

2C i n f

(10)

where nPWM is the number of PWM cycles elapsed with Mcapopen. From (10), it is possible to obtain VC i n f , which is thevoltage on Cin at the end of the VOC measurement procedure.

Fig. 9. Schematic of the complete system proposed.

IV. MPPT CONVERTERThis section presents the noninverting synchronous Buck

Boost dcdc converter, whose schematic diagram of the com-plete system is shown in Fig. 9. A generic TEG is representedby a voltage source VOC , an internal resistance Rint , and a par-asitic inductance Lp . An innovative snubber, described in theSection IV-A, is connected across the input of the synchronousBuckBoost converter to suppress overvoltage transients. Theconverter supplies power to a battery and to an auxiliary elec-tronic load. A microcontroller, measuring the input and outputvoltages, computes the MPPT algorithm and controls the gatedrivers of the converters MOSFETs. The power stage is de-scribed in Section IV-B.

A. Overvoltage SnubberWhen a TEG is suddenly disconnected from the load, it goes

to the open circuit after a very fast underdamped oscillationwith frequency usually in the order of megahertz [27]. Thisis due to the fact that a parasitic inductance LP is built up inthe many solder connections between pellets in the TEG, inthe cables from the TE device to its load, and in the printed-circuit board (PCB)s tracks. Such parasitic inductance forms aresonating tank with the parasitic capacitances of the circuit andit is damped by the TEGs internal resistance Rint .

In the circuit of Fig. 6, when Mcap is closed and M1 opensat the beginning of to , Iin finds an alternative path into Cin ,which is a fairly big capacitance. This cannot happen whenMcap is open, hence the TEG is suddenly open-circuited. Thecurrent in Lp cannot stop flowing instantaneously and its energyis dissipated in the ringing with the parasitic capacitances of thecircuit, damped by Rint , i.e., an RLC circuit. The decrease ofIin reverses the voltage across the parasitic inductance, so that avoltage considerably greater than VOC appears at the convertersinput.

Fig. 10 shows an experimental switching transient test un-dertaken on one of the TEG modules used. At the beginningof the transient, t0 , the voltage sharply rises from the operat-ing voltage Vload to Vmax ; this increases the switching tran-sition losses on M1 and it also requires M1 to have a higher


Fig. 10. TEGs voltage and current during a switching transient from at-loadoperation to open circuit.

maximum drainsource voltage rating. Due to the RLC oscilla-tory nature, when VTEG reaches Vmax the inductor current (inblue in Fig. 10) reverses and flows into the TEG; the Peltiereffect is reversed and the Joule heating is of similar magnitude,therefore it is not a problem for the TEG. The maximum voltagethat can be applied to a TE device in Peltier cooling mode ishigher than VOC and a TEG can stand high levels of Joule heat-ing; also, TE devices do not contain voltage insulating layers orother materials susceptible to voltage stress.

LP can be approximately calculated from Fig. 10. At the endof ton , the current Iin(ton) flows through LP . In order to avoidambiguity in the equations, Iin(ton) will be written Iin , ton . Theenergy contained into LP is

ELP =12LP I

2in,to n . (11)

This energy is completely transferred to the parasitic capacitancewhen VTEG = Vmax and Iin = 0. The basic inductor relation-ship vL (t) = Ldi(t)dt can be approximated for LP to

Vmax Vload = LP Iin,to ntmax t0 (12)

where tmax is the time at which VTEG = Vmax . LP can be cal-culated from (12) using the values obtained from the waveformsof Fig. 10. However, it should be noted that the rise of VTEGto VOC is not linear. The linear region is approximately be-tween 20% and 80% of the increase. Dividing T = tmax t0in three intervals where the middle interval T2 correspondsto the linear region, we can see that T2 (T1 + T3)/4.As a consequence, we can apply a correction factor to thecalculated value for LP , which now becomes

LP =T (Vmax Vload)

4Iin,to n. (13)

In order to damp the overvoltage, while still achieving a fasttransient of the TEGs voltage to the open circuit, a capacitor CSis added across the TEGs terminals. CS needs to be sufficientlylarge so that the energy transferred from LP does not charge itto much more than VOC , but small enough to let VTEG quicklysettle to VOC . The value of such capacitor can be chosen usingthe energy calculated in (11). Before the transient CS is already

Fig. 11. Experimental comparison of TEGs voltage and current during aswitching transient from at-load operation to open circuit, when using a dampingcapacitor only or with the proposed DCD snubber.

charged at Vload , with a stored energy 1/2CSV 2load . If we wantall the energy in LP to be transferred to CS when it reachesVOC , then the energy balance states that

12LP I

2in,to n =

12CS

(V 2OC V 2load

). (14)

When working at MP point VOC = 2Vload , therefore (14) leadsto CS = LP /3R2int . However, given the wide range of Vload(depending on the temperature difference), the choice of CS isby necessity a compromise. Our experiments have shown thefollowing solution to be the most satisfactory:

CS =LPR2int

(15)

which corresponds to removing the dc offset Vload in CS from(14), which becomes LP I2in,to n = CSV 2load . It is convenient todesign the snubber capacitor CS for IMP at Tmax .

Next, these results are applied to the experimental case ofFig. 10, in which T = 0.37s, Vmax Vload = 18 V andIin(ton) = 2.17 A. Using (11), LP is estimated at 767 nH, henceusing (15) the required snubber capacitor is 174 nF.

Fig. 11 shows the improvements to the TEGs transient re-sponse when adding a 220-nF ceramic capacitor (commercialvalue closest to 174 nF), during the same operating conditions.Also, two diodes, DS1 and DS2 , are used to add some dampingdue to their conduction resistances, and to provide a Schmitttrigger function because of their voltage drops. The resultingcircuit is effectively a diode capacitor diode (DCD) snubber,which suppresses overvoltages storing energy during to andreleasing it back during ton . Fig. 11 also includes results usingthe proposed DCD snubber circuit. The overvoltage is reducedfrom 18 to 1 V in both cases. Experimental and simulation re-sults have proven that the settling time is shorter when the twodiodes are used. By way of comparison, the settling time is re-duced from 2.5 to 2.09s with the capacitor and to 1.48s withthe proposed DCD snubber.


It is a design choice to use smaller values for the snubbercapacitor in order to reach a compromise between speed oftransient response and magnitude of overvoltage.

As an alternative, it would not be possible to use a tran-sient voltage suppressor, because the open circuit voltage varies,therefore a constant breakdown voltage cannot be selected.

B. Synchronous Buck-BoostA noninverting synchronous Buck-Boost was chosen because

of its adaptability to working with a wide range of input voltages,smaller or greater than the output voltage, which is fixed bythe battery voltage. The common noninverting synchronousBuckBoost converter [49][52] uses four switches, however,to prevent the battery from discharging in case the converterruns in the discontinuous conduction mode, the output switch isin this work replaced by a Schottky diode.

A Microchip PIC16F microcontroller activates the gatedrivers with two 180 anti-phase PWMs, running at 78 kHz.The microcontroller measures the TEG voltage at the convertersinput and the batterys voltage Vb at the output. After measur-ing the open-circuit voltage VOC , the algorithm calculates theinitial PWMs duty cycle using the ideal relation: 2Vb/VOC =D/(1D). At every successive microcontrollers program it-eration, the input voltage Vin is measured and a digital controlloop keeps on adjusting the duty cycle to maintain Vin = VOC/2.In this way, the converter minimizes parasitic effects and dealswith changes in the battery voltage, e.g., load transients. Theconverter is intended to be used with the three TEG devices de-scribed in Section II, electrically connected in series, howeverit can be used with other TEGs with different VI characteris-tics (Iin,max = 5 A, Vin,max = 30 V, Prated = 35 W). The threeTEGs in series produce a maximum open-circuit voltage of27 V and the MP is approximately 30.4 W at VMP = 13.5 V andIMP = 2.25 A. Fig. 12 shows the converters PCB, which mea-sures 75 55 mm2 . The n-MOSFETs used are IPD036N04L,the power Schottky is VS-12CWQ03FN, and the inductor is15H (Isat = 14 A), the input capacitors are a total of 440F(50 V) and the output ones a total of 660F (25 V). Both inputand output capacitors were chosen based on their RMS currentcapabilities. Using the electrical values at maximum availableTEG power and with a battery voltage of 12 V, the maximumRMS current in the input capacitors is calculated from (6) to be2.62 A.

The MP loss on Mcap is 21 mW (from (8), assuming an on-resistance of 3.6 m). This corresponds to 10.5 mJ lost every500 ms. As a comparison, with the common fractional open-circuit technique that waits for the input capacitors to charge upto open circuit through the TEGs internal resistance ( 6),the RC time constant is RC = 2.64 ms. Waiting for 3 RC notharvesting 30 W equates to losing 237 mJ.

The converters electrical efficiency was tested with a powersupply in series with a fixed 6- power resistor and the resultsare listed in Table III. The efficiency is 92.6% when tested at30.4 W(13.5 V, 2.25 A) input. It must be noted that the MPPTtechnique presented in Section III can be used with any othersimilar type of converter.

Fig. 12. Image of the PCB of the MPPT converter.

TABLE IIIELECTRICAL PERFORMANCE OF THE SYNCHRONOUS BUCK-BOOST TESTED

WITH A POWER SUPPLY IN SERIES WITH A 6- POWER RESISTOR

The VOC measurement is performed every 500 ms and it lastsfor eight switching cycles Tsw , which corresponds to less than110s. Considering a PWM duty cycle of 50%, the converter isdisconnected from the TEGs for just 0.011% of the time.

Fig. 13 shows the converters input voltage and current dur-ing the VOC measurement. The converter is initially runningat 13.35 V, 2.07 A at the input. After 45s Mcap is switchedOFF therefore the input voltage goes to VOC , during to , afteran overshoot of less than 6 V when using a DCD snubber with100- nF ceramic capacitor. The ADC measurement starts 2safter the PWM goes low. It can be noted that during ton currentis drawn from the TEGs and that during the VOC measurementthe voltage across the input capacitors decreases from 12.86to 12.46 V as described by (10). The initial drop from 13.35to 12.86 V is due to the voltage drop across the body diode ofMcap .


Fig. 13. Converters input voltage and current during the measurement of theopen-circuit voltage.

V. EXPERIMENTAL RESULTS

The choice of using three TEGs is dictated by the needof testing the MPPT converter around its power rating andwith a relatively high maximum TEG voltage. As explained inSection II-C not only are the performances of the three devicesalmost identical, but the mathematical characterization guaran-tees the estimation of performance relative to each independentTEG device.

Three experiments were designed to test the steady state andtransient performance of the proposed MPPT converter. First,the steady-state performance is measured using TEGs. Next, asudden VOC transient is created by substituting the TEGs with apower supply in series with a power resistor. Finally, a thermaltransient was created in the test rig to analyze the tracking per-formance of the MPPT converter during continuously changingthermal operating conditions.

The PCB used is not equipped with a current sensor, thereforeit cannot be used for experimental comparison with other MPPTtechniques. However, where possible the obtained performanceare compared to results found in the literature. In all the experi-ments, a 12 V, 7Ah leadacid battery is used to accumulate thepower transferred through the converter. An electronic load wasconnected to prevent the battery from overcharging.

A. Steady-State PerformanceThe aim of this experiment is to compare the power ex-

tracted by the MPPT converter to the MP available from thethree TEMs, maintained at the same temperature difference.Three separate tests have been undertaken, each one select-ing a different thermal operating point, i.e., temperature gra-dient across the devices. The temperature gradients used areT = 100 C, 150 C, 200 C, which are the same used for theelectrical characterization of the devices in Section II.

When the three modules are electrically connected in series,their open-circuit voltages and internal resistances sum so thatthe resulting array can still be represented by a voltage sourcein series with an internal resistance and the MPP remains at half

TABLE IVCOMPARISON OF THE STEADY-STATE TRACKING PERFORMANCE OF THE MPPT

CONVERTER WITH THE MAXIMUM AVAILABLE POWER FROM THESERIES-CONNECTED ARRAY

VOC . The procedure to compare the electrical operating pointset by the converter to the MPP is the following:

1) Confirm that the actual series open-circuit voltagecorresponds to VOC ,S = VOC ,1 + VOC ,2 + VOC ,3 fromTable II.

2) Calculate the theoretical current for MP: IMP =VO C , S

2(R1 +R2 +R3 )3) Calculate the theoretical MP: Pmax = VMPIMP =

V 2O C , S4(R1 +R2 +R3 )

4) Read the current Iop set by the MPPT converter5) Use Iop to calculate the actual power produced by each

of the three TEGs, using the individual mathematicalformulation from (3) (1.5% accuracy).

It is important to note that it is not possible to sum the indi-vidual values of MP from Table II (and thus replace points 1 to3) because those MPPs are relative to slightly different values ofcurrent, which it is not possible to have in a series array. As analternative, it would also be possible to use the voltage readingfrom the multimeter or the oscilloscope, however this procedureis less precise due to the switching noise; the current reading ismeasured with both a multimeter and an oscilloscope probe.

The results of the steady-state test are summarized in Ta-ble IV. The last column shows that the MPPT converter has anaccuracy, sometimes called tracking efficiency, of 99.85% (cal-culated with a maximum error of 1.5%). The fractional open-circuit voltage MPPT converter presented in [32] maintains theinput voltage within 5% of VOC/2 except for small values ofVOC . In [22], fractional short circuit and P&O are compared butthe MPPT efficiency is not calculated. The INC MPPT controlproposed in [30] shows a 95% tracking efficiency. The P&OMPPT converter of [29] is calculated to have around 99% track-ing efficiency, but this is not accurately proved experimentally,as done in this paper.

B. Sudden-Transient PerformanceThis test allows characterizing the settling response of the

converter after a step change in the open-circuit voltage. Sucha test cannot be performed with real TEGs: it is impossibleto instantaneously change their open-circuit voltage, thereforethe TEGs have been replaced by a power supply in series witha power resistor of 4.7. Fig. 14 shows the response of theMPPT converter after a VOC step from 10 to 20 V. After mea-suring the open-circuit voltage for 110s (DCD snubber with100-nF ceramic capacitor), the MPPT converter regulates theinput voltage to half of VOC in 8 ms. It can be noted that theinput voltage starts at 5 V and ends at 10 V which correspond to


Fig. 14. Converters input voltage after a VOC step-up from 10 to 20 V. Time:1 ms/div (x-axis); Voltage: 5 V/div (y-axis).

half of 10 V and 20 V, respectively, as expected. A similar testwas undertaken in [30], demonstrating a 300 ms settling time.

C. TEG Transient PerformanceThe third experiment assesses the ability of the MPPT con-

verter to respond to changes of the thermal input power, i.e.,changes of the temperature gradient. In the test rig, the fastestthermal transient occurs during the cool down of the TEGs. TheTEGs are initially maintained at 200 C, then the power to theheaters is disconnected and the temperature difference dimin-ishes at a rate of 0.25 C/s due to the heat absorption capacityof the water cooling system. A datalogger records all the tem-peratures, while two multimeters measure the converters inputvoltage and current. Both instruments are controlled by a VEEPro program that records all the data in spreadsheet format.

The temperature differences across the three devices are notalways exactly the same at any given instant, therefore the ac-tual power extracted by the MPPT converter is compared to thetheoretical MP available, as calculated for the steady-state ex-periment. This experiment is effectively a continuous series ofsteady-state experiments because the thermal time constant ofthe TEG system is much slower than the transient response ofthe converter, which adjusts the operating point every 0.5 s. Theresults (in blue) are shown in Fig. 15, where a 2% margin hasbeen added over the maximum available power (in red), to takeinto account the accuracy of the mathematical characterizationand measurement errors. Considering each point, the averagetracking efficiency of the MPPT converter is 98.7%. None ofthe MPPT converters for TEGs presented in the literature istested with a TEG thermal transient. The test rig used cannotprovide faster temperature transients, however it must be notedthat due to how this MPPT algorithm is computed, without anyintegral term, the converter can track the MPP every 500 ms,even if this period could be simply reduced in the microcon-trollers code. It has been selected based on practical experienceabout the thermal time constant of the TE system.

VI. CONCLUSIONThis paper presented an innovative technique to obtain the

open-circuit voltage measurement of a TEG, with minimal dis-connection of the load. The MPPT algorithm is programmedto a low-cost microcontroller and does not require expensive

Fig. 15. Thermal transient from T = 200 C to T = 100 C across thethree TEGs. Available and extracted output power on the left y-axis and tem-perature difference on the right y-axis.

sensors; it checks the open-circuit voltage every 500 ms and ac-curately adjusts the optimum operating point in less than 10 ms.

The converter used is a dcdc noninverting synchronousBuck-Boost (93% efficient), which can work in Boost, Buck-Boost or Buck mode; this guarantees the harvest of power overa wide range of temperature differences across the TEG.

The presented MPPT system was tested both under steadystate and transient conditions with real TEGs, demonstrating itsability to set the optimum electrical operating point quickly andvery accurately. It is able to harvest close to 100% of the MPthat can be produced by the TEG in the steady state and 98.7%during thermal transients. These results exceed the performanceof any other MPPT algorithm for TEG applications presentedin the literature so far.

Future work will focus on comparing the proposed MPPTtechnique to other MPPT algorithms, and on integrating severalMPPT converters together to form a DMPPT system.

ACKNOWLEDGMENT

The authors would like to thank M. Compadre Torrecilla.

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Andrea Montecucco (S10) received the B.Sc. andM.Sc. degrees from the University of Padova, Padua,Italy, in 2007 and 2009, and he is currently workingtoward the Ph.D. degree at the University of Glasgow,Glasgow, U.K.

He has previously been Research Assistant for twoyears at the University of Glasgow. He has authoredmore than ten papers in journals and at professionalconferences, and holds one International patent. Hisresearch interests include analog and embedded elec-tronics design, testing and simulation of thermoelec-

tric systems, maximum power and maximum efficiency tracking for thermo-electric generators, solar cells and solar thermal, and dcdc power converters.

Andrew R. Knox (SM00) received the B.Sc. andPh.D. degrees from the University of Glasgow, Glas-gow, U.K., in 1985 and 2000, respectively.

He is currently a Professor of Power Electronicsand Renewable Energy Systems at the University ofGlasgow. He is also a Director of the Energy Tech-nology Partnership and a Member of the NationalPhysical Laboratory Advisory Board. Previously, heheld senior managerial and technical positions in IBMManufacturing, R&D for more than 22 years, work-ing on Hi-Res displays, advanced graphics, electronic

security, and PC architectures. He has published more than 40 papers, coau-thored a book, contributed to International Standards, and holds more than 50patents. His current research interests include analog and embedded electronics,thermoelectric, PV and solar thermal systems design, and smart grids.

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