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Efficient Maximum Power Point Tracking andBattery Charging for an Underwater Thermoelectric

GeneratorCharles Alexander, Thomas Christen, Matthew Fister, Kimberly Maier, Z.L. Mink, and Reginald Pierce

Abstract—A thermoelectric power generation system was de-veloped to extend the mission time of an unmanned underwatervehicle. Thermoelectrics are used to convert available heat intoelectricity, which is then used to charge a lithium-ion (Li-Ion) battery. The proof-of-concept system uses free convectionover a heat sink to reject heat to the surrounding water.The battery charging circuit developed includes an integratedmaximum power point tracker (MPPT) and protection againstbattery overheating. The MPPT/charging circuit uses a ZETAconverter topology. The tested efficiency of the converter is47%, which is poor, but the overall heat conversion efficiencyof the system is 3.5%, which compares favorably to otherthermoelectric power generation systems. The proposed systemused a novel electrical and mechanical approach to investigate theapplication of thermoelectric systems in an unusual, underwaterenvironment. Improvements to the electrical design are suggested.The maximum power point tracking circuit developed may beapplicable to a wide range of small-scale generators if theefficiency can be improved.

I. INTRODUCTION

Boeing has developed an unmanned underwater vehicle(UUV) called the Echo Ranger whose batteries provide astandard mission time of 28 hours. To investigate the feasibilityof thermoelectrics as a range extending generator, a proof-of-concept power generation system was developed leveragingexpertise at RIT. Thermoelectric modules (TEMs) are solid-state semiconductor devices that convert heat directly to elec-tricity. TEMs are compact, durable, and modular, which makesthem uniquely suited for use in a UUV, where space is at apremium and maintenance cannot be performed on-line. Thepower from the TEMs is optimized by a maximum powerpoint tracker (MPPT), which consists of a microcontroller-operated DC-DC converter that balances the source and loadimpedances. In the system developed, the MPPT circuit alsofunctions as a battery charger for lithium-ion (Li-ion) batteries.

II. BACKGROUND

A. Thermoelectrics

Thermoelectrics are solid state devices that convert heatdirectly into electricity. They operate on the principle known asthe Seebeck effect, which states that a temperature-dependentelectric potential will be generated at the junction of dissimilarmaterials. Thermoelectrics typically have very low (< 5 %)thermal efficiency, but as previously mentioned, they havegood physical properties such as size and durability. Figure 1shows a typical commercial TEM.

Figure 1. Thermoelectric module construction. Adapted from Snyder, NatureMaterials, 2008.

The voltage and power response of a module is given byeq. (1) and (2) where α is a property of the module, I is thesteady state current, and R is the internal resistance of themodule [1].

V = α(TH − TC) − IR (1)

P = αI(TH − TC) − I2R (2)

To find the power output for a given heat input q and currentflow I , one needs to solve the following equations relating hot-side temperature TH and cold-side temperature TC to q, whereK is the thermal conductance of the module. The equationsare implicit and nonlinear, but a solution can be found quicklyby iterating.

q = αITH − 1

2I2R+K(TH − TC) (3)

q − P = αITC +1

2I2R+K(TH − TC) (4)

B. Heat Sink

In order to find TC , the heat sink must be modeled. Tosave power, our design uses free convection over a heat sink.Free convection relies on density differences within a fluid togenerate fluid motion instead of an external source, such asa pump or fan. Density variations due to temperature cause aconvection current to form which carries away the heat.

Free convection is governed by the Rayleigh number, eq.(5), which is a function of the acceleration of gravity, g; thecoefficient of thermal expansion, β; the temperature differencebetween the fins and the ambient water ∆T ; the length of thefins L; the Prandtl number of the fluid Pr; and the kinematic

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Figure 2. Free Convection Diagram

viscosity of fluid ν.

Ra =(gβ∆TL3Pr)

ν2(5)

Incropera gives the following relation between the Nusseltnumber, the Rayleigh number, and the dimensions of the finsfor vertical flow between flat, parallel fins where Nu = hL/kis the Nusselt number and S is the fin spacing [2].

Nu = (1/24)(RaS/L)(1 − exp(−35/(RaS/L)))0.75 (6)

Since the thermal conductivity of the fins k is known, findingthe Nusselt number gives the heat transfer coefficient h.Equation (7) gives TC in terms of h, q, and A, which is thetotal fin area.

TC = Tamb +q

hA(7)

Since the Rayleigh number depends on ∆T = TC − Tamb,iteration is required, but good convergence can be reached inas little as two iterations.

C. Maximum Power Point Tracking

A maximum power point tracker (MPPT) controls theimpedance seen by the TEMs to ensure that the load receivesthe maximum amount of power that the TEMs can provide.As the temperature difference across the TEMs changes, thepower available (eq. (2)) also changes. The MPPT adjust theeffective impedance seen by the TEMs to maximize poweroutput at all times.

The perturb and observe (P&O), incremental conductance,and current sweep methods are three algorithms found inMPPT literature. The P&O method is the simplest. First,the voltage is incremented and the power output measured.If the power output increases due to the voltage increment,the voltage is incremented again in the same direction. Ifthe power output decreases, the voltage is incremented in theopposite direction. In either case, the power is measured againand the cycle continues. The P&O method is very simple toimplement, but it will always oscillate around the maximumpower point because the controller will continue to incrementthe input voltage up and down.

The incremental conductance method is very similar tothe P&O method, except it uses a forward difference to

estimate dP/dV and adjusts the size of the voltage incrementaccordingly. A large absolute value of dP/dV will result ina large voltage increment and vice versa. The incrementalconductance method can find the maximum power point fasterand oscillate less around the maximum power point than theP&O method, however, the incremental conductance methodis more algorithmically complex and suceptible to noise dueto the calculation of the derivative.

The current sweep method periodically maps the entirecurrent-voltage relationship of the generator by sweepingacross a range of voltages. This method allows the maximumpower point to be computed exactly, but it adjusts to transientconditions more slowly than the previous methods because thesweep cannot be performed continuously.

D. DC-DC Converter

MPPT is typically implemented using a DC-DC con-verter. The DC-DC converter is commonly built using amicrocontroller-operated SEPIC topology, although analogcontrol systems have also been reported [3]. For high powerloads, the ZETA converter is of interest, due to the inherentlylow output capacitance requirement [4]. The ZETA converterhas a non-exponentially increasing output capacitance require-ment with respect to output power. The low output capacitancerequirement allows for ceramic capacitors with low equivalentseries resistance, which reduces electrical losses in the con-verter. A typical ZETA converter is shown in figure 3.

Figure 3. Example ZETA converter topology. D1 is typically a schottky diode,L1 and L2 may be coupled for halved current ripple, and Q1 is generally aPMOS FET.

III. DESIGN

The thermoelectric power system developed is a proof-of-concept design that uses TEMs to generate power to chargea battery. System requirements identified included the abilityto continuously generate power, operate efficiently, and incor-porate a heat source that provides a constant source of heat.Additionally, the system should be waterproof to a depth of 1meter and the thermoelectrics must develop 20W with minimaluser interactions.

A. Generator Subsystem

The thermoelectric generator subsystem generates powerunderwater from a heat source. For development purposes, a750W electric cartridge heater supplies the heat. In service,the heat would come from another source.

The construction of the generator subsystem is as follows:The aluminum heat sink (a) acts as the base for the assembly to

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Figure 4. Mechanical System Exploded View

allow the heat to flow through the thermoelectrics to the water.Three TEMs (b) (Thermonamic Electronics TEHP1-1264-0.8)are placed on the heat sink. A copper heat spreader (d) aroundthe cartridge heater (c) ensures a minimal temperature gradientacross the thermolectrics. To minimize heat loss, ceramicmillboard insulation (e) was placed between the heat spreaderand the clamping mechanism (f). 90 psi of clamping pressure isapplied to the TEMs by torquing the nuts to 5 in−lbs. Bellevillewashers (g) are used to moderate the pressure changes dueto thermal expansion. An aluminum enclosure (h) houses thegenerator subsystem, with the heat sink taking the place ofthe lid. An SBR rubber gasket (i) provides waterproofing.Power input to the cartridge heater and power output fromthe thermoelectrics is sent through the conduit connector (j)to the battery charging subsystem, which for developmentpurposes, is located out of the water. Thermocouples placed atthe hot side and cold sides of the thermoelectrics, the clampingplate and the enclosure wall monitor the device temperature.Aluminum legs hold the system upright.

B. Battery Charging Subsystem

Since the objective is to extend the life of a battery poweredvehicle, an intermediate electrical system is required to transferthe electrical energy from the thermoelectrics to the battery.This means that the voltage must be stepped up (or down,as needed) to the voltage needed to charge the battery. Amaximum power point tracker ensures that the impedanceseen by the thermoelectrics optimizes the power delivered.To accomplish this, a microcontroller-operated ZETA DC-DCconverter is connected between the thermoelectrics and thebattery. The battery charging system is designed to chargethe batteries at a constant power output to ensure that thepower from the thermoelectrics is not wasted. Although thisis an unusual charging method, adequately sized cells andtemperature monitoring enusres safe charging. Cell size isimportant because it ensures the battery is always in the slow

charging region, which allows for more complete charging.Output current and output voltage sensors provide feedbackto control the maximum power point tracking. Figure 5 showsthe layout of the circuit designed, with components labeled.Figure 6 shows the complete schematic.

Figure 5. Layout of main PCB for battery charging subsystem. Temperaturesensors are located on separate PCBs.

For the ZETA converter, capacitors were sized according toa Texas Instruments (TI) Analog Applications Journal article[4]. The equations are given below, where fsw is the switchingfrequency of the converter.

Cout =2Iripple

8Vripplefsw(8)

Cin =DIout

.01Voutfsw(9)

Cc =DIout

0.01Voutfsw(10)

To reduce device footprint and inductance required, coupledinductors were used. The minimum inductance needed forcontinuous conduction mode are given in eq. (11), where Lmin

is the minimum inductance for each inductor.

Lmin =V D

2∆ILfsw(11)

Transistors with very low on-resistance are desirable forswitched DC-DC converters to reduce losses. Gallium nitridefield effect transistors (GaN FETs) are an emerging technologythat boasts low on-resistance and gate charge, allowing forhigh-efficiency switching at high frequencies. EPC2015 GaNFETs with 4 mΩ on-resistance were selected.

GaN FETs require specialized driver circuitry to operate.The TI LM5113 is currently the only GaN FET driver availableon the market. It includes high-side drive capability with GaNFET specific voltage clamping, low propagation delays, lowpower consumption, and a small device package.

The GaN FET driver is controlled by an ATtiny85 microcon-troller programmed to implement the P&O algorithm. Sincethe output of the converter is connected directly to the battery,the ouput voltage is approximately constant, and output currentcan be substituted for power in the P&O algorithm. The inputvoltage is varied by changing the duty cycle.

In the circuit designed, output current is measured using acurrent sense resistor. The voltage drop across the resistor isamplified using a TI OPA192 op-amp, featuring both low noiseand low power consumption, and fed into a high resolutionADC. For an optimal balance of low capacitor and inductor

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Figure 6. Electrical Schematic for Charging Subsystem.

values and low high frequency losses, the PWM frequencywas set to 100 kHz. The P&O algorithm is programmedto increment the duty cycle by 0.007 as often as possible,which is constrained by the read times from the ADC. Everyfew seconds, the voltage and temperture of the battery arealso measured. Temperature measurement is performed by TITMP006 IR temperature sensors, which communicate withthe microcontroller via I2C. If the voltage or temperature falloutside the acceptable charging limits, the controller shutsdown the charging circuit. Table I shows the action chart.

Table IBATTERY CHARGING DECISION TABLE

Condition Charging External Load

Tcell > 40 C OFF OFFVbatt > 12V OFF ONVbatt < 10V ON OFF

A TI TPS54426 voltage regulator takes power from thebattery to power the electronics. This switching regulatorprovides high efficiency and accepts a wide input voltage rangewhich is essential for this circuit configuration in which theinput voltage swings based on the state of charge of the batteryas well as the output of the converter if it is extracting powerfrom the thermoelectrics.

The full system schematic is given in Figure 6 in which allof the reported subsystems may be seen.

IV. TESTING AND RESULTS

A. Thermoelectric Clamping

To ensure that the clamping pressure across the thermo-electrics was correct and uniform, pressure-sensitive film was

inserted between the modules and the heat sink. FujifilmPrescale pressure-sensitive film, rated for 70 to 350 psi, wasused. After sending the film in for analysis, the results cameback with a higher average pressure (182.84 psi) and less uni-form distribution than expected. The results were inconclusive;it appears that most of the surface meets or exceeds the designpressure of 90 psi and the non-uniformity in pressure is not anissue.

B. Insulation Testing

By placing quartz in the place of TEMs, one can determinethe heat losses through the insulation because the thermal con-ductivity of quartz is well known [5]. By assuming a reason-able value of thermal contact resistance (5 × 10−4 K−m2/W),one can determine the heat flow through the quartz fromthe measured temperature difference across the quartz. Theelectricity consumed by the heater was also measured. Thedifference between the heat input and the heat flowing throughthe quartz is the heat conducted through the insulation. Table IIshows the results of testing. The design of the thermal system

Table IIINSULATION TESTING RESULTS

Case Heat (W) TH (C) TC (C) Quartz Heat (W,%)

1 345 220 40 333.3 972 510 305 44.5 482.4 95

specified 96 % heat flow through the thermoelectrics. Ourmeasurments confirmed that this goal was achieved, withinexperimental uncertainty.

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C. Generator Subsystem

The performance of the generator subsystem was tested byattaching the output of the thermoelectrics to a Kikusui pro-grammable electronic load. The electrical input to the heaterwas measured with an RMS power analyzer. The temperatureof the water was kept relatively stable by a submersed ”coldplate” heat exchanger, and the temperatures of the system andthe water were monitored. MPPT was performed manuallyby adjusting the conductance of the electronic load. Thevoltage and power readings of the electronic load were usedto measure the thermoelectric output. Results are shown inTable III. With 630 W, the mechanical system meets therequired 20 W output. The conversion efficiency is 3.5 %.

Table IIIMECHANICAL SYSTEM TESTING RESULTS

Input Heat TH TC Twat Voltage Power OutW C C C V W

500 245.2 48.4 23.9 8.75 14.4630 296.6 54.8 26.5 9.85 20.19

D. Electronics Testing

Upon testing the electrical system, a major design flawof the ZETA converter was discovered. A low side N typetransistor was used in replacement of the typical schottkydiode. This would not allow current to flow from ground tothe drain of the device. Therefore, proper operation of theconverter required this design change. Also, the GaN FETdriver was found to not properly drive the high side transistor.This was likely due to source voltage fluctuations beyond thecapability of the GaN devices.

To obtain a working system, a simplified circuit was createdby replacing the low side transistor with a Schottky diode, asis used in ordinary ZETA converter designs. In the simplifiedcircuit, transistor Q1 (Fig. 3) was replaced with 3 parallel P-channel MOS power FET’s. The transistors were driven by asimple driver circuit using a pull-up resistor and N-channelMOSFET. The switching frequency was reduced to 108 kHz,down from the design frequency of 400 kHz.

The results of the converter testing are given in Figures 7and 8.

As figure 8 shows, the simplified circuit lost more thanhalf of the input power. We estimate that the diode dissipated1.4 W, the gate drive circuit 1 W, and there was 7 W dissipatedthrough the transistors due to switching losses. The switchinglosses were the result of an imperfect gate signal on the parallelPMOS’s.

Figure 7 shows that the maximum output voltage of thesystem was around 11V, which is too low to charge our sixcell lithium ion battery pack. As a result, we were unable totest whether the system could charge the battery.

Figure 7. Power Curve of the MPPT system connected to simulatedthermoelectric source

Figure 8. Power Curve of the MPPT system connected to simulatedthermoelectric source

V. CONCLUSION

The conversion efficiency (3.5 %) of the thermoelectricsystem compares favorably to generation systems created byBensaid et al, Casano and Piva, Headings et al, Kagawa etal, and Zhu et al [6]–[10]. However, the electrical systemperformed poorly, with an measured efficiency of only 47 %.The losses were primarily switching losses due to an inade-quate gate drive circuit constructed for the MOSFET designmodification.

To improve upon this system, the first step would be to use abetter gate drive circuit. Futher improvements may require analternate converter topology, perhaps SEPIC or non-invertingbuck boost, that allows the diode to be replaced by a transistorso that the losses from the Schottky diode part of the circuitcan be reduced.

ACKNOWLEDGEMENTS

This work was completed as part of the RIT Multidis-ciplinary Senior Design course. Funding was provided byBoeing. The project was guided by Rick Lux and RobertJ. Stevens. Additional thanks to Mark Indovina and JeffLonneville.

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