Thermoelectric Power Generation

Allison Duh and Joel Dungan

May 15, 2013

Introduction

A thermoelectric generator (TEG) is a device that converts heat energy directly into electrical

energy. Thermoelectric systems capitalize on semiconductor charge carriers excited by a temperature

difference to convert heat into useful current. TEGs fall under the broad domain of energy recycling, but

find use in a variety of difference niche applications. They can be used as stand-alone generators or to

recycle waste heat and make conventional systems more “green.” These solid-state systems have been

the subject of much recent research and investigation because of their potential to “reduce ozone

depletion, greenhouse gas emissions and fossil fuel usage” (Bell).

This investigation will aim to provide the reader with a basic understanding of mechanics behind

TEGs and their importance as a potential energy source. First, the thermoelectric effects relevant to

understanding TEG operation are introduced. A simple thermoelectric generator circuit is examined in

detail. An attempt then is made to find the optimal TEG and identify the material parameters important

to materials research in thermoelectrics. Further, current and future applications of thermoelectric

devices are discussed. And the market impact of TEGs is analyzed to understand where they stand today

and what role they may play in the future.

Thermoelectric Effects

Three thermoelectric phenomena are pertinent to thermoelectric generator design - the

Seebeck, Peltier, and Thomson effects. The former of these effects can be shown to result from the

latter two. Together, they provide correlations between heat flow and current flow at a conductor

junction.

The Seebeck effect states that when two different conductors form a closed loop, a current will

flow if the two junctions between the conductors are held at different temperatures. Equivalently, a

“Seebeck voltage” is formed under these conditions. The Seebeck voltage is linearly proportional to the

temperature difference and the coefficient of proportionality, , can be derived from material

properties. Formally,

The Peltier effect asserts that heat is released or absorbed when current flows across the

junction between two unlike conductors. The direction of heat flow is dependent on the direction of

current. The absorption rate of heat is proportional to current and can be expressed in terms of the

Peltier coefficient, , as,

Inefficiency in TEGs results primarily from the fact that Peltier heat varies linearly with current, while

Joule heating is quadratic in current.

Finally, the Thomson effect is seen only in one conductor and is included here mostly for

completeness. When a temperature gradient exists along a conductor, current flowing against the

temperature gradient in the conductor will provide cooling, while a heating effect is observed when

current flows along with thermal current. The relationship can be described in terms of a Thomson

coefficient, , as,

Thomson effects usually have a minimal impact, especially when the Thomson coefficients of the two

conductors in a thermocouple are well matched so that there is no net heat exchange.

Lord Kelvin proved that the coefficients are related by

and

.

The Seebeck effect results from the Peltier and Thomson effects. In contrast to Joule heating, all three

effects are all thermodynamically reversible and are independent of contact geometry at the junction.

Thermoelectric Efficiency

Figure 1 depicts a thermoelectric circuit

configured as a generator. Thermoelectric

generators can also be adapted into a heat

absorber, often used in cooling systems, by

replacing the load with a power source. The

contacts (dark grey) are maintained by a heat

source at a temperature difference . The n

and p type elements have associated electrical

resistivities, , thermal conductivities, , total

electrical resistances, , total thermal

resistances, , cross-sectional areas, , and

lengths, . Additionally, the two elements have a

relative Seebeck coefficient, , and relative

Peltier coefficient, .

We can balance the heat exchange at the junction by writing:

( ) ( )

( (

) (

)) ( ) ( (

) (

))

Figure 1: A basic thermocouple circuit.

where is the heat absorbed from the external source, refers to Joule heating, is due to the

Peltier effect, and is conduction heat.

The maximum power, , is delivered to the load when is equal to . Under this

condition, the current generated in the circuit is simply the Seebeck voltage divided by the total series

resistance of the loop, or

meaning that

( )

The efficiency of this generator would then be the ratio of the output power to the heat absorbed.

Substituting the maximum current into our equation for Qs, we find after considerable algebra:

( ( ) (

))( (

) (

))

The efficiency is maximized when the term,

( (

) (

))( (

) (

))

is minimized. Thus, the optimal thermocouple will maximize the Seebeck coefficient, while minimizing

the term above, which may be rewritten as a function of the form factor ( ⁄ ). We find:

( ⁄ ⁄ )( )

which is minimized when the derivative with respect to

is equal to zero, or

(

)

( )

⁄

⁄ √ ⁄

The term, , from the efficiency formula is minimized when its reciprocal is maximized. Thus, we arrive

at a term of merit , which should be maximized to create an optimal thermoelectric

generator. The figure of merit, which is expressed as

(√ √ )

is a function of the material properties of the two semiconductors in the thermocouple. is often

multiplied by an average temperature in the system to produce a dimensionless standard for

comparison of different thermoelements’ performance.

It should be noted that thermal and electric conductivity, as well as the Seebeck coefficient, are

actually temperature dependent themselves. Here we have assumed average values for these material

parameters provide an adequate representation since the parameters vary slowly over a wide

temperature range. The Thomson effect and contact resistance have also been neglected, as well as

thermal conduction outside of the thermopiles. These steady state calculations, though far from truly

rigorous, already bring to light many important relationships for TEG design and demonstrate some of

the challenges of finding good thermoelectric materials.

Thermoelectric Efficiency

The efficiency equation derived in the previous section provides insight into optimal TEG design

and operation. Good devices should be optimized in both their geometric configuration and should be

carefully selected (or synthesized) for specific material properties. The former optimization can be easily

accomplished by properly scaling the cross-sectional area of the thermocouple junctions, to match the

equation derived above. The latter issue of choosing the correct material properties can be reduced to

discovering a material with the high value of , which depends on electrical and thermal conductivity

and the Seebeck coefficient for particular material. Figure 2 plots the total efficiency of energy

conversion, , for typical figures of merit as the temperature gradient from which the TEG draws energy

is increased. This plot clearly shows the importance of selecting proper materials to maximize the figure

of merit. It is also immediately clear that significant temperature differences are needed to design an

effective system.

Figure 2: TEG efficiency plotted for several typical values of Z. Image generated in Matlab.

Besides manufacturing process development and design space research, materials science

investigations into maximizing the figure of merit in new materials constitutes the bulk of the ongoing

research in thermoelectric devices. Achieving higher values will make thermopower a much more

commercially viable option. However, developing high materials is not an easy task as the Seebeck

coefficient and the conductivity parameters tend to counter each other. Figure 3 depicts how these

parameters counterbalance each other for the simple case of a silicon thermoelement where the

semiconductor doping can be varied to optimize the figure of merit (which is proportional to ). The

thermal conductivity varies slightly with doping as well, but is often minimized seperately. In general, it

is difficult to produce large Seebeck coefficients and high electrical conductivities, but highly doped

semiconductors represent a good compromise. Many semiconductor thermoelements have been

proposed for TEG applications. Bismuth Telluride and its derivatives show the most potential for

attaining high figures of merit while maintaining other secondary qualities like material robustness.

Figure 3: A simulation optimizing the figure of merit by doping of silicon.

Total efficiencies for TEGs are quite low and applications are generally left to niche markets

where the reliability of a solid state device is more important than efficiency. The efficiency increases

with the temperature difference between the junctions, so most TEGs become a viable solution at above

100°C. Some of these applications areas where TEGs are most useful will be addressed specifically in the

sections that follow.

Applications

Because of their reliability and compact operability, for some time thermoelectric systems have

been popular in consumable electronics that can be powered by a TEG system’s low wattage generation.

These include systems such as personal cooling systems for desktops, climate-controlled car seating and

portable, and quiet, vibration-free beverage and food coolers. There are even products like watches that

can convert the temperature difference between a human body and the surrounding air into electrical

energy.

Cooling and temperature management is a major application of thermoelectric systems. Since

the Peltier effect is thermodynamically reversible, thermoelectric devices are often exploited to provide

cooling. Current efforts are being invested in higher-efficiency materials that will enable stronger

generation performance without suffering an increase in production and operation costs. For example,

there is significant interest in expanding these current consumer technologies into “commercial solid-

state heating, ventilating and air-cooling systems.” Widespread conversion from current electric-current

systems to thermoelectric systems would have strong impacts in more ways that simply cutting energy

usage. Current temperature control systems use “two-phase fluids” and refrigerants such as R-134A,

“which has a greenhouse gas equivalence of 1430 times that of CO2.” The solid-state structure of TE

cooling systems would eliminate the use of refrigerants while packaging and construction costs would

be much less compared to that of current systems with moving parts.

TEG systems have also been popular in applications such as space probes and spacecraft. In

these systems, consistent power, rather than cost of construction, is a priority. As solar or gasoline-

fueled combustion powers are unreliable sources in space, radioisotope thermoelectric systems have

been heavily favored. “All power sources for U.S. and former-USSR deep-space probes have used TE

heat engines to convert heat generated by nuclear fissile material to electricity.” A current area of

interest to both military and civilian applications is also solar thermoelectric generation, which is the

combination of “a solar thermal collector with a thermoelectric generator” rather than a nuclear

thermal collector.

While there is great potential the development of thermoelectric generator systems, many

opportunities lie in using TEG technology to recycle and reclaim energy that is wasted as heat in larger

systems. For example, gasoline-fueled combustion engines use “only about 25% of the fuel energy… for

vehicle mobility … the rest is lost in the form of waste heat in the exhaust and coolant…” Thermoelectric

junctions would already be able to use this waste heat to reclaim power, but this reclamation can also

be optimized and become more integrated into the engine system.

In his review of thermoelectric systems, Lon Bell refers to turbine engines, which are used in

“municipal electric power-generation systems,” and how these systems optimize the operating point of

each compression and expansion stage known as a “regenerative Brayton cycle.” This cycle has raised

efficiency to 60-65%. Bell discusses how the thermoelectric generator can be implemented in a similar

way, “by optimizing each element along the thermal gradient… rather than the less efficient cycle in

which the temperature and pressure of every element (TE junction) are the same.” Such optimization at

each stage could yield “efficiency… double that of a single module operating with all elements at the

same temperature.”

Whereas with generation systems the TEG is limited to low-wattage applications, in these types

of niche applications, a thermoelectric generator is not in competition with other generators but rather

seeks to “exploit the low grade heat, cheap or free, and to obtain additional benefits in terms of an

improved overall efficiency” (Min Chen). It is a simple, low-maintenance way in which systems may

capitalize on excess waste heat to generate energy that was previously lost.

Market

The market in thermoelectric generators has expanded in recent years to meet increasing

interest in alternative and inexhaustible energies. It is expected that a consumer cost function would

have a very low slope – almost flat – because “the cost of thermoelectrically producing electricity mainly

consists of the running cost and module cost” (Riffit, Ma). The running cost, “determined by its

conversion efficiency” is negligible compared with the module cost (“cost of its construction to produce

the required output”) because the fuel of a thermoelectric generator is either free or very cheap to

produce (Riffit, Ma). This leaves only the device construction cost and cost-per-watt of the devices to be

optimized. In current and future research, this is pursued through exploration of more efficient and high

ZT materials.

In terms of cost-per-watt, thermoelectric power is still significantly more expensive than sources

such as photovoltaic energy or oil. For example, a retail portfolio on photovoltaic pricing reported in

2012 a $2.29/W peak in the U.S. If it is assumed that a barrel of oil produces 1699 KW/H for $70 dollar

then it yields a value of $0.05 per KWH.

For thermoelectric energy, a standard device measuring 75 mm2 such as the 20 Watt Module

HZ-20 on www.hi-z.com is assumed. It consists of 71 thermocouples and has a power output of

approximately 19 W. Each is $125 and the cost of peripheral devices such as inverters and DC/DC

converters add up to approximately $120. Assuming that the device runs for %65 of a year and

generating 19 watts yields an annual average output of 108.18 kWh/yr. Over a ten year lifespan and

depending on peripheral device cost, the cost of power generation can vary from between $0.11/kWh

to $0.22/kWh.

However, the relatively high price of thermoelectric technology does not outweigh the benefits

of its low-maintenance clean energy. In 2012 IDTechEx reported that approximately 33 million dollars

was invested in thermoelectric markets, with a project $35 million in 2013 and $43 million in 2014. 30 of

the 33 million dollars were attributed to military and aerospace consumption, indicating the military and

private aerospace sector’s strong continued interest in expanding the production of thermoelectric

technologies. Another firm, Pike Research, forecasts that between 2011 and 2015, thermoelectric

energy harvesting will represent approximately 12% of the consumer energy harvesting market against

the 40% of photovoltaic harvesting. Even though thermoelectric power generation is limited in its

applications and runs at a higher cost per watt than does other energy harvesting technologies like

photovoltaic harvesting, it is clear that the TE market will continue to grow and expand in the future.

Conclusion

Through natural phenomena known as the Peltier and Seebeck effects, thermoelectric

generators and systems are able to generate or reclaim power from thermal differences. Although they

have been used the mostly in expensive large-scale systems such as space probes, they have been

successful and invaluable in boosting the energy efficiencies of these systems when other fuel sources

run out or are inaccessible. As a solid-state system, it is very robust and has few moving parts. TE

systems have expanded in consumer electronics and applications but its largest drawback in “real-

world” application is its bulk and weight. In terms of further development, researchers are working to

optimize devices in terms of thermocouple material properties such as a high Z value. However, the

performance of the TE system is also largely dependent on the environment and application within

which it is applied.

In the current age of environmental toxicity and energy crises, thermoelectric technology is an

unique and mostly untapped resource. Whereas forays into natural gas and new oil reserves damage the

environment and photovoltaics require chemical processing and cleaning, thermoelectric technology

has a comparatively small footprint. For example, the immense amounts of chemicals and energy used

in civilian/consumer heating and cooling would be drastically reduced by wider use of thermoelectric

technology. Furthermore, the system as a whole would be cheaper to maintain. Although currently

preferred by military and aerospace applications, investment in thermoelectric technology within the

clean energy market continues to rise and these systems have strong potential for wide-spread use in

the future.

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