# Calculating the output power of Thermoelectric generator

This question is related with my previous question here

I am trying to calculate the output power from a specific TEG, here is it specifications,

• Open Circuit voltage (Voc) = 5.29V
• Current (I) = 0.93A
• Electrical resistance (Re) = 3.85Ω
• Seebeck (α) = 0.056V/k
• Number of PN couple(N) = 127N
• Air temperature (Tair) = 30 degree C
• Max temp (Tmax) =100 degree C
• Thermal conductance (k) = 0.35 W/k
• Resistance junction to case (Rjc) = 2.45 k/W
• Resistance case to source (Rcs) = 1 k/W
• heat flow on hot side (Qhot) = 53.1
• Temperature difference (∆T) = 50degree C

first I calculate the heat flow on the hot side,

Qhot=(Re/2×I^2 )-(α×I×Tmax)-(k×∆T)=(3.85/2×0.93*0.93 )-(0.056×0.93×100)-(0.35×50)=20.39 degree C/W

Now I find the,Resistance surface to air

Rsa = ((Tmax-Tair)/Qhot) - Rjc - Rcs = ((100-30)/20.39)-2.45-1 = 0.0192 degree C/W

Now i calculate the Rmodule,

Rmodule= Rcs+Rjc+Rsa=2.45+1+0.0192 = 3.46 degree C/W

Now using the formula for power,

P = (N * α^2 * ∆T^2)/(4*Rmodule) = (127 0.0031 50*50)/(4*3.46)= 71.1 Watts

the calculated output power is 71.1 watss, I think this very much, how can it produce 71 watts at temperature difference of 50 degree C? Where am I making mistake.

I assume you're referring to the same or similar device you linked to in your other question.

Did you check the datasheet? Right on page 2 they have charts and a table with all kinds of figures, including max. output power at different delta-T.

From that, I read for example that at a delta-T of 140-50°C=90°C roughly 26W of heat are conducted through the device of which about 0.8W can be converted to electricity.

That order of magnitude may give you a hint on what result to expect when trying to derive some formula.

Given the figures from the datasheet the rest of the calculations become quite simple, if you don't account for hard-to-predict variations, for instance the exact thermal resistance of a layer of thermal grease manually applied between the components.

A couple of sanity checks...

Assuming this is a Heat to Electricity (not Electricity to Heat) generator:

why would you expect the output power to be greater than OC voltage * current?

Also, Rsa is an absurdly low value. Do some thermodynamics reading and calculations for the actual heatsink surface area, (or if its a commercial heatsink, use its rated value in K/W) then work backwards from that to calculate an actual delta-T for your heat flow (or alternatively the max heat flow for your allowable delta-T.)

While you know that there must be errors in your method, there are two result that make this clear.

Power in = 5.29V x 0.93 A ~= 5 Watts but calculated output = 71 Watts.
So you have a 'COP'of 71/5 = 14+.
Nice if you manage it.
But, alas, you can't.

Max possible conversion efficiency is Carnot efficiency =
Delta-T/Thot
= 50 / (273 + 100C) ~= 13.4%
In practice you'll get a substantially lower amount- well under 50% of Carnot at low delta-T's typically.

You used V and I of TEG, buy you used formulae of TEC .

Reverse efficiency (as in TEG) is very less as compared to TEC.

Formulae are modified for TEG.