The emission from a black-body at each photon energy, hf, is determined by one parameter, its temperature. Higher efficiency is possible if the emission of light at each energy is optimised separately. Staying with black-body models, a converter which allows this, in principle, is shown in Fig. 3.4. Here, photovoltaics has a real advantage over solar thermal approaches. Using tandem cell stacks, a conceptually equivalent geometry can be implemented much more elegantly, as shown later.
The analysis becomes much more complex but, as shown later, results in an optimum temperature for the black-bodies for each photon energy given by:
1 + (1 – TA/Topt )(hf/kTA )-exp(-hf/kTopt) ‘ 1 + [(1 – Ta/Topt )(hf/kTA )-1] exp(-hf/kTopt)_
The efficiency is marginally increased to 86.8% from 85.4% for a single black – body, clearly not worth the effort, especially as each black-body absorber in Fig.
3.4 is connected to its own Carnot converter.
We will see later that a photovoltaic cell in combination with a monochromatic filter (Fig. 3.5) can convert energy from a black-body at the Carnot efficiency.
Fig. 3.5 : An ideal solar cell combined with an ideal monochromatic light filter acts as an ideal Carnot converter of heat emitted by a black-body.
Hence, each black-body absorber in Fig. 3.4 and its associated Carnot converter can be replaced by an idealised photovoltaic cell of bandgap appropriate for converting its assigned colour (Fig. 5.1 later in the text shows a similar configuration).
An elegant simplification of this modified system is to use the cells to do the filtering as in the tandem stack of Fig. 3.6. This gives the same limiting efficiency as before but with much reduced system complexity.
The author has argued elsewhere that this multi-colour efficiency limit of 86.8% is the highest solar energy conversion efficiency possible in a solar system with reciprocity between light absorption and emission (Green 2001).
Decreasing band gap
Fig. 3.6 : Tandem cell stack giving the same limiting efficiency as the more complex system of Fig. 3.4.