Using the AM1.5 direct solar spectrum as a baseline, we can model the amount of energy that can be converted into electricity by a solar cell if a portion of the solar spectrum is diverted to algae production and only the remainder is provided to the solar cells. This allows us to determine the viability of a cultivation system based on this concept in terms of generating electivity or increasing the portion of specifically targeted PAR available for cultivation. The proposed lossless system places a filter or device above the algae pond to split the spectrum into the appropriate compo­nents. We do not consider the mechanism used to redirect the light or the specifics of how the system will function. However, one candidate technology would be the luminescent solar concentrator or a variation thereof. Although the exact mecha­nism is not described, the model assumes all the light not provided to the algae is directed to a solar cell. The model assumes there are no losses associated with transmission of light through the filter or reflections from the surfaces of the filter or solar cell. The model also disregards electrical resistance in the transmission of the generated electricity.

The first aspect of this model is to determine the component of the spectra absorbed by the microalgae. As can be seen from Fig. 15.2, on average the main chlorophyll absorption peaks are centered at 434 and 662 nm. The portion of the spectrum transmitted to the algae was varied by changing the threshold around these peaks. For example, full-width half-maximum (50 % threshold) meant the spectra from 400 to 492 nm and 644 to 678 nm was transmitted to the algae, while for a threshold of 80 %, only the spectra from 417 to 458 nm and 656 to 670 nm were transmitted to the algae. Additionally, the light given to the algae is limited to between 400 and 700 nm as this is the region typically considered PAR (photo­synthetically active radiation). All energy not transmitted to the algae is provided to the photovoltaic device for producing electricity. To calculate the power absorbed by the different microalgae species, the AM1.5 solar spectrum is multiplied by the absorbance spectrum (Fig. 15.2). The allocation of the solar spectrum as the bandwidth changes and the power absorbed by the microalgae (nannochloropsis) can be seen in Fig. 15.4.

With this allocation of the solar spectrum, we can calculate the power generated by a solar cell in hypothetical system using the reported spectral response graphs and parameters for crystalline silicon (Beardall et al. 2009) and amorphous silicon (Meier et al. 2004).

The short-circuit current density (Jsc) generated by a solar cell is calculated from:

where EQEQ.) is the external quantum efficiency as a function of wavelength, Ф(к)АМ1 5 is the photon flux density calculated from the AM1.5 (Global Tilted) solar spectrum, PV(k) is function defining the portion of spectrum not transmitted to the microalgae, and q is the charge of an electron.

The open-circuit voltage (VOC) of the solar cell is dependent on the short-circuit current density and will vary with the irradiance that is incident upon the cell. This can be calculated from (Messenger and Ventre 2010):

where Eg is the bandgap of the semiconductor material, k is Boltzmann’s constant, T is the cell temperature in K, and J0 is derived from the published parameters of each device.

The power generated (P) in W. m 2 from the cell is then:

P = FF. Isc ■Voc

where the fill factor (FF) is the value published in the literature for each cell type.

The power generated by the photovoltaic modules from this limited spectrum and as the bandwidth changed can be seen in Fig. 15.4. The power produced from the solar cells can be directed to the powering facilities associated with the growth of microalgae (pumps and monitoring systems) or to provide additional illumina­tion to the microalgae. The former would reduce the costs of running the plant whereas the latter can boost growth productivity. Light emitting diode (LED) arrays can be used to most efficiently provide additional lighting to the microalgae at a specific wavelength. LEDs are highly efficient solid-state devices for converting electricity into light. They can be designed to emit light in a range of wavelengths to match the spectral. The internal quantum efficiency of high quality LEDs can exceed 99 %. This sounds extremely efficient, and however, there are difficulties in extracting the light from the LED which leads to low external quantum efficiencies (EQE) in the order of only a few percent (Schnitzer et al. 1993).

There is a significant amount of research effort into increasing the external quantum efficiencies of LEDs. As a result, LEDs are produced from a range of materials and use a variety of technologies. Some of the resulting LEDs include blue emitting InGaN-GaN LED’s with a EQE of 40 % (Gardner et al. 2007), thin — film GaAs LEDs with a 30 % EQE, (Schnitzer et al. 1993), and organic LEDs with an EQE of 30 % (Kim et al. 2013). In some cases, careful texturing can improve the light extraction efficiency which yields LEDs with an EQE greater than 50 % and in some cases up to 60.9 % (Krames et al. 1999a).

The most useful LED for adding targeted illumination to a microalgae pond would be those LEDs with high external quantum efficiencies at particular wave­lengths, such as those discussed by Krames et al. with efficiencies of 60.9 % (Krames et al. 1999a).

The additional power (P) in Wm 2 that can be produced using the power gen­erated (Pin) using the system modeled above can be calculated from:

P = EQELed .Pin

where EQELed is the external quantum efficiency of the LED.

The additional irradiance from these LEDs is assumed to be tailored to the peak absorbance of the respective microalgae species. The total power absorbed by the algae is thus the irradiance absorbed directly by the microalgae and the peak absorbance multiplied by P.