Experimental Determination of Power Losses and Heat Generation in Solar Cells for Photovoltaic-Thermal Applications

Abstract

Solar cell thermal recovery has recently attracted more and more attention as a viable solution to increase photovoltaic efficiency. However, the convenience of the implementation of such a strategy is bound to the precise evaluation of the recoverable thermal power and to a proper definition of the losses occurring within the solar device. In this work, we establish a framework in which all solar cell losses are defined and described. The aim is to determine the components of the thermal fraction. We therefore describe an experimental method to precisely compute these components from the measurement of the external quantum efficiency, the current–voltage characteristics, and the reflectivity of the solar cell. Applying this method to three different types of devices (bulk, thin film, and multi-junction), we could exploit the relationships among losses for the main three generations of PV cells available nowadays. In addition, since the model is explicitly wavelength dependent, we could show how thermal losses in all cells occur over the whole solar spectrum, and not only in the infrared region. This demonstrates that profitable thermal harvesting technologies should enable heat recovery over the whole solar spectral range.

Appendix A: Computation of \(\varvec{L}_{4}\) Components

In this section, we show how to split the $L_{4}$ components. As mentioned in section 2, $L_{4}$ losses are voltage drops associated with $L_{3}$ losses. Actually, current losses $L_{3}$ impact the generation–recombination balance, reducing the voltage that the device can generate and are the reason why solar cells exhibit voltages smaller than $E_{\text{g}} /q$. The sum of these voltage losses actually accounts for the difference between $E_{\text{g}} /q$ and voltage at maximum power $V_{\text{mp}}$.

Previous studies (Ref 15, 26, 32,33,34) showed how the sum of two of such losses corresponds to the radiative recombination $L_{{3{\text{rad}}}}$. The first is called Carnot loss ($L_{{4{\text{carnot}}}}$) with a corresponding voltage drop firstly derived by Landsberg and Badescu (Ref 35):

$$\Delta V_{{4{\text{carnot}}}} \approx \frac{{E_{\text{g}} }}{q}\frac{{T_{\text{c}} }}{{T_{\text{s}} }}$$

(25)

with $T_{\text{c}}$ the cell temperature and $T_{\text{s}}$ the temperature of the Sun. This loss takes into account only radiative emission in the solid angle within which the device absorbs the solar spectrum. The second is instead the so-called Boltzmann voltage loss ($L_{{4{\text{boltz}}}}$) which takes into account the difference between the solid angle within which the solar cell absorbs the solar power, and the solid angle within which it emits. The voltage drop associated can be calculated as

$$\Delta V_{{4{\text{boltz}}}} \approx \frac{{k_{\text{B}} T_{\text{c}} }}{q}{ \ln }\left( {\frac{{\varOmega_{\text{emit}} }}{{\varOmega_{\text{abs}} }}} \right)$$

(26)

where $k_{\text{B}}$ is the Boltzmann constant and $\varOmega_{\text{emit}}$ and $\varOmega_{\text{abs}}$, respectively, the emission and absorption solid angles.

We then define with $L_{{4{\text{Nrad}} - {\text{V}}}}$, and $L_{{4{\text{s}}}}$ the voltage drops corresponding to non-radiative recombination and to electrical shunts.

The total voltage drop due to $L_{4}$ (hereafter $\Delta V_{4}$) is therefore equal to

$$\Delta V_{4} = \frac{{E_{\text{g}} }}{q} - V_{\text{mp}} = \Delta V_{{4{\text{carnot}}}} + \Delta V_{{4{\text{boltz}}}} + \Delta V_{{4{\text{Nrad}} - {\text{V}}}} + \Delta V_{{4{\text{s}}}}$$

(27)

While $V_{\text{mp}}$ is known from the solar cell current–voltage characteristic, and the Carnot and Boltzmann contributions are known from Eq 25 and 26, one can obtain the sum of the two unknown voltage drops as

$$\Delta V_{{4{\text{Nrad}} - {\text{V}}}} + \Delta V_{{4{\text{s}}}} = \frac{{E_{\text{g}} }}{q} - V_{\text{mp}} - \Delta V_{{4{\text{carnot}}}} - \Delta V_{{4{\text{boltz}}}}$$

(28)

Finally, knowing from Eq 18, the total $L_{4}$, and from Eq 25, 26, and 28, the ratio between the different components, one can sort out the loss components $L_{{4{\text{carnot}}}}$, $L_{{4{\text{boltz}}}}$, and ($L_{{4{\text{Nrad}} - {\text{V}}}} + L_{{4{\text{s}}}}$).

It is worth to point out that ${{\Delta }}V_{{4{\text{s}}}}$ can also be extracted by the determination of the solar cell series resistance as

$$\Delta V_{{4{\text{s}}}} = R_{\text{s}} I_{\text{mp}}$$

(29)

where $R_{\text{s}}$ is the series resistance which can be obtained from the solar cell IV characteristic by several methods (Ref 36) and $I_{\text{mp}}$ is the solar cell current at maximum power.

Note that the method does not allow to obtain the spectral dependency of the $L_{4}$ components.