Teoretiske studier i solcellefysikk

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Alfredo Ignacio Sanchez Garcia fra Fakultet for teknologi og realfag ved UiA disputerer for ph.d.-graden med avhandlingen «Theoretical Studies in Solar Cell Physics» mandag 12. desember 2022.

Han har fulgt doktorgradsprogrammet ved Fakultet for teknologi og realfag ved UiA, med spesialisering i ingeniørvitenskap, forskningsområde fornybar energi.

Slik oppsummerer Alfredo Ignacio Sanchez Garcia selv avhandlingen:

Theoretical Studies in Solar Cell Physics

Solar cells are devices capable of converting sunlight into electricity which can be extracted and utilized. Modern solar cells are approaching their conversion efficiency limit. Because of this, a deeper understanding of what prevents a solar cell from achieving its limiting efficiency is necessary. The goal of my PhD thesis has therefore been the development of analytical models that describe some of the physical mechanisms that negatively affects the efficiency of solar cells; mainly focusing in three distinct topics: (i) fundamental energy losses, (ii) the temperature sensitivity of solar cells and (iii) the effect of the series resistance on the maximum power point.

The maximum power point

The maximum power point (MPP) of a solar cell is the operational point in which the output power from the cell is the maximum attainable. Solar panels in the field are usually connected to optimizers, devices that, among other things, ensure that the solar cells are operating at their MPP. Even though the MPP is of such importance, it has not been explored much, from an analytical perspective, in the scientific literature. The reason for this is that, traditionally, the MPP is computed numerically. It was not until recently (2013) that it was discovered that a not so well-known mathematical function, called Lambert’s W, allowed for analytical expressions that described the MPP. This function and its possible applications in the field of solar cell physics has motivated a huge part of the PhD work.

Fundamental energy losses

The maximum obtainable efficiency of conventional solar cells is 40% under ideal conditions and under concentrated light. The natural question that follows is what happens to the remaining 60%. In the scientific literature, one can read about the five mechanisms of energy loss that are intrinsic to the solar cell’s nature. With the help of Lambert’s W function, we develop a set of analytical expressions that can accurately describe these mechanisms.

Temperature sensitivity of solar cells

Solar cells are usually characterized at 25°C. However, real operating conditions can differ substantially. Depending on the climate, operating solar panels can easily achieve temperatures of 55°C or even higher. An increase in temperature from 25°C to 55°C results in a 12% power drop for conventional silicon solar cells.

Changes in solar cell parameters (efficiency, open-circuit voltage, fill factor, etc.) due to temperature variations are quantified by means of parameters called temperature coefficients (TCs). Because of the importance of being able to accurately predict the output power at different temperature conditions, TCs have been studied in depth in the scientific literature. The MPP, however, has not been much explored. The reason for this is, once again, the lack of analytical models describing the MPP. We filled this gap in the scientific literature by using Lambert’s W function to develop analytical expressions for the TCs of the voltage, current and power at the MPP. The new model allowed for a new analytical expression for the

TC of the fill factor. This represents an improvement, as only empirical models are known for the TC of this solar cell parameter.

Still within the topic of temperature sensitivity, we have developed an analytical model that connects the TCs to physical properties of the material of which a solar cell is made of. Furthermore, with this new model, we have been able to show analytically how the TCs relate to impurities present in the cell. This new theory sets the ground for future novel characterization techniques.

The effect of the series resistance

In real cells, power is not only lost through the internal processes occurring within the cell but also due to current leakages and resistance with metal contacts. Accounting for the effect of series resistance in the usual models used for describing solar cells results in expressions that are not straightforward to work with. Particularly, trying to describe analytically the effect of the series resistance on the MPP results in a transcendental equation. This type of equation cannot, in general, be solved analytically. Because of this, the effect of the series resistance on the MPP has not been much explored. A model was developed back in 1981, but it is difficult to use and implement. Motivated by this gap in the scientific literature and with the goal of improving previous existing models, we made use of Lambert’s W function to derive analytical expressions that describe how the series resistance affects the MPP.

Intensive Lambert’s W function application in the solar cell analysis

This PhD work has expanded the knowledge of some of the internal mechanisms that limit the efficiency of solar cells. We have shown that Lambert’s W function allows for the development of analytical models that describe fundamental energy losses, the temperature sensitivity of the MPP and the effects of the series resistance on the MPP, potentially improving current characterization techniques.

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