We investigate the mechanisms leading to electrically insulated cell parts in a photovoltaic module under mechanical load. For this we measure the resistances across a crack in a laminated solar cell during bending that is typical in the field. The cracks in the solar cell are detected with electroluminescence imaging. The resistance over the aluminum paste increases continuously by negligible 30 mΩ whereas the front finger resistance increases by 15.4 kΩ stepwise. This difference is the result of the higher ductility of the aluminum paste in comparison to the front finger metallization. We associate the steps in the front finger resistance measurement to breakage of single fingers with an equivalent circuit model. Furthermore we found that a silicon crack widths lower 2μm has no influence on the resistances. Crack widths higher than 7μm leads to a complete front finger interruption. We determine that the specific resistance of such a crack causes nearly 100% of the power loss, which is caused by a completely electrically insulating crack in a photovoltaic module

This paper proposes a method for tuning the fractional exponent of different types of fractional order resonant controllers for a voltage source converter in a weak AC grid context. The main objective is to ensure the stability of the controlled system in a weak AC grid environment and to achieve an adequate dynamic response under disturbances. Therefore, six commonly used integer order proportional resonant (PR) control structures are selected from the literature and compared with each other according to their frequency behaviour. Afterwards, a rational approximation for the fractional order term is selected based on continuous fraction expansion technique. The inclusion of a fractional exponent in each integer order PR structure generates the fractional order proportional resonant (FPR) control transfer functions. Once the FPR controllers have been obtained, their closed-loop responses are tested via eigenvalue trajectory analysis. For each FPR control structure, a range of the fractional exponent that ensures stability is obtained. The conclusions of eigenvalue trajectory analysis are tested by implementing the FPR control structures in an specific application consisting in a modular multi-level converter (MMC) connected to a weak AC grid with adjustable short-circuit ratio. By means of time-domain simulations, not only the previous eigenvalue analyses are validated, but also new tuning criteria are given for the fractional exponent in combination with other control parameters, such as the damping frequency and the inductance of the complementary feedback branch. Moreover, a sensitivity analysis of the tuning criteria is carried out for other sizes of the AC filter inductance.