This paper introduces a method to enforce balanced power distribution between the stages of a single-phase transformer-based cascaded multilevel inverter using the new asymmetric ratio 6:7:8:9 between stages. Since the inverter is fed by a single DC source, asymmetry is enforced by means of the transformer turns ratio providing multiple redundant switching patterns to synthesize an output signal of until 35 levels. As it is developed in the paper, optimum switching patterns for the proposed ratio allow reducing typical power unbalance produced by commonly used ratios in four stage multilevel inverters (1:2:4:8 and 1:3:9:27). The proposed method consists on determining off-line the best switching patterns for minimizing deviation error, and then, storing them as lock-up tables in the digital device controlling the inverter. By permanently reproducing the selected switching patterns, balanced power distribution is achieved. A closed-loop control approach to regulate the RMS value of the output voltage compatible with the proposed method is also developed. The experimental results using a laboratory prototype are presented validating the entire approach.INDEX TERMS Balanced power distribution, cascaded asymmetrical multilevel inverter, transformer-based multilevel inverter.

Hardness is one of the most important mechanical properties of materials, since it is used to estimate their quality and to determine their suitability for a particular application. One method of determining quality is the Vickers hardness test, in which the resistance to plastic deformation at the surface of the material is measured after applying force with an indenter. The hardness is measured from the sample image, which is a tedious, time-consuming, and prone to human error procedure. Therefore, in this work, a new automatic method based on image processing techniques is proposed, allowing for obtaining results quickly and more accurately even with high irregularities in the indentation mark. For the development and validation of the method, a set of microscopy images of samples indented with applied forces of 5N and 10N on AISI D2 steel with and without quenching, tempering heat treatment and samples coated with titanium niobium nitride (TiNbN) was used. The proposed method was implemented as a plugin of the ImageJ program, allowing for obtaining reproducible Vickers hardness results in an average time of 2.05 seconds with an accuracy of 98.3% and a maximum error of 4.5% with respect to the values obtained manually, used as a golden standard.

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Phase congruence technique developed by Kovesi allows the detection of edges in images by analyzing the phases of their frequency components. A limitation of this technique is that it does not allow the detection of closely spaced edges that have different intensities. However, this situation occurs frequently in images, which therefore limits the use of this method. This study aims to propose a method that can overcome this limitation. Unlike the original technique, the proposed study uses a high degree of overlap between different frequency components to allow the detection of contiguous edges of low intensity. To avoid the problems that arise from high overlap, we modify the sensitivity of the phase congruence, allowing us to detect weak edges while discarding the noise associated with the proposed changes. We present our results and compare them with the results obtained using the existing technique.