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Selective harmonic elimination technology has been widely used in many medium and high power converters which operating at very low switching frequency, however, it is still a challenging work to solve the switching angles from a group of nonlinear transcendental equations, especially for the multilevel converters. Based on the Groebner bases and symmetric polynomial theory, an algebraic method is proposed for selective harmonic elimination. The SHE equations are transformed to an equivalent canonical system which consists of a univariate high order equations and a group of univariate linear equations, thus, the solving procedure is simplified dramatically. In order to solve the final solutions from the definition of the elementary symmetric polynomials, a univariate polynomial equation is constructed according to the intermediate solutions and two criteria are given to check whether the results are true or not. Unlike the commonly used numerical and random searching methods, this method has no requirement on choosing initial values and can find all the solutions. Compared with the existing algebraic methods, such as the resultant elimination method, the calculation efficiency is improved, and the maximum solvable switching angles is 9. Experiments on three-phase two-level and 13-level inverters verify the correctness of the switching angles solved by the proposed method.

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A hybrid system electrode made from biomass-based material sodium lignosulfonate-derived hierarchical porous graphitic carbon (PGLS) and an organic redox compound (alizarin) is demonstrated. A derivative of alizarin called “alizarin red...

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The effect of the amount of BiVO 4 as visible light sensitizer on the photocatalytic activity of BiVO 4 /3DOM TiO 2 nanocomposites was highlighted. The low amount of BiVO 4 nanoparticles favors the transfer of photogenerated electrons to 3DOM TiO 2 while photogenerated electrons will remain at the surface of BiVO 4 at high amount of BiVO 4 , leading to the recombination of electrons-holes and reduced photocatalytic activity. 1 0 0.6 0.4 0.2 0.08 0.04 0.0209 0.0381 0.0256 0.0152 0.110 0.0078 0.0062 100 75 50 25 10 5 0 0.040 0.035 0.030 0.025 0.020 0.015 0.010 0.005 0.000 Rate Constant (min -1 ) mol % BiVO 4 -1 0 1 2 3 E (NHE) CB VB O 2 /O 2 .-OH . /H 2 O Oxidation Highlights -BiVO 4 @3DOM TiO 2 exhibit highly enhanced visible light photocatalytic activity -The effect of the amount of BiVO 4 as visible light sensitizer is highlighted -The electronic interactions BiVO 4 /TiO 2 lead to an improved charge separation -High BiVO 4 content leads to the accumulation of the electron/hole pairs at the surface of the BiVO 4 4 Abstract A series of BiVO 4 /3DOM TiO 2 nanocomposites have been synthesized and their photocatalytic activity was investigated under visible light irradiation using the RhB dye as model pollutant molecule in an aqueous solution. The effect of the amount of BiVO 4 as visible light sensitizer on the photocatalytic activity of BiVO 4 /3DOM TiO 2 nanocomposites was highlighted. The heterostructured composite system leads to much higher photocatalytic efficiencies than bare 3DOM TiO 2 and BiVO 4 nanoparticles. As the proportion of BiVO 4 in BiVO 4 /3DOM TiO 2 nanocomposites increases from 0.04 to 0.6, the photocatalytic performance of the BiVO 4 /3DOM TiO 2 nanocomposites increases and then decreases after reaching a maximum at 0.2. This improvement in photocatalytic perfomance is related to 1) the interfacial electron transfer efficiency between the coupled materials, 2) the 3DOM TiO 2 inverse opal structure with interconnected pores providing an easy mass transfer of the reactant molecules and high accessibility to the active sites and large surface area and 3) the effect of light sensitizer of BiVO 4 . Intensive studies on structural, textural, optical and surface properties reveal that the electronic interactions between BiVO 4 and TiO 2 lead to an improved charge separation of the coupled BiVO 4 /TiO 2 system. The photogenerated charge carrier densities increase with increasing the BiVO 4 content, which acts as visible light sensitizer to the TiO 2 and is responsible for the enhancement in the rate of photocatalytic degradation. However, the photocatalytic activity is reduced when the BiVO 4 amount is much higher than that of 3DOM TiO 2 . Two reasons could account for this behavior. First, with increasing BiVO 4 content, the photogenerated electron/hole pairs are accumulated at the surface of the BiVO 4 nanoparticles and the recombination rate increases as shown by the PL results. Second, decreasing the amount of 3DOM TiO 2 in the nanocomposite decreases the surface area as shown by the BET results. Mo...

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