Sorghum [Sorghum bicolor (L.) Moench] biomass hybrids with high productivity and enhanced levels of lignin are seen as a promising alternative of feedstock for direct burning in ovens designed for cogeneration of electricity. The objective of this study was to estimate the genetic combing capacity of biomass sorghum lines and conduct multivariable selection of photosensitive biomass sorghum hybrids for use in cogeneration. Thirty‐six photosensitive hybrids, the control BRS716, and 12 parental lines were evaluated in a seven‐by‐seven triple lattice design at two locations, and 12 characters were evaluated. There was superiority of additive effects on the genetic control of all the characteristics studied in both environments, less for female lines in the diallelic analysis of F1 hybrids. The inclusion of parents in the estimates of combining capacities indicated predominance of dominance effects involved in the genetic control of the traits analyzed. The results demonstrate the action of epistasis of the dwarf genes present in the female lines for the biomass parameter and the false interpretation when these lines are included in the diallelic analysis. With the use of the index based on factor analysis and genotype–ideotype distance (FAI‐BLUP index), four factors were established, which separated the characteristics of production and quality, as well as the two environments, resulting from the high hybrid × environment interaction. With the index, five hybrids with higher potential for burning (H5‐5, H2‐1, H1‐1, H1‐5, and H5‐1) were selected. However, no hybrids obtained gains for the characteristics of production and quality, simultaneously, which indicates the need for genetic improvement of the parents used in the program.