The microcalorimeter detects the energy of incident X-ray photon by the slight temperature rise of a device at a very low temperature, and the detector of a superconducting transition-edge sensor (TES) microcalorimeter has been developed for the measurement of energy dispersive X-ray photons of the energy of 10 to 20 keV with the energy resolution better than 100 eV of FWHM value by having the counting rate over 100 counts per second. A FE-SEM with a detector of TES microcalorimeter (SEM-TES) has already been developed for the extra-high resolution energy-dispersive X-ray spectrometry system to apply in electron-microprobe chemical analyses. Recently, we developed the sensitive correct function on the observed X-ray intensity data measured in the system. Then, the high energy resolution of revised SEM-TES system is precisely able to determine the element contents on the sample. In addition, the chemical bonding states can be clarified by the fluorescent X-ray intensities in the lower energy region derived with a low accelerating voltage of SEM-TES system. We applied the revised SEM-TES system to analyze chemical state on the electrode of nanosheets-derived Hx(Ni1/3Co1/3Mn 1/3)O2 for newly developing electrochemical capacitors. We investigated the chemical state of cations by not the M-lines but the L-beta and L-alpha lines as the lower energy lines having relative large contribution on chemical bonding. As a result, we revealed a specific chemical state of the Mn different from that of Li(Ni1/3Co1/3Mn 1/3)O2 electrode in LiB, that was supported by the result of TEM-EELS analysis. These results show that the SEM-TES system can be a useful analytical tool for the chemical bonding state and electronic structure determinations in a wide range of materials.