Within the dielectric continuum model and the model of effective masses for the electron, self-consistent solutions to the Schrödinger-Poisson system of equations taking into account the contribution of piezoelectric and spontaneous polarizations were found.The theory of stationary electronic states, taking into account the internal fields caused by piezoelectric and spontaneous polarizations occurring in the nanostructure was developed for the three-barrier wurtzite anisotropic resonance-tunneling structure with binary and ternary components.For nanostructure, which functioned as a cascade of experimentally realized quantum cascade detector, the calculation of the potential profile, stationary electron energy spectrum and oscillator strengths of quantum transitions was carried out. The geometric configurations of the nanostructure, for which the intensity of the detector quantum transitions between the working energetic states is the largest, were established.