We develop a formalism to model the luminosity functions (LFs) of radio-loud Active Galactic Nuclei (AGN) at GHz frequencies by the cosmological evolution of the supermassive black hole (SMBH). The mass function and Eddington ratio distributions of SMBHs have been taken as starting point for this analysis. Our approach is based on physical and phenomenological relations that allow to statistically calculate the radio luminosity of AGN cores, corrected for beaming effects, by linking it with the SMBH at their center, through the Fundamental Plane of black hole activity. Moreover, radio luminosity from extended jets and lobes is also computed through a power-law relationship that reflects the expected correlation between the inner radio core and the extended jets/lobes. Radio-loud AGN are further divided in two classes, characterized by different accretion modes onto the central BH. If the Eddington ratio is <0.01 they are called low-kinetic (LK-mode) AGN; if >0.01, they are called high-kinetic (HK-mode) AGN, being this critical value roughly corresponding to the transition between radiatively inefficient and efficient accretion flows. The few free parameters used in the present model are determined by fitting two different types of observational data sets: local LFs of radio-loud AGN at 1.4 GHz and differential number counts of extragalactic radio sources at 1.4 and 5 GHz. Our present model fits well almost all published data on LFs of LK-mode AGN and of the total AGN population up to redshifts z<=1.5 and, moreover, in the full range of luminosities currently probed by data. On the other hand, it tends to underestimate some recent measures of the LF of HK-mode AGN at low redshifts, but only at low radio luminosities. The present model is also able to provide a very good fit to almost all data on number counts of radio-loud sources at 1.4 and 5 GHz. (abridged)
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