A critical evaluation and thermodynamic modeling study including key phase diagram experiments was performed to investigate the K2O-Al2O3 and K2O-MgO-Al2O3 systems. For the first time, potassium β- and βʹʹ-alumina solid solutions were described using the Compound Energy Formalism with accurate cation distributions in their sublattices. From the new experimental results, the stability of potassium βʹʹ-alumina was assured up to 1600 °C. A large discrepancy reported in the literature, the eutectic temperature between KAlO2 and β-alumina in the K2O-Al2O3 system, was resolved. A set of self-consistent Gibbs energy functions for all stable phases in the K2O-MgO-Al2O3 system was obtained. As a result, any phase diagram sections and thermodynamic properties of the K2O-MgO-Al2O3 system can be calculated from the optimized Gibbs energy functions. In particular, the cation distribution in the β- and βʹʹ-alumina solid solutions is calculated depending on the non-stoichiometry of solution and temperature.