A two-dimensional (2-D) cellular automaton (CA) model considering phase equilibria according to the Calphad method is proposed for the simulation of solidification microstructures and microsegregation of Al-Si-Mg alloys. The present model encompasses the essential aspects of thermodynamics and kinetics of phase transformation during solidification of ternary Al-rich alloys, particularly nucleation and growth of primary dendrites, irregular binary and ternary eutectic phases, as well as the time-dependent mass transport of two solutes. The proposed CA model is applied to simulate the evolution of primary dendrites and irregular eutectic microstructures of Al-Si-Mg alloys. The influence of the cooling rate on the solidified microstructures and microsegregation is investigated. The following features are reproduced well by the CA simulations: microstructural length scales correlate with the cooling rate; the homogeneity of the primary alpha-phase is quantified depending on the cooling rate and deviates considerably from Scheil-type calculations; back diffusion is accompanied by a decrease in the eutectic fraction, considering that some amount of eutectic beta-phase is dissolved to maintain solute conservation and adjustment of equilibrium in the eutectic. (C) 2018 Elsevier Ltd. All rights reserved.