Imbalance of generation and load caused by volatile generations poses challenges on frequency regulation. AGC is required to respond to the generation fluctuations without violating operational and security constraints. While explicit model predictive control (EMPC) provides an approach, the partition number of the piecewise affine control laws grows exponentially with the number of constraints and prediction/control horizons, which hinders its application in large systems. In this paper, we propose an EMPC approach for AGC by approximating the control laws using Legendre polynomial series expansions, thus entirely eliminating the partition issue. Galerkin method is applied to the KKT conditions of EMPC's multiparametric quadratic programming (mp-QP) problem to compute the approximations. Case study in New England 39-bus system verifies the performance and efficiency of the proposed controller.