In electric grids with large photovoltaic (PV) integration, the PV system dynamics triggered by irradiance variation is an important factor for the power system stability. Although there are models in the literature that describe these dynamics, they are usually formulated as block diagrams or flowcharts and employ implicit equations for the PV generator, thus requiring application-specific software and iterative solution algorithms. Alternatively, to provide a rigorous mathematical formulation, a state-space representation of the PV system dynamics driven by irradiance variation is presented in this paper. This is the first PV dynamic model in entirely state-space form that incorporates the maximum power point tracking function. To this end, the Lambert W function is used to express the PV generator's equations in an explicit form. Simulations are performed in MATLAB/Simulink to evaluate and compare the proposed dynamic model over the detailed switching modeling approach in terms of accuracy and computational performance.