Sufficient conditions for almost global synchronization of second-order multi-machine power systems with radial topology are provided. The analysis is based on the recently proposed multivariable cell structure approach using Leonov functions-an extension of the powerful cell structure principle developed by Leonov and Noldus to nonlinear systems, the dynamics of which are periodic with respect to several state variables and possess multiple invariant solutions. The efficiency of the derived conditions is illustrated via a numerical example.