We discuss the large deviations asymptotic of the time-averaged empirical current in stochastic lattice gases in the limit in which both the number of particles and the time window diverges. For some models it has been shown that dynamical phase transitions occur: the optimal density profile to realize such deviations is given by travelling waves rather than by homogeneous profiles. We shall prove a variational representation, proposed by Varadhan, for the corresponding rate function that is obtained by projecting the large deviations at the level of the empirical process.