In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector with the time derivative of the solution. It is dynamically updated within each Newton-Raphson iteration. The method is applied to an analytic benchmark problem and to an LC oscillator. It provides better convergence properties than when using the popular phase-shift condition. It also does not need additional information about the solution. The method can also easily be implemented within the Harmonic Balance framework.