This paper considers the problem of balanced model reduction for a class of smooth nonlinear systems. The nonlinear system is approximated by local linearizations model around a continuum of constant operating points. An upper bound on the error of approximation is presented. The obtained linearization model can be considered as a linear time-varying (LTV) system model. Three different problems of balanced truncation for LTV systems are considered and the corresponding upper bound on the error between the full order and reduced order models is shown.