Higher harmonic cavities are used in light sources to lengthen the bunch and increase the beam lifetime without effects on beam brightness. Some longitudinal beam dynamic equations with higher harmonic cavity are derived. Calculations for Hefei Light Source II (HLS-II) with a third harmonic cavity under the optimum conditions are presented. The results show that the factor of lifetime improvement is 2.9 and the bunch length is 45.65 mm. The transient beam loading effect on the bunch length in harmonic cavity may be neglected for uniform fill of all rf buckets. Meanwhile, a third harmonic cavity with higher order modes damping was optimized through a large number of simulations.