A single-phase energy-stored quasi-Z-source inverter (ES-qZSI) can not only realize the function of boosting and inversion in a single stage, but can also smooth the fluctuation of photovoltaic power. However, it has second harmonic ripples on the DC side, which greatly affects performance. In order to limit the second harmonic ripples to an allowable range, system parameters need to be optimized. First, based on the state-space average model and the second order derivative, a detailed second harmonic component model is established for a single-phase qZSI with energy storage branch. Then, based on the built model, the influence of system parameters on the second harmonic ripple is analyzed. Finally, a system parameter design method used for second harmonic ripple suppression is proposed. The accuracy of the built model and the efficiency of the system parameter design method are verified by simulation and experiment. This work is supported by National Natural Science Foundation of China (No. 51707126) and Science and Technology Project of State Grid Corporation of China (No. SGLNDK00DWJS1800020).