The use of a multi-parallel converter system has many advantages in increased scalability, better maintenance, scheduling, and improved output current quality. However, a periodic zero-sequence circulating current (ZSCC) may occur due to the asymmetry of parallel-connected converters. ZSCC produces additional losses and possible instability of the system. Therefore, proper control must be applied to suppress this harmful ZSCC. In order to design an effective controller for suppressing ZSCC, it is necessary to analyze the circulating current. However, most of the studies conducted so far have applied the controller without detailed analysis. This paper mathematically analyzes the ZSCC spectrum by using the Fourier series to identify which harmonics are included in ZSCC. From the results of the analysis, the necessity of multi-resonant controllers to suppress the ZSCC at specific harmonics is demonstrated. Simulation and experiments are conducted to validate the analysis results and necessity of multi-resonant controllers.