In modular power converters, the dc-link capacitor has the highest failure rate due to thermal stress, reducing system performance and reliability. Current harmonics are one of the prominent causes of thermal stress on the dc-link capacitor that may get instigated by the resonance between the dc-link capacitor and stray inductance of the busbar. The dc-link capacitor current harmonics mitigation through busbar design optimization has not been reported. The challenge lies in analyzing the profound resonance characteristics of high order dc-link busbar impedance network as no insightful information can be obtained from impedance analyzers. This paper features a new strategy for high power modular converters that splits the high order dc-link busbar impedance network into corresponding lower-order sub-units. Then, the required relationship between resonating components and corresponding resonance frequencies is attained by exploiting the structural symmetry of the standard modular power unit as well as the inheritance relationship between sub-circuit units and the combined network. Finally, leveraging the derived resonant frequencies expressions, busbar structure is optimized, and up to 23% reduction in capacitor RMS current is achieved. Simulation and experimental results are provided to validate the efficacy of the proposed analysis method. The in-depth theoretical study featured in this paper can dictate not only the busbar design optimization but also a key to improve capacitor lifetime and reliability of the system.