The use of quasi-Z-source inverters (qZSIs) for DC-DC power conversion applications has gained much recognition when dealing with grid-tied renewable energy resource integrations. This paper proposes a novel self-powered dynamic system (SPDS) involving a piezoelectric vibration energy harvester (PVEH) using qZSI to establish interoperability with a DC load rated at 16.15 mW. Based on uncertain output performances from a piezoelectric cantilever beam (CB), the qZSI-based PVEH serves as a dynamic voltage restoration unit that establishes load-following synchronisation. It uses a proportional-integral based boost controller (PI-based BC) to generate strategic ordering of shoot-through voltage amplification into pulse-width modulation (PWM) gating sequences. The SPDS was modelled using two software based on commercially available product specifications: (i) COMSOL Multiphysics to mechanically design and optimise a CB. (ii) PSCAD/EMTDC to electronically design and integrate the qZSI with the optimised CB, while functioning as a testbed to model the SPDS against arbitrary wind speed and structural vibration frequency data collected from an above-ground mass rapid transit (MRT) train station in Khatib, Singapore. The acquired simulation results have depicted desirable transient responses at respective sub-systems, procuring fast settling-time responses, negligible steady-state error, as well as high efficiencies of 94.07% and 91.64% for the CB and SPDS respectively.