Small-signal instability is easy to occur when the single-delta bridge-cell-based static synchronous compensator (SDBC-STATCOM) is connected to the weak receiving grid. This paper first presents the harmonic state-space (HSS) model of the SDBC-STATCOM. Then, to assess interaction stability, the multi-input multi-output (MIMO) impedance model and the single-input single-output (SISO) equivalent impedance model are further deduced. Furthermore, the impedance characteristics of the SDBC-STATCOM and the influence of parameter variation are analyzed to provide physical insights into the harmonic oscillation in the weak grid. The impedance characteristic analysis indicates AC voltage control loop will deteriorate the stability of SDBC-STATCOM. In addition, an improved AC voltage control is proposed to improve impedance characteristics and suppress harmonic oscillation. Finally, the effectiveness of the derived model and proposed oscillation suppression strategy is verified by simulation results.