Helical-coil steam generator (HCSG) technology is a major design candidate for small modular reactors due to its compactness and capability to produce superheated steam with high generation efficiency. In this paper, we investigate the feasibility of the passively autonomous power maneuvering by coupling the 3-D transient multi-physics of a soluble-boron-free (SBF) core with a time-dependent HCSG model. The predictor corrector quasi-static method was used to reduce the cost of the transient 3-D neutronic solution. In the numerical system simulations, the feedwater flow rate to the secondary of the HCSGs is adjusted to extract the demanded power from the primary loop. This varies the coolant temperature at the inlet of the SBF core, which governs the passively autonomous power maneuvering due to the strongly negative coolant reactivity feedback. Here, we simulate a 100-50-100 load-follow operation with a 5%/minute power ramping speed to investigate the feasibility of the passively autonomous load-follow in a 450 MWth SBF PWR. In addition, the passively autonomous frequency control operation is investigated. The various system models are coupled, and they are solved by an in-house Fortran-95 code. The results of this work demonstrate constant steam temperature in the secondary side and limited variation of the primary coolant temperature. Meanwhile, the variations of the core axial shape index and the core power peaking are sufficiently small.