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We describe methodologies for comprehensive and reduced-order modeling of solid-oxide-fuel-cell (SOFC) power-conditioning system (PCS) at the subsystem/component and system levels to resolve the interactions among SOFC, balance-of-plant subsystem, and power-electronics subsystem (PES) and application loads (ALs). Using these models, we analyze the impacts of electrical-feedback effects (e.g., ripple-current dynamics and load transients) on the performance and reliability of the SOFC. Subsequently, we investigate the effects of harmonics in the current, drawn from the SOFC by a PES, on the temperature and fuel utilization of the SOFC. We explore the impacts of inverter space-vector modulation strategies on the transient response, flow parameters, and current density of the SOFC during load transients and demonstrate how these two traditionally known superior modulation/control methodologies may in fact have a negative effect on the performance and durability of the SOFC unless carefully implemented. Further, we resolve the impacts of the current drawn by the PES from the SOFC, on its microcrack density and electrode/electrolyte degradation. The comprehensive analytical models and interaction-analysis methodologies and the results provided in this paper lead to an improved understanding, and may yield realizations of cost-effective, reliable, and optimal PESs, in particular, and SOFC PCSs, in general.