Hydrogen is a promising energy carrier, and the port fuel injection (PFI) is a fuel-flexible, durable, and relatively cheap method of energy conversion. However, the contradiction of increasing the power density and controlling NOx emissions limits the wide application of PFI hydrogen internal combustion engines. To address this issue, two typical thermodynamic cycles the Miller and Otto cycles are studied based on the calculation model proposed in this study. The thermodynamic cycle analyses of the two cycles are compared and results show that the thermal efficiency of the Miller cycle (eta(Miller)) is higher than eta(Otto), when the multiplied result of the inlet pressure and Miller cycle coefficient (delta(M gamma M)) is larger than that of the Otto cycle (i.e., the value of the inlet pressure ratio multiplied by the Miller cycle coefficient is larger than the value of the inlet pressure ratio of the Otto cycle). The results also show that the intake valve closure (IVC) of the Miller cycle is limited by the inlet pressure and valve lift. The two factors show the boundaries of the Miller cycle in increasing the power density of the turbocharged PFI hydrogen engine. The ways of lean burn + Otto cycle (LO), stoichiometric equivalence ratio burn + EGR + Otto cycle (SEO) and Miller cycle in turbocharged hydrogen engine are compared, the results show that the Miller cycle has the highest power density and the lowest BSFC among the three methods at an engine speed of 2800 rpm and NOx emissions below 100 ppm. The brake power of the Miller cycle increases by 37.7% higher than that of the LO and 26.3% higher than that of SEO, when gamma(M) is 0.7. The BSFC of the Miller cycle decreases by 16% lower than that of the LO and 22% lower than that of SEO. However, the advantage of the Miller cycle decreases with an increase in engine speed. These findings can be used as guidelines in developing turbocharged PFI hydrogen engines with the Miller cycle and indicate the boundaries for the development of new hydrogen engines. (C) 2016 Elsevier Ltd. All rights reserved.