The state of charge (SOC) is a key indicator to show whether a compressed hydrogen tank meets refueling requirements, so it is worth to study effects of the refueling parameters on it. A new SOC analytical solution is obtained based on a simple thermodynamic model. By applying a mass balance equation and an energy balance equation for a hydrogen storage system, a differential equation was obtained. An analytical solution of hydrogen temperature was deduced from the solution of the differential equation, then an analytical solution of hydrogen mass was further deduced based on the analytical solution of hydrogen temperature with some mathematical modifications. By assuming the hydrogen density inside the tank is uniform, the SOC, which defined as a ratio of hydrogen density to the full-fill density, can be transformed to be the ratio of hydrogen mass to the full-fill mass. The hydrogen mass can be calculated from analytical solution of hydrogen mass, while the full-fill mass is supposed to be a constant value. The full-fill density of 35 MPa and 70 MPa tanks at 15 °C are respectively 24.0 g/L and 40.2 g/L, and if the volume of the tank is known, the full-fill mass can also be calculated. The analytical solution of SOC can be unitized to express the reference data, the contributions of inflow temperature and mass flow rate on SOC are presented for a Dynetek type III tank (40 L, metallic liner) and a Hexagon type IV tank (29 L, plastic liner). In addition, the two-parameter effect of inflow temperature and mass flow rate on SOC are presented. The Nusselt number and Reynolds number are utilized to modify the analytical model, the relationship between SOC and refueling parameters can be obtained through the method of fitting. The fittings show a good agreement. The SOC can be determined from the refueling parameters based on the model with more physical meaning. The method developed in this research can be applied to the control algorithm of refueling stations to ensure safety and efficiency.
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