We calculate thermodynamic potentials and their derivatives for the three-dimensional O(2) model using tensor-network methods to investigate the well-known second-order phase transition. We also consider the model at nonzero chemical potential to study the Silver Blaze phenomenon, which is related to the particle number density at zero temperature. Furthermore, the temperature dependence of the number density is explored using asymmetric lattices. Our results for both zero and nonzero magnetic field, temperature, and chemical potential are consistent with those obtained using other methods.