This paper presents an analytical study on the energy dissipation capacity of unbonded post-tensioned self-centering precast concrete beam-column connections that have a friction device only below the beam or on the web. The energy dissipation capacity is quantified using an effective energy dissipation ratio. To quantitatively evaluate the influence of three design parameters on the energy dissipation capacity, nonlinear analyses were carried out using a section-analysis method to predict the relationship between the moment and the relative rotation at the beam-column interface under cyclic loading. The design parameters were the initial post-tensioning force in the unbonded post-tensioning tendon, the friction force, and the location of the friction device. The analysis results show that the effective energy dissipation ratios for connections whose friction devices are in the same location can be related to the ratio of the friction force to the initial post-tensioning force.