Geomagnetically induced currents (GICs) result from the interaction of the time variation of ground magnetic field during a geomagnetic disturbance with the Earth's deep electrical resistivity structure. In this study, we simulate induced GICs in a hypothetical representation of a low-latitude power transmission network located mainly over the large Paleozoic Paraná basin (PB) in southern Brazil. Two intense geomagnetic storms in June and December 2015 are chosen and geoelectric fields are calculated by convolving a three-dimensional (3-D) Earth resistivity model with recorded geomagnetic variations. The dB/dt proxy often used to characterize GIC activity fails during the June storm mainly due to the relationship of the instantaneous geoelectric field to previous magnetic field values. Precise resistances of network components are unknown, so assumptions are made for calculating GIC flows from the derived geoelectric field. The largest GICs are modeled in regions of low conductance in the 3-D resistivity model, concentrated in an isolated substation at the northern edge of the network and in a cluster of substations in its central part where the east-west (E-W) oriented transmission lines coincide with the orientation of the instantaneous geoelectric field. The maximum magnitude of the modeled GIC was obtained during the main phase of the June storm, modeled at a northern substation, while the lowest magnitudes were found over prominent crustal anomalies along the PB axis and bordering the continental margin. The simulation results will be used to prospect the optimal substations for installation of GIC monitoring equipment.