A pump system for a water supply mains has at least one pump device, a pressure detecting sensor at the pressure side of the pump device, a flow detecting sensor of the pump device, several pressure sensor units (D) remote arranged remotely from the pump device in different part regions of the mains, and a pump control device. The control device includes a model formation module designed in each case to produce a model (A) representing pressure loss from the pressure sensor to the position of the respective pressure sensor unit (D), based on several pressure measured values of at least two pressure sensor units (D) for the at least two associated part regions. The control device is designed for regulation of the pump device based on produced models (A), as well as to a corresponding method for regulation of a pump device in a water supply mains.