Synchronous machines have found wide application in a variety of technological fields, ranging from domestic to industrial, to transportation. In particular, Permanent Magnet Synchronous Machines are the most common typology thanks to their higher power density and simpler construction. Hence, they have attracted scientific attention with the aim of optimizing their design and control strategies and, also, techniques for sensorless operation have received particular focus. In fact, eliminating the need for mechanical sensors skews in the advantage of using such machines due to the consequent reduction of space and cost of the driving system. Many techniques for the estimation of the electrical rotor position from electrical measurements have been proposed, either relying on the exploitation of the back-EMF voltage or on machine anisotropies. This work lies in this research field and proposes to offer a mathematical description of the so-called Direct Flux Control (DFC) sensorless technique. This technique, differently from the majority of other proposed approaches, exploits machine anisotropies by measuring the zero-sequence voltage of the machine, i.e. requiring measurements of the star-point voltage. After deriving a mathematical formulation of the DFC technique for generic synchronous machines first and for PMSMs later, an experimental investigation is presented. Moreover, an insight into sensorless condition monitoring based on the DFC technique is provided.