This paper presents a self-identification approach for reluctance synchronous machines (RSMs) in combination with analytical flux linkage prototype functions. Due to the severe magnetic saturation, good machine knowledge is required for high-performance electrical drive systems. The proposed self-identification method injects bipolar voltage pulses to an inverter-fed machine at standstill, without additional test equipment and requirements. Within an extremely short time, nonlinear flux linkages, including the magnetic saturation and cross-coupling effects, can be obtained. Instead of saving the samples as lookup tables (LUTs), they are approximated by analytical flux linkage prototype functions, which are parametrized by few parameters, and continuously differentiable throughout the whole operation range. The effectiveness of the developed self-identification method is experimentally validated for a nonlinear 4.0kW RSM. The results prove (i) the simple and time-saving procedure of the self-identification method, (ii) the high approximation accuracy and (iii) the benefits of the flux linkage prototype functions for real-time applications.