The POG technique for Modelling Multi-phase Permanent Magnet Synchronous Motors

In the paper the Power-Oriented Graphs (POG) technique is used for modelling n-phase permanent magnet synchronous motors. The POG technique is a graphical modelling technique which uses only two basic blocks (the elaboration and connection blocks) for modelling physical systems. Its main characteristics are the following: it keeps a direct correspondence between pairs of system variables and real power flows; the POG blocks represent real parts of the system; it is suitable for representing physical systems both in scalar and vectorial fashion; the POG schemes can be easily transformed, both graphically and mathematically; the POG schemes are simple, modular, easy to use and suitable for education. The POG model of the considered electrical motor shows very well, from a ``power'' point of view, its internal structure: the electric part of the motor interacts with the mechanical part by means of a ``connection'' block which neither store nor dissipate energy. The dynamic model of the motor is as general as possible and it considers an arbitrary odd number of phases and an arbitrary number of harmonics of the rotor flux waveform. Generalized orthonormal transformations allow to write the dynamic equations of the system in a very compact way. The model is finally implemented with Matlab/Simulink software. The Simulink structure of the motor clearly reflects its POG representation. Simulation results are then presented to validate the machine model.