Monday 25-Oct-21 |

Power Oriented Graph modelling of electrical systems

Contributor

Roberto ZANASI (lecturer)

 

Objective

The main characteristics of the Power-Oriented Graphs (POG) modelling technique will be presented and compared with the well known Bond Graphs technique.

 

Outline

The main characteristics of the Power-Oriented Graphs (POG) modelling technique will be presented. Then, the POG modelling technique will be compared with the well known Bond Graphs technique. A few POG modelling examples, mainly in the field of the electrical systems, will be illustrated. In particular, the following physical systems will be considered: a three-phase brushless motor, a three-phase asynchronous motor and an electronic control of a multi-phase lighting system.
POG uses only two basic graphical blocks (the "elaboration" and "connection'" blocks) for modelling physical systems; 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 state space mathematical model of a system can be "directly" obtained from the corresponding POG representation; when some dynamic parameters of the system tend to zero (or to infinity), the "reduced" POG model can be easily obtained by using a proper ''congruent transformation''.
The POG technique is used for modelling the following electrical systems: a three-phase brushless motor, a three-phase asynchronous motor and an electronic control of a multi-phase lighting system. The POG models of the electrical motors show very well, from a "power" point of view, their 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. With a proper choice of the reference frame, the dynamic models of the electric motors become very simple and clear. For obtaining the dynamic models of the motors, a Lagrangian/Hamiltonian methodology has been used. For describing and transforming the dynamic models of the motors, a very compact ''exponential'' notation has been used.

Fig. 1: Electronic control of a multi-phase lighting system: the POG model

 

References

R. Morselli, R. Zanasi, R. Cirsone, E. Sereni, E. Bedogni, E. Sedoni,
"Dynamic modeling and control of electro-hydraulic wet clutches",
IEEE-Intelligent Transportation Systems'03,
2004, vol. 1, pp. 660-665.

R. Morselli, R. Zanasi,
"Control of mechatronic systems by dissipative devices: application to semi-active vehicle suspensions",
American Control Conference, 2006

R. Morselli, R. Zanasi, G. Sandoni, E. Sedoni,
"Detailed and reduced dynamic models of passive and active limited-slip car di?erentials",
Mathematical and Computer Modelling of Dynamical Systems
Vol. 12, no. 4, August 2006, pp. 347–362


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