Federica Grossi

Optimal rotor flux shape for multi-phase permanent magnet synchronous motors

In the paper the power-oriented graphs (POG) technique is used for modeling m-phase permanent magnet synchronous motors and a study on the optimal rotor flux is given. The POG model shows the ldquopowerrdquo internal structure of the considered electrical motor: the electric part interacts with the mechanical part by means of a ldquoconnectionrdquo block which neither stores nor dissipates energy. The dynamic model of the motor is as general as possible and it considers an arbitrary odd number of phases. The rotor flux is analyzed, in particular in order to minimize the currents needed for the torque generation, and its optimal shape is given. The model is finally implemented in Matlab/Simulink and the presented simulation results validate the machine model and the rotor flux choice.

The POG technique for modeling planetary gears and hybrid automotive systems

In this paper the Power-Oriented Graphs (POG) technique is used for modeling planetary gears and hybrid automotive systems. Some basic properties of the POG technique are firstly given. An extended dynamic model of a planetary gear with internal elasticity is presented. Then a POG congruent state space transformation is used to transform and reduce the system when the elasticities or the inertias go to zero. The obtained reduced model is used as central element of an hybrid automotive power structure (endothermic engine, multi-phase synchronous motor and vehicle dynamics). Simulation results of the modeled hybrid system ends the paper.

Differences and common aspects of POG and EMR energy-based graphical techniques

Three main modeling techniques have been proposed in the past years: Bond Graphs (BG), Power-Oriented Graphs (POG) and Energetic Macroscopic Representation (EMR). These modeling techniques are energy-based graphical techniques which exploits the power interaction between subsystems as basic concept for modeling. In this paper a comparison between the POG and EMR techniques is presented. These techniques have many aspects in common and also differences that are pointed out in the paper. The POG schemes have a well-defined mathematical structure and use vectorial compact forms when the system complexity increases. The EMR constitutes a graphical tool useful for modeling, simulation and control of dynamical systems.

Complex Dynamic Models of Multi-Phase Permanent Magnet Synchronous Motors

Abstract In the paper two power-invariant real and complex state space transformations for modeling multi-phase electrical machines in a compact and general form are proposed. In particular the paper deals with the modeling of multi-phase permanent magnet synchronous machines with an arbitrary number of phases and an arbitrary shape of the rotor flux. The dynamic model of the motor is obtained using a Lagrangian approach and in the frame of the Power-Oriented Graphs technique. The obtained models are equivalent from a mathematical point of view and can be directly implemented in Simulink. The complex transformed model is quite compact and uses a reduced order state vector. Some simulation results end the paper.

The POG technique for modeling multi-phase asynchronous motors

In this paper the dynamic model of a multi-phase asynchronous motor has been obtained using the Power-Oriented Graphs (POG) technique and applying the Lagrangian approach. The “power” internal structure of the motor has been clearly identified. The steady-state behaviour of the motor has been analyzed putting in evidence the mathematical relations between the current and voltage vectors in the transformed rotating frame. In particular an interesting expression for the generated motor torque has been obtained. Some simulation results are finally reported.

Vectorial control of multi-phase synchronous motors using POG approach

This paper deals with the vectorial control of multiphase permanent magnet synchronous machines. The dynamic model of the motor is obtained using the Power-Oriented Graphs technique which clearly shows the power flows within the system and allows to write the dynamic equations of the system in a proper rotating reference frame. Moreover the obtained model can be directly implemented in Simulink. Starting from the model of the motor, a torque control law with saturated input voltages is proposed based on a new “current” approach. The obtained control is very effective and with a simple structure. Simulation results are provided.

Modeling of multi-phase permanent magnet synchronous motors under open-phase fault condition

This paper deals with the modeling of multi-phase permanent magnet synchronous motors under open-phase fault condition. Multi-phase electrical motors offer high reliability thanks to their capability to operate safely even in case of faults such the loss of some phase. In this paper the model of a multi phase PM machine in the case of open phase fault condition is proposed. The model is suitable for faults occurring at any phases: the faults can happen on one single phase or more than one phase (both adjacent and not adjacent phases). Moreover the model holds for any shape of the rotor flux and for a generic odd number of phases.

Modeling and control of Power-split hybrid electric vehicles

In this paper a Power-split hybrid automotive system is considered, including a multi-phase synchronous motor, an internal combustion engine and a planetary gear as key element to split power in this propulsion system. The dynamic model of a planetary gear with internal elasticity is presented and the model of the whole vehicle is given using the Power-Oriented Graphs approach. A global control is designed to obtain different operation modes of the vehicle: engine start, battery charging, hybrid traction, recovery of braking energy. Simulation results of the modeled HEV are provided showing the effectiveness of the proposed model and control.

Modelling of an internal combustion engine using power-oriented graphs and electrical analogy

In this paper, the power-oriented graphs (POG) technique is used for modelling an internal combustion engine through electrical analogy. The aim of the authors, starting from an analogy with electrical systems, is to simplify the approach eliminating the space dynamics, while preserving the time dynamics. In this way, one can obtain an engine description similar to an electric circuit, with all the useful consequences in terms of existence and numerical availability of the solution. The advantages are in the specific correspondence found between the engine components and variables with electrical counterparts. The main benefit achievable with this methodology is the simplicity to compose the whole engine model and customise it including the differential equations of the engine in state space form. The POG technique is a graphical modelling technique which uses only two basic blocks for modelling physical systems and the state space mathematical model of a system can be ‘directly’ obtained from the corresp...

Modelling and control of a vehicle with tire-road interaction using energy-based techniques

In this paper a vehicle with the modelling of its tire-road interaction is described using two different energy-based graphical techniques: Power-Oriented Graphs (POG) and Energetic Macroscopic Representation (EMR). The main features of both approaches are presented and an integration between them is proposed: they can be used together to model different parts of the same system. Using the two techniques the whole vehicle can be represented with either a mathematical or a macroscopic view. From EMR an inversion-based control is given in order to control the vehicle velocity.