Objectives:
Multi Conductor systems exhibit a large number of self and mutual coupling inductances & capacitances in their operating environments.
Need to create a numerically viable model of multi conductor systems without reduced accuracy.
Developing an optimum multi-conductor equivalent model of a 3-phase induction machine a multi conductor example.
Model used for the 3D-FE evaluation of radiated electromagnetic field emissions and signature in a multi-machine environment.
The results were compared with the detailed geometrical model of the machine in 3DFE quasi-static electromagnetic domain.
An optimum equivalent model was developed through an optimization process based upon the difference between the observed electric and magnetic far fields from detail geometrical and equivalent models.
The equivalent model was validated in several examples.
Far and Near Fields in Multi Conductor Systems:
The far field appears with just one local maximum in any arbitrary plane parallel to the component. It also appear when the distance of the measurement plane to the largest machine conductive part become large. The near field appears with more than one local maximum in any arbitrary plane parallel to component .
The propagated quasi-static far electric and magnetic fields from electrical components can be the most effective index in investigating EMI and signature studies.
Optimal Equivalent Shape for an Example of Induction Machine:
The symmetry of far field, calculated by the detailed geometrical model, along the axial direction of the machine in any X=a, Y=b planes, and the symmetry of the far field, calculated by detail geometrical model in radial direction in any Z=c plane, are the main factor of the choice of an equivalent cubic shape.
Equivalent cubic model Variables
- Currents in cube sides: (ix0 … ix3, iy0 … iy3, iz0 … iz3)
- Voltages at the Cube nodes: (V1, V2),
- Length of the cube sides: (A, B, C)
The Model Variables:
An evolutionary-based Optimization problem is defined with and Objective Function
Bi(x, y, z)3DFE, and Ei(x, y, z)3DFE, are normal magnetic flux density and normal electric fields that are calculated along three finite lines for detail geometrical models. Bi(x, y, z)Eq.model, and electric field, Ei(x, y, z)Eq.model are the corresponding measurements from the equivalent cube model.
Quasi-Static Field Formulation:
Normal Magnetic flux density throughout X-Y plane for the equivalent model (a), for the detail geometrical model (b), Normal electric field throughout XY plane for the equivalent model (c), for the detail geometrical model (d), all for the one motor case of study
Model Validation with two Induction Motors:
Model Revision:
(a) Revised version of the cube model
(b) Normal Magnetic flux density in X-Y plane for the equivalent model
(c) for the detailed geometrical model
(d) Normal electric field throughout XY plane for the equivalent model
(e) for the detail geometrical model (e), all for the one motor case of study
Conclusion:
- Since the assumption of quasi static fields in this problem is valid, the equivalent model does not change with fundamental component of machine frequency. Moreover, if the iron core saturation is ignored, there is a linear relationship among the magnetic field and the actual phase current of the machine and the current in sides of the equivalent model.
- As long as the terminal voltage and phase currents are fixed, in a balanced three-phase induction machine, the far field does not change with time.
- The equivalent models can be simply recreated when the phases current, terminal voltage, or the frequency of the machine changes over the time.
- Revision of the model by adding an additional current loop or curving the current flowing in each side improves the results of the magnetic field computed by the equivalent model.