Electromagnetic modeling of Electric Motors

Electromagnetic analysis techniques used in motor design usually fit into one of the following two categories:

• Analytical Methods
• Numerical Methods (Finite Element Analysis) (as used in Motor-CAD):

A brief description of the two methods together with a list of their main advantages/disadvantages is given below:

Analytical Methods

The analytical modeling of the electric motors relies on the electromagnetic field and generalized forces theorem. In a simplified form, the latter theorem states that the electromagnetic torque (or force) is given by the system coenergy or energy variation with incremental rotor displacement, if the currents and flux-linkages are constant during the elemental rotor movement. As the system is an electrical motor, the energy or coenergy can be expressed as a function of products between flux-linkages and currents. Furthermore, the flux-linkages are expressed as products between reactances and currents. Consequently, all the developed analytical models that compute the electromagnetic torques in AC motors are relying on the equivalent circuits parameters (resistances and reactances) that can have fixed or variable (linear or non-linear) values. Thus, the precision of any analytical model that estimates the electromagnetic torque in a rotating motor depends on the accuracy level that characterizes the motor parameters.

Advantages:

• it gives an important starting point to any preliminary design and analysis of an electrical motor.
• the analytical methods are based on measurable physical parameters and permit the inclusion of non-linear effects. Therefore, many electrical machinery designers address new prototypes development through the use of analytical tools.

Disadvantages:

• there are still physical phenomena that occur in rotating motors (e.g., stray load losses) and cannot yet be mathematically modelled.
• several simplifying assumptions are necessary for any analytical motor model.
• the accuracy can be low unless significantly improved if the most important non-linear effects (i.e., saturation, core loss, windage and friction loss, and harmonics) are modeled through a sufficiently high number of elements in the mathematical model of the motor.

Numerical modeling

The numerical modeling of electric motors has its basics in the electromagnetic fields theory. There are several mathematical approaches such as finite-element method (FEM), finite-difference method (FDM), boundary element method (BEM) to solving the system equations in numerical methods. Regardless of the mathematics of these methods, the electromagnetic torque is estimated using either the Maxwell stress theory, virtual work (energy variation) or Laplace method (magnetizing currents).

Advantages:

• Progressive improvement in the power and speed of computers has resulted in a situation in which the numerical analysis of electrical machines is successfully used as both a research and design tool. In rotating machines, the model most widely employed is two-dimensional
• If the problem settings are correctly formulated, the numerical modeling of rotating motors will usually lead to a higher accuracy level for the estimated results than the analytical modeling

Disadvantages:

• 2D models still ignore the end-effects and the three-dimensional eddy currents effect.
• 3D models though potentially more accurate, require one or two orders of magnitude more of computer resources;
• 3D models are still beyond the bounds of economic viability, especially in the electrical machinery industry where tens of design versions for only one motor might be requested in one day..

In modern practise, a combination of analytical modeling and numerical modeling is required. A preliminary design optimised through analytical modeling represents the best initial solution for a further numerical model. There are also very well established combined numerical and analytical models that will numerically simulate the electrical motor and analytically simulate the external circuits from the drive system (inverters, connections, etc.)