IEEE TRANSACTIONS ON MAGNETICS, VOL. 48, NO. 2, FEBRUARY 2012 1011 Optimum Equivalent Models of Multi-Source Systems for the Study of Electromagnetic Signatures and Radiated Emissions From Electric Drives A. Sarikhani, M. Barzegaran, and O. A. Mohammed, Fellow, IEEE Energy Systems Research Lab., Electrical and Computer Eng. Dept., Florida International University, Miami, FL 33174 USA An optimum equivalent electric machine model for 3-D finite element (3DFE) simulation and evaluation of radiated electromagnetic field emissions in a multi-machine environment is presented. A typical example of such systems includes electric motors and cable runs electric drives. Initially, the detailed geometrical model of the machine was simulated in a 3DFE quasi-static electromagnetic domain. An optimum equivalent model was created using an optimization process based upon the difference between the observed electric and mag- netic far fields from both the detailed geometrical and the equivalent models. The equivalent model was validated in several examples. The computed electromagnetic signature results from the equivalent model show acceptable accuracy as compared with the detailed geometrical model of the machine. The equivalent machine model was obtained with significant reduction in computation time needed for the evaluation of the radiated fields. The proposed model can be used as an effective method for the simulation of signatures and radiated electromagnetic field emissions from electric drives in computationally intensive environments. Index Terms—Electromagnetic interference (EMI), multi-source environments, signature analysis, wave propagation. I. INTRODUCTION E VALUATION of electromagnetic signatures and radiated fields for the computational assessment of electromag- netic interference (EMI) can be computationally demanding. During the design stage, this problem can be challenging and contribute to increasing cost. We are proposing a model that can contribute to optimally minimizing the product cost, reduce time-to-market and lessen trial-and error approaches. Such a model can also be used to develop mitigation strategies to meet product safety and compliance standards [1]–[3]. Electrical machines are the backbone of many industries. Be- cause of their complex structure, numerical modeling in an en- vironment with finite computational boundaries for quasi-static EMI at relatively far distances represent a challenging computa- tional problem especially when the number of multi conductor systems in the environment are increased. In the recent years, there has been an increased interest in the expansion of multi- level numerical simulation tools for the investigation of EMC, EMI, and signature issues in the early design stages of electrical apparatus and specially their utilization environments. Some studies evaluating the signature patterns and radiated emissions from multi-machine environments represent a progress in this important area of product development [4]–[6]. Physics-based numerical modeling of multi-source environments, from the de- vice level to the environment level remains challenging problem in computational electromagnetics. As the number of the con- ductive components within the environment is increased, the number of self and mutual coupling capacitances and induc- tances are increase. Therefore, without a proper model reduc- tion, the FE-based simulation of the physical system may be difficult to achieve. Also, the simplification of each independent subsystem within the environment is vital for the creation of nu- merically viable and simpler environment. Manuscript received July 07, 2011; revised October 02, 2011 and October 16, 2011; accepted October 16, 2011. Date of current version January 25, 2012. Corresponding author: O. A. Mohammed (e-mail: mohammed@fiu.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2011.2173794 This paper offers an optimal equivalent model for an example induction machine representing a multi conductor system in a study environment. The model was created for simulating quasi-static far electromagnetic fields propagated from a multi conductor environment with a large number of degrees of freedom. The proposed model makes it possible to reduce the mesh size and make the numerical computation possible. With this model, it is possible to reduce the number the mesh sizes and the freedom in the finite element domain in a quasi-static EMI problem with complex geometrical components. II. CREATION OF OPTIMAL EQUIVALENT MODELS A. Theoretical Definitions In a given environment, the far field is defined as the field at a distance at which the normal magnetic flux density or normal electric field propagated from the multi-conductor component in any arbitrary plane parallel to the component has only one local maximum. The near field defined, vice versa, as when more than one local maximum appear in any arbitrary plane. Figs. 1 and 2 show examples of the near and far magnetic fields, respectively. These figures are the stationary solutions of a two-machine en- vironment simulated by 3-D quasi-static finite element analysis. It is seen that the far field almost appeared when the distance of the measurement plane to the largest machine conductive part become significant enough. The propagated quasi-static electric and magnetic fields from the electrical components specifically at a far distance from the device is the most effective index in investigating EMI issues. In [7] and [8], the basis of the analytical methods for the far field solution is presented. Although the analytical solutions offer low computational complexity, it fails to handle the multipart envi- ronments. The role of the numerical simulation tools becomes more im- portant when material diversities and geometrical complexities increase from a certain level. However, these methods also have serious computational capacity limitations. In the static magnetic field domain, the far field definition de- fines the fact that the normal magnetic flux density of a magnetic dipole is always coincident with the definition of the far field 0018-9464/$31.00 © 2012 IEEE