PEEC modeling and verification for broadband analysis of air-core reactors

Abstract: There is an increasing utilization of modern Power Electronic (PE) devices in power systems, in for example, harmonic filters, reactive power compensation, and current limiting applications. The operational frequencies and switching rates of the PE devices now cover up to the megahertz range. As a consequence, an understanding of the functionality of static components like transformers, inductors (reactors), and capacitors in the presence of these high frequency signals are challenging issues. Present standards and legislation on EMC also put more constraints on the design of these power components. The focus of this work is the creation of high frequency electromagnetic models for power electronic components, with emphasis on air-core reactors. Attempts to model air-core reactors include lumped models, which typically consists of a series of mutually coupled lumped section, neglecting internal couplings within each section. This approach is limited to low frequencies where the voltage distribution along the turns in each section can be considered linear. For higher frequencies (several MHz), a more distributed model accounting for the electromagnetic couplings is inevitable. The Partial Element Equivalent Circuit (PEEC) modeling approach is suitable for mixed circuit and electromagnetic problems. It is based on the integral forms of Maxwell's equations upon which an equivalent circuit based model is developed. In this study, a broadband model for air-core reactors is created using the PEEC approach. Each reactor turn is represented by a finite number of interconnected bars or volume cells. From the volume cells equivalent circuit parameters, mainly the partial inductances, the coefficients of potential, and the resistances are evaluated using analytical routines. The electromagnetic coupling between the cells is represented by mutual partial inductances and the mutual coefficients of potential. The parameters are assembled into matrix equations, whose solution gives the current and voltage distribution in the model windings. The current distribution is post-processed to obtain the field distribution in the vicinity of the reactor. The PEEC reactor model was validated by comparing model results with measurements done on a laboratory air-core reactors and showed good agreement in both time and frequency domain. The time complexity for the PEEC simulation is greater compared to the corresponding lumped models, but the PEEC models give a better characterization at high frequencies. Using the frequency response from the PEEC model, smaller RLC resonance circuits replicating the same behaviour, can be synthesized. These reduced circuits can be easily included in system simulations as lumped components along side other power components. The PEEC model could also be helpful in design and diagnosis work for air-core reactors. Though the focus is on air-core reactors, the model could be enhanced to characterize other devices like power transformers.