PRZEGLĄD ELEKTROTECHNICZNY (Electrical Review), ISSN 0033-2097, R. 85 NR 7/2009 31
Arash H. ISFAHANI, Sadegh VAEZ-ZADEH, and Abbas N. KHODABAKHSH
School of Electrical and Computer Engineering, University of Tehran
Calculation of Maximum Short Circuit Electromagnetic Forces in the IPB Using Time Stepping Finite Element Method
Abstract. Calculation of maximum short circuit electromagnetic forces is one of the most important factors in the mechanical design and optimization of isolated phase buses which is required by the manufacturing companies. In this paper, these forces as well as associated eddy currents and magnetic fields are calculated using finite element method. A software program is developed to find the worst conditions at which a maximum short circuit electromagnetic force occurs. It is shown that the maximum force strongly depends on the initial phase current angle at the instance the short circuit occurs. Two common enclosure material i.e. aluminum and steel are also compared regarding short circuit forces.
Streszczenie..Maksymalne siáy elektromagnetyczne zwarciowe to jeden z najwaĪniejszych parametrów mechanicznych przy projektowaniu i optymalizacji izolowanych szyn fazowych. W artykule obliczono te siáy metodą elementu skoĔczonego przy uwzglĊdnieniu prądów wirowych i i pola magnetycznego. Oprogramowanie obliczeniowe udoskonalono aby moĪna byáo znaleĨü krytyczne warunki wystĊpujące w stanach zwarcia.
Wykazano Īe maksymalna siáa zaleĪy od początkowej fazy prądu w momencie zwarcia. Dwa typowe materiaáy obudowy – aluminium i stal zostaáy porównane. (Obliczenia maksymalnej elektromagnetycznej siáy zwarciowej w izolowanej szynie przy wykorzystaniu metody elementów skoĔczonych)
Keywords: Isolated phase bus, Electromagnetic force, Magnetic field, Short Circuit, Finite element method, Enclosure material Sáowa kluczowe:.
Introduction
Three phase isolated phase buses (IPBs) are increasingly used in power plants to carry electricity from generators to main and auxiliary transformers. Using IPBs, instead of other types of connecting buses, the magnetic field density reduces and the security of system increases because of the isolation between phases. To achieve a reliable design of an IPB, accurate understanding of its magnetic field distribution, eddy current losses, thermal conditions, insulation and shielding problems and short circuit forces are required. The magnetic fields, eddy currents and electrical losses in IPBs have been extensively investigated [1-6]. The thermal behavior of IPBs and other heavy current busbars is also consider in many researches so far [7-15]
Short circuit forces are the most important factor in mechanical design of IPBs since they may cause permanent damage to IPBs. Therefore, these forces must be considered accurately. Different methods can be employed to calculate the forces, e.g. the empirical method, the image current method, the complex vector potential method, and numerical methods. The empirical method has been used to evaluate the forces by certain companies and researchers [16, 17]. This method uses a scaled down experimental system and is very costly and difficult. Also, using the scaled model rather than the real model may lead to inaccurate results. Imaging method has been applied to calculate the forces on IPBs in many researches [18-19].
However, this method cannot consider the distribution of eddy currents and may cause erroneous results at large currents [20]. An analytical method has been developed for the IPB field and force computation [20]. This method uses the complex potential and solves the Maxwell equations analytically. Some simplifications, e.g. neglecting enclosure thickness and assuming conductors as current filaments, are used in the method causing a reduction of computation accuracy.
Numerical methods are one of the best solutions for field and force computation in IPBs, as they can consider the real shape of conductors and enclosures as well as their thicknesses. These methods can also take into account the skin effect, eddy current distribution and nonlinearity of materials. Finite element method (FEM) is a widely used and well suited numerical method for electromagnetic problems [21]. FEM has been successfully applied to IPBs for fields, eddy currents and losses calculations [7, 9, 12and 22]. It is also used to compute transient electromagnetic
forces in several types of bus bars [23-28]. Whereas, the calculation of transient short circuit forces in IPBs via FEM has not gained enough attention. Authors, has used FEM method to investigate the effect of IPB dimensions and its material properties on short circuit forces [29-30]. However, finding the worst conditions from forces point of view still needs to be investigated.
In this paper the magnetic field distribution and the eddy current characteristics as well as transient short circuit forces of IPBs are investigated using 2D time stepping finite element method. A FEM based program is then developed which provides easy determination of maximum force on IPB systems under the worst conditions. The results are useable for the mechanical design of IPBs.
System structure and model
A real IPB carrying current to a transformer is shown in Fig. 1. The IPB system consists of three tubular conductors housed in three cylindrical shaped enclosures. The conductor is supported by insulators made of porcelain or epoxy materials. The conductors and enclosures are formed by rolling aluminum sheets and welding the joints.
Fig. 1: A real IPB structure (courtesy of MAPNA Company, Tehran, Iran)
The enclosures are connected together at both ends by bonding plates and are grounded at one end. The cross section of one phase is shown in Fig. 2. Enclosures, conductors and insulators are seen in this figure.
