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This paper presents the application of a numerical approach known as proper generalized decomposition (PGD) to calculate the per-unit length (PUL) ac resistance of rectangular conductors. PGD has been successfully used in areas such as fluid mechanics and biomedical applications. It solves a partial differential equation (PDE) by decomposing the answer into a set of unknown one-dimensional (1D) functions in an iterative approach until it reaches a predetermined convergence. In this paper, a frequency-dependent meshing scheme is employed in the PGD technique at each frequency to properly take skin and proximity effects into account. One of the main advantages of PGD over traditional numerical approaches such as finite element or finite difference methods is that it confines the answers within a set of one-dimensional functions, which require fewer computational resources. Different examples of single and multiple rectangular conductors are considered to study skin and proximity effects. The PGD results are compared with those obtained using a commercial finite element method (FEM) software to verify the accuracy of the model. This approach can be used in applications such as white box modeling of transformers, EMC analysis, hairpin winding design used in electric vehicles, and busbar simulation. [ABSTRACT FROM AUTHOR]

This paper presents an accurate quasi-analytical approximation of frequency-dependent ac resistance of single rectangular conductors. In this work, first, a two-dimensional analytical ac resistance of rectangular conductors is derived. Unlike circular conductors, where current density distributes evenly in each layer of the conductor's cross-section, the edge effect is involved for rectangular conductors. Due to the edge effect, one cannot define an accurate boundary condition for solving the two-dimensional partial differential equation of magnetic field or current density of rectangular conductors. Hence, the calculated two-dimensional analytical current density result is not accurate and is modified and fitted on FEM simulation, taking the conductor's thickness into account using the least-square problem to improve its accuracy. Unlike numerical approaches, the proposed method yields an easy-to-use formula applicable to industrial applications in different fields. Contrary to the one-dimensional approach, which is only valid for very thin rectangular conductors, this method takes edge effect into account and can be used for any thickness (from square to very thin rectangular conductors). The proposed method can be used in applications where an accurate ac resistance of rectangular conductors over a wide frequency range is required, such as white-box modeling of power transformers and interpreting its frequency response analysis (FRA), and calculating the resistance of electric machine winding, busbars, and printed circuit board traces. [ABSTRACT FROM AUTHOR]

A selective fault clearing scheme is proposed for a hybrid voltage source converter (VSC)-line commutated converter (LCC) multi-terminal high voltage direct current (HVdc) transmission structure in which two small capacity VSC stations tap into the main transmission line of a high capacity LCC-HVdc link. The use of dc circuit breakers (dc CBs) on the branches connecting to VSCs at the tapping points is explored to minimize the impact of tapping on the reliability of the main LCC link. This arrangement allows clearing of temporary faults on the main LCC line as usual by force retardation of the LCC rectifier. The faults on the branches connecting to VSC stations can be cleared by blocking insulated gate bipolar transistors (IGBTs) and opening ac circuit breakers (ac CB), without affecting the main line's performance. A local voltage and current measurement based fault discrimination scheme is developed to identify the faulted sections and pole(s), and trigger appropriate fault recovery functions. This fault discrimination scheme is capable of detecting and discriminating short circuits and high resistances faults in any branch well before 2 ms. For the test grid considered, 6 kA, 2 ms dc CBs can easily facilitate the intended fault clearing functions and maintain the power transfer through healthy pole during single-pole faults. [ABSTRACT FROM AUTHOR]