Five-Dimensional Switching-Table-Based Direct Torque Control of Six-Phase Drives
Mohammad Hosein Holakooie, Grzegorz Iwański, Tomasz Miazga
Abstract
This article proposes a novel 5-D switching-table-based direct torque control (5D-DTC) strategy for asymmetrical six-phase induction machines (6PIMs). As is well-known, classical DTC of 6PIM is penalized by significant stator current harmonics, which are mapped into the nonenergy subspace ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> subspace). The concept of virtual voltage vectors (VVs) has been frequently perceived as able to tackle the problem of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents. Such a concept maintains zero average volt-second in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> subspace, which in turn suppresses current harmonics due to discrete pulsewidth modulation implementation to a great extent compared to the classical DTC. However, it still cannot effectively compensate for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents, mainly arising from dead band effect and machine/converter asymmetry, due to lack of dedicated regulators for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents. Indeed, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents can be fully suppressed only in the presence of active control over them. This article incorporates additional hysteresis regulators of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents into the direct torque control strategy. In the proposed 5D-DTC scheme, there are in total five indexes for optimal selection of VVs as torque, stator flux, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents, and stator flux position indexes. In this way, a clustering method is developed for synthesizing VVs to cover all possible cases of the switching table. A beneficial feature in comparison with 3-D switching-table-based DTC is effective suppression of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x-y$</tex-math></inline-formula> currents with a rather simple structure, without increasing the switching frequency, and without decreasing dc-link utilization. Experimental results confirm the effectiveness of the proposed technique.