Kepler's Problem in Rotating Reference Frames Part I: Prime Integrals, Vectorial Regularization

Manuscript submitted to the Twenty-second IEEE Workshop on Control and Modeling for Power Electronics (COMPEL 2021).<div>Abstract: Dual-sequence current controllers of voltage source converters (VSCs) feature two separate rotating reference frames (RRFs), commonly named dq frames, and rely on techniques that isolate the positive and negative sequences of three-phase measurements. One of these techniques is the delayed signal cancellation (DSC). It is performed in the stationary reference frame (SRF), also known as αβ frame. The DSC combines old values of one axis with new values of the other axis of the SRF. The results are, then, transformed into the RRFs for use in the current controller. This filtering process introduces an extra layer of complexity for dual-sequence current controllers, which could otherwise operate solely in the RRFs. This paper introduces a frequency adaptive DSC method that operates directly in the RRF. Moreover, an averaging of two of the proposed DSC filters with contiguous integer delays is employed for reducing discretization errors caused by grid frequency excursions. A formal proof of the equivalence between the αβ and dq DSC methods is presented. Furthermore, computer simulations of a case study support the interpretation of the results.</div>

Download Full-text

Quantum effects in rotating reference frames

AVS Quantum Science ◽

10.1116/5.0073436 ◽

2022 ◽

Vol 4 (1) ◽

pp. 011401

Author(s):

S. P. Kish ◽

T. C. Ralph

Keyword(s):

Reference Frames ◽

Quantum Effects ◽

Rotating Reference Frames

Download Full-text

Dual Sequence Controller with Delayed Signal Cancellation in the Rotating Reference Frame

10.36227/techrxiv.17142341 ◽

2021 ◽

Author(s):

Daniel Mota ◽

Erick Alves ◽

Elisabetta Tedeschi

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Formal Proof ◽

Voltage Source ◽

Phase Measurements ◽

Current Controller ◽

Signal Cancellation ◽

Rotating Reference Frames ◽

Dsc Method ◽

Dual Sequence

Manuscript submitted to the Twenty-second IEEE Workshop on Control and Modeling for Power Electronics (COMPEL 2021).<div>Abstract: Dual-sequence current controllers of voltage source converters (VSCs) feature two separate rotating reference frames (RRFs), commonly named dq frames, and rely on techniques that isolate the positive and negative sequences of three-phase measurements. One of these techniques is the delayed signal cancellation (DSC). It is performed in the stationary reference frame (SRF), also known as αβ frame. The DSC combines old values of one axis with new values of the other axis of the SRF. The results are, then, transformed into the RRFs for use in the current controller. This filtering process introduces an extra layer of complexity for dual-sequence current controllers, which could otherwise operate solely in the RRFs. This paper introduces a frequency adaptive DSC method that operates directly in the RRF. Moreover, an averaging of two of the proposed DSC filters with contiguous integer delays is employed for reducing discretization errors caused by grid frequency excursions. A formal proof of the equivalence between the αβ and dq DSC methods is presented. Furthermore, computer simulations of a case study support the interpretation of the results.</div>

Download Full-text

Rotating Reference Frames and Resonance

Magnetic Resonance Imaging ◽

10.1002/9781118633953.ch3 ◽

2014 ◽

pp. 37-51

Keyword(s):

Reference Frames ◽

Rotating Reference Frames

Download Full-text

Modulated wavy vortex flow in laboratory and rotating reference frames

Physics Letters A ◽

10.1016/0375-9601(82)90758-7 ◽

1982 ◽

Vol 87 (9) ◽

pp. 457-460 ◽

Cited By ~ 9

Author(s):

J.B. Swift ◽

M. Gorman ◽

Harry L. Swinney

Keyword(s):

Vortex Flow ◽

Reference Frames ◽

Rotating Reference Frames

Download Full-text

Rotordynamic Analysis Using the Complex Transfer Matrix

Volume 6: 1st Biennial International Conference on Dynamics for Design; 14th International Conference on Advanced Vehicle Technologies ◽

10.1115/detc2012-70643 ◽

2012 ◽

Cited By ~ 1

Author(s):

Philip Varney ◽

Itzhak Green

Keyword(s):

Reference Frame ◽

Transfer Matrix ◽

Reference Frames ◽

Detection System ◽

Numerical Technique ◽

External Support ◽

Starting Point ◽

Rotating Reference Frame ◽

Rotating Reference Frames ◽

Lumped Masses

The transfer matrix method is an expedient numerical technique for determining the dynamic behavior of a rotordynamic system (e.g., whirl frequencies, steady-state response to forcing). The typical 8 × 8 transfer matrix suffers from several deficiencies. First, for a system incorporating damping, the method generates a characteristic polynomial of degree 8N for a model of N lumped masses (degree 4N for an undamped model). The high degree of the polynomial results in lengthy computation times and decreased accuracy. Second, as discussed herein, the 8 × 8 formulation fails to distinguish between forward and backward whirl. These deficiencies are overcome by a novel complex-valued state variable redefinition resulting in a 4×4 transfer matrix including external support stiffness and damping. The complex transfer matrix is then modified to account for analysis within a rotating reference frame. Analysis in a rotating reference frame is a judicious means to determine unique system fault characteristics, which serve as a starting point for the development of an on-line fault detection system. Insights into using the complex transfer matrix in a rotating reference frame are discussed. Analytical results in both inertial and rotating reference frames for an overhung rotor model are provided.

Download Full-text