Search NASA⌕ Search

SEARCH · Search NASA

Results for “vector spaces”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

A Computational Efficient Space-Vector Modulation Scheme for A Hybrid Seven-Level Converter for Medium Voltage Grid-Tied Applications

In this paper, a fast space-vector modulation (SVM) scheme is proposed for a hybrid 7-level (7-L) converter, i.e., cascaded T-type converter and H-bridge converters, for grid-tied applications. Using oblique coordinate reference, the proposed SVM can quickly locate the switching triangle enclosing the reference vector in the 7-L space vector diagram. Then all available switching sequences and vector duty cycles are acquired by straightforward calculation without using any look-up tables, which significantly reduces the computational cost. The floating capacitor voltages are also stabilized by using the proposed SVM. Experimental studies on a scale-down prototype are presented in this work to validate the effectiveness of the proposed scheme.

Diao, Fei↗

A Digital Three Level Space Vector Modulator for High Frequency Vector Sequence Generation

This letter proposes a digital high-speed three-level space vector pulse width modulator (3L-SVPWM). A conventional 3L-SVPWM is typically computation-based, involving a sequential execution of sub-tasks on a digital signal processor (DSP) based controller. The resulting high computation time of 5.4 μs limits the implementation of additional control blocks for switching frequencies greater than 100 kHz. This is overcome by transforming sub-tasks into digital blocks with 1-0 decisions and simpler arithmetic operations. The sub-task blocks are executed concurrently on a programmable logic device (PLD). Hence, a fast 3L-SVPWM execution in 140 ns is achieved. The proposed digital 3L-SVPWM enables high switching frequency operation of wide bandgap (WBG) device-based 3 L inverters to generate high fundamental frequency waveforms. A finite state machine is an integral part of the proposed implementation with the ability to generate any vector sequence, maximizing the usage of redundant vector states in 3L-SVPWM. Here, the proposed digital 3L-SVPWM operation is demonstrated with a GaN-based 3 L active neutral point clamped (3L-ANPC) inverter. Experimental results are presented at 250 kHz switching frequency to generate vector sequences for center-aligned SVPWM (CA-SVPWM) and common mode voltage reduced SVPWM (CMVR-SVPWM). The results also showcase a high fundamental frequency generation capability of 10 kHz.

active neutral point clamped inverter↗

A Virtual Space Vector Model Predictive Control for a Seven-Level Hybrid Multilevel Converter

This paper proposes a virtual space vector (VSV) model predictive control (MPC) for a three-phase seven-level (7L) hybrid multilevel converter (HMC), where each phase consists of an active-neutral-point-clamped converter with a floating H-bridge. To achieve the best current tracking, which is the primary goal of the proposed algorithm, a novel geometrical positioning approach is proposed to select the optimal voltage vector among all the realspace vectors and VSVs. Then, all the possible switching sequences that belong to the optimal voltage vector are evaluated to realize the dc capacitor voltage balancing and common-mode voltage reduction. Through an external modulator, the optimal voltage vector can be synthesized by using either one-, three-, or seven-segment switching sequence. Compared with the conventional MPC, the proposed VSV-MPC can reduce not only the computational burden but also the current THD. Both simulation and experimental results obtained on silicon carbide based 7L-HMC prototype are presented to validate the feasibility and effectiveness of the proposed VSVMPC strategy.

42 ENGINEERING↗

A Six-Phase Space Vector PWM Technique for Wide Bandgap Device-Based Three-Level Inverters

This article presents a space vector pulsewidth modulation (SVPWM) technique for wide bandgap (WBG) device-based three-level (3L) six-phase inverters. Implementation of the SVPWM techniques for any six-phase inverter is complex for its high number of possible voltage vectors. Different six-phase load configurations are also possible depending on the angle between two consecutive phases and neutral point connections. The implementation techniques change depending on the load configuration. Moreover, a common neutral point for all six phases leads to circulating currents. Capacitor voltage balancing is also needed for 3L inverters. Capacitor voltage balancing and addressing the circulating current problem further increases the implementation complexity. In this article, a generalized SVPWM technique is proposed for the six-phase 3L inverters that is implementable using two three-phase 3L SVPWM blocks. The SVPWM technique also ensures dc bus capacitor voltage balancing and minimizes circulating current. Here, the SVPWM technique is experimentally verified using a GaN-based 3L six-phase active neutral point clamped (ANPC) inverter prototype, and the results are presented in this article.

42 ENGINEERING↗

Vector space methods of photometric analysis - Applications to O stars and interstellar reddening

A multivariate vector-space formulation of photometry is developed which accounts for error propagation. An analysis of uvby and H-beta photometry of O stars is presented, with attention given to observational errors, reddening, general uvby photometry, early stars, and models of O stars. The number of observable parameters in O-star continua is investigated, the way these quantities compare with model-atmosphere predictions is considered, and an interstellar reddening law is derived. It is suggested that photospheric expansion affects the formation of the continuum in at least some O stars.

Massa, D.↗

A Simple Space Vector Modulation of High-Frequency AC Linked Three-Phase-to-Single-Phase/DC Converter

High frequency (HF) ac linked converter functions well to interface between buses with different voltage types. Using a three-phase-to-single-phase matrix converter, a single-phase cyclo converter, and a HF transformer, we can compose a HF ac linked converter to interface between three-phase ac grids and single-phase ac or dc distributed generations (DGs). In this paper, a novel space vector modulation (SVM) method is proposed for such kind of converter. The proposed SVM method converts the mains three-phase ac voltage to a HF ac voltage at the primary side of transformer, and then unfolds the HF ac voltage to a single-phase ac or dc voltage at the secondary side of transformer. Without need to compute separate switching signals for the primary and secondary converters and then coordinate their operations elaborately, the proposed SVM method can be easily implemented by incorporating the HF chopping into the SVM of traditional indirect matrix converter. Therefore, no complicated duty cycle computation or elaborate switching states combination is required. Simulation and hardware-in-loop implementation demonstrate the validity of the proposed method.

42 ENGINEERING↗

Discrete Fourier Transform Analysis in a Complex Vector Space

Alternative computational strategies for the Discrete Fourier Transform (DFT) have been developed using analysis of geometric manifolds. This approach provides a general framework for performing DFT calculations, and suggests a more efficient implementation of the DFT for applications using iterative transform methods, particularly phase retrieval. The DFT can thus be implemented using fewer operations when compared to the usual DFT counterpart. The software decreases the run time of the DFT in certain applications such as phase retrieval that iteratively call the DFT function. The algorithm exploits a special computational approach based on analysis of the DFT as a transformation in a complex vector space. As such, this approach has the potential to realize a DFT computation that approaches N operations versus Nlog(N) operations for the equivalent Fast Fourier Transform (FFT) calculation.

Dean, Bruce H.↗

How to Maneuver Around in Eccentricity Vector Space

The GRAIL mission to the Moon will be the first time that two separate robotic orbiters will be placed into formation in orbit around a body other than Earth. The need to design an efficient series of maneuvers to shape the orbits and phasing of the two orbiters after arrival presents a significant challenge to mission designers. This paper presents a simple geometric method for relating in-plane impulsive maneuvers to changes in the eccentricity vector, which determines the shape and orientation of an orbit in the orbit plane. Examples then show how such maneuvers can accommodate desired changes to other orbital elements such as period, incination, and longitude of the ascending node.

orbit maneuvers↗

Online adaptive basis refinement and compression for reduced-order models via vector-space sieving

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these approximate solutions are accurate; their accuracy depends on the ability of the low-dimensional trial basis to represent the FOM solution. As a result, ROMs can generate inaccurate approximate solutions, e.g., when the FOM solution at the online prediction point is not well represented by training data used to construct the trial basis. To address this fundamental deficiency of standard model-reduction approaches, this work proposes a novel online-adaptive mechanism for efficiently enriching the trial basis in a manner that ensures convergence of the ROM to the FOM, yet does not incur any FOM solves. The mechanism is based on the previously proposed adaptive $h$-refinement method for ROMs, but improves upon this work in two crucial ways. First, the proposed method enables basis refinement with respect to any orthogonal basis (not just the Kronecker basis), thereby generalizing the refinement mechanism and enabling it to be tailored to the physics characterizing the problem at hand. Second, the proposed method provides a fast online algorithm for periodically compressing the enriched basis via an efficient proper orthogonal decomposition (POD) method, which does not incur any operations that scale with the FOM dimension. We report these two features allow the proposed method to serve as (1) a failsafe mechanism for ROMs, as the method enables the ROM to satisfy any prescribed error tolerance online (even in the case of inadequate training), and (2) an efficient online basis-adaptation mechanism, as the combination of basis enrichment and compression enables the basis to adapt online while controlling its dimension.

42 ENGINEERING↗

Vector space methods of photometric analysis. II - Refinement of the MK grid for B stars. III - The two components of ultraviolet reddening

This paper discusses systematic errors which arise from exclusive use of the MK system to determine reddening. It is found that implementation of uvby, beta photometry to refine the qualitative MK grid substantially reduces stellar mismatch error. A working definition of 'identical' ubvy, beta types is investigated and the relationship of uvby to B-V color excesses is determined. A comparison is also made of the hydrogen based uvby, beta types with the MK system based on He and metal lines. A small core correlated effective temperature luminosity error in the MK system for the early B stars is observed along with a breakdown of the MK luminosity criteria for the late B stars. The second part investigates the wavelength dependence of interstellar extinction in the ultraviolet wavelength range observed with the TD-1 satellite. In this study the sets of identical stars employed to find reddening are determined more precisely than in previous studies and consist only of normal, nonsupergiant stars. A multivariate analysis of variance techniques in an unbiased coordinate system is used for determining the wavelength dependence of reddening.

Massa, D.↗

Robot Acquisition of Active Maps Through Teleoperation and Vector Space Analysis

The work performed under this contract was in the area of intelligent robotics. The problem being studied was the acquisition of intelligent behaviors by a robot. The method was to acquire action maps that describe tasks as sequences of reflexive behaviors. Action maps (a.k.a. topological maps) are graphs whose nodes represent sensorimotor states and whose edges represent the motor actions that cause the robot to proceed from one state to the next. The maps were acquired by the robot after being teleoperated or otherwise guided by a person through a task several times. During a guided task, the robot records all its sensorimotor signals. The signals from several task trials are partitioned into episodes of static behavior. The corresponding episodes from each trial are averaged to produce a task description as a sequence of characteristic episodes. The sensorimotor states that indicate episode boundaries become the nodes, and the static behaviors, the edges. It was demonstrated that if compound maps are constructed from a set of tasks then the robot can perform new tasks in which it was never explicitly trained.

Peters, Richard Alan, II↗

Discrete Fourier Transform in a Complex Vector Space

An image-based phase retrieval technique has been developed that can be used on board a space based iterative transformation system. Image-based wavefront sensing is computationally demanding due to the floating-point nature of the process. The discrete Fourier transform (DFT) calculation is presented in "diagonal" form. By diagonal we mean that a transformation of basis is introduced by an application of the similarity transform of linear algebra. The current method exploits the diagonal structure of the DFT in a special way, particularly when parts of the calculation do not have to be repeated at each iteration to converge to an acceptable solution in order to focus an image.

Dean, Bruce H.↗

On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators

The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined.

Bykhovskiy, E. B.↗

Generating accurate density matrices on the tangent space of a Grassmann manifold

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Chemistry↗