On the Theory of Near-Vector Spaces
We give a brief introduction to near-vector spaces.
97 MATHEMATICS AND COMPUTING↗
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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↗
Islanding Detection of Distributed Generation Using Electrical Variables in Space Vector Domain
This paper presents a new approach for islanding detection in distribution systems incorporating synchronous generator-based distributed generations. The proposed method first utilizes the dynamic equations of three electrical variables under islanding situations. The variables are: change of frequency; rate of change of frequency; and rotor angle deviation. Second, transformation of these variables is conducted in the space vector domain, which gives rise to three parameters, namely, semi-major axis, semi-minor axis, and inclination angle. Finally, exploiting these parameters, a decision boundary is established to classify grid events resulting in the formation of an island or not. The proposed method is comprehensively investigated under different operating conditions, which include excess/deficit of reactive/active power imbalance scenarios in the formed island containing different load-types (constant impedance, constant power, and constant current) with varying quality factor. A large variety of islanding and non-islanding events are generated using a practical distribution network simulated in real time on OPAL-RT digital simulation platform under the aforementioned operating conditions. A detailed evaluation of the proposed approach is conducted and it demonstrates the effectiveness of the method.
F-measure↗
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↗
Analytical Analysis of Ac and Dc Side Harmonics of Three-level Active Neutral Point Clamped Inverter with Space Vector Modulation
This paper presents a comprehensive analytical analysis of the ac and dc side harmonics of the three-level active neutral point clamped (ANPC) inverter with space vector modulation (SVM) scheme. An analytical model to calculate the harmonics of a three-level converter with SVM is developed. The ac side output voltage harmonics and dc side current harmonics characteristics are calculated and analyzed. With the developed models, the impact of interleaving on both sides harmonics are studied which considers the modulation index, interleaving angle, and power factor. The analysis provides guideline for interleaving angle optimization to reduce the ac side power filter and dc side dc-link capacitor. The relationship between electromagnetic interference (EMI) filter corner frequency and switching frequency is also analytically derived which provides guideline for switching frequency and EMI filter design optimization. Two paralleled three-level ANPC inverters are constructed and experimental results are presented to verify the analytical analysis.
Chen, Ruirui↗
General Space Vector Modulation of A High-Frequency AC Linked Universal Converter for Distributed Generations
A high-frequency (HF) ac linked universal converter is proposed for distributed generations interfacing three-phase ac with single-phase ac or dc. The primary and secondary of the HF isolation transformer are, respectively, formed by a three-to-single-phase matrix converter and a cyclo converter. Based on the operating principle, a general and simple to be implemented space vector modulation (SVM) is developed from that for the conventional indirect matrix converter and constantly operated virtual dual-active-bridge converter. Simulation studies carried out on different amplitudes and frequencies of single-phase ac output and dc output demonstrate effectiveness and simplicity of the proposed converter with the SVM solution.
Liu, Yushan↗
A Model Predictive Voltage Control using Virtual Space Vectors for Grid-Forming Energy Storage Converters
Sinusoidal output voltages with low harmonic distortion can be achieved using three-level converters along with LC filters, which have been proven to be suitable for energy storage systems (ESSs). Model predictive control (MPC) as been applied to such energy storage converters due to its simplicity and effectiveness. However, selecting the weighting factor of the additional neutral-point (NP) voltage balancing term in the cost function is time consuming and may also affect the main objective of MPC. To address this issue, in this paper, additional virtual space vectors (VSVs), which do not affect the NP capacitor voltages, are adopted in the proposed MPC. Both simulation and experimental results using controller hardware-in-the-loop are presented to show that NP capacitor voltages can be well controlled using a particularly small NP voltage balancing weighting factor in the cost function. In addition, the total harmonic distortion of the voltage at the point of common coupling is reduced while retaining the fast dynamic response of MPC.
Alhosaini, Waleed↗
An Enhanced Model Predictive Control Using Virtual Space Vectors for Grid-Connected Three-Level Neutral-Point Clamped Inverters
Reliability of power systems can be improved by the use of voltage source inverters (VSIs) with fast dynamic control, which can handle uncertainties induced by renewable energy resources and nonlinear loads. To ensure fast-dynamic response and simplified controller design, various model predictive control (MPC) methods are investigated in this paper. In the conventional MPC design for three-level VSIs, the cost function requires an additional term to ensure the balance of the neutral-point voltage (NP-V), which however can considerably impact the main goal of the MPC. To address this issue, an enhanced MPC using virtual space vectors is proposed, which allows the use of a significantly reduced weighting factor for the term in the cost function for NP-V balancing, while retaining fast-dynamic response. Additionally, the proposed MPC leads to reduced harmonic distortion in the VSI output voltage and current. Both simulation and controller hardware-in-the-loop studies are performed to demonstrate the effectiveness of the proposed enhanced MPC in an operating microgrid under both steady-state and fast-transient conditions.
30 DIRECT ENERGY CONVERSION↗
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↗
Instrument-model refinement in normalized reciprocal-vector space for X-ray Laue diffraction
Abstract not provided
Kami↗
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↗
Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group
In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
A resolution independent neural operator
The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.
Deep operator network (DeepONet)↗
Error Analysis of ZFP Compression for Floating-Point Data
Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to bound its errors when used to store look-up tables, simulation results, or even the solution state during the computation. In this paper, we analyze the round-off error introduced by ZFP, a lossy compression algorithm. Here, the stopping criteria for ZFP depends on the compression mode specified by the user: fixed rate, fixed accuracy, or fixed precision [P. Lindstrom, ZFP 0.5.3 Documentation, 2018]. While most of our discussion is focused on the fixed precision mode of ZFP, we establish a bound on the error introduced by all three compression modes. In order to tightly capture the error, first we introduce a vector space that allows us to work with binary representations of components. Under this vector space, we define operators that implement each step of the ZFP compression and decompression to establish a bound on the error caused by ZFP. To conclude, numerical tests are provided to demonstrate the accuracy of the established bounds.
97 MATHEMATICS AND COMPUTING↗