Three-dimensional Space Vector Research Articles

New Three-Dimensional Space Vector-Based Switching Signal Generation Technique Without Null Vectors and With Reduced Switching Losses for a Grid-Connected Four-Leg Inverter

In this paper, the performance of the new three-dimensional space vector-based switching signal generation technique for a grid-connected four-leg voltage source inverter used as a shunt compensator is proposed. The shunt compensator can be used for reactive power compensation, harmonic elimination, load balancing, and neutral current elimination in a three-phase four-wire grid-connected system. It is shown through experimental studies that switching losses in the four-leg voltage source inverter are appreciably reduced to a maximum of 33% in three-dimensional space vector modulation without NULL vector as the number of switches controlled at any instant of time is six out of eight. The new proposed technique is compared with three-dimensional space vector modulation with null vector. Experimental results are given to show the validity of the proposed switching control strategy.

The Vector Algebra War: A Historical Perspective

There are a wide variety of different vector formalisms currently utilized in engineering and physics. For example, Gibbs' three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford's multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.

Power quality improvement using a dual unified power quality conditioner/uninterruptible power supply in three‐phase four‐wire systems

Using a dual compensation strategy, this study proposes the analysis and implementation of active power quality conditioners (PQCs), which are applied for power quality improvement in three-phase four-wire (3P4W) systems. By means of similar control strategy use, the topology employed to implement the PQCs can operate as unified PQC (UPQC), or, through some circuit modifications, as uninterruptible power supply (UPS) system. Considering 3P4W systems, the use of the dual compensation strategy into the PQCs comprised of two four-leg (4-Leg) converters is the main contribution of this study. Different from the conventional strategies, in the dual compensation strategy, the 4-Leg converter connected in parallel with the load is controlled to operate as a sinusoidal voltage source, whereas the 4-Leg converter connected in series between the grid and the load is controlled to operate as a sinusoidal current source. Both the voltage and current controllers are implemented into the synchronous rotating reference frame, and the converters use the three-dimensional space vector modulation technique. Experimental tests, based on a digital signal processor, are performed in order to validate the theoretical development and to verify both static and dynamic performance of the PQC operating as UPQC, as well as UPS system.

Kinematics and dynamics of planar mechanisms reinterpreted in rigid-body’s configuration space

Mechanisms with lower mobility can be studied by using tools that are directly deduced from those of spatial kinematics as screw theory. Nevertheless, ad-hoc tools that fully exploit the peculiarities of the displacement subgroups these mechanisms move in are usually more efficient both in showing mechanisms’ features and when used to conceive numerical algorithms. Planar displacements constitute a three-dimensional subgroup with many peculiarities that allow the use of simplified tools (e.g., complex numbers) for studying planar mechanisms. Here, the systematic use of three-dimensional vector spaces to represent link poses and velocities in planar motion and planar system of forces is investigated. The result is a novel coherent set of tools that make it possible to geometrically describe kinematics and dynamics of planar mechanisms in the three-dimensional configuration space of links’ planar poses. The effectiveness of this novel approach is shown through a case study.

Representation of symmetric second-rank III tensor in the space of resultant eigenvectors

The article examines the possibility of representation of a symmetric second rank III tensor in the three-dimensional vector space of resultant eigenvectors. It has been shown that the vector space of resultant eigenvalues consists of six independent segments. Vector symmetric tensor may be represented in any of the segments independently. The authors introduce a local vector basis for each of the sectors. It is shown that the previously proposed by A.A. Ilyushin and K.F. Chernykh vector basis of the stress tensor are the second and third segments of the vector space of principal stresses.

Key Image Processing Techniques Used in Laser Welding

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00270001/03.jpg"" width=""500"" /> Welding image and weld pool edge</div> Machine vision techniques are widely used with automatic laser-welding robots. Existing systems acquire geometrical information on both the weld seams and molten pool by using a single camera and then processing a single image. The recognition of weld seams is thus obviously affected by the arc, plasma, spatter, etc. This study examined a novel, cost-effective weld image acquisition and processing system with real-time performance, which is based on an advanced RISC machine (ARM). The software and hardware platforms of a weld seam image processing system were designed, and theoretical and experimental studies were undertaken. A novel image-processing method for the laser welding molten pool, based on a quaternion and self-organizing feature map (SOFM) neural network is also proposed. The edge characteristic vector of the molten pool is acquired based on the rotational characteristic of the quaternion in a three-dimensional vector space. The geometric features of the molten pool image are acquired by the self-organizing feature map neural network. The measured results pointed to the possibility of improving the reliability and precision of the automatic laser welding system by combining the two machine vision systems. </span>

A real-time American Sign Language word recognition system based on neural networks and a probabilistic model

The photovoltaic power generation and active filter (PV-AF) system can realize photovoltaic grid-connected power regulation, and meanwhile it can also improve the power quality of power grid effectively. The four-leg grid-connected inverter has successfully been used in the three-phase four-wire system. In this paper, a three-dimensional space vector pulse width modulation (3D-SVPWM) method based on the gh$\gamma $ coordinate system for a four-leg inverter has been proposed. As the switching vectors of the four-leg inverter are in the three-dimensional space, it is difficult to realize the complex modulation process. In order to simplify the modulation process, the reference vector is placed into gh$\gamma $ coordinates in the proposed modulation strategy, and then the vectors are selected and the duration times are acquired directly by a group of intermediate variables, which could be obtained by linear transformation of the coordinates. As the intermediate variables are used, the modulation can be easily implemented by the proposed modulation strategy without excessive mathematical calculations. The simulation and experimental results all confirmed the validity and effectiveness of this strategy.

New three-dimensional space vector pulse width modulation of PV-AF system based on the gh$\gamma $ coordinate system

The photovoltaic power generation and active filter (PV-AF) system can realize photovoltaic grid-connected power regulation, and meanwhile it can also improve the power quality of power grid effectively. The four-leg grid-connected inverter has successfully been used in the three-phase four-wire system. In this paper, a three-dimensional space vector pulse width modulation (3D-SVPWM) method based on the gh$\gamma $ coordinate system for a four-leg inverter has been proposed. As the switching vectors of the four-leg inverter are in the three-dimensional space, it is difficult to realize the complex modulation process. In order to simplify the modulation process, the reference vector is placed into gh$\gamma $ coordinates in the proposed modulation strategy, and then the vectors are selected and the duration times are acquired directly by a group of intermediate variables, which could be obtained by linear transformation of the coordinates. As the intermediate variables are used, the modulation can be easily implemented by the proposed modulation strategy without excessive mathematical calculations. The simulation and experimental results all confirmed the validity and effectiveness of this strategy.

A Near-State Three-Dimensional Space Vector Modulation for a Three-Phase Four-Leg Voltage Source Inverter

A near-state three-dimensional space-vector modulation (NS 3-D SVM) switching scheme, which aims to reduce the common-mode noise in a three-phase four-leg voltage source inverter, is proposed. The impact of common-mode noise, which is related to electromagnetic interference issues for a high-voltage level four-leg system, is investigated first. Identification of the section in a 3-D space, selection of the near-state switching vectors, and sequence of the selected switching vectors are then introduced in steps to describe the proposed switching scheme. The proposed switching scheme is based on classical 3-D SVM, producing higher dc-link utilization, less harmonic content, and reduced switching loss compared to sinusoidal PWM. Theory, simulation, and experimental results show that the near-state 3-D SVM can work under both balanced and unbalanced load conditions.

Motor Control System Based on DSP Four-Bridge Arm Topology

This paper proposes a space vector motor control system based on DSP four-legged bridge topology A three-dimensional space vector control principle based on four-bridge arm three-phase inverter is introduced with a MATLAB model using space vector Motor Control Algorithm instead of traditional Motor Control method. A DSP experimental setup is also carried out to verify the control theory and simulation result. The experiment and simulation results show that the speed control system helps the asynchronous motor to achieve the consistent response characteristics with separately excited DC machine. When the motor doesn't work or the load is unstable, asynchronous motor can still achieve excellent electrical characteristics with the proposed speed control system, such as quick start, small overshoot and static torque ripple.

Implementation of digital FCS-MP controller for a three-phase inverter

In this paper, a digital current control of a three-phase four-leg inverter based on predictive cost function is studied. Inverters are important for power electronics applications in three-phase four-wire systems, such as active power filters and uninterruptible power supplies. There are many methods for control of inverters, such as pulse-width modulation and three-dimensional space vector modulation. These methods are complex. In this paper, a simple way for current control of a three-phase four-leg inverter is presented. Here, by using a predictive cost function and fixed-point computations, the optimal switching state to be applied in the next sampling is selected. Finally, to evaluate the accuracy of the fixed-point computations, several cases for balanced and unbalanced loading conditions are verified. In each case, the parameter that measured to confirm computation accuracy is total harmonic distortion.

Analysis of Rectangular Waveguides – An Intuitive Approach

ABSTRACTCustomarily, the field solutions of rectangular waveguides are achieved by solving Maxwell's equation for three-dimensional vector space. The field expressions obtained from the solutions of differential equations are often too mathematical to develop any physical understanding of the subject. In this article, the field solutions are obtained mostly through the analysis of underlying physics; this approach provides a firm conceptual grasp over the subject and is best suited to accomplish pedagogical objectives along with being a supplementary text for undergraduate studies.

Comprehensive Mathematical Description and Harmonic Analysis of Hybrid Two-Dimensional–Three-Dimensional Space Vector Modulation

This paper presents the mathematical and harmonic analyses of output phase voltages of three-phase voltage source inverters which employ a hybrid two-dimensional-three-dimensional (2-D-3-D) space vector modulation (SVM) voltage control algorithm. The explicit time-domain representation of the harmonic components in addition to the total harmonic distortion (THD) of the output phase voltages is given in terms of system and control parameters. This paper also investigates the harmonic characteristics and THD performance against the linearity of the modulation region which helps in the harmonic performance and design studies of such inverters employing the hybrid 2-D-3-D SVM. The fundamental component of the output voltages follows the reference with lower THD in the linear modulation region rather than the overmodulation region. Experimental results are used to validate these analyses as well as the effectiveness of the hybrid 2-D-3-D SVM algorithm for generating balanced and low THD phase voltages.

A Fast Digital 3D-SVPWM Algorithm for Four-Leg Converter

The three-phase four-leg converter can be obtained by adding a bridge into the traditional three-phase three-leg converter. The average mathematical model of three-phase four-leg converter is described in this paper. The three-dimensional space vector PWM (3D-SVPWM) is analyzed. For simplifying the modulation, a fast digital SVPWM algorithm which eliminates coordinate transformation and saves calculating time was proposed. The feasibility of the proposed modulation technique is verified by computer simulation. These results show that the proposed fast digital 3D-SVPWM technique can be easily implemented without conventional computational burden.

Digital current control of a three‐phase four‐leg voltage source inverter by using p – q – r theory

In this study, balanced/unbalanced linear/non-linear current control in three-phase four-leg voltage source inverter (VSI) is carried out by using modified p - q - r method instead of the classical p - q - r method, digital proportional integral derivative (PID) control rule and three-dimensional (3D) space vector pulse width modulation (3D SVPWM). For this purpose, three-phase four-leg power inverter and PWM signal generation circuits are designed and modelled separately. Even if the power source voltage is unsymmetrical, the proposed modified p - q - r method leads to measurement and to generating the instantaneous harmonic and reactive components of load current accurately. The performance of the classical p - q - r theory under non-ideal mains voltages is improved and the accuracy of the proposed modified p - q - r theory is demonstrated both through simulation and real-time application. Each phase of the three-phase four-leg VSI modelled directly in abc reference frame is decoupled from each other This simplifies the digital PID controller design significantly. Modelling of the whole system, modified p - q - r measurement and digital PID design steps are given in detail. Real-time experimental results for the designed three-phase four-leg VSI in stand-alone mode are compared with the simulation results.

Estymacja parametrów składowej podstawowej prądu wtórnego przekładnika prądowego odkształconego na skutek nasycenia rdzenia magnetycznego

In the paper a new algorithm is described that is intended for estimation of fundamental component parameters of the distorted secondary CT current due to magnetic core saturation. The algorithm presented was derived with use of the innovative methodology where the current samples measured are treated as components of three-dimensional space vector. Simulative investigations with use of ATP/EMTP package confirm high efficiency of the proposed algorithm. (Estimation of the fundamental component parameters of the secondary CT current distorted due to magnetic core saturation).

The use of the BIC set in the characterization of used nuclear fuel assemblies by nondestructive assay

This paper explains why the burnup, initial enrichment, and cooling time of a used fuel assembly – collectively called the BIC set of variables – characterize it to first order for the purposes of nuclear-materials safeguards and burnup credit. From an analysis by basic nuclear engineering, it is shown that the physical properties and the isotopic content of a used fuel assembly are basically three-dimensional vector spaces. By extensive referencing of the NDA literature, the paper then shows that the BIC variables are independent variables with respect to the physical properties and the isotopes. Therefore, the knowledge of all three BIC variables is a necessary condition for the accurate characterization of a used low- or high-enriched uranium (LEU or HEU) fuel assembly. For a plutonium mixed-oxide (MOX) fuel assembly, a fourth variable for the BIC set (the curium-producing ability) is also necessary. The paper also discusses other possible variables besides the BIC set, to demonstrate that the knowledge of the BIC set is also a sufficient condition in many cases. Logically, it is therefore necessary to make at least three independent NDA measurements (or four, for MOX) to achieve a unique solution (characterization) if a reliance on information provided by the reactor operator is to be avoided. By this fact, the common question, “What is the accuracy of a particular NDA technique?” is revealed to be a poorly posed one with regard to used fuel assemblies. The result of the paper is a better paradigm for interpreting and improving the NDA practice of both the safeguards community and the burnup-credit community.

A Dead Time Compensation Algorithm of Independent Multi-Phase PMSM with Three-Dimensional Space Vector Control

This paper proposes a new dead time compensation method of independent six-phase permanent magnet synchronous motors (IS-PMSM). The current of the independent phase machines contains odd-numbered harmonics because of the dead time and the nonlinear characteristics of the switching devices. By using the d-q-n three-dimensional vector analysis, these harmonics can be extracted at the n-axis current. Thus, the current distortion can be compensated by controlling the n-axis current of the IS-PMSM to zero. The proposed method is simple and can be easily implemented without additional hardware setup. The validity of the proposed compensation method is verified with simulations and several experiments.

Spatial color image processing using Clifford algebras: application to color active contour

In the literature, the color information of the pixels of an image has been represented by different structures. Recently, algebraic entities such as quaternions or Clifford algebras have been used to perform image processing for example. This paper presents the embedding of color information into the vectorial parts of a multivector. This multivector is an element of the geometric or Clifford algebra constructed from a three-dimensional vector space. This formalism presents the advantage of algebraically separating colors which are handled entities from the geometric operations done to them. We propose to introduce several contributions for color image processing by using this Clifford algebra. First, as colors are represented by 1-vectors, we point out that a color pixel given in the RGB color space can be expressed algebraically by its hue saturation and value using the geometry. Then, we illustrate how this formalism can be used to define color alterations with algebraic operations. We generalize linear filtering algorithms already defined with quaternions and define a new color edge detector. Finally, the application of the new color gradient is illustrated by a new color formulation of snakes. Thus, we propose in this paper the definition and exploitation of a formalism in which we geometrically handle colors with algebraic entities and expressions.

A mapping of an ensemble of mitochondrial sequences for various organisms into 3D space based on the word composition

To visualize a bird’s-eye view of an ensemble of mitochondrial genome sequences for various species, we recently developed a novel method of mapping a biological sequence ensemble into Three-Dimensional (3D) vector space. First, we represented a biological sequence of a species s by a word-composition vector x(s), where its length ∣x(s)∣represents the sequence length, and its unit vector x(s)/∣x(s)∣represents the relative composition of the K-tuple words through the sequence and the size of the dimension, N=4K, is the number of all possible words with the length of K. Second, we mapped the vector x(s) to the 3D position vector y(s), based on the two following simple principles: (1) ∣y(s)∣=∣x(s)∣and (2) the angle between y(s) and y(t) maximally correlates with the angle between x(s) and x(t). The mitochondrial genome sequences for 311 species, including 177 Animalia, 85 Fungi and 49 Green plants, were mapped into 3D space by using K=7. The mapping was successful because the angles between vectors before and after the mapping highly correlated with each other (correlation coefficients were 0.92–0.97). Interestingly, the Animalia kingdom is distributed along a single arc belt (just like the Milky Way on a Celestial Globe), and the Fungi and Green plant kingdoms are distributed in a similar arc belt. These two arc belts intersect at their respective middle regions and form a cross structure just like a jet aircraft fuselage and its wings. This new mapping method will allow researchers to intuitively interpret the visual information presented in the maps in a highly effective manner.