Orthogonal Reference Frame Research Articles

Dead time effects compensation strategy by third harmonic injection for a five-phase inverter

This paper proposes a method for compensation of dead-time effects for a fivephase inverter. In the proposed method an additional control subsystem was added to the field-oriented control (FOC) scheme in the coordinate system mapped to the third harmonic. The additional control loop operates in the fixed, orthogonal reference frame ( α - β coordinates) without the need for additional Park transformations. The purpose of this method is to minimize the dead-time effects by third harmonic injection in two modes of operation of the FOC control system: with sinusoidal supply and with trapezoidal supply. The effectiveness of the proposed control method was verified experimentally on a laboratory setup with a prototype five-phase interior permanent magnet synchronous machine (IPMSM). All experimental results were presented and discussed in the following paper.

On the objectivity of mathematical description of ion transport processes using general temporal Caputo and Riemann-Liouville fractional partial derivatives

It is shown that the mathematical description of the ion transport across passive or active biological neuron membrane, voltage propagation along neuron axons and dendrites having passive or active membrane and ion transport in biological neuron networks, using general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, is objective. The basic idea is that different observers using this type of description obtain results which can be reconciled, i.e., transformed into each other using only formulas that link the coordinates of a point in two fixed orthogonal reference frames and the numbers representing a moment of time in two different choices of the origin of time measurement. This requirement was pointed out by Galileo Galilee (1564–1642), Isaac Newton (1643–1727), Albert Einstein (1879–1955) in the context of mathematical description of mechanical movement: “The mechanical event is independent on the observer “.

Rotor Current Feedback Based Direct Power Control of a Doubly Fed Induction Generator Operating with Unbalanced Grid

The paper presents a decoupled direct power-controlled (DPC) of a doubly fed induction generator (DFIG) connected to an unbalanced power grid, executed in an orthogonal stationary reference frame related to the stator side. The control allows to maintain constant electromagnetic torque despite stator connection to the unbalanced power grid and to achieve controllable low-voltage ride through (LVRT) capability. The control does not require any signal decomposition into positive and negative sequence order, which allows to reduce its complexity and computational requirements. Then, the paper presents positive influence of rotor current feedback in the stator-controlled reference frame on control performance. It facilitates significant transient reduction and minor steady state control improvement. All the mentioned functionalities were validated both in simulation and in laboratory conditions and the obtained results are described in the paper.

Mathematical description of the bulk fluid flow and that of the contained impurity dispersion which uses Caputo or Riemann-Liouville fractional order partial derivatives is nonobjective

In this paper it is shown that the mathematical description of a Newtonian, incompressible, viscous bulk fluid flow and that of the contained impurity dispersion which uses Caputo or Riemann-Liouville fractional order derivative, having integral representation on finite interval, is nonobjective. This means that, two different observers describing the flow or the contained impurity dispersion with these tools obtain two different results which cannot be reconciled i.e. transformed into each other using only formulas that link the coordinates of a point in two fixed orthogonal reference frames and formulas that link the numbers representing a moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which of the obtained results is correct?

Vector Control of Three-Phase Solar Farm Converters Based on Fictive-Axis Emulation

In this paper, a new method for adjusting the current of three-phase voltage source DC-AC converter in orthogonal (DQ) reference frame is presented. In the DQ reference system, AC variable appears in the constant form of DC, making the controller design the same as the DC-DC converter [1]. It provides controllable gain benefits at the steady-state operating point, and finally realizes zero steady-state error [2]. In addition, the creative analytical model is dedicated to building up a series of virtual quantities orthogonal to the actual single-phase system. In general, orthogonal imaginary numbers get the reference signal by delaying the real quantity by a quarter period. However, the introduction of such time delay makes the dynamic response of the system worse. In this paper, orthogonal quantities are generated from a virtual axis system parallel to the real axis, which can effectively improve the dynamic performance of traditional methods without increasing the complexity of controller structure. Through PSCAD simulation, the ideal experimental results are obtained.

On the Existence of Lagrangians for Clarke and Park Transformed Switched-Mode Electrical Networks

It is well-known that the classical passivity-based control (PBC) design is founded on the existence of the Euler-Lagrange (EL) equations. For a large class of systems, including mechanical, electrical, and electro-mechanical systems, its application is usually rather straightforward and requires a standard Lagrangian formulation. For three-phase electrical networks, with or without switches, it is often desirable to reformulate the resulting equations of motion into an orthogonal reference frame using the Clarke or Park transformation, or a combination of both. However, such transformations are always performed after the EL equations have been set up and a formal procedure to obtain the transformed equations directly from a Lagrangian thus far lacks in the literature. The contribution of this paper is to show that, by invoking the Helmholtz conditions and the concept of the traditor, such Lagrangians do exist, but require the inclusion of certain non-energetic cross terms.

The human visual system estimates angle features in an internal reference frame: A computational and psychophysical study.

Angle perception is an important middle-level visual process, combining line features to generate an integrated shape percept. Previous studies have proposed two theories of angle perception-a combination of lines and a holistic feature following Weber's law. However, both theories failed to explain the dual-peak fluctuations of the just-noticeable difference (JND) across angle sizes. In this study, we found that the human visual system processes the angle feature in two stages: first, by encoding the orientation of the bounding lines and combining them into an angle feature; and second, by estimating the angle in an orthogonal internal reference frame (IRF). The IRF model fits well with the dual-peak fluctuations of the JND that neither the theory of line combinations nor Weber's law can explain. A statistical image analysis of natural images revealed that the IRF was in alignment with the distribution of the angle features in the natural environment, suggesting that the IRF reflects human prior knowledge of angles in the real world. This study provides a new computational framework for angle discrimination, thereby resolving a long-standing debate on angle perception.

A Flexible Nonorthogonal-Reference-Frame-Based SVPWM Framework for Multilevel Inverters

A generalized SVPWM framework is proposed based on the convenient definition of three nonorthogonal static reference frames, alternative to the $\alpha \beta$ -frame. The definition of these reference frames is exploited in order to get appropriate switching sequences and duty cycles taking into account the redundancy property of constructive vectors. The redundancy property is transparent to the algorithm, given that the proposed method takes advantage of it by following a straightforward algebraic procedure, without postprocessing stages or lookup tables. Furthermore, according to the number of levels and the region of the control space, a detailed analysis on the viability of time averaged common-mode voltage (CMV) elimination, is given. If it is viable, the algorithm achieves zero time-averaged CMV by selecting appropriate switching sequences and duty cycles. The method is based on very simple, low-dimensional, algebraic matrix computations, which make it flexible for implementation. Every detail on the algorithm and its theoretical base is carefully provided in the manuscript. Both, the proposed strategy that optimally provides switching sequences eliminating CMV, and its viability analysis, are applicable to other types of modulation approaches based on orthogonal or nonorthogonal reference frames. A test is proposed on a real-time emulated five-level cascaded H-bridge topology.

Musical intervals under 12-note equal temperament: a geometrical interpretation

Musical intervals in multiple of semitones under 12-note equal temperament, or more specifically pitch-class subsets of assigned cardinality ($n$-chords) are conceived as positive integer points within an Euclidean $n$-space. The number of distinct $n$-chords is inferred from combinatorics with the extension to $n=0$, involving an Euclidean 0-space. The number of repeating $n$-chords, or points which are turned into themselves during a circular permutation, $T_n$, of their coordinates, is inferred from algebraic considerations. Finally, the total number of $n$-chords and the number of $T_n$ set classes are determined. Palindrome and pseudo palindrome $n$-chords are defined and included among repeating $n$-chords, with regard to an equivalence relation, $T_n/T_nI$, where reflection is added to circular permutation. To this respect, the number of $T_n$ set classes is inferred concerning palindrome and pseudo palindrome $n$-chords and the remaining $n$-chords. The above results are reproduced within the framework of a geometrical interpretation, where positive integer points related to $n$-chords of cardinality, $n$, belong to a regular inclined $n$-hedron, $\Psi_{12}^n$, the vertexes lying on the coordinate axes of a Cartesian orthogonal reference frame at a distance, $x_i=12$, $1\le i\le n$, from the origin. Considering $\Psi_{12}^n$ as special cases of lattice polytopes, the number of related nonnegative integer points is also determined for completeness. A comparison is performed with the results inferred from group theory.

Unbalanced Power Flow in Distribution Systems With Embedded Transformers Using the Complex Theory in <formula formulatype="inline"> <tex Notation="TeX">$\alpha \beta 0\;$</tex></formula> Stationary Reference Frame

This paper presents three new contributions to power flow analysis of unbalanced three-phase distribution systems. First, a complex vector based model in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\alpha \beta 0\;$</tex> </formula> stationary reference frame is developed to state the power flow equations using a compact matrix formulation. The proposed model is based on Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). Then, a general and exact power transformer model in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\alpha \beta 0\;$</tex></formula> reference frame is proposed. Finally, this transformer model is incorporated into the power flow problem. It will be shown that the use of an orthogonal reference frame simplifies the modeling of the distribution network components. In this work, both the network and the power transformer, as well as PQ type loads, PQ and PV type generators and a slack bus are modeled. By using the node incidence matrix instead of the admittance matrix, the information about the grid topology and the grid parameters (including power transformers) is separately organized. As it will be demonstrated, the proposed formulation is ready to incorporate other complex models of loads, generators or storage devices. The model is tested by using the IEEE 4-Node and the IEEE 123-Node Test Feeders with different transformer connections and balanced and unbalanced lines and loads.

Natural geometric representation for electron local observables

An existence of the quartic identities for the electron local observables that define orthogonality relations for the 3D quantities quadratic in the electron observables is found. It is shown that the joint solution of the quartic and bilinear identities for the electron observables defines a unique natural representation of the observables. In the natural representation the vector type electron local observables have well-defined fixed positions with respect to a local 3D orthogonal reference frame. It is shown that the natural representation of the electron local observables can be defined in six different forms depending on a choice of the orthogonal unit vectors. The natural representation is used to determine the functional dependence of the electron wave functions on the local observables valid for any shape of the electron wave packet.

A Control Technique for Integration of DG Units to the Electrical Networks

This paper deals with a multiobjective control technique for integration of distributed generation (DG) resources to the electrical power network. The proposed strategy provides compensation for active, reactive, and harmonic load current components during connection of DG link to the grid. The dynamic model of the proposed system is first elaborated in the stationary reference frame and then transformed into the synchronous orthogonal reference frame. The transformed variables are used in control of the voltage source converter as the heart of the interfacing system between DG resources and utility grid. By setting an appropriate compensation current references from the sensed load currents in control circuit loop of DG, the active, reactive, and harmonic load current components will be compensated with fast dynamic response, thereby achieving sinusoidal grid currents in phase with load voltages, while required power of the load is more than the maximum injected power of the DG to the grid. In addition, the proposed control method of this paper does not need a phase-locked loop in control circuit and has fast dynamic response in providing active and reactive power components of the grid-connected loads. The effectiveness of the proposed control technique in DG application is demonstrated with injection of maximum available power from the DG to the grid, increased power factor of the utility grid, and reduced total harmonic distortion of grid current through simulation and experimental results under steady-state and dynamic operating conditions.

PMSM servo‐drive control system with a state feedback and a load torque feedforward compensation

Purpose – The purpose of this paper is to discuss the design and verification of a non‐classical structure of servo‐drive controller with the state feedback and a load torque feedforward compensation.Design/methodology/approach – First a well known nonlinear mathematical model of a PMSM is transformed into a linear form by introducing new variables. The state space new model presented in rotated orthogonal reference frame is decoupled by means of equation in d and q axis. To achieve correct dynamic performance of the servo‐drive system the state feedback with an internal input model and load torque feedforward compensation is proposed. The observed load torque has been used as an input signal for the feedforward compensator. The design of the control system and simulation analysis were performed in Matlab/Simulink. The proposed control algorithm was implemented in a DSP controller (TMS320F2812). The experiments were carried out by using a 0.6 kW PMSM drive system.Findings – It is shown that the proposed c...

The frequency-independent control method for distributed generation systems

In this paper a novel frequency-independent control method suitable for distributed generation (DG) is presented. This strategy is derived based on the abc/αβ transformation and abc/dq transformation of the ac system variables. The active and reactive currents injected by the DG are controlled in the synchronously rotating orthogonal dq reference frame. The transformed variables are used in control of the voltage source inverter that connects DG to distribution network. Due to importance of distributed resources in modern power systems, development of new, practical, cost-effective and simple control strategies is obligatory. The new control method of this paper does not need a Phase Locked Loop (PLL) in control circuit and has fast dynamic response in providing active and reactive power to nonlinear load. From extensive simulation results, high performance of this control strategy in DG application is demonstrated with improved voltage profile, increased power factor and reduced total harmonic distortion.

Instantaneous active and reactive current control technique of shunt active power filter based on the three‐level NPC inverter

AbstractIn this paper, the synthesis and performance of a shunt active power filter (SAPF) based on instantaneous active, and reactive current components (id − iq) technique is presented. The proposed active filter acts as a current source, which is connected in parallel with a nonlinear load and controlled to generate the required compensation currents. The proposed control technique for SAPF aims to compensate the harmonic current contents of nonlinear loads by connection of distributed generation (DG) resources based on renewable energy sources to distribution network. This modeling is derived from the 123(abc) to αβ and αβ to dq transformation of the ac system variables. The injected currents by the SAPF to polluted grid are controlled in synchronous orthogonal dq reference frame by using of decoupled current control technique. By use of phase locked loop (PLL) in control circuit of proposed technique, the angle of positive sequence has been detected, in order to synchronize the SAPF injected currents to distribution network. The proposed control strategy has this ability to eliminate wide range of harmonic frequency draws from utility grid, and provide the compensation currents by DG resources. By this control method, replacement of distributed power generation systems as an active power filter can be possible. Three‐phase three‐level neutral‐point‐clamped (NPC) voltage source inverter (VSI) is proposed for the interfacing between renewable energy resources and polluted distribution network. The simulation results demonstrate high performances of proposed SAPF technique. Copyright © 2010 John Wiley &amp; Sons, Ltd.

A multi-objective control strategy for grid connection of DG (distributed generation) resources

Abstract This paper presents a flexible control technique for connection of DG (distributed generation) resources to distribution networks, especially during ride-through on faulty grid. This strategy is derived from the abc/αβ and αβ/dq transformations of the ac system variables. The active and reactive currents injected by the DG source are controlled in the synchronously rotating orthogonal dq reference frame. The transformed variables are used to control the VSI (voltage source inverter) which connects the DG to the distribution network. Using a P.L.L. (phase locked loop) in circuit of proposed control technique, the angle of positive sequence has been detected, in order to synchronize the currents to the distribution network. The proposed control technique has the capability of providing active and reactive powers and harmonic currents to nonlinear loads with a fast dynamic response. Simulation results and mathematical analysis have been completed in order to achieve a reduced THD (total harmonic distortion), increased power factor and compensated load’s active and reactive powers. The analyses show the high performance of this control strategy in DG applications in comparison with other existing strategies.

A New Control Technique for Three-Phase Shunt Hybrid Power Filter

This paper presents a nonlinear control technique for a three-phase shunt hybrid power filter (SHPF) to enhance its dynamic response when it is used to compensate for harmonic currents and reactive power. The dynamic model of the SHPF system is first elaborated in the stationary ldquoabcrdquo reference frame and then transformed into the synchronous orthogonal ldquodqrdquo reference frame. The ldquodqrdquo frame model is divided into two separate loops, namely, the two current dynamic inner loops and the dc-voltage dynamic outer loop. Proportional-integral (PI) controllers are utilized to control the SHPF input currents and dc-bus voltage. The currents track closely their references so that the SHPF behaves as a quasi-ideal current source connected in parallel with the load. It provides the reactive power and harmonic currents required by the nonlinear load, thereby achieving sinusoidal supply currents in phase with supply voltages under dynamic and steady-state conditions. The SHPF consists of a small-rating voltage-source inverter (VSI) in series with a fifth-harmonic tuned <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> passive filter. The rating of the VSI in the SHPF system is much smaller than that in the conventional shunt active power filter because the passive filter takes care of the major burden of compensation. The effectiveness of the control technique is demonstrated through simulation and experimentation under steady-state and dynamic operating conditions.

Robust Model-Following control of a three-level Neutral Point Clamped shunt active filter in the medium voltage range

This paper presents a robust control technique applied to a three-phase shunt active filter based on an NPC inverter, showing the modelling procedure needed to carry out the proposed control. The transfer functions for the control of the currents injected by the active filter are derived. The modelling is based on the abc/dq Park transformation of the AC system variables. The currents injected by the active filter are controlled in the synchronous orthogonal dq reference frame. The proposed robust current control technique is compared to a conventional PI controller in the dq frame, and to a PIS controller in the dq frame, consisting of a PI and resonant controllers synchronized to the frequencies of the nonlinear load current harmonics. On one hand, it is shown that the proposed technique improves the current harmonics compensation obtained by conventional PI control. On the other hand, it is found that the PIS controller is the best suited for current harmonics compensation among the controllers under study. Nevertheless, the RMF controller results in a simpler implementation than the PIS controller. Moreover, the proposed robust control has been applied to the DC-link voltage regulation, and it has been compared to a PI controller. It is shown that the robust control technique improves the dynamic response of the inverter to load steps without the need of a high crossover frequency of the DC-link voltage loop.

A multi-band shunt hybrid active filter with reduced sensor count

A Shunt Hybrid Active Filter (SHAF) is an attractive option for realizing low-cost harmonic compensation solutions. This paper proposes a SHAF with multiple harmonic compensation capability using a single Voltage Source Inverter and reduced sensor count. This strategy is apt for harmonic filtering solutions where low cost is the exclusive priority. In this paper, a new estimation approach is proposed to obviate requirement of a large number of sensors. Multiple Synchronous Reference Frames (MSRF) and low pass filters are used to measure 5th and 7th harmonic components separately from load as well as filter currents. Individual current controllers are designed for the 5th and 7th harmonic currents. Control is realized in the synchronously rotating, orthogonal (dq) reference frame. Performance of the controller is validated through simulation, using realistic plant and controller models. Experimental results are provided to corroborate the analytical and simulation results.

Assessing talonavicular joint rotations in three dimension

The union of the spherical talar head with the cupped shaped navicular shows the general characteristics of a ball-and-socket joint [1]. As such, the talonavicular joint should be expected to demonstrate three rotational degrees of freedom. Yet, conventional approaches to foot motion analysis provide little opportunity to assess motion of the intrinsic foot joints. A new approach, and perspective, is adopted that permits an appreciation of the talonavicular joint that is not restricted to the confines of marker dependence or the orthogonal reference frame. Data will be presented that shows talonavicular rotation about independent axes that possess orientations that are not orthogonal to any conventional reference frame.