Modal transformation obtained from Clarke's matrix - Asymmetrical three-phase case

Some constant matrices can be used as phase-mode transformation matrices for transposed three-phase transmission lines. Clarke's matrix is one of these options. Its application as a phase-mode transformation matrix for untransposed three-phase transmission lines has been analyzed through error and frequency scan comparisons. Based on an actual untransposed asymmetrical three-phase transmission line example, a correction procedure is applied searching for better results from the Clarke's matrix applicaton as a phase-mode transformation matrix. The error analyses are carried out using Clarke's matrix and the new transformation matrices obtained from the correction procedure. Applying Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. If the the corrected transformation matrices are used, the relative values of the off-diagonal elements are decreased. Based on the results of these analyses, the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2007 IEEE.

Voltage regulator modeling for the three-phase power flow in distribution networks

In this paper a three-phase power flow for electrical distribution systems considering different models of voltage regulators is presented. A voltage regulator (VR) is an equipment that maintains the voltage level in a predefined value in a distribution line in spite of the load variations within its nominal power. Three different types of connections are analyzed: 1) wye-connected regulators, 2) open delta-connected regulators and 3) closed delta-connected regulators. To calculate the power flow, the three-phase backward/forward sweep algorithm is used. The methodology is tested on the IEEE 34 bus distribution system. ©2008 IEEE.

A comparative analysis of FBD, PQ and CPT current decompositions - Part II: Three-phase four-wire systems

This paper investigates the major similarities and discrepancies among three important current decompositions proposed for the interpretation of unbalanced and/or non linear three-phase four-wire power circuits. The considered approaches were the so-called FBD Theory, the pq-Theory and the CPT. Although the methods are based on different concepts, the results obtained under ideal conditions (sinusoidal and balanced signals) are very similar. The main differences appear in the presence of unbalanced and non linear load conditions. It will be demonstrated and discussed how the choice of the voltage referential and the return conductor impedance can influence in the resulting current components, as well as, the way of interpreting a power circuit with return conductor. Under linear unbalanced conditions, both FBD and pq-Theory suggest that the some current components contain a third-order harmonic. Besides, neither pq-Theory nor FBD method are able to provide accurate information for reactive current under unbalanced and distorted conditions, what can be done by means of the CPT. © 2009 IEEE.

Three-phase four-wire circuits interpretation by means of different power theories

In order to contribute to the discussion of defining a generalized power theory, valid for unbalanced and non linear circuits, this paper discusses the relationship and discrepancies among four modern power theories. Three-phase four-wire circuits, under different conditions, have been analyzed, since the most conflicting and intriguing interpretations take place in case of return conductor occurrence. Simulation results of different load, power supply and line conditions will be discussed in order to elucidate the author's conclusions and to provoke the readers for additional discussions. © 2010 IEEE.

Innovation and technology policy (ITP) for catching up: a three phase life cycle framework for industrializing economies

Includes bibliography

Distributed generation modelling for unbalanced three-phase power flow calculations in smart grids

Distributed Generators (DG) are generally modeled as PQ or PV buses in power flow studies. But in order to integrate DG units into the distribution systems and control the reactive power injection it is necessary to know the operation mode and the type of connection to the system. This paper presents a single-phase and a three-phase mathematical model to integrate DG in power flow calculations in distribution systems, especially suited for Smart Grid calculations. If the DG is in PV mode, each step of the power flow algorithm calculates the reactive power injection from the DG to the system to keep the voltage in the bus in a predefined level, if the DG is in PQ mode, the power injection is considered as a negative load. The method is tested on two well known test system, presenting single-phase results on 85 bus system, and three-phase results in the IEEE 34 bus test system. © 2011 IEEE.

Comparative analysis for reactive energy measurement methodologies, under non-sinusoidal conditions in three-phase four-wire circuits

This paper presents some methodologies for reactive energy measurement, considering three modern power theories that are suitable for three-phase four-wire non-sinusoidal and unbalanced circuits. The theories were applied in some profiles collected in electrical distribution systems which have real characteristics for voltages and currents measured by commercial reactive energy meters. The experimental results are presented in order to analyze the accuracy of the methodologies, considering the standard IEEE 1459-2010 as a reference. Finally, for additional comparisons, the theories will be confronted with the modern Yokogawa WT3000 energy meter and three samples of a commercial energy meter through an experimental setup. © 2011 IEEE.

An analysis of Generalized Symmetrical Components in non sinusoidal three phase systems

This paper presents the study of the so called Generalized Symmetrical Components, proposed by Tenti et. al. to the analysis of unbalanced periodic non sinusoidal three phase systems. As a result, it was possible to establish a proper relationship between such of generalized symmetrical components and Fortescue symmetrical components to the harmonic frequencies that compose a generic periodic non sinusoidal three phase system. © 2011 IEEE.

Tri-state Space Vector Modulation for Three-phase integrated inverters

The aim of this work is to present a modified Space Vector Modulation (SVM) suitable for Tri-state Three-phase inverters. A standard SVM algorithm and the Tri-state PWM (Pulse Width Modulation) are presented and their concept are mixed into the novel SVM. The proposed SVM is applied to a three-phase tri-state integrated Boost inverter, intended to Photovoltaic Energy Applications. The main features for this novel SVM are validated through simulations and also by experimental tests. The obtained results prove the feasibility of the proposal. © 2011 IEEE.

Three-phase tri-state integrated boost inverter with special space vector and dq0 control

This paper presents a three-phase integrated inverter suitable for stand-alone and grid-connected applications. Furthermore, the utilization of the special features of the tri-state coupled with the new space vector modulation allows the converter to present an attractive degree of freedom for the designing of the controllers. Additionally, the control is derived through dq0 transformation, all the system is described and interesting simulation results are available to confirm the proposal. © 2012 IEEE.

A new design methodology for multipulse rectifiers with Delta auto-connected transformers and a retrofit application in Adjustable Speed Drives (ASDs)

Multipulse rectifiers can replace a conventional six pulse three-phase rectifier (diode bridge) providing a DC voltage with low ripple, low Total Harmonic Distortion of current (THDi) and a high Power Factor (PF). In this context is presented a multipulse rectifier with generalized Delta-differential autotransformer topology, which can provide any level of DC output voltage for any level of three-phase AC input voltage. This paper presents all the possible configurations for Delta topology in order to choose, through graphics, one configuration that presents reduced weight and volume. The average voltage on the DC bus must be compatible with the DC voltage in the six pulse rectifier used in commercial ASDs. Therefore, it is possible to apply the retrofit technique to replace the conventional bridge rectifier by the proposed multipulse rectifier. Based on mathematic models and simulation results, an 18-pulse rectifier with Delta topology, 220 V of line voltage, 315 V of DC output, and rating 2.5 kW of power was designed, implemented and applied for three different commercial ASDs. Experimental results as voltage and current waveforms and results about PF and THDi will be presented. © 2012 IEEE.

Eigenvalue analyses for non-transposed three-phase transmission line considering non-implicit ground wires

This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency range considered in this case. This transformation matrix is an approximation to the exact transformation matrix. For those elements related to the phases of the considered system, the transformation matrix is composed of the elements of Clarke's matrix. In part related to the ground wires, the elements of the transformation matrix must establish a relationship with the elements of the phases considering the establishment of a single homopolar reference in the mode domain. In the case of three-phase lines with the presence of two ground wires, it is unable to get the full diagonalization of the matrices Z and Y in the mode domain. This leads to the second proposal for the composition of real transformation matrix: obtain such transformation matrix from the multiplication of two real and constant matrices. In this case, the inclusion of a second matrix had the objective to minimize errors from the first proposal for the composition of the transformation matrix mentioned. © 2012 IEEE.

Three-phase tri-state buck-boost integrated inverter

This paper presents a three-phase integrated inverter suitable for stand-alone and/or grid-connected applications. The usage of the special features of the tri-state coupled with the special space vector modulation allows the inverter to present an attractive degree of freedom for the controllers' design, i.e. input and output can be controlled independently. Additionally all controllers are based on dq0 transformation, the system are described and interesting simulation results are available to confirm the proposal. Finally, this paper presents experimental evaluations of the inverter feeding a three-phase stand-alone load confirming the remarkable features of the decoupling control. © 2013 IEEE.

Using Universal Line Model (ULM) for Representing Electromagnetic Transients in Three-Phase Transmission Lines

The second-order differential equations that describe the polyphase transmission line are difficult to solve due to the mutual coupling among them and the fact that the parameters are distributed along their length. A method for the analysis of polyphase systems is the technique that decouples their phases. Thus, a system that has n phases coupled can be represented by n decoupled single-phase systems which are mathematically identical to the original system. Once obtained the n-phase circuit, it's possible to calculate the voltages and currents at any point on the line using computational methods. The Universal Line Model (ULM) transforms the differential equations in the time domain to algebraic equations in the frequency domain, solve them and obtain the solution in the frequency domain using the inverse Laplace transform. This work will analyze the method of modal decomposition in a three-phase transmission line for the evaluation of voltages and currents of the line during the energizing process.

Instantaneous complex power applied to three-phase machines

The theory presented in this paper was primarily developed to give a physical interpretation for the instantaneous power flow on a three-phase induction machine, without a neutral conductor, on any operational state and may be extended to any three-phase load. It is a vectorial interpretation of the instantaneous reactive power theory presented by Akagi et al. Which, believe the authors, isn't enough developed and its physical meaning not yet completely understood. This vectorial interpretation is based on the instantaneous complex power concept defined by Torrens for single-phase, ac, steady-state circuits, and leads to a better understanding of the power phenomenon, particularly of the distortion power. This concept has been extended by the authors to three-phase systems, through the utilization of the instantaneous space vectors. The results of measurements of instantaneous complex power on a self-excited induction generator's terminals, during an over-load application transient, are presented for illustration. The compensation of reactive power proposed by Akagi is discussed and a new horizon for the theory application is opened.