Space Vector Transients of Three-phase Transformers

This paper is devoted to the transient analysis of three-phase transformers by means of the space vector tool. Space vector definition is based on the Clarke transformation, operating in the time domain. Thus, the space vector is better suited to transient analysis when compared with approximate approaches based on the phasor symmetrical-component transformation. Space-vector equivalent circuits are derived for three-phase transformers with Wye and Delta connections. A case study, consisting in the transient due to a capacitor bank insertion, shows that the proposed space-vector approach can clearly evidence the asymmetrical transient behavior of the phase variables in terms of different peak levels and oscillations amplitude.

Clarke Transformation Solution of Asymmetrical Transients in Three-Phase Circuits

This work deals with the use of the Clarke transformation for the theoretical derivation of circuit models for the analysis of asymmetrical transients in three-phase circuits. Asymmetrical transients occur when only one or two phases of a three-phase power system are involved in a switch operation. Such a condition is critical from a theoretical viewpoint since the Clarke transformation is based on the assumption of circuit symmetry between the three phases. If the symmetry assumption is not met, the equivalent circuits in the transformed variables α, β, and 0 are not uncoupled. The literature concerning numerical approaches for asymmetrical transient analysis is very rich, but a comprehensive and rigorous analytical investigation of circuit models within the framework of the Clarke transformation is still lacking. Contrary to numerical approaches, analytical solutions provide deeper insight into the phenomenon and allow for theoretical interpretation and better understanding of the transient behavior. The proposed circuit models show that the β variables are always uncoupled with α and 0 variables, whereas coupling between α and 0 variables can be properly represented by an ideal transformer. Moreover, in the case of single-line switching, the β variables have no transient, i.e., they keep the steady-state behavior. Transient properties can be readily and effectively observed by representing the trajectory of the space vector on the complex plane. All the analytical results have been checked numerically through the Simulink (Matlab R2020a, The MathWorks, Inc., Natick, MA, USA) implementation of a specific three-phase circuit introduced to illustrate the main theoretical issues.

Tan-Sun Transformation-Based Phase-Locked Loop in Detection of the Grid Synchronous Signals under Distorted Grid Conditions

When three-phase voltages are polluted with unbalance, DC offsets, or higher harmonics, it is a challenge to quickly detect their parameters such as phases, frequency, and amplitudes. This paper proposes a phase-locked loop (PLL) for the three-phase non-ideal voltages based on the decoupling network composed of two submodules. One submodule is used to detect the parameters of the fundamental and direct-current voltages based on Tan-Sun transformation, and the other is used to detect the parameters of the higher-harmonic voltages based on Clarke transformation. By selecting the proper decoupling vector by mapping Hilbert space to Euclidean space, the decoupling control for each estimated parameter can be realized. The settling time of the control law can be set the same for each estimated parameter to further improve the response speed of the whole PLL system. The system order equals the number of the estimated parameters in each submodule except that a low-pass filter is required to estimate the average amplitude of the fundamental voltages, so the whole PLL structure is very simple. The simulation and experimental results are provided in the end to validate the effectiveness of the proposed PLL technique in terms of the steady and transient performance.

Designing A Protective Relay for Differential Protection of Power Transformers Using Clarks Transform and S Transform

Given that power transformers are one of the most important components of each network, their protection is an important part that the power transformer errors must be accurately identified and distinguished from each other. Therefore, identification and differentiation of transient phenomena of power transformers, including internal and external errors and magnetic inrush current are essential. In this research, Clarke transform and S transform were used to distinguish between these phenomena that the proposed algorithm is very suitable in terms of three characteristics of accuracy, speed and computational cost. Initially, the simulation of internal, external errors and magnetic inrush current of the transformer was performed for different transformer scenarios. For this purpose, 1060 signal tests were performed under different conditions. Subsequently, the signals of differential current obtained by Clarke transformation and S transformation were analyzed and appropriate criteria were extracted for detecting the current of internal errors from external errors and inrush current. The simulated internal and external errors include three- phase, three-phase to ground, two- phase, two- phase to ground and phase to ground error. Simulations were performed using PSCAD software and implementation of the proposed algorithm in MATLAB environment. The results of this study prevent the unwanted performance of differential protection to prevent undesirable electrifying. It is clear that the description of transient phenomena is the first step towards improving new ideas and criteria for protection with the greater reliability of power transformer which can be controlled better such unusual conditions that are currently used in equipment and relay.

Optimization of efficiency for power system using three phase AC to AC matrix converter with the algorithm of fuzzy controller

This paper suggested a new contribution of three phase AC to AC matrix converter MC via fuzzy logic controller FLC to enhance the whole system. However, the weakness of matrix converter is that the input- output voltage transfer is control to 87% for input and output waveform. Also, matrix converter is more sensitive to the trouble of input voltage which deteriorates the system performance. To overcome these problems, and to improve the efficiency of system, FLC with matrix converter is proposed to minimize the sensitivity to the load, and to increase voltage transfer. In this paper the currents a,b,c are converted to alpha and beta current via Clarke transformation . In this method two FLC are used. The error (between alpha current and reference current) (e) and the change of this error (de) will apply to first FLC. The output of FLC is actual alpha current. In the other hand, the error of beta current and the change of error are also passes through the second FLC to produce the actual beta current. The actual alpha and beta current is converted to direct and quadrature d-q current by park transformation. The d-q current is converted to (a, b, c) out currents by inverse park transformation, the results of this method express that the matrix converter with FLC is more capable, high accuracy with better efficiency as compared with conventional matrix converter system.

EXTENDED CLARKE TRANSFORMATION FOR n-PHASE SYSTEMS

The article describes how to convert space vectors written in a stationary multiphase system, consisting of a number of phases where n > 3, to the stationary alfa beta orthogonal coordinate system. The transformation of vectors from a stationary n-phase system to the stationary alfa beta orthogonal coordinate system is defined The inverse transformation of a vector written in the orthogonal coordinate system to a stationary n-phase system is also defined. The application of the extended Clarke transformation allows control calculations to be performed in both stationary alfa beta or rotating dq orthogonal coordinate systems. This gives the possibility of performing different control strategies. It has a practical application for drive systems with five-phase, six-phase or dual three-phase motors.