Application of Haar functions for transmission line and transformer differential protection

The development of algorithms, based on Haar functions, for extracting the desired frequency components from transient power-system relaying signals is presented. The applications of these algorithms to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. For transmission line protection, three modes of application of the Haar algorithms are described: a full-cycle window algorithm, an approximate full-cycle window algorithm, and a half-cycle window algorithm. For power transformer differential protection, the combined second and fifth harmonic magnitude of the differential current is compared with that of fundamental to arrive at a trip decision. The proposed line protection algorithms are evaluated, under different fault conditions, using realistic relaying signals obtained from transient analysis conducted on a model 400 kV, 3-phase system. The transformer differential protection algorithms are also evaluated using a variety of simulated inrush and internal fault signals.

Combined Use of Solid of Revolution, Thin Shell, and Interphase Elements for Analysis of Cylindrical Shells

Near the boundaries of shells, thin shell theories cannot always provide a satisfactory description of the kinematic situation. This imposes severe limitations on simulating the boundary conditions in theoretical shell models. Here an attempt is made to overcome the above limitation. Three-dimensional theory of elasticity is used near boundaries, while thin shell theory covers the major part of the shell away from the boundaries. Both regions are connected by means of an “interphase element.” This method is used to study typical static stress and natural vibration problems

Ratio transformer bridge for the measurement of dielectric constant of lossy liquids

A three-terminal capacitance bridge is developed for the measurement of the dielectric constant of lossy liquids. Using this modified ratio transformer bridge, the capacitance shunted by a resistance as low as 50 Omega is measured at 10 kHz. The capacitance error associated with the inductance of the connecting wire is compensated using the novel method of introducing an additional transformer to the existing ratio transformer bridge. Other sources of capacitance errors, such as the non-zero output impedence of the ratio transformer and the shield capacitances of the cables, are discussed.

Temperature Distribution in Resin Impregnated Paper Insulation for Transformer Bushings

The overall reliability of a power transformer depends to a great extent on the sound operation of the bushings thereof. Oil impregnated paper (OIP) insulated bushings have been in use for a long time now. In many situations, it becomes necessary to avoid OIP insulation in bushings. In the recent past, a new technological breakthrough has been achieved whereby the OIP is replaced by epoxy resin impregnated crepe paper (RIP) insulation. This new system has several advantages over OIP and has now become the insulation of choice. However, its long time thermal and electrical performance need to be carefully assessed. This paper reports the results of a study of temperature distribution in the body of insulation, based on the ac conductivity of RIP insulation. A method of computing the maximum thermal voltage of this system is also given.

Liquid-Liquid Interphase (Biphasic) as the Reaction Medium in the Assembly of a Hierarchy of Structures of 4,4 `-Azodibenzoic Acid with Zinc and Cadmium

The compounds Zn(C12H8N2)](2)C12N2H8(COO)(2)](2)center dot(C6H12O)center dot(H2O), I, Zn(C12H8N2)]C12N2H8(COO)(2)], II, Cd(C12H8N2)(H2O)]C12N2H8(COO)(2)]center dot(H2O), III, Zn(C10N2H8)]C12N2H8(COO)(2)]center dot 0.5(C10N2H8), IV, Cd(C12N2H8(COO)(2)center dot H2O], V, and Zn-3(mu(2)-O)(mu(3)-O)(3)]C12N2H8(COO)(2)], VI, have been synthesized by using a biphasic approach (I, III, V, VI) or regular hydrothermal method (II, IV). The compounds exhibit one (I and II), two (In), and three dimensionally (IV, V, VI) extended structures. The flexible azodibenzoate ligand gives rise to a 3-fold interpenetration (IV) when the synthesis was carried out using normal hydrothermal methods. The biphasic approach forms structures without any interpenetrations, especially in the three-dimensional structures of V and VI. Formation of Cd2O2 dimers in V and extended M-O(H)-M two-dimensional layers in VI suggests the subtle structural control achieved by the biphasic method. Transformation studies indicate that it is possible to transform I to II. Lewis acid catalytic studies have been performed to evaluate the role of the coordination environment in such reactions. All the compounds have been characterized by a variety of techniques that includes powder X-ray diffraction, infrared, thermogravitric analysis, UV-vis, photoluminescence studies.

Localisation of discrete change in a transformer winding: a network-function-loci approach

An entirely different approach for localisation of winding deformation based on terminal measurements is presented. Within the context of this study, winding deformation means, a discrete and specific change externally imposed at a particular position on the winding. The proposed method is based on pre-computing and plotting the complex network-function loci e.g. driving-point impedance (DPI)] at a selected frequency, for a meaningful range of values for each element (increasing and decreasing) of the ladder network which represents the winding. This loci diagram is called the nomogram. After introducing a discrete change, amplitude and phase of DPI are measured. By plotting this single measurement on the nomogram, it is possible to estimate the location and identify the extent of change. In contrast to the existing approach, the proposed method is fast, non-iterative and yields reasonably good localisation. Experimental results for actual transformer windings (interleaved and continuous disc) are presented.

Improved utilisation of an HF transformer in DC–AC application

Power conversion using high frequency (HF) link converters is popular because of compact size and light weight of highfrequency transformer. This study focuses on improved utilisation of HF transformer in DC–AC applications. In practical application, the operating condition of the power converter deviates significantly from the designed considerations. These deviating factors are commutation requirements (dead-time, overlap), mismatch in device drops and presence of the fundamental frequency in load current. As a result, the HF transformer handles some amount of low-frequency components (including DC) other than desired HF components. This causes the operating point in B-H curve to shift away from its normal or idealised position and hence results poor utilisation of the HF transformer and unwanted losses. This study investigates the nature of the problem with experimental determination of approximate lumped parameter modelling and saturation behaviour (B-H curve) of the HF transformer. A simple closed-loop control algorithm with online tuning of the controller parameters is proposed to improve the utilisation of the isolation transformer. The simulation and experimental results are presented.

Influence of Phase Connection and Terminal Conditions on Natural Frequencies of Three-Phase Transformer Windings

With the increasing use of extra high-voltage transmission in power system expansion, the manufacturers of power apparatus and the electric utilities are studying the nature of overvoltages in power systems due to lightning and, in particular, switching operations. For such analyses, knowledge of the natural frequencies of the windings of transformers under a wide variety of conditions is important. The work reported by the author in a previous paper is extended and equivalent circuits have been developed to represent several sets of terminal conditions. These equivalent circuits can be used to determine the natural frequencies and transient voltages in the windings. Comparison of the measured and the computed results obtained with a model transformer indicates that they are in good agreement. Hence, this method of analysis provides a satisfactory procedure for the estimation of natural frequencies and transient voltages in transformer windings.

Natural Frequencies of 3-Pkase Transformer Windings

Natural frequencies and surge response of the windings of 3-phase transformers have been determined in the past by neglecting the capacitive and inductive couplings between the phase windings. This paper shows that these assumptions are not valid and presents a new method of formulating equivalent networks of 3-phase transformer windings for the various winding connections and terminal conditions. By utilizing these equivalent networks the natural frequencies and surge response of the windings can be determined. Tests made on a model transformer showed good correlation with calculated results.

Estimation of Series Capacitance of a Transformer Winding Based on Frequency-Response Data: An Indirect Measurement Approach

A novel procedure to determine the series capacitance of a transformer winding, based on frequency-response measurements, is reported. It is based on converting the measured driving-point impedance magnitude response into a rational function and thereafter exploiting the ratio of a specific coefficient in the numerator and denominator polynomial, which leads to the direct estimation of series capacitance. The theoretical formulations are derived for a mutually coupled ladder-network model, followed by sample calculations. The results obtained are accurate and its feasibility is demonstrated by experiments on model-coil and on actual, single, isolated transformer windings (layered, continuous disc, and interleaved disc). The authors believe that the proposed method is the closest one can get to indirectly measuring series capacitance.

Construction of Equivalent Circuit of a Single and Isolated Transformer Winding From FRA Data Using the ABC Algorithm

This paper reports the results of employing an artificial bee colony search algorithm for synthesizing a mutually coupled lumped-parameter ladder-network representation of a transformer winding, starting from its measured magnitude frequency response. The existing bee colony algorithm is suitably adopted by appropriately defining constraints, inequalities, and bounds to restrict the search space and thereby ensure synthesis of a nearly unique ladder network corresponding to each frequency response. Ensuring near-uniqueness while constructing the reference circuit (i.e., representation of healthy winding) is the objective. Furthermore, the synthesized circuits must exhibit physical realizability. The proposed method is easy to implement, time efficient, and problems associated with the supply of initial guess in existing methods are circumvented. Experimental results are reported on two types of actual, single, and isolated transformer windings (continuous disc and interleaved disc).

Construction of equivalent circuit of a transformer winding from driving-point impedance function - analytical approach

Analytical solution is presented to convert a given driving-point impedance function (in s-domain) into a physically realisable ladder network with inductive coupling between any two sections and losses considered. The number of sections in the ladder network can vary, but its topology is assumed fixed. A study of the coefficients of the numerator and denominator polynomials of the driving-point impedance function of the ladder network, for increasing number of sections, led to the identification of certain coefficients, which exhibit very special properties. Generalised expressions for these specific coefficients have also been derived. Exploiting their properties, it is demonstrated that the synthesis method essentially turns out to be an exercise of solving a set of linear, simultaneous, algebraic equations, whose solution directly yields the ladder network elements. The proposed solution is novel, simple and guarantees a unique network. Presently, the formulation can synthesise a unique ladder network up to six sections.