1,721,030 research outputs found
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Total Electric Field due to an Electron Avalanche and it's coupling to Transmission Line Conductors
No full textTransmission of bulk electric power from the generating stations to the load centres can be carried out only through high voltages transmission lines. One of the main issues in the design and maintenance of extra and ultra-high voltage transmission system is the phenomenon named corona. It is the local electrical breakdown of air in the vicinity of the line conductors and hardware. Even though the design and dimensions of these elements are made considering the corona onset, surface abrasions arising either during installation or operation can lead to intolerable corona. Apart from producing some insignificant chemical reactions and noticeable acoustic noise, they can be a significant source of electromagnetic interference. In the early days, this interference was of concern only to radio and television receptions, however, with extensive use of wide frequency bands for modern applications, it has assumed prime importance.
The EMI due to the transmission line corona has been extensively studied and reliable empirical formulas have been proposed. The basis for all the earlier studies was the experimentally measured corona currents. This approach fails for new line designs especially with higher and higher voltages being employed due to non-availability of experimental data. A second approach assumed corona current to be injected into the line and subsequent analysis was carried out based on transmission line model. However, there were assumptions made on the mode of corona current injection into the conductor and the frequency range involved were also not adequate for the modern-day applications. Applicability of transmission line model for analysis is also questionable.
From a theoretical perspective, the coupling of the field produced by corona to the conductor was hardly investigated and the total field produced by the corona itself was not quantified. In order to address these serious lacunae, the present work was taken up and it can be considered as the first leap towards the correct picturization, as well as, quantification of the problem.
The field produced by the electron avalanche involves noticeable retardation effects. In the literature, only the field produced by arbitrarily moving point charge of fixed strength is given by the Heaviside-Feynman equation. On the contrary, the avalanche involves an arbitrarily moving charge of time varying strength at its head with trailing positive charge, which is almost stationary. Starting from the basics, an analytical expression for the electric field due to an arbitrarily moving point charge of time varying strength is derived which forms a fundamental contribution to Electrodynamics. This is extended to deduce an expression for the total electric field due to an avalanche for the very first time. Suitable validation of the expression is provided through
numerical simulation of electric field integral equation.
Corona discharge is a complex phenomenon having many distinctly different modes which differ in their visual, as well as, electrical characteristics. Innumerable electron avalanches contribute to the measured corona current with their space-charge acting as a moderator. Therefore, in order to model the corona on conductors, an indirect approach based on linear system theory is proposed. An equivalent spatio-temporal dipole distribution was obtained to produce the measured current on the conductor. The general expression derived for the isolated avalanche is extended for this purpose.
Using the above, the means of induction, spatial decay rate of corona current in the close range, its propagation mode and field produced by both avalanche/equivalent dipole and that due to induced current in the conductor, have all been investigated and quantified.
In summary, the contributions made in this work are more of fundamental in nature and would be of significant interest to the high voltage power transmission line, as well as, to the communication engineers
Upper Frequency Bound on Circuit-Based Models for Transformer Windings
No full textThe power generation, transmission and utilisation are necessarily being carried out at different
voltage levels, and require transformers for performing the voltage level conversions.
As a result, transformers form one of the most critical elements of the power system. Incidentally,
they are also one of the costliest equipments in any electric power stations, with
cost ranging up to millions of dollars. Their repair work also proves to be quite expensive
and time consuming. Moreover, the revenue loss due to the consequential line outages can
be intolerable.
The electrical insulation in the transformers age under electrical, thermal, mechanical
and synergy of these stresses. The electrical stresses are due to the continuous operating
voltage, temporary overvoltages and the transient overvoltages. Classically, the surges generated
by switching operation and natural lightning formed mainly the transient overvoltages.
An adequate design of the transformer insulation requires a detailed knowledge on the electrical
stress distribution all along the winding. Unlike that in simple airgaps found in the
transmission lines, the transformer winding complicates the stress distribution by modulating
its spatio-temporal distribution. This necessitated a detailed modelling of the winding,
well beyond the normal two-port network model employed in power system studies.
Both distributed and ladder network models have been proposed in the earlier literature
to accurately depict the response of the simplified winding models for fast rising lightning and
switching surges. Depending on the adopted model, varieties of theoretical approaches ranging
from travelling and standing wave theory-based approaches to finite-difference-equation
based approaches, have been proposed. With the advent of digital computers, ladder network
models assumed priority and non-uniform winding could be modelled.
There was also another experimental based approach in which the frequency or time
domain response of the winding at its terminals (and taps if made available) were measured and various system identi fication approaches were attempted to either describe the terminal
response for different surges or use it for possible identification of the physical (geometric)
changes in the winding structure. However, as this approach cannot be employed for the
winding that are yet to be fabricated and further cannot provide any insight into various
interior stresses, they will not be considered hereafter.
With the increase in power rating of the transformers, the size of the winding also became
bigger. Then the adequacy of the above said modelling approaches for analysing the stress
under the chopped lightning impulse was questioned. Meanwhile, the propagation of the
Partial Discharge (PD) pulse, which can have rise time of the order of few nanoseconds, could
not be e ectively analysed by the classical approaches. With the advent of Gas Insulated
Substation (GIS), another overvoltage called the Very Fast Transient Overvoltage (VFTO),
caused by the operation of mainly the disconnector switches became a matter of concern.
These overvoltages have frequency spectrum ranging up to tens to hundreds of MHz. The
higher frequency content of the above said entities have led to serious concern over the
validity of the circuit-based modelling.
To overcome the problem, transmission line modelling for the turns/coils of the winding
were proposed and commonly employed. In this approach, both Single Transmission Line
model (STL) and Multi-Conductor Transmission Line Model (MTL) were adopted to evaluate
the surge distribution along the winding. The same was also employed for the modelling
of the propagation of PD pulses. However, the transmission line modelling requires the existence
of Transverse Electro Magnetic (TEM) mode of wave propagation, which is rather
di cult to realise for the initial critical part of VFTO and for the entire PD waveforms.
Incidentally, the laboratory validation provided in some of the literature were plagued by
the electromagnetic scaling issues, which render the validation provided quite inadequate. In
other words, it has become highly essential to trace the underlying dynamic electromagnetic
fields, rather than resorting to convenient simplified modelling approaches.
The present work was taken up to address this basic problem. Its scope is identified
as: (i) Find a suitable numerical electromagnetic field calculation approach for the problem
in hand, and (ii) Noting that the circuit-based modelling is the language of electrical engineers,
provide an upper frequency bound to such modelling approaches for the transformer
windings. Simplifications which are routinely made in evaluating the surge response of the
windings like neglecting role of bushing, tank and other phases, are also made in this work.
At the same time, it is worth noting here that the present work can be considered as a first step in finding the full-wave response of winding
Lightning Threat to Cables on Tall Towers and the Question of Electrical Isolation
Full text linkElectromagnetic effects of lightning currents during a direct hit to tall communication towers, other instrumented towers and chimneys can be hazardous to associated cables, as well as, electrical and electronics systems. The standard practice in telecommunication and other related fields is to bond the cable sheath to the tower and ground connection is made before it enters the base station. However, in some specific cases when power, signal and data logging cables are to be supported on the same tower, isolation of power cables is demanded. In a totally different situation, attempts are also made to have a dedicated isolated down conductor.
A critical review of the situation demanded a more quantitative answer to the following questions: (i) whether it is possible to electrically isolate a dedicated down conductor, (ii) is it possible to electrically isolate the cables and their terminal equipment both mounted on towers serving as down conductor and if so, what will be the nature of current induced in the cables and (iii) as per the standard practice, if the cable sheaths are connected to the tower/structure, what will be the nature of the current shared by them. Addressing these important issues formed the scope of the present work.
For the tall structures considered in this work, for the critical time periods, wave nature of the current dominates. This called for electromagnetic modeling covering Transverse Magnetic (TM) mode of the wave propagation. Owing to the complex geometrical features involved with the problem, both experiments on electromagnetically scaled laboratory models, as well as, theoretical simulation is attempted.
An electromagnetically scaled laboratory model is employed for the time domain experimental investigation. This approach, which has been validated earlier, is further scrutinized to ensure its adequacy. In order to achieve generality and noting the fact that the associated parameters are rather difficult to be varied in the experimentation, theoretical investigation is also employed. For this, both NEC-2, as well as, an in-house thin wire time domain code developed for this work is employed. NEC-2 could handle multi-wire multi-radius junctions, while in-house time domain code could handle proximity and non-cylindrical shapes encountered with tower lattice elements.
The investigation of induction to isolated cables on simple down conductors and towers is considered first. The induced current is shown to be bipolar oscillatory with the period of oscillation governed by the length of the cable. It is shown that the level of induction for good earth termination is below 5 – 10 % while that with moderate inductance in the earth termination can enhance the induction to higher levels. The level of induction is shown to be not critically dependent on the length of the cable, gap between cable and down conductor/tower. When multiple cables are mounted, they seem to influence each other and individually carry currents of lower amplitude. Also, the effect of shape and proximity of the tower lattice elements on induction is investigated. If the cable is housed inside a metallic tray, the amplitude of induced current is shown to be quite small.
Subsequently, the evaluation of electrical stress between the isolated down conductor on tower and simplified representation of the structure is considered. A suitable definition of the electric stress for the wave regime is evolved and then it is shown that, at present, the voltage difference defined by the path integral of electric field across shortest path between the two entities is the best indicator for the stress. The electrical stress in the case of isolated down conductor on tower, as well as, down conductor with isolated cable is shown to reach very dangerous levels. On the other hand, the stress on the isolated cables on towers also serving as down conductors is shown to be relatively moderate. Interestingly, it is shown that the electrical stress and the voltage difference is dependent on the gap and for the critical time period, can be much lower than that calculated as a product of equivalent tower surge impedance and the stroke current, even before the arrival of ground end reflections.
Finally, the current shared by cables connected to the down conductor is investigated. For the case of simple cylindrical down conductor with cable connected to it at the top, it is shown that the amount of current shared by the cable is not dependent on its length and the relative radii (cross section) have only a weak influence. For the case with down conductor formed by L and + angles, it is shown that the placement of cable at their interior corner can reduce the initial current shared by the cable. In order to model best possible situation with towers, experiments are conducted with cable inside an aluminum pipe. Even in this case, cable current builds up with successive reflections to become comparable with the current through the pipe itself. Subsequent investigation with 1:40 and 1:20 tower models lead to several interesting observations. Cables running along leg/face of the tower whether placed inside or outside the tower, always shares good amount of current. Further, frequent bonding of the sheath to the tower increases the current shared by the cable. Cable when housed in a metallic tray shares less than 50% of the current shared without the tray.
Even though a complete quantification is not to be achieved in this work, it has made a good beginning with some significant contribution towards lightning protection issues pertaining to tall towers and structures
Lightning Protection System To Indian Satellite Launch Pads : Stroke Classification And Evaluation Of Current In The Intercepted Strokes
No full textSatellites have become absolute necessity in the growing modern space technology. At present, launch pads are the only means for launching of satellites or any other space vehicles. Due to the large magnitude of current and the associated rate of rise, a lightning strike to launch pads can be quite disastrous.
Satellite launch complex forms typically the tallest object in that region. This makes them the more vulnerable to cloud-to-ground lightning. In addition, most of the launch pads are situated near the coastal area, where the isokeraunic levels are quite high. In view of these, almost all the satellite launch pads are provided with suitable Lightning Protection Systems (LPS). The LPS is basically intended for protecting against a direct lightning hit. The present work is related with the LPS to Indian satellite launch pads, Pad-I and Pad-II.
The protection system for Pad-I consists of three 120 m tall towers placed approximately at the vertices of an equilateral triangle of 180 m. The same for Pad-II consist of 120 m tall towers placed at vertices of rectangle of size 90 m x 105 m. Towers are interconnected by 6 shield wires at the top. A mast of 10m length forms the top of the tower.
Significant work on the analysis of interception efficacy of these protection systems has been reported in the literature. The lightning surge response of these systems have also been analysed and reported.
The interception efficacy of these LPS in field can be ascertained by pertinent measurements. Measuring the lightning current on LPS seems to be one of the most suitable choices for this purpose. It would also greatly facilitate collection of local lightning current statistics, data on which is almost absent. Several considerations suggest that the tower bases form ideal place for such measurement.
However, such lightning current records would involve mainly the current resulting from stroke interception, as well as, induced current due to strokes nearby. Literature on categorisation of measured currents to the type of stroke and correlation of measured currents to the incident stroke currents is rather limited. This is especially true for interconnected protection system of the type dealt in the present work.
Considering these the present work is taken up and its scope is defined as:
(i) Evolve a suitable model for study of current distribution in LPS due to
Lightning and using the same deduce the current due to stroke interception and that due to stroke nearby.
(ii) For the purpose of categorization identify the salient characteristics of current due to the intercepted strokes and that due to bypass/nearby strokes
(iii) For the intercepted strokes, develop a processor for estimating the injected stroke current from the measured tower base currents.
Lightning event, apart from other associated physical phenomena, is strongly governed by electromagnetic fields. Any method employed for the analysis, either theoretical or experimental, should satisfy the governing electromagnetic equations. As experimentation on actual system, as well as, their laboratory simulation is nearly impossible, theoretical modelling approach is selected. Modelling involves modelling of the channel along with its excitation, modelling of the LPS and modelling of the ground. Channel, following the literature, is represented as a loaded conductor with a lumped current source at the junction point. Such models have quite successfully predicted the electromagnetic fields and current in other places on the down conductor.
For the LPS, some simplifications on the geometry are very essential. Tower lattice elements of dimensions much smaller than the wavelength of highest dominant frequency component of lightning current spectrum are neglected. Suitable modification is made for the tower top involving a plate and interconnection of several short members.
For the close range within 200 – 400 m, even for the induced currents, the influence of ground in the literature has been reported to be small. Also, there is an extensive grounding network in these systems. In view of the same, a perfectly conducting ground along with suitable ground termination impedance is considered.
Only the numerical solution of the problem is feasible and for the same, following the literature, NEC-2 is employed. All the guidelines of NEC are respected in the discretisation. Geometric mean radius is employed for modelling the complex tower elements. Fourier Transform Techniques are employed for time domain conversion of the computed frequency domain quantities. Occasionally, numerical inversion error of magnitude less than 5% is encountered. For the validation of the numerical modelling for both direct stroke and that nearby, time domain experimentation on electromagnetically reduced scale models (35:1) is employed.
As the channel electrical and geometrical parameters are stochastic in nature, it is necessary to ensure that the deduction made using the model is practically relevant. For this, some parametric studies are conducted. The influence of channel length and inclination, stroke current velocity etc. has been shown to be insignificant for the case of intercepted strokes. Simulations are carried out for the stroke intercepted (i.e. direct strikes) by the LPS. The characteristics of the tower base currents are investigated. The base currents indicate a dispersive propagation along the towers and further a frequency dependent current division at the tower-shield wire junctions. Base currents contain superimposed oscillations, which basically originate from various junctions of the system. The magnitude of the oscillations is obviously dependent on the rise time of the incident currents. The tower base currents settle within about 10 -15 µs, which is shorter than that for isolated tower. Further, the full-frequency model could be limited to this time period. The corresponding current transfer functions are deduced.
For the stroke interception by shield wires, based on the earlier work, only stroke to midspan is found to be relevant and hence it is considered. The nature of tower base currents for a stroke to midspan of the shield wires seem to be similar. However there are some distinct features, which are helpful in identifying the stroke location on the LPS. From the time correlated tower base currents, a suitable methodology for identifying the stroke interception location on LPS is developed.
Next, simulations for induced current due to a bypass stroke, as well as, stroke to ground outside the LPS, however, within 1 km radius are taken up. In fact, it is estimated that latter is nearly 5 – 13 times higher than the strokes collected by LPS, indicating it as the most probable event. The objective here is characterization, rather than correlation. In this study, the influence of charge induced on the LPS by the descending leader is neglected and the upward leader activity is approximately considered. To the best of author’s knowledge, studies on such induced currents in down conductors are very scarce. Considering this and noting that the number of parameters is quite large, first the basic study is taken up on simple cylindrical down conductors. Many important and interesting deductions are made.
The nature of the induced current is highly dependent on the rate of rise as well as the velocity of propagation of the stroke current. The magnitude and to some extent, the wave shape of the induced current is found to depend on the average as well as maximum di/dt of the stroke current. For a given wave shape, the magnitude of the induced current increases with rate of rise of the wave front; however, saturating trend will onset after some point. The height of the down conductor mainly governs the frequency of the oscillatory component of the induced current. The dependency of the induced current on the radius of the down conductor seems to be logarithmic (which is in accordance with the antenna theory). Based on these results, the parameters for the corresponding study on LPS under consideration, is chosen.
The results of the investigation on the induced currents in LPS show that they have quite distinct waveform. They are basically bipolar and oscillatory in nature, with relatively short duration. These unique features facilitate clear distinction of the induced currents from that due to stroke interception. Basic characteristics are reasonably insensitive to the separation distance of the protection system and the channel, current propagation velocity along the channel, channel inclination and shape of the current front. The salient features of the induced current due to a bypass stroke are also enumerated.
• The noise, if any, in the measured current can be addressed only after acquiring sufficient data. Based on the above, the following procedure is suggested for the stroke classification and estimation.
• By employing the distinct features of the resulting tower base currents, analyze the measured tower base currents and classify the strokes into the intercepted stroke or stroke to ground.
• For the latter case, using the salient features of the bypass strokes, further classify the strokes to bypass strokes and stroke to ground outside the protected volume.
• For the intercepted strokes, using the relative strengths and wave shapes, identify the interception point to either tower top or the midspan of the shield wires.
• Then by using the corresponding transfer functions and Fourier Transform techniques, compute the injected stroke current.
• Using the above, other tower base currents are computed and compared with the measured currents. This gives quantification for the accuracy of the method.
In summary the present work has made some original contribution to the classification and estimation of stroke currents measured on the interconnected LPS
Stable Galerkin Finite Element Formulation for the Simulation of Electromagnetic Flowmeter
Full text linkElectromagnetic flow meters are simple, rugged, non-invasive flow measuring instruments, which are extensively employed in many applications. In particular, they are ideally suited for the flow rate measurement of liquid metals, which serve as coolants in fast breeder reactors. In such applications, theoretical evaluation of the sensitivity turns out to be the best possible choice. Invariably, an evaluation of the associated electromagnetic fields forms the first step. However, due to the complexity of the problem, only numerical field computational approach would be feasible. In the pertinent literature, couple of e orts could be found which employ the well-known Galerkin Finite Element Method (GFEM) for the required task. However, GFEM is known to suffer from the numerical stability problem even at moderate flow rates. This problem is quite common in fluid dynamics area and several stabilization schemes have been suggested as a remedial measure. Among such schemes, the Streamline Upwinding Petrov Galerkin (SU/PG) method is a simple and widely employed approach. The same has been adopted in some of the moving conductor literatures for obtaining a stable solution.
Nevertheless, in fluid dynamics literature, it has been shown that the SU/PG solution can suffer from distortion/peaking at the boundary. The remedial measures proposed are nonlinear in nature and hence are computationally demanding. Also, even the SU/PG scheme by itself requires significant additional computation for quadratic and higher order elements. Further, the value of stabilization parameter is not accurately known for 2D and 3D problems.
The present work is basically an attempt to address the above problem for flow meter and other rectilinearly moving conductor problems. More specifically, but for the requirement of (graded) structured mesh along the flow direction, it basically aims to address a more general class of problems not just limited to the flow meter.
Following the classical approach employed in fluid dynamics literature, first the problem is studied in its 1D form. It was observed that a relatively better performance of GFEM over FDM scheme is basically due to the difference in their Right Hand Side (RHS) terms, which represents the applied magnetic field. Taking clue from this, it was envisaged that a better insight to the numerical problem can be obtained by using the control system theory's transfer function approach.
An application of FDM or GFEM to the 1D form of the governing equation, leads to flalge-braic equations with space variable in discrete form. Hence, a Z-transform based approach is employed to relate the applied magnetic field to the vector potential of the resulting reaction magnetic field. It is then shown that the presence of a pole at Z = -1 is basically responsible for the oscillations in the numerical solution.
It is then proposed that by using the control systems pole-zero cancellation principle, stability can be brought into the numerical solution. This requires suitable modification of RHS terms in the discretised equations and accordingly, two novel schemes have been proposed which works within the framework of GFEM. In author's considered opinion, the use of Z-transform for analysing the stability of the numerical schemes and the idea of employing pole-zero cancellation to bring in stability, are first of its kind.
In the first of the proposed schemes, the pole-zero cancellation is achieved by simply restating the input magnetic field in terms its vector potential. Solving the difference equations given by the application of FDM or GFEM to 1D version of the governing equation, it is analytically shown that the proposed scheme is absolutely stable at high flow rates. However, at midrange of flow rates there is a small error, which is analytically quantified.
Then the scheme is applied to the original flow meter problem which has only axially varying applied field and the stability is demonstrated for an extensive range of flow rates. Note that the discretisation along the flow direction was restricted in the above exercise to graded regular mesh, which can readily be realised for problems involving rectilinearly moving conductors.
In order to cater for more general cases in which the applied field varies in both axial and transverse directions, a second scheme is developed. Here the RHS term representing the input magnetic field is considered in a generic weighted average form. The required weights are evaluated by imposing apart from the need for an essential zero yielding term, the flux preservation and other symmetry conditions. The stability of this scheme is proven analytically for both 1D and 2D version of the problem using respectively, the 1D and 2D Z-transform based approaches. The analytical inferences are adequately validated with numerical exercises. Also, the small error present for the midrange of flow rates is analytically quantified. Then the second scheme is applied to the actual flow meter with a general magnetic field pro le. The proposed scheme is shown to be very stable and accurate even at very high flow rates. As before, the discretisation was restricted to graded regular mesh along the flow direction.
By solving for the standard TEAM No. 9 benchmark problem, applicability of the second scheme for other rectilinearly moving conductor problem has been adequately demonstrated.
Even though the problems considered in this work readily permits the use of a graded regular mesh along the flow direction, for the sake of completeness, discretisation with arbitrary quadrilateral and triangular mesh is also considered. The performance of the proposed schemes for such cases even though found to deteriorate, is still shown to be considerably better than the GFEM.
In summary, this work has successfully proposed two novel, computationally effcient and stable GFEM schemes for the simulation of electromagnetic flow meters and other rectilin early moving conductor problems
A Macroscopic Physical Model For Lightning Return Stroke
Full text linkIn the design of most of the modern systems, lightning threat needs to be considered at the design phase itself. This demands a suitable model and owing to associated complexity, only simplified modeling have been attempted. As a consequence, it does not provide adequate insight into the phenomena. Considering these, a more realistic time-¬ domain electromagnetic model for the return stroke current evolution has been developed by incorporating the following underlying physical processes: (i) excitation formed by the electric field due to charge distribution along the channel, cloud and that induced on ground, (ii) the transient enhancement of series conductance at the bridging regime, which initiates the return stroke,( iii) the non¬linear variation of channel conductance along with (iv) the associated dynamic Electromagnetic Fields(EMFs) that supports the current evolution.
The intended modeling begins from the instant of bridging and the pre-¬return stroke charge distribution along the channel is calculated using Charge Simulation Method(CSM). For the calculation of dynamic EMFs, the thin wire Time Domain Electric Field Integral Equation(TD¬EFIE) is employed The transient enhancement of conductance at the bridging/streamer region is emulated using Toepler’s spark law while that along the matured section of the channel is described by first order arc model. The macroscopic physical model developed depicts most of the salient features of current evolution and resulting remote electromagnetic fields in a self¬ consistent manner. The work is not limited by the simplifications adopted for the channel geometry.
The strength of the model was exploited for investigating a couple of practically important questions, one of which had divided opinion in the literature. Firstly, analysis showed that the "secondary" current waves generated by successive reflection within struck TGO and that fed by branches do not get reflected at the main wave front. It is shown that the dynamic spatial resistance profile of the channel at the main wave front is primarily responsible for this behavior. Secondly, it is shown that the abrupt change in radii at TGO ¬channel junction is mainly responsible for reflection at the junction.
In summary, a novel time-¬domain macroscopic physical model for the first return stroke of a downward cloud¬-to-¬ ground lightning has been successfully developed, which is capable of providing much deeper insight in to the complex phenomena
Improved Understanding of Standing Waves in Single Layer Coils and Elegant Methods to Estimate Transformer Winding Parameters
No full textAnalyzing the effect of impulse voltages (like lightning, switching) on transformer winding has occupied centerstage in core electrical engineering research for over a century. These investigations gather great significance and relevance as it eventually governs the design of insulation in the winding. Notwithstanding the colossal contribution this domain has witnessed from stalwarts in the past century, a closer scrutiny surprisingly reveals that there still exists tiny grey areas that demands attention. Pursuing this line of thought, the first part of this thesis aims to clearly describe what this grey area is and resolving it would provide a deeper insight about fundamental understanding of surge response in transformer windings – with special emphasis on its standing wave phenomenon. Following this, in the latter part, elegant procedures are stitched together to determine a few electrical parameters of the transformer winding equivalent circuit that have the potential to help in assessing mechanical status of windings. Objectives of the thesis are -
1. Formulate an analytical method to determine the exact shape of standing waves for all modes in a uniform single layer coil as a solution of its governing partial differential equation
2. Estimate series capacitance of a uniform transformer winding from its measured driving point impedance
3. Determine effective air-core inductance of an iron-core uniform winding as a function of its axial length from measured driving point impedance
First part of the thesis revisits a century-old classical theory of standing waves on uniform single layer coils. Accurate information about natural frequencies and shapes of the corresponding standing waves are essential for gaining a deeper understanding of the response of coils to impulse excitations. Analytical studies on coils have largely been based on the assumption that standing waves are sinusoids in both space and time. However, this contradicts the results from numerical circuit analysis and practical measurements. So, this thesis attempts to bridge this discrepancy by revisiting the classical standing wave phenomena in coils. It not only assesses the reason for the aforementioned inconsistency, but also makes a contribution by analytically deriving the exact mode shape of standing waves for both neutral open/short conditions. For this, the coil is modelled as a distributed network of elemental inductances and capacitances, while an exponential function describes the spatial variation of mutual inductance between turns. Initially, an elegant derivation of the governing partial differential equation (in terms of voltage as the variable instead of flux) for surge distribution is presented and to the best of our knowledge, for the first time, an analytical solution for the same has been found by the variable-separable method to find the complete solution (sum of time and spatial terms). Hyperbolic terms in the spatial part of the solution have always been neglected but are included here, thus, yielding the exact mode shapes. For verification, both voltage and current standing waves computed from the analytical solution were plotted and compared with PSPICE simulation results on a 100-section ladder network representing a uniform single-layer coil. Then, practical measurements were made on a tailor-made large-sized single layer coil with a length of 2.02 m, diameter of ~1 m and having 640 turns. It turns out that even in such simple single layer coils, the shape of standing waves of all modes deviates considerably from being sinusoidal. It was further observed that this deviation depends on spatial variation of mutual inductance, capacitive coupling, and order of the standing waves.
In the second part, an elegant method for determining the series capacitance (Cs) and air-core equivalent inductance of a uniform winding as a function of its axial length (termed as M0x in this thesis) of a uniform transformer winding, from its measured DPI magnitude, is discussed. Knowledge about the series capacitance of the winding is essential, which along with shunt capacitance, determines the initial impulse voltage distribution when a surge impinges on the winding. Unlike previously published approaches, the proposed method does not involve any cumbersome and time-consuming curve-fitting or running of optimization/search algorithms. Neither does it require winding geometry data. The proposed procedure for finding series capacitance relies on a property that is observable in the driving point impedance (DPI) function of a lossless winding with an open neutral condition, viz., the ratio of the product of squares of open circuit natural frequencies to the product of squares of short circuit natural frequencies bears a particular relation to the coefficients of the DPI function. A simple procedure involving a deft manipulation and combination of a few well-known properties that correlate the roots of a polynomial to its coefficients are then utilized for determining series capacitance.
Knowledge about equivalent air-core inductance distribution as a function of its axial length (i.e., M0x) is useful for localizing a minor/incipient mechanical fault in the winding. A physically realizable empirical relationship to estimate M0x is initially proposed. The corresponding constants of the empirical relationship are then calculated from the measured DPI. The proposed method requires three DPI measurements: one with neutral-end open and the other with neutral-end shorted. The third DPI is measured with a known external lumped capacitance connected between the neutral and ground. This method requires only the first few dominant natural frequencies observable in the first two of the DPIs.
Feasibility of proposed methods for estimating Cs and M0x was initially verified by simulation on an N-section ladder network and then by experiments on small-sized continuous-disk and interleaved-disk windings, and finally on a large-sized 33 kV, 3.5 MVA continuous-disk winding. Salient features of the proposed methods are – they are simple, elegant and involve minimum post-processing after measuring the DPI. Given its inherent simplicity and their relevance, the author is hopeful that industry will come forward to implement these procedures on an existing FRA measuring instruments – thus opening a new dimension to FRA measurements
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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