etd@IISc Collection:
http://hdl.handle.net/2005/20
Fri, 09 Feb 2018 08:10:54 GMT2018-02-09T08:10:54ZVoltage Stability Analysis of Unbalanced Power Systems
http://hdl.handle.net/2005/3065
Title: Voltage Stability Analysis of Unbalanced Power Systems
Authors: Santosh Kumar, A
Abstract: The modern day power system is witnessing a tremendous change. There has been a rapid rise in the distributed generation, along with this the deregulation has resulted in a more complex system. The power demand is on a rise, the generation and trans-mission infrastructure hasn't yet adapted to this growing demand. The economic and operational constraints have forced the system to be operated close to its design limits, making the system vulnerable to disturbances and possible grid failure. This makes the study of voltage stability of the system important more than ever.
Generally, voltage stability studies are carried on a single phase equivalent system assuming that the system is perfectly balanced. However, the three phase power system is not always in balanced state. There are a number of untransposed lines, single phase and double phase lines. This thesis deals with three phase voltage stability analysis, in particular the voltage stability index known as L-Index. The equivalent single phase analysis for voltage stability fails to work in case of any unbalance in the system or in presence of asymmetrical contingency. Moreover, as the system operators are giving importance to synchrophasor measurements, PMUs are being installed throughout the system. Hence, the three phase voltages can be obtained, making three phase analysis easier.
To study the effect of unbalanced system on voltage stability a three phase L-Index based on traditional L-Index has been proposed. The proposed index takes into consideration the unbalance resulting due to untransposed transmission lines and unbalanced
loads in the system. This index can handle any unbalance in the system and is much more realistic. To obtain bus voltages during unbalanced operation of the system a three phase decoupled Newton Raphson load ow was used.
Reactive power distribution in a system can be altered using generators voltage set-ting, transformers OLTC settings and SVC settings. All these settings are usually in balanced mode i.e. all the phases have the same setting. Based on this reactive power optimization using LP technique on an equivalent single phase system is proposed. This method takes into account generator voltage settings, OLTC settings of transformers and SVC settings. The optimal settings so obtained are applied to corresponding three phase system. The effectiveness of the optimal settings during unbalanced scenario is studied. This method ensures better voltage pro les and decrease in power loss.
Case studies of the proposed methods are carried on 12 bus and 24 bus EHV systems of southern Indian grid and a modified IEEE 30 bus system. Both balanced and unbalanced systems are studied and the results are compared.Tue, 06 Feb 2018 18:30:00 GMThttp://hdl.handle.net/2005/30652018-02-06T18:30:00ZAdaptive Sampling Pattern Design Methods for MR Imaging
http://hdl.handle.net/2005/3066
Title: Adaptive Sampling Pattern Design Methods for MR Imaging
Authors: Chennakeshava, K
Abstract: MRI is a very useful imaging modality in medical imaging for both diagnostic as well as functional studies. It provides excellent soft tissue contrast in several diagnostic studies. It is widely used to study the functional aspects of brain and to study the diffusion of water molecules across tissues. Image acquisition in MR is slow due to longer data acquisition time, gradient ramp-up and stabilization delays. Repetitive scans are also needed to overcome any artefacts due to patient motion, field inhomogeneity and to improve signal to noise ratio (SNR). Scanning becomes di cult in case of claustrophobic patients, and in younger/older patients who are unable to cooperate and prone to uncontrollable motions inside the scanner. New MR procedures, advanced research in neuro and functional imaging are demanding better resolutions and scan speeds which implies there is need to acquire more data in a shorter time frame. The hardware approach to faster k-space scanning methods involves efficient pulse sequence and gradient waveform design methods. Such methods have reached a physical and physiological limit. Alternately, methods have been proposed to reduce the scan time by under sampling the k-space data. Since the advent of Compressive Sensing (CS), there has been a tremendous interest in developing under sampling matrices for MRI. Mathematical assumptions on the probability distribution function (pdf) of k-space have led researchers to come up with efficient under sampling matrices for sampling MR k-space data. The recent approaches adaptively sample the k-space, based on the k-space of reference image as the probability distribution instead of a mathematical distribution, to come with an efficient under sampling scheme. In general, the methods use a deterministic central circular/square region and probabilistic sampling of the rest of the k-space. In these methods, the sampling distribution may not follow the selected pdf and
viii Adaptive Sampling Pattern Design Methods for MR Images the selection of deterministic and probabilistic sampling distribution parameters are heuristic in nature.
Two novel adaptive Variable Density Sampling (VDS) methods are proposed to address the heuristic nature of the sampling k-space such that the selected pdf matches the k-space energy distribution of a given fully sampled reference k-space or the MR image. The proposed methods use a novel approach of binning the pdf derived from the fully sampled k-space energy distribution of a reference image. The normalized k-space magnitude spectrum of the reference image is taken as a 2D probability distribution function which is divided in to number of exponentially weighted magnitude bins obtained from the corresponding histogram of the k-space magnitude spectrum.
In the first method, the normalized k-space histogram is binned exponentially, and the resulting exponentially binned 2D pdf is used with a suitable control parameter to obtain a sampling pattern of desired under sampling ratio. The resulting sampling pattern is an adaptive VDS pattern mimicking the energy distribution of the original k-space.
In the second method, the binning of the magnitude spectrum of k-space is followed by ranking of the bins by its spectral energy content. A cost function is de ned to evaluate the k-space energy being captured by the bin. The samples are selected from the energy rank ordered bins using a Knapsack constraint. The energy ranking and the Knapsack criterion result in the selection of sampling points from the highly relevant bins and gives a very robust sampling grid with well defined sparsity level.
Finally, the feasibility of developing a single adaptive VDS sampling pattern for a organ specific or multi-slice MR imaging, using the concept of binning of magnitude spectrum of the k-space, is investigated. Based on the premise that k-space of different organs have a different energy distribution structure to one another, the MR images of organs can be classified based on their spectral content and develop a single adaptive VDS sampling pattern for imaging an organ or multiple slices of the same. The classification is done using the k-space bin histogram as feature vectors and k-means clustering. Based on the nearest distance to the centroid of the organ cluster, a template image is selected to generate the sampling grid for the organ under consideration.
Using the state of the art MR reconstruction algorithms, the performance of the proposed novel adaptive Variable Density Sampling (VDS) methods using image quality measures is evaluated and compared with other VDS methods. The reconstructions show significant improvement in image quality parameters quantitatively and visual reduction in artefacts at 20% 15%, 10% and 5% under samplingTue, 06 Feb 2018 18:30:00 GMThttp://hdl.handle.net/2005/30662018-02-06T18:30:00ZStable Galerkin Finite Element Formulation for the Simulation of Electromagnetic Flowmeter
http://hdl.handle.net/2005/3068
Title: Stable Galerkin Finite Element Formulation for the Simulation of Electromagnetic Flowmeter
Authors: Sethupathy, S
Abstract: Electromagnetic 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.Tue, 06 Feb 2018 18:30:00 GMThttp://hdl.handle.net/2005/30682018-02-06T18:30:00ZThermal and Electrical Degradation of Resin Impregnated Paper Insulation for High Voltage Transformer Bushings
http://hdl.handle.net/2005/3044
Title: Thermal and Electrical Degradation of Resin Impregnated Paper Insulation for High Voltage Transformer Bushings
Authors: Jyothi, N S
Abstract: The overall reliability of a power transformer depends to a great extent on the sound operation of the bushings thereof. In view of its overwhelming advantages, resin impregnated paper (RIP) is acquiring prominence over conventional oil impregnated paper (OIP) in transformer bushings. The main advantages of RIP bushings are low dielectric loss and capability of positioning them at any desired angle over the transformer. The RIP structure, being an all-solid system, is completely free from oil phase.
The temperature rise in RIP bushings under normal operating conditions is seen to be a diﬃcult parameter to control in view of the limited options for eﬀective cooling. The degradation of dry-type insulation such as RIP is often due to thermal and electrical stresses. The long time performance thereof, depends strongly, on the maximum operating temperature. In order to be able to predict the regional temperature, it is necessary to consider the thermal and electrical parameters of insulation in question; and to identify and solve the governing equations under the relevant boundary conditions.
Electrical failure of insulation is known to be an extremal random process wherein nominally identical specimens of equipment insulation, at constant stress fails at inordinately diﬀerent times. In order to be able to estimate the life of power equipment like transformer bushing, it is necessary to run long duration ageing experiments under accelerated stresses, to acquire and analyze insulation speciﬁc failure data. The present work is an attempt to provide reliability and life estimation of High Voltage RIP bushing insulation. The literature survey carried out in this view indicate that investigation on thermal and electric ﬁeld distribution and the models for failure under combined stress and analysis of the data so as to be able to estimate the possible life of RIP bushing is scanty. Having these aspects in focus, the scope of the present work is deﬁned as:
(i) Mapping of the temperature and electric ﬁeld distribution in the body of 400kV RIP bushing
(ii) Deduction of parameters of the probabilistic models for the failure under electrical and thermal ageing
(iii) Estimation of life based on diagnostic testing using PD
With this in view, the temperature distribution in the body of a 400kV RIP bushing is studied considering the heat generation both in central conductor and that in the insulation. Presence of multiple materials with non-conﬁrming interfaces makes analytical solution rather diﬃcult and hence numerical approach is adopted. In the present work, vertex-centered Finite Volume Method (FVM) is employed for both thermal and electrical analysis. The electric stress distribution is accurately evaluated considering both the non-zero conductivity of the RIP material and the presence of capacitive grading foils. These analysis has clearly shown that Stress grading foils uniforms the stress across the major portion of the bushing insulation
Enhancement of the electric conductivity by the temperature is not found to be aﬀective in changing the electric ﬁeld distribution
The temperature distribution is shown to have a maxima near the ﬂange due to the inﬂuence of top oil temperature of the transformer
Heat generated in the dielectric due to the prevailing electric stress is shown to be insigniﬁcant. This ruled out the possibility of thermal runaway and hence the dielectric temperature is within the safe working limits for the bushing considered.
The deduction of physical models governing insulation failure depends on the nature of stress. In this work, the insulation failure at constant accelerated stress has been considered and the estimation of life is computed based on inverse power law coupled with Arrhenius law. A high degree of scatter is generic to the experimental data forming the ingredients to develop the models. In view of this, the concept of a random process is invoked. Probabilistic models for the failure of RIP bushing under synergy are adopted and an attempt is made to estimate the life. The well known Weibull distribution and probability plotting of life data is used in this endeavor. The maximum likelihood estimation is used to determine the scale and shape parameters of the Weibull distribution.
In the diagnosis of the extent of degradation of insulation due to PD, under long duration electric stress, a non-conventional voltage application method called the classical stepped stress method is adopted. In this technique, the voltage is applied in pre-determined steps over predetermined duration of time. The magnitude of voltage steps is carefully computed based on Miners law and the end-of-life is computed using inverse power law.
In summary, this thesis work has contributed to the thermal and electrical degradation of resin impregnated paper insulation for high voltage transformer bushing. The thermal and electrical ﬁeld distributions computed in the body of bushing clearly shown that these stresses are well within the limit, thereby ruling out the possibility of a thermal runaway. Comparing the estimates of the most probable life of RIP, based on several methods appears to show that any of the method can be adopted. However, as matter of caution and safety, the lowest among them can be taken as a reasonable estimate.Mon, 29 Jan 2018 18:30:00 GMThttp://hdl.handle.net/2005/30442018-01-29T18:30:00Z