Güç transformatörlerinin optimum tasarımına yönelik çalışmaların incelenmesi
Başlık çevirisi mevcut değil.
- Tez No: 75302
- Danışmanlar: PROF. DR. NURDAN GÜZELBEYOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1998
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektrik Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 93
Özet
ÖZET Bu çalışmada, güç transformatörlerinin optimum tasarımına yönelik çalışmalar incelenmektedir. Tüm bu çalışmalar, transformatörlerin daha küçük hacim ve maliyetle ve daha yüksek verimle üretilebilmelerine yöneliktir. öncelikle transformatör çekirdeklerinde oluşan kayıpların azaltılması için yapılan çalışmalardan bahsedilmekte ve amorphous metalli çekirdeklerin toplam maliyete etkileri incelenmektedir. Ardından, bir transformatörün optimum tasarımı için geliştirilen bir yöntemin adımları verilmektedir. Yöntemde, oluşturulan bir optimizasyon probleminin çözümüyle elde edilen eğrilerin kullanılmasıyla optimum tasarıma ulaşılmaktadır. Son olarak, transformatörlerin optimum tasarımında kullanılan bilgisayar programlarından bazıları incelenmekte ve bu yöntemlerden birisi incelenerek optimum çözüme hangi aşamalarla ulaşıldığı açıklanmaktadır.
Özet (Çeviri)
SEARCH OF WORKS ABOUT OPTIMUM DESIGN OF POWER TRANSFORMERS SUMMARY Influence of Transformer Core Design on Power Losses The magnetic properties of a transformer core are influenced by three basic factors : grade of material, processing of steel sheet during core manufacture and core design. The results of an investigation of the influence of the core design on the core losses are given in this work. In order to present the results in a more convenient way, the losses are given in per-unit values by means of the so-called 'building factor1. The building factor kb is the ratio between the specific losses of the core and of the used material. The aim of this part's is to investigate some of the phenomena described in previous works using an extensive experimental approach, and also to investigate the influence of some new parameters and new core forms on the building factor and in particular : - to compare the building factors of single phase and three phase cores ; - to compare the building factors of cores having different corner and T-joint designs ; - to determine the influence of overlap length, of the number of laminations per. stagger layer, and of the yoke cross-section form on the building factor. Procedure In this investigations, each experiment is repeated on five samples, and two measurements are performed on each of the samples. In each experiment all models are made from steel sheets of the same quality. This is achieved by cutting the laminations for all the models in each experiment from the same steel coil. In order to reduce the yoke leakage flux occuring at higher flux densities ( 1.7 T and higher ), which is significant on small models and can considerably affect the accuracy of investigation, additional excitation coils are fitted on the yoke. On the single phase models, all four excitation coils are series connected, while on the three phase models the additional coils are parallel connected to the main excitation coil of the corresponding limb. The material used to build the models is 0.3 mm thick grain-oriented silicon-iron with typical losses of 1.33 VWkg at 1.7 T and 50 Hz ( grade M5 ). After cutting, ail laminations are stress-relief annealed. The core losses are measured at flux densities of 1.5, 1.6, 1.7 and 1.8 T in a conventional way using a precision electrodynamic wattmeter. A precision digital XIvoltmeter, which indicated the average value of voltage, is also connected to the secondary coil. The resuts given in this work are an average of measurements on all five samples. Building Factor of a 100 kVA 3 Phase Distribution Transformer Core The no load iron loss in laminated transformer cores is always greater than the nominal loss of the electrical steel laminations, by a factor known as the building factor. It is as important to improve the building factor of the transformer cores as it is to attempt to improve the basic properties of the steel. Because, it is meaningless to build a transformer with a poor building factor using good quality steel. In this work an attempt made to break down the measured loss of a 100 kVA 3 phase distribution transformer into several components to obtain a good indication of the most important parameters which affect the building factor. Typically, the building factor is about 1.5 for a 3-phase 3-limb core and it becomes higher as the core geometry more complex. The losses additional to the intrinsic loss may be attributed to ; possible variation above the intrinsic loss in the bulk of the core material, handling losses due to punching, slitting, cropping and core assembly ( these losses should be removed by annealing processes ), design of core joints, deviation of flux from the rolling directions in the corners, the rotational flux in the T-sections ( this loss takes the angular direction of the flux flow into account ), circulating harmonic flux in the limbs, stress in the core and stacking method. The object of the investigation has been to determine the effect of these various factors on the building factor for a 100 kVA 3-phase distribution transformer over a range of core flux densities. Experimental Apparatus The core was built with grain-oriented electrical steel sheets having a nominal power loss of 1.02 W/kg at peak flux density of 1.5 T, and a typical induction of 1.84 T at 1000 A/m. The material had a density of 7560 kg/m3 and was 0.35 mm thick. The popular 45-90° joint configuration was used at T-sections and 45° mitred overlap joint was employed at the outside corners. The overall dimension of the core was 50 cm x 46.5 cm x 8.4 cm and its limbs and yokes were made from packets of five different widths. Primary windings were connected in a star configuration to a 50 Hz three phase 415 V supply via variacs and the core was magnetized sinusoidally to obtain three different flux densities of 0.9, 1.3 and 1.7 T. A single turn search coil was wound over each limb to enable to monitor the core flux density. In order to determine the mechanical stress levels in xnthe laminations, an array of strain gauges was placed on an individual lamination in the center of the core. Results The experiments showed that forty two percent of the loss occured in the limbs and yokes, the central limb contributing most of it. Although the loss in the T-sections was small, a properly designed T-joint would lower the magnitude of overall third harmonic flux and also the loss due to the stacking method. The losses due to the third harmonic circulating flux, the stress level and the stacking method were estimated to be %10, %17 and %18 respectively. The unaccounted loss of %8 could be partly attributed to the higher harmonics and some errors in estimation. This method of breaking the loss down into components due to magnetization conditions within the core and the presence of stress works quite well. There is probably as much scope for improvement in building techniques and usage of the material as in improvements of the basic material properties. Amorphous Alloys for Distribution Transformers : Design Considerations and Economic Impact The potential benefits of using amorphous ferromagnetic alloys as a replacement for grain-oriented iron-silicon steels in distribution transformers are generally assessed on the basis of their impact on the no-load core losses. However, the cost of such materials, their low stacking factor, low saturation value, brittleness, handling problems, etc. are all considered serious disadvantages. This work presents an economic justification for the use of such alloys and discusses the impact of the transformer design on the cost evaluation. Overall Cost Analysis Amorphous alloys promise a significant reduction in no-load core losses, the overall cost of the transformer must next be considered before a definite decision can be made about the viability of amorphous alloy cores. This work assesses various designs in the context of an analysis of the overall cost of the transformer, i.e. initial purchase cost and the cost of the copper and iron losses over the expected life of the transformer ( about 30 years ). The use of new materials with unique physical and mechanical properties is also considered. Copper Loss Evaluation Evaluation of the copper losses calls for knowledge of the transformer load which, for any given distribution network, varies daily, weekly and seasonally. The typical ratio of the nominal copper loss to the average copper losses is between 1.5 and 12, depending on the load factor. XlllIron Loss Evaluation Contrary to the copper losses, which fluctuate with the loading, the no-load losses are continuous throughout the life of the transformer. Materials Selected Three ferromagnetic alloys were selected for the comparison. The first is an amorphous alloy, Allied Metglass 2605S2. The accepted loss values used for analysis are not the best avaible but represent the present state of the art for this alloy used in a transformer configuration ; the cost of this material was assumed to be 3.30 $/kg. The other two alloys evaluated were grade M4 and grade M6, corresponding to a common material used in distribution transformers. Design Optimization of Small Low-Frequency Power Transformers A number of computer-aided design procedures for power transformers have appeared in the literature. While in some design techniques the word optimum has been used to describe the resulting design, each is in effect based on a heuristic technique often involving a modified process of direct enumeration. The principal design objectives in these proposed techniques are usually minimum physical size or mass, maximum efficiency,and cost. Unfortunately, a number of assumptions are often made which are not only contradictory, but tend to artificially constrain the resulting design away from the optimum the technique was intended to find. For example, in a technique is suggested for choosing an optimum core geometry which is intended to minimize transformer weight, losses, volume or cost. Unfortunately, this is done while assuming that flux density, current density, and other electrical or magnetic parameters are fixed. Thus, while some interesting curves are presented which are an aid in comparing different core types, they do not suggest to the designer how to complete his design ( i.e., how to choose the best values for the electrical and magnetic parameters). In addition, the designer may be misled into thinking that by choosing the core geometry suggested in procedure, he will automatically achieve an optimum design. In reality this choice may result in a transformer which does not meet power, temperature rise, or regulation requirements. This unhappy situation occurs because, the ultimate design is critically dependent on the choice of electrical and magnetic parameters. As a result of these problems, some transformer designers have implied that a transformer design cannot be unique for a given set of ratings and specifications. The lack of a unique design, however, is not an inherent property of the transformer design problem. It can be shown that uniqueness or nonuniqueness is solely xivdependent on how the design procedure is organized. For example, if the design procedure is based on the solution to a well posed mathematical optimization problem, then the uniqueness of the resulting design can be guaranteed relative to the design objectives. In this work a mathematical optimization problem is developed whose solution is a set of parameter values characterizing the maximum VA output design for an assumed core structure. The questions of existence and uniqueness of the solution this problem are briefly discussed, and a set of closed form expressions are presented for the optimum design parameters. It is recognized that in any practical transformers design such parameters as current density and flux density must occasionally be constrained away from their optimum values. A constraint solution to the original optimization problem is then presented in the form of curves showing maximum VA capability as a function of operating frequency for each of a set of example core structures. These curves are used to develop an improved design technique. In addition to designing specific transformers, the technique can also simplify the comparison of units with different properties. For example, comparisors are given in this work of transformers with class A ( 105 °C maximum operating temperature ) and class B (130 °C maximum operating temperature ) insulation, and those with 0.15 mm and 0.35 mm laminations. Although El-laminated transformers are discussed in this work, the techniques presented here can be readily extended to a variety of other core types including ferrites. In addition, secondary design objectives such as minimizing total losses and transformer regulation can also be included in such a computer aided design program. Computer Aided Instruction of Power Transformer Design The design of the electric and magnetic portions of a power transformer is successfully completed in this work. Designers are provided with a computer analysis program to assist them in performing routine calculations and most importantly, otimize their designs. Each designer optimizes his/her design by observing the effect of the parameter variation on the transformer performance. The following assumptions for the design proceedure are made: - The flux density is uniform throughout the core, - The low-voltage coil has been wound closest to the core, - The high voltage coil has been wound over the top of the low-voltage coil, - The number of turns are rounded to the nearest integer, - The cost of non-metals is ignored, - The temperature is uniform. The transformer operates at 60 degrees centigrate. xv
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