Generatör ve transfarmatör bloğundan oluşan sistemin yüksek frekans davranışı
Başlık çevirisi mevcut değil.
- Tez No: 39300
- Danışmanlar: PROF.DR. M. KEMAL SARIOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol, Computer Engineering and Computer Science and Control
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1994
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 121
Özet
ÖZET Gerilim darbeleri ve açma-kapama işlemleri, elektrik makinalarmda yüksele frekanslı salımmlara yol açarlar. Bu tür geçici salınımlar, genellikle geometrik boyutlar dan hareketle hesaplanan R, L, C parametrelerinin oluş turduğu eşdeğer devreler yardımıyla incelenmektedir. Te2de geliştirilen yeni bir yöntem, sargıların uç empe- dans karakteristiğinden hareketle modellenmesine olanak vermiştir. Bu yöntem, sargı iç yapısının bilinmesine gerek göstermediğinden, özellikle, enerji iletim ve dağıtım sistemlerinde yer alan transformatörlerde ortaya çıkan geçici olayların incelenmesinde kolaylık sağlamaktadır. Tezde yapılan çalışmalar aşağıdaki gibi özetlenebilir : Tezin ikinci bölümünde, aradevreli frekans eviricileri incelenmiştir. Bu elemanlar döner alan makinalarma yol vermede, artık gelişen güç elektroniği yardımıyla da hayli yoğun bir şekilde kullanılmaktadır. Tezin konusu içinde eviriciler, senkron generatörlere ilk çalışma anında asenkron motor olarak yol verme şeklinde kullanılmaktadır. Tezin üçüncü bölümünde, yüksek frekanslı alan değişimlerinde demir çekirdeğin davranışı incelenmiştir. Hem teorik hemde deneysel yollardan yapılan incelemeler, nötr noktası topraklanmış bir sargıda ortaya çıkan geçici olyların demir çekirdek tarafından fazla etkilenmediğini ortaya koymuştur. Dördünccü bölümde, sargı iki uçlu bir eleman gibi düşünülerek uç empedans fonksiyonu tanımlanmış, bu fonksiyonun geçeçe hal davranışı açısından anlamı üzerinde durulmuştur. Beşinci bölümde, sargıya ilişkin uç empedans fonksiyonunu sağlayan kanonik devrelerin sentezi gösterilmiş, elde edilen Cauer ve Foster biçimindeki devrelerin durum denklemleri yazılmıştır. Altında bölümde ise pratik bir uygulama olması açısından özellikleri ek-1 ve ek-2 'de verilmiş deney transformatörü ve generator üzerinde bu geliştirilen yöntem uygulanmıştır.
Özet (Çeviri)
SUMMARY Voltage surges due to atmospheric discharges and switching operations cause high frequency transient oscillations of very short duration in electrical transmission and distribution systems. In the course of such transient phenomena, various points of the network transformer and generator windings are subjected to overvoltage stresses. An accurate calculation of these voltage stresses is of-prime importance for the design of power trans formes and high voltage generator. On the other hand, some recent transient phenomena causing failures in power systems have shown that the transient behavior must be taken into account to provide a suitable insulation coordination and protection for high voltage networks [29], [301. Since the beginning of the century, extensive works of theoretical and experimentel basis have been carried out to investigate the surge response of electric machines (transformers and generators). In the past, attempts were made to find analytical solutions for integro-differential equations written for distributed parameter winding models of the machines (about above). Unfortunately, even with many assumptions to simplify the solution of the problem, complete calculations were laborious and unsuitable for routine design. Wide-spread use of digital computers in recent years made it possible to solve the large number of system equations in the time domain. Thus, various models of the transformers and generators with lumped parameters were developed and the transient behavior of the these machines have been determined in terras of the state equations. Computer aided analysis is obviously the most convenient and powerful method for determining the transient phenomena which occur in power transmission and distribution systems. In general, such a methot consists of building a mathematical model for the entire system involving transmission lines, transformers and generators; then solving the state equations in the time domain. All possible switching and foult conditions can be simulated in this way, in order to predict the complete behavior of the system.Methods of modelling for transmission lines, transformers, synchronous machines and the others are extensively covered in the litterature. For transmission lines, lumped parameter models based on inductance, capacitance and resistance per unit length are available. The conventionel equivalent circuits developed for transformers and synchronous machmees consist of RLC ladder networks similar to those representing transmission lines; the main difference being the presence of a series capacitances and mutual inductances between sections. The network parameters are normally calculated from the geometric dimensions of windings. It is opvious that the determination of those parameters is not difficult at the design stage of a transformer, since all the constructional details and material properties are known. However, when the task of building a model of a complex electrical power system for high speed switching or impulse surge analysis arises, one must think of two important problems: a- Generally, no sufficient information is available about the internal structre, winding geometry and material properties of electric machines ( to trans formers and generators ) already manufactured and operating in the network. In such a case, conventional transformer and generator models become unsuitable since it is not possible to determine the parameters. b- Electric power supply systems consist of several transformers, voltage generator, switches and cutters interconnected by transmission lines. When transformers and generators are represented by equivalent circuits which consist of large number of tandem sections as it has been proposed in early works in literature, the number of the system dynamic equations to be solved, reaches easily several hundreds. Since the system matrix is generally plain for these equations, the solution in computer requires large memory and long computation time. In this thesis, a new method is proposed to build a mathematical model of power transformers and voltage generators by means of terminal impedance measurements. This method offers two advantages in the study of switching surges in power systems. First, all the parameters related to transformer and generators models are determined from the terminal measurements, and a detailed knowledge of the internal structure is not required. These measurements can be performed easily on viiany transformer or / and generator existing in electric power systems. Second, the canonic structure of the network permits the use of sparse matrix techniques and offers advantages in numerical integration of state equations. In the 2 nd. chapter, we mvesteged to using source by current frequency connvertor to first initialising to generators as a asynchronous motors. By the this ways syncronous machine works better from the clasic methods. But also note that rememmer this ways produced more harmonxcs and electrical noises from the others kniwn methods. In this way, recently more used power electronics circuit and its component like transistor, tristor, GTO and extra. In this section this subject are investeged. In the 3 rd. chapter, the effect of the iron core is examined both in theoretical and experimental ways. By the relations derived from the Maxwell equations, it is shown thaqt at high frequenciens, the magnetic flux is attenuated in the internal regions of the core, and condensed on the surface. Besides, experimental works also has shown that an iron core winding behaves frequency-dependent up to 10 kHz; however, for higher frequenciens, self and mutual inductances approach asymptotically to the values of the air core winding. Time domain measurements on a power transformer agreed with the above observations and have shown clearly that, for a winding with the neutral pointh earthed, the iron core has a negligible effect on the high speed transients either in the cases of the secondary winding open or short circuited. According to these observations, it has been assumed that the iron core can be ignored in the analysis of high speed transients in order to rebresent the transformer and generator windings by linear passive RLC networks. In the 4 th. chapter, the transformer and generator windings are considered as a two terminal component and the terminal impedance function is defined with the following relation: Vo(t) » Z io (t) (i) where, Vo is the terminal voltage and io is the terminal current. Linearity of the system implies that Z does not viiidepent neither of current nor voltage. The terminal (driving point) impedance funtion can be expressed in the s domain in terms of the coefficient matrices of the state equations by a rational function in the from: P(s) Z(s) = (ii) Q(s) In the case of a lossless winding for which all resistances and conductances of the equivalent circuit (fig. 4. 2) are zero, the poles and zeros are pure imaginary and they are located alternatively on the jw axis as shown in fig. 4. 4 for the values of angular frequencies corresponding to the poles, the impedance tends to infinity, whereas it goes to zero for the values corresponding to the zeros. Experiments have shown that, when ohmic resistance of the winding is present, the poles and zeros shift leftward in the complex plane, in such a way that imaginary parts remain almost unchanged (fig. 4. 5). Thus, in the general case, it may be assumed that the magnitude of winding terminal impedance takes maximum and minumum values for angular frequencies corresponding to the imaginary part of poles and zeros respectively. Synthesis of a passive LC network described by an impedance function is a solved problem and several algorithms were developed. In order to realise (ii) written in the from 2 2 2 2 2 2 k.s. (s+w2) (s+w4) (s+w2n) Z(s)= (iii) 2 2 2 2 2 2 (S+Wl) (S+W3) (S+W2n+1) for a lossless winding, either Cauer or Foster synthesis methods can be used. Once the LC network is realised, ohmic resistances are added to the sections. The resistance values and the scaling factor k are determined ixcharacteristic obtained by terminal measurements be minumum. As an application to the above mentioned procedure, the equivalent circuit af Foster type is developed for a laboratory size model transformer and generator. Optimal gradient algorithm is applied to calculate the resistor values and the scaling factors, and the parameters determined for this 'synthetic model' are fictitious values and they do not correspond to any physical section of the windings. However, the model have the same driving point impedance function as the windings. In the developing chapter, the constituents of a power supply network: such as transmission lines, power switches, lightning arresters, compensating capacitors and filters are considered as two or three terminal components and their state equations are given. Deals with the determination of the mathematical model of a power system comprising several transformers and generators, interconnected by transmission lines and the other circuit compenents. To establish the mathematical model for such a system, the graph should be constituted by using the terminal grabhs is next chosen according to the following rules: a. All voltage sources must be takren on branches and all current sources on chords. b. Components for which the terminal current is chosen as input function, should be on branches. Reciprocally, components for which the terminal voltage is the input function, should be on chords. The components on branches and chords are grouped to write the state equations of the whole system in the following form: d I xd I I Ad-BdQ2Gk(xkr) BdQlCk: | xd | | 0 Bd.Q3 | Ve | = T T + T (İV) dt LxkJ L-BkQlCd Akr-BkQ2Rd(xkr) J_xkJ L-Bk.Q3 0_LîjJ XIwhere, the indice d denotes the branches and the indice k denotes the chords. A, B, C are the coefficient matrices of the corresponding state equations. Ql, Q2, Q3 are the cutset matrices corresponding respectively to the components which comprise reactive elements; resistances and conductances; cur rend and voltage sources. As the system may include non-linear resistors (lightning arresters) Gk and Rd are taken in the general nonlinear form. To illustrate the proposed method of modelling power systems and determination of switching surges, two examples are given. The first one corresponds to the model system built in the laboratorye with an experemental transformer and a line model. The asystem was driven by a step function generator and the terminal voltage of the transformer was opserved by means of a storage oscilloscope. On the other hand, the state equations were solved in digital computer. A good agreement was obtained between measured and calculated values. The second application is an example of the supply network of a steel manufacturing plant in which heavy arc furnaces take place. The mathematical model of this system is obtained and simulation of switching operations is shown. jcu
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