Büyük boyutlu şebekelerin diakoptics yöntemi ile kısa devre analizi

Başlık çevirisi mevcut değil.

Tez No: 46531
Yazar: ÖMER GÜL
Danışmanlar: DOÇ.DR. ADNAN KAYPMAZ
Tez Türü: Yüksek Lisans
Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
Anahtar Kelimeler: Belirtilmemiş.
Yıl: 1995
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Fen Bilimleri Enstitüsü
Ana Bilim Dalı: Belirtilmemiş.
Bilim Dalı: Belirtilmemiş.
Sayfa Sayısı: 87

Özet

ÖZET Bu çalışmada, nitelikleri ve boyutları giderek büyüyen şebekelerin analizinde, çeşitli basitleştirici yöntem arayışları ve bunlardan biri olan diakoptics yöntem kısaca analtılmıştır. Şebekenin modellenmesi için yapılan çalışmalar ayrıntılı olarak ayrıca bir bölüm halinde incelenmektedir. Sisteme ait matematiksel model oluşturulurken, sistem alt-şebekelere ayrılmakta ve herbir alt-şebeke modeli için bu gün modern devre teorisinde fazlaca bilinen çok-uçlu eleman kavramı kullanılmaktadır. Her faz devresinin aynı grafı içermesi ve birbiriden yalıtılmış oluşu yaklaşımı ile transformatör ve hat modelleri verilmektedir. Simetrili bileşen transformatör modeli ise, elde edilen modelden simetrili bileşen genişletilmiş dönüşüm matrisi yardımı ile elde edilmektedir. Sadece hatlardan oluşmuş bir şebekenin uç denklemleri, ele alınan şebekenin devre grafının her faz devresinin aynı grafı içermesi ve birbiriden yalıtılmış oluşu yaklaşımını esas alan faz bileşenleri ve simetrili bileşenler yöntemleriyle analizde aynı olmasının bir sonucu olarak iki farklı yolla elde edilmiştir. Bu çalışmada kısa devre analizde her bir hata türü için türetilmiş denklemler yerine, kısa devrenin genel denklemleri kullanılmakta olup hata türünün verilmesinde bir sınırlamaya gidilmemiştir. Hata türünün hata empedans veya admitans matrisi ile verilmesi şeklinde bir yol tutulmuştur. önerilen yöntemler kullanılarak örnek bir şebekenin bara admitans matrisi oluşturan ve bunu kullanarak kısa devre analizi yapan iki ayrı program G dilinde yazılmıştır. Elde edilen sonuçların, başka kaynakta elde edilen ile aynı olduğu tespit edilmiştir. ix

Özet (Çeviri)

SUMMARY A DİAKOPTİCAL TECHNIQUE FOR SHORT CİRCUİT STUDIES OF LARGE SİZE POWER SYSTEM NETWORKS In recent years, the need of the electric energy is rapidly increasing because of the technological developments. However, the generating of electrical energy from the primary energy sources is not increasing at the same rate, therefore present energy sources must be used more effi- cientiy than before and optimum operating efficiently must be maintained during the operating of electrical power systems. In order to maintain maximum operating efficiency, several different power systems are inter connected, moreover some countries share the same large scale power systems. Thus the structure, the quality and the dimension of the electrical power systems are to change and become more complex. The analysis of these kind of network can not be managed without using the computer. In the analysis of electrical power systems having large number of buses, it is necessary to solve a group of nonlinear algebraic equation of the following form. Ax=b where A is a square matrix having complex elements and whose order is equal to the large number of buses in the network. It is necessary to use of same type of automatic calculators or computers to get the solution of this system. This led to the design of special purpose analog computer, called a.c. network analyzer (about the year 1929). Digital computer for the analysis gained importance during the beginning of 1950 and first the planning studies on the digital computer was completed by the year of 1956. Today, most of the studies for electrical power systems are carried out on digital computers. This change from the network analyzer to digital computer has resulted in greater flexibility, economy, accuracy and quicker operation. On the other hand, while the electrical power systems, having large number of buses is analyzed, the need of computation time and storage requirement is excessive. For this reason, in order to provide some simpli fication in computer computations, new approaches for the formulation oftearing is performed at the nodes of the network, the order of coefficient matrix can be kept to a minimum. Therefore this method is useful for analyzing electrical power systems having a large number of buses. It is in this thesis and it is shown that coefficient matrix is sparse and has a block-diagonal band form. The normal operating mode of a power system is balanced three-phase ac. A number of undesirable but unavoidable incidents can temporarily disrupt this condition. If the insulation of the system fails at any point or rf a conducting object comes in contact with a bare power conductor, a short circuit, or fault, is said to occur, the causes of faults are many; they include lightning, wind damage, trees falling across lines, vehicles colliding with towers or poles, birds shorting lines, aircraft colliding with lines, vandalism, small animals entering switch gear, and line breaks due to excessive ice loading, power system faults may be categorized as one of four types; in order of frequency of occurrence, they are: single line to ground, line to line, double line to ground, and balanced three phase. The first three types constitute severe unbalanced operating condition. It is important to determine the values of system voltage and currents during faulted conditions, so that protective devices may be set to detect and minimize the harmful effects of such contingencies. Therefor, it necessary to analyze the power system operating in unbalanced modes. The time constants of the associated transients are such that sinusoidal steady-state methods may be used. The method of symmetrical compo nents is admirably suited to unbalanced system analysis. Short circuit calculations provide currents and voltages on a power system during fault conditions. This information is required to design an adequate protective relaying system and to determine interrupting requirements for circuit breakers at each switching location. Relaying systems must recognize the existence of a fault and initiate circuit breaker operation to disconnected faulted facilities. This action is required to assure minimum disruption of electrical service and to limit damage in the faulted equipment. The currents and voltages resulting from various types of faults occurring at many locations throughout the power system must be calculated to provide sufficient data to develop an effective relaying and switching system. To obtain the required information a special purpose analog computer, called a network analyzer, was used extensively for short circuit studies before digital techniques were available. The bus frame of reference in admittance form was employed in the first application of digital computers to short circuit studies. This method, which was patterned after similar techniques employed for load flow calculation, used an iterative technique. This required a complete iterative solution for each fault type and location. The procedure was time-consuming, particularly if, as was usually the case, the currents and voltages were required for a large number of fault locations. Consequently, this method was not adopted generally. xithe electrical power systems have recently being considered and still some Intensive works continues. After completing the literature survey associated with large scale systems studies, it is apparent that matrix A is usually diagonally dominant and has a sparse form. In some studies, this matrix is triangulated and non-zero elements are added in the upper triangle so that the solution of Ax=b becomes easier. In other group of studies large-scale power systems are analyzed by using Tearing and Reconstruction Technique(Diakoptics) and [A] becomes a sparse and block-diagonal band matrix form. Thus, computation time and storage requirements are reduced. In reference studies is directed mainly on the use of multi-terminal competent as the fundamental components in the analysis of large-scale systems, it became possible to investigate, in detail various problems of power systems in this approach. This study presents a diakoptical technique for deriving the impedance matrixes required for short circuit of large size power system networks by tearing into smaller subsystems by removing some elements from the network or splitting some nodes in the network. The bus admittance matrix is formed for the sequence networks of each of each subsystem and then modified later by means of diakoptics The essence of Diakoptics is to solve a network having large number of elements by firs tearing it into subnetworks each of which considered as a multi-terminal component, then to obtain the solution (or modeling) of each network. The solution of the original network is then constructed by the aid of the model, for each subnetworks as well as the interconnected pattern of these subnetwork which form the original network. The purpose of the diakoptics analysis are fallow: - Reducing the number of network equation to a minimum - Obtaining sparse network equation. On the other hand, the works on diakoptics can also be devided in two groups according to its actual realization: - Tearing is performed by removing some elements from network. - tearing is performed by splitting some nodes in the network. The diakoptics or picewise analysis as introduced by Kron, if carried out by removing elements from the network, the resulting network equations are then in the hybrid form and the coefficient matrix of these equations is sparse. However, the order of coefficient matrix increases by the number of removed elements compared to those obtained by the regular method, if the current variables of the removed elements are eliminated from these equation, then the spares pror of the coefficient matrix disappears. If the xiiThe development of techniques for applying a digital computer to form the bus impedance matrix made it feasible to use Thevenin" s theorem for short circuit calculation. This approach provide an efficient means of determining short circuit currents and voltages because these values can be obtained with few arithmetic operation involving only related portion of the bus impedance matrix. We shall use the zero, positive, and negative-equivalent circuits for the power system. Certain simplifications are possible that will not substantially affect the accuracy of the results. The simplified three-phase is the following: - Representing each machine by a constant voltage behind the machine reactance, transient or sub transient. - Neglecting shunt connections, e.g., loads, line charging, etc. - Setting all transformers at nominal taps. - Shunt elements in the transformer model that account for magnetizing current and core loss will be neglected. - All prefault bus voltages have one per unit value and prefault currents are zeros. Positive and negative sequence network are identical. The use of the bus impedance matrix provide a convenient means of calculating short circuit currents and voltages when the ground is selected as refe- rence. One of the distinct advantages is that, once the bus impedance matrix is formed, the elements of this matrix can be used directly to calculate the currents and voltage associated with various types of faults and fault location. This study presents the application of diacoptics for short circuit analize. The key step in the calculation of short circuits is the computation of the sequence networks thevenin equivalents from the point of the fault. These equivalents can be obtained from either a Z (impedance) bus formulation or a Y (admittance) bus formulation, propesed method is based on factorized bus admittance matrices and full exploitation of sparsity. this approce has been recommended over other approach of using explicit bus admittance matrices for use with recent methods for fault analysis as it offers great advantages concerning computational and storage requirements. Mi»The overall solution is performed partly In sequence coordinate and partly in phase coordinates. The most important outcome is the possibility of using parallel computation with the propesed method. XIV

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