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Simetrik olmayan 3-fazlı dengesiz yüklü enerji sistemlerinde yük akışının yeni bir yaklaşımla analizi

A Different approach to three phase element matrices in load flow studying

  1. Tez No: 19244
  2. Yazar: HAKAN LEVENT YÜCEL
  3. Danışmanlar: DOÇ.DR. ADNAN KAYPMAZ
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1991
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 64

Özet

ÖZET Bu çalışmada, üç fazlı elektrik şebekelerinin mümkün olan bütün dengesizlik koşullarında, yani hem şebekelerdeki yapısal simetrisizlikleri (örneğin, çaprazl anmamış çok yüksek gerilim hatlarını içeren şebeke) hem de şebeke yükündeki dengesiz durumları (örneğin, tek fazlı yüklenme, tek kutuplu, tek kutuplu kısa devre anahtarlama) içeren genel bir şebeke modeli verilmiş ve bu model üzerinde üç fazlı yük akışı analizi Newton-Raphson metodu kullanılarak yapılmıştır. Sisteme ait matematiksel model oluşturulurken, sistem alt şebekelere ayrılmış ve herbir alt şebeke modeli için bugün modern devre teorisinde çok iyi bilinen bir kavram olan çok-uçlu eleman kavramı kullanılmıştır. Sonuçta tüm sistem için parçalama ve yeniden birleştirme yöntemi ile elde edilen matematiksel modelde, herbir fazın kendi elemanları ve diğer faz elemanları ile olan elektriksel ve magnetik bağları açık ve net olarak ifade edilebilmiştir. Burada, herbir fazın, diğer fazlarla eş grafa sahip olduğu, fazlar arası kuplajların da gene aynı grafa sahip bir kuplaj devresi ile ifade edilebildiği gösterilmiştir. Sonuçta üç fazlı sistem, A, B,C fazları ve bunlar arasındaki kuplajları temsil eden A- B, A-C, B-C, ve karşı kuplaj devrelerinin ayrı ayrı hesaplanabileceği bir yapıda modellenebilmiştir. Sonuçta önerilen model kullanılarak örnek bir şebeke üzerinde Newton-Raphson Yöntemi ile C programlama dilinde yük akış analizi yapılmış ve bu programın hem üç fazlı hem de bir fazlı yük akışlarına kolayca uygulanabileceği gösterilmiştir. iv

Özet (Çeviri)

SUMMARY A Different Approach to Three Phase Element Matrices in Load Flow Studying : An electric power system consists of three major components. These are the generating stations, the transmission lines and the distribution systems. Linking is made between the generating stations and the distribution systems by transmission lines. Also transmission lines lead to other power systems over interconnections. A distribution system connects all the individual loads in a given place to the transmission lines. In this dissertation, 3-phase unsymmetrical load flow analysis is made through a different point of view. Compound matrix prototype is changed. An electric power system is considered to be seperated into its phases and these three phases are thought to be isolated with each other constituting subsystems. Reasons for interconnection are : a) Large capacity stations are in operation to lower the initial cost per kVA. Therefore regardless of geographical position, it is more economical to use these efficient stations to full capacity all day and transmit energy to far distances than to use less efficient, more local stations, so that this faces us the interconnected large capacity stations feed into the general system (the main base load) not to a particular load. b) Jn order to supply sudden increases in load a certain amount of generating capacity is required. This consists of generators running at normal speed ready to supply power. If the machines are stationary, time is required to run. It is more economical to have certain stations only serving this condition than to have each station carrying its own individual reserve. c) The electricity supplies over the entire country are synchronized and a common frequency maintained. d) In an interconnected network continuity of supply is maintained.Load Flow Studies : With the help of a load study we can determine the voltage, current, power and power factor or reactive power at various points in an electric network under normal operation. The satisfactorily operation of the system depends on knowing the effects of interconnections with other power systems, of new loads, new generating stations, and new transmission lines before they are installed. Associated with each bus there are four quantities. The real and reactive power, the voltage magnitude and the phase angle. Three types of buses are defined in a load flow calculation and two of the four quantities are specified for each bus. Since the transmission losses are unknown, it is necessary to select one bus to provide the additional real and reactive power to supply the transmission losses. This bus is called slack bus. At this bus the voltage magnitude and phase angle are specified. The second bus is named voltage controlled bus, the third one is a load bus. The real power and voltage magnitude are specified at the second bus. The real and reactive powers are specified at the third one. There are two primary considerations to develop an effective engineering computer program. The formulation of a mathematical description of a problem and the application of a numerical method for a solution. The relationships of these two factors must also considered. in analyzing the problem. Solutions of load flow studies on complex systems can be made with the help of digital computers The majority of load flow programs for large power system studies apply methods using the bus admittance matrix. This procedure remains the most economical for the computers to save time and memory. During the solution of load flow studies, the algebraic equations taking effect are in nonlinear type. An iterative technique must be used. The solution must satisfy Kirchhof's laws. The algebraic sum of all flows at a bus must equal zero, and the algebraic sum of all voltages in a loop must equal zero. Other limitations are the capability limits of reactive power sources, the tap setting range of tap changing under load transformers and the specified power interchange between interconnected systems. VIComparison Of Methods : The basic points of the methods for obtaining a load flow solution are : l.The computing time required to process system input data in order to obtain the parameters for the iterative calculation. 2. Computer programming and storage requirements. 3. Iterative solution time. 4. The computing time required to modify network data and to effect system operating changes. The computer time required during the iterative solution depends on the number of logical and arithmetic operations, the rate of convergence of the solution technique, the size and characteristics of the power system. A significant increase in the rate of convergence can be obtained by applying acceleration factors. The optimum values of acceleration factors for a load flow solution are difficult to calculate. The selection of the acceleration factors for the real and imaginary components of voltage, depends on the characteristics of the network and the method of solution. The tolerance required to obtain a solution varies with the different methods. The Newton-Raphson method using the bus admittance matrix uses the tolerances specified for the net real and reactive powers at a bus. Therefore the tolerances are meaningful to the user who indicates the desired accuracy. Tolerances of 0.001 per unit for the real and reactive bus powers were used in the test calculations and produced comparable results. The number of iterations for different size systems, for each method are summarized along with the acceleration factors and tolerances. The initial bus voltages were assumed equal to 1.0 +j0 for all tests done. For Gauss-Seidel method acceleration factors of 1.7 and 1.7 and tolerances of 0.0001 and 0.0001 per unit used for real and imaginary components of voltage. VI iTable 1. Number of iterations used for load flo^ solutions: For Newton-Raphson method tolerances of 0.001 and 0.001 per unit used for real and reactive bus powers. There is no acceleration. For the ZDUS used in Gauss-Seidel method tolerances of 0.001 and 0.001 per unit used for real and imaginary components of voltage. There is no acceleration. The time required for the iterative solution was least for the Newton-Raphson method using the bus admittance matrix. Time Unite 0 40 80 120 Sun,- Gauss-Seidel Yg^ Gauss-Seidel Vq Newton-Raphson Number of Buses Figure 1. Time for iterative solution The total iterative solution times for the methods are shown in figure 1. The selection of initial values for bus voltages have a great effect on solution time. When a series of load flow calculations are performed, the usual procedure is to use the last calculated bus voltages of each case as the initial voltages for the next case. This tends to reduce the number of iterations, when VI 11there are only minor changes in system conditions. The actual computer time required for a load flow solution is dependent also on the speed of computer used. A Guiding Explanation Of The Computer Program : The computer program given in this thesis to solve load flow consists of two parts. The first part is the main program. The second part consists of the functions. The main program calls the functions when it needs them to perform a specific task. Thus we can easily see what happens in the main program because with the help of functions the main part becomes shorter. The method used to solve the load flow is Newton- Raphson. Tolerance must be given to the program during its run time. When we run the program main menu comes to the screen. To write the basic cut set's data into the program press the“ K ”key. The required [i][j] th matrix data is asked by the computer. To give the ^primitive matrix data press the“ Y ”key. If you realize that you made a mistake go on writing other elements. You can always have a chance to change a particular element after turning to the main menu and by pressing the“ D ”key. After pressing the D key you are being asked which element you want to write over. If the matrix you are going to give is a diagonal matrix D key simplifies your task of writing the whole matrix. You needn't write the zeros. Initially the computer gives all the elements of a matrix zero values. The rest of the job is only writing diagonals. All the given data is saved to the hard disk automatically. You have a chance to run the program every time without writing it. From the main menu you can select“ B ”key to look up to the power systems Ygus matrix. We must also enter bus voltages by selecting“ A ”key. Quitting from the program during the main menu is always possible by pressing the“ Q ”key. IX

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