Çok makineli güç sisteminde açısal kararlılık analizi ve kontrolör parametre optimizasyonu
Angular stability analysis and controller parameter optimization in multi-machine power system
Yazar: SERDAR EKİNCİ
Danışman: PROF. DR. AYŞEN DEMİRÖREN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Elektrik Mühendisliği Ana Bilim Dalı
Derece: Doktora, 2015
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering

Özet:
Güç sistemlerinde en önemli araştırma konularından olan kararlılık, rotor açısı kararlılığı, gerilim kararlılığı ve frekans kararlılığı olmak üzere üç ana sınıfa ayrılmaktadır. Bu tezde temel olarak rotor açısı kararlılığına değinilmiştir. Rotor açısı kararlılığı, küçük veya büyük arızalara maruz kalan güç sisteminin senkronizasyonunu koruma yeteneğidir. 
Büyük güç sistemlerinde yaygın problemlerden biri düşük frekanslı güç sistem salınımlarıdır. Yeterli sönüm mevcut değilse, bu salınımlar giderek devam eder ve sistem senkronizasyonunu kaybedinceye kadar büyür. Senkron generatörlerin kararlı ve güvenilir çalışmasını sağlamak için güç mühendisliğinde çok sayıda çalışma yapılmıştır. Güç sistemi kararlı kılıcılar (Power System Stabilizers, PSSs) bu problem için alternatif çözümlerden biridir. PSS, yardımcı kararlı kılıcı işaretler kullanıp kendi uyarmasını kontrol ederek, generatör rotor salınımlarına sönüm eklemek için kullanılır. 
Son yıllarda, zor olan optimizasyon problemlerini çözmek amacıyla çeşitli sezgisel optimizasyon teknikleri önerilmiştir. Bu yöntemlerin birçoğu doğadan esinlenilmiş olup, evrimsel algoritmalar ve sürü zekâları olmak üzere iki önemli kategoride sınıflandırılabilir. Problem ve modelden bağımsız olan doğadan esinlenmiş sezgisel optimizasyon teknikleri, geleneksel optimizasyon tekniklerindeki eksikliklerin giderilmesi için önerilmektedir. Bu yöntemlere dayalı Genetik Algoritma (Genetic Algorithm, GA), Parçacık Sürüsü Optimizasyonu (Particle Swarm Optimization, PSO), Diferansiyel Gelişim (Differential Evolution, DE) algoritması ve yapay arı kolonisi (Artificial Bee Colony, ABC) algoritması gibi çeşitli algoritmalar optimum PSS parametrelerini etkin şekilde bulmak için yaygın olarak uygulandı.   
Güç sistemlerinde Power System Simulator (Simpow) ve DigSilent gibi hesaplama yönünden çok etkili ve yeterince kullanıcı dostu olan ticari programlar ile MATLAB tabanlı ücretsiz bir yazılım olan Power System Toolbox (PST) ve ticari bir yazılım olan SimPowerSystems (SPS) gibi çeşitli programlar mevcuttur. Bu programların çoğunda bileşen modellerini incelemek ve değişiklik yapmak zordur veya olanaksızdır. Ayrıca bu programların öğrenilmesi genellikle önemli eğitim gerektirmektedir ve bu sebepten ötürü normal derslik kullanımlarına uygun değildir. Akademik ve eğitim kullanımları için bileşen modellerinin şeffaf ve esnek olması ve öğrencilerin simülasyonlarını kolaylıkla yapabilmesi daha önemlidir.
Bu tezde, MATLAB ortamında çalışan ve grafiksel kullanıcı arabirimine (graphical user interfaces, GUI) sahip PowSysGUI adında yeni bir eğitimsel yazılım paketi, elektrik güç sistem analizi ve tasarımlarında kullanılması için geliştirildi. Bu program açık kaynak kodlu yazılımdır ve güç sistemleri alanında kod yazmayı öğrenmek isteyen biri bu programın içyapısını görebilir. Bu program paketi, araştırmacılar ve eğitimciler için kullanması ve değiştirmesi kolay olan bir simülasyon aracı olarak amaçlandı. PowSysGUI, anlaşılması ve değiştirilmesi için kodu basit tutarak olası en iyi performansı vermesi için tasarlandı. PowSysGUI yük akışı analizi, küçük işaret kararlılık analizi, zaman domeni simülasyonu ve evrimsel hesaplama tekniklerini kullanarak PSS tasarımı için verimli algoritmalara sahiptir ve kolay kodlamaya izin verir. 
Tezde geliştirilen programın kapasitelerini ve eğitim/araştırma amaçları için uygunluğunu göstermek amacıyla temel özellikleri, algoritmaları ve farklı güç sistemleri üzerinde çeşitli durum çalışmaları sunuldu. Simülasyon sonuçları, PowSysGUI paket programının elektrik güç sistem çalışmaları için güçlü ve gelecek vaat eden bir araç olduğunu gösterdi. Ayrıca PowSysGUI açısal kararlılık kavramının anlaşılmasında çok yararlıdır ve elektrik mühendisliğindeki özellikle kararlılık konularını içeren bazı lisans/yüksek lisans derslerinde etkin olarak kullanılabilir.

Abstract:
Load flow or power flow analysis is implemented in a power system analysis course for the determination of voltage magnitudes and angles of various bus bars as well as real and reactive power flow. It is, in fact, a problem of solving a system of nonlinear equations. To solve load flow problems as efficiently as possible, a myriad of different methods have been proposed in the literatures.
The stability of power systems has been and continues to be of a fundamental concern in system operations. Modern electrical power systems have grown to a complexity which is not easy to handle by conventional methods because of growing interconnections, installation of large generating units and extra high voltage tie-lines etc. The power system stability is usually categorized based on the following considerations: 
a)	Rotor angle stability
b)	Voltage stability
c)	Frequency stability
In this thesis, mainly the rotor angle stability is considered. Rotor angle stability denotes the ability of the grid's synchronous machines to remain in synchronism following being subjected to large and small disturbances. It can also be directly related to maintaining or restoring the equilibrium of the system between electromagnetic torque and mechanical torque of each synchronous machine in the system. There are two basic approaches of stability studies for exploring the impact of disturbances on the electromechanical dynamic behavior of the power system: steady-state and transient stability.
The steady-state or small signal stability of a power system refers to the ability of the system to maintain synchronism after being subjected to a small disturbance. Steady-state stability studies are usually less comprehensive than transient stability studies, and often perform on a single machine infinite bus or just a few machines undergoing one or more small disturbances. Hence, steady-state stability studies are used to examine the stability of the system under incremental variations in parameters or operating conditions at a steady-state equilibrium point. The nonlinear differential and algebraic equations of the system are replaced by a set of linear equations, which are solved by methods of linear analysis to check if the system is steady-state stable.
Transient stability or large-disturbance rotor angle stability denotes the ability of the power system to maintain synchronism while being subjected to severe disturbances, including a short circuits and/or outages of major transmission lines. In this case, the system's response is governed by the system nonlinearities; hence linearized of the system equations do not work. It is worth to note that while steady-state stability is a function only of operating conditions, transient stability is a function of both the operating conditions and disturbances. This complicates the analysis of transient stability substantially, but the resultant nonlinear differential and algebraic equations of the overall system can be solved by means of using either direct methods or iterative step-by-step procedures.
Power systems undergo low frequency oscillations when they are vulnerable to disturbances. The oscillations might continue and develop to trigger the system separation in the case of lack of sufficient damping. To augment the system damping, the generators are fitted out with the power system stabilizers (PSSs), which are designed to supply supplementary feedback stabilizing signals in the excitation systems. PSSs prolong the power system stability level through advancing the system damping of the low frequency oscillations, which are related to the electromechanical modes. 
A number of techniques, such as optimal control, adaptive control, variable structure control and intelligent control, have been used in the design of PSS. These existing techniques contain numerous disadvantages, since the control law is contingent upon a linearized machine model and the control parameters are arranged for definite nominal operating settings. The parameters of the controllers are not also valid, as the system conditions modify nonlinear in the situation of large disturbances. 
In the last two decades, several heuristic optimization techniques have been proposed in order to solve difficult optimization problems. Most of these methods are inspired by nature and can be classified into two main categories: evolutionary algorithms and swarm intelligence. Nature-inspired heuristic optimization algorithms, independent from the problem and model, have been proposed to explain deficiencies of conventional optimization algorithms. A number of algorithms based on these methods, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE) algorithm and Artificial Bee Colony (ABC) algorithm, have been widely proposed and applied to find the optimal set of parameters to effectively design the PSS. The outcomes are propitious and substantiate the potential of these algorithms for optimal PSS design. 
The simulation of power systems using special purpose tools is nowadays a well-established field and a number of commercial tools, such as Simpow, NEPLAN, EuroStag and PSS/E, are available. Although most of these tools are computationally very efficient and reasonably user-friendly, they have a closed architecture in which it is hard or impossible to view or change most of the component models. What is more, these simulators are not ideal for normal classroom use since they often require substantial training. For academic and educational use, it is more significant that the component modeling be transparent and flexible that help students quickly get started with their simulations. 
Over the last decade, a myriad of high-level scientific languages, including MATLAB, MATHEMATICA and MODELICA, have become more and more popular for both research and educational purposes. Any of these languages can lead to desired results in the field of power system analysis. Nevertheless, MATLAB proved to be the best user choice. Key features of MATLAB are the matrix-oriented programming, wonderful plotting capabilities and a graphical environment (SIMULINK) which greatly simplifies control scheme design. Therefore, several MATLAB-based commercial, research and educational power system tools have been proposed, such as Power System Toolbox (PST), Electromagnetic Transients Program in MATLAB (MatEMTP), Voltage Stability Toolbox (VST), Power Analysis Toolbox (PAT), Educational Simulation Tool (EST), SimPowerSystems (SPS), Power System Analysis Toolbox (PSAT), Matlab Power System Simulation Package (MatPower) and MatDyn. But only a few of them are entirely free and open source.
Graphical user interfaces (GUIs) are being increasingly used in the classroom to provide users of computer simulations with a friendly and visual approach to specify all input parameters and enhance the configuration flexibility. In this thesis, an educational software package called PowSysGUI (Power System GUI), which runs on MATLAB and uses GUIs, has been developed for analysis and design of electric power systems. It is open-source software and anyone can see the inner structure of the program to understand how to code a power-engineering problem. It is designed as a simulation tool for researchers and educators, as it is simple to use and modify. PowSysGUI is designed to give the best performance possible while keeping the code more simple and plain to understand and modify. 
PowSysGUI has efficient algorithms for power flow analysis, small signal stability analysis, time-domain simulation and PSS design using evolutionary computation methods. PowSysGUI also allows easy scripting, and comprises four main programs:
1) Power Flow Analysis (PFA) : PowSysGUI finds admittance matrix and uses the standard Newton-Raphson Method for power flow. 
2) Small Signal Stability Analysis (SSSA) : PowSysGUI allows computing and plotting all the eigenvalues and the participation factors of the system, once the power flow has been solved. To ensure high-precision results, the eigenvalues are calculated by using analytical Jacobian matrices. 
3) Time-domain Simulation (TDS) : This program is Simulink-based and plots system responses and gives reduced admittances matrices. It has to be bear in mind that a transient stability analysis is characteristically more complicated than power flow and small signal stability analysis. 
4) PSS Design : This program contains two types of objective functions: eigenvalue-based objective function and time domain-based objective function for PSS parameters tuning problem. In this program, some heuristic optimization techniques are applied to search for optimal PSS controller's parameters. 
Basic features, algorithms, and a variety of case studies based on the IEEE 9-bus, IEEE 39-bus and IEEE 68-bus test systems are presented in this thesis in order to illustrate the capabilities of the presented tool and its suitability for educational and research purposes. Simulation results show that PowSysGUI is a powerful and promising tool for electric power system studies, and very helpful to understand angle stability phenomena. Likewise, PowSysGUI could be effectively used to enhance power engineering undergraduate/graduate courses. PowSysGUI developed in this thesis is available to the reader. For more information, please contact the communicating author at ekinciser@yahoo.com.