Kararlılık analizinde kullanılan senkron makina modelleri
Synchronous machine models used in stability analysis
Yazar: MEHMET S. KÜÇÜK
Danışman: PROF. DR. M. EMİN TACER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1990
Konu: Elektrik ve Elektronik Mühendisliği = Electrical and Electronics Engineering
Dizin: Enerji sistemleri = Energy systems ; Kararlılık analizi = Stability analysis ; Senkron makineler = Synchronous machinery

Özet:
Elektrik Enerji Sistemlerinde Kararlılık Konusu, günümüzde güncelliğini muhafaza etmektedir. Bilim ve tek nolojideki hızlı değişimlere paralel olarak Kararlılık konusunda da çok yönlü çalışmalar yapılmaktadır. Bu konuda yapılan çalışmalarda Kararlılığın sağlan masında en önemli bileşen olan Senkron Makinalar büyük önem kazanmaktadırlar. Analiz açısından bir enerji sisteminde, tasarlanan elektriksel yük değişimini ve sistemde meydana gelebilecek arızalar neticesinde ortaya çıkacak olan dengesizlikleri en iyi şekilde dengeleyebilecek uygun Senkron Makina modellerinin belirlenmesi büyük önem taşı maktadır. Gerçeğe uygun Senkron Makina modellerinin gelişti rilebilmesi için, Senkron Makina parametrelerinin Kararlılık analizinde, doğru ve hassas bir şekilde elde edilmesi gerekmektedir. Bu yönde yapılan deney çalışmaları da Kararlılık bilgilerinin iyileştirilebilirliğinden hareketle makina modellerinin daha verimli tasarlanması yönünde büyük katkılar sağlamıştır. Yapılan bu çalışmada, senkron makinalar kararlılık analizi açısından incelenmiş, değişik araştırmacılar tara fından makina modelleri üzerinde yapılan araştırmalar ta nıtılmış ve gerçeğe uygun senkron makina modellerinin elde edilmesi yönündeki ilerlemeler anlatılmıştır. - iv -

Abstract:
After the years of the Second World War, man's de mand for and consumption of energy has increased. When Nikola Tesla in 1888 invented the induction motor, the energy became more necessary for the industrial world. During the civilization of the societies, a major portion of the energy needs is supplied in the form of electrical energy. In industrially developed countries, the supply of electrical power is increasing day by day. Therefore very complicated power systems have been built during the increasing need to energy consumption. Electrical energy is supplied to the consumers by the interconnected network of transmission lines, linking the loads and generators into large integrated systems. Generally generators are located thousands miles away from the cities. This loca tion presents many engineering problems such as planning, construction and operation. Power systems can only be operated under the condi tion that the system is stable, in other words when the mechanical input energy is balanced with the electrical energy during the production. Consumer needs a constant voltage and frequency at all the times. In the developed countries Electricity authorities are obliged by laws to present to their consumers voltage and frequency within close tolerances so that the consumer's electrical equip ments may operate satisfactorily. Therefore electrical energy required by the consumer must be supplied securely. The growing need to energy is generated by the ge nerators operating parallel in an interconnected system. In order to sustain the stability of energy systems, gene rators must be operated in synchronism. If any generator loses its synchronism with the rest of the system, volta ge and frequency may change and my be some of the systems tripped. In this case if any generator is seperated from the system, the energy must be supplied via the other transmission lines to the consumer; during this process, the generator which lost its synchronism must be re-synch ronized and loaded again. Frequently, it is supposed that the power system is being operated under the "Steady State". But this is not always achieved, since random changes in loads are occured at all the times. For example, any fault on the - v -network/ sudden change of, major loads, loss Of aline, or generating unit effect, the stability of energy system. The system may not operate in the steady state. For the Industrial countries, the stability of the energy system is a very most important engineering prob lem for the power engineers. Since in an efficient energy system, the requirement of the energy is achieved by the interconnected synchronous generators, the behavior of the synchronous machines specially during the transi ent periods must be investigated. If during the transi ent periods, the perturbations occured in the system do not involve any net change in power, there is no any problem, the machines sould return to their original ope rating state. But if any unbalance occured between the supply and demand by a change in load, or in generation, a new operating state must be reached. Consequently, if ?Öhe energy system is stable, in any case during the tansi- ent or subtransient periods, interconnected synchronous machines (generators) must be able to remain in synchronism that is to say they must all be operating in paral lel at the same speed. A system perturbation during the transient period is oscillation. If a system is stable, these oscillati ons are damped toward a new quiescent operating conditi on. If they are not damped (in unstable case) these os cillations are reflected in the power flow as fluctuati ons over the transmission lines. Energy system is called as "stable" if the oscilla tory response of a power system during the transient pe riod following a disturbance is damped and the system settles in a finite time to a new steady operating condi tion. So in the stability of the energy system, the cha racter of the disturbance is very important. Power system response to the different type of disturbance shows dif ferent behaviour so the distinctions must be made between the disturbances. Sudden and major impacts are generally called as "Large Impacts" while the known load changes in the electrical network or small faults which do not affect the stability of the system is called as "Small Impacts". A fault on the high voltage transmission lines, short circuits or loss of a generating unit in the system are examples to the "Large Impacts". This problem is ex plained as the Transient Stability problem. For attaining the stability of the system, the transient behavior of the stability must be dealth with., In order to make stability analysis, when any type of impacts is applied to the system, the type of the im pact and its duration. must be taken into account. Gene rally stability concept is considered in three classifi cations. - vi -1, Steady state stability 2, Transient state stability 3, Sub^tra,nşient (dynamic) stability. The transient stability study is the most specific one in stability analysis. Because during this state, the system may loose its Synchronism according to the type of the disturbance. During the steady state analysis, the known changes in load or faults do not affect the synchro nism. Stability basically depends upon the magnitude, lo cation and the duration of the disturbances. Since in the stability analysis, disturbance affect: directly the synchronism of synchronous generators depend ing upon the disturbance, the reliable synchronous machine models must be modelled and used in stability analysis. For this purpose, in my thesis I will deal with the synch ronous machine models used, in stability programs in a wide approach. The fault analysis on the transmission li nes, or the load changes during the distribution system will not be explained. A further information may be found and read from the references written on the last pages of this book. By this scope, the aim of the thesis is to define synchronous machine models, for use in stability studies and work on methods for determining the parameter values for use in the defined models either by calculation or by test. Also, the distinction between the derived models and the synchronous machine models reliable to the real world will be investigated. In 1928, Park and Robertson developed the ideas of several "Reactances for synchronous Machines" in both the direct axis and quadrature axis on the rotor. They also introduced the concepts of both the transient and sub- transient states in the fluxes, voltages and currents as sociated with some sudden change in the electrical network in which the synchronous machine was connected. In 1929, Par.£ and Robertson had extended the d and q axis concepts and they defined the well known (dqo) transformations which are latterly called "Park Transformations". The first test for the determination of the vari ous machine synchronous and transient quantities had been defined by Sherwin Wright in 1931. This test was accepted by the AIEE Synchronous Machine Subcommittee in 1945. The present IEEE 115 depends on this investigation After the 1960's, as computational tools developed stability concept was considered for larger and larger systems. As the computational tools became available, the machine modeling for stability concept became apparent - vii -since thirty years. At the same time, the requirement for the improyed stability models f(?r synchronous machines has increased considerably in the electric power systems during these years» The traditional approach to the synchronous machine modeling has been to describe it interms of parameters that are directly related to the observed machine behavi ours under standart test condition. The normal parameters used are the transient and sub-transient reactances and their corresponding time constants meant to characterize the open circuit and short circuit responses of machine flux in accordance with ANSI standards. But the ANSI data is often inadequate. Several new test procedures which explained in this thesis have been developed for accurate determination of synchronous machine dynamic characteris tics. Models that have been derived from the new derived approaches do not generally conform to the traditional mo dels used by most large scale stability programs. On the other hand during the modeling of the synchronous machines in conventional models, there are lot of assumptions which have been made for the calculation of the model parameters. During these assumptions some physical concepts of the synchronous machine have been ignored. In particular, it has been found necessary to account for the unequal mutual inductances between the d-axis stator and rotor circuits. It has also been found necessary to account for the q-axis saturation effects more accurately. Factory tests on synchronous generators provide im portant information for verification of new designs as well as yielding the parameters which are commonly used in synchronous machine models. The current standard fac tory tests have evolved into their present form over a long period of time and procedures governing then are fo und in IEEE 115 Although synchronous machine model ing has been growing in complexity and sophistication, the data available from factory tests remained the same. This is mostly due to two practical considerations. First, to put the load on the machine in the factory is not possib le. Neither the energy to drive the unit nor means to dump the energy is available. Therefore the only aperating po ints which are available are open circuit, short circuit, and zero power factor. These three conditions are charac terized by the fact that all of the flux and current are on the direct-axis. The tests are therefore direct axis tests yielding no information about the quadrature axis. Both experimental and analytical techniques have been put forth that provide data as a function of frequ ency, that can be used to characterize the mathematical representation of synchronous machines. These methods pro vide data about machines that is different from the time domain records of quantities measurable at machine - vili -terminals < Techniques for analyzing- these time domain re cords are well known,, but no widely recognized methods- exist for extracting a synchronous' machine model from functions expressed in the frequency domain.. Stand-still and on-line frequency response tests are good approaches for this purpose. In this thesis, at the fourth chapter, frequency response tests are widely investigated. Also some simulation examples are given for synchronous machine models. Operational impedances and transfer functions can be obtained from a synchronous machine either at rest (stand-still), or from small periodic disturbances impres sed during steady-state operation. It can either be chosen a structure for a synchronous machine model and then use these frequency domain functions to derive appropriate nu merical constants for the model specified. A flow-chart for this procedure apears on Fig.l. This procedure is widely applied with examples in Chapter 4. OBTAIN FREQUENCY DOMAIN OATA SELECT MODEL STRUCTURE DEFINE ERROR INDEX BETWEEN FREQUENCY DOMAIN DATA AND DERIVED MODEL SELECT PARAMETERS AND ESTIMATE VALUES FOR DERIVED MODEL ADJUST PARAMETER VALUES OF DERIVED MODEL TO ' MINIMIZE ERROR INDEX EVALUATE ADEOUACV OF DERIVED MODEL FIGURE 1. FLOW CHART FOR DERIVING A SYNCHRONOUS MACHINE MODEL, FROM FREQUENCY RESPONSE DATA As explained, during the flow-chart approach, the general aims of the tests performed, for obtaining the synchronous machine parameters are. as follows. 1. Determination of the simplest form of model that will adequately represent the dynamics of solid rotor mac hines. 2. Developement of test procedures and methods for derivation of necessary parameters for this model. 3. Demonstration of accuracy of predicted perfor mance with the proposed models and evaluate the accuracy requirements for various model parameters. 4. Suggestion of improvements in model structures as necessary to provide acceptable accuracy. - ix -