Geçici hal kararlılık probleminin sayısal çözüm metodları

Abstract

Geçici Hal Kararlılık Probleminin Sayısal Çözüm Metodları Herhangi bir bozucu etkiye maruz kalan enerji iletim «sisteminde senkron makinaları kararlılığı önemli bir problem olarak karşımıza çıkmaktadır. İletim ağının yaygınlaşmasıyla birlikte bu problem daha büyük bir önem arzetmektedir. Kararlılık, bozucu etki sonrası senkron makinenın senkronizmada kalma kabiliyetidir. İletim hatlarının empedansları, makineların geçici reaktansları ve eylemsizlikleri kararlılığı etkileyen faktörler arasında sayılabilir. İletim hatlarının muhtemel bir bozucu etkiye karşı tasarımlanmaları işletme şartları ve sürekli enerji nakli bakımından önemlidir.Bu amaçla, bu çalışmada çok makineli ve çok baralı bir sistem incelemeye tabi tutulmuştur. En basit şekilde; iletim hattı, transformatör ve senkron generatörden oluşan tek makineli sistem ikinci dereceden bir diferansiyel denklemle temsil edilmektedir. Bu denklemi çözmede farklı sayısal metodlar vardır.Çalışmadan beklenen doğruluk ve simülasyon zamanı göz önüne alınarak bunlardan sisteme en uygun olanı seçilir.Çok makineli sistemlerde durum değişkenleri sayısının artması, problemi çözmek için seçilecek sayısal metodun önemini artırmaktadır. Bu çalışmada değişik yöntemler ele alınmıştır ve değişik metodlarla programlama yapılarak aralarındaki avantaj ve dezavantajlar gösterilmeye çalşılmıştır. Yukarıda bahsedilen çok makinelı sistemin analizi sonucunda programlamasıyapılan tüm sayısal çözüm metodlarıyla sonuç alınabildiği gösterilmiştir.Ayrıca Runge-Kutta (dördüncü mertebeden) metodunun sayısal olarak en kararlı sonucu verdiği belirlenmiştir.

Numerical Solution Methods For Transient Stability Problem An electric; power system is a dynamic, nonlineer system» The dynamics occur due to changes in demand, generation, line switching, lightning surges, and faults. These dynamics m-e often classified by the speed of occurence. The models needed to study these dynamics vary in detail depending on the speed of occurence. The stability of power system is further classified according to the intensity of the disturbance admitted. When large disturbances are considered, the term "transient stability" applies to systems that retain synchronism» For small disturbances, the terms "small signal stability" or "small disturbance stability" apply. Older literature contains the term "dynamic stability", which was used to denote small signal stability. The guest i on of what constitutes a small disturbance is resolved by relegating small signal analysis to those problems in which linearisation is allowable. When linearization produces inaccuracy sufficient to alter the stability study, the term "transient stability study" appl i es. For synchronous machine dynamics significantly longer than 5 cycles <1 cycle -- 1/50 s at SO I-İ2 ), the stator circuits and interconnecting network may be con sidered to be in steady state. The field circuit, however, is controlled by an automatic voltage regulater as well as other stabilizing control lersş these devices are not high speed controllers and the long time con stants in the field itself usually preclude steady state analysis for this circuit. The most influential factor that determines the rotor dynamics, 6' it), is the electromechanical pVienomena of the rotor inertia. Transient stability studies provide information re lated to the capability of a power system to remain in synchronism during major disturbances resulting from either the loss of generating or transmission facilities, sudden or sustained load changes, or momentary faults. Specifically, these studies provide the changes in voltages, currents, powers, speeds, and torques of themachines of- the power system, as well as the changes in system voltaıjBE and power flows, during and immediately following a disturbance. The degree of stability of a power system is an important factor in the planning of now facilities. In order to provide the reliability required by the dependence on continuous electric sor v.i co, it is neccessary that power systems be designed to be stable under any conceivable* disturbance» Many years ago, at the inception of interconnection of power systems, stabi 1 i t i y occupied a less important role in power engineering than at present. This is due to two distinct factors early generators had very high inertia constants, and resulting angular accelerations were limited by these high values. Second, interconnec tion was not so extensive. High energy levels were un available from interties, and interconnection between generators was correspondingly limited. The gradual ap pear ance of the control of low inertia machines has resulted in increased importance of stability. This is reflected in the increasing importance of the control of energy avaible to machine rotors. This energy has the pot ant i ai of causing inappropriate fluctuation of i5'(t>, or wor s e, i n s t ab ili t y. In the caxse of electromechanical transients, it is necassary to consider stability more closely because dis turbances may cause machine rotors to loose synchronism with the power frequency. In this study, attention is focused on electromechanical transients of synchronous machines in an interconnected power system. The- pwi tor manee of the power system during the transient period can be obtained from the network perfor mance equations.. "the performance equation using the bus frame of reference in either the impedance or admittance form has been used in transient stability calculations. When ground is used as reference for the load flow calculation and the loads are represented solely as cur rent sources, the bus admittance matrix will include only capacitor, reactor, and line charging elements to ground. In this case the bus admittance matrix is ill-conditioned and convergence of ^ the solution usually is not obtained. On the other hand, the convergence characteristic, then these admittances and the bus adrni ttances matrix must be modified during the iterative solution for changes in bus vol t ages. The procedures-, described uses the bus impedance and admittance matrices and representing each machine vias a current, source between the machine terminal bus and ground and in parol lei with the machine impedance. This is an application of Norton's teorem. This el emi nates the need to establish an additional bus behind the im pedance of each machine. In general, a transient stability program is developed as an extension of- a load flow program. This provides, the ability to obtain a load -flow solution prior to the disturbance and thus the initial system values for the transients calculations:.» In addition, the load -flow data can be used in the transient study. If the bus admittance matrix is used for a tran sient: stability study, ground is usually taken as reference because all network bus voltages, except at the fault bus, change during the transient period. To eleminate the need to modify the bus admittance matrix for a change in the reference bus, ground is used also as a reference in the prefault load flow calculations. In transient stability studies a load flow calcula tion is made first to obtain system conditions prior to the disturbance or the load flow results used. In this calculi on the network is composed of system buses, trans mission lines, and transformers. The network repre sentation for transient stability studies includes, in addion to these components, equivalent circuits of the machines and static impedances or admittances to ground for loads. After the load flow calculation, therfore, the admittance matrix of the network must be modified to reflect the changes in the representation of the network. In this thesis essentially three phase faults examined, also the others arta taken into account. It is necassary to do this, only data file must be represented to reflect the faults. For this propose a computer progam prepared. During the iterative calculation the magnitudes and phase angles of bus voltages behind the machine equiv alent admittances are held constant. If a three phase fault is simulated, the voltage of the faulted bus is set to aero and held constant. V. Many faults &r& of the type that deenergization of the bus will result in clearing the fault. Reclosure speed, then, should be sufficiently rapid so that Si (t) is less then the critical value.