Birleşik Alternatif Akım-doğru Akım Sistemlerinde Geçici Hal Kararlılığına Değişik Bir Yaklaşım

Abstract

Sunulan bu çalışma ile ilk defa, birleşik alternatif akım-doğru akım enerji sistemlerinin geçici hal kararlılık analizi, geçici hal sırasında bara gerilim genliklerindeki değişimi gözönüne almak suretiyle, arıza yerine bağlı kararsız denge noktalan yöntemi ile yapılmıştır. Bara gerilimlerinin yeni değerleri, geçici halde doğru gerilimli hattan iletilen aktif gücün her integrasyon adımında değişmesi ve bu yeni güç değerine göre güç akışı analizinin ardışıl olarak tekrarlanmasıyla bulunmaktadır. Bu güç akışı analizi sonunda bara gerilimleri ile birlikte çeviriciler tarafından çekilen reaktif güç de her defasında yeniden hesaplanmaktadır. Bunun sonucunda bu gücün doğru gerilimli hattan iletilen aktif güce oram, geçici hal boyunca hesaplamalarda değişken bir değer olarak gözönüne alınmaktadır. Bu yöntem vasıtasıyla, geçici hal süresince bu oranın gerçek değeri hesaba katılarak geçici hal kararlılık analizi yapılmıştır. Böylece, şimdiye kadar geçici hal kararlılık analizinde bu oranın geçici hal sırasında yaklaşık sabit bir değeri alınarak yapılmış olan hata ortadan kaldırılmıştır. Sonuçların kararlılık bakımından daha iyimser olduğu gözlemlenmiştir. Yine bu çalışmada, arıza yerine bağlı kararsız denge noktalan yaklaşımının birleşik AC-DC sistem geçici hal kararlılık analizine uygulanabilirliği gösterilmiştir. Geliştirilen yeni bir algoritma ile, her integrasyon adımında yeniden hesaplanan DC hattan iletilen güç değerine göre arıza sonrası kararlı ve kararsız denge noktalarının düzeltilmesi ve buna bağlı olarak kritik enerjinin güncelleştirilmesi sağlanmıştır. Sistemdeki DC hatlar iki uçlu olarak gözönüne alınmış ve bağlı olduklan haralara akım enjeksiyonu şeklinde modellenmişlerdir. Sistemdeki yükler ise klasik sabit admitans şeklinde gösterildikleri gibi, DC hatta benzer şekilde bağlı oldukları haralara akım enjeksiyonu şeklinde olmak üzere iki farklı biçimde modellenmiştir. Yüklerin her iki modellerime biçimine ait saf AC sistem geçici hal kararlılık analizi, yine arıza yerine bağlı kararsız denge noktalan metodu ile yapılmıştır. Her iki durumda elde edilen sonuçlar ile, birleşik AC-DC sistem geçici hal kararlılık analizinden elde edilen sonuçlar kendi aralarında karşılaştırılmak suretiyle değerlendirmeler yapılmıştır. Bu çalışmada ayrıca, DC hatların sistemdeki yeri ile arıza yerine olan uzaklığının AC- DC sistem geçici hal kararlılığı üzerine etkisi incelenmiş ve sonuçlar birbirleriyle karşılaştırılmak suretiyle değerlendirilmiştir. Geçici hal esnasında DC hattan iletilen gücün kontrolünde oransal kontrolör kullanılmış ve bu kontrolör kazancına göre kararlılık bölgesinin değişimi incelenmiştir. Yukarıda genel hatları açıklanmış olan bu çalışma, literatürde yer alan dört generator ve altı barak örnek bir sistem üzerinde test edilmiştir.

Power system stability may be broadly defined as that property of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to disturbance. Stabilities in power systems are traditionally referred to as either voltage or rotor angle (phase angle) stability. 1. Voltage stability is the ability of a power system to maintain steady acceptable voltages at all busses in the system under normal operating conditions and after being subjected to a disturbance. A system enters a state of voltage instability when a disturbance, increase in load demand, or change in system condition causes a progressive and uncontrollable drop in voltage. The main factor causing instability is the inability of the power system to meet the demand for reactive power. The heart of the problem is usually the voltage drop that occurs when active power and reactive power flow through inductive reactances associated with the transmission network. 2. Rotor angle stability is the ability of interconnected synchronous machines of a power system to remain in synchronism. The stability problem involves the study of a electromechanical oscillations inherent in power systems. A fundamental factor in this problem is the manner in which the power outputs of synchronous machines vary as their rotors oscillate. Under steady state conditions, there is equilibrium between the input mechanical torque and the output electrical torque of each machine, and the speed remains constant. If the system is perturbed this equilibrium is upset, resulting in acceleration and deceleration of the rotors of the machines according to the laws of motion of a rotating body. If one generator temporarily runs faster than another, the angular position of its rotor relative to that of the slower machine will advance. The resulting angular difference transfers part of load from to slow machine to the fast machine, depending on the power angel relationship. This tends to reduce the speed difference and hence the angular separation. The power-angel relationship is nonlinear as seem from equation 1. Beyond a certain limit, an increase in angular separation is accompanied by a decrease in power transfer; this increases the angular separation further and leads to instability. For any given situation, the stability of the system xv depends on whether or not the deviations in angular positions of the rotors result in sufficient restoring torques. When a synchronous machine loses synchronism or "falls out of step" with the rest of the system, its rotor runs at a higher or lower speed than that required to generate voltages at system frequency. The "slip" between rotating stator field (corresponding to system frequency) and the rotor field result in large fluctuations in the machine power output, current, and voltage; this causes the protection system to isolate the unstable machine from the system. Pe=PmaxSin6 (1) Loss of synchronism can occur between one machine and the rest of the system groups of machines. In the latter case synchronism may be maintained within each group after its separation from the others. For convenience in analysis and for gaining useful insight into the nature of stability problems, it is usual to characterize the rotor angle stability phenomena in terms of the following three categories: 1. Small signal (steady-state) stability is the ability of the power system to maintain synchronism under small disturbances. Such disturbances occur continually on the system because of small variations in loads and generation. The disturbances are considered sufficiently small for linearization of system equations to be permissible for purposes of analysis. 2. Transient stability is the ability of the power system to maintain synchronism when subjected to a severe transient disturbance. The resulting system response involves large excursions of generator rotor angels and is influenced by the nonlinear power-angle relationship. Stability depends on both the initial operating state of the system and severity of the disturbance. Usually, the system is altered so that the post-disturbance steady-state operations differs from that prior to the disturbance. In transient stability studies the study period of interest is usually limited to 3 to 5 seconds following the disturbance, although it may extend to about ten seconds for very large systems with dominant interarea modes of oscillation. 3. The term dynamic stability has also been widely used in the literature as a class of rotor angle stability. However, it has been used to denote different aspects of the phenomenon by different authors. In recent years, loading of transmission networks in the industrialized countries has increased to levels which have brought the systems close to their stability limits. Consequently, getting near to the limit of power transmission give rise to a single or a group of generators being separated from the remainder of the system, even with small disturbances. In order to avoid this risk, which leads to interruption of the system continuation, power systems should be revised. This involves determining whether DC or AC transmission lines to be added to the original system. DC lines xvi have the advantages of fast controlling the active power through them and their low cost due to the use of recent semiconductor technologies. In a traditional AC power system, the dynamics are mainly determined by the rotors of the generators, the generators' excitation systems and stabilizers, the turbine governors, and the load dynamics. The faster dynamics, lasting up to about 10 second, as well as the different forms of voltage instability involved, are of primary interest in such systems. The means available for controlling the power swings in a conventional AC system revolve mainly around the excitation system of the synchronous machines: either the voltage is raised quickly after an earth fault or the voltage setpoint is modulated in a appropriate way when power swings occur. Although indirect, these methods have the required effect in the majority of cases. The control actions are initiated mainly in dynamic situations, being used only to a minor extent to control the steady-state active power flow in the network. Recent years have seen the introduction of a new concept, named FACTS (for Flexible AC Transmission Systems), in connection with AC system analysis. HVDC, static var compensators, fast controllable phase-shifters and series compensation all play a significant role in FACTS. Although the equipment which comes under this heading has existed for many years, what is new about FACTS is that these power components and their special features are systematically evaluated with the goal of increasing the power transfer limits of AC network. An important property of the mentioned components is their ability to control the power flow, both active and reactive, in power lines or the power infeed to a certain node. The controllability can be used either to regulate the power flows in the steady- state or to damp power swings dynamically. These are features that can be exploited quite easily for HVDC lines, usually at no significant extra cost. It is the possibility of fast control of the active and reactive power that makes the HVDC line capable of stabilizing power system. However, with the HVDC converters in use today, active and reactive power cannot be controlled independently, despite the fact that appropriate control strategies would in many cases yield the desired results. The HVDC lines for stabilizing of power systems can be considered in the manner as stabilization of parallel and stabilization of non parallel. The simplest and the most obvious system configuration for illustrating the stabilizing effect of HVDC line in the stabilization of parallel power swings is that shown in figure 1. A disturbance in this very simplified system will cause the rotor angles of generators Gi and G2 to oscillate in opposition to each other. If the HVDC line restarts fast enough, it will counteract the instability during the first swing. It goes without saying that the HVDC line can be used to damp power oscillations in the transmission path X2. By modulating the active power in response to the difference in frequency of the two systems, very effective damping is achieved. Another possibility xvii would be to measure the power flow in the parallel transmission path X2to obtain the input signal for the HVDC controller. This signal normally has to be filtered before being used in order to modulate the power order and avoid unwanted action by the controller. The HVDC line damps the power oscillations in line X2, since it is exactly parallel to the path in which the power oscillations occur. G X, Figure 1. Since the active and reactive power cannot be modulated independently, the power oscillation in X2 is also affected by the reactive power modulation. Whether or not this reactive power modulation is important or not depends on the magnitude of the reactances Xi and X3 as compared with X2. The modulation or the external control signal is derived from frequency deviations of the generating units. Thus it is suitable to chose to be difference between the rotor speeds of the generators nearest to the rectifier and the inverter bus terminals. In reality, the HVDC terminals are not always connected to the AC system in the way shown in figure 1. Other system configurations also allow HVDC lines to be used for improving network stability. Load characteristics have an important influence on system stability. The modelling of loads is complicated because a typical load bus represented in stability studies is composed of a large number of devices such as fluorescent and incandescent lamps, refrigerators, heaters, compressors, motors, furnaces, and so on. In the meantime the exact composition of load is difficult to estimate. Even if the load composition were known exactly, it would be impractical to represent each individual component as there are usually millions of such components in the total load supplied by a power system. Therefore, load representation in system studies is based on a considerable amount of simplification. In power system stability and power flow studies, the common practice is to represent the composite load characteristics as seen from bulk power delivery points. The load models are traditionally classified into two broad categories: static models and dynamic models. xvui A static load model expresses the characteristics of the load at any instant of time as algebraic functions of the bus voltage magnitude and frequency at that instant. The active power component P and the reactive power component Q are considered separately. Traditionally, the voltage dependency of load characteristics has been represented by the exponential model: P = P0(V)a (2) Q = Qo(V)b (3) where P and Q are active and reactive components of the load when the bus voltage magnitude is V. The subscript o identifies the values of the respective variables at the initial operating conditions. It is well known that the transfer conductances present in the internal bus description using the classical model pose a problem in constructing a valid Lyapunov function, as well as in computing tCT in the transient stability studies. These transfer conductances are mostly due to the system loads being converted to constant impedances depending on the magnitude and the frequency of the bus voltages at that time. For the AC-DC system transient analysis section in this thesis, the loads are represented as current injections to the buses where they are connected. The effect of these is reflected at the internal buses in the form of additional bus power injections. For the transient stability analysis of pure AC system that again accomplished by the controlling unstable equilibrium points approximation, the loads are represented as current injections to the buses where they are connected, together with classical constant admittance representations and the obtained results are compared. However the response of most composite loads to voltage and frequency changes is fast and the steady-state of the response is reached very quickly. This is true at least for modest amplitudes of voltage/frequency change. The DC lines are taken into consideration as two terminals. The DC lines are also represented as the current injections to the buses where they are connected and their effect is reflected at the internal buses in the form of additional bus power injections. In this thesis, first time, a sequential integrated AC-DC (alternating current-direct current) transient stability analysis is accomplished by taking into account the variation of the amplitude of the bus voltages during transient. This variation of the bus voltages is provided by power-flow analysis of the AC-DC system with respect to the modified power, since the active power transferred through the DC line changes at each integration step. Since the reactive power absorbed by the converters is also recalculated at the each integration step, together with the amplitude of the bus voltages, the ratio of the reactive power to the active power is taken into account as variable during transient. Thus, the AC-DC transient stability analysis is accomplished considering the true value of this ratio by the sequential approach. As a result of this, the error that is made by taking constant this ratio as in the steady-state is eliminated. xix In this study, again, the applicability of the controlling unstable equilibrium points approximation to the AC-DC system transient stability analysis is shown. The post fault stable and unstable equilibrium points are changed with respect to the active power through the DC line with a new algorithm developed and thus the critical energy is modified depending on the value of this power. The results obtained from the transient stability analysis of the AC-DC system are compared with those obtained from the transient stability analysis of pure AC system. Furthermore, the transient stability analysis of the AC-DC system has been accomplished with respect to where the DC line is connected to the AC system and how far it is to the faulted AC line and the results are compared. A proportional controller is used for controlling of the active power transferred through the DC line and the variation of the stability region is studied with respect to the gain of the controller. The sample system used in this study had four generators and six buses.