EMTP yardımıyla kısa devre akımının dinamik simülasyonu

Abstract

Elektrik güç sistemlerindeki geçici olay analizlerinin, tesisteki can ve mal güvenliği, koruma cihazlarının uygun şekilde boyutlandın İması, hesap yöntemlerinin ilgi çekiciliği açısından en önemlilerinden biri kısa devre incelemeleridir. Bu inceleme bir tesisin proje aşamasından işletmesine kadar çok geniş bir alanda karşımıza çıkmaktadır. Uluslararası standartların geçmişten günümüze kadar olan süreçte sürekli olarak yenilenmesi ve varılan anlaşmalar hep kısa devre akımının en doğru şekilde hesaplanabilmesine yönelik çalışmalardır. Bu standartların hemen hepsi, kısa devre akımının çeşitli büyüklüklerini çeşitli deneysel ve ampirik formüller yardımıyla hesaplamaktadır. Bu çoğu zaman kabul edilebilir oranda doğru sonuçlar vermekle birlikte, bir tesiste bulunan generator ve motor gibi cihazların davranışını ve kısa devre akımının zamana bağlılığını ortaya koymakta oldukça yetersiz kalmaktadır. Bu standartlarda senkron generatörler ve kısa devre anında arıza yerini besleyen asenkron motorlar basitçe bir reaktansla ifade edilmekte, bu makinelerin geçici olay sırasındaki davranışları ihmal edilmektedir. Bilgisayar teknolojisinin gelişmesiyle statik hesap yöntemleri adı verilen uluslararası standartların bir alternatifi veya bir tamamlayıcısı olarak dinamik hesap yöntemleri geliştirilmiştir. Gerçekte çok daha önceden beri bilinen bu yöntem elle hesaplamanın çok güç oluşu nedeniyle uygulamada kullanılamıyordu. Ancak bilgisayarlarda geliştirilen algoritmalarla, bir tesisin ayrıntılı olarak modellenebilmesi ve dolayısıyla kısa devre gibi birçok geçici olayın, çok daha doğru bir şekilde incelenebilmesi söz konusu olmuştur. Tezde, VDE / IEC ile ANSI standartları tanıtılmış, EMTP adı verilen ve tüm dünyada büyük ölçüde kabul görmüş ve FORTRAN yazılım dilinde derlenmiş program yardımıyla üç adet şebeke modeli incelenmiştir. Bunlardan ikisinden elde edilen sonuçlar VDE / IEC standardıyla hesaplanan sonuçlarla karşılaştırılmıştır. Sonunucusu ise, Conrad R.St.Pierre tarafından geliştirilen, temelini büyük ölçüde ANSI standartlarından alan ve bu standartlara çok yakın sonuçlar veren bir bilgisayar programının, birçok kısa devre analizinde örnek şebeke modeli olarak kullanılan 20 düğümlü gözlü bir şebekeye uygulanmasıyla elde edilmiş sonuçlarının, aynı şebekenin EMTP ile modellenmesi ile elde edilen sonuçlarla kıyaslanmasından ibarettir.

In 1918, one of the most powerful tools for predicting short circuit duties in balanced and unbalanced polyphase circuits was presented by Fortesque at a conference of the American Institute of Electrical Engineers procedures described in Fortesque's paper were applicable to both analytical solutions and to ac or dc calculating boards and were widely adopted in both Europe and the U.S. during the early years of the electrical industry. However, the complexity of short circuit calculations for any practical electrical system was well beyond the scope of manual calculation, regardless of the power of Fortesque's method. In time, it became clear that a standard method of approximating certain electrical interactions would be required to augment the method of symmetrical components. The first standard methodology for calculating short circuit currents was introduced in 1929 by the German Verband Deutscher Electrotechniker (VDE). During the same year, the ac network calculating board was developed jointly by the Massachusetts Institute of Technology and the General Electric Company Short circuits studies that could be performed on the dc calculating boards of the day could be performed more accurately on the ac calculating board. In the U.S., the early 1940's and 1950's saw the development of ASA standards similar to those of the VDE in their underlying basis in the method of symmetrical components, but different in the empirical factors each standard used to approximate such phenomena as ac an dc decay during a short circuit. Over the years, these empirical factors became more important, due to the fact that electrical equipment was rated in accordance with a particular method of calculation. Fortunately, until 1987, only two principal standards for calculating short circuit duties existed. In 1987, VDE Standard 0102 was absorbed into the new IEC Standard 909. Short circuit calculations based on these procedures were - and for the most part still are - performed at fixed points in time. ANSI standards generally define these fault times as corresponding to the momentary and interrupting times of the short circuit breakers being applied. Fault current duties for protective relaying are often calculated at approximately 30 cycles to allow for the decay of motor fault current contributions that occurred prior to the operation of inverse time relays. The early, as well as the current ANSI and IEC standards are essentially based on empirical procedures which calculate short circuit duties at static points in time. Current ANSI Standards (C37.06-1979 and C37.010-1979) as well as IEC 909 rely heavily on empirical multipliers and procedures that have been greatly refined over the years. A recent example of this is the change in the equivalent XJj of groups of small motors from 0,25 to 0,20. Today, most ANSI and IEC based short circuits studies are XIV performed by digital computers, and empirical procedures for predicting machine response have been combined with analytical network reduction techniques based upon the manipulation of large matrices in their sparse form. Dynamic short circuit algorithms have been developed to overcome limitations in the accuracy of standard procedures when applied to power system with local generation, large drives, or large motor groups in tightly interconnected networks. Calculation of dc components using more mathematically rigorous methods had shown evidence of increased asymmetry in fault currents of tightly interconnected networks. In some cases these dc component levels exceeded the proportions permitted for circuit breakers built to certain national standards. The concerns that prompted the development of dynamic short circuit algorithms are therefore in good part a response to advances in electrical power technology. 1)The ratings of individual motors units and motor groups was increasing steadily. Motor short circuit contributions could therefore be expected to be significant even at remote busbars. 2) Faster protection times were increasing the significance of motor contributions. Considering that the exponential decay of motor fault current contributions will have time constants of the order of three cycles, it will be clear that the difference between three and six cycle operation is very significant. 3) The empirical factors and other recommendations relating to fault current contributions by motors to remote busbars of the distribution network would not apply to the large tightly interconnected industrial power systems as oil platforms, power station auxiliary systems, cogeneration, etc. Initial investigations showed that any attempt to use static network methods to calculate the impedance seen by each machine between its terminals and the fault point would involve substantial errors. It was, therefore, decided to use an iteration approach. The main requirements were 1) to model the machine short circuit behavior as a continuous time function so that synchronous and induction machine contributions would be calculated and summed appropriately at all required times after fault incidents; 2) to calculate the effect of the network on the machine time constants and thus remove the need to make arbitrary value judgements or use empirical factors in the calculation of fault currents contributions by the various machines, for faults at remote busbars; 3) to pay particular attention to the modelling of the unidirectional components of fault current, the decay of which is largely controlled by the network losses. The process starts by modelling the machines using appropriate reactance and standard short circuit time constant values. A first estimate of the fault currents flowing in the network is calculated, from which effective "external" network impedance values seen by each machine are calculated. XV The external impedances are then used to calculate modified machine time constants and reactances, from which an updated value of fault currents is obtained. The process is repeated until the corrections calculated are below any set tolerance. Clearly, this procedure would put heavy demand on computing resources. This was minimized by full use of sparsity techniques and is also assisted by the fact that, although the first fault current estimate may involve an acceptable and high error in real engineering terms, it is an excellent first guess for the iterative loop that converges very quickly indeed. The synchronous machine models are based on the equations below: Xj +x" ?+ 1 1 ^Xj+Xe Xd+Xe \exp(-t/rd) + 1 1 Xj+Xe X'd+Xe exp(-t/TJ') Y' 4- Y T"-5^T<1° V» i Y ^ - ~ -_ Mo xd + xe I Ar- - 1 Ldc X2 + X, -exp(-t/Ta) where Ta = (X2 + Xe)/w(Ra + Re) Induction machines can be represented similarly but are usually better modelled by run and start parameters, as illustrated in the equations below: Y" = - 1 Lac ^st +Xe exp(-t/T') where T' = [Xs + Xe + Xr(s = 1)]/ wRr(s = 0) XVI Y^=ır4ırexp(-t/T-) where Ta = [X. + Xe + Xr(s = 1)]/ w(Rs + Re) The later model was based on large-scale tests and uses mode readily available data. The typical networks and machine data, the iterative solution gets within 2% of the final value in two iterations. When this work was completed an interesting result emerged: it was found that any further fine- tuning of the machine model had a smaller effect on fault current values compared with the method of calculating the change in time constants due to the network. The short circuit algorithm does not require the same quantity of data as a stability model since it does not consider the effects of mechanical time constants and field forcing. When such factors much be considered, an option exists to model them by using a dynamic stability algorithm, which utilizes common input data. Short circuit load flow, and stability algorithms interchange data as required in a user transparent manner and can all be controlled by a common menu-driven format. At first glance the requirement to input induction motor data such as the stator reactance Xs, starting rotor resistance Xr (s=1, running rotor resistance Rr (s=0), etc., seems quite daunting. However, these are parameters that may be readily obtained in the case of low-voltage motors, or for existing installations, where data may not be readily available, the engineer has a choice: to download "typical" data from a data base. To calculate an approximate starting reactance and running resistance from the starting current and power factor; or to model the motor as an asynchronous machine. Controlling the fault contribution and decay to some realistic expectation. When one considers that the error of any solution in summation of the error of the data and the error of the method of calculation, it is obvious that any of the above approaches is likely to give more reliable results than the use of empirical factors. The most detailed synchronous machine model requires that synchronous transient, and subtransient impedance and time constant data be entered. These permits peak, asymmetrical rms, symmetrical rms, or instantaneous dc values of fault current to be calculated at any user-defined point in time. A less detailed synchronous machine representation can be used to model the time-independent nature of utility fault current sources. In this case the utility's equivalent X and R values are entered in place of the source generator Ra and Xs parameters. Asymmetrical rms values calculated by dynamic procedures are directly comparable with ANSI circuit xvii breaker momentary and interrupting duties when defined at the proper point in time. Symmetrical rms values can be compared directly with ANSI low voltage switch gear ratings when defined at 8,33 ms or one-half cycle at 60 Hz. Peak short circuit values are used for comparison with VDE-type calculations. Symmetrical short circuit duties for high voltage switchgear can be compared with those obtained through VDE-type calculations; however, they do not correlate with symmetrical duties calculate for medium voltage ANSI circuit breakers. This is explained by the fact that ANSI symmetrical duties are not defined at the moment of contact parting, whereas the dynamically calculated values apply to any selected time point. In chapter 2 the international standards as German VDE / IEC (Verband Deutscher Elektrotechniker / International Electrotechnical Commission) and American ANSI (American National Standards Institute) standard have been analysed. In chapter 3 the evolution and definition of dynamic simulation have been represented. In chapter 4 EMTP (Electromagnetic Transients Program) has been introduced and card structures used in the models represented in the thesis have been analysed in detail. In chapter 5 three network models have been analysed in order to compare EMTP results with the standards and the data files, time dependent variations of short circuit and comparison tables have been represented.