Durum geçiş matrisi yöntemi ile yüksek gerilim hava iletim hatlarının güvenilirlik değerlendirilmesi

Abstract

ÖZET Sayısal güvenilirlik değerlendirilmesi sistemin uygun çalışmasını öngörüm için önemli bir ölçüdür. Bu çalışma da enterkonnekte şebekenin iletim hatları ile ilgili güvenilirlik hesaplamaları yapılmıştır. iletim hatlarında oluşan sürekli, geçici, aşırı yüklenme ve bakım devredışı kalma arıza biçimlerine ek olarak bağlantı nedenli devredışı kalmalar incelenmiştir ve bunların çakışma olasılıkları ifade edilmiştir. İle tim hatlarının değişik yük haralarında devredışı kalma sıklığı ve süresi gibi genel olarak kabul edilen güveni lirlik ölçümleri hesaplanmıştır. Güvenilirlik hesaplamalarında kullanılan yaklaşıklık ve Markov yöntemleri anlatılmıştır. Ağır hava koşullarında oluşan arıza yüzdesinin, sistemin güvenilirlik değeri üzerindeki etkisi açıklanmıştır. Bu çalışma da durum geçiş matrisi olarak adlandırılan yeni bir güvenilirlik hesaplama yöntemi geliştirilmiştir. Sistemin gireceği durumları içeren bir durum matrisi yardımıyla durum geçiş diyagramı oluşturulmuş bununla durum geçiş matrisi elde edilmiştir. Sistemin çalışırlık ve arızalı durumlarını gösteren matrisler tanımlanmıştır. Bir sistemin güvenilirlik ölçümleri olan arıza oranı ve onarım süreleri durum geçiş matrisi, çalışırlık durumu ve arızalı durum kolon matrisleri ile hesaplanmıştır. Ayrıca sistemin gireceği durum olasılıklarının eldesi için ifadeler verilmiştir. Bağlantı işlemi nedenli devredışı kalmalar sonrası sistemdeki yapısal değişimin, farklı yük baralarındaki güvenilirlik değerinde yapmış olduğu olumlu veya olumsuz etki gösterilmiştir. Buradan sisteme eklenen her yeni tesis elemanından sonra güvenilirlik hesaplamasının gerekliliği sonucuna varılmıştır. Bursa Yöresi iletim hatları sistemi için güvenilirlik değerlendirilmesi yapılmıştır. Bölüm 6 ' da bu çalışmadan çıkarılan sonuçlar kısa bir özet halinde verilmiştir. XV

SUMMARY RELIABILITY EVALUATION OF HIGH VOLTAGE OVERHEAD TRANSMISSION LINES BY THE STATE TRANSITIONAL MATRIX METHOD Reliability is probability of a system or a network weather it will succeed its duty at a specified time duration or not. Reliability has a quantitative property. Nowadays reliability studies have been performed from computers to space-ships and balistic missiles, from public or private exchanges to automobile factories, and in other fields. An adequate supply of power is an essential ingredient in any scheme to improve the standard of living in a developing country. The annual consumption of energy per head of population is usually an accurate measure of the degree of advancement or of prosperity. The economic implications associated with power development are relatively straight forward. The determination of what is an adequate supply, however, is not an easy problem. The increasing criticality of industrial processes as well as load concentration and customer reliance on electric energy calls for a virtually continuous uninterrupted supply. It is not possible to absolutely guarantee this requirement and any attempt to do so is impractical and uneconomical. It becomes essential to evaluate where the limited available funds should be utilized to produce the maximum returns. The incremental benefits associated with equipment and configuration changes cannot be evaluated by qualitative reliability criteria. Such measures are based on simple rules of thumb and do not adequately reflect the effect of equipment performance characteristics, network configuration, system operating conditions and in fact those elements that do influence the reliability of the system. These factors can only be incorporated in the analysis through quantitative reliability technigues which xviutilize probabilistic models of the system components. One objection often raised to the utilization of probability techniques is the absence of accurate component data. It should be appreciated, however, that the results obtained are simply estimation based upon the available information. As such, they can be extremely valuable in consistently comparing alternative configurations and the relative benefits of configuration changes. The maximum contribution to the total number of customer supply interruptions arises from the overhead distribution system. This is primarily due to the environment in which these systems operate. In heavy weather conditions, the physical stresses placed upon the system components can be very much higher than those encountered under normal weather conditions. Transmission facilities are normally concentrated over a relatively small area and therefore are more liable to be totally affected by heavy weather conditions. The application of probability techniques in the quantitative evaluation of transmission and distribution schemes received its present impetus with the publication of two papers in 1964 [4,5 ]. A considerable amount of work has been done in the establishment of consistent techniques since that time. The approximate equations described in reference [5] included the weather conditions by assuming a two state model in which weather was classified into normal and heavy periods. The method presented in this thesis gives results which compare very closely with those obtainned by a Markov approach and is flexible enough to consider the occurrence or nonoccurrence of repair of components during heavy weather conditions. This work also presents a method for the quantitative evaluation of temporary and permanent load bus interruptions. Temporary outages of components can cause many load bus outages and can be a major reason of customer dissatisfaction. This aspect is extended to include the two state weather environment. Maintenance of components is another event which can result in load bus interruptions. This study presents some matrices to represent the occurrence of this event. A useful approach in the study of systems involving a large number of components is that of failure mode and effect analysis. This technique has been used in this thesis and requires a thorough knowledge of the operation of the xviisystem and the effect of component failures on load buses The recognition of failure modes and their cause effect relationships is a valuable tool in improving customer servise continuity. If the reliability predictions do not meet a predetermined goal, a logical improvement procedure is to look for ways to mitigate the causes underlying the events that contributed most to failure. In the fourth part of this study, a new method has been developed for evaluation of power system reliability. This method has been named as the state-transitional matrix. The state matrix [ K] contains all states of the system and the state-transitional diagram with the aid of this [ K] matrix has been obtained. The state matrix [ K] and the state-transitional diagram can be written as follows for a two component system in the normal weather condition. [K] = 1 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 = [K] K] Elements dj,, d2 2, d3 3 / d4 4 of the state- transitional diagram are found as explained in the 4.2.1 paragraph of this study. Thus [ D], the state-transitional matrix can be expressed as XVXll~~ A. j `T A. 2 `? î x, [D] M2 Mi -fi2 -X 2 «1 -JU i -X ; Xi Mi M 2 -M ı -M 2 The steady state probabilities have been found with the aid of the state-transitional matrix. New [D.] matrix has been obtained by removing the first yi' column and ith row elements of [ D], the state-transitional matrix,,k. if y. i Kıl*-1* is evaluated as; P. = i H-i then ith probability of state D. 1 (-1) yıj 2k+l n i=ı (i = 1, 2, n and k = number of component) The metrices containing the operable and failure states of system have been defined as [ a] and [ q], respectively. As explained in the paragraph 4.3 of this study the operable state [ T], the frequency of operable state [ F], failure state [ L] and frequency of failure state [ G] matrices have been obtained with the aid of [ a], [ q] and [ D] matrices. The failure rate Xs and repair time rs of the series system can be written as follows with the aid of the state-transitional matrix. Xs=(-1) 2n+l Tand r.= (-l) 2n+i JL_ Fwhere n; the number of components,. The failure rate Xp and repair time rp of the parallel system are given as; xix»`+? G'`+> LApart from these, in this study, the connection failure mode has been added to the failure modes of a component. Thus, addition to the load bus failure modes have appeared. The positive and negative effects of the connection procedure on the reliability indices of developing systems have been established. Following an additional connection made at the transmission lines which comprises a part of an electrical installation, a change has been observed at the system's probabla failures which are found by minimal cut method [2]. Due to this change, there has been found change in the reliability indices of each load bus of the system. Following a connection incidence, the change in the reliability indices of a load bus at the system has been given below for the development of the sample system of figure 4.11 to the system showned in figure 4.12. When more than one connection to the system is programmed, it has been observed that it is necessary to make load flow calculations for the new planned system. The results obtained by using the matrices developed in this thesis have been continually compared with those obtained by a more sophisticated Markov approach. Within the bounds of distributional assumptions, all the applications considered can be analysed by the method of the state-transitional matrix. xx