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Elektrik Enerji İletim Şebekelerinin Optimal Genişletme Planlaması

Elektrik Enerji İletim Şebekelerinin Optimal Genişletme Planlaması

##### Dosyalar

##### Tarih

1994

##### Yazarlar

Sohtaoğlu, Nazif Hülagü

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Elektrik enerji iletim sistemi genişletme planlaması problemi» elektrik enerji sistemlerine ilişkin planlama çalışmaları içerisinde çözümü en zor olan problemlerden birisidir. Enerji iletim sistemi genişletme planlaması algoritmalarını geliştirmek üzere yapılan çalışmalarda genişletme planlaması problemine bir matematik optimizasyon problemi olarak yaklaşılarak, eşitlik ve/veya eşit sizliklerden oluşan bir kısıtlama kümesinin etkisi al tında bir amaç fonksiyonunun optimizasyonunu sağlamak yoluna gidilmiştir. Bu şekilde günümüze kadar önerilen yöntemlerin çok az bir bölümü dışında diğerleri, deneysel evrelerinin ötesinde geliştirilememiş veya gerçek planlama çalışmalarına uygulanamamıştır. Bu çalışmada önerilen yöntemde, daha önce yapılan çalışmalarda saptanan zorlamalardan kaçınılmış, teknik, ekonomik ve güvenilir şebeke yapılarının elde edilmesine yönelik olarak izlenen adımlar ile uygulamadaki planlama çalışmaları arasında uyum bulunmasına özen gösterilmiştir. Özellikle, başlangıçta enerji sisteminden ayrık bara bulunması durumunda ortaya çıkan güçlüklerin ortadan kaldırılması amaçlanmıştır. Önerilen yönteme göre, başlangıç şebeke yapısı tasarlanmakta ve bu yapıdan hareketle bu çalışmada tanımlanan etkinlik endeksi kullanılarak, etkin olmayan iletim hatları devreden çıkarılmaktadır. Bunun sonucun da, normal işletme koşulları altında optimal şebeke yapısı belirlenmektedir. Sürekli hal işletme koşullarında belirlenen optimal şebeke yapısı üzerinde açma analizi gerçekleştirilmektedir. Açma analizi sonuçlarına bağlı olarak, nominal şebeke yapısı aşırı yüklenmeler açısından kontrol edilmekte ve aşırı yüklenmenin mevcut olduğu durumlarda, aşırı yüklenmeleri ortadan kaldıracak en etkin iletim devresi eklemeleri bulunmaktadır. Bu işlem, geliştirilen şebeke yapısındaki hiçbir iletim devresi üzerinde aşırı yüklenme saptanmayıncaya kadar yinelenmekte ve sonuçta açmalı işletme koşullarında optimal şebeke yapısına ulaşılmaktadır. Çalışmada bütün bu işlemleri gerçekleştirecek bir bilgisayar algoritması verilmiş ve yöntemin geçerliliği, yayınlarda oldukça sık karşılaşılan Test Sistem üzerinde uygulama ile kanıtlanmıştır. Ayrıca, Türkiye Batı Anadolu Enter könekte Sistemi üzerinde gerçek verilere dayanarak yapılan uygulamalar sunulmuştur.

Dependence on electrical energy in all facets of life has made power system planning an important and critical tool in achieving higher living standards in all countries. Besides great social and economic significance of having continuous availability of power supplies, power systems need heavy financial investment. In all count ries investment in power systems constitute the major part of the total investments of the nation. One of the most significant problems confronting electric utility system planners is the problem of se lecting the best expansion alternative for their system. In general, this involves the specification of where, when, and in what capacity new electric generating plants and major transmission lines should be built. Today, every electric utility company performs both short-term and long-term planning. Here, the short range planning is defined as the analytical process that includes an assessment of the near future by evaluating alternative courses of action against desired objectives with the selection of a recommended course of action for the time period requiring immediate commitments. Where as the long-range planning is defined as the analytical process that includes an assessment of the future by evaluating alternative courses of action against desired objectives with the selection of a recommended course of action extending beyond the time period requiring imme diate commitments. The necessity for long-range system planning becomes more pressing than in the past because of the very fast changes in technology, fuel availabi lity, and environmental constraints. It enables plan ners to explore various alternatives in supplying elect rical energy and provides them with a guide for making short-range decisions and actions. It must be quantita tive as well as qualitative. In general, the long-range planning may cover 15-20 years into the future. However, the planning horizons are known to be 15-30 years for some power plant additions. xix - The objective of power system planning is to op timize the facilities necessary to provide an adequate electrical energy supply at the lowest reasonable cost. In general, the power system planning activities can be classified as CI D synthesis, that is, the development of initial plans to study the system; C2D analysis, that is technical evaluation of the system operation in terms of reserve requirements, load flow, and stability, under simulated conditions; and C33 optimization, that is, eco nomic evaluation of alternatives to determine the mini mum-cost alternative. The power system planning may include the following activities: - Load forecasting, - Generation system planning, - Transmission system planning, - Subtransmission system planning, - Distribution system planning, - Öper ati ons pi anni ng, - Fuel supply planning, - Environmental planning, - Fi nanci al pi anni ng, - Research & development planning. The forecasting of load increases and system re action to these increases is essential to the power sys tem planning process. In general, the long-range fore casting has a time horizon of 15-20 years, whereas the time horizon of short-range forecasting is somewhere between 1 and 5 years. The basic function of the load forecasting is to analyze the raw historical load data to develop models of peak demand for capacity planning and of energy for capacity planning and of energy for production costing. The risk of planning based on too low load projections is poor system reliability, whereas the risk of planning based on too high load projections is an uneconomical operation. Generation planning helps to identify the techno logy, size, the timing of the next generating plants to be added to the power system in order to ensure that adequate generation capacity is available to meet future demand for electricity and that the future cost of power generation is economical. The objective is the optimum generation planning that combines the aforementioned functions into one to develop economically optimum gene ration expansion patterns year -by-year over the planning horizon. Transmission planning is closely related to the generation planning. The objectives of transmission system planning is to develop year -by-year plans for the transmission system based on existing systems, future load and generation scenarios, right-of-way constraints, cost of construction, line capabilities, and reliability criteria. xx - The purpose of transmission system planning is to determine the timing and type of new transmission faci lities required in order to provide adequate transmissi on network capability to cope with the future generating capacity additions and power flow requirements. Trans mission system planning process may be repeated, with diminishing detail, for each year of a long-range C 15-20 year D planning horizon. The key objective is to minimi ze the long-range capital and operating costs involved in providing an adequate level of system reliability, with due consideration of environmental and other rele vant issues. Transmission planning may include not only existing but also new service areas. The starting point of the planning procedure is to develop load forecasts in terms of annual peak demand for the entire system, as well as for each region and each major present and futu re substation, and then finding specific alternatives that satisfy the new load conditions. The system per formance is tested under steady-state and contingency conditions. The transmission network expansion planning is a complicated mathematical optimization problem. The comp lication of the problem arises mainly from the large number of problem variables where a multitude of techni cal and economical constraints are to be considered. The general form of network expansion problem can be stated as follows: Given - load-generation patterns at target year, - existing network configuration, - all possible routes Clength and right-of -wayD, - available line types and the corresponding cost estimate the optimum network which feeds the loads with the required quality degree and realizes a prespecified reliability level. The solution tool for such problems is the stan dard mathematical programming techniques. The general form of these techniques are: Optimize: FCx,x,...,x ) ı 2 n subject to the constraints: G. Cx,x,...,x3>,. J I J where n. ; the set of buses directly connected to bus v i. P. ; the net active power injected at bus i. P. ; the active power generated at bus i. P. ; the active power consumed at bus i. B.. ; the susceptance of the line i - j connected l-j between buses i and j. <5. ; the voltage phase angle of bus i. n ; total number of network buses. This model contains branch susceptances as basic design variables, whose main properties are the consequ ence of their discrete, time dependent, stochastic cha racter, constrained by right-of-way limits, making even simple cases to become a complex computational problem. In addition, real transmission networks imply a high di mensionality of the problem, so that the use of simpli fied, but reliable methods for its solution is an impe rative. As far as optimization methods used for large transmission network expansion planning, the network and linear programming were most frequently applied. A simple transmission network expansion planning method especially suited for comparative studies of al ternate generation and transmission expansion schedules, has been presented in this thesis. The steps in this al gorithm follow the same logical steps that are carried out in practice during the process of network expansion planning activities. In the developed method, transmission network ex pansion planning problem is solved in three stages. In the first stage, DC power flow model is used to obtain power flow for all the possible as well as the existing xxin - transmission lines. In -the second stage, an optimizati on based tool is to be used to remove the 'worst* set of lines. The two stages may be repeated in an iterative manner until the nominal network configuration is achie ved. Reliability of the nominal network configuration is examined in a separate stage after finding the least cost configuration satisfying quality constraints. In the final stage, a new set of lines are added to realise reliability level constraints. The process is initialised by considering all possible right-of-ways with the maximum allowable number of parallel transmission lines for each right-of-way. For the determination of the optimal network configura tion under steady state conditions, the cost function was obtained based on initial network configuration de signed according to proposed transmission line additions The objective is to minimize the present worth value of the capital investment costs associated with the system expansion over the planning horizon. The cost function to be minimized is " J D. min Z = > D.. F.. C 33 where a ; the set of proposed transmission line addi tions in initial network configuration. F.. ; the present value of capital investment cost 3 for proposed line i-j. D.. ; a binary variable can be introduced for i. 1 each proposed line i - j to denote whether it is selected or not in the horizon year. {1, if line i-j is O, if line i-j is selected, not selected. Problems are being faced during the transmission network expansion planning studies in which bus or buses frequently disconnected from the existing network con figuration, evolve. In this study, to avoid this prob lems a measure has been identified to simplfy the compu tations and reduce the computation time. This measure called the effectiveness index has been introduced to the model with the intention of the removal of ineffec tive transmission lines in the initial network configu ration and obtaining the nominal network configuration. The effectiveness index defined in regard to pro posed transmission lines at the initial network configu ration can be stated as follows: - xxiv - where EI v J L.. K.. PC. <. J «. J L.. K.. PC. v J ı J C33 «. J K. ij PC. >. J t- J the length of line i - j, km. the capital investment cost per km of add ing new transmission lines to a new right- of-way. the power transmission limit of line i - j. the active power flow through line i - j from bus i and to bus j. The cost function, given by equation 1 2D, includ ing effect of interest and inflation rates over the planning time horizon can be taken into consideration as nun = 2 D. 1- J 1+i 1+r N F.. C4D where i ; nominal interest rate, r ; nominal inflation rate. n ; number of the time intervals in planning ho rizon. In the same manner, the effectiveness index given by equation C3D can be used as follows; EI ı J 1+i 1+r N L.. K.. PC. v J P.. t J 1+i 1+r %n L.. K.. PC <. J P.. C5D The cost function given by equations C2D or C 4D contains the capital cost of proposed transmission li nes represented actually in its discrete form and can be solved subject to the constraint equations contain Kirc- hhoff *s Laws CKCL and KVLD in addition to the transmis sion line loading constraint and maximum allowable num ber of transmission lines per right-of-way regarding constraint. - XXV - S P.. = P., i= 4,2,...,r, C63 Z. i. j t 2x.. P.. = O, 1= 1,2,...,l C73 \ Equation C 63 represents the power balance at each bus, the KCL, while equation C 73 represents the basic loop equation, the KVL. Since both Kirchoff 's law are modelled as constraints the solution of the problem is equivalent to the DC model. The power flow on any transmission line must be within the specified limits of that line i - j, _prnax £ p ^ pwax c 83 >- j i- j i j or IP.. I < P.'., i= i,2,...,r, ; turn j<=D. The number of transmission lines to be added to each right-of-way can be constrained to be below a cer tain number. n.. < n.. C 93 >- J >- J where Q. ; the set of buses directly connected to bus i. P.. ; the active power flow between buses i and j- P. ; the net active power injected at bus i. A ; the set of lines belonging to the basic loop L. x., : the reactance of line i - j connected betwe- i. i en buses i and j. P.', ; the power transmission limit of line i - j. n.. ; number of lines in any right-of-way i - j. n. '. ; maximum allowable number of lines in any ^J right-of-way i-j The effect of line outages on the active power flows of a system is analyzed using the DC power flow model. The analysis of contingencies, particularly line outages, is important to utilities in both operation and planning. If the potential outage of a line would result in the overload of another line, then the system is said - xxvi - to be vulnerable, a condition which should be quickly detected for possible corrective rescheduling actions in operation or for system redesign in planning. Depending on the results of the contingency anal ysis, the expansion of the nominal network configuration can be necessary. Transmission line contingencies are ranked accor ding to their expected severity. An intuitively appeal ing index for quantifying the severity of transmission line contingencies with respect to line overloads may be defined in terms of the active power flow performance index. The PICMW measures system difficulty in terms of line overloads in the network configuration. TO PICMW = ? I wi L = i Sot jpkj,2a _mox I CI OD where m ; the number of lines in the network. P ; in the case of the outage of the transmis sion line, k, power flow through line L. YCtfxa P ; the power transmission limit of line I. W ; real, non-negative weighting coefficient for line I may be used to reflect the importance tance of some lines and is normally taken to be unity under the assumption that all lines are weighted equally. en ; the order of the performance index C The va lue of ot has been taken as S so that the masking effect is reduced, thus providing better results?. The purpose of the contingency selection method is to efficiently identfy the contingencies. This may be achieved by predicting the values of the performance in dex for each line outage and subsequently ranking the contingencies from the most Important C largest value of the performance index} to the least important C small est value of the performance indexD. The criteria used in the addition of new trans mission lines to the nominal network configuration is exclusion of the sum of the maximum overloads for all lines by the addition of transmission line with minimum cost. This procedure is repeated until suggested relia bility constraint is achieved and in conclusion, under contingency state, optimal network configuration is de termined. - XXVI i - The numerical applications of the proposed method have been realized over the Test System which frequently appears in literature and the Turkish West Anatolian In terconnected System. In this thesis, the proposed approach for the po wer transmission network expansion planning especially through the incomplexity of the established model, can be subject to various developments in future network ex pansion planning studies.

Dependence on electrical energy in all facets of life has made power system planning an important and critical tool in achieving higher living standards in all countries. Besides great social and economic significance of having continuous availability of power supplies, power systems need heavy financial investment. In all count ries investment in power systems constitute the major part of the total investments of the nation. One of the most significant problems confronting electric utility system planners is the problem of se lecting the best expansion alternative for their system. In general, this involves the specification of where, when, and in what capacity new electric generating plants and major transmission lines should be built. Today, every electric utility company performs both short-term and long-term planning. Here, the short range planning is defined as the analytical process that includes an assessment of the near future by evaluating alternative courses of action against desired objectives with the selection of a recommended course of action for the time period requiring immediate commitments. Where as the long-range planning is defined as the analytical process that includes an assessment of the future by evaluating alternative courses of action against desired objectives with the selection of a recommended course of action extending beyond the time period requiring imme diate commitments. The necessity for long-range system planning becomes more pressing than in the past because of the very fast changes in technology, fuel availabi lity, and environmental constraints. It enables plan ners to explore various alternatives in supplying elect rical energy and provides them with a guide for making short-range decisions and actions. It must be quantita tive as well as qualitative. In general, the long-range planning may cover 15-20 years into the future. However, the planning horizons are known to be 15-30 years for some power plant additions. xix - The objective of power system planning is to op timize the facilities necessary to provide an adequate electrical energy supply at the lowest reasonable cost. In general, the power system planning activities can be classified as CI D synthesis, that is, the development of initial plans to study the system; C2D analysis, that is technical evaluation of the system operation in terms of reserve requirements, load flow, and stability, under simulated conditions; and C33 optimization, that is, eco nomic evaluation of alternatives to determine the mini mum-cost alternative. The power system planning may include the following activities: - Load forecasting, - Generation system planning, - Transmission system planning, - Subtransmission system planning, - Distribution system planning, - Öper ati ons pi anni ng, - Fuel supply planning, - Environmental planning, - Fi nanci al pi anni ng, - Research & development planning. The forecasting of load increases and system re action to these increases is essential to the power sys tem planning process. In general, the long-range fore casting has a time horizon of 15-20 years, whereas the time horizon of short-range forecasting is somewhere between 1 and 5 years. The basic function of the load forecasting is to analyze the raw historical load data to develop models of peak demand for capacity planning and of energy for capacity planning and of energy for production costing. The risk of planning based on too low load projections is poor system reliability, whereas the risk of planning based on too high load projections is an uneconomical operation. Generation planning helps to identify the techno logy, size, the timing of the next generating plants to be added to the power system in order to ensure that adequate generation capacity is available to meet future demand for electricity and that the future cost of power generation is economical. The objective is the optimum generation planning that combines the aforementioned functions into one to develop economically optimum gene ration expansion patterns year -by-year over the planning horizon. Transmission planning is closely related to the generation planning. The objectives of transmission system planning is to develop year -by-year plans for the transmission system based on existing systems, future load and generation scenarios, right-of-way constraints, cost of construction, line capabilities, and reliability criteria. xx - The purpose of transmission system planning is to determine the timing and type of new transmission faci lities required in order to provide adequate transmissi on network capability to cope with the future generating capacity additions and power flow requirements. Trans mission system planning process may be repeated, with diminishing detail, for each year of a long-range C 15-20 year D planning horizon. The key objective is to minimi ze the long-range capital and operating costs involved in providing an adequate level of system reliability, with due consideration of environmental and other rele vant issues. Transmission planning may include not only existing but also new service areas. The starting point of the planning procedure is to develop load forecasts in terms of annual peak demand for the entire system, as well as for each region and each major present and futu re substation, and then finding specific alternatives that satisfy the new load conditions. The system per formance is tested under steady-state and contingency conditions. The transmission network expansion planning is a complicated mathematical optimization problem. The comp lication of the problem arises mainly from the large number of problem variables where a multitude of techni cal and economical constraints are to be considered. The general form of network expansion problem can be stated as follows: Given - load-generation patterns at target year, - existing network configuration, - all possible routes Clength and right-of -wayD, - available line types and the corresponding cost estimate the optimum network which feeds the loads with the required quality degree and realizes a prespecified reliability level. The solution tool for such problems is the stan dard mathematical programming techniques. The general form of these techniques are: Optimize: FCx,x,...,x ) ı 2 n subject to the constraints: G. Cx,x,...,x3>,. J I J where n. ; the set of buses directly connected to bus v i. P. ; the net active power injected at bus i. P. ; the active power generated at bus i. P. ; the active power consumed at bus i. B.. ; the susceptance of the line i - j connected l-j between buses i and j. <5. ; the voltage phase angle of bus i. n ; total number of network buses. This model contains branch susceptances as basic design variables, whose main properties are the consequ ence of their discrete, time dependent, stochastic cha racter, constrained by right-of-way limits, making even simple cases to become a complex computational problem. In addition, real transmission networks imply a high di mensionality of the problem, so that the use of simpli fied, but reliable methods for its solution is an impe rative. As far as optimization methods used for large transmission network expansion planning, the network and linear programming were most frequently applied. A simple transmission network expansion planning method especially suited for comparative studies of al ternate generation and transmission expansion schedules, has been presented in this thesis. The steps in this al gorithm follow the same logical steps that are carried out in practice during the process of network expansion planning activities. In the developed method, transmission network ex pansion planning problem is solved in three stages. In the first stage, DC power flow model is used to obtain power flow for all the possible as well as the existing xxin - transmission lines. In -the second stage, an optimizati on based tool is to be used to remove the 'worst* set of lines. The two stages may be repeated in an iterative manner until the nominal network configuration is achie ved. Reliability of the nominal network configuration is examined in a separate stage after finding the least cost configuration satisfying quality constraints. In the final stage, a new set of lines are added to realise reliability level constraints. The process is initialised by considering all possible right-of-ways with the maximum allowable number of parallel transmission lines for each right-of-way. For the determination of the optimal network configura tion under steady state conditions, the cost function was obtained based on initial network configuration de signed according to proposed transmission line additions The objective is to minimize the present worth value of the capital investment costs associated with the system expansion over the planning horizon. The cost function to be minimized is " J D. min Z = > D.. F.. C 33 where a ; the set of proposed transmission line addi tions in initial network configuration. F.. ; the present value of capital investment cost 3 for proposed line i-j. D.. ; a binary variable can be introduced for i. 1 each proposed line i - j to denote whether it is selected or not in the horizon year. {1, if line i-j is O, if line i-j is selected, not selected. Problems are being faced during the transmission network expansion planning studies in which bus or buses frequently disconnected from the existing network con figuration, evolve. In this study, to avoid this prob lems a measure has been identified to simplfy the compu tations and reduce the computation time. This measure called the effectiveness index has been introduced to the model with the intention of the removal of ineffec tive transmission lines in the initial network configu ration and obtaining the nominal network configuration. The effectiveness index defined in regard to pro posed transmission lines at the initial network configu ration can be stated as follows: - xxiv - where EI v J L.. K.. PC. <. J «. J L.. K.. PC. v J ı J C33 «. J K. ij PC. >. J t- J the length of line i - j, km. the capital investment cost per km of add ing new transmission lines to a new right- of-way. the power transmission limit of line i - j. the active power flow through line i - j from bus i and to bus j. The cost function, given by equation 1 2D, includ ing effect of interest and inflation rates over the planning time horizon can be taken into consideration as nun = 2 D. 1- J 1+i 1+r N F.. C4D where i ; nominal interest rate, r ; nominal inflation rate. n ; number of the time intervals in planning ho rizon. In the same manner, the effectiveness index given by equation C3D can be used as follows; EI ı J 1+i 1+r N L.. K.. PC. v J P.. t J 1+i 1+r %n L.. K.. PC <. J P.. C5D The cost function given by equations C2D or C 4D contains the capital cost of proposed transmission li nes represented actually in its discrete form and can be solved subject to the constraint equations contain Kirc- hhoff *s Laws CKCL and KVLD in addition to the transmis sion line loading constraint and maximum allowable num ber of transmission lines per right-of-way regarding constraint. - XXV - S P.. = P., i= 4,2,...,r, C63 Z. i. j t 2x.. P.. = O, 1= 1,2,...,l C73 \ Equation C 63 represents the power balance at each bus, the KCL, while equation C 73 represents the basic loop equation, the KVL. Since both Kirchoff 's law are modelled as constraints the solution of the problem is equivalent to the DC model. The power flow on any transmission line must be within the specified limits of that line i - j, _prnax £ p ^ pwax c 83 >- j i- j i j or IP.. I < P.'., i= i,2,...,r, ; turn j<=D. The number of transmission lines to be added to each right-of-way can be constrained to be below a cer tain number. n.. < n.. C 93 >- J >- J where Q. ; the set of buses directly connected to bus i. P.. ; the active power flow between buses i and j- P. ; the net active power injected at bus i. A ; the set of lines belonging to the basic loop L. x., : the reactance of line i - j connected betwe- i. i en buses i and j. P.', ; the power transmission limit of line i - j. n.. ; number of lines in any right-of-way i - j. n. '. ; maximum allowable number of lines in any ^J right-of-way i-j The effect of line outages on the active power flows of a system is analyzed using the DC power flow model. The analysis of contingencies, particularly line outages, is important to utilities in both operation and planning. If the potential outage of a line would result in the overload of another line, then the system is said - xxvi - to be vulnerable, a condition which should be quickly detected for possible corrective rescheduling actions in operation or for system redesign in planning. Depending on the results of the contingency anal ysis, the expansion of the nominal network configuration can be necessary. Transmission line contingencies are ranked accor ding to their expected severity. An intuitively appeal ing index for quantifying the severity of transmission line contingencies with respect to line overloads may be defined in terms of the active power flow performance index. The PICMW measures system difficulty in terms of line overloads in the network configuration. TO PICMW = ? I wi L = i Sot jpkj,2a _mox I CI OD where m ; the number of lines in the network. P ; in the case of the outage of the transmis sion line, k, power flow through line L. YCtfxa P ; the power transmission limit of line I. W ; real, non-negative weighting coefficient for line I may be used to reflect the importance tance of some lines and is normally taken to be unity under the assumption that all lines are weighted equally. en ; the order of the performance index C The va lue of ot has been taken as S so that the masking effect is reduced, thus providing better results?. The purpose of the contingency selection method is to efficiently identfy the contingencies. This may be achieved by predicting the values of the performance in dex for each line outage and subsequently ranking the contingencies from the most Important C largest value of the performance index} to the least important C small est value of the performance indexD. The criteria used in the addition of new trans mission lines to the nominal network configuration is exclusion of the sum of the maximum overloads for all lines by the addition of transmission line with minimum cost. This procedure is repeated until suggested relia bility constraint is achieved and in conclusion, under contingency state, optimal network configuration is de termined. - XXVI i - The numerical applications of the proposed method have been realized over the Test System which frequently appears in literature and the Turkish West Anatolian In terconnected System. In this thesis, the proposed approach for the po wer transmission network expansion planning especially through the incomplexity of the established model, can be subject to various developments in future network ex pansion planning studies.

##### Açıklama

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1994

Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1994

##### Anahtar kelimeler

Elektrik enerjisi,
Enerji iletim sistemleri,
Planlama,
Electrical energy,
Energy transmission systems,
Planning