Kablolu Enerji Dağıtım Sistemlerinde Maliyet Minimizasyonunna Ait Yeni Bir Yaklaşım

Abstract

Bu tez çalışmasında, yerleşme yoğunluğu yüksek şehir bölgelerine ait kablolu enerji dağıtım sistemleri için yeni yaklaşımlar geliştirilmiştir. Önce sistemi meydana getiren alçak gerilim fiderleri, orta gerilim fiderleri, dağıtım transformatörleri ve kesici, ayırıcı vb. gibi elemanlardan meydana gelen dağıtım posta elemanlarına ait güç kayıpları ve buna bağlı olarak yıllık enerji kayıpları belirlenmiştir. Daha sonra, bugünkü değer analizi formülasyonuna göre her bir elemana ait ilk yatırım maliyetleri ve daha önce çıkarılan yıllık enerji kayıpları dikkate alınarak belirlenen işletme kayıpları ve bunların toplamlarından da toplam maliyet ifadeleri elde edilmiştir. Elde edilen işletme maliyeti ve toplam maliyet ifadelerindeki yük, kayıp faktörü ve enerji maliyetleri yıllık eşdeğer üniform büyüme oranları kullanılarak sabit, Lineer ve nonlineer modeller ile modellenmiş ve aralarındaki yirmiyedi ayrı durum için toplam işareti altında bu durumlara ait seri açılım toplamlarının tek ifade ile elde edilmesi gerçekleştirilmiştir. Ayrıca alçak gerilim ve orta gerilim fiderleri ile dağıtım transformatörleri için regresyon analizi kullanılarak çeşitli orjinal ilişkiler elde edilmiş ve bunların daha önce çıkarılan maliyet ifadelerinde yerleştirilmesi ile yeni yaklaşık maliyet ifadeleri bulun¬ muştur. Elde edilen son ifadeler kullanılarak, verilen bir yük için optimum alçak ve orta gerilim fider kesiti ile optimum norm transformatör gücünü veren yeni orjinal ifadeler elde edilmiştir. Son olarak, elde edilen yaklaşık maliyet ifadelerinin Nonlineer Programlama Tekniği ile kullanılması gerçekleştirilmiştir. Çalışmada, ülkemizde mevcut sistemlerde kullanılan gerçek sayısal değerler göz önünde bulundurularak hesaplamalar yapılmış ve sonuçlar grafik olarak verilmiştir.

Energy distribution systems have developed in the recent years, due to increasing population, new-technologies and load demand. it is clear that these systems have more complex structure and expensive cost. The most problem is planning of the distribution systems. in present planning is done more sensitive using various statistical methods and computer - aided approches depending on the new technology developments. The basis aim for the planning studiesconcernsload increase in the future and the factors affecting it. If a proper planning is not done, the most reason is that the increase in load can not be deter- mined and operating losses are not considered. As known, electrical energy generation and consumption amount mean whether a country is developed ör not. Similarly, great network losses mean that well - designed system and planning are not exist. If the system is non - efficient, i.e, annual load increase can not be determined, system components must be changed. Othervvise, operating costs increase and national economy is aîîected from this. Especially, from the point of our country, operating costs are very important. This study is applicable in terms of operation of the existing system and planning of new systems. First total cost equations to be used for long period planning are derived, considering energy losses vvhich are very important for planning of distribution transformers, low voltage and medium voltage feeders. Present value of total cost expression for low voltage feeders would be obtained as: PWTFC = IICF. CCR.USPVVF c N + 60, 33. r. I.LAF.LLF. YSm^LF. EC.q" (1) 0 n=1 n Present value of total cost expression tor medium voitage feeders can also be stated as: PVVTFC =IICF.CCR. USPWF + c c O Öp e N £i|r. r.I.LAF. LLF. 10 Y Sm2. LF.EC.q (2) V * nf,. " - n And, present value of total cost equati-on for distribution trans- formers can be given in the follovving from. Where: PWTDTC = IICDT. mt. CCR. USPVVF. v,t c N + NLT. LAF. NLLDT.Y EC.q" v'' n=1 n N. (3) + 8760. LAF. LLDT Y TYF. LF. EC. q" v.t _. n n n n-1 2 N 9 + LRLDT.VCC.CCR.TC Y TYF v'1 n=ı PWTDTC : Present vvorth of total distribution transformer's cost (subscripts v and t denote rated transformer povver number and primary voitage, respectively),$ IICDT : Initial investment cost of (similar) distribution transformer, $ mt : A coefficient dealing with distribution trans- formers, including as maintenance cost ete. (mt=1+sg) NLT : "No-load° operation time of distribution trans¬ former NLLDT : "No-load" Loss of similar transformer v,t LLDT : "Load° Loss of similar transformer V>t TLF= Sm/RTV RTV : Rated transformer value, kVA PRF : Peak responsibility factor ıx NLRLDT : 'No-load" reactive loss of distribution transformer, kVAr LRLDT : "Load° reactive loss of distribution transformer, kVAr FCC : Fixed compensaîor cost placed on the low voltage side of distribution transformer, $/kVAr VCC : Variable Compensator cost placed on the low voltage side of distribution transformer, $/kVAr PVVTFC : Present worth of total feeder cost (subscript c denotes cross sectional area-number) C = 1,..., CN (where CN is the last volue in the list) CCR : Carrying change rate, including vveighted cost of investment, depreciation, tax and insurance for three distribution components mentioned above, p.u. USPVVF : Uniform Series Present Worth Factor r : Alternating current resistance of the cable with n th number l : feeder length LAF : Loss Allovvance Factor LLF : Load Location Factor Smn : Maximum apparent power for nth year, kVA (MVA, if medium voltage considered) LF : Loss Factor for nth year n EC : Energy cost for nth year qn = 1/(1+f)-n f : Discount rate V : Primary Voltage, kV v : Number of primary voltage (v=1,.., VS; where VS is primary voltage number used) t : t-numbered rated transformer power (t=1,..., TS; where TS is total of rated transformer powers) x in this study, the terms-C, LF and EC shown, in "summing notation" represent constant, loss factor and energy cost, respectively. in first case, load is represented by constant model: S =S = S = constant (4) n o in Second case, load is represented by nonlinear model: S =So. (1 + by)""1 (5) n or defining 1 +by = b S =So.b"~1 (6) n 1 in third case, load represented by linear model: S =S [1 + (n-1)by] (7) n o Similarly, three case is valid for loss factor First case (constant) is: LF =LF =LF = constant (8) n o Second case (nonlinear model) is: LF =LF (1 + bk)"~1 (9) n o or defining 1+bk = b2 LF =LF.b"~1 (10) n o 2 Third case (linear model) is: LF =LF [1 + (n-1)bk] (11) n o Finally energy cost is also defined by the similar terminology. First case (constant) represents constant model. EC =EC =EC = constant (12) n o Second case (nonlinear model) is: EC = EC (1+be)""1 (13) n o or, defining 1 +be = b EC = EC.b ""1 (14) n 03 Third case (linear model) is EC =EC [1 + (n-1)be] (15) n o XI VVhere: S,LF,EC :"First year - end" value of load, load factor and energy cost, respectively. by :AnnuaI equivalent increase in load, p.u. bk :Annual equivalent increase in loss factor, p.u. be :Annual equivalent increase in energy cost. For low voltage and medium voltage distribution feeders and distribution transformers, initial costs of these components are ob- tained using regression analysis in the follovving form: For Iv/mv feeders: initial cost depending on cross sectional area of conductor For distribution transformers: initial cost depending on transformer's rated power For Iv/mv feeders: a relationship between conductor's resistance and cross sectional are of conductor For distribution transformers: a relationship betvveen no-load los- ses and rated power For substations: initial cost depending on operating voltage. Later, using the equaitions derived in chapter 3, approximate expressions are given, considering several loadings, as follovvs: For distribution transformer: cost versus rated povver Iv/mv distribution feeders: cost versus conductor's cross section¬ al area For mv cables: cost versus operating voltage. in this thesis for a given load value, the follovving parameters can be originally found with the aid of previous mathematica! models. These parameters are below: optimum value of iv feeders' cross sectional area optimum value of mv feeders' cross sectional area optimum value of distribution transformer Also, considering ali constraints (such as f(ö)-q, voltage drop -q and maximum loading capability) and several loadings, cost expres- sions of the system components mentioned above are obtained using "Nonlinear Optimization Technique." Ali expressions obtained in the thesis are depended on load¬ ing, loss factor and annual increase in the energy cost, therefore these xıı expressions are valid for both the existing systems and the future applications to be planned. The computation results give optimal Iv conductor's cross sec tional area per unit length, optimal mv feeder's cross sectional area depending on system voltage and their costs. Similarly, optimal transformer power per received load and its cost are also given. With the aid of total costs of energy distribution system which are obtained using cost expressions defined in the thesis, a relation ship is given among total cost, cross sectional area and system volt age. All expressions and definitions are in basis structure in terms of energy distribution calculations with reference to optimization analysis. As a result, there are twenty seven-case in the analysis. The equations originally derived are in the present worth for mulation, and each equation includes investment and operation costs. Using eqs.(1), (2), (3) and the actual values used in Turkey, cost variations depending on various loadings are shown in Figure 1, Figure 2 and Figure 3. 20000 PWTFC.Cfc) 0 0 S(kVA) 300 Figure 1. Present worth of total low voltage feeder costs depending on cross sectional area of conductor xm 40000 PWTFC(S) 10000 0 SCMVA) 30.0 Figure 2. Present worth of total medium voltage feeder costs depending on cross sectional area of conductor 90000 PWTDT(S) 20000 0 SCkVA) 2000 Figure 3. Present worth of total distribution transformer costs depending on transformer loads