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Dallı dağıtım şebekesi yük akışı çözüm metodları

Başlık çevirisi mevcut değil.

  1. Tez No: 66785
  2. Yazar: MUSTAFA ÇELENLİOĞLU
  3. Danışmanlar: DOÇ. DR. ADNAN KAYPMAZ
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Elektrik dağıtım sistemleri, Enerji iletim sistemleri, Yük akış modeli, Electric distribution systems, Energy transmission systems, Load flow model
  7. Yıl: 1997
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Elektrik-Elektronik Mühendisliği Ana Bilim Dalı
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: Belirtilmemiş.

Özet

ÖZET Bu tez çalışmasında dallı dağıtım şebekesine ait çeşitli yük akışı metodları incelenmiştir. Bu metodlar; yük modellerine göre sabit akımlar, sabit admitanslar ve sabit güçler olmak üzere şebekenin üç ayrı yük tipi için; yüklerin sabit akımlar ve sabit admitanslar olarak alındığı, bu sebeple lineer yük akış eşitliği içeren şebekelerde kullanılan iterasyonsuz düz çözüm, şebekede yüklerin sabit güçler olarak kabul edildiği modeller için ise Newton-Raphson ve Gauss-Siedel iteratif çözüm yöntemlerine içeren yük akış analizi metodlarıdır. Yük akış eşitliklerinin elde edilmesinde genel olarak hatların kapasitanslarını ve karşılıklı endüktanslarının ihmal edildiği, şebekede yüklerin dengeli olduğu hatlarda çap- razlaştırmanın yapıldığı kabul edilmiştir. Bununla beraber yüklerin sabit akımlar veya sabit admitanslar olarak alındığı yük modeli için tek fazlı, iki fazlı, üç fazlı hatlar ile tek fazlı, iki fazlı ve üç fazlı dengesiz yükleri ihtiva eden bir dağıtım şebekesinin yük akış eşitliklikleri oluşturulmuş ve çözüm metodu sunulmuştur. Bara yükleri sabit aktif ve reaktif yükler olarak verilmiş ana kol ile beraber yan kollar ve alt kollar içeren birradyal dağıtım şebekesi için iki ayrı matod ile yük akış programı yazılmış örnek 28 baralı bir şebeke için bu program çalıştırılmış yük akışı sonuç¬ ları elde edilmiştir.

Özet (Çeviri)

SUMMARY Introduction: Load flow is a very important and fundemental tool for the analysis of any power system and is used in the operational as well as planning stages. Certain applica- tions, particularly in distribution automations and optimizations of a power system, require repeated load flow solutions. in these applications it is very important to sol- ve the load flow problem as efficiently as posible. Since the invention and wide- speread use of digital computers, many methods for solving the load flow problem have been devoloped. Most of t he methods have grown up around transmission systems and, över the years, variations of the Nevvton method, have become the most vvidely used However for distribution system complexes which are mostly ra- dial in nature. These general purpose programmes are not normaly found suitable mainly because of the difficulties in convergence of the iterations and the large me- mory requirement of the computer. Not much work has been carried out on load flow analysis of distribution networks. Generally distribution netvvorks are radial and the R/X ratio is very high. For this rea- sion netvvorks are ill-conditioned, and conventional Newton Raphson and fast de- coupled load flow methods are in efficient in solving such netvvorks [1,2]. Many researchers have suggested modified versions of the conventional load flow solving ill-conditioned povver networks. Recently some researchers have paid much attention to obtaining solutions for radial distributions netvvorks [ 4, 5 ]. Kersting and mendive have presented a load flow technique based on the ladder netvvork theory [6]. Shir Mohammadi have presented a compansation based power flow method for weakly meshed distribution and transmission systems [ 7 ]. Baran and Wu and Chiang have obtained the load flow solution in a distribution system by iterative solu- tion of three fundemental equations representing real power, reactive and voltage magnitude [8,9]. Renato has proposed a method for obtaining the load flow solution of radial distribution networks. His technique seems to be quite promising because it solves for bus voltage magnitudes only [10]. Goswamİ and Basu have presented a ixdirect solution method for solving radial and meshed distribution networks [11]. Ho- wever, the main limitation of their method is that no node in the network is the junc- tion of more than three branches. Jasmond and Lee have proposed a new load flow method for obtaining the solution of the radial distribution netvvork using a single-line equivlent. in this thesis several solution algorithms for solving distribution power flow equati- ons are investigated. These proposed methods, for three different power loads mo- dels of network, constant current, constant admittance and constant power, are ba- sic solution and iterative solutions algoritms. The basic solution is uniterative tech- nique because of consisting linear equation. The other iterative solution technique is Newton Raphson ör Gauss Siedal iterative methods because of consisting non- linear equations. in obtaining of power flow equation, generally capacitance and mutual inductance of lines are neglected. Loads is balanced and each phase in- ductance is equal. in addition for any given constant current ör admittance load mo¬ del, radial distribution network consist of single, double and three phases line ör lo¬ ads, power flow equations and solutions methods are obtained. There are many kinds of power flow methods. Ali methods are based on backvvard orforward svveep method. For this reason the formulation and presentation of the proposed algorithms highlight the fact that these methods can be viewed as Newton methods and the backvvard, forvvard sweep methods based on Siedal iterativ method. They are based on updating voltages, currents, (ör power flows) along the paths from the and buses to source ör from the source bus to the end buses. The technique of ali these proposed methods are nearly sensitive to correctly indexing laterals ör buses. Solution methodology: A-) Loads are constant power: Power flow equations for distribution system are usually modelled differently from transmission systems. To simplify the presentation, the system is assumed to be a balanced three phase system. For presentational convenience firstly a special case where there is only öne main feder is considered. The general case for any distri¬ bution system is considered next. A piece of line (branch) between two buses of xRadial Distrubution netvvorks, branch flow eguation used in iterative solution techni- gue from below figüre. following equations can be written. 1 i i+1NB Substation ||Lj-* PL(i+1), QL(i+1) PL(NB), QL(NB) I/İN _ |V(i+1)k5(i)-|V(i+1)|ZS(i+1) 'U>> -R(İ)+JX(İ)ı P(i+1)-jQ(i+1)=V*(i+1).l(i)2 From eqns. 1 and 2, we have |V(i+1)|={[(P(i+1)R(i)+Q(i+1)X(i)-0.5|V(i)|2)2-(R2(i)+X2(i))(P2(i+1)+Q2(i+1))]1/2 - P(i+1 )R(i)+Q(i+1 )X(i)-0.5|V(i)|2}1/23 Eqn.3 is a recursive relation of voltage magnitude. Since the substation voltage |V(i)| is known, it is possible to find out the voltage magnitude of ali other nodes. The real and reactive power in used eqn.3 can be written in generalised form NBNB-1 P(i+1)= E PL(j)+ E LPÛ) j=l+1J=H-1 NBNB-1 Q(i+1)= E QLO)+ E LQö) for 1=1,2NB-2 4 j=i+1j=i+1 and the real and reactive power losses in branch (i) can be written in generalised form _ R(')(P2(Hi)+Q2(i+i)) X(i)fp2(i+1)+Q2(i+1)) LQ<P- IV,M,P xiinitially, if LP(i+1) and LQ(i+1) are set to zero for ali (i), it will be a very good initial estimated for obtaining the load flow solution of the proposed method. The conver- qence criteria of the proposed method are that if the difference of real and reactive power loses in successive iterations in each branch is less than 1 Watt and 1 VAr, respectively, the solution has converqed. B-) Loads are constant current ör admittans [I]=[A][J]6 where [J]: is the vector off the load currents, dimension [1xn], n is the number of branches [l]: is the vector off the relevant branch currents, dimension [1xn], and [A]: is the incidence square matrix, [nxn], where the rows correspond to the n branc¬ hes and the columns to the nodes. The elements of [A] describe the netvvork topology and equal to ay =1, if the node corresponding to column j is fed Via the branch corresponding to rowi 3y =0, otherwise The network complex impedance is equal to : [Z]=[A]t[Zb][A]7 VVhere, [Zb] is the diagonal matrix [nxn], the elements of which are the complex im¬ pedance of the corrosponding branches. Let VQ and VR r epresent the voltage vector at the origine and node k respectively, AVk the voltage drop on branch k and AUk the total voltage drop f rom the in feed up to node k AUk = AVı++ AVk=Vo-Vk8 then, [AU] = [A]l[AV]9 xiifrom 6 [AV]=[Zbira = [Zb][A][J]10 andfrom (7,9and 10) [AU] = [A]'[Zb][A][J] = [Z][J]11 i.e. the voltage drop from the origin to node k is AUk = 2ZkiJk12 vvhere Zki the elements of the row k of [Z] using 8. Vk = Vo-ZkjJj--ZkkJk--ZknJn13 C-) Loads are unbalanced and the conductors confiquration is an equilateral triangle Line Model: Some assumptions are made in that the solution of the load flow analysis in order to reduce the complexity of the calculation. The two fundemental assumptions are : 1.Balanced three-phase currents 2.Complete transposition of conductors with these two assumptions a simple equation is derived for phase inductance which includes the şelf inductance and the effect of the mutual inductance with the other two phases. For balanced three-phase system analysis. This is a viable method and the öne most commonly used in industry for the determination of impedance values to use in povver how studies of transmission systems. However, a distribition system does not lend itself to either of the two assumptions. Because of the dominance of single -phase loads the assumption of balanced three-phase currents is not justified. Distribition lines are never transposed nor can it be assumed that the conductor con- fiquration is an equilateral triangle. Carson's equations allow for the computation of conductor şelf impedance and the mutual impedances betvveen conductors for any number of conductors above ground. For a three-phase, four vvire grounded wye system, Carson's equations will lead to the development of a 3x3 impedance matrix. xiii14 Equation 14 represents the general equation used to calculate voltage drop on a line segment. In cases of double-phase and single-phase lines, only the physically pre sent phases will have current flow and voltage drops. This is accomplished by set ting to zero the appropriate terms for the missing phases. Load Model : All loads are assumed to be fixed complex power (S=P+jQ) by phase. It is further assumed that all three-phase loads are wye connected and all double-fhase and single-phase loads are connected line to grounded neutral. That complex power lands, Sa, Sb and Sc can be different values or even zero. Infact, double-phase and single - phase loads are modeled by setting the values of the complex power to zero for the non-exist phases. It is assumed that the complex powers of each phase are known that the line to neutral voltages have been specified. With this known the load currents are determi ned by la = (Sa/Vanr lb = (Sb/Vbn)* lc = (Sc/VCn)* 15 Consisting have only main feder, a distribution network, to get started a voltage Vn is assumed at end node n. With ln known, calculated using equation 15, the voltage drop in the line section (n-1 to n) can be calculated using equation 14 and in turn Vn-i is calculated. Now the load current at n-1 can be determined and this is added to the previous line current so the next line section voltage drop can be calculated. This proses is repeated until the voltage at the source (Vi) has been calculated. The calculated Vi is compared to the known input voltage Es. AV=ES-V1 16 The calculated delta voltage is applied to the assumed voltage add Vn. Using equ ation 16. Vn,new = Vn,old+AV 17 XIVWith the new Vn the system is analyzed by working from node n back to the source node. This procedure is continued until the calculated voltage Vi is within a specified tolerance of the known source voltage Es and final solution is achived. xv

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