Güç transformatörlerinde ayar bobinlerinin yerleştirilmesinin sargı kuvvetleri bakımından incelenmesi
The Proper location of the regulating coil in transformers from short circuit forces point of view
- Tez No: 39131
- Danışmanlar: PROF.DR. NURDAN GÜZELBEYOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1993
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 79
Özet
ÖZET Transformatörlerde nominal gerilimdeki kısa devre akimi büyük transformatörlerde nominal akimin 8-10 kati, küçük ünitelerde 20-25 katidir. Sargıların sarımlarında akan akımların etkileşiminden ve magnetik akının eksenel bileşeni radyal zorlamaya çalışırken, radyal akı bileşenleri de ekse nel kısa devre kuvvetlerini meydana getirir. Ayar bobininin olması halinde ayar bobininin çıkarılmasıy la oluşacak simetrisizlikler incelenmiştir. Çeşitli ayar bobini düzenlemeleri için radyal ve eksenel kuvvetler hesap lanmış ve ayar bobininin en uygun yerinin tayinine çalışıl mıştır» Kısa devre kuvvetlerinin hesabı, yaklaşık formüller, Roth metodu ve sonlu elemanlar yöntemiyle yapılmıştır. Çeşitli ayar bobini düzenlemeleri için radyal ve eksenel kuvvetler hesaplanıp tablo haline getirilmiştir. Ekte sonlu elemanlar yöntemiyle FLDİİ paket programı kullanılarak maksimum magnetik indüksiyon değerleri ve es potansiyel (magnetik vektör potansiyel) noktaların birleşti rilmesiyle elde edilen akı çizgileri de verilmiştir. Radyal ve eksenel kuvvetler nominal akım içindir, dolayısıyla kısa devre kuvvetlerini hesaplamak için bu kuvvetler (k/u ) ile carpılmalıdır. Ayrıca ekte verilen Roth metoduna ve sonlu elemanlara dayanan çıkışlar nominal akım için olduğundan tüm değerler 2 ile çarpılıp, akımın tepe değerine karsı düsen kuvvetler tablo haline getirilmiştir. Çeşitli ayar bobini düzenlemeleri için verilen derli toplu sonuçlar, transformatör tasarımında ayar bobininin yerinin kısa devre kuvvetlerine göre tayini ve buna göre konstrüksi- yonel önlemlerin alınması için temel öneme sahiptir. -VI-
Özet (Çeviri)
- SUMMARY - THE PROPER LOCATION OF THE REGULATING COIL IN TRANSFORMERS FROM SHORT CIRCUIT FORCES POINT OF VIEW For transformers operating at rated voltage, the short circuit forces are determined by the short circuit impedance of the transformer. The short circuit current is 8- İO times the rated current in larger transformers and 20-25 times in smaller units. As a result of interaction between the leak age field of the shorted winding system and current flowing in the turns ? short circuit forces will act on the turns of the winding» These short circuit forces are proportional to the square of the short circuit current. The phase position of voltage prevailing at the instant of the short circuit and the time constant of the short- circuit loop determine the maximum short- circuit current and force, and the forces act ing on the turns and windings after the first current peak keep the windings and their clamping structures in oscillation at double the network frequency until the short circuit is interrupted. The winding structure should he dimensioned against mechanical strains to prevent the stresses a- rising in component parts from causing permenant deformations and to limit the movement of the winding structure to a mi nimum during short circuits. The peak short circuit current is given by i = -/2Ifi + e R*5 (i) K This is the condition for occurrance of maximum amplitude of transient short circuit component. Thorough knowledge can be made use of from IEC Publication 76-5 as regards the ability to withstand the short circuits. For the sake of simplicity, electrodynamic forces are considered as the resultant of radial and axial forces. The forces resulting from the interaction of the current flowing in the turns of the winding and the axial components of the magnetic flux lines act in the radial direction, whereas the radial components cause axial short circuit forces. The radial forces act in such a way that the inner winding is compressed and the outer winding expanded. In symmetrical arrangement the axial forces tend to compress the coils so the forces acting on the individual turns have no resultant. -VII-In an asymmetrical winding system, however the axial forces also tend to compress the coil, but the axial forces acting on the turns have a resultant thus the directing forces resulting from the asymmetry is such as to cause the symmetry increase further» The ability of the transformer windings to withstand short circuits is checked as detailed below: a) The radial forces should not cause dangerous deformation in the outer winding. This checking is substantially similar to the calculation of mechanical stresses arising in a tube expanded from its inside. b) The radial forces should not crush the inner winding, i.e. the winding is checked for deformation as a tube compressed from the outside and braced from the inside at its generatrices along the spacers. c) The axial forces should not cause deformation of the windings. In the case of balanced ampere- turns, axial forces act on the windings as compressive forces. In layer windings the compressive stress arises on the surface of successive turns, whereas in pancake windings, the axial pressure is transferred through the spacers to the next turns, and the conductor sections between spacers are subject to bending. Since maximum axial forces act on the conductors at the win ding ends, the bending stresses are also the highest there. Resultant radial forces can be derived by differentiating the stored magnetic energy in the direction of radial dis placement of the winding. Since the forces arising due to the existance of asymmetry can exceed those occuring in windings of a transformer with balanced ampere-turns, it is of great importance to properly locate the regulating coil. The worst condition is that of the exclusion of ail turns of the regulating coil. For the simplest case, the radial forces are given by. F = (W i}- _ (ii) rrnax ^ Where I is the mean periphery of the stray channel, le is the length of the leakage channel. This is valid for symmetrical windings. These approximate formulations aren't extensively used. They are just to see what these forces are dependent on. Moreover, the force formulation for asymmetrical winding system is very complicated and formulae vary from arrangement to arrangement - -VIII-A second method taken in hand for determining the short circuit forces in transformers is Roth's method. Roth's method is based on the solution of Poisson's equation in two dimensional space written for the magnetic vector potential Ai -STA = fj 5 o (iii) where 5 is the total current density infA/ia J, A ±n fWb/mJ, Mo=1.25610~ö[H/ffll. A series solution. of vector potential A is substituted in (iii) also taking into account boundary conditions. Series solution is given by- 00 CO A* ~ Is 2 \k cos^ffli x' »iatöfe y) Clv> i=ı k=i Making the required substitutions in df =i B dl (v) and integrating it we get- dy dx, Fy. - dy dx t8/ml (vi) These are the forces per unit length. It »us t be noted that the direction of the winding currents should carefully be employed. Jfhatever the winding arrangement of the transformer is, Both' s method evaluates the radial and axial forces with great accurracy. A moderate accuracy is -IX-achieved in taking 20 terms for the series solution of (iii). The third method considered to estimate the radial and axial forces uses the 'Finite Elements'. The transformer problem is apt to be used in a>;i- symmetric finite element analysis. Finite element procedure comprises the fol - lowings; 1. Define the boundary-value problems by a partial differential equation or a set of equations. 2. Obtain a variational formulation for the partial differential equation in terms of an energy- related expression called the 'functional'. 3. Subdivide the field region into subregions (finite elements). 4. Choose a trial solution in terms of the nodal values of the potential weighted by interpolation functions. 5. Hinimize the functional with respect to each of the nodal potentials. 6. Solve the algebraic equations. 7. Convert the potential solution to useful design parameters. The functional corresponding to (iii) is specified to this case in cylindiric coordinates as follows: B ICA3 = j i-> b dbl i-> b dbl r dr öz - R 0 J A r dr dz (vii) A linear variation of A in each element yields simple values for B which is the target solution- The finite el ement program considered (called FLDli) divides the region up into 3496 triangular elements. The program can calculate the leakage reactance by means of stored magnetic energy. Leakage reactance is also a measure as regards short circuit forces. It must be emphasized that both Roth's method and finite element analysis yield accurate solutions indicating the direction of radial and axial forces. However, approximate -X-calculations yield coarse results not giving directly the sign of the forces. As a result, it is found that dividing the coil into subsections gives extremely decreased axial forces, however no significant change in radial forces occurs. Subdivision of high- voltage winding also ensures better cooling in large units. Since a compromise between constructional features and short- circuit effects exists, it is not possible to find out a unique regulating coil arrangement. The location of the regulating coil varies in accordance with transformer power, regulation range and short- circuit forces. During design the untapped winding can be split into se veral parts corresponding to the tapped side, and connected in parallel. Thus, ampere- turn balance is achieved. An output data from FLDİ1 for various winding arrangements are given in table. The transformer designer is faced the fact of estimating short- circuit forces. Roth's method or finite elements can be made use of during design and precautions are taken like clamping the winding structure. When calculating short circuit current, one must carefully refer to the nameplate of the transformer to read u, since it has different values for each tapping. -XI-
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