Güç transformatörlerinde aşırı gerilim harmoniklerinin incelenmesi
A Treatise on overvoltage harmonics in power transformers
- Tez No: 46502
- Danışmanlar: PROF.DR. NURDAN GÜZELBEYOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Aşırı gerilimler, Dönüştürücüler, Harmonikler, Overvoltage, Transformers, Harmonics
- Yıl: 1995
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Şebekelerde meydana gelen aşırı gerilimler ışık hızı ile yürüyerek transTofmâTöfsargısından içeri girer. Bu aşırı gerilimler, transformatör sargısının nötr noktasının topraklanmış ve topraklanmamış olmasına göre, sargının sarımlar arası, sargıyla toprak arası kapasiteleri ile sargı endüktansı ve direncine göre sargı boyunca dağılır. Çalışmada iç ve dış etkiler sonucu oluşan aşırı gerilim dağılımları incelenmiştir. Gerek sonu topraklanmış silindirik sarılmış güç transformatörlerinin sargılarında ve gerekse sonu topraklanmamış silindirik sarılmış güç transformatörlerinin sargılarında başlangıç gerilim dağılımlarının matematiksel ifadeleri ve son gerilim dağılımlarının matematiksel ifadeleri sırasıyla incelenmiştir. Ayrıca başlangıç gerilim dağılımından son gerilim dağılımı oluşuncaya kadar sargı içinde yüksek dereceli harmoniklerin matematiksel ifadeleri incelenmiştir. Transformatör sargısının eşdeğer devre parametrelerinin gerilim dağılışının matematiksel ifadeleri çıkartılmıştır. Transformatör sargılarında oluşan başlangıç gerilim dağılımı, son gerilim dağılımı ve serbest titreşimlerin harmonikleri ile bu harmoniklerin zarf eğrileri Turbo C bilgisayar programlama dilinde hazırlanan bir program yardımıyla t=0 anında al' nin çeşitli değerleri için çizdirtilmiştir. V
Özet (Çeviri)
SUMMARY A TREATISE ON OVERVOLTAGE HARMONICS IN POWER TRANSFORMERS This is a study about the higher order harmonics in power transformers due to the over voltages in windings. Both for the earthed-end cylindrical windings and for the open-end cylindrical windings, the analysis is carried out on a theoretical basis yielding a family of parametric curves, which, in turn has turned out to be the structure of a Turbo - C program for the application part of this thesis. Transformers, one of the most functional devices of networks, are sometimes exposed to different types of over voltages occurring in the networks, the reasons being; switching in the network, atmospheric effects and earth faults along the lines. These over voltages propagate with the speed of light and enter into the transformer windings. Depending on whether the neutral line of the winding is earthed or not and according to the functional winding parameters like the mutual capacitance, self capacitance, self inductance, resistive impedance of the winding the distribution of those over voltages vary along the winding. The simplified mathematical model for such a winding is a single loop LC circuit formed by series and parallel capacitances and inductances. The family of partial differential equations expressing the transients in the windings is as follows: ox ox dt VI*cs - ^s S2u dxdt du _ d'h *L one: ox dt The above three equations can be reduced to a single ia2u_ tfu a4u _ Lax2 _x dt1 ^sdx2dt This equation is the most general expression for the distributions on a cylindrical winding with the input point at a potential of u(x,t) volts. In this equation, Cj [ F/m ] is the self capacitance of the winding, C§ [ Fm ]is the series capacitance per unit length and L [ H/m ]is the series inductance per unit length of the winding. This equation defines the parameter a. The value of the parameteroc / =0 is related with the final voltage distribution which is equal to the initial voltage distribution. Nonetheless practically it is almost impossible to realize this a / =0 condition for the normal winding structures. Thus, the general expression for the initial voltage distribution is as follows when the over voltage urj enters into the earthed-end winding: Sha(l-x) u = u0 - 0 Shod For the open-end windings that will be as follows: VIICha(l-x) u = u0 - 0 Chal For the earthed-end cylindrical windings, the mathematical expression for the voltage distribution occurring after time t will be as follows; Uks=U0(l-y) The above expression for the open-end windings will be: u]B=l.u0 In both of these windings, when the over voltage loading occurs, up to the final voltage distribution formation, the transient process is caused by free voltage oscillations along the windings. Generally for t=0 condition, these free oscillations are expressed by: uo(x)=u(x,0)+Uks(x,0) Here, uo(x) is the initial voltage distribution; u(x,0) is the value of free oscillations and u[<s(x,0) is the final voltage distribution. On a very general basis, these oscillations are expressed as: u(x, t) = ^ (ancos Xn x+ bnsin Xn x) coswnt For the earthed-end cylindrical winding at the application of a unit voltage on the input node of the winding, when x=0 ( that is, at the very beginning of the winding ), this most general expression is reduced to u(0,t)=0 and when x=l (at the end of the winding), the result will be u(/,t)=0. That means; there is no oscillation at the boundaries ( the beginning and the end points ) of the winding. Using the boundary conditions for this most general expression, VIIIa =0 and 2 a2l2 bn =? n% a"l +n 7t When the above analysis is carried out for an open-end winding with the boundary conditions u(0,t)=0 for x=0 and ( - ) for x=l the parameters are obtained as follows: 8x an=0 and 4 a2!2 'n 2 2 iitc 2l2 n 7i a2r+ b =- If, along the winding, the initial voltage distribution differs much from the final one, then the free oscillations will possess very large amplitudes ending up with a possible breakdown of the insulation material and with a short circuit fault. To prevent such results, the factor a / should have small values. For a / =0, the initial voltage distribution is linear. Since, this was stated to be practically impossible to realize, in order to provide a I =0 approximately; it is necessary either to increase Cş (the series capacitance) or decrease Cj ( the self capacitance of the winding) and that will yield the required approximate linear characteristics. To decrease Cj it is necessary to distort the electromagnetic space distribution of the present fields in and around the winding. Several screens placed on the certain points of the winding will be sufficient for this distortion. IXIncreasing C$ provides higher winding insulation. Many different methods have been developed for this aim. One is to increase the mutual inductance between the windings, which is, very expensive when applied to the whole winding. Hence only the input windings are supplied with better insulation which normally are exposed to very high voltages. Another method is to electrically separate the windings. This application is capable of increasing 200 - 400 times the series capacitance. In this case there is no need to increase the insulation threshold values for the windings. It is clearly seen that, when a / has larger values the free oscillation harmonics have also great amplitudes and the relevant envelope belongs to the area on the winding (first %20 part) where over voltage stresses also present. Practically, it is known that the envelope of free oscillation harmonics obtained mathematically and its experimental value are nearly equal. Thus, a computer program on free oscillation harmonics is valuable tool for the determination of the most stressed winding due to over voltages for different values of a /, which is also effectively used in this analysis. X
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