Güç transformatörlerinde aşırı gerilim dağılım sorunu ve alınan önlemler

Abstract

Çalışmada enerji iletim hatlarında her türlü elektriksel iç ve dış etkilere açık olan güç transformatörlerin sargılarında oluşan aşın gerilim dağılışı bulunmuştur. Gerilim dağılışını belirleyen transformatör sargı kapasitelerinin matematiksel ifadeleri çıkarılmıştır. Daha sonra başlangıç gerilim dağılışım düzelten yöntemler incelenmiştir. Önce seri kapasitenin artırılması yöntemi ve buna bağlı olarak sargıda oluşabilecek düzgünsüzlüğün etkileri örneklerle incelenmiştir. Ardından bu yöntemlerden biri olan ve pratikte de uygulama bulan toprağa karşı paralel kapasitelerin etkilerini yok eden yöntemin matematiksel bağıntıları çıkarılmış ve ekranın sargıyla yapması gereken açı hesaplanmıştır. Çıkan sonucu bir örnek transformatör üzerinde uygulayarak gerçekte yapılanla bir uyum gösterip göstermediği kontrol edilmiştir.

First of all, the main purpose of this study is to investigate the problem of the overvoltage distribution along a power transformer. Since a transformer is subjected to various external and internal harmful effects, optimum solution for this problem, that is to construct a transformer which withstands overvoltages and also works in normal conditions without increasing cost of transformer, should be found. So far various methods of the transformer protection, for example, different kinds of dischargers, special spark gaps called co-ordinators, proper choice of the transmission line route, the reactive coils and capacitors, were employed. These ones are not used today, since experience has shown and subsequent analysis has confirmed that the efficiency of such protection is insufficient. Nowadays, concepts of reinforcement of the input and output coil insulation, interleaving coil windings and capacitive protection are argued. In the first chapter, this study investigates overvoltage waves along a transformer windings on the basis of standing and travelling waves and according to Wagner theory, starting from the sets of differential equations describing the transient process and using the simplified mathematical model of a winding, the equations giving the voltage distribution within the transformer winding are given. In this chapter depending on if the winding end is open or earthed, the initial and the final voltage distribution are studied on and found as follows: "C-* For at one end earthed winding; the initial voltage u(-j,0) sinhaCl- j) U sinha the final voltage U 1 -vi- For an open end winding; the initial voltage u{^,0) coshccCL-^) U cosha the final voltage u Here:...... U : Terminal voltage, [kV] I : the full winding length, [m] x : the coordinate of a given point of the winding, [m] a=J £ Cr = C.l the resultant parallel capacitance, [F] Kr = K/l the resultant series capacitance, [F] And then voltage oscilations taking place between these two processes are found out. The primary importance of the Wagner model and of the calculation based on it, is the very informative qualitative picture provided by the phenomena taking place in transformer windings under the effect of steep-front overvoltage waves. Also from a practical point of view, the factor calculated from the resultant shunt and series capacitances is of great significance, since conclusions can be drawn from it also as to the uniformity of initial voltage distribution within the winding and to the liability of the latter oscillations. This method, however, is unsuitable for the purpose of voltage distribution calculations required for the insulation design. The infinitesmall homogenous winding model proposed by Wagner, where the series and parallel capacitances and the self-inductances are alone taken into account, idealizes the real conditions very much. Therefore Wagner's classic model is also criticized. As a matter of fact, a real transformer winding is composed of a finite number of elements (e.g. discs, pairs of discs), therefore it is more obvious to present it by a model consisting of a finite number of elements than by an infinitesmall model. Thus in the case of disc type transformer windings, it is convenient to consider each disc, each pair of discs or each group of discs as a separate element. Further, real transformer windings are not homogeneous in every case but generally at the beginning and end of the winding, and sometimes inside it, often contain winding elements (discs) in which the number of turns, geometrical arrangement or shape deviates from the majority of elements constituting the winding. The Wagner model also simplifies real condition by neglecting the mutual inductance within the winding and the damping effect of eddy current losses on voltage oscillations. Finally, in the majority of cases, it is not a single winding that is to be investigated, but a transformer or a winding system consisting of two or more windings. Then according to these opinions overvoltage distribution along a transformer winding is -vii- investigated. As it is known that there are capacitances present between transformer windings, series capacitances, and earthed parts (core, tank, etc.), grounded or parallel capacitances, within each winding between discs, turns and layers, and between individual coils. These series and parallel capacitances determine the voltage distribution. Therefore expression of the series and the parallel capacitances are found out in details. The series capacitance of normal disc windings is, N 2nbt 3 26 1 ^ 6a- and the parallel capacitance between two concentric cylindrical windings of heights H, and H? is 21, BD x 2 C= -?. 1(T12F Here. D : the mean winding diameter, [m] N : the number of layers n : the number of turns in a layer h : the size of copper conductor used for calculating the turn capacitance, [m] (\ : the thickness of inter turn insulation, [m] £, : its permittivity. [F/m] r : radial size of winding, [m] S,, : the thickness of spacers between discs, [in] £,, : the resultant permittivity of (oil and solid) insulation of thickness 5,,, [F/m] <5%1 : the thickness of oil insulation between the surface of two cylinders, [m] <5S : the thickness of solid insulation between the two surfaces, [m] c" : the permittivity of the oil insulation, [F/m] e,i : the permittivity of the solid insulation, [F/m] Meanwhile, since one of the methods of increasing the series capacitance is interleaving disc windings, series capacitances of interleaved disc windings are studied. The series capacitance of a normal disc winding can be increased by several orders of magnitude by interleaving the turns, i.e. by removing geometrically adjacent turns farther away from each other electrically, thereby increasing the voltage between adjacent turns. Although it is not necessary to reinforce the intertum insulation. The series capacitances of windings wound of several wires in parallel can.be influenced by modifying the arrangement of the parallel wires. If these parallel wires line one next to the other, the series capacitance remains -viii- unchanged. If. however, the wires in parallel are separated from one another the series capacitance of the winding increases considerably. Thus the series capacitance can be varied in the ratio of 1/32 without modifying either its geometrical dimensions and operating characteristics. For the purpose of calculation the voltage distribution more accurately than Wagner self and mutual inductances and damping resistances are taken into account. As a requirement of primary importance, the voltage oscillations calculated on the basis of the model should as closely as possible approach the oscillations taking place in the real winding or winding system. Therefore it is important to choose the rigt number of element in the model. Because the higher the number of winding sections, the higher the probability of making an error in determining characteristics of individual elements. Experience has shown that for the purpose of voltage distributions calculations, when not only the initial distribution but also the voltage oscillations arc to be determined, it is not expedient to use models consisting of more than 10 - 12 elements. This is enough for calculation of large transformers. A voltage distribution satisfying practical requirements can be calculated within an accuracy of + 20 %. The discs next to the line terminals of disc type transformers often differ from the discs inside the winding. Generally, the outermost discs contain a reduced number of turns for constructional reasons, to provide space for end insulation and to reinforce the insulation to cope with the higher mechanical stresses arising here. This kind of inhomogeneous design of windings may considerably influence the voltage distribution. Generally, it is sufficient to examine the effect of inhomogeneity by checking the initial voltage distribution, i.e. on the basis of a network containing capacitances only. The effect on the initial voltage distribution of an inhomogeneity arising at the initial section and final section of the winding are calculated on the basis of the n-element capacitance network. An inhomogeneity in the initial section of the winding primarily affects the voltage distribution prevailing at the initial section of the winding and has a minor influence on its remaining sections. Similarly, a winding-end inhomogeneity will mainly modify the stresses arising there, and will but slightly affect the voltage distribution of the initial section of the winding. Generally, two or more windings are mounted on a limb of a transformer. An overvoltage directly affecting one of the windings will, due to existing capacitance and inductive couplings, also give rise to overvoltage in the other windings, thereby also indirectly jeopardizing the latter. The investigations described here, mainly serving the purpose of demonstrating the nature of the phenomenon, relate to single phase transformer containing two homogeneous concentric windings. One winding of" the transformer being investigated is that directly hit by the overvoltage ( referred to as impulsed ). while the other is the winding not directly affected ( referred to as non-impulsed ). The case is investigated, depending on whether one end of the non- -ix- impulsed winding is earthed or not, the five different connections are distinguished. As regards initial voltage distribution, three of them are found as identical. Therefore just three of them are examined. For these 3 basic cases, 3 different sets of equations are written, considering the respective boundary conditions. It is convenient to treat the three cases in common by means of matrix calculus and to express the result also in matrix form. Starting from the relations given in this section and regarding the equations derived for winding capacitances, the voltage distribution developing along the impulsed and non-impulsed windings can be determined by computer for all concrete cases. The above methini is not only suitable for describing the phenomenon of voltage transfer, but by its means the transferred voltages of given winding systems divided in not too many elementary sections and consisting of two homogeneous windings can be calculated. In systems consisting of more than two windings or when the number of elementary windings is too high, instead of solving the matrix equations directly, it is more practical to employ some method utilizing computer capacity more economically, e.g. some iteration method or Gaussian elimination. In the last chapter, transformer overvoltage protection ( especially capacitive one) is investigated. As it is known that there are two kinds of transformer protection from overvoltages. They are external and internal protection. The object of external protection is to render sufficiently harmless the wave hitting the transformer, by lowering its amplitude and making it flatter. Internal transformer protection from overvoltages includes the required reinforcement of the input and output coil insulation where the maximum voltage gradients can be expected, the capacitive protection of transformers and interleaving coil windings. In transformers for 110 kV and higher, in addition to coil end insulation, capacitive protection is used so that overvoltage pulses are distributed along the winding approximately in the same manner as the final voltage distribution, i.e. sufficiently uniformly. The idea of capacitive protection consists in the following. If a winding could be made so that the parallel (grounded) capacitance is C=0- we would have, for a N -^0 A' The case of " u = 0 " corresponds uniform distribution. Unfortunately, it is physically impossible to eliminate the grounded capacitances but it is possible to compensate the currents required for charging these capacitances with the currents flowing from the line through a system of screening protective capacitors C" connected to the winding. The protective capacitor has the form of a special screen made of an insulating material with a metal-coated surface and connected to the line end of the winding. The important thing is the appropriate choice of the screening capacitance and the screening angle between screen and the surface of the winding. -x- In this method the equation giving the screening capacitance is. Ck=C(£-l) *=1..77-] * k and the equation giving the screening angle necessary for obtaining the above capacitance is 271er. e=Arctan ( 1- ) Here, C : Winding parallel capacitance, [F] r. : Permittivity of oil and solid, [F/m] r,: The radius of mean winding, [m] n : The number of division in the winding, k : The number of division belonging to the screening capacitance to be found, And then in order to prove that the equation investigated for the angle is right, some data of a transformer to be protected are taken and as it is expected to be small, it is found as a small angle. It is a general practice to assume that it is zero degree and to wind the screen parallel to the winding.