Senkron generatörün akı dağılımının FLDII programı ile incelenmesi

Abstract

FLDll programx, elektromagnetik alan problemleri nin çözümünde kullanılan sonlu elemanlar yöntemini esas alarak işlem yapan bir paket programdır. Bu programdan, elektrik makinelarındakı dağılımlarının incelenmesinde yararlanılmaktadır. Bu çalışmada, 2214 kVA ve 150 dev/dak'lık çıkık ku tuplu bir senkron generatörün yarım kutup, uyarma sargı sı, oluklar ve endüvinin bir parçasından oluşan kısmında ki magnetik alan dağılımı, FLDll programı yardımıyla çiz- dirilmiştir. Bölüm 2' de, ele alınan senkron generatörün hesapla rı yapılmış, Bölüm 3' de FLDll paket programı hakkında gerekli bilgiler verilerek, makinaya nasıl uygulandığı açıklanmıştır. Bu bölümde, hesaplar ve programa girilen veriler sonucunda elde edilen çıktılarla akı dağılımını içeren şekil de yer almaktadır.

FLDll is a computer program which is used to examine the flux lines of electrical machines. Finite element method is included in this program. The finite element method was provided by Courant in 1943 and was not applied to electromagnetic problems until 1968. The finite element analysis of any problem involves basically four steps: 1) Discretizing the solution region into finite number of subregions or elements, 2) Deriving governing equations for a typical element, 3) Assembling of all elements in the solution region, 4) Solving the system of equations obtained. To construct an approximate solution by a simple finite element method, the problem region is subdivided into triangular elements. The essence of the method lies in first approximating the potential within each element in a standardized fashion and thereafter interrelating the potential distributions in the various element so as the constraint in the potential to be continuous accross interelement boundaries. FLDll can apply all these steps to an electrical machine. A synchronous generator is chosen and the necessary calculations are done in this thesis. Therefo re, FLDll is applied to the machine and the figure conta ining the flux lines was obtained. below: Nominal values of the synchronous machine is given Apparent power P =» 2214 kVA Power factor cos = 0,8 Nominal terminal voltage U = 3695 V/phase Nominal current I = 200 A n Synchronous speed n =-150 min S - v - Humber of poles 2p - 40 Number of slots N - 240.Some basic dimensions of the generator: Total length of the stator Circular distance between two poles Circular distance between two slots Internal diameter of the stator External diameter of the stator Height of a pole Height of a slot Width of a slot Air gap Width of the excitation winding Cartesian and polar coordinates can be used separa tely in the program FLD11. Flux lines of the figures which have horizontal, vertical and diagonal lines can be drawn with Cartesian coordinates. If polar coordinates are used, the figure has to have radial lines and circular arcs. However, in Cartesian coordinates, some preprogram med shapes such as circular arcs, rectangles, sharp right angles and curved right angles can be added to the basic figure using a special code (9000 mm). In this program, each coordinate usually consists of a five digit number, with one digit after the decimal point. Then, there is a blank before the next coordinate. The x or r coordinate is entered first, then the y or z coordinate. Here x and y are for cartesian coordinates, r and z are for polar coordinates. When a coordinate is less than 1000 mm, it is entered with leading zeros. Example : 0000.0 0100.0 0030.2 0400.5 x y x z point 1 point 2 - vi - In FLDll, the identification which can consist of up to 80 characters is entered in line 1 (table 1). Line 2: Even through it is not mentioned on the input sheet (table 1) / a zero can also be entered in column 1. This signifies that. the contour lines are speci fied in polar coordinates, and that the initial grid con sists of circular arcs and radial lines.. The scale of the input drawing should nearly speci fied as one. The periodicity condition can be used both with cartesian and polar coordinates. Lines 3 to 8: Line numbers are entered for verti cal grid lines, where the grid density changes (grid den sity break lines). Flux densities are assumed to be constant within each triangle in the numerical solution, and the grid should be fine enough for this to be true within acceptab le accuracy, especially in critical regions. In any case, the grid lines must be close enough, so that contour line points are at least as far apart as the grid lines in the same region. Line(s) 9: One or more lines which contain x or r coordinates of the grid density break lines are entered here. Lines 10 to 15: Line numbers are entered for hori zontal grid lines, where the grid density changes. Line(s) 16: y or z coordinates of the horizontal grid density break lines are entered here. Lines 17 to 19: The detailed output information increases the bulk of the output and the computing time significantly, and should therefore be limited to those areas where it is of real interest. The information inclu des node coordinates, vector potentials, permeabilities and flux densities. Line 20: The scale of the flux plot is unimportant for the plot on the screen. It is used for the plot on the plotter. The plot is automatically tilted 90 degrees if this permits a better utilization of the paper. Lines > 21: It is important that the contour lines are entered in a proper sequence since the grid is fitted to line segments that are common for two or more lines only the first time they are entered. This usually means that flux lines should fc>e entered first, so that they receive the proper code throughout. - vii - DEIFICATION (line 1) t TABLE 1 Explanatory table Max.. 80 characters, including blanks For each contour line:. »0.1 if no air gap - viii -. When a flux line is entered with code 2, the vector potential A will be kept constant equal to zero along the line (and within the line if it is a closed curve). This also serves the purpose of providing a reference potential for the program. Therefore, it is necessary to enter at least one flux line. However, it can be specified as a single point. The number of points (col.l, line 21) is used only to enable the program to read the input properly. It actu ally means the number of pairs of five digit numbers, entered in coordinate line format. This should be kept in mind when preprogrammed shapes are used to describe the contour line. The program FLD11 is applied to the synchronous generator following the steps above.