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Çıkık kutuplu senkron generatörlerde uyarma alanları ve alan harmoniklerinin incelenmesi

Çıkık kutuplu senkron generatörlerde uyarma alanları ve alan harmoniklerinin incelenmesi

##### Dosyalar

##### Tarih

1995

##### Yazarlar

Tükenmez, Lale

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

Institute of Science and Technology

Institute of Science and Technology

##### Özet

Son yıllarda elektrik enerjisine olan ihtiyacın artması sonucunda, yapılan çalışmaların büyük çoğunluğu enerji üretim sistemlerinin tasarımında en yüksek verime ulaşmaya yönelik olmuştur. Elektrik enerjisi üretiminin ayrılmaz bir parçası olan senkron generatörler; yuvarlak rotorlu ve çıkık kutuplu olmak üzere ikiye ayrılabilirlar. Çıkık kutuplu senkron generatörlerde hava aralığının değişken olması sonucunda endüklenen gerilimin şekli de hava aralığının şekline bağlı olarak değişmektedir. Bir senkron generator için standartlarda istenen en önemli özellik çıkış geriliminin sinüs formunda olmasıdır. Çıkık kutuplu senkron generatörlerde hava aralığındaki uyarma alan şekli kutup ayaklarına form verilerek değiştirilebilir. Bu sonuç, senkron generator tasarımında kutup ayaklarına form vermenin önemini ortaya koymaktadır. Bu tez çalışmasında konvansiyonel yolla hesabı yapılan bir çıkık kutuplu senkron generatörün hava aralığındaki uyarma alan şekli beş farklı kutup ayağı modeli için incelenmiştir. Modellere ait hava aralığı akı dağılımı sonlu elemanlar yöntemi kullanılarak hazırlanmış FLD13 paket programı kullanılarak çıkarılmış ve modellere ait harmonik analizi yapılarak alan harmonikleri çizdirilmiştir.

The basic aim of this work is to observe the excitation fields for air gaps in synchronous generators and to determine the measures to come close to sinusoidal form designing level. Another aim will be to determine the most ideal method by applicating the proposed methods for a salient pole synchronous generators having conventional calculations. As it is known, synchronous generator is one of the most fundamental parts of the electrical power systems. These machines used for converting mechanical energy to electrical energy have an important portion (like %99) in industry as a generator. As we head towards to produce more powerful synchronous generators to cover the increasing energy demand, also the rise at power bring additional problems during designing level in the same way. E.g., as it is not very important for the shape of the pole tip either it is straight or in the shape of the segment of a circle, it causes very serious problems in high powered machines. The most important feature proposed in standarts for synchronous machines is that the wave form of the generator voltage to be sinusoidal. Naturally, different methods to make the wave form to come close to sinusoidal form is used due to difference in construction of salient pole generators and generators with cylindiricai rotor. The most significant difference between the generators with cylindiricai rotor and the salient pole generators is air gap. As the air gap in generator with cylindiricai rotor is uniform and constant, it is varying in salient pole synchronous generators. According to Faraday's Law, to make voltage wave form sinusoidal, the wave form of the air gap field must be sinusoidal. Faraday's Law given by Equation (1) is a result of the flux change[1] -c Bav)1 (1) vi If synchronous machines are observed, I and v are constant in Faraday's Law, so the wave form of the induced e.m.f. is affected by the shape of B. The analysis of the wave form of air gap field gives the shape of induced voltage directly in both the synchronous generators with cylindrical rotor and salient pole synchronous generators. During this work, FLD13 packet program is used to get the air gap field belonging to the sample salient pole synchronous generator. FLD13 packet program is prepared by using Finite Element Method. This program works as a sub program of FLD1 1; a program to draw the field form in elektrical machines prepared by using the same method. This field program is prepared for synchronous machines and it is written in Fortran. The program wants 22 entry datas belonging the problem that is taken into account. The program gives the air gap field form for four different conditions of a synchroous machine. [12] This can be done by changing a code in data. Excitation forms and the codes of them are: 1. Field winding excited. 2.Armature winding excited in the d-axis. 3. Armature winding excited in the q-axis. 4.Amortisseur bar nearest the pole centerline excited in the q-axis. Harmonic analysis is done for the air gap field in the output of the program. The harmonic analysis is important for both predicting the wave form of induced voltage and the core loss at the teeth. The effect of the shape change of the pole tip on the wave form can be seen by the help of this analysis. This work is based on this fundamental. The reason for using a program depending on Finite Element Method is this, the method is highly practical tool for electromagnetic field calculations by digital computers. It is well suited for automatic grid generation, which greatly simplifies the preperation of the program input. Complicated shapes of electrical machines and the other boundaries can be handled easily. The Finite Element Method offers significant advantages over other methods, which have been used for this purpose. It is fast, reliable, easy to use, gives sufficient details, boundary conditions and curvature are properly accounted for, and both numerical representation of the result can be provided. For considerable two dimensional field applications have been given to Finite Element Method in recent years.[9][13] The field region is covered by a grid and magnetic vector potentials are calculated at the nodes giving a numerical solution for the flux densities. In the first chapter of this work, a general view over problem and the steps that the work will follow is given. The constructive features of synchronous machines are mentioned. The main differences between synchronous generators with cylindiricaî rotor and salient pole synchronous generators are shown and the cross sections of four pole machines are given. vii In the second chapter of this work, the change of excitation field in synchronous machine is observed. During this observation the form of the excitation field for synchronous generators with cylindrical rotor and salient pole synchronous generators is dealed one by one. First the measures to make the excitation fields to come close to sinusoidal form in synchronous generators with cylindirical rotor is given in a short way. After this the measures to make the excitation fields to come close to sinusoidal form in salient pole synchronous generators is dealed. In salient pole syncronous generators a form is given to the pole tips to change the excitation field in air gap. Here, the air gap excitation fields for different pole tip forms are given. These forms of the excitation fields are obtained by five different methods. At the end of the this chapter, for one of the these methods that is to make pole tips eccentric with the armature's cylinder, the relationship is obtained with equations. In the thirth chapter, Finite Element Method is presented. This method depends on writing the unknown variables thai are finite in the system in the name of the known variables. First, the fundamentals and then the steps of the method is given. The steps of the method are discretization, writing the basic equations for one element, combining all the elements and solving the equation system, respect iveiy. In the fourth chapter, FLD13 packet program written in Fortran programming language by Finite Element Method is presented. The input data of the program is given by a table. The equations of the electromagnetic field used in the program is derived in polar coordinates. The reason to write the equations in polar coordinates is that the structure of the synchronous machine is more suitable for polar coordinates than the cartesian coordinates. in the fifth chapter, the calculation results belonging to the sample salient pole synchronous generator which were calculated by using conventional method are given.[2] These calculation results are : Number of poles 2p=40 Inside stator diameter D^STIO mm Minimum air gap (actual) <5n=4.3 mm Carter's coefficient £,=1.164 Depth of pole tip at centeriine hpl=35 mm Width of pole tip bp=200 mm viii Depth of the poie body hpç =143 mm Width of the pole body *K=150mm Width of the field winding b« =25 mm Maximum air gap ^mx =9.1 mm Pole face radius(inner) R =1850.7 mm Pole face radius (outer) R =1845.9 mm For the sample salient pole synchronous generator, five different poie tip models are improved. In this chapter, these five different models are introduced one by one. By using FLD13 packet program, shapes of pole tips are plotted in real dimension for every model. And then, shapes of the excitation fields in air gap are plotted by using MAT-LAB program. For this, output datas of the FLD13 packet program are used. By using MAT-LAB program again, excitation field harmonics are plotted for every model. In MODEL 1, the air gap was taken constant along all the pole tip. In MODEL 2, shaping of the air gap is to be got a cosinus function from the pole centeriine to each x distance. This variation of the air gap is given by Equation 2.(£0:Minimum air gap, <^:Air gap at x distance) *,=- ^- (2) x 71. X cos In MODEL 3, the air gap was taken constant (at minimum value) below the middle of the poie up to 0.4 tp and after that the air gap was widened to 25 3 at the end of the pole tip. In MODEL 4, pole tips were taken eccentric in respect of the armature centeriine. In other words, the center of the armature cylinder and the center of the circle forming the pole arc is not congruent. In MODEL 5, the air gap was taken constant (at minimum value) below the middle of the pole up to 1/3 TP. After that the air gap was widened to «5"maxat the end of the pole tip. ix In the sixth chapter, the harmonic analysis results belonging the models were given and curves of the excitation fields were demonstrated in collected form. The differences among the models were considered. By using these output datas belonging the models, the ideal pole tip shape was determined.

The basic aim of this work is to observe the excitation fields for air gaps in synchronous generators and to determine the measures to come close to sinusoidal form designing level. Another aim will be to determine the most ideal method by applicating the proposed methods for a salient pole synchronous generators having conventional calculations. As it is known, synchronous generator is one of the most fundamental parts of the electrical power systems. These machines used for converting mechanical energy to electrical energy have an important portion (like %99) in industry as a generator. As we head towards to produce more powerful synchronous generators to cover the increasing energy demand, also the rise at power bring additional problems during designing level in the same way. E.g., as it is not very important for the shape of the pole tip either it is straight or in the shape of the segment of a circle, it causes very serious problems in high powered machines. The most important feature proposed in standarts for synchronous machines is that the wave form of the generator voltage to be sinusoidal. Naturally, different methods to make the wave form to come close to sinusoidal form is used due to difference in construction of salient pole generators and generators with cylindiricai rotor. The most significant difference between the generators with cylindiricai rotor and the salient pole generators is air gap. As the air gap in generator with cylindiricai rotor is uniform and constant, it is varying in salient pole synchronous generators. According to Faraday's Law, to make voltage wave form sinusoidal, the wave form of the air gap field must be sinusoidal. Faraday's Law given by Equation (1) is a result of the flux change[1] -c Bav)1 (1) vi If synchronous machines are observed, I and v are constant in Faraday's Law, so the wave form of the induced e.m.f. is affected by the shape of B. The analysis of the wave form of air gap field gives the shape of induced voltage directly in both the synchronous generators with cylindrical rotor and salient pole synchronous generators. During this work, FLD13 packet program is used to get the air gap field belonging to the sample salient pole synchronous generator. FLD13 packet program is prepared by using Finite Element Method. This program works as a sub program of FLD1 1; a program to draw the field form in elektrical machines prepared by using the same method. This field program is prepared for synchronous machines and it is written in Fortran. The program wants 22 entry datas belonging the problem that is taken into account. The program gives the air gap field form for four different conditions of a synchroous machine. [12] This can be done by changing a code in data. Excitation forms and the codes of them are: 1. Field winding excited. 2.Armature winding excited in the d-axis. 3. Armature winding excited in the q-axis. 4.Amortisseur bar nearest the pole centerline excited in the q-axis. Harmonic analysis is done for the air gap field in the output of the program. The harmonic analysis is important for both predicting the wave form of induced voltage and the core loss at the teeth. The effect of the shape change of the pole tip on the wave form can be seen by the help of this analysis. This work is based on this fundamental. The reason for using a program depending on Finite Element Method is this, the method is highly practical tool for electromagnetic field calculations by digital computers. It is well suited for automatic grid generation, which greatly simplifies the preperation of the program input. Complicated shapes of electrical machines and the other boundaries can be handled easily. The Finite Element Method offers significant advantages over other methods, which have been used for this purpose. It is fast, reliable, easy to use, gives sufficient details, boundary conditions and curvature are properly accounted for, and both numerical representation of the result can be provided. For considerable two dimensional field applications have been given to Finite Element Method in recent years.[9][13] The field region is covered by a grid and magnetic vector potentials are calculated at the nodes giving a numerical solution for the flux densities. In the first chapter of this work, a general view over problem and the steps that the work will follow is given. The constructive features of synchronous machines are mentioned. The main differences between synchronous generators with cylindiricaî rotor and salient pole synchronous generators are shown and the cross sections of four pole machines are given. vii In the second chapter of this work, the change of excitation field in synchronous machine is observed. During this observation the form of the excitation field for synchronous generators with cylindrical rotor and salient pole synchronous generators is dealed one by one. First the measures to make the excitation fields to come close to sinusoidal form in synchronous generators with cylindirical rotor is given in a short way. After this the measures to make the excitation fields to come close to sinusoidal form in salient pole synchronous generators is dealed. In salient pole syncronous generators a form is given to the pole tips to change the excitation field in air gap. Here, the air gap excitation fields for different pole tip forms are given. These forms of the excitation fields are obtained by five different methods. At the end of the this chapter, for one of the these methods that is to make pole tips eccentric with the armature's cylinder, the relationship is obtained with equations. In the thirth chapter, Finite Element Method is presented. This method depends on writing the unknown variables thai are finite in the system in the name of the known variables. First, the fundamentals and then the steps of the method is given. The steps of the method are discretization, writing the basic equations for one element, combining all the elements and solving the equation system, respect iveiy. In the fourth chapter, FLD13 packet program written in Fortran programming language by Finite Element Method is presented. The input data of the program is given by a table. The equations of the electromagnetic field used in the program is derived in polar coordinates. The reason to write the equations in polar coordinates is that the structure of the synchronous machine is more suitable for polar coordinates than the cartesian coordinates. in the fifth chapter, the calculation results belonging to the sample salient pole synchronous generator which were calculated by using conventional method are given.[2] These calculation results are : Number of poles 2p=40 Inside stator diameter D^STIO mm Minimum air gap (actual) <5n=4.3 mm Carter's coefficient £,=1.164 Depth of pole tip at centeriine hpl=35 mm Width of pole tip bp=200 mm viii Depth of the poie body hpç =143 mm Width of the pole body *K=150mm Width of the field winding b« =25 mm Maximum air gap ^mx =9.1 mm Pole face radius(inner) R =1850.7 mm Pole face radius (outer) R =1845.9 mm For the sample salient pole synchronous generator, five different poie tip models are improved. In this chapter, these five different models are introduced one by one. By using FLD13 packet program, shapes of pole tips are plotted in real dimension for every model. And then, shapes of the excitation fields in air gap are plotted by using MAT-LAB program. For this, output datas of the FLD13 packet program are used. By using MAT-LAB program again, excitation field harmonics are plotted for every model. In MODEL 1, the air gap was taken constant along all the pole tip. In MODEL 2, shaping of the air gap is to be got a cosinus function from the pole centeriine to each x distance. This variation of the air gap is given by Equation 2.(£0:Minimum air gap, <^:Air gap at x distance) *,=- ^- (2) x 71. X cos In MODEL 3, the air gap was taken constant (at minimum value) below the middle of the poie up to 0.4 tp and after that the air gap was widened to 25 3 at the end of the pole tip. In MODEL 4, pole tips were taken eccentric in respect of the armature centeriine. In other words, the center of the armature cylinder and the center of the circle forming the pole arc is not congruent. In MODEL 5, the air gap was taken constant (at minimum value) below the middle of the pole up to 1/3 TP. After that the air gap was widened to «5"maxat the end of the pole tip. ix In the sixth chapter, the harmonic analysis results belonging the models were given and curves of the excitation fields were demonstrated in collected form. The differences among the models were considered. By using these output datas belonging the models, the ideal pole tip shape was determined.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1995

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1995

Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 1995

##### Anahtar kelimeler

Harmonikler,
Jeneratörler,
Senkron jeneratör,
Harmonics,
Generators,
Synchronous generator