Sažetak (engleski) | Nominal power and characteristics of the synchronous generator are determined by the temperature that develops within the machine. Nowadays the strong competition demands a higher grade of efficiency and consequently new materials are introduced in the machine development process. Using simplified or only standard techniques of calculation can lead to the development of the synchronous generator that does not satisfy such high demands therefore, the need for more accurate thermal analysis is required. Comprehensive understanding of the machines thermal condition demands an application of multiple engineering disciplines such as electromagnetism, heat transfer and fluid dynamics. Review of the existing research shows the need for development of new methodologies of calculation that combine multiple engineering disciplines (electromagnetism and thermal calculation) with intent to provide more accurate values of temperatures and losses during the development state of the machine. The idea is to implement an appropriate model with simplified procedure of the initial two-dimensional (2D) modeling and to obtain the corresponding model with accurate results. Thermal conditions and losses inside the machine have to be studied with respect to several engineering disciplines like electromagnetism, heat transfer and fluid dynamics. Due to the complexity of both the calculation and the geometry the numerical electromagnetic and thermal calculation based on the finite elements method (FEM) is often applied. Applying the methodology of sequential coupling of such calculations allows an independent execution of each calculation and results with detailed and accurate modeling for every individual model. Applying an appropriate methodology and coupling algorithm, which is formulated through this thesis enables the losses and temperatures inside the synchronous generator to be determined automatically. This thesis describes the development of the methodology for coupled calculation of the electromagnetic and thermal conditions of the synchronous generator using the numerical methods. Diversity of problems in the electromagnetic and thermal field and different physical significance of fields of interest requires an application of different meshes for each model. This also requires the development of an appropriate method for loss and temperature transfer between different meshes. The methodology of the electromagnetic and thermal calculation coupling through the FEM mesh using the projection of loss and temperature values on 2D mesh is applied. Value transfer through the mesh of finite elements allows automatic transfer of temperature and loss values between individual models and automatic model coupling. For loss calculation, this thesis applies an electromagnetic numerical simulation of 2D FEM in time domain. External electrical circuit is directly included in the FEM, rotation of rotor is simulated by moving rotor’s mesh regarding to the stator. The losses in the windings and iron losses are calculated using the appropriate postprocesing expressions. The value of losses represents a heat source for thermal calculation. This thesis shows simplified three-dimensional (3D) thermal model based on FEM numerical method. New methodology for automatic creation of synchronous generators 3D thermal model from initial 2D mesh is provided in this thesis. In machines with one ventilation circuit, which contains multiple radial and axial cooling channels and has considerable coolant temperatures, the assumption of constant average temperature of fluids in the whole area of the machine is not accurate enough. Therefore, the cooling circuit which allows more accurate temperature calculation in electric machines is introduced. Thermal calculation based on 3D FEM is coupled with cooling circuit which uses the parameters from ventilation calculation. The results of the numerical thermal calculation are the stationary values of temperatures. Temperature values further affect the values of losses obtained by electromagnetic calculation through the material characteristics dependent of the temperature. The applications of mentioned methodology as well as the specific individual models require implementation of algorithms which are formulated through this thesis into a programming system. The thesis is organized into ten chapters. Chapter 1. - Introduction contains the review of the research area related to the thesis and introduction to related modeling and methodologies. Chapter 2. - Synchronous generator data contains basic data about the synchronous generator which is the model for research in this thesis. Chapter 3. - Ventilation of electric machines describes cooling principle and ventilation of electric machine. This chapter shows two methods for calculating the ventilation. Simplified one-dimensional (1D) method for calculating the ventilation based on determination of ventilation network is described in detail. The second method shown uses CFD and 2D modeling for calculating the flow rate. The results of calculation are shown for each method. The cooling circuit is implemented in order to include the effect of fluid heating during the circulation through the machine and affects heat transfer in the thermal calculation. As described in this chapter, the modeling of the cooling circuit is performed by dividing the area of fluid flow into control volumes. Calculation of average fluid temperatures for each control volume based on absorbed losses, flow rate from ventilation calculation and temperatures from previous control volumes is presented in detail. Knowledge of absorbed losses and fluid temperature allows coupling of thermal calculation by applying FEM and cooling circuit with calculation of coolant heating. Chapter 4. - Heat transfer in electrical machines describes thermal modeling and thermal calculation of the machine. Existing research for individual specific parts of the machine is used to determine the heat transfer coefficient. Their overview is shown in this chapter. Thermal modeling for individual parts of the electric machine is presented. This chapter describes numerical procedure using FEM for thermal calculation of synchronous generator's 3D model. This chapter also shows the new methodology for automatic creation of synchronous generator's 3D model based on 2D mesh. From 2D thermal mesh with triangular elements, the 3D mesh model is automatically created by applying prism as the element of FEM. Model created using this technique consists of a 3D shape and 3D FEM mesh. As shown in this chapter, the appropriate heat transfer coefficients are added to the surfaces of 3D model. Flow chart for coupling thermal calculation with cooling circuit is shown. Chapter 5. - Electromagnetic calculation describes numerical method applied for electromagnetic calculation. Non-sinusoidal waveform of flux density, induced current and voltage are taken into consideration using the time domain calculation. This chapter describes applied numerical procedure for 2D FEM in time domain. Modeling of the nominal operating condition is accomplished using the 2D FEM and the external electric circuit. In this chapter, numerical procedures for including external electric circuit into magnetic FEM calculation are presented. Modeling of rotor movement according to the stator based on rotors movement along the line of rotation in the air gap is described. This chapter describes the methodology and numerical procedure for modeling of stator's skewed slots which is solved by slicing the 3D model into multiple cross sections along the axial direction. This chapter also contains the results of electromagnetic calculation. Due to the affect of mesh on calculation results, the electromagnetic calculation has been performed both for the model with and for the model without slot skew. Also, the electromagnetic calculation with increased number of mesh elements is performed for the model without slot skew. Results of electromagnetic calculation are given and these results are used for loss calculation in the next chapter. Chapter 6. - Losses in synchronous generator describes methods for loss calculation of the synchronous generator, which have direct influence on the thermal calculation, this includes ohmic and iron losses. An overview of the losses in synchronous generator is discussed. This chapter describes the method for calculating the ohmic losses based on known analytical expression for loss calculation. After comparing the results of the calculation with the measured values of required excitation current for the nominal working point, good agreement is shown. An overview of iron losses and methods for determining the iron losses which are based on postprocessing expressions are discussed in this chapter. Also, method based on the implementation of correctional factors for loss calculation as the relation between measured and calculated values is discussed. This chapter describes three methods for the calculation of iron losses. All stated methods are based on separating losses in to three components. First method calculates losses based on the maximum flux density value in each finite element. Second method calculates losses in frequency domain. Losses are calculated as the sum of individual losses of both orthogonal directions. This method also performs the harmonic analysis and calculates the contribution of individual flux density harmonics. Third method calculates the iron losses in time domain. Models of equivalent hysteresis loop and minor hysteresis loop is presented. Techniques for determination of material loss coefficients are described. Chapter shows the result comparison of iron losses obtained from different postprocessing expressions. Also, the results of the iron loss calculation and iron loss measurement for no load condition are presented. The correctional factor has been determined for each method and results have been shown. Loss distribution analysis was performed and presented with images at the cross section of the machine along with the areas that are significantly influenced by higher harmonic components. Results of calculated iron losses for nominal operating point for presented methods and models with different number of mesh elements are also shown. Chapter 7. - Coupling of the magnetic and thermal models describes methods for coupling of the electromagnetic and thermal model. At the beginning of the chapter, a detailed description of sequential coupling method of the electromagnetic and thermal FEM models is described. Also, the flow chart of the sequential calculating algorithm is shown. Chapter describes the temperature dependency of materials used for determining new values of losses in the machine. The chapter contains descriptions of different methods for data projection between FEM mesh. Applying the method of weighted residuals where the temperature values have been projected from thermal into electromagnetic mesh is described in detail. Losses obtained from the electromagnetic calculation are included in thermal calculation using new method, through the mesh elements of the numerical calculation. The proposed method is described in detail. Chapter shows the result of projecting loss and temperature values between meshes with minimal error. Due to the complexity of geometry and calculation, the electromagnetic and thermal FEM models are coupled using weak coupling method. The calculation is divided on magnetic and thermal model. Electromagnetic and thermal model of calculation are coupled through calculated values of temperature and losses. Applying the projection of temperature and loss through the mesh of finite elements allows automatic model coupling. Chapter 8. - Results of the numerical analysis of the thermal and electromagnetic calculation contain an overview of the results of the coupled numerical analysis of the thermal and electromagnetic calculation of the synchronous generator. Stated results are given for the nominal working point. Results of the numerical analysis are presented with the images of temperature distribution in the 3D model of synchronous generator. Measurement of the temperature rise and local temperature values have been performed for the actual generator. Result comparison shows good agreement between measured values and calculated results. Chapter 9. - Structure of software package describes modules contained by the software which was developed for performing the complete analysis. By applying presented methods and algorithms the computer software which performs numerical electromagnetic and thermal analysis was created. Also, additional part of program was created for coupling of the previously stated analysis and transfer of losses and temperatures between individual calculations. Thesis shows the development of methodology for coupling of electromagnetic and thermal calculation based on FEM. Coupling algorithm that performs loss and temperature data projection between 2D FEM mesh is applied. Simplified 3D model was created using an algorithm for automatic creation of 3D model from 2D mesh. Thermal 3D calculation of synchronous generator has been performed using numerical procedure with FEM. Thermal calculation is coupled with cooling circuit. Magnetic FEM calculation with an external electrical circuit has been performed for determining the losses of the synchronous generator. Ohmic and iron losses have been analyzed. For validation purposes of previously stated methodologies, the coupled electromagnetic and thermal computational calculation procedure is carried out for the actual generator. Stationary values of losses and temperatures are determined and the results of temperatures are compared with measured values. The scientific contributions of the thesis are: 1. Development of coupling methodology for magnetic, thermal and ventilation computation by means of finite element mesh connected to external circuit. 2. Formulation of algorithm for coupled computation of magnetic and thermal state by application of numerical methods that enable automatic determination of losses and temperatures in synchronous generator. 3. Implementation of algorithms into a programming system and verification of results by comparison with measurements. |