Simulation of a Time Dependent 2D Generator Model Using Comsol Multiphysics

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1 Simulation of a Time Dependent 2D Generator Model Using Comsol Multiphysics M. Rambabu 1, K. Naresh 2, A. Balaji 3, J.Sai Siva Kalyan 4 Usha Rama College of Engineering and Technology Department of Electrical and Electronics Engineering 1 ramhoney05@gmail.com, 2 naresh5kelothu@gmail.com, 3 baluurce@gmail.com, 4 jsskalyan@gmail.com Abstract COMSOL Multi physics is designed to be an extremely flexible package applicable to virtually many areas of research, science, and engineering. A consequence of this flexibility is that it becomes necessary to set up COMSOL Multi physics for a specific modeling task. It familiarizes with the modeling of generator (2D) in the AC/DC Module and illustrates different aspects of the simulation process. It steps through all the stages of modeling, from geometry creation to post processing. The program must mesh the geometry of the generator model before it can solve the problem. The powerful visualization of COMSOL Multi physics tools is accessible in the program s post-processing mode. With this visualization time varying flux distribution and corresponding voltage output of the generator is possible to represent. Reliable output voltage of the generator depends upon the number of flux lines cut by the stator winding that depends on material property of stator and rotor. The materials may be magnetic or nonmagnetic. With various combinations of these materials corresponding output voltage and flux distribution are shown here with the process of modeling, defining, solving, and post processing using the COMSOL Multi physics graphical user interface. The purpose of this modeling is to find out best material combination which would produce significant amount of output voltage with least harmonic.. Index Terms COMSOL, 2D-generator model, Multi Physics tools, MATLAB/Simulink I. INTRODUCTION This paper shows how the circular motion of a rotor with permanent magnets generates an induced EMF in a stator winding. The generated voltage is calculated as a function of time during the rotation. The model also shows the influence on the voltage from material parameters, rotation velocity, and number of turns in the winding the center of the rotor consists of annealed medium carbon steel, which is a material with a high relative permeability. The center is surrounded with several blocks of a permanent magnet made of samarium and cobalt, creating a strong magnetic field. The stator is made of the same permeable material as the center of the rotor, confining the field in closed loops through the winding. The winding is wound around the stator poles. Figure1 shows the generator with part of the stator sliced in order to show the winding and the rotor. Fig. 1 Drawing of a generator showing how the rotor, stator, and stator winding are constructed. The winding is also connected between the loops, interacting to give the highest possible voltage. a) MODELLING IN COMSOL MULTIPHYSICS The COMSOL Multi physics model of the generator is a time-dependent 2D problem on a cross section through the generator [1]. This is a true time-dependent model where the motion of the magnetic sources in the rotor is accounted for in the boundary condition between the stator and rotor geometries. Thus, there is no Lorentz term in the equation, resulting in the PDE where the magnetic vector potential only has a z component Rotation is modeled using a ready-made physics interface for rotating machinery. The center part of the geometry, containing the rotor and part of the air-gap, rotates relative to 2204

2 the coordinate system of the stator. The rotor and the stator are imported as two separate geometry objects, so it is possible to use an assembly (see the section finalizing the Geometry in the COMSOL Multi physics Reference Manual for further details). This has several advantages: the coupling between the rotor and the stator is done automatically, the parts are meshed independently, and it allows for a discontinuity in the vector potential at the interface between the two geometry objects (called slits). The rotor problem is solved in a rotating coordinate system where the rotor is fixed (the rotor frame), whereas the stator problem is solved in a coordinate system that is fixed with respect to the stator (the stator frame). An identity pair connecting the rotating rotor frame with the fixed stator frame is created between the rotor and the stator. The identity pair enforces continuity for the vector potential in the global fixed coordinate system (the stator frame). The stator and center of the rotor are made of nnealed medium-carbon steel (soft iron), which is implemented in COMSOL Multi physics as an interpolation function of the B-H curve of the material; see Fig. 2. The function can be used in the domain settings. Usually B-H curves are specified as modules B versus H, but the rotating machinery, Magnetic interface must have modules H versus B. It is therefore important that the H-data is entered as f(x)-data of the interpolation function and the B-data entered as x-data This relationship for modules H is predefined for the material Soft Iron (withoutlosses) in the materials library that is shipped with the AC/DC Module. Fig. 2 The norm of the magnetic flux, B, versus the norm of the magnetic field, H, for the rotor and stator materials. The inverse of this curve is used in the calculation. The generated voltage is computed as the line integral of the electric field, E, along the winding. Because the winding sections are not connected in the 2D geometry, a proper line integral cannot be carried out. A simple approximation is to neglect the voltage contributions from the ends of the rotor, where the winding sections connect. The voltage is then obtained by taking the average z component of the E field for each winding cross-section, multiplying it by the axial length of the rotor, and taking the sum over all winding cross sections. Where L is the length of the generator in the third dimension, NN is the number of turns in the winding, and A is the total area of the winding cross-section a) Introduction II. COMSOL COMSOLMultiphysics is a comprehensive simulation software environment for a wide array of applications, but structured and user-friendly for all to use. Engineers and scientists have long had to make assumptions in order to be able to realize their design ideas [2]. As time progresses these assumptions are being refined and in some cases even eliminated allowing for more accurate results. Multiphysics is one major enabler in eliminating assumptions. How? By coupling related physical applications together to include all the necessary factors for a complete model. COMSOL Multiphysics is a simulation software designed to provide the most accurate results by minimizing the assumptions its users must make. Users of COMSOL Multiphysics are free from the restrictive nature generally associated with simulation software. The COMSOL user has complete control of his or her model. The ability to couple any number of physics together and input user-defined physics and expressions directly into a model allows COMSOL users to be creative in a way that is not possible or just a lot harder with other simulation software. COMSOL is a simulation environment, designed with real-world applications in mind. The point of all simulation of course is to mimic, as closely as possible, effects that are observed in reality. Be they in an engineering or scientific context. To do this, there is the need of multiphysics; that is multiple scientific models that include the things that you are interested in. Some of these are: acoustics, electromagnetics, chemical reactions, mechanics, fluid flow, and heat transfer. Because the real world includes all of these effects, your simulation environment should also. This is what COMSOL seeks to deliver, and we do so in an easy-to-use interface geared toward making scientists and engineers more productive in their day-to-day work Engineers are designing better products faster and at less cost. Scientists are exploring new discoveries. Physicians are researching innovative medical treatments. Educators are connecting with students, and the list goes on. We re confident you ll be impressed that 2205

3 the users of COMSOL multiphysics are producing simulations that make a big impact in the real world. b) Steps of COMSOL We can create a new model guided by the Model Wizard or start from a Blank Model. 1. Start by selecting the space dimension for your model component: 3D, 2D Axisymmetric, 2D, 1D Axisymmetric, or 0D. 2. Now, add one or more physics interfaces. These are organized in a number of Physics branches in order to make them easy to locate. These branches do not directly correspond to products. When products are added to your COMSOL installation, one or more branches will be populated with additional physics Interfaces. 3. Select the Study type that represents the solver or set of solvers that will be used for the computation. 4. Finally, click Done. The desktop is now displayed with the model tree configured according to the choices you made in the Model Wizard c) Model Builder Finally, click Done. The desktop is now displayed with the model tree configured according to the choices you made in the Model Wizard It is worth noting that if you have the Help window open (which is achieved either by SE selecting Help from the File menu, or by pressing the function key F1), then you will also get dynamic help (in English only) when you click on a node. Workflow and gives an overview of the functionality available for each modeling step. Physics, building the mesh, running a study, and visualizing the simulation results. Physics, Mesh, Study, and Results Contextual tabs are shown only if and when they are needed, such as the 3D Plot Group tab which is shown when the corresponding plot group is added or when the node is selected in the model tree. Modal tabs are used for very specific operations, when other operations in the ribbon may become temporarily irrelevant. An example is the Work Plane modal It is worth noting that if you have the Help window open (which is achieved either by SE selecting Help from the File menu, or by pressing the function key F1), then you will also get dynamic help (in English only) when you click on a node. The Home tab has buttons for the most common operations for making changes to a model and for running simulations. Examples include changing model parameters for a parameterized geometry, reviewing material properties and All of the nodes in the default model tree are top-level parent nodes. You can right-click on them to see a list of child nodes, or subnodes, that you can add beneath them. This is the means by which nodes are added to the tree tab. When working with Work Planes, other tabs are not shown since they do not present operations relevant to. The ribbon gives quick access to available commands and complements the model tree in the Model Builder window. Most of the functionally accessed from the ribbon is also accessible from contextual menus by right-clicking nodes in the model tree. Certain operations are only available from the ribbon, such as selecting which desktop window to display. In the COMSOL Desktop interface for OS X and Linux, this functionality is available from toolbars which replace the ribbon on these platforms. THE QUICK A CCESS TOOLBAR There are standard tabs for each of the main steps in the modeling process. These are ordered from left to right according to the workflow: Definitions, Geometry A model tree always has a root node (initially labeled Untitled.mph), a Global Definitions node, and a Results nodethe Label on the root node is the name of the multiphysics model file, or MPH file, that this model is saved to. The root node has settings for author name, default unit system, and more In the COMSOL Desktop environment for OS X and Linux, the ribbon is replaced by a set of menus and toolbars You build a model by starting with the default model tree, adding nodes, and editing the node settings. When you click on a child node, then you will see its node settings in the settings window. It is here that you can edit node settings. Export: defines numerical data, images, and animations to be exported to files has no sett settings, but its child nodes have plenty of them. Reports: contains automatically generated or custom reports about the Global Definitions node is where you define parameters, variables, functions, and couplings that can be used throughout the model tree. They can be used, for The Results node is where you access the solution after performing a simulation and where you find tools for processing the data. The Results node initially has example, to define the values and functional dependencies of material properties, forces, geometry, and other relevant features. The Global definitions node itself. The Model Builder is the tool where you define the model and its components: how to solve it, the analysis of results, and the reports. You do that by building a model tree. Derived Values or for Results generated by probes that monitor the solution in real-time while the simulation is running in the Graphics window or in Plot windows model in HTML or Microsoft Word format To these five default subnodes, you may also add additional Plot Group subnodes some of these may be created automatically, depending on the type of simulations you are performing, but you may add additional figures by right-clicking on the results node and choosing from the list of plot types. In addition to the three nodes just described, there are two additional top-level node types: Component nodes and Study nodes. These are usually created by the Model Wizard when you create a new model [3]. After using the Model Wizard to 2206

4 specify what type of physics you are modeling, and what type of Study (e.g. steady-state, time-dependent, frequency-domain, or eigen frequency analysis) you will carry out, the Wizard automatically creates one node of each type and shows you their contents. Data Sets: contains a list of solutions you can work with that define graphs to be displayed Derived Values: defines values to be derived from the solution using a number of post processing tools. Specifying mesh element sizes. Defining parametric sweeps (that is, simulations that are repeated for a variety of different values of a parameter such as a frequency or a load). A Parameter Expression can contain numbers, parameters, built-in constants, functions with Parameter Expressions as arguments, and unary and binary operators. For a list of available operators, see Appendix C Language Elements and Reserved Names on page 131. Because these expressions are evaluated before a simulation begins, Parameters may not depend on the time variable t. Likewise, they may not depend on spatial variables, like x, y, or z, nor on the dependent variables that your equations are solving for. b) Scope The scope of a Parameter or Variable is a statement about where it may be used in a expression. All Parameters are defined in the Global Definition node of the model tree. This means that they are global in scope and can be used throughout the model tree. A Variable may also be defined in the Global Definitions node and have global scope, but they are subject to other limitations. For example, Variables may not be used in Geometry, Mesh, or Study nodes (with the one exception that a Variable may be used in an expression that determines when the simulation should stop). Fig. 3. Model Builder III. PARAMETERS, VARIABLES AND SCOPE a) Parameters To be more specific, suppose that you build a model that simulates a coil assembly that is made up of two parts, a coil and a coil housing. You can create two component nodes, one models the coil and the other the coil housing. You can then rename each of the nodes with the name of the object. Similarly, you can also create two Study nodes, the first simulating the stationary, or steady-state, behavior of the assembly and the second simulating the frequency response. You can rename these two nodes to be Stationary and Frequency Domain. When the model is complete, save it to a file named Coil Assembly.mph. At that point, the model tree in the Model Builder looks like the above figure. In this figure, the root node is named CoilAssembly.mph, indicating the file in which the model is saved. The Global Definitions node and the Results node each have their default name. In addition there are two Component nodes and two Study nodes with the names chosen in the previous paragraph. You define Parameters in the model tree under Global Definitions. Parameterizing geometric dimensions. Fig. 4 Scope of parameters A Variable that is defined, instead, in the Definitions subnode of a Component node has local scope and is intended for use in that particular Component. They may be used, for example, to specify material properties in the Materials subnode or to specify boundary conditions or interactions. It is sometimes valuable to limit the scope of the variable to only a certain part of the geometry, such as certain boundaries. For that purpose, 2207

5 provisions are available in the settings for a Variable to select whether to apply the definition either to the entire geometry of the Component, or only to certain Domains, Boundaries [4]. Variables can be defined either in the Global Definitions node or in the Definitions subnode of any Component node. Naturally, the choice of where to define the variable depends on whether you want it to be global (that is, usable throughout the model tree) or locally defined within a single Component node. Like a Parameter Expression, a Variable Expression may contain numbers, parameters, built-in constants, and unary and binary operators. However, it may also contain Variables, like t, x, y, or z, functions with Variable Expressions as arguments, and dependent variables that you are solving for in addition to their space and time derivatives. Although Variables defined in the Definitions subnode of a Component node are intended to have local scope, they can still be accessed outside of the Component node in the model tree by being sufficiently specific about their identity. This is done by using a dot-notation where the Variable name is preceded by the name of the Component node in which it is defined and they are joined by a dot. In other words, if a Variable named is defined in a Component node named MyModel, then this variable may be accessed outside of the Component node by using MyModel.foo. This can be useful, for example, when you want to use the variable to make plots in the Results node. orange (a warning) or red (an error) and you will get a tooltip message if you select the text string. IV. GEOMETRY Import the geometry of the generator cross section from an external CAD file. It deals with the construction and representation of free-form curves, surfaces, or volumes. Core problems are curve and surface modelling and representation. GD studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. The most important instruments here are parametric curves and parametric surfaces, such as Bézie curves, spline curves and surfaces. An important non-parametric approach is the level set method. Application areas include shipbuilding, aircraft, and automotive industries, as well as architectural design. The modern ubiquity and power of computers means that even perfume bottles and shampoo dispensers are designed using techniques unheard of by shipbuilders of 1960s. Geometric models can be built for objects of any dimension in any geometric space. Both 2D and 3D geometric models are extensively used in computer graphics. 2D models are important in computer typography and technical drawing. 3D models are central to computer-aided design. Geometric models are usually distinguished from procedure and object-oriented models, which define the shape implicitly by an algorithm. They are also contrasted with digital images and volumetric models and with implicit mathematical models such as the zero set of an arbitrary polynomial. However, the distinction is often blurred, for instance, geometric shapes can be represented by objects, a digital image can be interpreted as a collection of colored squares; and geometric shapes such as circles are defined by implicit mathematical equations. Also, the modeling of fractal objects often requires a combination of geometric and procedural techniques. Fig. 5. Flow chart for all above process COMSOL comes with many built-in constants, variables and functions. They have reserved names that cannot be redefined by the user. If you use a reserved name for a user-defined variable, parameter, or function, the text you enter will turn Fig. 6. AutoCad Geometry 2208

6 Fig. 7. Conductor Area Selection V. MATERIAL SELECTION In COMSOL Multiphysics, you can create your own completely customized materials. It's simple: Add a blank template material to your model, assign it to the necessary parts of your model geometry, and describe how the material behaves through specifying material properties[5]. Use constants, parameters, and/or write an expression to define the value for each material property. You can also control the appearance of the material in the Graphics window. After creating the material, you can save it for future simulations by adding it to the User-Defined Material Library. Fig. 9 Selection of soft iron VI. ROTATING MACHINERY, MAGNETIC (RMM) Apply a Prescribed Rotational Velocity feature to the rotor, and specify its rotational velocity using the parameter rpm. a) Prescribed Rotational Velocity 1 1. on the Physics toolbar, click Domains and choose Prescribed Rotational Velocity. 2. Select Domains only. 3. In the Settings window for Prescribed Rotational Velocity, locate the Prescribed Rotational Velocity section. 4. In the rps text field, type rpm. The permanent magnets on the rotor have a radial field. Use the cylindrical coordinate system specified earlier to define it. Fig. 8. Air gap of generator Fig. 10 Selection of rotating part 2209

7 b) Ampere s Law 2 1. On the Physics toolbar, click Domains and choose Ampere s Law. 2. Select Domains 20, 23, 24, and 27 only. 3. In the Settings window for Ampere s Law, locate the Coordinate System Selection section. 4. From the Coordinate system list, choose Cylindrical System 2 (sys2). 5. Locate the Magnetic Field section. From the Constitutive relation list, choose Remanent flux density. 6. Specify the Br vector as The other four magnets are reversed Tetrahedral elements are the default element type for most physics within COMSOL. Tetrahedra are also known as a simplex, which simply means that any 3D volume, regardless of shape or topology, can be meshed with tets. They are also the only kind of elements that can be used with adaptive mesh refinement. For these reasons, tets can usually be your first choice [6]. The other three element types (bricks, prisms, and pyramids) should be used only when it is motivated to do so. It is first worth noting that these elements will not always be able to mesh a particular geometry. The meshing algorithm usually requires some more user input to create such a mesh, so before going through this effort, you need to ask yourself if it is motivated. Here we will talk about the Motivations behind using brick and prism elements. The pyramids are only used when creating a transition in the mesh between bricks and tets. Fig. 10 Selection of north poles(colored) rest south poles VII. MESHING & STUDY One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. In this post, we will delve deeper into how to choose an appropriate mesh to start your mesh convergence studies for linear static finite element problems. As we saw earlier, there are four different 3D element typesets, bricks, prisms, and pyramids: These four elements can be used, in various combinations, to mesh any 3D model. (For 2D models, you have triangular and quadrilateral elements available. We won t discuss 2D very much here, since it is a logical subset of 3D that doesn t require much extra explanation.) What we haven t spoken in-depth about yet is why you would want to use these various elements. Fig. 11 Meshing of generator VIII. RESULTS Magnetic Flux Density (rmm) Now, plot the solution in the spatial frame (the stator's fixed frame) at time t = 0.2 s Data Sets 1. In the Model Builder window, expand the Results>Data Sets node, then click Study 1/ Solution In the Settings window for Solution, locate the Solution section. 3. From the Frame list, choose Spatial (x, y, z). Magnetic Flux Density (rmm) 1. In the Model Builder window, under Results click Magnetic Flux Density (rmm). 2. In the Settings window for 2D Plot Group, locate the Data section. 3. From the Time (s) list, choose In the Model Builder window, right-click Magnetic Flux Density (rmm) and choose Contour. 2210

8 5. In the Settings window for Contour, click Replace Expression in the upper-right corner of the Expression section. From the menu, choose Model>Component1>Rotating Machinery, Magnetic (Magnetic Fields)>Magnetic>Magnetic vector potential (Material)>Az - Magnetic vector potential, Z component. 6. Locate the Coloring and Style section. From the Coloring list, choose Uniform. 7. From the Color list, choose Black. 8. Locate the Levels section. In the Total levels text field, type On the 2D plot group toolbar, click Plot Fig. 13 Resultant Induced Voltage The plot shows an induced EMF with an amplitude of about 4.2 V. Fig. 12 Resultant flux density of generator The plot will show the rotor position at t = 0.2 s, the magnetic flux density norm and magnetic flux lines. Next, plot the induced EMF in a quarter of the cycle 1D Plot Group 2 1. On the Model toolbar, click Add Plot Group and choose 1D Plot Group. 2. In the Settings window for 1D Plot Group, click to expand the Title section. 3. From the Title type list, choose Manual. 4. In the Title text area, type Induced voltage. 5. Locate the Plot Settings section. Select the x-axis label check box. 6. In the associated text field, type Time (s). 7. Select the y-axis label check box. 8. In the associated text field, type Voltage (V). 9. On the 1D plot group toolbar, click Global. 10. In the Settings window for Global, click Replace Expression in the upper-right corner of the y-axis data section. From the menu, choose Model>Global Definitions>Variables>Vi - Induced voltage in winding IX. CONCLUSION Independent of the structure size, the AC/DC Module of COMSOL Multiphysics accommodates any case of nonlinear, inhomogeneous, or anisotropic media. It also handles materials with properties that vary as a function of time as well as frequency-dispersive materials. Applications that can successfully simulate with the AC/DC Module include electric motors, generators, permanent magnets, induction heating devices, dielectric heating, capacitors, and electrical machinery. The simulation of the generator model can be used to design small power generator with high efficiency, compactness and low wait to torque ratio. This simulation experiment clearly demonstrate the output voltage characteristics for different material under rotating condition and also shows the strong effect of permeability and conductivity on output voltage magnitude. In future experiment Neodymium Iron-Boron (NdFeB) is likely to be used instead of Samarium Cobalt due to its High remanent flux density & low cost ACKNOWLEDGMENT We are thankful to URCET Chairmen, Principal, A. Lokesh and J. Ravi Kumar supported for this research. REFERENCES [1] Software version- Comsol multiphysics Module 5.0, Model [2] William T. Ryan, Design of Electrical Machinery Volume 3; New York;John Wiley & Sons, [3] W. S. Franklin and R. B. Williamson, The Elements of Alternating Currents ; The Macmillan company, London, [4] Alfred Still, Principles of Electrical Design dc and ac Generators ; Mcgraw-Hill book company, New York, [5] Mark, James E. (Ed.), Physical Properties of Polymers Handbook. [6] S.O Kasap, Principles of Electronic Materials and Devices ; March 05,