Introduction to Machinery Principles-Power Electronics-Handout, Exercises of Power Electronics

Download Introduction to Machinery Principles-Power Electronics-Handout and more Exercises Power Electronics in PDF only on Docsity! EE2401 Electromechanical Systems-Chapter 01 1/19 CHAPTER 1 - Introduction to Machinery Principles Summary: 1. Basic concept of electrical machines fundamentals: o Rotational component measurements  Angular Velocity, Acceleration  Torque, Work, Power  Newton’s Law of Rotation o Magnetic Field study  Production of a Magnetic Field  Magnetic Circuits 2. Magnetic Behaviour of Ferromagnetic Materials 3. How magnetic field can affect its surroundings:  Faraday’s Law – Induced Voltage from a Time-Changing Magnetic Field.  Production of Induced Force on a Wire.  Induced Voltage on a Conductor moving in a Magnetic Field Introduction 1. Electric Machines  mechanical energy to electric energy or vice versa Mechanical energy  Electric energy: GENERATOR Electric energy  mechanical energy: MOTOR 2. Almost all practical motors and generators convert energy from one form to another through the action of a magnetic field. 3. Only machines using magnetic fields to perform such conversions will be considered in this course. 4. When we talk about machines, another related device is the transformer. A transformer is a device that converts ac electric energy at one voltage level to ac electric energy at another voltage level. 5. Transformers are usually studied together with generators and motors because they operate on the same principle; the difference is just in the action of a magnetic field to accomplish the change in voltage level. 6. Why are electric motors and generators so common? - Electric power is a clean and efficient energy source that is very easy to transmit over long distances and easy to control. - Does not require constant ventilation and fuel (compare to internal- combustion engine), free from pollutant associated with combustion 1. Basic concept of electrical machines fundamentals 1.1 Rotational Motion, Newton’s Law and Power Relationship docsity.com EE2401 Electromechanical Systems-Chapter 01 2/19 Almost all electric machines rotate about an axis, called the shaft of the machines. It is important to have a basic understanding of rotational motion. Angular position,  - is the angle at which it is oriented, measured from some arbitrary reference point. Its measurement units are in radians (rad) or in degrees. It is similar to the linear concept of distance along a line. Conventional notation: + ve value for anticlockwise rotation - ve value for clockwise rotation Angular Velocity,  - Defined as the velocity at which the measured point is moving. Similar to the concept of standard velocity where: dr v dt  Where: r – distance traverse by the body t – time taken to travel the distance r For a rotating body, angular velocity is formulated as: d dt   (rad/s) Where:  - angular position/ angular distance traversed by the rotating body t – time taken for the rotating body to traverse the specified distance, . Angular acceleration,  - is defined as the rate of change in angular velocity with respect to time. Its formulation is as shown: d dt   (rad/s2) Torque,  1. In linear motion, a force applied to an object causes its velocity to change. In the absence of a net force on the object, its velocity is constant. The greater the force applied to the object, the more rapidly its velocity changes. 2. Similarly in the concept of rotation, when an object is rotating, its angular velocity is constant unless a torque is present on it. Greater the torque, more rapid the angular velocity changes. 3. Torque is known as a rotational force applied to a rotating body giving angular acceleration, a.k.a. ‘twisting force’. 4. Definition of Torque: (Nm) ‘Product of force applied to the object and the smallest distance between the line of action of the force and the object’s axis of rotation’ docsity.com EE2401 Electromechanical Systems-Chapter 01 5/19 HB  3. Applying Ampere’s law, the total amount of magnetic field induced will be proportional to the amount of current flowing through the conductor wound with N turns around the ferromagnetic material as shown. Since the core is made of ferromagnetic material, it is assume that a majority of the magnetic field will be confined to the core. 4. The path of integration in Ampere’s law is the mean path length of the core, lc. The current passing within the path of integration Inet is then Ni, since the coil of wires cuts the path of integration N times while carrying the current i. Hence Ampere’s Law becomes, c c Hl Ni Ni H l    5. In this sense, H (Ampere turns per meter) is known as the effort required to induce a magnetic field. The strength of the magnetic field flux produced in the core also depends on the material of the core. Thus, B = magnetic flux density (webers per square meter, Tesla (T)) µ= magnetic permeability of material (Henrys per meter) H = magnetic field intensity (ampere-turns per meter) 6. The constant  may be further expanded to include relative permeability which can be defined as below: r o    Where: o – permeability of free space (air) 7. Hence the permeability value is a combination of the relative permeability and the permeability of free space. The value of relative permeability is dependent upon the type of material used. The higher the amount permeability, the higher the amount of flux induced in the core. Relative permeability is a convenient way to compare the magnetizability of materials. 8. Also, because the permeability of iron is so much higher than that of air, the majority of the flux in an iron core remains inside the core instead of travelling through the surrounding air, which has lower permeability. The small leakage flux that does leave the iron core is important in determining the flux linkages between coils and the self- inductances of coils in transformers and motors. 9. In a core such as in the figure, B = H = cl Ni Now, to measure the total flux flowing in the ferromagnetic core, consideration has to be made in terms of its cross sectional area (CSA). Therefore, docsity.com EE2401 Electromechanical Systems-Chapter 01 6/19 Where: A – cross sectional area throughout the core Assuming that the flux density in the ferromagnetic core is constant throughout hence constant A, the equation simplifies to be: BA  Taking into account past derivation of B, c NiA l   2. Magnetic Circuits The flow of magnetic flux induced in the ferromagnetic core can be made analogous to an electrical circuit hence the name magnetic circuit. The analogy is as follows: + - A RV + -  Reluctance, RF=Ni (mmf) Electric Circuit Analogy Magnetic Circuit Analogy Electric Circuit Magnetic Circuit RIV  Rf  V: electromotive force (emf) i.e. voltage f: magnetomotive force (mmf) I: current  : flux R: resistance R: reluctance Conductor Conductor A l R  Core Core A l relR )(  : resistivity yreluctivitrel    1  1  yreluctivitrel  : conductivity  : permeability  A BdA docsity.com EE2401 Electromechanical Systems-Chapter 01 7/19 Conductor Conductor Conductor Conductor A l A l R         1 Core Core Core Core A l A l R         1 E: Electric field intensity )/( 11 mvolt d V d V dq W dq dF q F E  H: Magnetic field intensity l R l iN l f H   D: Electric flux density B: magnetic flux density ED  HB   cos. EAAEe   cos. BAABm  d A C   l AN R N L 22  dceElas tan A ceElas 1 tan  A d ceElas tan A d ElastivityceElas )(tan  d A ElastivityceElas        1 tan 1 d A yPermitivitceCapaci tan d A C   tivdtivdtPW RRRRRR        LLL L LLLLL diLidtidt di LdtivWdtPW )0( 2 2 2 1 2 L L LLL iL i LdiLiW   docsity.com EE2401 Electromechanical Systems-Chapter 01 10/19        C Cor l A N R N L 22 )( Cor C A l R   5. By using the magnetic circuit approach, it simplifies calculations related to the magnetic field in a ferromagnetic material; however, this approach has inaccuracy embedded into it due to assumptions made in creating this approach (within 5% of the real answer). Possible reason of inaccuracy is due to: a) The magnetic circuit assumes that all flux are confined within the core, but in reality a small fraction of the flux escapes from the core into the surrounding low- permeability air, and this flux is called leakage flux. b) The reluctance calculation assumes a certain mean path length and cross sectional area (csa) of the core. This is alright if the core is just one block of ferromagnetic material with no corners, for practical ferromagnetic cores which have corners due to its design, this assumption is not accurate. c) In ferromagnetic materials, the permeability varies with the amount of flux already in the material. The material permeability is not constant hence there is an existence of non-linearity of permeability. d) For ferromagnetic core which has air gaps, there are fringing effects that should be taken into account as shown: N S (a) Magnetic Behaviour of Ferromagnetic Materials 1. Materials which are classified as non-magnetic all show a linear relationship between the flux density B and coil current I. In other words, they have constant permeability. Thus, for example, in free space, the permeability is constant. But in iron and other ferromagnetic materials it is not constant. 2. For magnetic materials, a much larger value of B is produced in these materials than in free space. Therefore, the permeability of magnetic materials is much higher than µo. However, the permeability is not linear anymore but does depend on the current over a wide range. 3. Thus, the permeability is the property of a medium that determines its magnetic characteristics. In other words, the concept of magnetic permeability corresponds to the ability of the material to permit the flow of magnetic flux through it. docsity.com EE2401 Electromechanical Systems-Chapter 01 11/19  4. In electrical machines and electromechanical devices a somewhat linear relationship between B and I is desired, which is normally approached by limiting the current. 5. Look at the magnetization curve and B-H curve. Note: The curve corresponds to an increase of DC current flow through a coil wrapped around the ferromagnetic core (ref: Electrical Machinery Fundamentals 4th Ed. – Stephen J Chapman). 6. When the flux produced in the core is plotted versus the mmf producing it, the resulting plot looks like this (a). This plot is called a saturation curve or a magnetization curve. A small increase in the mmf produces a huge increase in the resulting flux. After a certain point, further increases in the mmf produce relatively smaller increases in the flux. Finally, there will be no change at all as you increase mmf further. The region in which the curve flattens out is called saturation region, and the core is said to be saturated. The region where the flux changes rapidly is called the unsaturated region. The transition region is called the ‘knee’ of the curve. 7. It can be seen that magnetizing intensity is directly proportional to mmf and magnetic flux density is directly proportional to flux for any given core. B=µH  slope of curve is the permeability of the core at that magnetizing intensity. The curve (b) shows that the permeability is large and relatively constant in the unsaturated region and then gradually drops to a low value as the core become heavily saturated. 8. Advantage of using a ferromagnetic material for cores in electric machines and transformers is that one gets more flux for a given mmf than with air (free space). 9. If the resulting flux has to be proportional to the mmf, then the core must be operated in the unsaturated region. 10. Generators and motors depend on magnetic flux to produce voltage and torque, so they need as much flux as possible. So, they operate near the knee of the magnetization curve (flux not linearly related to the mmf). This non-linearity as a result gives peculiar behaviour to machines. 11. As magnetizing intensity H increased, the relative permeability first increases and then starts to drop off. docsity.com EE2401 Electromechanical Systems-Chapter 01 12/19 Energy Losses in a Ferromagnetic Core I. Hysteresis Loss 1. Discussions made before concentrates on the application of a DC current through the coil. Now let’s move the discussion into the application of AC current source at the coil. Using our understanding previously, we can predict that the curve would be as shown,  F 1st Positive Cycle 2nd Negative Cycle Theoretical ac magnetic behaviour for flux in a ferromagnetic core 2. Unfortunately, the above assumption is only correct provided that the core is ‘perfect’ i.e. there are no residual flux present during the negative cycle of the ac current flow. A typical flux behaviour (or known as hysteresis loop) in a ferromagnetic core is as shown in the next page. Typical Hysterisis loop when ac current is applied docsity.com EE2401 Electromechanical Systems-Chapter 01 15/19 dt d eind   dt d Neind   Conclusion: Core loss is extremely important in practice, since it greatly affects operating temperatures, efficiencies, and ratings of magnetic devices. 3. How Magnetic Field can affect its surroundings 3.1 FARADAY’S LAW – Induced Voltage from a Time-Changing Magnetic Field Before, we looked at the production of a magnetic field and on its properties. Now, we will look at the various ways in which an existing magnetic field can affect its surroundings. 1. Faraday’s Law: ‘If a flux passes through a turn of a coil of wire, voltage will be induced in the turn of the wire that is directly proportional to the rate of change in the flux with respect of time’ If there is N number of turns in the coil with the same amount of flux flowing through it, hence: where: N – number of turns of wire in coil. Note the negative sign at the equation above which is in accordance to Lenz’ Law which states: ‘The direction of the build-up voltage in the coil is as such that if the coils were short circuited, it would produce current that would cause a flux opposing the original flux change.’ Examine the figure below: docsity.com EE2401 Electromechanical Systems-Chapter 01 16/19    N i iind ee 1    N i i dt d 1           N i idt d 1   If the flux shown is increasing in strength, then the voltage built up in the coil will tend to establish a flux that will oppose the increase.  A current flowing as shown in the figure would produce a flux opposing the increase.  So, the voltage on the coil must be built up with the polarity required to drive the current through the external circuit. So, -eind  NOTE: In Chapman, the minus sign is often left out because the polarity of the resulting voltage can be determined from physical considerations. 2. Equation eind = -d /dt assumes that exactly the same flux is present in each turn of the coil. This is not true, since there is leakage flux. This equation will give valid answer if the windings are tightly coupled, so that the vast majority of the flux passing thru one turn of the coil does indeed pass through all of them. 3. Now consider the induced voltage in the ith turn of the coil, i i d e dt   Since there is N number of turns, The equation above may be rewritten into, ind d e dt   docsity.com EE2401 Electromechanical Systems-Chapter 01 17/19 where  (flux linkage) is defined as: 1 N i i      (weber-turns) 4. Faraday’s law is the fundamental property of magnetic fields involved in transformer operation. 5. Lenz’s Law in transformers is used to predict the polarity of the voltages induced in transformer windings. 3.2 Production of Induced Force on a Wire. 1. A current carrying conductor present in a uniform magnetic field of flux density B, would produce a force to the conductor/wire. Dependent upon the direction of the surrounding magnetic field, the force induced is given by: )()( B t l tiFBliF  )( BVqF  )( tiqt q i  where: i – represents the current flow in the conductor l – length of wire, with direction of l defined to be in the direction of current flow B – magnetic field density 2. The direction of the force is given by the right-hand rule. Direction of the force depends on the direction of current flow and the direction of the surrounding magnetic field. A rule of thumb to determine the direction can be found using the right-hand rule as shown below: Thumb (resultant force) Index Finger (current direction) Middle Finger (Magnetic Flux Direction) Right Hand rule 3. The induced force formula shown earlier is true if the current carrying conductor is perpendicular to the direction of the magnetic field. If the current carrying conductor is position at an angle to the magnetic field, the formula is modified to be as follows: sinF ilB  docsity.com