Power Engineering EPO460Chapter 1 – Magnetic Circuit Magnets Objects which produce their own magnetic field are called magnets. Magnetism is a force of attraction or repulsion that produced by magnets to the other materials. The orientation of electrons is the reason behind the production of magnetic field and magnetism. o In a natural state of an object, the electrons are scattered. o If the orientation of electrons is aligned in one direction, it becomes a magnet. Magnets have 2 poles: North and South. There are 3 major groups of magnets: Permanent magnets Temporary magnets Electromagnets o Objects that o Become o Magnets made by wire loops around a retain their magnetized when core material when electricity pass magnetism once they come within through a wire, it produces magnetic magnetized range of magnet field o The magnetic o The magnetism o Magnetic property become strong if: properties last lasts for a short i. The core is made of ferromagnetic for a long period period material o Example: fridge, o Example: nail, ii. A coil is used instead of straight wire cabinet door, etc. needle, paper clips, etc. iii. Current is high o Example: transformers, motors, generators, floating bullet train, etc. Ferromagnetic materials exhibit a strong attraction to magnetic fields and retain their magnetic properties after the external field has been removed. Iron, nickel, manganese and cobalt are the example of ferromagnetic materials. It is used as a core of transformers and stator of motors. Electromagnets Magnetic field (or flux) is the region around a magnet where magnetic effects can be experienced. (magnetic flux symbol: Φ, unit: Weber (Wb)) A magnetic line of force (or flux line) is a continuous line whose direction at any point is the direction of the magnetic field at that point. D. Johari, FKE UiTM-modified by NZA 1 Power Engineering EPO460 Fig. 1: Magnetic field The magnetic flux through a region is a measure of the number of magnetic field lines passing through the region. The strength of magnetic flux is measured using magnetic field intensity. (magnetic flux intensity symbol: H, unit: ampere turn per meter, At/m) The direction of magnetic field intensity can be determined by the right-hand grip rule. Figure 2: Right hand grip rule Magnetic flux intensity produces magnetic flux density everywhere it exists. (magnetic flux density symbol: B, unit: Tesla (T). 1Wb/m2 = 1T) Magnetic flux density indicates the magnitude and direction of a magnetic field of an area. (how to increase the magnetic flux density?) The ease with which a material will conduct magnetic lines force is called permeability. The concept of electromagnetism and electromagnetic induction are applied in many electrical appliances such as motors, transformers and generators. o Electromagnetism is a process of making magnetism using electrical current. A current carrying wire produces a magnetic field in the area around it. o Electromagnetic induction is a process of creating an electrical current using magnetism. D. Johari, FKE UiTM-modified by NZA 2 Power Engineering EPO460 Laws related to electromagnetic induction (*refer to video at I-learn) Faraday’s law: o First law: Whenever the magnetic flux linked with a circuit changes, an electromotive- force (EMF) is always induced in it OR whenever a conductor cuts magnetic flux, an EMF is induced in that conductor (*when EMF is induced, the current is also induced) o Second law: The magnitude of the induced EMF is equal to the rate of change of flux linkages The direction of motion or direction of induced current can be determined using Fleming’s right and left hand rules o Right hand rule: applicable for generator o Left hand rule: applicable for motor Fore finger: direction of magnetic field Middle finger: direction of current Thumb: direction of force Fig. 3: Fleming’s right hand rule Lenz’s law states that when EMF is induced as in Faraday's law, the polarity (direction) of that induced EMF is such that it opposes the cause of its production. Three basic principles that describe how magnetic fields are used in transformers, motors and generators are as follows: 1. A time-changing magnetic field induces EMF/voltage in a coil of wire if it passes through that coil. (This is the basis of transformer) 2. A current-carrying wire in the presence of a magnetic field has a force induced on it (This is the basis of motor action) 3. A moving wire in the presence of a magnetic field has a voltage induced in it (This is the basis of generator action) In most electrical machines (except permanent magnet machines), magnetic flux is produced by passing an electrical current through coils looped on ferromagnetic materials. D. Johari, FKE UiTM-modified by NZA 3 Power Engineering EPO460 Magnetic Field The relation between current, i and magnetic flux intensity, H (i-H relation) can be obtained using Ampere’s law. This law stated that the line integral of the magnetic flux intensity, H, around a closed path is equal to the total current linked by the contour. It is given by: Hlc Ni Where H – the magnetic field intensity produced by total current Ni lc – the mean path length of the core (in meter) Cross-sectional area, A Mean path length lc Fig. 4: Simple magnetic core The magnitude of the magnetic field intensity, H in the core due to the applied current is Ni H lc The relationship between the magnetic field intensity H and the resulting magnetic flux density B produced within a material is given by B H or B 0 r H Where H – magnetic field intensity (ampere-turn per meter) µ – magnetic permeability of material (henrys per meter) B – resulting magnetic flux density produced (Weber per square meter or Tesla) µr – relative permeability µo – permeability of free space (4 x 10-7H/m) The permeability of any material compared to the permeability of free space is called relative permeability given by: r o D. Johari, FKE UiTM-modified by NZA 4 Power Engineering EPO460 The magnetic flux density for magnetic core in Fig. 2 is, therefore, given by: Ni B H lc Now the total flux in a given area is given by BA Where A is the cross-sectional area of the core (in meter square-m2) Thus, the total flux in the core in Fig. 2 due to the current i, in the winding is NiA BA lc The core shapes can be of rectangular, toroid, solenoid and shell type (**how to determine the length and area of each core shapes?) Relationship between B and H The relationship between B and H of any magnetic materials is generally shown by Fig. 4. This curve is also known as magnetization curve In the core, magnetic intensity, H is increased proportionally by the increasing current The flux density, B in the core changes in the way shown below: Fig. 4: General magnetization curve From Fig. 4, the flux density, B increases almost linearly with the increase of flux intensity, H, at initial condition However, at higher value of H, the change of B is nonlinear and shows the effect of saturation D. Johari, FKE UiTM-modified by NZA 5 Power Engineering EPO460 Fig. 5: Sample of magnetization curve of a few magnetic materials From magnetization curve, information of B and/or H of magnetic core can be obtained. Magnetic Circuits Magnetic flux circulated in a closed area or path of ferromagnetic materials is called as magnetic circuit. If the flux is divided into 2 or more path of magnetic flux, it is called as parallel magnetic circuit. Otherwise, it has series magnetic circuit. A circulating force called Magneto Motive Force (MMF) or magnetic potential is responsible for establishing magnetic flux in a magnetic circuit. Unit of MMF is Ampere-turn (At) The magnetic circuit can be drawn analogous to an electric circuit as shown below: Fig. 6 a) A simple electric circuit (b) The magnetic circuit D. Johari, FKE UiTM-modified by NZA 6 Power Engineering EPO460 The electrical terms used in electric and magnetic circuits Electric circuit Magnetic circuit The voltage or electromotive force The magnetomotive force (mmf) causes (emf) causes current I, to flow. flux to be produced. V IR F V = voltage or electromotive force F = magnetomotive force (mmf) of circuit I = current = Flux of circuit R = resistance = Reluctance of circuit 1 1 G (conductance) = (permeance) = R Core Reluctance Each core (ferromagnetic material) has its own reluctance. Reluctance is the opposite of permeability. Magnetic property of the core can be improved by using material that has very low reluctance. The resulting flux in a core (as shown in Fig. 4) is given by: NiA A A Ni F lc lc lc We can see that the reluctance of the core is lc A Reluctance in a magnetic circuit obeys the same rules as resistance in an electric circuit. The equivalent reluctance of several reluctances in series is just the sum of the individual reluctances: eq 1 2 3 ....... Similarly, reluctances in parallel combine according to the equation 1 1 1 1 ......... eq 1 2 3 D. Johari, FKE UiTM-modified by NZA 7 Power Engineering EPO460 Magnetic circuit with air gap In electric machines, the rotor is isolated from the stator by the air gap to reduce the saturation effect at the core (or poles) A magnetic circuit having 2 or more medium (magnetic core and air gap) is known as a composite structure. Magnetic equivalent circuit for magnetic core with air gap is shown below: Figure 7: Composite structure. (a) Magnetic core with air gap (b) magnetic equivalent circuit In Fig. 7(a) lc lg c g c A and 0 A Thus, the resulting flux for magnetic circuit with air gap is: F Ni c g Ni H c lc H g l g The flux densities are: c g Bc and Bg Ac Ag At the air gap, magnetic fluxes flowing in a magnetic core spreads out (or fringes out) into the surrounding medium. This is called fringing of the flux as shown below: Figure 7: Fringing effect at the air gap D. Johari, FKE UiTM-modified by NZA 8 Power Engineering EPO460 Fringing is directly proportional to the length of the air gap. If the length increases, the fringing effect will increase and vice versa Leakage flux is defined as the magnetic flux which does not follow the intended path in a magnetic circuit Useful flux is the flux that passes through the core and is utilized in the magnetic circuit Ferromagnetic Materials All substances are affected by magnetic fields. They are classified into 3 according to the way they are affected: o Diamagnetic materials Show very weak magnetic effects μr is very slightly less than one (typically 0.99999) o Paramagnetic materials Show very weak magnetic effects μr is very slightly greater than one (typically 1.001) o Ferromagnetic materials Exhibit very strong magnetic effects Have very large values of μr (typically 104) Examples are iron, nickel and cobalt D. Johari, FKE UiTM-modified by NZA 9 Power Engineering EPO460 Losses in Ferromagnetic Core There are 2 types of losses occur in the magnetic core; one is Eddy Current Loss (ECL) and the other is hysteresis loss. ECL takes place when a coil is wrapped around a core and alternating ac supply is applied to it As the supply to the coil is alternating, the flux produced in the coil is also alternating By Faradays law of electromagnetic induction, the change in flux through the core causes EMF induction inside the core Due to induction of EMF, eddy current starts to flow in the core and exist as loss in the form of heat energy Eddy current losses can be reduced by laminations in the core Thin sheet steels must be used which are insulated from each other Due to insulated sheets the amount of current which flows get reduced and hence the eddy current losses Lamination of core to reduce ECL Hysteresis loss occurs when the amount of energy absorbed by magnetic material does not returned to its original path (refer to hysteresis curve) Hysteresis curve D. Johari, FKE UiTM-modified by NZA 10 Power Engineering EPO460 When the magnetic field strength or the current is increased the flux density increase proportionally until it (flux) gets saturated When we reduce the current from saturation to zero side the flux density starts to decrease But when the current value reaches zero the flux density should also be zero but it is not For zero current there is still some flux density present in the material, this is known as residual magnetic flux Hence the amount of power is never recovered The power which gets trapped in the core of the material is lost in the form of heat The area of the B-H curve determines the amount of hysteresis loss The larger the area greater is the loss and vice versa Since hysteresis loss depends on the material of the core, then to reduce such loss, it is recommended to use high permeability material for the core Since both losses (hysteresis and ECL) occur within the metal of the core, they are usually lumped together and called as core losses. Example 1 A ferromagnetic core is shown in Fig. 8. Three sides of this core are of uniform width, while the fourth side is somewhat thinner. The depth of the core (in to page) is 10cm, and the other dimensions are shown in the figure. There is a 200-turn coil wrapped around the left side of the core. Assuming relative permeability µr of 2500, how much flux will be produced by a 1A input current? D. Johari, FKE UiTM-modified by NZA 11 Power Engineering EPO460 Fig. 8: The Ferromagnetic Core Example 2 Fig. 9 shows a ferromagnetic core whose mean path length is 40cm. There is a small gap of 0.05cm in the structure of the otherwise whole core. The cross-sectional area of the core is 12cm2, the relative permeability of the core is 4000, and the coil of wire on the core has 400 turns. Assume that fringing (border) in the air gap increases the effective cross-sectional area of the air gap by 5 percent. Given this information, find: a) the total reluctance of the flux path (iron plus air gap) and b) the current required to produce a flux density of 0.5T in the air gap Fig. 9: The Ferromagnetic Core D. Johari, FKE UiTM-modified by NZA 12 Power Engineering EPO460 Example 3 Fig. 10 shows a simplified rotor and stator for a DC motor. The mean path length of the stator is 50cm, and its cross-sectional area is 12 cm2. The mean path length of the rotor is 5cm, and its cross-sectional area also may be assumed to be 12cm2. Each air gap between the rotor and the stator is 0.05cm wide, and the cross-sectional area of each air gap (including fringing) is 14 cm2. The iron of the core has a relative permeability of 2000, and there are 200 turns of wire in the core. If the current in the wire is adjusted to be 1 A, what will the resulting flux density in the air gaps be? Fig. 10: A simplified diagram of a rotor and stator for a dc motor. D. Johari, FKE UiTM-modified by NZA 13