Chapter 1 Introduction to Electromechanical Energy Conversion

1. Chapter 1 Introduction to Electromechanical Energy Conversion Dr Awang Jusoh/Dr Makbul

2. 1.1 Magnetic Circuits Dr Awang Jusoh/Dr Makbul

3. Magnetic Field Concept Magnetic Fields: • Magnetic fields are the fundamental mechanism by which energy is converted (transferred) from one form to another in electrical machines. • Magnetic Material • Definition : A material that has potential to attract other materials toward it, materials such as iron, cobalt, nickel • Function: Act as a medium to shape and direct the magnetic field in the energy conversion process Dr Awang Jusoh/Dr Makbul

4. Magnetic Field Concept • Magnetic field around a bar magnet • Two “poles” dictated by direction of the field • Opposite poles attract (aligned magnetic field) • Same poles repel (opposing magnetic field) Dr Awang Jusoh/Dr Makbul

5. Magnetic Field Concept Magnetic Flux/ Flux Line Characteristic 1. Outside - Leaves the north pole (N) and enters the south pole (S) of a magnet. Inside - Leaves the south pole (S) and enters the north pole (N) of a magnet. 2. Like (NN, SS) magnetic poles repel each other. 3. Unlike (NS) magnetic poles attracts each other. 4. Magnetic lines of force (flux) are always continuous (closed) loops, and try to make as shortest distance loop. 5. Flux line never cross each others Dr Awang Jusoh/Dr Makbul

6. Magnetic Field Concept Dr Awang Jusoh/Dr Makbul

7. Machines Basic Requirements • Presence of a “magnetic fields” can be produced by: • Use of permanent magnets • Use of electromagnets • Then one of the following method is needed: • Motion to produce electric current (generator) • Electric current to produce motion (motor) Dr Awang Jusoh/Dr Makbul

8. Ampere’s Law • Any current carrying wire will produce magnetic field around itself. Magnetic field around a wire: • Thumb indicates direction of current flow • Finger curl indicates the direction of field Dr Awang Jusoh/Dr Makbul

9. Ampere’s Law Ampere’s law: the line integral of magnetic field intensity around a closed path is equal to the sum of the currents flowing through the surface bounded by the path H I1 I2 q dl Recall that the vector dot product is given by in which q is the angle between H and dl. Dr Awang Jusoh/Dr Makbul

10. Ampere’s Law If the magnetic intensity has constant magnitude and points in the same direction as the incremental length dl everywhere along the path, Ampere’s law reduces to in which l is the length of the path. Examples of such cases: (i) Magnetic field around a long straight wire, (ii) Solenoid Dr Awang Jusoh/Dr Makbul

11. Example 1: ( a long straight Wire) Example 2: (Solenoid) Dr Awang Jusoh/Dr Makbul

12. Flux Density • Number of lines of magnetic force (flux) passing through unit area or Wb/m2 Dr Awang Jusoh/Dr Makbul

13. Field Intensity • The effort made by the current in the wire to setup a magnetic field. • Magnetomotive force (mmf) per unit length is known as the “magnetizing force” H • Magnetizing force and flux density related by: Dr Awang Jusoh/Dr Makbul

14. Permeability • Permeability is a measure of the ease by which a magnetic flux can pass through a material (Wb/Am). The higher the better flux can flow in the magnetic materials. • Permeability of free space o = 4 x 10-7 (Wb/Am) • Relative permeability, r : Dr Awang Jusoh/Dr Makbul

15. Reluctance • Reluctance, which is similar to resistance, is the opposition to the establishment of a magnetic field, i.e." resistance” to flow of magnetic flux. Depends on length of magnetic path , cross-section area A and permeability of material . Dr Awang Jusoh/Dr Makbul

16. Magnetomotive Force • The product of the number of turns and the current in the wire wrapped around the core’s arm. (The ability of a coil to produce flux) N Dr Awang Jusoh/Dr Makbul

17. Magnetomotive Force • The MMF is generated by the coil • Strength related to number of turns and current, Symbol F, measured in Ampere turns (At) Dr Awang Jusoh/Dr Makbul

18. Magnetization Curve Behavior of flux density compared with magnetic field strength, if magnetic intensity H increases by increase of current I, the flux density B in the core changes as shown.  flux () Near saturation linear  current (I) Dr Awang Jusoh/Dr Makbul

19. Magnetic Equivalent Circuit Analogy between magnetic circuit and electric circuit Dr Awang Jusoh/Dr Makbul

20. Magnetic Circuit with Air Gap Dr Awang Jusoh/Dr Makbul

21. Parallel Magnetic Circuit l2 l1 I l3 N • Loop I • NI = S33 + S11 • = H3l3 + H1l1 • Loop II • NI = S33 + S22 • = H3l3 + H2l2 • Loop III • 0 = S11 + S22 • = H1l1 + H2l2 3 1 II 2 S3 S2 S1 I + NI - Dr Awang Jusoh/Dr Makbul

22. Electric vs Magnetic Circuit Magnetic circuit Electric circuit Dr Awang Jusoh/Dr Makbul

23. Leakage Flux • Part of the flux generated by a current-carrying coil wrapped around a leg of a magnetic core stays outside the core. This flux is called leakage flux. Useful flux Dr Awang Jusoh/Dr Makbul

24. Fringing Effect • The effective area provided for the flow of lines of magnetic force (flux) in an air gap is larger than the cross-sectional area of the core. This is due to a phenomenon known as fringing effect. Air gap – to avoid flux saturation when too much current flows - To increase reluctance Dr Awang Jusoh/Dr Makbul

25. Example 1 Refer to Figure below, calculate:-1) Flux 2) Flux density 3) Magnetic intensity Given r = 1,000; no of turn, N = 500; current, i = 0.1 A. cross sectional area, A = 0.0001m2 , and means length core lC = 0.36m. • 1.75x10-5 Wb • 0.175 Wb/m2 • 139 AT/Wb Dr Awang Jusoh/Dr Makbul

26. Example 2 Data- 1T – 700 at/m • The Figure represents the magnetic circuit of a relay. The coil has 500 turns and the mean core path is lc = 400 mm. When the air-gap lengths are 2 mm each, a flux density of 1.0 Tesla is required to actuate the relay. The core is cast steel. a. Find the current in the coil. (6.93 A) b. Compute the values of permeability and relative permeability of the core. (1.14 x 103 , 1.27) c. If the air-gap is zero, find the current in the coil for the same flux density (1 T) in the core. ( 0.6 A) Pg 8 : SEN Dr Awang Jusoh/Dr Makbul

27. Electromagnetic Induction • An emf can be induced in a coil if the magnetic flux through the coil is changed. This phenomenon is known as electromagnetic induction. • The induced emf is given by • Faraday’s law: The induced emf is proportional to the rate of change of the magnetic flux. • This law is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators.

28. Electromagnetic Induction • Faraday's law is a single equation describing two different phenomena: The motional emf generated by a magnetic force on a moving wire, and the transformer emf generated by an electric force due to a changing magnetic field. • The negative sign in Faraday's law comes from the fact that the emf induced in the coil acts to oppose any change in the magnetic flux. • Lenz's law: The induced emf generates a current that sets up a magnetic field which acts to oppose the change in magnetic flux.

29. Lenz’s Law An induced current has a direction such that the magnetic field due to the induced currentopposes the change in the magnetic flux that induces the current. As the magnet is moved toward the loop, the B through the loop increases, therefore a counter-clockwise current is induced in the loop. The current produces its own magnetic field to oppose the motion of the magnet If we pull the magnet away from the loop, the B through the loop decreases, inducing a current in the loop. In this case, the loop will have a south pole facing the retreating north pole of the magnet as to oppose the retreat. Therefore, the induced current will be clockwise.

30. Self-Inductance • From Faraday’s law • Where l is the flux linkage of the winding is defined as • For a magnetic circuit composed of constant magnetic permeability, the relationship between f and i will be linear and we can define the inductance L as • It can be shown later that

31. Self-Inductance • For a magnetic circuit having constant magnetic permeability • So, Henry

32. Mutual Inductance i1  i2 + + N1 N2 g l1 l2 turns turns - - Notice the current i1 and i2 have been chosen to produce the flux in the same direction. It is also assumed that the flux is confined solely to the core and its air gap. Magnetic core Permeability m, Mean core length lc, Cross-sectional area Ac

33. Mutual Inductance The total mmf is therefore with the reluctance of the core neglected and assuming that Ac = Ag the core flux is If the equation is broken up into terms attributable to the individual current, the flux linkages of coil 1 can be expressed as

34. Mutual Inductance where is the self-inductance of coil 1 and is the flux linkage of coil 1 due to its own current i1. The mutual inductance between coils 1 and 2 is and is the flux linkage of coil 1 due to current i2.

35. Mutual Inductance Similarly, the flux linkage of coil 2 is where is the mutual inductance and is the self-inductance of coil 2.

36. Mutual Inductance: Example i1  i2 + + N1 N2 g l1 l2 turns turns - - Magnetic core Permeability m >> mo, Cross-sectional area Ac = Ag = 1 cm X 1.5916 cm Air gap length, g = 2 mm N1 = 100 turns, N2 =200 turns Find L11, L22, and L12 = L21 = M

37. Magnetic Stored Energy We know that for a magnetic circuit with a single winding and For a static magnetic circuit the inductance L is fixed For a electromechanical energy device, L is time varying

38. Magnetic Stored Energy The power p is Thus the change in magnetic stored energy The total stored energy at any l is given by setting l1 = 0: