ELEN-30083 Electrical Machines I Lesson 1 and 2 PDF (SY 2024-2025)

Lesson 1 - Introduction to Electrical Machines 1 Unit 1: Generator Principles Overview: This lesson will give the students what are the general principles of a Direct Current Generators. Learning Objectives: After successful completion of this lesson, you should be able to:...

Lesson 1 - Introduction to Electrical Machines 1 Unit 1: Generator Principles Overview: This lesson will give the students what are the general principles of a Direct Current Generators. Learning Objectives: After successful completion of this lesson, you should be able to: 1. Discuss what are the general principles of a direct current generator 2. Explain what a direct current generator is Course Materials: Direct Current Generator An electrical generator is a machine which converts mechanical energy (or power) into electrical energy (or power). The energy conversion is based on the principle of the production of dynamically (or motionally) induced e.m.f. As seen from Fig. 1.1, whenever a conductor cuts magnetic flux, dynamically induced e.m.f. is produced in it according to Faraday’s Laws of Electromagnetic Induction. This e.m.f. causes a current to flow if the conductor circuit is closed. Hence, two basic essential parts of an electrical generator are (i) a magnetic field and (ii) a conductor or conductors which can so move as to cut the flux. Figure 1.1 1 Principle of Operation The scientific principle on which generators operate was discovered almost simultaneously in about 1831 by the English chemist and physicist, Michael Faraday, and the American physicist, Joseph Henry. Imagine that a coil of wire is placed within a magnetic field, with the ends of the coil attached to some electrical device, such as a galvanometer. If the coil is rotated within the magnetic field, the galvanometer shows that a current has been induced within the coil. The magnitude of the induced current depends on three factors: the strength of the magnetic field, the length of the coil, and the speed with which the coil moves within the field In fact, it makes no difference as to whether the coil rotates within the magnetic field or the magnetic field is caused to rotate around the coil. The important factor is that the wire and the magnetic field are in motion in relation to each other. In general, most DC generators have a stationary magnetic field and a rotating coil, while most AC generators have a stationary coil and a rotating magnetic field. According to Faraday’s laws of electromagnetic induction, whenever a conductor is placed in a varying magnetic field (OR a conductor is moved in a magnetic field), an emf (electromotive force) gets induced in the conductor. The magnitude of induced emf can be calculated from the emf equation of dc generator. If the conductor is provided with the closed path, the induced current will circulate within the path. In a DC generator, field coils produce an electromagnetic field and the armature conductors are rotated into the field. Thus, an electromagnetically induced emf is generated in the armature conductors. The direction of induced current is given by Fleming’s right hand rule. According to Fleming’s right hand rule, the direction of induced current changes whenever the direction of motion of the conductor changes. Let’s consider an armature rotating clockwise and a conductor at the left is moving upward. When the armature completes a half rotation, the direction of motion of that particular conductor will be reversed to downward. Hence, the direction of current in every armature conductor will be alternating. If you look at the above figure, you will know how the direction of the induced current is alternating in an armature conductor. But with a split ring commutator, connections of the armature conductors also gets reversed when the current reversal occurs. And therefore, we get unidirectional current at the terminals. 2 Reference: https://www.electrical4u.com/principle-of-dc-generator/ Electrical Machines Second Edition by Siskind Complete Electrical Engineering Formulas and Principles by Romeo A. Rojas Jr. Activities/Assessments: Assignment: Answer the following questions briefly: 1. What is generator? 2. Explain briefly the general principles of a DC Generator. 3 Lesson 1 - Introduction to Electrical Machines 1 Unit 2: Simple Loop Generator Introduction: This lesson focuses on Construction and Working Principles of a DC Generator Learning Objectives: After successful completion of this lesson, you should be able to: 1. Describe construction and working principles of a DC Generator Course Materials: Construction In Fig. 2.1 is shown a single-turn rectangular copper coil ABCD rotating about its own axis in a magnetic field provided by either permanent magnet or electromagnets. The two ends of the coil Figure 2.1 are joined to two slip-rings ‘a’ and ‘b’ which are insulated from each other and from the central shaft. Two collecting brushes (of carbon or copper) press against the slip-rings. Their function is to collect the current induced in the coil and to convey it to the external load resistance R. The rotating coil may be called ‘armature’ and the magnets as ‘field magnets’. Working Imagine the coil to be rotating in clock-wise direction (Fig. 2.2). As the coil assumes successive positions in the field, the flux linked with changes. Hence, an e.m.f. is induced in it which is 4 proportional to the rate of change of flux linkages. When the plane of the coil is at the right angles to line to flux i.e. when it is position, 1, then flux linked with the coil is maximum but rate of change of flux linkages is minimum. It is so because in this position, the coil sides AB and CD do not cut or shear the flux, rather they slide along them i.e. they move parallel to them. Hence, there is no induced e.m.f. in the coil. Let us take this no-e.m.f. or vertical position of the coil as the starting position. The angle of rotation or time will be measured from this position. Figure 2.2 Figure 2.3 As the coil continues rotating further, the rate of change of flux linkages (and hence induced e.m.f. in it) increases, till position 3 is reached where ϴ = 90º. Hence, the coil plane is horizontal i.e. parallel to the lines of flux. As seen, the flux linked with the coil is minimum but rate of change of flux linkages is maximum. Hence, maximum e.m.f. is induced in the coil when in this position (Figure 2.3). In the next quarter revolution i.e. from 90º to 180º, the flux linked with the coil gradually increases but the rate of change of flux linkages decreases. Hence, the induced e.m.f. decreases gradually till in position 5 of the coil, it is reduced to zero value. So, we find that in the first half revolution of the coil, no (or minimum) e.m.f. is induced in it when in position 1, maximum when in position 3 and no e.m.f. when in position 5. The direction of this induced e.m.f. can be found by applying Fleming’s Right-hand rule which gives its direction from A to B and C to D. Hence, the direction of current flow is ABMLCD (Fig. 2.1). The current through the load resistance R flows from M to L during the first half revolution of the coil. In the next half revolution i.e. from 180º to 360º, the variations in the magnitude of e.m.f are similar to those in the first half revolution. Its value is maximum when coil in in position 7 and minimum when in position1. But it will be found that the direction of the induced current is from D to C and B to A as shown in Fig. 2.1 (b). Hence, the path of current flow is along DCLMBA which is just the reverse of the previous direction of flow. Therefore, we find that the current which we obtain from such a simple generator reverses its direction after every half revolution. Such a current undergoing periodic reversal is known as alternating current. It is, obviously, different from a direct current which continuously flows in one and the same direction. It should be noted that alternating current not only reverses its direction, 5 it does not even keep its magnitude constant while flowing in any one direction. The two half- cycle may be called positive and negative half-cycles respectively (Fig.2.3) For making the flow of current unidirectional in the external circuit, the slip-rings are replaced by split-rings (Fig. 2.4). The split-rings are made out of a conducting cylinder which is cut into two halves or segments insulated from each other by a thin sheet of mica or some other insulation material (Fig. 2.5). As before, the coil ends are joined to these segments on which rest the carbon or copper brushes. It is seen [Fig. 2.6 (a)] that in the first half revolution current flows along (ABMNLCD) i.e. the brush No. 1 in contact with segment ‘a’ acts as the positive end of the supply and ‘b’ as the negative end. In the next half revolution [Fig. 2.6 (b)], the direction of the induced current in Figure 2.4 Figure 2.5 the coil has reversed. But at the same time, the positions of segments ‘a’ and ‘b’ have also reversed with the result that brush No. 1 comes in touch with the segment which is positive i.e. segment ‘b’ in this case. Hence, current in the load resistance again flows from M to L. The waveform of the current through the external circuit is as shown in Fig. 2.7. This current is unidirectional but not continuous like pure direct current. Figure 2.6 Figure 2.7 It should be noted that the position of brushes is so arranged that the change over of segments ‘a’ and ‘b’ from one brush to the other takes place when the plane of the rotating coil is at right angles to the plane of the lines of lux. It is so because in that position, the induced e.m.f in the coil is zero. 6 Another important point worth remembering is that even now the current induced in the coil sides is alternating as before. It is only due to the rectifying action of the split-rings (also called commutator) that it becomes unidirectional in the external circuit. Hence, it should be clearly understood that even in the armature of a d.c. generator, the induced voltage is alternating. Reference: https://www.electrical4u.com/principle-of-dc-generator/ Electrical Machines Second Edition by Siskind Complete Electrical Engineering Formulas and Principles by Romeo A. Rojas Jr. Activities/Assessments: Assignment: Answer the question: 1. Explain briefly the working principles and construction of a DC Generator. 7 Lesson 1 - Introduction to Electrical Machines 1 Unit 3: Practical Generator Introduction: This lesson focuses on Practical Generator and Parts of DC Generator Learning Objectives: After successful completion of this lesson, you should be able to: 1. Describe parts of a DC Generator Course Materials: Practical Generator The simple loop generator has been considered in detail merely to bring out basic principle underlying construction and working of an actual generator illustrated in Fig. 2.8 which consists of the following essentials parts: 1. Magnetic Frame or Yoke 2. Pole-Cores and Pole- Shoes 3. Pole Coils or Field Coils 4. Armature Core 5. Armature Windings or Conductors 6. Commutator 7. Brushes and Bearings Of these, the yoke, the pole cores, the armature cores and air gaps between the poles and the armature core or the magnetic circuit whereas the rest form the electrical circuit. Figure 2.8 8 Yoke The outer frame or yoke serves double purpose: (i) It provides mechanical support for the poles and acts as a protecting cover for the whole machine and (ii) It carries the magnetic flux produced by the poles. In small generators where cheapness rather than weight is the main consideration, yokes are made of cast iron. But for large machines usually cast steel or rolled steel is employed. The modern process of forming the yoke consists of rolling a steel slab round a cylindrical mandrel and then welding it at the bottom. The feet and the terminal box etc. are welded to the frame afterwards. Such yokes possess sufficient mechanical strength and have high permeability. Pole Cores and Pole Shoes The field magnets consist of pole cores and pole shoes. The pole shoes serve two purposes (i) they spread out the flux in the air gap and also, being of larger cross-section, reduce the reluctance of the magnetic path (ii) the support the exciting coils (or field coils) as shown in Fig. 2.14 There are two main types of pole construction (a) The pole core itself may be a solid piece of made out of either cast iron or cast steel but the pole shoe is laminated and is fastened to the pole face by means of counter sunk screws as shown in Fig. 2.10 (b) In modern design, the complete pole cores and pole shoes are built of thin laminations of annealed steel which are riveted together under hydraulic pressure (Fig. 2.11). The thickness of laminations varies from 1 mm to 0.25mm. The laminated poles may be secured to the yoke in any of the following two ways: (i) Either the pole is secured to the yoke by means of screws bolted through the yoke and into the pole body or (ii) The holding screws are bolted into a steel bar which passes through the pole across the plane laminations (Fig. 2.12) Figure 2.9 Figure 2.10 9  Figure 2.11 Figure 2.12 Pole Coils The field coils, which consist of copper wire or strip, are former-wound for the correct dimension (Fig. 2.13). Then, the former is removed and wound coil is put into place over the core as shown in Fig. 2.14. When current is passed through these coils, they electromagnetise the poles which produce the necessary flux that is cut by revolving armature conductors. Armature Core It houses the armature conductors or coils and causes them to rotate and hence cut the magnetic flux of the field magnets. In addition to this, it’s most important function is to provide a path of very low reluctance to the flux through the armature from a N-pole to a S-pole. It is cylindrical or drum-shaped and is built up of usually circular sheet steel discs or laminations approximately 0.5mm thick (Fig. 2.15). It is keyed to the shaft. The slots are either die-cut or punched on the outer periphery of the disc and the keyway is located in the inner diameter shown. In small machines, the armature stampings are keyed directly to the shaft. Usually, these laminations are perforated for air ducts which permits axial flow of air through the armature cooling purposes. Such ventilating channels are clearly visible in the laminations shown in Fig. 2.16 and Fig. 2.17. Figure 2.13 Figure 2.14 Up to armature to diameters of about one metre, the circular stampings are cut out in one piece as shown in Fig. 2.16. But above this size, these circles, especially of such thin sections, are 10 difficult to handle because they tend to distort and become wavy when assembled together. Hence, the circular laminations, instead of being cut out in one piece, are cut in a number of suitable sections or segments which form part of a complete ring (Fig. 2.17) Figure 2.15 Figure 2.16 A complete circular lamination is made up of four or six or even eight segmental laminations. Usually, two keyways are notched in each segment and are dove-tailed o wedge –shaped to make laminations self-locking in position. The purpose of using laminations is to reduce the loss due to eddy currents. Thinner the laminations, greater is the resistance offered to the induced e.m.f., smaller the current and hence lesser the I² R loss in the core. Figure 2.17 Armature Windings The armature windings are usually former-wound. These are first wound in the form of flat rectangular coils and are then pulled into their proper shape in a coil puller. Various conductors of the coils are insulated from each other. The conductors are placed in the armature slots which are lined with tough insulating material. This slot insulation is folder over above the armature conductors placed in the slot and is secured in place by the special hard wooden or fibre wedges. 11 Commutator The function of the commutator is to facilitate collection of current from the armature conductors. As shown in Art. 26.2, it rectified i.e. converts the alternating current induced in the armature conductors into unidirectional current in the external load circuit. It is of cylindrical structure and is built up of wedge-shaped segments of highly-conductivity hard-drawn or drop forged copper. Figure 2.18 Figure 2.19 These segments are insulated from each other by thin layer of mica. The number of segments is equal to the number of armature coils. Each commutator segments is connected to the armature conductor by means of a copper lug o strip (or riser). To prevent them from flying out under the action of centrifugal forces, the segments have V-grooves, these grooves being insulted by conical micanite rings. A sectional view of commutator is shown in Fig. 2.18 whose general appearance when completed is shown in Fig. 2.19. Brushes and Bearings The brushed whose function is to collect current from commutator, are usually made of carbon or graphite and are in the shape of rectangular block. These brushes are housed in brush- holders usually of the box-type variety. As shown in Fig. 2.20, the brush-holder is mounted on a spindle and the brushes can be slide in a rectangular box open at both ends. The brushes are made to bear down on the commutator by a spring whose tension can be adjusted by changing the position of lever in the notches. A flexible copper pigtail mounted at the top of the brush conveys current from the brushes to the holder. The number of brushes per spindle depends on the magnitude of the current to be collected from the commutator. Figure 2.20 12 Because of their reliability, ball-bearings are frequently employed, though for heavy duties, roller bearings are preferable. The ball and rollers are generally packed in hard oil for quieter operation and for reduced bearing wear, sleeve bearing are used which are lubricated by ring oilers fed from oil reservoir in the bearing bracket. Reference: https://www.electrical4u.com/principle-of-dc-generator/ Electrical Machines Second Edition by Siskind Complete Electrical Engineering Formulas and Principles by Romeo A. Rojas Jr. Activities/Assessments: Assignment: Answer the following question briefly: 1. Give the parts of a DC Generator. 13 Lesson 2 – Armature Windings Unit 1: Lap Winding Overview: This lesson will give the students on how to determine the lap winding. Learning Objectives: After successful completion of this lesson, you should be able to: 1. Compute lap winding in the armature core 2. Explain what lap winding is. Course Materials: Lap Winding This winding forms a loop as it expands around the armature core. Commutator Segments Yb = Yf + 2m Where: Yb= back pitch (must be an odd number) = the number of elements that the coil advances on the back of the armature core Yf= front pitch (must be an odd number) = the number of elements spanned on the commutator end of armature m= multiplicity factor = 1, for simplex winding = 2, for duplex winding … etc. +(sign) = for progressive winding = winding expands from left to right -(sign) = for retrogressive winding = winding expands from right to left 14 In lap winding, the conductors are joined in such a way that their parallel paths and poles are equal in number. The end of each armature coil is connected to the adjacent segment on the commutator. The number of brushes in the lap winding is equal to the number of parallel paths, and these brushes are equally divided into negative and positive polarity. The lap winding is mainly used in low voltage, high current machine applications. They are three types Simplex Lap Winding Duplex Lap Winding Triplex Lap Winding 1. Simplex Lap Winding: In simplex lap winding, the terminating end of one coil is joined to the commutator segment and the starting end of the next coil is placed under the same pole. Also, the number of parallel paths is similar to the number of poles of the windings. 2. Duplex Winding: In duplex winding the number of parallel paths between the pole is twice the number of poles. The duplex lap winding is mainly used for heavy current applications. Such type of winding is obtained by placing the two similar winding on the same armature and connecting the even number commutator bars to one winding and the odd number to the second winding. 15 3. Triplex Lap Winding: In triplex lap winding the windings are connected to the one-third of the commutator bars. The lap winding has many paths and hence it is used for the larger current applications. The only disadvantage of the lap winding is that it requires many conductors which increase the cost of the winding. Reference: https://circuitglobe.com/lap-and-wave-winding.html Electrical Machines Second Edition by Siskind Complete Electrical Engineering Formulas and Principles by Romeo A. Rojas Jr. Activities/Assessments: Assignment: Answer the following questions briefly: 1. What is lap winding of a DC Generator? 16 Lesson 2 – Armature Windings Unit 2: Wave Winding Overview: This lesson will give the students on how to determine the wave winding. Learning Objectives: After successful completion of this lesson, you should be able to: 1. Compute wave winding in the armature core 2. Explain what wave winding is. Course Materials: Wave Winding This winding forms a wave as it expands around the armature core. Y = Z ± 2m Y = Yb + Yf P 2 Where: Y= average pitch (must be an integer) Z = total number of winding elements on the surface of the armature core P = number of poles Minimum number of elements or conductors per slot (if not specified): Types of Winding Elements per slot Simplex 2 Duplex 4 Triplex 6 Quadruplex 8 Total number of elements or conductors (Z): Z = (elements/ slot) (total number of slots) 17 Number of brushes (N): N (lap) = P N (wave) = 2 Number of commutator segments (Nc): Nc = Z 2 Number of armature current paths (a): a (lap) = mP a (wave)= 2m Coil pitch (Ys): Ys = coil span in slots slots per pole In wave winding, only two parallel paths are provided between the positive and negative brushes. The finishing end of the one armature coil is connected to the starting end of the other armature coil commutator segment at some distance apart. In this winding, the conductors are connected to two parallel paths irrespective of the number of poles of the machine. The number of brushes is equal to the number of parallel paths. The wave winding is mainly used in high voltage, low current machines. If after passing one round, the armature winding falls into a slot to the left of its initial point, then the winding is said to be retrogressive. And if the armature windings fall on one slot to the right then it is called progressive winding. 18 Assume the two layers winding and suppose that the conductor AB must be at the upper layer half of the slot on the left or right. Consider that the YB is the back pitch and YF is the front pitch. The sum of the back pitch and the front pitch is nearly equal to the pole pitch of the winding. Sample Problems: 1. In a lap winding the front pitch is 17 and the back is 19. What is the average pitch? Yave= Yb + Yf = 19+17 = 18 2 2 2. The difference between the back pitch and the front pitch is 2. The front pitch is 21. If the winding is lap retrogressive, what is the back pitch? Note: Since the difference between the back pitch and the front pitches is 2, the winding is simplex (m = 1). Yb = Yf -2m for retrogressive lap Yb = 21- 2(1) Yb = 19 19 3. If the armature of an eight-pole machine were wound with a simplex wave winding, how many parallel paths would there be? Note: Since simplex, multiplicity factor (m) = 1 A= 2m for wave winding A = 2(1) = 2 paths 4. A four pole, DC generator with lap winding has 48 slots and 4 elements per slot. How many coils does it have? Assume one conductor per coil side. Note: One conductor per coil side means two conductors or elements per coil. N= 4 elements x 1 coil x 48 slots slot 2 elements n = 96 coils 5. A duplex lap wound, four-pole dc generator has 120 slots and four elements per slot. How many commutator segments are there? Z = 4 elements x 120 slots = 480 elements slot Nc = Z = 480 = 240 segments 2 2 Reference: https://circuitglobe.com/lap-and-wave-winding.html Electrical Machines Second Edition by Siskind Complete Electrical Engineering Formulas and Principles by Romeo A. Rojas Jr. Activities/Assessments: Assignment: Problem Solving. 1. A 4-pole wave wound armature has 744 armature conductors in 62 slots. If the commutator has 186 segments, determine a. the coil span b. the number of conductors per coil Explanation: 2. Differentiate lap winding and wave winding. 20