LECTURE NOTES ON ELECTRICAL MACHINE-II Subject Code-PCEL4302 For B.Tech 5 th Semester Electrical Engineering MODULE-III SYNERGY INSTITUTE OF ENGINEERING AND TECHNOLOGY Department of Electrical Engineering Dhenkanal
Syllabus PCEL4302 ELECTRICAL MACHINES-II (3-1-0) MODULE-I [15 HOURS] 1. Three Phase Synchronous Generators (5 hours) Synchronous Generator Construction (both Cylinderical Rotor and Salient Pole type), The Speed of Rotation of a Synchronous Generator, Induced voltage in A.C. Machines, The Internal Generated Voltage of a Synchronous Generator, The Effect of Coil Pitch on A.C. Machines, Distributed Windings in A.C. Machines, The Rotating Magnetic Field, The Equivalent Circuit of a Synchronous Generator (Armature Reaction Reactance, Synchronous Reactance and Impedance). [Chapman: Ch. 5.1, 5.2, 4.4, 5.3, B.1, B.2, 4.2, 5.4] 2. Cylindrical Rotor type Three Phase Synchronous Generators (4+2=6 hours) (a) The Phasor Diagram of a Synchronous Generator, Power and Torque in Synchronous Generators (Power Angle Equation and Power Angle Characteristic), Measuring Synchronous Generator Model Parameters (Open Circuit and Short Circuit Tests and Determination of Synchronous Impedance and Reactance, The Short Circuit Ratio), Voltage Regulation and Speed Regulation. [Chapman: Ch. 5.5, 5.6, 5.7, 4.8] (4 hours) (b) Zero Power Factor characteristic, Potier Reactance, Voltage Regulation by Synchronous Impedance Method, Potier Reactance (Zero Power Factor = ZPF) Method. [M.G.Say: Selected Portions of Ch.10.2, 10.3, 10.4, 10.15] (2 hours) 3. Salient Pole type Three Phase Synchronous Generators (3+1=4 hours) Two Reaction Concept, Development of the Equivalent Circuit of a Salient Pole type Three Phase Synchronous Generator (Direct axis and Quadrature axis Reactances, Phasor Diagram for various load power factors,), Torque and Power Equations of Salient Pole Synchronous Generator (Power Angle Equation and Power Angle Characteristic with stator resistance neglected). [Chapman: Appendix C.1, C.2] (3 hours) Slip Test for determination of Direct axis and Quadrature axis Reactances. [M.G.Say: Ch.10.15] (1hour) MODULE-II [12 HOURS] 4. Parallel operation of Three Phase A.C. Synchronous Generators (4 hours) The Conditions Required for Paralleling, The General Procedure for Paralleling Generators, Frequency - Real Power and Voltage Reactive Power Characteristics of a Three Phase Synchronous Generator, Operation of Generators in Parallel with large Power Systems, Operation of generators in parallel with other Generators of the same size. [Chapman: Ch.5.9] 5. Three Phase Synchronous Motors (8 hours) Basic Principles of Motor operation, Steady State Synchronous Motor operation, Starting Synchronous Motors, Synchronous Generators and Synchronous Motors, Synchronous Motor Ratings. [Chapman: Ch.6.1, 6.2, 6.3, 6.4, 6.5] MODULE-III [13 HOURS] 6. Three Phase Transformers (5+3=8 hours) Constructional features, Three-Phase Transformer connections, The per unit system for Three Phase Transformer, Transformer Ratings and Related problems, Two Single-Phase Transformers connected in Open Delta (V-Connection) and their rating, T-
Connection (Scott Connection) of Two Single-Phase Transformers to convert Three-Phase balanced supply to Two-Phase balanced supply.[chapman: Ch.2.10, 2.11, 2.12] (5 hours) o o o o Transformer Three phase Connections: Various Phase Displacements (0, 180,+30 and -30 ), Connection Diagrams and Phasor Diagrams of various Vector Groups (Yy0, Dd0, Dz0, Yy6, Dd6, Dz6, Yd1, Dy1, Yz1, Yd11, Dy11, Yz11), Parallel operation of three phase transformers. [M.G.Say: Ch.5.9, 5.15] (3 hours) 7. Single Phase and Special Purpose Motors (5 hours) The Universal Motor, Introduction to Single Phase Induction Motors, Starting of Single Phase Induction Motors, Speed Control of Single Phase Induction Motors, The Circuit Model of a Single Phase Induction Motor, Other types of Motors: Reluctance Motors, Stepper Motors. [Chapman: Ch.10.1, 10.2, 10.3, 10.4, 10.5, 10.6] TEXT BOOKS: (1) Stephen J. Chapman- Electric Machinery and Fundamentals - McGraw Hill International Edition, (Fourth Edition), 2005. (2) M.G.Say- Alternating Current Machines, English Language Book Society (ELBS) /Longman, 5 th Edition, Reprinted 1990. REFERENCE BOOKS: (1) P.C.Sen- Principles of Electric Machines and Power Electronics -2 nd Edition, John Wiley and Sons, Wiley India Reprint, 2007.
Sub: Electrical Machine -II LESSON PLAN 2015-16 Sem: 5 th Electrical Engineering PCEL4302 (3-1-0) Module No Class No Topic 1. Three Phase Synchronous Generators[Chapman: Ch. 5.1, 5.2, 4.4, 5.3, B.1, B.2, 4.2, 5.4] 1 Introduction,Synchronous Generator Construction (both Cylinderical Rotor and Salient Pole type), 2 The Speed of Rotation of a Synchronous Generator, Induced voltage in A.C. Machines, 3 The Internal Generated Voltage of a Synchronous Generator, The Effect of Coil Pitch on A.C. Machines, 4 Distributed Windings in A.C. Machines, The Rotating Magnetic Field, 5 The Equivalent Circuit of a Synchronous Generator (Armature Reaction Reactance, Synchronous Reactance and Impedance) 6 Problem Solving Module No 1 2. Cylindrical Rotor type Three Phase Synchronous Generators a.[chapman: Ch. 5.5, 5.6, 5.7, 4.8] b. [M.G.Say: Selected Portions of Ch.10.2, 10.3, 10.4, 10.15] 7 (a) The Phasor Diagram of a Synchronous Generator, 8 Power and Torque in Synchronous Generators (Power Angle Equation and Power Angle Characteristic), 9 Measuring Synchronous Generator Model Parameters (Open Circuit and Short Circuit Tests and Determination of Synchronous Impedance and Reactance, The Short Circuit Ratio), 10 Voltage Regulation and Speed Regulation. 11 (b) Zero Power Factor characteristic, Potier Reactance, 12 Voltage Regulation by Synchronous Impedance Method, Potier Reactance (Zero Power Factor = ZPF) Method. 3.Salient Pole type Three Phase Synchronous Generators [Chapman: Appendix C.1, C.2] 13 Two Reaction Concept,
14 Development of the Equivalent Circuit of a Salient Pole type Three Phase Synchronous Generator (Direct axis and Quadrature axis Reactances, Phasor Diagram for various load power factors,), 15 Torque and Power Equations of Salient Pole Synchronous Generator (Power Angle Equation and Power Angle Characteristic with stator resistance neglected) 16 Slip Test for determination of Direct axis and Quadrature axis Reactances. [M.G.Say: Ch.10.15] 17 Problem Solving 4. Parallel operation of Three Phase A.C. Synchronous Generators [Chapman: Ch.5.9] 18 The Conditions Required for Paralleling, The General Procedure for Paralleling Generators, 19 Frequency - Real Power and Voltage Reactive Power Characteristics of a Three Phase Synchronous Generator, 20 Operation of Generators in Parallel with large Power Systems, 21 Operation of generators in parallel with other Generators of the same size. 22 Problem solving 5. Three Phase Synchronous Motors [Chapman: Ch.6.1, 6.2, 6.3, 6.4, 6.5] Module No 2 23 Basic Principles of Motor operation, 24 Steady State Synchronous Motor operation 25 Starting of Synchronous Motors 26 Synchronous Generators and Synchronous Motors 27 Synchronous Motor Ratings. 28 Problem solving 6. Three Phase Transformers [Chapman: Ch.2.10, 2.11, 2.12] 29 Constructional features, Three-Phase Transformer connections, 30 The per unit system for Three Phase Transformer, Transformer Ratings and Related problems, 31 Two Single-Phase Transformers connected in Open Delta (V-Connection) and their rating, 32 T-Connection (Scott Connection) of Two Single-Phase Transformers to convert Three- Phase balanced supply to Two-Phase balanced supply
33 Problem solving Module No 3 34 Transformer Three phase Connections: Various Phase Displacements (0 o, 180 o,+30 o o and -30 ), [M.G.Say: Ch.5.9, 5.15] 35 Connection Diagrams and Phasor Diagrams of various Vector Groups (Yy0, Dd0, Dz0, Yy6, Dd6, Dz6, Yd1, Dy1, Yz1, Yd11, Dy11, Yz11), 36 Parallel operation of three phase transformers 37 Problem solving 7. Single Phase and Special Purpose Motors [M.G.Say: Ch.5.9, 5.15] 38 The Universal Motor, Introduction to Single Phase Induction Motors, 39 Starting of Single Phase Induction Motors, Speed Control of Single Phase Induction Motors, 40 The Circuit Model of a Single Phase Induction Motor, Other types of Motors: 41 Reluctance Motors, Stepper Motors. 42 Problem solving and discussion TEXT BOOKS: (1) Stephen J. Chapman- Electric Machinery and Fundamentals - McGraw Hill International Edition, (Fourth Edition), 2005. (2) M.G.Say- Alternating Current Machines, English Language Book Society (ELBS) /Longman, 5 th Edition, Reprinted 1990. REFERENCE BOOKS: (1) P.C.Sen- Principles of Electric Machines and Power Electronics -2 nd Edition, John Wiley and Sons, Wiley India Reprint, 2007. Prepared by Mr S.S.Pati Asso Prof
6. Three Phase Transformers LECTURE: 29 Constructional features, Three-Phase Transformer connections Constructional
LECTURE: 30 The per unit system for Three Phase Transformer, Transformer Ratings and Related problems,
LECTURE: 31 Two Single-Phase Transformers connected in Open Delta (V-Connection) and their rating,
LECTURE: 32 T-Connection (Scott Connection) of Two Single-Phase Transformers to convert Three-Phase balanced supply to Two-Phase balanced supply
LECTURE: 33 Problem solving
LECTURE: 34 o Transformer Three phase Connections: Various Phase Displacements (0, 180 [M.G.Say: Ch.5.9, 5.15] o,+30 o o and -30 ),
LECTURE: 35 Connection Diagrams and Phasor Diagrams of various Vector Groups (Yy0, Dd0, Dz0, Yy6, Dd6, Dz6, Yd1, Dy1, Yz1, Yd11, Dy11, Yz11),
Parallel operation of three phase transformers LECTURE: 36
LECTURE: 37 Problem solving
7. Single Phase and Special Purpose Motors LECTURE: 38 The Universal Motor, Introduction to Single Phase Induction Motors
LECTURE: 39 Starting of Single Phase Induction Motors, Speed Control of Single Phase Induction Motors,
LECTURE: 40 Single Phase Induction Motor Circuit Model The steady state model for a single winding of a single phase induction motor is developed in this section. It should be noted that the steady state circuit model does not include effects such as pulsating torques. It also doesn't apply to the case where a split-phase winding is used (with or without capacitors). In that case, the backwards rotating field may be completely or partially eliminated. Assuming a single-phase single-winding motor, the equivalent circuit at standstill may be drawn as Note that this circuit is identical to the the per-phase circuit of a multi-phase induction machine at standstill. Now, assuming that the pulsating field in the motor can be described using forwards and backwards rotating fields, the standstill circuit can be modified as shown below.
In the diagram shown above, the total impedance is equal to the original circuit, but the magnetising and rotor branches have been divided into two equal components, with forwards and backwards currents to represent the forwards and backwards magnetic fields. Now, if the rotor rotates, the equivalent rotor resistance in each of the forwards and backwards circuits will be divided by slip, relative to the forwards or backwards rotating field.
In the final circuit, shown above, forwards slip is shown as s f and backwards slip is shown as s b. These slips are defined as Analyzing the circuit, rather than solve for the currents in the various parallel paths, it is easier to think in terms of impedances of the different parts of the circuit and the power flow into each part of the circuit. The phase input impedance is given by Considering the circuit and remembering that air gap power is defined as the input power minus the power losses in the stator, the air gap power can be defined using When considering the torque components, we must remember that the forwards and backwards torques correspond to positive and negative synchronous speeds. Using knowledge from threephase machines, torque is given be airgap power divided by synchronous speed:
Power converted to mechanical energy can be found from the torque and mechanical speed The losses in the rotor circuits can be found from the difference between airgap power and output power Finally, the output power available on the shaft is given by the mechanical power converter minus the rotational losses. P out = P conv - P rot Points to note The air gap power is the sum of both forwards and backwards components. If the motor is rotating in the forwards direction, the backwards field is in the braking or plugging region and the rotor copper losses will be higher than the backwards air gap power. (Power flows into the rotor from both the stator and the backwards torque component) The text derivation of this theory (and example) contains some errors. If you consider example 10-1 on p 663 of the 4th edition, the output power plus losses don't add up to the input power. Use the definitions in these notes.
Stepper Motors., Reluctance Motors LECTURE: 41
Problem solving and discussion Example LECTURE: 42 A 2-pole, 120V, 50hz, single-phase induction motor is running at 3420 rpm. The equivalent circuit parameters are: R 1 = 3.5Ω, R 2 = 3.2Ω, X 1 = 4.1Ω, X 2 = 4.1Ω, X m = 80Ω, P rot = 42.5W Calculate the input current, input power, power factor, output power and efficiency This is a 2-pole 60hz motor, therefore synchronous speed and forwards slip are given by To find current, first find phase impedance Input current can be found as
power factor is given by cos(44.5)=0.717 Power in a single phase system is VI cosθ = 328W To find output power: Therefore efficiency is given by η =200/327=61%