Technological University of the Philippines-Manila Electrical Engineering Department PEE5-M Electrical Machines 1 2024

Technological University of the Philippines-Manila Ayala Blvd, Ermita, Manila, 1000 Metro Manila College of Engineering Electrical Engineering Department...

Technological University of the Philippines-Manila Ayala Blvd, Ermita, Manila, 1000 Metro Manila College of Engineering Electrical Engineering Department MODULE 1 : INTRODUCTION TO MACHINERY PRINCIPLES CONTENTS: I. Electrical Machines II. Notes on Units and Notation III. Rotational Motion, Newton’s Law, and Power Relationships IV. Magnetic Field V. Faraday’s Law VI. Production of Induced Force on a Wire www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. ELECTRICAL MACHINES Electrical Machine An electrical machine is a device that can convert either mechanical energy to electrical energy or electrical energy to mechanical energy. When such a device is used to convert mechanical energy to electrical energy, it is called generator. When it converts electrical energy to mechanical energy, it is called motor. The transformer on the other hand, is an electrical device that is closely related to electrical machines. It converts electrical energy at one voltage level to ac electrical energy at another voltage level. Since transformers operate on the same principles as generators and motors, depending on the action of the magnetic field to accomplish the change in voltage level, they are usually studied together with generators and motors. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. NOTES ON UNITS AND NOTATION The design and study of electric machines and power systems are among the oldest areas of electrical engineering. Study began in the latter part of the nineteenth century. At that time, electrical units were being standardized internationally, and these units came to be universally used by engineers. Volts, amperes, ohms, watts, and similar units, which are part of the metric system of units have long been used to describe electrical quantities in machines. In 1954, a comprehensive system of units based on the metric system was adopted as an international standard. This system of units became known as the Systeme International (SI) and has been adopted throughout most of the world. The SI possesses a number of remarkable features shared by no other system units: 1. It is a decimal system. 2. It employs many units commonly used in industry and commerce: for example, volt, ampere, kilogram, and watt. 3. It is a coherent system that expresses with startling simplicity some of the most basic relationships in electricity, mechanics, and heat. 4. It can be used by research scientist, the technician, the practicing engineer, and by the layman, thereby blending the theoretical and practical worlds. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. NOTES ON UNITS AND NOTATION BASE UNITS OF THE SI QUANTITY UNIT SYMBOL Length meter m Mass kilogram kg Time second s Electric Current ampere A Temperature kelvin K Luminous Intensity candela cd Amount of Substance mole mol DERIVED UNITS OF THE SI QUANTITY UNIT SYMBOL Electric Capacitance farad F Electric Charge coulomb C Electric Conductance siemens S Electric Potential volt V Electric Resistance ohm Ω Energy joule J Force newton N Frequency hertz Hz Illumination lux lx Inductance henry H Luminous Flux lumen lm Magnetic Flux weber Wb Magnetic Flux Density tesla T Plane Angle radian rad Power watt W Pressure pascal Pa Solid Angle steradian sr www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. NOTES ON UNITS AND NOTATION COMMON UNITS IN ELECTRICITY AND MAGNETISM QUANTITY UNIT SYMBOL Capacitance farad F Conductance siemens S Electric Charge coulomb C Electric Current ampere A Energy Joule J Frequency Hertz Hz Inductance newton N Potential Difference volt V Power watt W Resistance ohm Ω Resistivity ohm meter Ω m Magnetic Field Strength ampere/meter A/m Magnetic Flux weber Wb Magnetic Flux Density tesla T Magnetomotive Force ampere turns A t or Fm www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. ROTATIONAL MOTION, NEWTON’S LAW, AND POWER RELATIONSHIPS Almost all electric machines rotate about an axis, called the shaft of the machine. Because of the rotational nature of the machinery, it is important to have a basic understanding of rotational motion. Each major concept of rotational motion is defined below and is related to the corresponding idea from linear motion. Angular Position, θ Refers to the orientation of a line with respect to a reference direction, often measured in radians or degrees or revolution. It describes how far an object has rotated or the angle at which it is positioned relative to a fixed axis. Angular Velocity, ω Is the rate at which an object changes its angular position. It describes how fast something is spinning or rotating. It quantifies the rate of change of angular position with respect to time. 𝒅r v= – linear velocity 𝒅𝒕 𝒅θ ω= (radians per second)– angular velocity 𝒅𝒕 ωm – angular velocity in radians per second fm – angular velocity in revolutions per second nm – angular velocity in revolutions per minute ω fm = m nm = 60 fm 𝟐𝝅 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. ROTATIONAL MOTION, NEWTON’S LAW, AND POWER RELATIONSHIPS Angular Acceleration, α Measures how fast the angular velocity is changing. If an object is rotating and its speed of rotation is increasing or decreasing, it experiences angular acceleration. 𝒅v α= – linear acceleration 𝒅𝒕 𝒅ω α= (radians per second2)– angular acceleration 𝒅𝒕 Torque, τ ▪ Also called the “twisting force” on an object. ▪ Torque is a measure of the rotational force applied to an object, causing it to rotate around an axis. ▪ Torque is defined as the product of the force (𝐹) applied and the perpendicular distance (𝑟) from the point of rotation (the axis) to where the force is applied. τ = (force applied)(perpendicular distance) τ = F x r sinθ τ = rF sinθ (N m or lb ft) www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. ROTATIONAL MOTION, NEWTON’S LAW, AND POWER RELATIONSHIPS Newton’s Law of Rotation F = 𝒎𝒂 (Newton) – linear form τ = Ia (N m or lb ft) – rotational form Work, W The product of the force applied to an object and the displacement of the object in the direction of the force. W = ‫𝒓𝒅 𝑭 ׬‬ – linear form W = Fr – constant force W = ‫ ׬‬τ 𝒅𝜽 (Joule) – rotational form W = τθ (Joule) – constant torque Power, P Defined as the amount of work done (𝑊) divided by the time (𝑡) taken to do that work. 𝒅W P= (Joules per second, watts, ft lb/sec, horsepower) 𝒅𝒕 𝒅W 𝒅 𝒅𝒓 P= = (Fr) = F = 𝑭𝒗 – constant force 𝒅𝒕 𝒅𝒕 𝒅𝒕 𝒅W 𝒅 𝒅𝜽 P= = (τθ) = τ = τω – constant torque 𝒅𝒕 𝒅𝒕 𝒅𝒕 τ 𝑙𝑏 𝑓𝑡 𝒏 ( 𝑟 ) P= 𝑚𝑖𝑛 (watts) 𝟕.𝟎𝟒 𝑟 τ 𝑙𝑏 𝑓𝑡 𝒏 ( ) P= 𝑚𝑖𝑛 (horsepower) 𝟓𝟐𝟓𝟐 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. MAGNETIC FIELD Four basic principles to describe how magnetic fields are used in the devices 1. A current-carrying wire produces magnetic field in the area around it. 2. A time-changing magnetic field induces a voltage in a coil of wire if it passes through that coil. 3. A current-carrying wire in the presence of a magnetic field has a force induced on it. 4. A moving wire in the presence of the magnetic field has a voltage induced in it. Production of Magnetic Field When an electric current flows through a conductor, such as a wire, it generates a magnetic field around the conductor. This phenomenon is described by Ampere’s Law Ampere’s Law Relates the magnetic field around a closed loop to the electric current passing through the loop. ∮ H⋅ dl = Inet H = magnetic field intensity produced by the current Inet dl = differential length element along the path Inet = the net current passing through the surface enclosed by the loop. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. MAGNETIC FIELD Ampere’s Law ‫ ׬‬B 𝒄𝒐𝒔𝜽 𝒅𝒔 = µ𝟎𝑰𝒆𝒏𝒄 B = magnetic flux density cosθ = angle between the direction of the magnetic field and the direction of the differential area ds = differential element of area µ0 = permeability of free space or magnetic constant = 4π x 10-7 Henry/meter or 4π x 10-7 Newtons/Amperes2 Ienc = enclosed current Magnetic Field Intensity, H and Magnetic Flux Density, B ❑ Magnetic Field Intensity (Magnetizing Force), H Is a measure of the ability of a magnetic field to induce magnetization in a material. It is essentially the "push" given by the electric current that creates the magnetic field. Unit : Ampere/meter ❑ Magnetic Flux Density, B Is the amount of magnetic flux passing through a unit area perpendicular to the direction of the magnetic field. It tells you how strong the magnetic field is in a given area. Unit : Tesla (T) B=μH , B=φ/Area www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  V. FARADAY’S LAW Faraday’s Law of electromagnetic induction states: 1. If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals. 2. The value of the induced voltage is proportional to the rate of change of flux. 𝜟𝝋 E=N 𝜟𝒕 E = induced voltage N = number of turns Δφ = change in flux inside the coil (Wb) Δt = time interval during which the flux changes (secs) Example No. 1 A coil of 2000 turns surrounds a flux of 5 mWb produced by a permanent magnet. The magnet is suddenly withdrawn causing the flux inside the coil to drop uniformly to 2 mWb in 1/10 of a second. What is the volage induced? www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  VI. PRODUCTION OF INDUCED FORCE ON A WIRE Voltage Induced in a Conductor It is easier to calculate the induced voltage with reference to the conductors, rather than with reference to the coil itself. In effect, whenever a conductor cuts a magnetic field, a voltage is induced across its terminals. The value of the voltage induced is given by: E = Blv E = Induced voltage B = flux density (T) l = active length of the conductor in the magnetic field (m) v = relative speed of the conductor (m/s) Example No. 2 The stationary conductors of a large generator have an active length of 2m and are cut by a field of 0.6 tesla moving at a speed of 100 m/s. Calculate the voltage induced in each conductor. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  VI. PRODUCTION OF INDUCED FORCE ON A WIRE Lorentz Force on a Conductor When a current-carrying conductor is placed in a magnetic field, it is subject to a force which we call electromagnetic force or Lorentz force. The maximum force acting on a straight conductor is given by: F = Bil F = force acting on the conductor (N) B = flux density of the field (T) I = current in the conductor (A) l = active length of the conductor (m) Example No. 3 A conductor 3m long carrying a current of 200 A is placed in a magnetic field whose density is 0.5 T. Calculate the force of the conductor if it is perpendicular to the lines of force. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  VI. PRODUCTION OF INDUCED FORCE ON A WIRE Assignment : ( A4-size bond paper) 1. What is DC generator? 2. What is the difference between ac and dc generators? 3. Give the construction of DC Generators 4. What is the difference between shunt generator and compound generator? Late submission will not be entertained. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  QUIZ NO. 1 THANK YOU FOR LISTENING!! www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  Technological University of the Philippines-Manila Ayala Blvd, Ermita, Manila, 1000 Metro Manila College of Engineering Electrical Engineering Department MODULE 2 : DC MACHINERY FUNDAMENTALS CONTENTS: I. Voltage Induced in a Rotating Loop II. Internal Generated Voltage and Induced Torque Equations www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. VOLTAGE INDUCED IN A ROTATING LOOP The voltage induced in a rotating loop is a classic example of electromagnetic induction, which is described by Faraday's Law of Electromagnetic Induction. When a loop of wire rotates in a magnetic field, an electromotive force (EMF) or voltage is induced in the loop due to the changing magnetic flux through the loop over time. WORKING PRINCIPLE OF DC MACHINE 1. DC Generator ▪ Magnetic Field - A magnetic field is produced by field windings or permanent magnets in the stator of the machine. ▪ Armature (Rotor) - The armature, which is typically a coil or loop of wire, is mechanically rotated within this magnetic field. This rotation is usually provided by an external mechanical force (like a turbine, engine, or hand crank). ▪ Induced EMF - As the armature rotates, the conductors cut through the magnetic flux lines, and according to Faraday's Law, an EMF is induced in the conductors. ▪ Commutation - The commutator, which is connected to the rotating armature, converts the alternating EMF generated in the armature into direct current (DC) by reversing the direction of current in the armature windings each time the polarity of the induced EMF changes. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. VOLTAGE INDUCED IN A ROTATING LOOP WORKING PRINCIPLE OF DC MACHINE (Cont’d..) www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. VOLTAGE INDUCED IN A ROTATING LOOP The voltage induced in a rotating loop is a classic example of electromagnetic induction, which is described by Faraday's Law of Electromagnetic Induction. When a loop of wire rotates in a magnetic field, an electromotive force (EMF) or voltage is induced in the loop due to the changing magnetic flux through the loop over time. WORKING PRINCIPLE OF DC MACHINE 2. DC Motor ▪ Magnetic Field - Similar to a generator, a magnetic field is established in the stator of the motor by either field windings or permanent magnets. ▪ Current in Armature - When DC voltage is applied to the motor terminals, current flows through the armature winding, which is placed in the magnetic field. ▪ Lorentz Force - The interaction between the magnetic field and the current-carrying conductors in the armature generates a force (Lorentz force) on the conductors. According to Fleming's Left-Hand Rule, the direction of this force is such that it causes the armature to rotate. ▪ Commutation: The commutator and brushes in a DC motor ensure that the direction of current in the armature windings changes as the armature rotates. This allows for continuous rotation of the armature in the same direction, producing mechanical motion. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. VOLTAGE INDUCED IN A ROTATING LOOP WORKING PRINCIPLE OF DC MACHINE (Cont’d..) www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. VOLTAGE INDUCED IN A ROTATING LOOP Overview of Rectangular Loop The voltage in each segment is given by: Eind = v x B x l ❑ Segments AB and CD - These are the sides of the loop that are parallel to each other and perpendicular to the magnetic field. Force Direction: ▪ For segment AB, the force acts in one direction (say upwards), while for segment CD, the force acts in the opposite direction (downwards). ▪ These forces are equal in magnitude but opposite in direction, creating a couple that tends to rotate the loop. Torque Contribution: The forces on AB and CD contribute to the torque that rotates the loop. This torque is responsible for the rotational motion of the loop in the magnetic field. Eab = vBl Ecd = vBl www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Overview of Rectangular Loop ❑ Segments BC and DA - These are the sides of the loop that are parallel to each other and parallel to the magnetic field. Magnetic Force: In segments BC and DA, the current-carrying wires are parallel to the magnetic field. According to the Lorentz force law, the magnetic force on these segments is zero because the angle between the current direction and the magnetic field is 0° (or 180°), and the sine of 0° (or 180°) is zero. No Force, No Torque: Since there is no magnetic force acting on segments BC and DA, they do not contribute to the torque that rotates the loop. They simply connect the current paths between AB and CD. Ebc = 0 Eda = 0 The total induced voltage in a loop: Eind = Eab + Ebc + Ecd + Eda = 2vBl www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS The Induced Torque in the Rotating Loop When a rectangular loop or coil rotates in a magnetic field, it experiences an induced torque due to the interaction between the magnetic field and the current flowing through the loop. This induced torque is the key principle behind the operation of electric motors (where electrical energy is converted into mechanical energy) and electric generators (where mechanical energy is converted into electrical energy). Induced Torque and Forces on each Segment AB and CD Force: These segments experience forces due to their perpendicular orientation to the magnetic field. Fab = Fcd = Bil Torque: The forces on AB and CD create a torque that tends to rotate the loop around its axis. τab = τcd = rFsinθ = r(Bil)sin90° = rBil (counterclockwise) BC and DA Force: These segments do not experience any magnetic force because they are aligned with the magnetic field. Fbc = Fda = Bil = 0 (since l is parallel to B) Torque: These segments do not contribute to the torque, but they are essential for completing the circuit in the loop. τbc = τda = 0 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS The resulting total induced torque on the loop is given by: τind = τab + τbc + τcd + τda = ቐ𝟐𝒓𝑩𝒊𝒍 𝟎 By using the facts that Ap≈ πrl and φ = ApB , the torque expression can be reduced to: τind = ቐ𝟐/𝝅(𝝋𝒊) 𝟎 Thus; The torque produced in the machine is the product of the flux in the machine and the current in the machine, times some quantity representing the mechanical construction of the machine. In general, the torque in any real machine will depend on the same three factors: 1. The flux in the machine 2. The current in the machine 3. A constant representing the construction of the machine www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Example No. 1 A simple rotating loop between curved pole faces connected to a battery and a resistor through a switch. The resistor shown models the total resistance of the battery and the wire in the machine. The physical dimensions and characteristics of this machine are: r = 0.5 m R = 0.3 Ω Vs = 120 V l = 1.0 m B = 0.25 T www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Example No. 1 (Cont’d..) (a) What happens when the switch is closed? (b) What is the machine’s maximum starting current? What is it’s’ steady-state angular velocity at no load? (c) Suppose a load is attached to the loop, and the resulting load torque is 10 N m. What would the new steady-state speed be? How much power isa supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or generator? www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Example No. 1 (Cont’d..) (a) What happens when the switch is closed? ❑ When the switch is closed, a current will flow in the loop. Since the loop is initially stationary, Eind = 0. 𝑽 −𝑬𝒊𝒏𝒅 𝑽𝑩 i= 𝑩 = 𝑹 𝑹 ❑ The current flows through the rotor loop, producing torque. 𝟐 τind = φi (CCW) 𝝅 ❑ The induced torque produces angular acceleration in a counterclockwise direction, so the rotor of the machine begins to turn, an induced voltage is produced in the motor. 𝟐 Eind = φωm 𝝅 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Example No. 1 (Cont’d..) (b) What is the machine’s maximum starting current? What is it’s’ steady-state angular velocity at no load? ❑ At starting conditions, the machine’s current is 𝑽 𝟏𝟐𝟎 𝑽 i= 𝑩= = 400A 𝑹 𝟎.𝟑 𝛀 ❑ At no-load steady-state conditions, the induced torque (τind = 0) is zero. The fact that the i=0 means 𝑽𝑩 = 𝑬𝒊𝒏𝒅 𝟐 𝑽𝑩 = 𝑬𝒊𝒏d = φωm 𝝅 𝑽𝑩 𝑽𝑩 𝟏𝟐𝟎 𝑽 ω= 𝟐 = = = 𝟒𝟖𝟎 𝒓𝒂𝒅/𝒔 𝝋 𝟐𝒓𝒍𝑩 𝟐 𝟎.𝟓𝒎 𝟏.𝟎 𝒎 (𝟎.𝟐𝟓𝑻) 𝝅 (c) Suppose a load is attached to the loop, and the resulting load torque is 10 N m. What would the new steady-state speed be? How much power isa supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or generator? ❑ If a load Torque of 10 N m is applied to the shaft of the machine, It will began to slow down. But as the ω decreases, Eind = 𝟐/𝝅 φωm(decreases) and the rotor current increases V −Eind↓ [i= B ]. As the rotor current increases,| τind | increases too, until | τind |= | τload | at 𝑹 a lower speed (ω). ❑ At steady-state, | τind |= | τload | = 𝟐/𝝅 φωi 𝝉𝒊𝒏𝒅 𝝉𝒊𝒏𝒅 𝟏𝟎 𝑵 𝒎 i= 𝟐 = = = 𝟒𝟎 𝑨 𝝋 𝟐𝒓𝒍𝑩 𝟐 𝟎.𝟓 𝒎 𝟏.𝟎 𝒎 (𝟎.𝟐𝟓 𝑻) 𝝅 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. INTERNAL GENERATING VOLTAGE AND INDUCED TORQUE EQUATIONS Example No. 1 (Cont’d..) (c) Suppose a load is attached to the loop, and the resulting load torque is 10 N m. What would the new steady-state speed be? How much power isa supplied to the shaft of the machine? How much power is being supplied by the battery? Is this machine a motor or generator? ❑ If a load Torque of 10 N m is applied to the shaft of the machine, It will began to slow down. But as the ω decreases, Eind = 𝟐/𝝅 φωm(decreases) and the rotor current increases V −Eind↓ [i= B ]. As the rotor current increases,| τind | increases too, until | τind |= | τload | at 𝑹 a lower speed (ω). ❑ At steady-state, | τind |= | τload | = 𝟐/𝝅 φωi 𝝉𝒊𝒏𝒅 𝝉𝒊𝒏𝒅 𝟏𝟎 𝑵 𝒎 i= 𝟐 = = = 𝟒𝟎 𝑨 𝝋 𝟐𝒓𝒍𝑩 𝟐 𝟎.𝟓 𝒎 𝟏.𝟎 𝒎 (𝟎.𝟐𝟓 𝑻) 𝝅 ▪ By Kirchoff’s Voltage Law, Eind = VB−iR Eind = VB−iR = 120 V – 40 A (0.3Ω) = 108 V ▪ The speed of the shaft is E 𝑬 108 V ω = 𝟐ind = 𝒊𝒏𝒅 = = 432 rad/s 𝝋 𝟐𝒓𝒍𝑩 𝟐 𝟎.𝟓 𝒎 𝟏.𝟎 𝒎 (𝟎.𝟐𝟓 𝑻) 𝝅 ▪ The power supplied to the shaft is P = τ ωm = (10 N m) (432 rad/s1) = 4320 W ▪ The power out of the battery is P = Vbi = (120 V) (40A) = 4800 W www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  QUIZ NO. 1 THANK YOU FOR LISTENING!! www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  Technological University of the Philippines-Manila Ayala Blvd, Ermita, Manila, 1000 Metro Manila College of Engineering Electrical Engineering Department MODULE 3 : DIRECT-CURRENT GENERATORS CONTENTS: I. Difference between AC and DC Generators II. Practical Generator III. Windings IV. Types of Generators V. Problem Solving www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR Generating an AC Voltage Irrelevant as it may seem, the study of a direct-current (dc) generator has to begin with a knowledge of the alternating-current (ac) generator. The reason is that the voltage generated in any dc generator is inherently alternating and only becomes dc after it has been rectified by the commutator. AC Generator DC Generator VIDEO REFERENCE: https://www.youtube.com/watch?v=xrAIj9OeZ9g www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR AC Generator vs DC Generator The elementary ac and dc generators are essentially built the same way. In each case, a coil rotates between the poles of a magnet and an ac voltage is induced in the coil. The machines only differ in a way the coils are connected to the external circuit. AC Generators carry slip rings, while DC Generators require a commutator. Sometimes machines are built which carry both slip rings and commutator. Such machine can function simultaneously as ac and dc generators. The three armatures (a), (b), and (c) have identical windings. Depending upon how they are connected (to slip rings or commutator), an ac or dc voltage is obtained. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR Improving the Waveshape By increasing the number of coils and segments, we can obtain a dc voltage that is very smooth. Modern generators produce voltages having a ripple of less than 5 percent. The coils are lodged in the slots of laminated iron cylinder. The coils and the cylinder constitute the armature of the machine. Effect of a Single Coil If the generator has only a single coil, the output DC voltage will vary significantly. There will be moments where the coil is aligned such that it is perpendicular to the magnetic field, producing the maximum voltage, but as the coil rotates, there will be points where it is parallel to the magnetic field, resulting in zero voltage. This creates a pulsating DC output with a lot of ripple. Increasing the Number of Coils ▪ More Coils = Smoother Voltage - By adding more coils (windings) to the armature, the generator can reduce the ripple in the output DC voltage. Each coil is positioned at a different angle relative to the magnetic field, so while one coil's voltage output is dropping to zero, another coil’s voltage output may be at its peak. This overlapping of voltage contributions from multiple coils smooths out the waveform. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR ▪ Distributed Coil Layout - The coils are distributed around the armature in such a way that they span different angular positions relative to the magnetic field. With more coils, there are more instances when at least one coil is generating near-maximum voltage, preventing the sharp dips and peaks that occur with just one or two coils. The armature has The armature has 12 4 slots, 4 coils, and slots, 12 coils, and 4 commutator bars 12 commutator bars www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR ▪ Distributed Coil Layout - The coils are distributed around the armature in such a way that they span different angular positions relative to the magnetic field. With more coils, there are more instances when at least one coil is generating near-maximum voltage, preventing the sharp dips and peaks that occur with just one or two coils. VALUE OF THE INDUCED VOLTAGE The voltage induced in a dc generator having a lap winding is given by the equation: E0 = Znφ/60 Where: E0 = Voltage between the brushes (V) Z = Total number of conductors on the armature n = Speed of rotation (r/min) φ = Flux per pole (Wb) Lap Winding - In this winding configuration, the ends of each coil are connected to adjacent commutator segments in such a way that the coil "laps" or overlaps with the neighboring coil. This type of winding is primarily used in machines designed for high current, low voltage applications. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  I. DIFERENCE BETWEEN AC GENERATOR AND DC GENERATOR Example No. 1 The armature of a 6-pole, 600 r/min generator has 90 slots. Each coil has 4 turns and the flux per pole is 0.04 Wb. Calculate the value of the induced voltage. Solution: Z = 90 coils x 4turns/coil x 2 conductors/turn = 720 n = 600 r/min E0 = Znφ/60 = (720 x 600 x 0.04) / 60 = 288 V www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR The simple loop generator has been considered in detail merely to bring out the basic principle underlying construction and working of an actual generator which consists of the following essential 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 www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 1. Magnetic Frame or Yoke -The outer frame or yoke serves double purpose : ▪ It provides mechanical support for the poles and acts as a protecting cover for the whole machine and ▪ It carries the magnetic flux produced by the poles. 2. Pole Cores and Pole Shoes - The field magnets consist of pole cores and pole shoes. The pole shoes serve two purposes: ▪ They spread out the flux in the air gap and also, being of larger cross-section, reduce the reluctance of the magnetic path ▪ They support the exciting coils (or field coils) www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR The laminated poles may be secured to the yoke in any of the following two ways : ▪ Either the pole is secured to the yoke by means of screws bolted through the yoke and into the pole body or ▪ The holding screws are bolted into a steel bar which passes through the pole across the plane of laminations 3. Pole Coils - The field coils or pole coils, which consist of copper wire or strip, are former-wound for the correct dimension. Then, the former is removed and wound coil is put into place over the core. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 4. 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, its 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. 5. 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 folded over above the armature conductors placed in the slot and is secured in place by special hard wooden or fibre wedges. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 6. Commutator - The function of the commutator is to facilitate collection of current from the armature conductors. 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 high-conductivity hard-drawn or drop forged copper. 7. Brushes and Bearings - The brushes whose function is to collect current from commutator, are usually made of carbon or graphite and are in the shape of a rectangular block. the brush-holder is mounted on a spindle and the brushes can slide in the 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. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 8. Pole Pitch - It may be variously defined as : ▪ The periphery of the armature divided by the number of poles of the generator i.e. the distance between two adjacent poles. ▪ It is equal to the number of armature conductors (or armature slots) per pole. If there are 48 conductors and 4 poles, the pole pitch is 48/4 = 12. 9. Conductor - The length of a wire lying in the magnetic field and in which an e.m.f. is induced, is called a conductor (or inductor) as, for example, length AB or CD. 10. Coil and Winding Element - The two conductors AB and CD along with their end connections constitute one coil of the armature winding. The coil may be single-turn coil or multi turn coil. A single-turn coil will have two conductors. But a multi-turn coil may have many conductors per coil side. For example, each coil side has 3 conductors. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 11. Coil Span or Coil Pitch (YS) - It is the distance, measured in terms of armature slots (or armature conductors) between two sides of a coil. It is, in fact, the periphery of the armature spanned by the two sides of the coil. If the pole span or coil pitch is equal to the pole pitch (as in the case of coil A where pole pitch of 4 has been assumed), then winding is called full-pitched. It means that coil span is 180 electrical degrees. In this case, the coil sides lie under opposite poles, hence the induced e.m.fs. in them are additive. Therefore, maximum e.m.f. is induced in the coil as a whole, it being the sum of the e.m.f.s induced in the two coil sides. For example, if there are 36 slots and 4 poles, then coil span is 36/4 = 9 slots. If number of slots is 35, then YS = 35/4 = 8 because it is customary to drop fractions. If the coil span is less than the pole pitch (as in coil B where coil pitch is 3/4th of the pole pitch), then thewinding is fractional-pitched. In this case, there is a phase difference between the e.m.fs. in the two sides of the coil. Hence, the total e.m.f. round the coil which is the vector sum of e.m.fs. in the two coil sides, is less in this case as compared to that in the first case. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  II. PRACTICAL GENERATOR 12. Pitch of a Winding (Y)- In general, it may be defined as the distance round the armature between two successive conductors which are directly connected together. Or, it is the distance between the beginnings of two consecutive turns. Y = YB – YF - Lap Winding Y = YB + YF - Wave Winding In practice, coil-pitches as low as eight-tenths of a pole pitch are employed without much serious reduction in the e.m.f. Fractional-pitched windings are purposely used to effect substantial saving in the copper of the end connections and for improving commutation. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. WINDINGS 1. Single-Layer Winding - It is that winding in which one conductor or one coil side is placed in each armature slot. Such a winding is not much used. 2. Two-Layer Winding - Each slot of the armature contains two coils: an upper and a lower coil. This is a common method in electrical machines like alternators and motors, particularly for improving the winding arrangement and performance. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. WINDINGS 4. Multiplex Winding - The term "multiplex" indicates that multiple sets of windings are used, increasing the complexity and the number of parallel paths for current to flow through. Multiplex windings are used to handle higher currents and improve the overall performance of the machine. Types of Multiplex Winding The most common types of multiplex windings are: ▪ Duplex Winding - This is a two-layer winding, where two identical winding sets are connected in parallel. It doubles the number of parallel paths compared to a simplex winding. ▪ Triplex Winding - In this, three identical windings are connected in parallel, tripling the number of parallel paths. ▪ Quadruplex Winding - Four winding sets are connected in parallel, quadrupling the number of parallel paths. 5. Lap and Wave Winding - Two types of windings mostly employed for drum- type armatures are known as Lap Winding and Wave Winding. Lap winding is best for high-current, low-voltage applications due to its numerous parallel paths.Wave winding is ideal for high-voltage, low-current applications with its simplified two-path configuration. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. WINDINGS 5. Lap and Wave Winding (Cont’d..) Feature Lap Winding Wave Winding Number of Parallel Equal to the number of Always 2 Paths (A) poles (P) Lower voltage, more Higher voltage, fewer Voltage parallel paths parallel paths Current Higher current capacity Lower current capacity A = P (parallel paths = A = 2 (always 2 parallel Winding Formula poles) paths) Low-voltage, high-current High-voltage, low-current Applications machines machines Less armature reaction due More armature reaction Armature Reaction to more paths due to fewer paths More complex, more Simpler design, fewer Complexity conductors required commutator segments www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. WINDINGS 5. Lap and Wave Winding (Cont’d..) Simplex Lap Winding - This type of winding derives its name from the fact it doubles or laps back with its succeeding coils. Following points regarding simplex lap winding should be carefully noted : ▪ The back and front pitches are odd and of opposite sign. But they cannot be equal. They differ by 2 or some multiple thereof. ▪ Both YB and YF should be nearly equal to a pole pitch. ▪ The average pitch YA = (YB+YF)/2. It equals pole pitch Z/P ▪ Commutator pitch YC = ±1. (In general, YC = ± m) ▪ Resultant pitch YR is even, being the arithmetical difference of two odd numbers, i.e., YR = YB − YF. ▪ The number of slots for a 2-layer winding is equal to the number of coils (i.e. half the number of coil sides). The number of commutator segments is also the same. Simplex Wave Winding - Like lap winding, a wave winding may be duplex, triplex or may have any degree of multiplicity. A simplex wave winding has two paths, a duplex wave winding four paths and a triplex one six paths etc. Points to Note: ▪ Both pitches YB and YF are odd and of the same sign. ▪ Back and front pitches are nearly equal to the pole pitch and may be equal or differ by 2, in which case, they are respectively one more or one less than the average pitch. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  III. WINDINGS ▪ Resultant pitch YR = YF + YB. ▪ Commutator pitch, YC = YA (in lap winding YC = ±1). Also, YC = No. of Commutator bars ±1 / Number of Pair of Poles ▪ The average pitch which must be an integer is given by YA = Z+2 / P = (Z/2 +1 ) / (P/2) = No. of Commutator bars ±1 / Number of Pair of Poles www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. TYPES OF GENERATORS Generators are usually classified according to the way in which their fields are excited. Generators may be divided into (a) separately-excited generators and (b) self-excited generators. (a) Separately-excited generators are those whose field magnets are energised from an independent external source of d.c. current. (b) Self-excited generators are those whose field magnets are energised by the current produced by the generators themselves. Due to residual magnetism, there is always present some flux in the poles. When the armature is rotated, some e.m.f. and hence some induced current is produced which is partly or fully passed through the field coils thereby strengthening the residual pole flux. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. TYPES OF GENERATORS (b) Self-excited generators (cont’d..) There are three types of self-excited generators named according to the manner in which their field coils (or windings) are connected to the armature. 1. Shunt Wound - The field windings are connected across or in parallel with the armature conductors and have the full voltage of the generator applied across them. 2. Series Wound - In this case, the field windings are joined in series with the armature conductors As they carry full load current, they consist of relatively few turns of thick wire or strips. Such generators are rarely used except for special purposes i.e. as boosters etc. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. TYPES OF GENERATORS C. Compound Wound - It is a combination of a few series and a few shunt windings and can be either short-shunt or long-shunt. In a compound generator, the shunt field is stronger than the series field. When series field aids the shunt field, generator is said to be commutatively-compounded. On the other hand if series field opposes the shunt field, the generator is said to be differentially compounded. Short Shunt Long Shunt Compound Wond Compound Wond www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. TYPES OF GENERATORS www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  IV. TYPES OF GENERATORS Brush Contact Drop It is the voltage drop over the brush contact resistance when current passes from commutator segments to brushes and finally to the external load. Its value depends on the amount of current and the value of contact resistance. This drop is usually small and includes brushes of both polarities. However, in practice, the brush contact drop is assumed to have the following constant values for all loads. 0.5 V for metal-graphite brushes. 2.0 V for carbon brushes. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  V. PROBLEM SOLVING 1. A dc machine has 8 poles and a rated current of 100 A. How much current will flow in each path at rated conditions if the armature is (a) simplex lap-wound, (b) duplex lap-wound, (c) simplex wave-wound? 2. A shunt generator delivers 450 A at 230 V and the resistance of the shunt field and armature are 50 Ω and 0.03 Ω respectively. Calculate the generated e.m.f. 3. A long-shunt compound generator delivers a load current of 50 A at 500 V and has armature, series field and shunt field resistances of 0.05 Ω, 0.03 Ω and 250 Ω respectively. Calculate the generated voltage and the armature current. Allow 1 V per brush for contact drop. 4. A short-shunt compound generator delivers a load current of 30 A at 220 V, and has armature, series-field and shunt-field resistances of 0.05 Ω, 0.30 Ω and 200 Ω respectively. Calculate the induced e.m.f. and the armature current. Allow 1.0 V per brush for contact drop. 5. In a long-shunt compound generator, the terminal voltage is 230 V when gen erator delivers 150 A. Determine (i) induced e.m.f. (ii) total power generated and (iii) distribution of this power. Given that shunt field, series field, divertor and armature resistance are 92 Ω, 0.015 Ω, 0.03 Ω and 0.032 Ω respectively. 6. The following information is given for a 300-kW, 600-V, long-shunt compound generator : Shunt field resistance = 75 Ω, armature resistance including brush resistance = 0.03 Ω commutating field winding resistance = 0.011 Ω series field resistance = 0.012 Ω, divertor resistance = 0.036 Ω. When the machine is delivering full load, calculate the voltage and power generated by the armature. www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  ASSIGNMENT 1. A dc machine has 8 poles and a rated current of 120 A. How much current will flow in each path at rated conditions if the armature is (a) simplex lap-wound, (b) duplex lap-wound, (c) simplex wave-wound? www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024  QUIZ NO. 1 THANK YOU FOR LISTENING!! www.tup.edu.ph PEE5-M | ELECTRICAL MACHINES 1 ENGR. EVA B. BELGAR, RME 2024