1) Single-Phase Transformer =

A transformer is an electrical device designed to transfer electrical energy from one circuit to another through electromagnetic induction. It achieves voltage conversion, either stepping up or stepping down, without altering the frequency of the electrical current. Transformers are composed of two or more windings: the primary winding receives energy, and the secondary winding delivers it to the load.

• Equivalent Circuit: The concept of equivalent circuit parameters is used to simplify the analysis of transformers. This model represents the transformer’s resistance, reactance, and losses, which allows for easier calculation of performance metrics such as voltage regulation, efficiency, and power factor.

• Phasor Diagram: While not explicitly described with a general diagram, specific examples in the sources illustrate phasor diagrams for synchronous motors operating under various conditions, which conceptually involve representing voltages and currents as phasors.

• Open Circuit and Short Circuit Tests: These tests are performed to accurately assess a transformer’s performance.

    ◦ The Open-Circuit Test is used to determine the core loss and no-load current.

    ◦ The Short-Circuit Test helps in determining the copper loss and equivalent impedance.

• Regulation and Efficiency:

    ◦ Efficiency: Transformers are known for their high efficiency, often exceeding 95%, primarily because they operate without moving parts, relying on magnetic fields to transfer energy. Losses are minimised through careful design, maintaining low levels of core losses (iron losses, including hysteresis and eddy current losses) and copper losses (I²R losses from winding resistance). Efficiency can be calculated using the formula: Efficiency = (Output Power / Input Power) * 100.

    ◦ Voltage Regulation: This parameter indicates the change in output voltage under varying load conditions. It is defined as the percentage difference between the no-load and full-load output voltage, relative to the full-load voltage. Understanding voltage regulation is crucial for ensuring reliable and quality electrical supply.

2) Three-Phase Transformers =

Three-phase transformers are integral to electrical power systems.

• Connections: These include various configurations, which are typically discussed in detail in electrical engineering curricula. The specific types of connections (e.g., star-delta transformation) are part of the broader study of electric circuits.

• Vector Groups: The grouping of vectors is a consideration for three-phase transformers.

• Parallel Operation: Multiple three-phase transformers can be operated in parallel to enhance system reliability and efficiency. For successful parallel operation, they must have the same voltage rating and share the load proportionally based on their kVA ratings and leakage impedances. Incorrect connections can lead to circulating currents, uneven load sharing, and potential damage due to overloads. Proper polarity and matching of voltage ratios are essential for safe and efficient operation.

Auto-Transformer

An auto-transformer is a type of transformer with a single winding that functions as both the primary and secondary winding. In the context of motors, auto-transformers are notably used to reduce the applied voltage during starting for devices like synchronous motors. This reduction in voltage helps to decrease the starting current, which can be very high in direct-on-line starting. However, reducing the voltage also reduces the starting torque, which varies approximately as the square of the applied voltage. For synchronous motors, auto-transformers are typically used to apply 50% to 80% of the full-line voltage. They are cut out of the circuit once the motor has accelerated.

Electromechanical Energy Conversion Principles

Electromechanical energy conversion involves the transformation of various forms of energy into electrical energy and vice versa. The primary advantage of converting other energy forms into electrical energy is that electrical energy can be transmitted, utilised, and controlled more easily, reliably, and efficiently.

• Categories of Devices: Energy conversion devices are broadly categorised into:

    1. Low-energy signal devices such as telephones and microphones, which process small motions.

    2. Force or torque-producing devices like electromagnets and actuators, which have limited motions.

    3. Continuous energy conversion devices such as motors and generators, which are crucial for bulk energy conversion.

• Fundamental Principles: The operation of these devices is guided by the principle of conservation of energy, stating that total input energy equals the sum of output energy, stored energy, and energy dissipated as losses.

    ◦ For motors: Electrical energy input = Mechanical energy output + Energy dissipated + Energy stored.

    ◦ For generators: Mechanical energy input = Electrical energy output + Energy dissipated + Energy stored.

    ◦ The coupling between electrical and mechanical systems occurs through magnetic or electric fields.

    ◦ Energy storage in magnetic fields is significantly greater (about 25,000 times) than in electric fields, making magnetic field coupling more efficient for commercial applications.

• Force and Torque Calculations: Forces in electromechanical systems can often be derived from changes in stored energy (F = dW/dx). Torque in rotating machines results from the interaction of magnetic fields produced by stator and rotor currents.

• Electrical Losses: Electrical losses, including ohmic (copper), hysteresis, and eddy-current losses, are always present. While they do not significantly alter the fundamental energy conversion process, they are crucial for calculating the overall efficiency and output of these systems.

3) DC Machines =

D.C. machines are highly versatile energy conversion devices, particularly valued for applications requiring high starting torque and precise variable speed control.

• Motoring and Generating Mode: D.C. machines can operate as either motors (converting electrical energy to mechanical energy) or generators (converting mechanical energy to electrical energy).

    ◦ In a D.C. motor, a back e.m.f. (Eb) is generated in the armature that opposes the applied voltage (V). The armature current is determined by the difference between the applied voltage and the back e.m.f. divided by the armature resistance.

    ◦ D.C. generators provide an efficient power source for industrial applications.

• Characteristics: The fundamental principles of torque production and e.m.f. generation in D.C. machines are the same as for A.C. machines, differing mainly in construction. They feature homopolar field systems and armature-commutator systems.

• Types:

    ◦ Separately Excited: The field winding is supplied from an independent DC source.

    ◦ Series: The field winding is connected in series with the armature winding.

    ◦ Shunt: The field winding is connected in parallel (shunt) with the armature winding.

    ◦ The sources also discuss compound motors, implying these types are part of the broader classification.

• Construction: D.C. machines typically consist of a stator (stationary member) and a rotor (rotating member), separated by an air-gap. Field windings are usually concentrated on salient poles, while armature windings are distributed around the core. Laminated armature cores are used to reduce eddy currents, while stationary field structures may not require lamination. Key components include the yoke, field poles, interpoles, and brushes.

• Applications: D.C. motors are widely used in starter motors, windshield wipers, elevators, heavy machinery, steel and aluminium rolling mills, power shovels, electric locomotives, and cranes due to their precise speed and torque control capabilities.

Speed Control of D.C. Motors

The ability to precisely control speed over a wide range is a significant advantage of D.C. motors in industrial applications. There are three main methods for controlling their speed:

1. Flux Control Method (Varying Φ): The speed is inversely proportional to the flux per pole (N ∝ 1/Φ).

    ◦ Tapped Field Control: This involves reducing the number of turns in the series field winding to decrease the flux, thereby increasing the motor’s speed.

    ◦ Paralleling Field Coils: Used in applications like fan motors, regrouping field coils can achieve several fixed speeds.

2. Armature Control Method (Varying R_a): This method involves varying the resistance in the armature circuit.

    ◦ Armature Resistance Control: A variable resistance is connected in series with the motor’s supply, reducing the voltage across the armature and thus decreasing the speed. This is common for D.C. series motors, especially where speed regulation is less critical.

    ◦ Armature Diverter: A variable resistance is connected in parallel with the armature. This diverts some line current, reducing armature current, which for a given load, causes the flux to increase (T ∝ ΦIa), thereby decreasing motor speed.

3. Voltage Control Method (Varying V): In this method, the armature is supplied by a variable voltage source, separate from the field winding’s supply.

    ◦ Multiple Voltage Control: The shunt field is connected to a fixed voltage, while the armature can be connected across different voltage levels using switchgear. Speed is approximately proportional to the armature voltage. This method is expensive but provides good speed regulation and high efficiency, making it suitable for large motors.

4. Series-Parallel Control (for D.C. Series Motors): This method, widely used in traction systems, involves mechanically coupling two or more similar D.C. series motors to the same load.

    ◦ Series Connection: Motors connected in series will each receive half the normal voltage, resulting in a low speed.

    ◦ Parallel Connection: Motors connected in parallel will each receive the normal voltage, achieving a higher speed. This method is often combined with resistance control, where a starting rheostat is gradually cut out to increase speed.

4) Three-Phase Induction Machines

A three-phase induction motor is a singly-excited A.C. machine, meaning it is supplied power from a single A.C. source.

• Principle of Operation: When connected to a balanced three-phase A.C. supply, the stator windings produce a rotating magnetic field of constant amplitude. This rotating field induces a current in the rotor conductors via electromagnetic induction, which in turn creates a magnetic field in the rotor. The interaction between the stator’s rotating magnetic field and the rotor’s magnetic field produces torque, causing the rotor to turn. A key characteristic is that an induction motor cannot run at synchronous speed, but rather at a slightly lower speed, allowing for continuous induction and torque production.

• Types: The main types include polyphase induction motors and squirrel cage induction motors. Three-phase induction generators are also a type of induction machine relevant for applications like wind energy.

• Performance: The efficiency and power factor of induction motors tend to be lower under no-load conditions. As the shaft load increases, the rotor’s magnetomotive force (m.m.f.) reacts on the stator winding to draw more power from the A.C. source.

• Torque-Speed Characteristics (Torque-Slip Characteristics): This plot illustrates the relationship between the torque produced by the motor and its slip (the difference between synchronous speed and rotor speed). These characteristics are divided into three main regions:

    ◦ Low Slip Region: The motor speed is close to synchronous speed. Torque developed is proportional to the square of the slip and remains relatively constant, with a slight decrease as slip increases. The starting torque is high in this region.

    ◦ Medium Slip Region: Slip is moderate, and the motor operates below synchronous speed. Torque decreases rapidly with increasing slip but remains stable. This region includes the breakdown torque, which is the maximum torque the motor can produce.

    ◦ High Slip Region: In this region, torque becomes inversely proportional to slip. If the slip increases beyond the maximum torque, the torque value decreases, and the motor may eventually stop, resulting in a blocked rotor.

    ◦ Motoring Region: This is the operational region where the motor converts electrical energy into mechanical energy. Slip is positive (between 0 and 1), and the torque produced is positive and directly proportional to the slip.

    ◦ Generating Region: In this region, the slip is negative, meaning the rotor speed is higher than synchronous speed. The motor receives mechanical energy and generates electrical energy. The torque is negative, acting as a retarding force.

• No-Load and Blocked-Rotor Tests: These are specific tests conducted to determine the parameters of the induction motor’s equivalent circuit and its performance characteristics.

• Equivalent Circuit: The equivalent circuit of an induction motor resembles that of a transformer, showing the relationships between various electrical parameters.

• Starting Methods: Common methods include direct-on-line (DOL) starting, star-delta starting, and autotransformer starting. DOL is simple but can lead to high starting currents.

• Losses and Efficiency: Types of losses include core, copper, and mechanical losses. Efficiency generally increases with load up to a certain point before decreasing beyond the motor’s capacity.

Operating Principle of Single-Phase Induction Motors

A single-phase induction motor consists of a single-phase winding on the stator and a cage winding on the rotor. A key characteristic is that it is not self-starting. When a single-phase supply is connected to the stator winding, it produces a pulsating magnetic field rather than a rotating one. Due to inertia, this pulsating field alone cannot initiate rotor rotation.

• Starting Principle: To overcome the non-self-starting nature, a second phase, known as an auxiliary phase or start phase, is produced to create a rotating magnetic field in the stator, enabling the motor to start.

• Theories of Operation: The performance of a single-phase induction motor is explained by two main theories: the Double Revolving Field Theory and the Cross-Field Theory. The cross-field theory suggests that as the rotor begins to turn, an e.m.f. is induced in the rotor conductors. This voltage increases with rotor speed, causing currents that produce an A.C. flux acting at right angles to the stator flux, contributing to torque production.

• Starting Methods: Common methods to start single-phase motors include:

    ◦ Split Phase or Resistance Start.

    ◦ Capacitor Start.

    ◦ Permanent Split Capacitor.

    ◦ Capacitor Start Capacitor Run.

    ◦ Electronic Starter for Single-Phase Motor.

• Hysteresis Motor: A unique type of single-phase motor. Its rotor is a solid steel cylinder capable of retaining magnetism well. An electric current in the stator coils produces a magnetic field, which magnetizes parts of the steel rotor. As this magnetic field changes direction, the magnetised parts of the rotor follow it, causing continuous rotation. Hysteresis motors are known for their smooth, quiet operation with no mechanical vibrations, making them suitable for precision devices like clocks, timers, and audio players, though they have low power output and efficiency.

5) Synchronous Machines =

A synchronous motor is electrically identical to an alternator or A.C. generator. These machines are generally rated between 150 kW and 15 MW, operating at speeds from 150 to 1800 r.p.m..

• Principle of Operation: A key characteristic is that a synchronous motor runs at a constant (synchronous) speed or not at all. This synchronous speed is determined by the supply frequency and the number of poles (Ns = 120 * f / P). When a three-phase winding is supplied by a three-phase source, it produces a magnetic flux of constant magnitude that rotates at synchronous speed. The rotor, which is excited by a D.C. source, magnetically locks into position with the stator’s rotating magnetic field, forcing it to run synchronously. When a load is applied, the rotor progressively falls back in phase (load angle or coupling angle, α), but its speed remains constant. The torque developed by the motor is directly dependent on this load angle.

• Types (Cylindrical and Salient Pole Machines):

    ◦ Cylindrical-Rotor Generators are structurally designed to minimise centrifugal forces, making them ideal for high-speed steam-turbine applications (turbo-generators).

    ◦ Salient-Pole Generators are characterised by a large diameter and short core length, suited for low-speed hydro-turbine applications. The two-reaction theory is applied to salient-pole synchronous machines to account for the varying reluctance along the direct and quadrature axes, which affects armature M.M.F. and air-gap flux, leading to more precise performance analysis.

• Performance and Characteristics:

    ◦ Back E.M.F. (Eb): A back e.m.f. is set up in the armature (stator) by the rotor flux, which opposes the applied voltage (V). This back e.m.f. depends only on the rotor excitation, not on speed. The net voltage in the armature is the vector difference between V and Eb.

    ◦ Effect of Excitation:

        ▪ Normal Excitation: Occurs when Eb = V. At light loads, the power factor is close to unity. As load increases, the armature current increases more significantly than the power factor changes, and the power factor tends to become increasingly lagging.

        ▪ Under-Excitation: Occurs when Eb < V. The motor operates with a lagging power factor. As the load increases, the power factor tends to approach unity.

        ▪ Over-Excitation: Occurs when Eb > V. The motor operates with a leading power factor. Over-excited synchronous motors are widely used for power factor correction in systems with lagging loads (e.g., induction motors, transformers), effectively acting as synchronous capacitors by supplying leading reactive power.

    ◦ Load Increase with Constant Excitation: When the load increases, the armature current (Ia) increases irrespective of excitation. The power factor tends to approach unity for under- and over-excited motors, while for normally excited motors, it becomes increasingly lagging.

• Regulation and Parallel Operation of Generators: Voltage regulation is a critical parameter in synchronous machine operation. Under-excitation can cause a voltage drop, while over-excitation can increase the terminal voltage. The parallel operation of synchronous generators is a topic in electrical power systems.

• Starting of Synchronous Motors: Synchronous motors are not inherently self-starting as they do not produce starting torque by themselves.

    ◦ Methods: The rotor, initially unexcited, is sped up to or near synchronous speed by some external means before being synchronised to the supply. This can involve using damper windings (squirrel-cage winding), which allow the synchronous motor to start as an induction motor.

    ◦ Starting Procedure:

        1. The main field winding is initially short-circuited.

        2. Reduced voltage, often 50% to 80% of full line voltage, is applied to the stator terminals using auto-transformers to limit high starting currents (which can be 5 to 7 times full-load current).

        3. The motor starts as an induction motor and accelerates.

        4. Once it reaches near synchronous speed, a weak D.C. excitation is applied by removing the short-circuit on the field winding, causing the machine to pull into synchronism.

        5. The auto-transformers are then cut out, and full supply voltage is applied.

        6. The motor’s power factor can then be adjusted by varying the D.C. excitation.

    ◦ Challenges: Besides the lack of self-starting torque, a large e.m.f. can be induced in the rotor field windings during starting (requiring high insulation), and high starting currents need to be managed.

• Hunting or Surging: This refers to the oscillatory behaviour of the rotor around its synchronous position when the motor is driving a varying load or if the supply frequency is pulsating. Damper bars (or squirrel-cage windings), embedded in the field poles, are used to mitigate these oscillations and stabilise operation.

Types of Losses and Efficiency Calculations of Electric Machines

In all electric machines, the principle of energy conservation dictates that the total input energy is equal to the sum of the output energy, stored energy, and energy losses. Understanding and accounting for these losses are critical for calculating and optimising the efficiency of machines.

• General Losses:

    ◦ Copper Losses (I²R Losses): These are ohmic losses due to the resistance of the windings in both the armature and field circuits. In synchronous motors, rotor copper losses are met by the D.C. excitation source, not the A.C. input.

    ◦ Core Losses (Iron Losses): These include hysteresis losses (due to the magnetisation and demagnetisation of the core material) and eddy current losses (induced currents in the core material). Laminated cores are used to reduce eddy currents.

    ◦ Friction and Windage Losses (Mechanical Losses): These losses arise from friction in bearings and air resistance (windage).

    ◦ Stray Load Losses: These are minor losses that are not easily accounted for in other categories.

    ◦ Excitation Losses: Power consumed by the field excitation system, particularly in D.C. and synchronous machines.

• Efficiency Calculation: The efficiency of any electric machine is generally calculated as the ratio of output power to input power, expressed as a percentage.

    ◦ Efficiency = (Output Power / Input Power) * 100.

    ◦ The gross mechanical power developed in the armature is the electrical input minus the stator copper losses. The net mechanical power output at the shaft is the gross mechanical power minus the iron, friction, and excitation losses.

    ◦ Examples provided illustrate calculating input power, armature current, mechanical power developed, and efficiency by considering various losses (armature copper loss, iron and friction losses, excitation losses).

• Impact of Losses: While electrical losses may not significantly affect the energy conversion process itself, they are crucial for determining the actual efficiency and useful output of energy conversion systems. A machine with higher efficiency and fewer energy losses is generally preferred.

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