FUNDAMENTALS OF ELECTRICAL ENGINEERING [ ENT 163 ] LECTURE #10 ELECTRICAL MACHINES HASIMAH ALI Programme of Mechatronics, School of Mechatronics Engineering, UniMAP.

CONTENTS INTRODUCTION TO TRANSFORMER MUTUAL INDUCTANCE COEFFICIENT OF COUPLING IDEAL TRANSFORMER DC GENERATOR

 A transformer is a stationary electric machine which transfers electrical energy (power) from one voltage level to another voltage level.  Unlike in rotating machines, there is no electrical to mechanical energy conversion  A transformer is a static device and all currents and voltages are AC.  The transfer of energy takes place through the magnetic filed. INTRODUCTION TO TRANSFORMER

 When two loops with or without contacts between them affect each other through the magnetic field generated by one of them, they are said to be magnetically coupled.  Transformer is an electrical device designed on the basis of the concept of magnetically coupling. It uses magnetically coupled coils to transfer energy from one circuit to another.  Function of transformer – stepping up or stepping down ac voltage or currents

INTRODUCTION TO TRANSFORMER  It has 2 electric circuits called primary and secondary.  A magnetic circuit provides the link between primary and secondary.  When an AC voltage is applied to the primary winding (Vp) of transformer, an AC current will result (Ip). Ip sets up a time-varying magnetic flux  in the core.  A voltage is induced to the secondary circuit (Vs) according to the Faraday’s law. Transformer Principles Primary voltage Iron core

MUTUAL INDUCTANCE  When two coils are magnetically coupled, they provide electrical isolation because there is no electrical connection between them, only magnetic link.  The amount of voltage induced in the second coil as a result of the current in the first coil is dependent on the mutual inductance.  The mutual inductance is established by the inductance of each coil (L 1 and L 2 ) and by the amount of coupling k between the two coils.  Mutual inductance is the ability of one inductor to induce a voltage across a neighboring inductor, measured in Henrys (H).  To maximize coupling, the two coils are wound on the same core.  When a second coil is placed very close to the first coil so that the changing magnetic lines of force cut through the second coil, the coils are magnetically coupled and a voltage is induced.

COEFFICIENT OF COUPLING  Coefficient of coupling, k, between the primary and secondary windings of a transformer is the ratio of the flux ( lines of force) produced by the primary linking of secondary (  1-2 ) to the total flux produced by the primary (  1 ):  E.g. if half of the total flux produced by coil 1 links coil 2, then k=0.5.  Greater value of k means that more voltage is induced in coil 2 for a certain rate of change of current in coil 1.  k- depends on the physical closeness of the coils, the type of core material on which they are wound, the construction and shape of the cores. k =  1-2 / 1

COEFFICIENT OF COUPLING Example: One coil produces a total magnetic flux of 50µW, and 20µW link coil 2. What is the coefficient of coupling k?

IDEAL TRANSFORMER  Transformer is a magnetic device, constructed of four-terminal device comprising two magnetically coupled coils which have the mutual inductance phenomenon.  One coil – primary winding ( connected to the voltage source), other coil – secondary winding (connected to the load):

IDEAL TRANSFORMER  Ideal transformer is one with perfect coupling (k=1).  Ideal transformer is a unity-coupled, lossless transformer in which the primary and secondary coils have infinite self – inductances.

IDEAL TRANSFORMER  An important characteristic in ideal transformer = turns ratio/ transformation ratio n: V 1 = primary voltage V 2 = secondary voltage N 1 = number of turns of the primary winding N 2 = number of turns of the secondary winding I 1 = primary current I 2 = secondary current Where,

IDEAL TRANSFORMER 1.A transformer primary winding has 100 turns, and the secondary winding has winding 400 turns. What is the turns ratio? 2.A certain transformer has a turn ratio of 10. If N pri = 500, what is N sec ?

IDEAL TRANSFORMER 1.A transformer primary winding has 100 turns, and the secondary winding has winding 400 turns. What is the turns ratio? n = N sec / N pri = 400/100 = 4 2.A certain transformer has a turn ratio of 10. If N pri = 500, what is N sec ? n = 10, Npri = 500 N sec = n X N pri = 10 X 500 = 5000

IDEAL TRANSFORMER  For an ideal transformer, the complex power (VA) in the primary winding is equal to the secondary: S 1 = V 1 I 1 = V 2 I 2 =S 2 where, S 1 = power in the primary winding S 2 =power in secondary winding (This shows that the complex power supplied to the primary is delivered to the secondary without loss, since ideal transformer is lossless).  There are two types of a transformer:  A step-down transformer  A step-up transformer

IDEAL TRANSFORMER  Applications:  Electrical distribution networks (to reduce the voltage from medium voltage (10,000 V – V) to low voltage (110 V – 208 V) for different customers).  To reduce plug voltage (110 V) to lower voltages in electronic. Equipments/ circuits such as radio, phone, laptop, adaptors,… Step-down Transformer A step-down transformer is one whose secondary is less than its primary voltage Distribution Transformers used by Hydro companies to deliver the electric energy

IDEAL TRANSFORMER  Applications:  Power plants to increase the generated voltage and send it to high voltage transmission lines.  To increase the voltage in order to get higher electrical field (TVs, Radar and Microwaves,…) Step-up Transformer A step-up transformer is one whose secondary is greater than its primary voltage

DC GENERATOR  Simplified dc generator. Consist of:  A single loop of wire – rotates in a permanent magnetic field  Commutator – split-ring arrangement, connected at each end of the loop.  Brushes – the fixed contacts that connects wire to external circuit.

DC GENERATOR

 When driven by an external mechanical force – loop rotates through the magnetic field and cuts through the flux lines at varying angles:  At A – loop is effectively moving parallel with the magnetic field – the rate at which it is cutting through the magnetic flux lines is zero.  From A to B – the loop cuts through the flux lines at an increasing rate.  From B to C – the rate at which it cuts the flux lines decreases to minimum (zero) at C. N S AC B D

DC GENERATOR  From C to D – the rate at which the loop cuts the flux lines increases to a maximum at D, and then back to minimum again at A.  Recall from Faraday’s law:  When a wire moves through a magnetic field, a voltage is induced.  According to Faraday’s Law – amount of induced voltage is proportional to the number of loops turns in the wire and the rate at which it is moving with respect to the magnetic field.  The angle at which the wire moves with respect to the magnetic flux lines determines the amount of induced voltage because the rate at which the wire cuts through the flux lines depends on the angle of motion.

DC GENERATOR  Operation:  Assume that the loop is in its instantaneous horizontal position (induced voltage = 0).  As the loop continuous in its rotation, the induced voltage builds up to a maximum at B.  As the loop continuous to rotate from B to C, the voltage decreases to zero at C.  During the second half of the revolution, the brushes switch to opposite commutator sections, so the polarity of the voltage remains the same across the output.  Thus, as the loop rotates from position C to D and then back to A, the voltage increase from zero at C to a maximum at D and back to zero at A.

DC GENERATOR

 Final output (shows how the induced voltage varies as a wire in a dc generator goes through several rotations)

DC GENERATOR  Voltage = dc voltage (polarity does not change)  When more wire loops are added, the voltage induced across each loop are combined across the output – resulting a smoother dc voltage.

DC GENERATOR  Comparison of a dc generator and a dc motor: DC GeneratorDC Motor No source is connected to the commutator circuit A DC source is connected to the commutator circuit, producing current through the wire loop. External mechanical energy is used to rotate the loop to produce an induced voltage External electrical energy is used to rotate the loop to produce a mechanical rotation.

FURTHER READING 1.Electrical Machines, Drives, And Power System, 6 th Edition, Pearson Prientice Hall, Wildi. 2.Principles of Electric Circuits; Conventional Current version, 8 th Edition, Pearson, Floyd.