Fundamental Electrical Theory

Objectives Basic electrical theory including ohm's law and its derivationsBasic electrical theory including ohm's law and its derivations Generator theoryGenerator theory Generator construction and control mechanisms including prime movers and power ratingsGenerator construction and control mechanisms including prime movers and power ratings

Objectives Fundamentals of electric motor theory including construction, power rating, usage, and control mechanisms.Fundamentals of electric motor theory including construction, power rating, usage, and control mechanisms. Compare the uses for AC and DC electric power and their transmission methods.Compare the uses for AC and DC electric power and their transmission methods.

References References INE Ch 16 ( )INE Ch 16 ( ) PNE Ch 20 (1 - 20) ***PNE Ch 20 (1 - 20) *** HW: L.G. #19HW: L.G. #19

Definitions Current (I): flow of electric charges per unit time or “flow rate”, measured in “amperes” or “amps” (A)Current (I): flow of electric charges per unit time or “flow rate”, measured in “amperes” or “amps” (A) Electromotive Force (emf) (E): a potential difference or “electric pressure” which drives the flow of charges, measured in “volts” (V)Electromotive Force (emf) (E): a potential difference or “electric pressure” which drives the flow of charges, measured in “volts” (V) Resistance (R): an electrical circuit’s opposition to current flow, measured in “ohms” (  )Resistance (R): an electrical circuit’s opposition to current flow, measured in “ohms” (  ) Conductor: a material which offers little resistance to current flow, e.g. silver, copper, iron, etc…Conductor: a material which offers little resistance to current flow, e.g. silver, copper, iron, etc… Insulator: a material which offers high resistance to current flow, e.g. wood, paper, plastic, etc...Insulator: a material which offers high resistance to current flow, e.g. wood, paper, plastic, etc...

ELECTRICAL THEORY

Direct Current (DC) Current flow is unidirectional and of constant magnitudeCurrent flow is unidirectional and of constant magnitude Ohm’s Law: current in a circuit is directly proportional to the applied voltage and inversely proportional to the circuit resistanceOhm’s Law: current in a circuit is directly proportional to the applied voltage and inversely proportional to the circuit resistance E = I R P = I E = I 2 R P = I E = I 2 R (W)

Basic Circuit Properties Electrons flow (-) to (+)Electrons flow (-) to (+) Kirchoff’s Law of VoltagesKirchoff’s Law of Voltages –Sum of all voltages in a complete ckt is zero –Choose arbitrary current flow –If current encounters (+) terminal 1st, then (+) voltage –Voltage drops preceded by (-) sign if in the same direction as electron flow Current into and out of a point is constantCurrent into and out of a point is constant

Basic Circuit Properties SeriesSeries –Current is constant (flowrate) –Voltage drops across each resistor (pressure) –R = R 1 + R 2 + R 3 + etc ParallelParallel –Voltage drop constant –I in = I 1 + I 2 + I 3 +etc –1/R = 1/ R 1 + 1/R 2 + 1/R 3 + etc

Induction of Voltage (Faraday) RequiresRequires –Magnetic field –Conductor –Relative motion Conductor cuts lines of magnetic flux, a voltage is induced in the conductorConductor cuts lines of magnetic flux, a voltage is induced in the conductor Direction/Speed importantDirection/Speed important

Electromagnetic Induction N S MAGNET RELATIVE MOTION COIL (CONDUCTOR) VOLTMETER INDUCED CURRENT

Direction of Induced emf B MOTION OF CONDUCTOR INDUCED EMF NS “LEFT HAND GENERATOR RULE” (electron flow)

Electro-Magnet B  (N x I)

Generator Parts Prime mover: mechanical work which turns the rotor, may be a steam turbine, gas turbine, diesel engine...Prime mover: mechanical work which turns the rotor, may be a steam turbine, gas turbine, diesel engine... Armature windings: the conductor in which the output voltage is inducedArmature windings: the conductor in which the output voltage is induced Field windings: the conductors used to produce the electromagnetic field (needs a DC power supply)Field windings: the conductors used to produce the electromagnetic field (needs a DC power supply) Stator: stationary housing of the generatorStator: stationary housing of the generator Rotor: rotates inside the stator, moved by a prime mover (steam turbine, gas turbine, diesel…)Rotor: rotates inside the stator, moved by a prime mover (steam turbine, gas turbine, diesel…) Sliding contacts (slip-rings and brushes): used to conduct the field or armature current to and from the rotorSliding contacts (slip-rings and brushes): used to conduct the field or armature current to and from the rotor Commutator - maintains output current in one direction (DC generators)Commutator - maintains output current in one direction (DC generators)

DC Generator

DC Motors Similar in construction to DC generatorsSimilar in construction to DC generators A DC generator may be made to act as a DC motor by applying a suitable voltage across its output terminals (a DC motor acts as a DC generator operating in reverse)A DC generator may be made to act as a DC motor by applying a suitable voltage across its output terminals (a DC motor acts as a DC generator operating in reverse) Operates based on the principle that a current carrying conductor placed in, and at right angles to, a magnetic field tends to move in a direction perpendicular to the magnetic lines of force (right- hand rule)Operates based on the principle that a current carrying conductor placed in, and at right angles to, a magnetic field tends to move in a direction perpendicular to the magnetic lines of force (right- hand rule)

AC Power

Alternating Current (AC) Theory Method of single phase AC voltage generation:Method of single phase AC voltage generation: –Frequency (f) –Amplitude (max value) –Phase (number of signals)

Alternating Current (AC) Current is constantly changing in magnitude and direction at regular intervalsCurrent is constantly changing in magnitude and direction at regular intervals Current is a function of time and usually varies as a sine functionCurrent is a function of time and usually varies as a sine function I t

Two Types of AC Generators Revolving armatureRevolving armature –rotor is an armature which is rotating inside a stationary electromagnetic field –seldom used since output power must be transmitted through slip-rings and brushes Revolving fieldRevolving field –dc current is supplied to the rotor which makes a rotating electromagnetic field inside the stator –more practical since the current required to supply a field is much smaller than the output current of the armature

Revolving Armature (Low Power/Voltage)

Revolving Field

Most electrical equipment in the United States operates on 60 Hz AC electrical power (some foreign countries use 50 Hz)Most electrical equipment in the United States operates on 60 Hz AC electrical power (some foreign countries use 50 Hz) How fast must a 2-pole generator be rotating to produce a 60 Hz output?How fast must a 2-pole generator be rotating to produce a 60 Hz output? N x P = 120 x f N - rpm P - poles f - frequency (Hz) Relationship Between Generator Speed and Frequency

Classifying Generators Number of phases: most shipboard electrical power is 3 phaseNumber of phases: most shipboard electrical power is 3 phase Frequency: most shipboard electrical power is 60 Hz, some electronic equipment operate at 400 Hz or higherFrequency: most shipboard electrical power is 60 Hz, some electronic equipment operate at 400 Hz or higher Voltage: usually 450 V, smaller appliances use 120 VVoltage: usually 450 V, smaller appliances use 120 V Power rating: measured in kW, most shipboard generators are 2, ,000 kWPower rating: measured in kW, most shipboard generators are 2, ,000 kW

Three-Phase Electrical Power Uses three sets of armature windings to produce three separate outputsUses three sets of armature windings to produce three separate outputs Armature windings are physically separated 120 o from each other, and therefore, each phase is 120 o apart from anotherArmature windings are physically separated 120 o from each other, and therefore, each phase is 120 o apart from another More power may be generated by a generator of a given size and weightMore power may be generated by a generator of a given size and weight Provides continuous power to electrical equipment even if one phase is damagedProvides continuous power to electrical equipment even if one phase is damaged

3 Phase

Three Phase

AC Motors

Synchronous Motor Constructed exactly like a generatorConstructed exactly like a generator In a synchronous motor, the field is on the statorIn a synchronous motor, the field is on the stator

Synchronous Motor

Induction Motor Synchronous motor is not a practical motor for shipboard useSynchronous motor is not a practical motor for shipboard use Induction motor - simple, reliable and cheapInduction motor - simple, reliable and cheap Difference - the construction of the rotorDifference - the construction of the rotor Rotating field generated on statorRotating field generated on stator No slip-rings or external source of power to the rotorNo slip-rings or external source of power to the rotor Ideal for constant speed, varying torque applicationsIdeal for constant speed, varying torque applications

Induction Motor N S

Other Electrical Devices

Batteries Dry-cell batteries: cylindrical zinc container, carbon electrode, and ammonium chloride/water electrolyteDry-cell batteries: cylindrical zinc container, carbon electrode, and ammonium chloride/water electrolyte Wet-cell batteries: lead-acid battery is the most common, can be charged by forcibly changing the direction of electrical currentWet-cell batteries: lead-acid battery is the most common, can be charged by forcibly changing the direction of electrical current

Lead-acid Battery PbPbO 2 +- H 2 SO 4 Pb + PbO 2 + 2H 2 SO 4 2PbSO 4 + 2H 2 0   Load

Transformers A device that transfers energy by electromagnetic inductionA device that transfers energy by electromagnetic induction Primary and secondary windings (insulated from each other electrically) are mounted on opposite sides of a ferromagnetic corePrimary and secondary windings (insulated from each other electrically) are mounted on opposite sides of a ferromagnetic core Used to raise voltage (“step-up transformer”) or lower voltage (“step-down transformer”)Used to raise voltage (“step-up transformer”) or lower voltage (“step-down transformer”) Voltage is raised when the primary winding has fewer turns than the secondary winding, and voltage is lowered when the primary winding has more turns than the secondary windingVoltage is raised when the primary winding has fewer turns than the secondary winding, and voltage is lowered when the primary winding has more turns than the secondary winding

A Simple Transformer CORE PRIMARY WINDING SECONDARY WINDING

Rectifiers Uses diodes to convert alternating current into direct currentUses diodes to convert alternating current into direct current Diodes have a small resistance to current flow in one direction and a very large resistance to current flow in the opposite direction (act as a conductor for half of the cycle and as an insulator for the other half)Diodes have a small resistance to current flow in one direction and a very large resistance to current flow in the opposite direction (act as a conductor for half of the cycle and as an insulator for the other half)

Rectifying Device Output tt II INPUTOUTPUT DIODE

Voltage Kills It is the volume of the current that flows that kills.It is the volume of the current that flows that kills amps = 1 milliamp Tingles0.001 amps = 1 milliamp Tingles 0.01 amps = 10 milliamps Severe shock, uncontrolled muscle spasms0.01 amps = 10 milliamps Severe shock, uncontrolled muscle spasms 0.1 amps = 100 milliamps DEATH ! If the current passes through vital organs such as the heart.0.1 amps = 100 milliamps DEATH ! If the current passes through vital organs such as the heart.

Example Problem #1 Determine V 1, V 2, V 3, V 4, and I. V1V1 V2V2 V4V4 V3V3 I 90V  55 10 

Example Problem #2 Determine I 1, I 2, I 3, I 4 and total circuit resistance. I1I1 75V + - I4I4 I3I3 I2I2 20  30  20 

Summary