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3-PHASE POWER APPARATUS

BY: MUBAREK KURT

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BASIC CONCEPT-MAGNETIC FIELD-

Ampere’s Law – the basic law governing the production of a magnetic field by a current:

Where H is the magnetic field intensity produced by the current Inet and dl is the differential element of length along the path of integration.

netIdlH

mean path length, lc

I

N turns

CSA

c

c

Hl NiNiHl

BASIC CONCEPT-MAGNETIC FIELD-• H is known as the effort to induce a magnetic

field. The amount of H is depend on permeability of the material to form flux density B.

HB B = magnetic flux density (webers per square meter, Tesla (T))µ= magnetic permeability of material (Henrys per meter)H = magnetic field intensity (ampere-turns per meter)r

o

where: o – permeability of free space (4π x 10-7 H/m)Mubarek Kurt

BASIC CONCEPT-MAGNETIC FIELD-Measuring the total flux in the core B = H =

Now the total flux in a given area is given by

Where: A – cross sectional areaAssuming the flux density in the core is constant

clNi

A

BdA

BA c

NiAl

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ROTATING MACHINE-GENERAL-

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ROTATING MACHINE• Rotor is a moving component of an

electromagnetic system. Its rotation is due to the interaction between the windings and magnetic fields which produces torque around the rotor’s axis.

• Stator is the stationary part of a rotary system. The main use of the stator is to keep the field aligned.

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ROTATING MACHINE• Armature Winding: the winding that carries only

load current.• Field Winding: the winding that carries only

magnetizing current.

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ROTATING MACHINE

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ROTATING MACHINE-APPLICATION-• Could beGeneratorsAlternatorMotorsTransmission gears

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AC MACHINE-STRUCTURE-

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AC MACHINE-STRUCTURE-

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AC MACHINE-STRUCTURE-

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AC MACHINE – 3-PHASE-STRUCTURE-

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DC MACHINE-STRUCTURE-

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DC MACHINE-STRUCTURE-

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AC MACHINERY FUNDAMENTALS• AC machines are generators that convert

mechanical energy.• The fundamentals principles of ac

machines are very simple, but unfortunately, they are somewhat obscured by the complicated construction of real machines.

• There are two major classes of ac machines

i. Synchronous Machinesii. Induction machines

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A SIMPLE LOOP IN A UNIFORM MAGNETIC FIELD

• We will start our study of ac machines with a simple loop of wire rotating within a uniform magnetic field.

• A loop of wire in a uniform magnetic field is the simplest possible machines that produces a sinusoidal ac voltage.

• This case is not representative of real ac machines, since the flux in real ac machines is not constant in either magnitude or direction.

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THE VOLTAGE INDUCED IN A SIMPLE ROTATING LOOP

• If the rotor of this machine is rotated, a voltage will be induced in the wire loop.

• To determine the magnitude and shape of the voltage, examine figure below

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Total induced voltage on the loop eind = eba + ecb + edc + ead

= vBl sin θab + vBl sin θcd = 2 vBL sinθ, note that

v=velocity=2rωBLsinθ, where v=rω

 

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MOTOR-INDUCED TORQUE-

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sin2sinsin

rilBrilBrilB cdab

dacdbcabind

The total induced torque on the loop:

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INDUCED VOLTAGE AND TORQUEAs a conclusion, the induced voltage is dependent upon:a. Flux level (the B component)b. Speed of Rotation (the v component)c. Machine Constants (the l component and machine materials)Also for the torque is dependent upon:a. Strength of rotor magnetic fieldb. Strength of stator magnetic fieldc. Angle between the 2 fieldsd. Machine constants

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RELATIONSHIP BETWEEN FREQUENCY AND SPEED

Since one electrical cycle is 360 electrical degrees, and mechanical motion is 180 mechanical degrees, the relationship between the electrical angle θe and the mechanical θm in this stator is θe = 2 θm Thus, for a four pole winding, the electrical frequency of the current is twice the mechanical frequency of rotation: fe = 2 fmωe = 2 ωm

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2

2

2

e m

e m

e m

P

Pf f

P

60

120

mm

me

nsince f where n is the number of rotation

nf P

Therefore the general format will be as follows:

Also,

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INDUCED VOLTAGE IN 3-PHASEThe induced voltages at each phase will be as follows:

'

'

'

sin

sin( 120 )

sin( 240 )

aa

obb

occ

e N t V

e N t V

e N t V

The maximum induced voltage is when sin has a value of 1, hence,

max

max

, since 2 ,2

E N fE N f

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Therefore, the rms voltage at the 3 phase stator:

2AE N f

Note: These are induced voltages at each phase, as for the line-line voltage values; it will depend upon how the stator windings are connected, whether as Y or D.

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INDUCED TORQUE IN 3-PHASE

sinind r s r sKH B KH B

ind r skB B

ind r net r r netkB B B kB B

sinind r netkB B

Therefore the torque equation may be represented in the following form:

Note that K is a constant value.Since BR= HR,

The constant k is a value which will be dependent upon the permeabilityof the machine’s material. Since the total magnetic field density will be the summation of the BS and BR, hence:

If there is an angle between Bnet and BR,

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EXAMPLE 1The simple loop is rotating in a uniform magnetic field shown in Figure has the following characteristics:B = 0.5 T to the right r = 0.1 ml = 0.5 m ω = 103 rad/s(a) Calculate the voltage e t tot( )induced in this rotating loop.(b) Suppose that a 5 Ω resistor is connected as a load across the terminals of the loop. Calculate the current that would flow through the resistor.(c) Calculate the magnitude and direction of the induced torque on the loop for the conditions in (b).(d) Calculate the electric power being generated by the loop for the conditions in (b).(e) Calculate the mechanical power being consumed by the loop for the conditions in (b). How does this number compare to the amount of electric power being generated by the loop?

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EXAMPLE 2A three-phase four-pole winding is installed in 12 slots on a stator. There are 40 turns of wire in each slot of the windings. All coils in each phase are connected in series, and the three phases are connected in Δ. The flux per pole in the machine is 0.060 Wb, and the speed of rotation of the magnetic field is 1800 r/min.

(a) What is the frequency of the voltage produced in this winding?(b) What are the resulting phase and terminal voltages of this stator?

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AC MACHINE POWER FLOWS AND LOSSES

• AC generators take in mechanical power and produce electric power, while AC motors take in electric power and produce mechanical power.

• In either case, not all the power input to the machine appears in useful form at the other end-there is always some loss associate with the process.

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THE LOSSES IN AC MACHINES

• The losses that occur in ac machines can be divided into 4 basic categories:

a) Electrical or Copper losses (I2R losses)b) Core lossesc) Mechanical lossesd) Stray Load losses

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(A) COPPER LOSSES

• Copper losses are the resistive heating losses that occur in the stator (armature) and rotor (field) winding of the machine.

• The stator copper losses (SCL) in 3 phase ac machine

Where IA is armature current and RA is the resistance of each armature phase.

AASCL RIP 23

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(A) COPPER LOSSES CONT.

• The rotor copper losses (RCL) of a synchronous ac machine ac are given by

Where IF is field current and RF is the resistance of field winding.

FFRCL RIP 23

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(B) CORE LOSSES

• The core losses are the hysteresis losses and eddy current losses metal occurring in the metal of the motor.

• Both hysteresis and eddy current losses cause heating in the core material.

• Since both losses occur within the metal of the core, they are usually lumped together and called core losses.

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(C) MECHANICAL LOSSES

• The mechanical losses in an AC machine are the losses associated with mechanical effects.

• There are two basic types of mechanical losses: friction and windage.

• Friction losses are losses caused by the friction of the bearing in the n between machine.

• Windage losses are caused by the friction between the moving parts of the machine and the air inside the motor’s casing.

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(C) MECHANICAL LOSSES CONT.

• The Mechanical and Core losses of a machine are often lumped together and called the no-load rotational loss of the machine.

• At the no load, all the input power must be used to overcome these losses.

• Therefore, measuring the input power to the stator of an AC machine acting as a motor at no load will give approximate values of these losses.

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(D) STRAY LOSSES

• Stray or miscellaneous losses are losses that cannot be placed in one of the previous categories.

• No matter how carefully losses are accounted for, some always escape inclusion in one of the above categories.

• All such losses are lumped into stray losses.• For most machines, stray losses are taken by

convention to be 1 percent of full load.

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THE POWER FLOW DIAGRAM• One of the most convenient techniques for

accounting for power losses in a machine is the power-flow diagram.

Pconv=the remaining power converted from Mechanical to Electrical and vice versa

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EFFICIENCY

• The efficiency of an AC machine is defined by the equation

%100PinPout

%100

PinPlossPin

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VOLTAGE REGULATION

• Generators are often compared to each other using a figure of merit called voltage regulation.

• Voltage Regulation (VR) is a measure of ability of a generator to keep a constant voltage at its terminals as load varies.

%100

fl

flnl

VVVVR

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SPEED REGULATION

• Similarly, motors are often compared to each other by using a figure of merit called speed regulation.

• Speed Regulation (SR) is a measure of the ability of a motor to keep a constant shaft speed as load varies.

%100

fl

flnl

nnnSR %100

fl

flnlSR

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GENERATOR-TESTING-• Insulation test• Test of dielectric withstanding voltage (DWV)• Impulse test• Partial discharge test

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MOTOR-TESTING-• Insulation test• Voltage test• Current test• Impulse test• Continuity test• Impedance test