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ELECTRICAL MACHINES – II (AC MACHINES) Presented by C.GOKUL AP/EEE Velalar College of Engg & Tech,Erode EMAIL: [email protected]

Syllabus EE6502 Electrical Machines -II

BOOKS Reference

LOCAL AUTHORS: {For THEORY use this books} 1.Electrical Machines-II by “Gnanavadivel” – Anuradha Publication 2. Electrical Machines-II by “Godse” – Technical Publication For Problems: Electric Machines by Nagrath & Kothari {Refer Solved Problems} Electric Machinery by A.E.Fitgerald {Refer Solved Problems}

Important Website Reference Electrical Machines-II by S. B. Sivasubramaniyan -MSEC, Chennai http://yourelectrichome.blogspot.in/ http://www.electricaleasy.com/p/electri cal-machines.html

NPTEL Reference • Electrical Machines II by Dr. Krishna Vasudevan & Prof. G. Sridhara Rao Department of Electrical Engineering , IIT Madras. • Basic Electrical Technology by Prof. L. Umanand - IISc Bangalore {video}

BASICS OF ELECTRICAL MACHINES

Electrical Machine? Electrical machine is a device which can convert

Mechanical energy into electrical energy (Generators/alternators) Electrical energy into mechanical energy (Motors) AC current from one voltage level to other voltage level without changing its frequency (Transformers) Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

Fundamental Principle..

Electrical Machines (irrespective of AC or DC) work on the fundamental principle of Faraday’s law of Electromagnetic Induction.

Faraday’s Law Faraday’s Law of Electromagnetic Induction states that an EMF is induced in a coil when the magnetic flux linking this coil changes with time or The EMF generated is proportional to the rate at which flux is changed.

dψ dϕ e= − = −N dt dt

Faraday’s Law – Illustration

Two forms of Induced EMF ! The effect is same if the magnet is moved and the coil is made stationery We call it as statically induced EMF The previous case is referred to as Dynamically induced EMF

Governing Rules

It becomes evident that there exists a relationship between mechanical energy, electrical energy and magnetic field. These three can be combined and precisely put as governing rules each for generator and for motor

Fleming’s Right hand rule

For Generator

Fleming's Right hand rule(for Generator)

Fleming’s Left hand rule

For Motor

Fleming's left hand rule (for motors)

First finger - direction of magnetic field (N-S)

Second finger - direction of current

(positive to negative) Thumb - movements of the wire

Maxwell’s Corkscrew rule

If the electric current is moving away from the observer, the direction of lines of force of the magnetic field surrounding the conductor is clockwise and that if the electric current is moving towards an observer, the direction of lines of force is anti-clockwise

Corkscrew (Screw driver) rule Illustration

Coiling of Conductor

To augment the effect of flux, we coil the conductor as the flux lines aid each other when they are in the same direction and cancel each other when they are in the opposite direction Many a times, conductor is coiled around a magnetic material as surrounding air weakens the flux We refer the magnetic material as armature core

Electromagnet

The magnetic property of current carrying conductor can be exploited to make the conductor act as a magnet – Electromagnet

This is useful because it is very difficult to find permanent magnets with such high field Also permanent magnets are prone to ageing problems

AC Fundamentals

AC Fundamentals - continued

Whenever current passes through a conductor…

Opposition to flow of current Opposition to sudden change in current Opposition to sudden change in voltage Flux lines around the conductor

Inductive Effect

Reactance EMF Lenz Law An induced current is always in such a direction as to oppose the motion or change causing it

Capacitive effect

V= (t ) ⇒ i (t )=

Q C = V q (t ) 1 = C C dq (t ) = dt

∫ i (t ) dt

dv (t ) C dt

Resistive Network – Vector diagram

Inductive Network – Vector Diagram

Capacitive Network – Vector Diagram

Inductive & Capacitive effects combined

Pure L & C networks – not at all possible!

R-L network

Pure L & C networks – not at all possible! – contd.

R-C network

Current & Flux

As already mentioned, As the current, so the flux

3 phase AC

Star and Delta

Star connection

=

V L

3V ph

I L = I ph

Delta Connection

V L

= V ph

IL =

3I ph

Maxwell's Right Hand Grip Rule

Right Handed Cork Screw Rule

Generators

Input

The Generator converts mechanical power into electrical power.

Synchronous generators (Alternator) are constant speed generators.

The conversion of mechanical power into electrical power is done through a coupling field (magnetic field).

Mechanical

Magnetic

Electrical

Output

Electric Generator Mechanical Energy

G

Stationary magnets - rotating magnets - electromagnets

Electrical Energy

Motor

The Motor converts electrical power into mechanical power.

Electrical Energy

Input

M

Magnetic Electrical

Mechanical Energy

Mechanical

Output

Basic Construction Parts Stationary Part

Stator

Armature

Electrical

Mechanical

Rotor Rotating Part

Field

AC MACHINES Two categories: 1.Synchronous Machines:

Synchronous Generators(Alternator)

Primary Source of Electrical Energy Synchronous Motor

2.Asynchronous Machines(Induction Machines)

UNIT-1 Synchronous Generator (Alternator)

UNIT-1 Syllabus

Synchronous Generators

Generator

Exciter View of a two-pole round rotor generator and exciter. (Westinghouse)

Synchronous Machines • Synchronous generators or alternators are used to convert mechanical power derived from steam, gas, or hydraulic-turbine to ac electric power • Synchronous generators are the primary source of electrical energy we consume today • Large ac power networks rely almost exclusively on synchronous generators • Synchronous motors are built in large units compare to induction motors (Induction motors are cheaper for smaller ratings) and used for constant speed industrial drives

Construction Basic parts of a synchronous generator: • •

Rotor - dc excited winding Stator - 3-phase winding in which the ac emf is generated

The manner in which the active parts of a synchronous machine are cooled determines its overall physical size and structure

Armature Windings (On Stator) • Armature windings connected are 3-phase and are either star or delta connected

• It is the stationary part of the machine and is built up of sheet-steel laminations having slots on its inner periphery. • The windings are 120 degrees apart and normally use distributed windings

Field Windings (on Rotor) • The field winding of a synchronous machine is always energized with direct current • Under steady state condition, the field or exciting current is given

Ir = Vf/Rf Vf = Direct voltage applied to the field winding Rf= Field winding Resistance

Rotor • Rotor is the rotating part of the machine • Can be classified as: (a) Cylindrical Rotor and (b) Salient Pole rotor

• Large salient-pole rotors are made of laminated poles retaining the winding under the pole head.

Various Types of ROTOR

Salient-pole Rotor

Cylindrical or round rotor

a. Salient-Pole Rotor 1. Most hydraulic turbines have to turn at low speeds (between 50 and 300 r/min) 2. A large number of poles are required on the rotor d-axis

Non-uniform air-gap

N

D ≈ 10 m q-axis

S

S

Turbine Hydro (water)

Hydrogenerator

N

• Salient pole type rotor is used in low and medium speed alternators • This type of rotor consists of large number of projected poles (called salient poles) • Poles are also laminated to minimize the eddy current losses. • This type of rotor are large in diameters and short in axial length.

Salient-Pole Synchronous Generator

Stator

b. Cylindrical-Rotor(Non-Salient Pole)

D≈1m

Turbine

L ≈ 10 m Steam

d-axis Stator winding

High speed

3600 r/min ⇒ 2-pole

Uniform airgap Stato r

1800 r/min ⇒ 4-pole

Direct-conductor cooling (using hydrogen or water as coolant)

N

q-axis

Rotor winding Roto r

Rating up to 2000 MVA S

Turbogenerator

• Cylindrical type rotors are used in high speed alternators (turbo alternators) • This type of rotor consists of a smooth and solid steel cylinder having slots along its outer periphery. • Field windings are placed in these slots.

Cylindrical-Rotor Synchronous Generator

Stator

Cylindrical rotor

Working of Alternator & frequency of Induced EMF

Working Principle • It works on the principle of Electromagnetic induction • In the synchronous generator field system is rotating and armature winding is steady. • Its works on principle opposite to the DC generator • High voltage AC output coming from the armature terminal

Working Principle • Armature Stator • Field Rotor • No commutator is required {No need for commutator because we need AC only}

Frequency of Induced EMF Every time a complete pair of poles crosses the conductor, the induced voltage goes through one complete cycle. Therefore, the generator frequency is given by

p n pn f = . = 2 60 120 N=Rotor speed in r.p.m P=number of rotor poles f=frequency of induced EMF in Hz No of cycles/revolution = No of pairs of poles = P/2 No of revolutions/second = N/60 No of cycles/second {Frequency}= (P/2)*(N/60)=PN/120

Advantages of stationary armature • At high voltages, it easier to insulate stationary armature winding(30 kV or more) • The high voltage output can be directly taken out from the stationary armature. • Rotor is Field winding. So low dc voltage can be transferred safely • Due to simple construction High speed of Rotating DC field is possible. Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

Winding Factors( K , Kd) p

K

p

= cos

α

2 m sin 2 m sin 2

β

Kd

=

β

Pitch factor (Kp)

Consider 4 pole, 3 phase machine having 24 conductors Pole pitch = 24 / 4 = 6 slots If Coil Pitch or Coil Span = pole pitch, then it is referred to as full-pitched winding If Coil Pitch < pole pitch, it is referred to as short-pitched winding

Coil Span = 5 / 6 of pole pitch If falls short by 1 / 6 of pole pitch or 180 / 6 = 30 degrees

This is done primarily to Save copper of end connections Improve the wave-form of the generated emf (sine wave) Eliminate the high frequency harmonics There is a disadvantage attached to it Total voltage around the coil gets reduced because, the emf induced in the two sides of the coil is slightly out of phase Due to that, their resultant vectorial sum is less than the arithmetic sum This is denoted by a factor Pitch factor, Kp or Kc

Pitch factor – Kp

Vectorsum Kp = Arithmaticsum

Pitch factor – contd.

Arithmatic sum

Pitch factor – contd.

Vector sum

Pitch factor – contd.

Pitch factor – contd.

Kp

=

Vector _ sum = Arithmatic _ sum

2 Es cos 2 Es

= cos

α

2

α 2

Pitch factor - Problem

Distribution factor (Kd)

As we know, each phase consists of conductors distributed in number of slots to form polar groups under each pole The result is that the emf induced in the conductors constituting the polar group are not in phase rather differ by an angle equal to angular displacement of the slots

For a 3 phase machine with 36 conductors, 4 pole, no. of slots (conductors) / pole / phase is equal to 3 Each phase consists of 3 slots Angular displacement between any two adjacent slots = 180 / 9 = 20 degrees If the 3 coils are bunched in 1 slot, emf induced is equal to the arithmetic sum (3Es) Practically, in distributed winding, vector sum has to be calculated Kd = Vector sum / Arithmetic sum

emf _ with _ distributed _ winding Kd = emf _ with _ concentrated _ winding

β

0

180 180 = no.of _ slots _ per _ pole n

0

For calculating Vector sum

Kd

Kd

mβ 2 r sin 2 = β m 2 r sin 2 mβ sin 2 = β m sin 2

Problem: Distribution factor /Breadth factor

EMF Equation of Alternator

Equation of Induced EMF

Average emf induced per conductor = dφ / dt Here, dφ = φP If P is number of poles and flux / pole is φ Weber dt = time for N revolution = 60 / N second Therefore, Average emf = dφ / dt = φP / (60 / N)

=

ϕ NP 60

Equation of Induced EMF – contd. We know, N = 120 f / P Substituting, N we get Avg. emf per conductor = 2 f φ Volt If there are Z conductors / ph, then Avg. emf induced / ph = 2 f φ Z Volt Ave emf induced (in turns) / ph = 4 f φ T Volt

Equation of Induced EMF – contd.

We know, RMS value / Avg. Value = 1.11 Therefore, RMS value of emf induced / ph = 1.11 (4 f φ T) V = 4.44 f φ T Volt This is the actual value, but we have two other factors coming in the picture, Kc and Kd These two reduces the emf induced

RMS value of emf induced = (Kd) (Kc) 4.44 f φ T

Volt

Armature Reaction of Alternator

Armature Reaction

Main Flux Field Winding Secondary Flux Armature Winding Effect of Armature Flux on the Main Flux is called Armature Reaction

Armature Reaction in alternator I.) When load p.f. is unity II.) When load p.f. is zero lagging III.) When load p.f. is zero leading

Armature Reaction in alternator I.) When load p.f. is unity distorted but not weakened.- the average flux in the air-gap practically remains unaltered. II.) When load p.f. is zero lagging the flux in the air-gap is weakened- the field excitation will have to be increased to compensate III.) When load p.f. is zero leading

the effect of armature reaction is wholly magnetizing- the field excitation will have to be reduced

1. Unity Power Factor Load

Consider a purely resistive load connected to the alternator, having unity power factor. As induced e.m.f. Eph drives a current of Iaph and load power factor is unity, Eph and Iph are in phase with each other. If Φf is the main flux produced by the field winding responsible for producing Eph then Eph lags Φf by 90o . Now current through armature Ia, produces the armature flux say Φa. So flux Φa and Ia are always in the same direction.

• Phase difference of 90o between the armature flux and the main flux • the two fluxes oppose each other on the left half of each pole while assist each other on the right half of each pole. • Average flux in the air gap remains constant but its distribution gets distorted. • Due to such distortion of the flux, there is small drop in the terminal voltage

2. Zero Lagging Power Factor Load

Consider a purely inductive load connected to the alternator, having zero lagging power factor. Iaph driven by Eph lags Eph by 90o which is the power factor angle Φ. Induced e.m.f. Eph lags main flux Φf by 90o while Φa is in the same direction as that of Ia. the armature flux and the main flux are exactly in opposite direction to each other.

• As this effect causes reduction in the main flux, the terminal voltage drops. This drop in the terminal voltage is more than the drop corresponding to the unity p.f. load.

3. Zero Leading Power Factor Load

Consider a purely capacitive load connected to the alternator having zero leading power factor. This means that armature current Iaph driven by Eph, leads Eph by 90o, which is the power factor angle Φ. Induced e.m.f. Eph lags Φf by 90o while Iaph and Φa are always in the same direction. the armature flux and the main field flux are in the same direction

• As this effect adds the flux to the main flux, greater e.m.f. gets induced in the armature. Hence there is increase in the terminal voltage for leading power factor loads.

Phasor Diagram for Synchronous Generator/Alternator

Phasor Diagram of loaded Alternator Ef which denotes excitation voltage Vt which denotes terminal voltage Ia which denotes the armature current θ which denotes the phase angle between Vt and Ia ᴪ which denotes the angle between the Ef and Ia δ which denotes the angle between the Ef and Vt ra which denotes the armature per phase resistance Two important points: (1) If a machine is working as a synchronous generator then direction of Ia will be in phase to that of the Ef. (2) Phasor Ef is always ahead of Vt.

Lagging PF

Unity PF

Leading PF

a. Alternator at Lagging PF Ef by first taking the component of the Vt in the direction of Ia Component of Vt in the direction of Ia is Vtcosθ , Total voltage drop is (Vtcosθ+Iara) along the Ia. we can calculate the voltage drop along the direction perpendicular to Ia. The total voltage drop perpendicular to Ia is (Vtsinθ+IaXs). With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as

b. Alternator at Unity PF

Ef by first taking the component of the Vt in the direction of Ia. θ = 0 hence we have ᴪ=δ. With the help of triangle BOD in the second phasor diagram we can directly write the expression for Ef as

c. Alternator at Leading PF

Component in the direction of Ia is Vtcosθ. As the direction of Ia is same to that of the Vt thus the total voltage drop is (Vtcosθ+Iara). Similarly we can write expression for the voltage drop along the direction perpendicular to Ia. The total voltage drop comes out to be (Vtsinθ-IaXs). With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as

Determination of the parameters of the equivalent circuit from test data The equivalent circuit of a synchronous generator that has been derived contains three quantities that must be determined in order to completely describe the behaviour of a real synchronous generator: The saturation characteristic: relationship between If and φ (and therefore between If and Ef) The synchronous reactance, Xs The armature resistance, Ra

VOLTAGE REGULATION Voltage regulation of an alternator is defined as the rise in terminal voltage of the machine expressed as a fraction of percentage of the initial voltage when specified load at a particular power factor is reduced to zero, the speed and excitation remaining unchanged.

Voltage Regulation A convenient way to compare the voltage behaviour of two generators is by their voltage regulation (VR). The VR of a synchronous generator at a given load, power factor, and at rated speed is defined as

VR =

Enl − V fl V fl

× 100%

Voltage Regulation Case 1: Lagging power factor: A generator operating at a lagging power factor has a positive voltage regulation.

Case 2: Unity power factor: A generator operating at a unity power factor has a small positive voltage regulation.

Case 3: Leading power factor: A generator operating at a leading power factor has a negative voltage regulation.

Voltage Regulation This value may be readily determined from the phasor diagram for full load operation. If the regulation is excessive, automatic control of field current may be employed to maintain a nearly constant terminal voltage as load varies

Methods of Determination of voltage regulation

Methods of Determination of voltage regulation Synchronous Impedance Method / E.M.F. Method Ampere-turns method / M.M.F. method ZPF(Zero Power Factor) Method / Potier ASA Method

1. Synchronous Impedance Method / E.M.F. Method The method is also called E.M.F. method of determining the regulation. The method requires following data to calculate the regulation. 1. The armature resistance per phase (Ra). 2. Open circuit characteristics which is the graph of open circuit voltage against the field current. This is possible by conducting open circuit test on the alternator. 3. Short circuit characteristics which is the graph of short circuit current against field current. This is possible by conducting short circuit test on the alternator.

The alternator is coupled to a prime mover capable of driving the alternator at its synchronous speed. The armature is connected to the terminals of a switch. The other terminals of the switch are short circuited through an ammeter. The voltmeter is connected across the lines to measure the open circuit voltage of the alternator. The field winding is connected to a suitable d.c. supply with rheostat connected in series. The field excitation i.e. field current can be varied with the help of this rheostat. The circuit diagram is shown in the Fig.

Circuit Diagram for OC & SC test

a. Open Circuit Test Procedure to conduct this test is as follows : i) Start the prime mover and adjust the speed to the synchronous speed of the alternator. ii) Keeping rheostat in the field circuit maximum, switch on the d.c. supply. iii) The T.P.S.T switch in the armature circuit is kept open. iv) With the help of rheostat, field current is varied from its minimum value to the rated value. Due to this, flux increasing the induced e.m.f. Hence voltmeter reading, which is measuring line value of open circuit voltage increases. For various values of field current, voltmeter readings are observed.

Open-circuit test Characteristics The generator is turned at the rated speed The terminals are disconnected from all loads, and the field current is set to zero. Then the field current is gradually increased in steps, and the terminal voltage is measured at each step along the way. It is thus possible to obtain an open-circuit characteristic of a generator (Ef or Vt versus If) from this information

Connection for Open Circuit Test

Open-Circuit Characteristic

Short-circuit test Adjust the field current to zero and shortcircuit the terminals of the generator through a set of ammeters. Record the armature current Isc as the field current is increased. Such a plot is called short-circuit characteristic.

Short-circuit test After completing the open circuit test observation, the field rheostat is brought to maximum position, reducing field current to a minimum value. The T.P.S.T switch is closed. As ammeter has negligible resistance, the armature gets short circuited. Then the field excitation is gradually increased till full load current is obtained through armature winding. This can be observed on the ammeter connected in the armature circuit. The graph of short circuit armature current against field current is plotted from the observation table of short circuit test. This graph is called short circuit characteristics, S.C.C.

Short-circuit test Adjust the field current to zero and short-circuit the terminals of the generator through a set of ammeters. Record the armature current Isc as the field current is increased. Such a plot is called short-circuit characteristic.

Connection for Short Circuit Test

Open and short circuit characteristic

Curve feature The OCC will be nonlinear due to the saturation of the magnetic core at higher levels of field current. The SCC will be linear since the magnetic core does not saturate under short-circuit conditions.

Determination of Xs For a particular field current IfA, the internal voltage Ef (=VA) could be found from the occ and the short-circuit current flow Isc,A could be found from the scc. Then the synchronous reactance Xs could be obtained using

Z s ,unsat = Ef or Vt (V)

Air-gap line OCC

Vrated

Isc (A) SCC

VA

IfB

2 s ,unsat

=

V A (= E f

)

I scA

X s ,unsat = Z s2,unsat − Ra2 : Ra is known from the DC test.

Isc,B

IfA

R +X 2 a

Isc, A If (A)

Since Xs,unsat>>Ra,

X s ,unsat ≈

Ef I scA

=

Vt , oc I scA

Xs under saturated condition Ef or Vt (V)

Air-gap line OCC

Vrated

SCC

VA

Isc,B

At V = Vrated, Z s , sat =

R +X 2 a

2 s ,sat

=

Vrated (= E f

)

Isc (A)

Isc, A IfA

If (A) IfB

I scB

X s , sat = Z s2, sat − Ra2: Ra is known from the DC test.

Advantages and Limitations of Synchronous Impedance Method The value of synchronous impedance Zs for any load condition can be calculated. Hence regulation of the alternator at any load condition and load power factor can be determined. Actual load need not be connected to the alternator and hence method can be used for very high capacity alternators. The main limitation of this method is that the method gives large values of synchronous reactance. This leads to high values of percentage regulation than the actual results. Hence this method is called pessimistic method

Equivalent circuit & phasor diagram under condition

jXs

Ra Vt=0

+

Ef

Ia Ef

jIaXs

+ Vt=0

Ia

I aR a

Short-circuit Ratio Another parameter used to describe synchronous generators is the short-circuit ratio (SCR). The SCR of a generator defined as the ratio of the field current required for the rated voltage at open circuit to the field current required for the rated armature current at short circuit. SCR is just the reciprocal of the per unit value of the saturated synchronous reactance calculated by Ef or Vt (V)

Air-gap line

Isc (A) OCC

Vrated

SCC Isc,rated

I f _ Vrated SCR = I f _ Iscrated =

If_V rated

If_Isc rated

If (A)

1

X s _ sat [in p .u .]

Synchronous Generator Capability Curves Synchronous generator capability curves are used to determine the stability of the generator at various points of operation. A particular capability curve generated in Lab VIEW for an apparent power of 50,000W is shown in Fig. The maximum prime-mover power is also reflected in it.

Capability Curve

2. MMF method (Ampere turns method) Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF

3. ZPF method (Potier method) Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF ZPF (for rated current and rated voltage) Armature Resistance (if required)

Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

4. ASA method Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF ZPF (for rated current and rated voltage) Armature Resistance (if required)

Losses and Efficiency The losses in synchronous generator include: 1. Copper losses in a) Armature b) Field winding c) The contacts between brushes 2. Core losses, Eddy current losses and Hysteresis losses

Losses 3. Friction and windage losses,the brush friction at the slip rings. 4. Stray load losses caused by eddy currents in the armature conductors and by additional core loss due to the distribution of magnetic field under load conditions.

synchronous generator power flow diagram

The three-phase synchronous generator power flow diagram

Synchronization & Parallel operation of Alternator

Parallel operation of synchronous generators

There are several major advantages to operate generators in parallel: • • •

Several generators can supply a bigger load than one machine by itself. Having many generators increases the reliability of the power system. It allows one or more generators to be removed for shutdown or preventive maintenance.

Synchronization Before connecting a generator in parallel with another generator, it must be synchronized. A generator is said to be synchronized when it meets all the following conditions: • • • •

The rms line voltages of the two generators must be equal. The two generators must have the same phase sequence. The phase angles of the two a phases must be equal. The oncoming generator frequency is equal to the running system frequency. a Generator 1

b

Load

c Switch

a/ Generator 2

b/ c/

Parallel operation of synchronous generators Most of synchronous generators are operating in parallel with other synchronous generators to supply power to the same power system. Obvious advantages of this arrangement are: 1. Several generators can supply a bigger load; 2. A failure of a single generator does not result in a total power loss to the load increasing reliability of the power system; 3. Individual generators may be removed from the power system for maintenance without shutting down the load; 4. A single generator not operating at near full load might be quite inefficient. While having several generators in parallel, it is possible to turn off some of them when operating the rest at near full-load condition.

Conditions required for paralleling A diagram shows that Generator 2 (oncoming generator) will be connected in parallel when the switch S1 is closed. However, closing the switch at an arbitrary moment can severely damage both generators! If voltages are not exactly the same in both lines (i.e. in a and a’, b and b’ etc.), a very large current will flow when the switch is closed. Therefore, to avoid this, voltages coming from both generators must be exactly the same. Therefore, the following conditions must be met: 1. 2. 3. 4.

The rms line voltages of the two generators must be equal. The two generators must have the same phase sequence. The phase angles of two a phases must be equal. The frequency of the oncoming generator must be slightly higher than the frequency of the running system.

Conditions required for paralleling If the phase sequences are different, then even if one pair of voltages (phases a) are in phase, the other two pairs will be 1200 out of phase creating huge currents in these phases.

If the frequencies of the generators are different, a large power transient may occur until the generators stabilize at a common frequency. The frequencies of two machines must be very close to each other but not exactly equal. If frequencies differ by a small amount, the phase angles of the oncoming generator will change slowly with respect to the phase angles of the running system. If the angles between the voltages can be observed, it is possible to close the switch S1 when the machines are in phase.

General procedure for paralleling generators When connecting the generator G2 to the running system, the following steps should be taken: 1. Adjust the field current of the oncoming generator to make its terminal voltage equal to the line voltage of the system (use a voltmeter). 2. Compare the phase sequences of the oncoming generator and the running system. This can be done by different ways: 1) Connect a small induction motor to the terminals of the oncoming generator and then to the terminals of the running system. If the motor rotates in the same direction, the phase sequence is the same; 2) Connect three light bulbs across the open terminals of the switch. As the phase changes between the two generators, light bulbs get brighter (large phase difference) or dimmer (small phase difference). If all three bulbs get bright and dark together, both generators have the same phase sequences.

General procedure for paralleling generators If phase sequences are different, two of the conductors on the oncoming generator must be reversed. 3. The frequency of the oncoming generator is adjusted to be slightly higher than the system’s frequency. 4. Turn on the switch connecting G2 to the system when phase angles are equal. The simplest way to determine the moment when two generators are in phase is by observing the same three light bulbs. When all three lights go out, the voltage across them is zero and, therefore, machines are in phase. A more accurate way is to use a synchroscope – a meter measuring the difference in phase angles between two a phases. However, a synchroscope does not check the phase sequence since it only measures the phase difference in one phase. The whole process is usually automated…

Synchronization

Generat or

Load

Rest of the power system

Xs1 Ef1 Xs2 Ef2

Generato r

G

Xsn Efn

Infinite bus V, f are constant Xs eq = 0

Concept of the infinite bus When a synchronous generator is connected to a power system, the power system is often so large that nothing, the operator of the generator does, will have much of an effect on the power system. An example of this situation is the connection of a single generator to the power grid. Our power grid is so large that no reasonable action on the part of one generator can cause an observable change in overall grid frequency. This idea is idealized in the concept of an infinite bus. An infinite bus is a power system so large that its voltage and frequency do not vary regardless of how much real or reactive power is drawn from or supplied to it.

Steady-state powerangle characteristics

Active and reactive power-angle characteristics

Pm

Pe, Qe Vt

Fig. Synchronous generator connected to an infinite bus.

• P>0: generator operation • P

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Syllabus EE6502 Electrical Machines -II

BOOKS Reference

LOCAL AUTHORS: {For THEORY use this books} 1.Electrical Machines-II by “Gnanavadivel” – Anuradha Publication 2. Electrical Machines-II by “Godse” – Technical Publication For Problems: Electric Machines by Nagrath & Kothari {Refer Solved Problems} Electric Machinery by A.E.Fitgerald {Refer Solved Problems}

Important Website Reference Electrical Machines-II by S. B. Sivasubramaniyan -MSEC, Chennai http://yourelectrichome.blogspot.in/ http://www.electricaleasy.com/p/electri cal-machines.html

NPTEL Reference • Electrical Machines II by Dr. Krishna Vasudevan & Prof. G. Sridhara Rao Department of Electrical Engineering , IIT Madras. • Basic Electrical Technology by Prof. L. Umanand - IISc Bangalore {video}

BASICS OF ELECTRICAL MACHINES

Electrical Machine? Electrical machine is a device which can convert

Mechanical energy into electrical energy (Generators/alternators) Electrical energy into mechanical energy (Motors) AC current from one voltage level to other voltage level without changing its frequency (Transformers) Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

Fundamental Principle..

Electrical Machines (irrespective of AC or DC) work on the fundamental principle of Faraday’s law of Electromagnetic Induction.

Faraday’s Law Faraday’s Law of Electromagnetic Induction states that an EMF is induced in a coil when the magnetic flux linking this coil changes with time or The EMF generated is proportional to the rate at which flux is changed.

dψ dϕ e= − = −N dt dt

Faraday’s Law – Illustration

Two forms of Induced EMF ! The effect is same if the magnet is moved and the coil is made stationery We call it as statically induced EMF The previous case is referred to as Dynamically induced EMF

Governing Rules

It becomes evident that there exists a relationship between mechanical energy, electrical energy and magnetic field. These three can be combined and precisely put as governing rules each for generator and for motor

Fleming’s Right hand rule

For Generator

Fleming's Right hand rule(for Generator)

Fleming’s Left hand rule

For Motor

Fleming's left hand rule (for motors)

First finger - direction of magnetic field (N-S)

Second finger - direction of current

(positive to negative) Thumb - movements of the wire

Maxwell’s Corkscrew rule

If the electric current is moving away from the observer, the direction of lines of force of the magnetic field surrounding the conductor is clockwise and that if the electric current is moving towards an observer, the direction of lines of force is anti-clockwise

Corkscrew (Screw driver) rule Illustration

Coiling of Conductor

To augment the effect of flux, we coil the conductor as the flux lines aid each other when they are in the same direction and cancel each other when they are in the opposite direction Many a times, conductor is coiled around a magnetic material as surrounding air weakens the flux We refer the magnetic material as armature core

Electromagnet

The magnetic property of current carrying conductor can be exploited to make the conductor act as a magnet – Electromagnet

This is useful because it is very difficult to find permanent magnets with such high field Also permanent magnets are prone to ageing problems

AC Fundamentals

AC Fundamentals - continued

Whenever current passes through a conductor…

Opposition to flow of current Opposition to sudden change in current Opposition to sudden change in voltage Flux lines around the conductor

Inductive Effect

Reactance EMF Lenz Law An induced current is always in such a direction as to oppose the motion or change causing it

Capacitive effect

V= (t ) ⇒ i (t )=

Q C = V q (t ) 1 = C C dq (t ) = dt

∫ i (t ) dt

dv (t ) C dt

Resistive Network – Vector diagram

Inductive Network – Vector Diagram

Capacitive Network – Vector Diagram

Inductive & Capacitive effects combined

Pure L & C networks – not at all possible!

R-L network

Pure L & C networks – not at all possible! – contd.

R-C network

Current & Flux

As already mentioned, As the current, so the flux

3 phase AC

Star and Delta

Star connection

=

V L

3V ph

I L = I ph

Delta Connection

V L

= V ph

IL =

3I ph

Maxwell's Right Hand Grip Rule

Right Handed Cork Screw Rule

Generators

Input

The Generator converts mechanical power into electrical power.

Synchronous generators (Alternator) are constant speed generators.

The conversion of mechanical power into electrical power is done through a coupling field (magnetic field).

Mechanical

Magnetic

Electrical

Output

Electric Generator Mechanical Energy

G

Stationary magnets - rotating magnets - electromagnets

Electrical Energy

Motor

The Motor converts electrical power into mechanical power.

Electrical Energy

Input

M

Magnetic Electrical

Mechanical Energy

Mechanical

Output

Basic Construction Parts Stationary Part

Stator

Armature

Electrical

Mechanical

Rotor Rotating Part

Field

AC MACHINES Two categories: 1.Synchronous Machines:

Synchronous Generators(Alternator)

Primary Source of Electrical Energy Synchronous Motor

2.Asynchronous Machines(Induction Machines)

UNIT-1 Synchronous Generator (Alternator)

UNIT-1 Syllabus

Synchronous Generators

Generator

Exciter View of a two-pole round rotor generator and exciter. (Westinghouse)

Synchronous Machines • Synchronous generators or alternators are used to convert mechanical power derived from steam, gas, or hydraulic-turbine to ac electric power • Synchronous generators are the primary source of electrical energy we consume today • Large ac power networks rely almost exclusively on synchronous generators • Synchronous motors are built in large units compare to induction motors (Induction motors are cheaper for smaller ratings) and used for constant speed industrial drives

Construction Basic parts of a synchronous generator: • •

Rotor - dc excited winding Stator - 3-phase winding in which the ac emf is generated

The manner in which the active parts of a synchronous machine are cooled determines its overall physical size and structure

Armature Windings (On Stator) • Armature windings connected are 3-phase and are either star or delta connected

• It is the stationary part of the machine and is built up of sheet-steel laminations having slots on its inner periphery. • The windings are 120 degrees apart and normally use distributed windings

Field Windings (on Rotor) • The field winding of a synchronous machine is always energized with direct current • Under steady state condition, the field or exciting current is given

Ir = Vf/Rf Vf = Direct voltage applied to the field winding Rf= Field winding Resistance

Rotor • Rotor is the rotating part of the machine • Can be classified as: (a) Cylindrical Rotor and (b) Salient Pole rotor

• Large salient-pole rotors are made of laminated poles retaining the winding under the pole head.

Various Types of ROTOR

Salient-pole Rotor

Cylindrical or round rotor

a. Salient-Pole Rotor 1. Most hydraulic turbines have to turn at low speeds (between 50 and 300 r/min) 2. A large number of poles are required on the rotor d-axis

Non-uniform air-gap

N

D ≈ 10 m q-axis

S

S

Turbine Hydro (water)

Hydrogenerator

N

• Salient pole type rotor is used in low and medium speed alternators • This type of rotor consists of large number of projected poles (called salient poles) • Poles are also laminated to minimize the eddy current losses. • This type of rotor are large in diameters and short in axial length.

Salient-Pole Synchronous Generator

Stator

b. Cylindrical-Rotor(Non-Salient Pole)

D≈1m

Turbine

L ≈ 10 m Steam

d-axis Stator winding

High speed

3600 r/min ⇒ 2-pole

Uniform airgap Stato r

1800 r/min ⇒ 4-pole

Direct-conductor cooling (using hydrogen or water as coolant)

N

q-axis

Rotor winding Roto r

Rating up to 2000 MVA S

Turbogenerator

• Cylindrical type rotors are used in high speed alternators (turbo alternators) • This type of rotor consists of a smooth and solid steel cylinder having slots along its outer periphery. • Field windings are placed in these slots.

Cylindrical-Rotor Synchronous Generator

Stator

Cylindrical rotor

Working of Alternator & frequency of Induced EMF

Working Principle • It works on the principle of Electromagnetic induction • In the synchronous generator field system is rotating and armature winding is steady. • Its works on principle opposite to the DC generator • High voltage AC output coming from the armature terminal

Working Principle • Armature Stator • Field Rotor • No commutator is required {No need for commutator because we need AC only}

Frequency of Induced EMF Every time a complete pair of poles crosses the conductor, the induced voltage goes through one complete cycle. Therefore, the generator frequency is given by

p n pn f = . = 2 60 120 N=Rotor speed in r.p.m P=number of rotor poles f=frequency of induced EMF in Hz No of cycles/revolution = No of pairs of poles = P/2 No of revolutions/second = N/60 No of cycles/second {Frequency}= (P/2)*(N/60)=PN/120

Advantages of stationary armature • At high voltages, it easier to insulate stationary armature winding(30 kV or more) • The high voltage output can be directly taken out from the stationary armature. • Rotor is Field winding. So low dc voltage can be transferred safely • Due to simple construction High speed of Rotating DC field is possible. Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

Winding Factors( K , Kd) p

K

p

= cos

α

2 m sin 2 m sin 2

β

Kd

=

β

Pitch factor (Kp)

Consider 4 pole, 3 phase machine having 24 conductors Pole pitch = 24 / 4 = 6 slots If Coil Pitch or Coil Span = pole pitch, then it is referred to as full-pitched winding If Coil Pitch < pole pitch, it is referred to as short-pitched winding

Coil Span = 5 / 6 of pole pitch If falls short by 1 / 6 of pole pitch or 180 / 6 = 30 degrees

This is done primarily to Save copper of end connections Improve the wave-form of the generated emf (sine wave) Eliminate the high frequency harmonics There is a disadvantage attached to it Total voltage around the coil gets reduced because, the emf induced in the two sides of the coil is slightly out of phase Due to that, their resultant vectorial sum is less than the arithmetic sum This is denoted by a factor Pitch factor, Kp or Kc

Pitch factor – Kp

Vectorsum Kp = Arithmaticsum

Pitch factor – contd.

Arithmatic sum

Pitch factor – contd.

Vector sum

Pitch factor – contd.

Pitch factor – contd.

Kp

=

Vector _ sum = Arithmatic _ sum

2 Es cos 2 Es

= cos

α

2

α 2

Pitch factor - Problem

Distribution factor (Kd)

As we know, each phase consists of conductors distributed in number of slots to form polar groups under each pole The result is that the emf induced in the conductors constituting the polar group are not in phase rather differ by an angle equal to angular displacement of the slots

For a 3 phase machine with 36 conductors, 4 pole, no. of slots (conductors) / pole / phase is equal to 3 Each phase consists of 3 slots Angular displacement between any two adjacent slots = 180 / 9 = 20 degrees If the 3 coils are bunched in 1 slot, emf induced is equal to the arithmetic sum (3Es) Practically, in distributed winding, vector sum has to be calculated Kd = Vector sum / Arithmetic sum

emf _ with _ distributed _ winding Kd = emf _ with _ concentrated _ winding

β

0

180 180 = no.of _ slots _ per _ pole n

0

For calculating Vector sum

Kd

Kd

mβ 2 r sin 2 = β m 2 r sin 2 mβ sin 2 = β m sin 2

Problem: Distribution factor /Breadth factor

EMF Equation of Alternator

Equation of Induced EMF

Average emf induced per conductor = dφ / dt Here, dφ = φP If P is number of poles and flux / pole is φ Weber dt = time for N revolution = 60 / N second Therefore, Average emf = dφ / dt = φP / (60 / N)

=

ϕ NP 60

Equation of Induced EMF – contd. We know, N = 120 f / P Substituting, N we get Avg. emf per conductor = 2 f φ Volt If there are Z conductors / ph, then Avg. emf induced / ph = 2 f φ Z Volt Ave emf induced (in turns) / ph = 4 f φ T Volt

Equation of Induced EMF – contd.

We know, RMS value / Avg. Value = 1.11 Therefore, RMS value of emf induced / ph = 1.11 (4 f φ T) V = 4.44 f φ T Volt This is the actual value, but we have two other factors coming in the picture, Kc and Kd These two reduces the emf induced

RMS value of emf induced = (Kd) (Kc) 4.44 f φ T

Volt

Armature Reaction of Alternator

Armature Reaction

Main Flux Field Winding Secondary Flux Armature Winding Effect of Armature Flux on the Main Flux is called Armature Reaction

Armature Reaction in alternator I.) When load p.f. is unity II.) When load p.f. is zero lagging III.) When load p.f. is zero leading

Armature Reaction in alternator I.) When load p.f. is unity distorted but not weakened.- the average flux in the air-gap practically remains unaltered. II.) When load p.f. is zero lagging the flux in the air-gap is weakened- the field excitation will have to be increased to compensate III.) When load p.f. is zero leading

the effect of armature reaction is wholly magnetizing- the field excitation will have to be reduced

1. Unity Power Factor Load

Consider a purely resistive load connected to the alternator, having unity power factor. As induced e.m.f. Eph drives a current of Iaph and load power factor is unity, Eph and Iph are in phase with each other. If Φf is the main flux produced by the field winding responsible for producing Eph then Eph lags Φf by 90o . Now current through armature Ia, produces the armature flux say Φa. So flux Φa and Ia are always in the same direction.

• Phase difference of 90o between the armature flux and the main flux • the two fluxes oppose each other on the left half of each pole while assist each other on the right half of each pole. • Average flux in the air gap remains constant but its distribution gets distorted. • Due to such distortion of the flux, there is small drop in the terminal voltage

2. Zero Lagging Power Factor Load

Consider a purely inductive load connected to the alternator, having zero lagging power factor. Iaph driven by Eph lags Eph by 90o which is the power factor angle Φ. Induced e.m.f. Eph lags main flux Φf by 90o while Φa is in the same direction as that of Ia. the armature flux and the main flux are exactly in opposite direction to each other.

• As this effect causes reduction in the main flux, the terminal voltage drops. This drop in the terminal voltage is more than the drop corresponding to the unity p.f. load.

3. Zero Leading Power Factor Load

Consider a purely capacitive load connected to the alternator having zero leading power factor. This means that armature current Iaph driven by Eph, leads Eph by 90o, which is the power factor angle Φ. Induced e.m.f. Eph lags Φf by 90o while Iaph and Φa are always in the same direction. the armature flux and the main field flux are in the same direction

• As this effect adds the flux to the main flux, greater e.m.f. gets induced in the armature. Hence there is increase in the terminal voltage for leading power factor loads.

Phasor Diagram for Synchronous Generator/Alternator

Phasor Diagram of loaded Alternator Ef which denotes excitation voltage Vt which denotes terminal voltage Ia which denotes the armature current θ which denotes the phase angle between Vt and Ia ᴪ which denotes the angle between the Ef and Ia δ which denotes the angle between the Ef and Vt ra which denotes the armature per phase resistance Two important points: (1) If a machine is working as a synchronous generator then direction of Ia will be in phase to that of the Ef. (2) Phasor Ef is always ahead of Vt.

Lagging PF

Unity PF

Leading PF

a. Alternator at Lagging PF Ef by first taking the component of the Vt in the direction of Ia Component of Vt in the direction of Ia is Vtcosθ , Total voltage drop is (Vtcosθ+Iara) along the Ia. we can calculate the voltage drop along the direction perpendicular to Ia. The total voltage drop perpendicular to Ia is (Vtsinθ+IaXs). With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as

b. Alternator at Unity PF

Ef by first taking the component of the Vt in the direction of Ia. θ = 0 hence we have ᴪ=δ. With the help of triangle BOD in the second phasor diagram we can directly write the expression for Ef as

c. Alternator at Leading PF

Component in the direction of Ia is Vtcosθ. As the direction of Ia is same to that of the Vt thus the total voltage drop is (Vtcosθ+Iara). Similarly we can write expression for the voltage drop along the direction perpendicular to Ia. The total voltage drop comes out to be (Vtsinθ-IaXs). With the help of triangle BOD in the first phasor diagram we can write the expression for Ef as

Determination of the parameters of the equivalent circuit from test data The equivalent circuit of a synchronous generator that has been derived contains three quantities that must be determined in order to completely describe the behaviour of a real synchronous generator: The saturation characteristic: relationship between If and φ (and therefore between If and Ef) The synchronous reactance, Xs The armature resistance, Ra

VOLTAGE REGULATION Voltage regulation of an alternator is defined as the rise in terminal voltage of the machine expressed as a fraction of percentage of the initial voltage when specified load at a particular power factor is reduced to zero, the speed and excitation remaining unchanged.

Voltage Regulation A convenient way to compare the voltage behaviour of two generators is by their voltage regulation (VR). The VR of a synchronous generator at a given load, power factor, and at rated speed is defined as

VR =

Enl − V fl V fl

× 100%

Voltage Regulation Case 1: Lagging power factor: A generator operating at a lagging power factor has a positive voltage regulation.

Case 2: Unity power factor: A generator operating at a unity power factor has a small positive voltage regulation.

Case 3: Leading power factor: A generator operating at a leading power factor has a negative voltage regulation.

Voltage Regulation This value may be readily determined from the phasor diagram for full load operation. If the regulation is excessive, automatic control of field current may be employed to maintain a nearly constant terminal voltage as load varies

Methods of Determination of voltage regulation

Methods of Determination of voltage regulation Synchronous Impedance Method / E.M.F. Method Ampere-turns method / M.M.F. method ZPF(Zero Power Factor) Method / Potier ASA Method

1. Synchronous Impedance Method / E.M.F. Method The method is also called E.M.F. method of determining the regulation. The method requires following data to calculate the regulation. 1. The armature resistance per phase (Ra). 2. Open circuit characteristics which is the graph of open circuit voltage against the field current. This is possible by conducting open circuit test on the alternator. 3. Short circuit characteristics which is the graph of short circuit current against field current. This is possible by conducting short circuit test on the alternator.

The alternator is coupled to a prime mover capable of driving the alternator at its synchronous speed. The armature is connected to the terminals of a switch. The other terminals of the switch are short circuited through an ammeter. The voltmeter is connected across the lines to measure the open circuit voltage of the alternator. The field winding is connected to a suitable d.c. supply with rheostat connected in series. The field excitation i.e. field current can be varied with the help of this rheostat. The circuit diagram is shown in the Fig.

Circuit Diagram for OC & SC test

a. Open Circuit Test Procedure to conduct this test is as follows : i) Start the prime mover and adjust the speed to the synchronous speed of the alternator. ii) Keeping rheostat in the field circuit maximum, switch on the d.c. supply. iii) The T.P.S.T switch in the armature circuit is kept open. iv) With the help of rheostat, field current is varied from its minimum value to the rated value. Due to this, flux increasing the induced e.m.f. Hence voltmeter reading, which is measuring line value of open circuit voltage increases. For various values of field current, voltmeter readings are observed.

Open-circuit test Characteristics The generator is turned at the rated speed The terminals are disconnected from all loads, and the field current is set to zero. Then the field current is gradually increased in steps, and the terminal voltage is measured at each step along the way. It is thus possible to obtain an open-circuit characteristic of a generator (Ef or Vt versus If) from this information

Connection for Open Circuit Test

Open-Circuit Characteristic

Short-circuit test Adjust the field current to zero and shortcircuit the terminals of the generator through a set of ammeters. Record the armature current Isc as the field current is increased. Such a plot is called short-circuit characteristic.

Short-circuit test After completing the open circuit test observation, the field rheostat is brought to maximum position, reducing field current to a minimum value. The T.P.S.T switch is closed. As ammeter has negligible resistance, the armature gets short circuited. Then the field excitation is gradually increased till full load current is obtained through armature winding. This can be observed on the ammeter connected in the armature circuit. The graph of short circuit armature current against field current is plotted from the observation table of short circuit test. This graph is called short circuit characteristics, S.C.C.

Short-circuit test Adjust the field current to zero and short-circuit the terminals of the generator through a set of ammeters. Record the armature current Isc as the field current is increased. Such a plot is called short-circuit characteristic.

Connection for Short Circuit Test

Open and short circuit characteristic

Curve feature The OCC will be nonlinear due to the saturation of the magnetic core at higher levels of field current. The SCC will be linear since the magnetic core does not saturate under short-circuit conditions.

Determination of Xs For a particular field current IfA, the internal voltage Ef (=VA) could be found from the occ and the short-circuit current flow Isc,A could be found from the scc. Then the synchronous reactance Xs could be obtained using

Z s ,unsat = Ef or Vt (V)

Air-gap line OCC

Vrated

Isc (A) SCC

VA

IfB

2 s ,unsat

=

V A (= E f

)

I scA

X s ,unsat = Z s2,unsat − Ra2 : Ra is known from the DC test.

Isc,B

IfA

R +X 2 a

Isc, A If (A)

Since Xs,unsat>>Ra,

X s ,unsat ≈

Ef I scA

=

Vt , oc I scA

Xs under saturated condition Ef or Vt (V)

Air-gap line OCC

Vrated

SCC

VA

Isc,B

At V = Vrated, Z s , sat =

R +X 2 a

2 s ,sat

=

Vrated (= E f

)

Isc (A)

Isc, A IfA

If (A) IfB

I scB

X s , sat = Z s2, sat − Ra2: Ra is known from the DC test.

Advantages and Limitations of Synchronous Impedance Method The value of synchronous impedance Zs for any load condition can be calculated. Hence regulation of the alternator at any load condition and load power factor can be determined. Actual load need not be connected to the alternator and hence method can be used for very high capacity alternators. The main limitation of this method is that the method gives large values of synchronous reactance. This leads to high values of percentage regulation than the actual results. Hence this method is called pessimistic method

Equivalent circuit & phasor diagram under condition

jXs

Ra Vt=0

+

Ef

Ia Ef

jIaXs

+ Vt=0

Ia

I aR a

Short-circuit Ratio Another parameter used to describe synchronous generators is the short-circuit ratio (SCR). The SCR of a generator defined as the ratio of the field current required for the rated voltage at open circuit to the field current required for the rated armature current at short circuit. SCR is just the reciprocal of the per unit value of the saturated synchronous reactance calculated by Ef or Vt (V)

Air-gap line

Isc (A) OCC

Vrated

SCC Isc,rated

I f _ Vrated SCR = I f _ Iscrated =

If_V rated

If_Isc rated

If (A)

1

X s _ sat [in p .u .]

Synchronous Generator Capability Curves Synchronous generator capability curves are used to determine the stability of the generator at various points of operation. A particular capability curve generated in Lab VIEW for an apparent power of 50,000W is shown in Fig. The maximum prime-mover power is also reflected in it.

Capability Curve

2. MMF method (Ampere turns method) Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF

3. ZPF method (Potier method) Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF ZPF (for rated current and rated voltage) Armature Resistance (if required)

Presented by C.GOKUL,AP/EEE Velalar College of Engg & Tech , Erode

4. ASA method Tests: Conduct tests to find OCC (up to 125% of rated voltage) refer diagram EMF SCC (for rated current) refer diagram EMF ZPF (for rated current and rated voltage) Armature Resistance (if required)

Losses and Efficiency The losses in synchronous generator include: 1. Copper losses in a) Armature b) Field winding c) The contacts between brushes 2. Core losses, Eddy current losses and Hysteresis losses

Losses 3. Friction and windage losses,the brush friction at the slip rings. 4. Stray load losses caused by eddy currents in the armature conductors and by additional core loss due to the distribution of magnetic field under load conditions.

synchronous generator power flow diagram

The three-phase synchronous generator power flow diagram

Synchronization & Parallel operation of Alternator

Parallel operation of synchronous generators

There are several major advantages to operate generators in parallel: • • •

Several generators can supply a bigger load than one machine by itself. Having many generators increases the reliability of the power system. It allows one or more generators to be removed for shutdown or preventive maintenance.

Synchronization Before connecting a generator in parallel with another generator, it must be synchronized. A generator is said to be synchronized when it meets all the following conditions: • • • •

The rms line voltages of the two generators must be equal. The two generators must have the same phase sequence. The phase angles of the two a phases must be equal. The oncoming generator frequency is equal to the running system frequency. a Generator 1

b

Load

c Switch

a/ Generator 2

b/ c/

Parallel operation of synchronous generators Most of synchronous generators are operating in parallel with other synchronous generators to supply power to the same power system. Obvious advantages of this arrangement are: 1. Several generators can supply a bigger load; 2. A failure of a single generator does not result in a total power loss to the load increasing reliability of the power system; 3. Individual generators may be removed from the power system for maintenance without shutting down the load; 4. A single generator not operating at near full load might be quite inefficient. While having several generators in parallel, it is possible to turn off some of them when operating the rest at near full-load condition.

Conditions required for paralleling A diagram shows that Generator 2 (oncoming generator) will be connected in parallel when the switch S1 is closed. However, closing the switch at an arbitrary moment can severely damage both generators! If voltages are not exactly the same in both lines (i.e. in a and a’, b and b’ etc.), a very large current will flow when the switch is closed. Therefore, to avoid this, voltages coming from both generators must be exactly the same. Therefore, the following conditions must be met: 1. 2. 3. 4.

The rms line voltages of the two generators must be equal. The two generators must have the same phase sequence. The phase angles of two a phases must be equal. The frequency of the oncoming generator must be slightly higher than the frequency of the running system.

Conditions required for paralleling If the phase sequences are different, then even if one pair of voltages (phases a) are in phase, the other two pairs will be 1200 out of phase creating huge currents in these phases.

If the frequencies of the generators are different, a large power transient may occur until the generators stabilize at a common frequency. The frequencies of two machines must be very close to each other but not exactly equal. If frequencies differ by a small amount, the phase angles of the oncoming generator will change slowly with respect to the phase angles of the running system. If the angles between the voltages can be observed, it is possible to close the switch S1 when the machines are in phase.

General procedure for paralleling generators When connecting the generator G2 to the running system, the following steps should be taken: 1. Adjust the field current of the oncoming generator to make its terminal voltage equal to the line voltage of the system (use a voltmeter). 2. Compare the phase sequences of the oncoming generator and the running system. This can be done by different ways: 1) Connect a small induction motor to the terminals of the oncoming generator and then to the terminals of the running system. If the motor rotates in the same direction, the phase sequence is the same; 2) Connect three light bulbs across the open terminals of the switch. As the phase changes between the two generators, light bulbs get brighter (large phase difference) or dimmer (small phase difference). If all three bulbs get bright and dark together, both generators have the same phase sequences.

General procedure for paralleling generators If phase sequences are different, two of the conductors on the oncoming generator must be reversed. 3. The frequency of the oncoming generator is adjusted to be slightly higher than the system’s frequency. 4. Turn on the switch connecting G2 to the system when phase angles are equal. The simplest way to determine the moment when two generators are in phase is by observing the same three light bulbs. When all three lights go out, the voltage across them is zero and, therefore, machines are in phase. A more accurate way is to use a synchroscope – a meter measuring the difference in phase angles between two a phases. However, a synchroscope does not check the phase sequence since it only measures the phase difference in one phase. The whole process is usually automated…

Synchronization

Generat or

Load

Rest of the power system

Xs1 Ef1 Xs2 Ef2

Generato r

G

Xsn Efn

Infinite bus V, f are constant Xs eq = 0

Concept of the infinite bus When a synchronous generator is connected to a power system, the power system is often so large that nothing, the operator of the generator does, will have much of an effect on the power system. An example of this situation is the connection of a single generator to the power grid. Our power grid is so large that no reasonable action on the part of one generator can cause an observable change in overall grid frequency. This idea is idealized in the concept of an infinite bus. An infinite bus is a power system so large that its voltage and frequency do not vary regardless of how much real or reactive power is drawn from or supplied to it.

Steady-state powerangle characteristics

Active and reactive power-angle characteristics

Pm

Pe, Qe Vt

Fig. Synchronous generator connected to an infinite bus.

• P>0: generator operation • P

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