EET 221 Synchronous Machines Rafiqi. Synchronous Machines (Introduction) A synchronous machine...

EET 221

Synchronous Machines

Rafiqi


(Introduction)

A synchronous machine rotates at a constant speed in the steady state.

Unlike induction machine, the rotating air gap field and the rotor in the synchronous machine at the same speed, called the synchronous speed.

Synchronous machine can operate as both a generator and a motor.

Synchronous machines are used primarily as generators of electrical power.

Synchronous machine can be used to compensate the reactive power in the power system.


(Introduction)

Synchronous Generator

Synchronous Motor


(Introduction)

A synchronous motor can draw either lagging or leading reactive current from the ac supply.

A synchronous machine is a double excited machine. Its rotor poles are excited by a dc current and its stator windings (armature winding) are connected to the ac supply.

The air gap flux is the resultant of the fluxes due to both rotor current and stator current.

In induction machines, the only source of excitation is the stator current, because rotor currents are induced currents. Therefore induction motors always operate at a lagging power factor.

Construction of Three Phase Synchronous Machines

The stator winding of the three phase synchronous machines has a three phase distributed winding similar to that of the three phase induction machine.

Unlike the dc machine, the stator winding, which is connected to ac supply system is called the armature winding.

The rotor winding has a winding called the field winding, which is carries direct current. The field winding on the rotating structure is fed from an external dc source through slip rings and brushes.


Two common approaches to supplying the dc supply to the rotor winding (filed winding):

• Supply the power from an external dc source to the rotor by means of slip rings and brushes.

• Supply the dc power from a special power source mounted directly on the shaft of the generator.

On the larger synchronous machine, brushless exciter are used to supply the dc field current to the machines. A brushless exciter is a small ac generator with its field circuit mounted on the stator and its armature circuit mounted on the rotor shaft.

Construction of Three Phase Synchronous Machines (A Brushless Exciter Circuit)

A small three phase current is rectified and used to supply the field circuit of the exciter, which is located on the stator. The output of the armature of the exciter (on the rotor) is then rectified and used to supply the field current of the main winding.

Synchronous machines can be divided into two groups:


1. High speed machines with cylindrical (or non salient pole) rotor.

2. Low speed machines with salient pole rotors.

The cylindrical or non salient pole rotor has one distributed winding and essentially uniform air gap while salient pole rotors have concentrated winding on the poles and a uniform air gap.

Generator

Exciter

View of a two-pole round rotor generator and exciter

Round Rotor Generator

Cross-section of a large turbo generator. (Courtesy Westinghouse)


Laminated iron core with slots

Insulated copper bars are placed in the slots to form the three-phase winding

Metal frame

Details of a generator stator


Rotor block of a large generator. (Courtesy Westinghouse)


Generator rotor with conductors placed in the slots


DC current terminals

Shaft

Steelretaining

ring

DC currentterminals

Wedges

Shaft

Large generator rotor completely assembled. (Courtesy Westinghouse)


Salient pole generator

Stator of a large salient pole hydro generator; inset shows the insulated conductors and spacers


Large hydro generator rotor with view of the vertical poles


Pole

DC excitationwinding

Fan

Sliprings

Rotor of a four-pole salient pole generator

Synchronous generator

Mechanism of ac voltage generation• Rotor flux is produced by a dc field current If.• Rotor is driven by a prime mover, producing rotating field in the air gap.• A voltage is induced in the stator winding due tothe rotating field.Induced voltage is sinusoidal due to the sinusoidal distributed flux density in the air gap.

Synchronous generator

(The Speed of Rotation of a Synchronous Generator)

Synchronous generators are by definition synchronous, meaning that the electrical frequency produced is locked in or synchronized with the mechanical rate of rotation of the generator.

The rate of rotation of the magnetic fields in the machined is related to the stator electrical frequency is

120

Pnf m

e

Where fe = electrical frequency (Hz)

nm = mechanical speed of the magnetic field, rpm (= speed of rotor)

P = number of poles

The Internal Generated Voltage of a Synchronous Generator

The magnitude of the voltage induced in a stator phase is

fNE CA 2

or

KEA

Where

NC = no of conductors at an angle of 00

2CN

K

The Equivalent Circuit of a Synchronous Generator

The voltage EA is the internal voltage generated produced in one phase of a synchronous generator. However, this voltage EA is not usually the voltage that appears at the terminals of the generator.

There are many factors that cause the difference between EA and VФ.

1. The distortion of the air gap magnetic filed by the current flowing in the stator called armature reaction.

2. The self inductance of the armature coils.

3. The resistance of the armature coils.

4. The effect of salient pole rotor shapes.

The Development of a Model for Armature Reaction

Figure (a) shows a two pole rotor spinning inside a three phase stator. A rotating magnetic field produces the internal

generated voltage EA.

There is no load connected to the stator. The rotor magnetic field BR produces an internal generated voltage EA whose peak value coincides with the direction of BR. With no load on the generator, there is no armature current flow, and EA will be equal to the phase voltage VФ.


Figure (b): The resulting voltage produces a lagging current flow when connected to a lagging load


Figure (c): The stator current produces its own magnetic filed BS, which produces its own voltage Estat in the stator

windings of the machine

The current flowing in the stator in the stator windings produces a magnetic filed of its own. This stator magnetic filed is called BS and its direction is given by the right hand rule. The stator magnetic filed Bs produces a voltage of its own in the stator, and this voltage is called Estat.


Figure (d): The field BS adds to BR, distorting it into Bnet. The voltage Estat adds to EA, producing VФ at the output of the phase.

With two voltages present in the stator windings, the total voltage in a phase is just the sum of the internal generated EA and the armature reaction voltage Estat:

statA EEV


The net magnetic field Bnet is just the sum of the rotor and the stator magnetic fields:

SRnet BBB

Since the angles of EA and BR are the same and the angles of Estat and Bs, are the same, the resulting magnetic field Bnet will coincide with the net voltage VФ.

We know, the voltage Estat is directly proportional to the current IA. If X is a constant of proportionality, then the armature reaction voltage can be expressed as:

Astat jXIE


The voltage on a phase is

AA jXIEV


In addition to the effects of armature reaction, the stator coils have a self inductance and a resistance. If the stator self inductance is called LA (and its corresponding reactance is called XA) while the stator resistance is called RA, then the total difference between EA and VФ is given by

AAAAAA IRIjXjXIEV

Combine the armature reaction effects and the self inductance in the machine

AS XXX


So

AAASA IRIjXEV


If the machine is Wye (Y ) connection

VVT 3

If the machine is Delta (Δ) connection

VVT

The Per Phase Equivalent Circuit of a Synchronous Generator

The Phasor Diagram of A Synchronous Generator

The Phasor Diagram of A Synchronous Generator at Unity Power Factor

The Phasor Diagram of A Synchronous Generator

(a) Lagging (b) Leading

Per Unit System

Definition:

value Base

value Actualpu,Unit Per

Base value (in normal):– Choose rated power for base value of power– Choose rated voltage for base value of voltage

Other variables:

ratedbase SS ratedbase VV

base

basebase V

SI

base

basebase S

VZ

2

3rated,LL

baseratedbase

VV,SS

base

basebaserated,L

base

basebase I

VZ,I

V

SI

3

base

Lpu

base

LLpu I

II and

V

/VV

3

base

ApuA,

base

Spu,S Z

RR and

Z

XX

Select

then

Per Unit System

X S , p u R A , p u

+

-

E A , p u V T , p u

I f , p u

IA ,p u

Per Unit System

Equivalent circuit in per unit system

Tpu,Spu,Apu,Apu,A V)jXR(IE

Usually

VT,pu = 1.0, which is the rated voltage of the generator

Power and Torque in Synchronous Generator

cosIEP AAmindconv 3

Power converted from mechanical to electrical is

mappinP Input mechanical power

Where γ is the angle between EA and IA


The difference between the input power to the generator and the power converted in generator is mechanical (friction & windage), core and stray losses.

Real output power is

cosIVP LTout 3 (Line quantities)

cosIVP Aout 3 (Phase quantities)

Reactive output power is

sinIVQ LTout 3

sinIVQ Aout 3

(Line quantities)

(Phase quantities)


If the armature resistance RA is ignored (since Xs >> RA)


Since the resistances are assumed to be zero

s

Aoutconv X

sinEVPPP

3

Where torque angle, δ is the angle between VФ and EA

The power of the generator is maximum when δ = 900

s

Amax X

EVP

3

The maximum power indicated by this equation called static stability limit of the generator.

The induced torque is

sm

Aind X

sinEV

3

EXAMPLE 1

A 25kVA, 415V, three phase, 4 pole, 60Hz, wye connected synchronous generator has a synchronous reactances of 1.5Ω/phase and negligible stator resistance. The generator is connected to an infinite bus (of constant voltage magnitude and constant frequency) at 415V and 60Hz.

a) Determine the excitation voltage, EA when the machine is delivering rated kVA at 0.8 pf lagging.

b) The field excitation current If increased by 20% without changing the power input from the prime mover. Find the stator current IA, power factor, and reactive power Q supplied by the machine.

c) With the field excitation current If as in part (a), the input power from the prime mover is increased very slowly. What is the steady state limit? Determine stator current IA, power factor, and reactive power Q.

Measuring synchronous generator model parameter

The behavior of a real synchronous generator is determine by

• The relationship between field current and flux (and therefore between field current and EA)

• The synchronous reactance, Xs

• The armature resistance, RA

The quantities above are determined by open circuit test and short circuit test

Open Circuit Test

• To perform this test, the generator is turned at the rated speed.

• The terminals are disconnected from all loads.

• The field current is set to zero.

First step:

Second step:

The field current is gradually increased in steps, and the terminal voltage is measured at each step along the way with the terminals open. (IA = 0, so EA is equal to VФ)

Plot EA or VA versus IF from this information

Air gap line

This plot called open circuit characteristics

Open Circuit Test

The curve almost perfectly linear, until some saturation is observed at high field currents.

The unsaturated iron in the frame of the synchronous machine has a relunctance several thousand times lower than the air gap reluctance, so at the first almost all the magnetomotive force is across the air gap, and the resulting flux increase is linear.

When the iron finally saturates, the reluctance of the iron increases dramatically, and the flux increases much more slowly with an increase in magnetomotive forces. The linear portion of an OCC is called the air gap line of characteristic.

Short Circuit Test

Adjust the field current to zero again and short circuit terminals of the generator through a set of ammeters. Then the armature current IA or the line current IL is measured as the field increased.

Short Circuit Test

When the terminals are short circuited, the armature currents IA is

SA

AA jXR

EI

Its magnitude is

22SA

AA

jXR

EI

Refer to Figure (b), BS almost cancels BR, the net magnetic field Bnet is very small, so the machine is unsaturated and the SCC is linear.

Short Circuit TestThe internal machine impedance is

A

A)unsat(SA)unsat(S I

EXRZ 22

If XS >> RA, this equation reduces to

A

OC,

A

AS I

V

I

EX

1) Get the internal generated voltage EA from the OCC at the field changing.

2) Get the short circuit current flow IA,SC at that field current from SCC.

3) Find XS by equation above.

Therefore, an approximate method for determining the synchronous reactances at a given field current is

The saturated synchronous reactance may also found by taking the rated terminal voltage (line to line) measured on the OCC and dividing by the current read from SCC corresponding to the field current that produces at rated terminal voltage.

ba

A

SC,A

rated,A)sat(SA)sat(S I

E

I

EjXRZ

EET 221 Synchronous Machines Rafiqi. Synchronous Machines (Introduction) A synchronous machine...

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