Synchronous Generator

ELE-351Electrical Energy ConversionElectrical Energy Conversion

Chapter 5Synchronous GeneratorsSynchronous Generators

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OutlineSynchronous generator construction

The rotor circuit

The speed of rotation and the frequency of the electrical power

An equivalent circuit for a synchronous generator

The phasor diagram

Voltage regulation

Power & torque in synchronous generators

Measuring SG parameters

Frequency and voltage control of SG

Effects of load variations (voltage regulation) for isolated generators.generators.

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Synchronous generatorSynchronous generator

A prime mover (diesel engine or turbine) isA prime mover (diesel engine or turbine) isconnected to the shaft (rotor) to supplymechanical powermechanical power.

A dc current is applied to the rotor or fieldwinding producing a rotating magnetic fieldwinding producing a rotating magnetic field(Br).

A 3φ f l i i d d hA 3φ set of voltages is induced on the statoror armature windings.

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Elementary Synchronous generator

The rotating magnetic field is created by the dc current applied to the field winding on the spinningcurrent applied to the field winding on the spinning rotor!

Voltage is induced on the 3 windings placed on the o tage s duced o t e 3 d gs p aced o t estator by the variation of the magnetic flux.

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The rotor circuit (magnet)( g )

2 and 4-pole machines have nonsalient(cylindrical) poles while machines with 4 ormore poles have salient (sticking out)poles.

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The rotor circuit (magnet)

Photograph of a salient 8 pole synchronous machine rotorPhotograph of a salient 8‐pole synchronous machine rotor

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The rotor circuit (magnet)DC current is supplied to therotor by means of slip ringsy p gand brushes.Slip Rings: are metal rings p g gencircling shaft and are insulated from it

O d f t i di iOne end of rotor winding is connected to each of the 2 slip ringsA stationary brush mounted on the machine casing ride on each slip ringon each slip ring

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A brushless exciter systemThe dc current that appears on the rotor isobtained from a rectified induced voltage.

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Another brushless exciter system

Notice the small pilot exciter (extra windings,permanent magnet and rectifiers).permanent magnet and rectifiers).

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The speed of rotation of a synchronous generatorgenerator

The electrical frequency is synchronized to therotor speedrotor speed.Recall that the magnetic field created by a 3φ 4-pole machine moves 180° while the stator currentspole machine moves 180 while the stator currentsvary 360°.

Therefore a 2-pole generator must turn at 3600Therefore, a 2 pole generator must turn at 3600 r/min to produce a 60 Hz voltage while a 4-pole must turn at 1500 r/min to produce 50 Hz power.

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The induced voltageThe “internal generated voltage” (no load) is:

where ω is given in Electrical rad/s2

NKKE CA == ,ωϕ

How can this voltage be varied?

2

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The output voltage of the generator

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Last figure shows a 2 pole rotor spinning inside a 3 phase stator without loadinside a 3 phase stator, without load Rotor magnetic field BR develops a voltage EAis positive out of conductors, at top, and p , p,negative into the conductors at bottom of figureWhen there is no load on generator, the armature current is zero, EA=VφIf th t i t d t l i PFIf the generator is connected to a lagging PF load, the peak current occurs at an angle behind the peak voltage as in fig (b)behind the peak voltage as in fig (b)

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The output voltage of the generatorCurrent flowing in stator windings produces its magnetic field BS

The direction of BS is found by R.H.R. as shown in fig(c). This BS produces another voltage in stator,

d E h i finamed Estat as shown in figureHaving these two voltage components in stator

i di t t l lt i h i f E dwindings, total voltage in one phase is sum of EA and Estat :

V E + E and B B + BVφ = EA + Estat and Bnet = BR + BS

The angle of Bnet coincide with angle of Vφ shown in fig (d)fig (d)

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To model the effect of armature reaction, note:E li l f 90 b hi d l fEstat lies at an angle of 90◦ behind plane of maximum current IA

E directly proportional to I and X isEstat directly proportional to IA and X is constant of proportionality

Estat = -j X IA

voltage in one phase Vφ = EA - j X IA

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The output voltage of the generatorFactors that affect the output voltage (Vφ):

Armature reaction: Field created by the stator orarmature currents.Self-inductance and resistance of the statorwindings.

These can be modeled by an inductivereactance and resistance in series with the“internal generated voltage”

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Stator self-inductance named LA (its reactance X ) and stator resistance is R :XA) and stator resistance is RA :

Vφ= EA- jXIA- jXAIA- RAIAφ

Armature reaction & self-inductance in machineArmature reaction & self inductance in machine both represented by reactances, normally they are combined to a single reactance as :

XS = X + XA

V = EA- jXSIA- RAIAVφ EA jXSIA RAIA

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Equivalent model of a 3φ synchronous generatorgenerator

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The per-phase equivalent circuit and phasor diagramsphasor diagrams

How does V /Ε vary with the load type?How does Vφ/ΕΑ vary with the load type?9:54 PM 19

Synchronous GeneratorsPower and TorquePower and Torque

Not all mechanical power goes to a h b l i lsynchronous generator becomes electrical

powerThe difference between input & output power represent the losses.

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Synchronous Generators Power and TorqueThe input mechanical power is the shaft power in the synchronous generator

PPin = τapp ωm

The power converted from mechanical to electrical fform

Pconv = τind ωm

3E I= 3EA IA cos γwhere γ is the angle between EA and IA)The difference between Pin and Pconv in generator represents mechanical, core, and stray losses of the

himachine 9:54 PM 21

Synchronous Generators Power and TorqueTh l l t i l t t f h t iThe real electrical output power of synchronous generator in line quantities:

Pout=√3 VT IL cos θout T Lin phase quantities:

Pout= 3 Vφ IA cos θ

The reactive power output:Q =√3 V I sin θQout=√3 VT IL sin θ

in phase quantities:p qQout= 3 Vφ IA sin θ

Ignoring the armature resistance RA (XS >> RA), a useful l ti b d i d t i t th t t frelation can be derived to approximate the output power of

the Generator.9:54 PM 22

Synchronous Generators Power and Torque

To derive that useful equation with the statorTo derive that useful equation with the stator resistance ignored, a simplified phasor diagram is usedis used

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The vertical segment bc is EA sinδ or XS IA cos θIA cos θ = EA sin δ / XS

Substituting this in the equation of Pout

Pout = (3Vφ EA sinδ) / XS

Since resistances assumed zero, no electrical losses in the generator and Pconv = Pout

Th b ti h th t th d d bThe above equation shows that the power produced by a the generator depends on the angle δ (between Vφ and EA), the torque angleA), q gMaximum power that the generator can supply occurs when δ = 90◦.

Pmax = (3Vφ EA ) / XS9:54 PM 24


From chapter 4, torque developed in a generator can be expressed as:

τind= k BR × BS

τind= k BR × Bnet

Magnitude of torque in this equation is:τind= k BR Bnet sin δind R net

δ is the angle between the rotor field and the net magnetic field Since BR produces voltage EA, and Bnet produces Vφ, the angle δ between EA and Vφ is same as angle b t B d Bbetween BR and Bnet

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Alternative expression for this torque in syn. Gen is deri edGen. is derived Using Pconv= τind ωm

Ad

EV3 δτ φ sin

=

This equation gives torque in terms of circuitSm

ind Xωτ =

This equation gives torque in terms of circuit parameters.

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Measurement of Synchronous Generator Model ParametersModel Parameters

Main parameters: IF × EA relationship, XS and RA.

Open-circuit test → EA= VT

Short-circuit test → A2S

2AS I

EXRZ =+=

Since XS >> RA,

AI

ocAS I

VIEX ,φ=≈,

DC voltage test in the armature AA II

DCA I

VR2 =V

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DCI

DC

DCA I2

VR =

Measurement of Synchronous Generator Model ParametersModel Parameters

EA from the open circuit test and IA from the shorti i k h d fi ld I

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circuit test are taken at the rated field current If, rated

The Effect of Load Changes on a Synchronous Generator Operating AloneSynchronous Generator Operating Alone

For EA constant, if the load changes, the voltage drop X d V l hacross XS and Vφ also change →

How can Vφ be regulated? By varying If9:54 PM 29

Synchronous Generator

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