Synchronous Generators

Introduction

• source of all the electrical energy

• largest energy converters

• Convert mechanical energy into electrical energy up to 1500 MW

Commercial Synchronous Generator• Stationary –field synchronous generator

• same appearance as dc generator

• salient poles – create the dc field, cut by a revolving armature

• Armature possesses a 3-phase winding – connected to 3 slip ring mounted on shaft

• a set of brush sliding on the slip ring – connected to an external 3-phase load

• as the armature rotates, 3-phase voltage is induced – depend upon a speed of rotation and dc exciting current in the stationary poles

• frequency of the voltage – depend upon the speed and number of poles on the field

Commercial Synchronous Generator

• Revolving –field synchronous generator

• stationary armature called stator

• 3-phase stator winding is connected to the load

• stationary stator – easier to insulate the winding – not subjected to centrifugal forces

Number of poles

• Depends upon the speed of rotation and the wanted frequency

f = pn / 120

f = frequency of the induced voltage

p = number of poles on the rotor

n = speed of the rotor

Example

A hydraulic turbine turning at 200 r/min is connected to a synchronous generator. If the induced voltage has a frequency of 60 Hz, how many poles does the rotor have?

Stator – main features

• identical to that of 3-phase induction motor

• composed of cylindrical laminated core

• wye connection on windings

• voltage per phase is only 1/√3 (58%) of the voltage between the lines

• the highest voltage between a stator conductor and grounded stator core is 58% of the line voltage

• reduce the number of insulation in the slot

• increase the cross section of the conductors – larger conductor increases the current – increase the power output

• avoid line to neutral harmonics

Rotor – main features

• two types:

• salient poles

• cylindrical rotors

• Salient poles

• mounted on a large circular steel frame which is fixed to a revolving vertical shaft

• made of bare copper bars – ensure good cooling

• Cylindrical rotors

• long rotor, solid steel cylinder, contains a series of longitudinal slot

No-load saturation curve

• Ix – current to produce a flux in the air gap

• Ix gradually increased

• small value of Ix, Eo changes proportionally

• as the iron begins to saturate, the voltage rises much less

No-load saturation curve

Synchronous Reactance

• N1 and N2 is not connected as the load is balanced

Synchronous Reactance

• the field carries an exciting current, produces flux as the field revolves, the flux induces in the stator• each phase of the stator possesses a resistance R and inductance L

Xs = 2πfL

Xs = synchronous reactancef = generator frequencyL = apparent inductance of the stator

Synchronous Reactance

• simplified circuit – per phase• R (winding resistance) is neglected• Ix – produces the flux which induces the internal voltage Eo• E – voltage at the terminal of the generator – depend on Eo and Z• E and Eo – line to neutral voltage• I – line current

Determining the value of Xs

• open circuit and short-circuit test• the generator is driven at rated speed• exciting current is raised until the rated line to line voltage is attained• exciting current Ixn and line to neutral En is recorded• the excitation is reduced to zero and the three stator is short circuited together• the generator is running at rated speed, the exciting current is gradually raised to Ixn• resulting short circuit current Isc in the stator is measured

Xs = En / Isc

Xs = synchronous reactanceEn = rated open circuit line to neutral voltageIsc = short circuit current

Example

A 3-phase synchronous generator produces an open circuit line voltage of 6928 V when the dc exciting current is 50 A. The ac terminals are then short circuited, and the three line currents are found to be 800 A. Calculate

• the synchronous reactance per phase• the terminal voltage if three 12 Ω resistors are connected in wye across the terminals

Synchronous generator under load

• types of load applied to the generator• Isolated loads• Infinite bus

• in order to construct the phasor diagram for this circuit, following fact applies:• Current I lags behind terminal voltage E by an angle θ• cos θ = power factor of the load• voltage Ex across the synchronous reactance leads current I by 90o.• Ex = jIXs• voltage Eo generated by the flux is equal to the phasor sum of E plus Ex• both Eo and Ex are voltages that exist inside the synchronous generator windings and cannot be measured directly• flux is that produced by the dc exciting current Ix

Synchronous generator under load

• lagging power factor load •Eo leads E by δ degrees

• leading power factor load •Eo leads E by δ degrees

Example

A 36 MVA, 20.8 kV, 3-phase alternator has a synchronous reactance of 9 Ωand nominal current of 1 kA. No-load saturation as figure below. The excitation is adjusted so that the terminal voltage remain fixed at 21 kV, calculate the exciting current required and draw the phasor diagram for:

• no-load• resistive load of 36 MW• capacitive load 12 Mvar

Synchronization of a generator

• Connecting two or more generators in parallel to supply a common load• the load varies depend on power demand• the selected generators are temporarily disconnected if the demand falls• the generators must be synchronized• synchronization achieved when:

• the generator frequency is equal to the system frequency• the generator voltage is equal to the system voltage• the generator voltage is in phase with the system voltage• the phase sequence of the generator is the same as that of the system

• to synchronize:• adjust the speed regulator of the turbine so that the generator frequency is close to the system frequency• adjust the excitation so that the generator voltage Eo is equal to the system voltage E• observe the phase angle between Eo and E using synchroscope• the line circuit breaker is closed – connecting the generator to the system

Active power delivered by the generator

P = EoEsinδ/Xs

P = active powerEo = induced voltageE = terminal voltageXs = synchronous reactanceδ = torque angle between Eo and E

Example

A 36 MVA, 21kV, 1800 r/min, 3-phase generator connected to a power grid, has a synchronous reactance of 9 Ω per phase. If the exciting voltage is 12kV (line to neutral) and the system voltage is 17.3 kV (line to line), calculate:

• active power which the machine delivers when the torque angle is 30o

• the peak power that the generator can deliver before it falls out of step (loses synchronization)

Power transfer between two sources

• Only interested in the active power transmitted from source A to B or vice versa• E1 = E2 + jIX• I lags behind E2 by θ•E1 leads E2 by δ• IX leads I by 90o

• active power absorbed by B:P = E2Icosθ

• IX/sinδ = E1/sinψ= E1/sin (90 + θ)= E1/cos θ

• Icosθ = E1sinδ/X

P = E1E2sinδ/X

Power transfer between two sources

• Example

• Referring to the figure, source A generates a voltage E1 = 20 kV /50o and source B generates a voltage E2 = 15kV / 42o . The transmission line connecting them has an inductive reactance of 14 Ω. Calculate the active power that flows over the line and specify which source is actually a load