Synchronous machines - geuzaine/ELEC0431/3_ machines 1 Synchronous machines Turbo -alternator...

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Transcript of Synchronous machines - geuzaine/ELEC0431/3_ machines 1 Synchronous machines Turbo -alternator...

  • Synchronous machines 1

    Synchronous machines

    Turbo-alternator Saliant poles

    p/=!Rotor (inductor) : 2p poles with excitationwindings carrying DC current; non-laminated magnetic material

    Stator: polyphase (e.g. 3-phase) windingin slots; laminated magnetic material

    Synchronous generator (alternator): transforms mechanical energy into electric energy;designed to generate sinusoidal voltages and currents; used in most power plants, for caralternators, etc.Synchronous motor: transforms electric energy into mechanical energy; used for high-power applications (ships, original TGV)

    ...

    01/03/2018

  • 2

    No-load characteristic

    Evolution of the voltage Ev in a stator phasevs. intensity of the excitation current Ie, for agiven rotation speed and with no generatedstator current

    =

    ==

    0Iconstantevitesse

    avec)I(fE ev!

    )I(kE evEv = !

    Magnetic flux producedby the inductor and seen by the stator winding

    Non linearity with hysteresis

    due due remanent magnetization

    The rotor winding, carrying the DC current Ie and rotatingat speed /p, produces in the airgap a sliding m.m.f. Fe(as seen from the stator).

    Fe generates a magnetic flux density Br (with the samephase) in the airgap, which induces sinusoidal e.m.f.s Evin the stator windings, with a phase lag of /2.

    Synchronous machines

    average characteristicaverage characteristic

    withconstant speed

  • 3

    Vector diagram with loadDiagram of magnetomotive forces and magnetic flux densities

    resulting m.m.f. (3) = (1)+(2)

    m.m.f. from Ie(1)

    m.m.f. from I(2)

    (1) The rotor winding, carrying the DC current Ie androtating at speed /p, produces in the airgap a slidingm.m.f. Fe (as seen from the stator)..

    (2) The polyphase current I in the stator winding produces asliding m.m.mf. FI (in phase with I).

    (3) The resulting m.m.f. is Fr = Fe+FI.

    (4) Fr generates a magnetic flux density Br (with the samephase) in the airgap,, which induces sinusoidal e.m.f.s inthe stator windings, with a phase lag of /2.

    (4b)

    rB (4a)

    ee IF = IFI =and

    Synchronous machines

  • 4

    Vector diagram with loadStator leakage flux

    1tm

    3tm2tm1ti)(

    iii)t(e=

    =

    IXjE f= )(X mf =

    Slot leakage flux

    End-winding leakage flux IXjEE frt =

    IRIXjEU fr =

    0iii 321 =++

    (seen by the stator but not coming from the rotor)

    e.m.f. induced by leakage flux

    because

    with

    Stator leakage reactance

    total e.m.f.

    Resistance of stator winding

    ee IF = IFI =andIIF er +=

    IIFI erdefr

    +=

    =

    Equivalent excitation current

    Diagrams

    Er no-load e.m.f. produced by IrSynchronous machines

  • 5

    Which excitation current Ie should one impose in the synchronousmachine to reach the functioning point corresponding to a givenvoltage U and current I in the stator, with a phase shift of between U and I?

    Potier diagram

    IXjIRUE fr ++=

    (1)(0)

    (2)(3)

    (4)

    (5)

    (2)

    (3)III re

    =

    Er no-load e.m.f produced by theequivalent current Ir

    Synchronous machines

  • 6

    Reaction

    Demagnetizing reaction Magnetizing reaction

    The m.m.f. is smaller than the no-load m.m.f. (Ir < Ie)The m.m.f. is larger thanthe no-load m.m.f. (Ir > Ie)

    Inductive behaviour of the load(I lagging behind U)

    Capacitive behaviour of the load(I in front of U)

    Synchronous machines

  • 7

    Zero power factor characteristic

    Evolution of the stator voltage U as a function of theexcitation current Ie, for a given rotation speed and statorcurrent, with a zero power factor

    ==

    =

    =

    =

    )2/(0cosconstanteI

    constantevitesseavec)I(fU e

    !

    Example: = /2

    IXEU fr

    III re

    +

    Synchronous machines

    with

    speed constant constant

  • 8

    Short-circuit characteristic

    Evolution of the stator current as a function of the excitationcurrent Ie, for a given rotation speed and with the statorwindings in short-circuit

    =

    ==

    0Uconstantevitesse

    avec)I(fI e!

    IXjIRE fr +=

    IXjIRUE fr ++=

    0U =with

    rr IE =

    IXE fr

    III re

    +

    ef

    IX

    I

    +

    Non saturatedmachine

    Synchronous machines

    with speed constant

  • 9

    When the magnetic materials are not saturated, the combined effectof the reaction and of stator leakage fluxes can be taken intoaccount thanks to a single parameter: the synchronous reactance

    Simplified vector diagramBehn-Eschenburgs method Synchronous reactance Xs

    constanteIE

    IE

    r

    r

    e

    v ==

    Synchronousreactance

    IXjIRUE sv ++=

    Synchronous machines

    constant

    Equal angles OAB and AOB

    Similar triangles OAB and OAB

    A, B and C colinear

  • 10

    Experimental determination of XsBehn-Eschenburgs method Synchronous reactance Xs

    )I(I)I(EXecc

    evs

    ( ) ccsv IXjRE +=

    cc

    vs IEXjR =+ sXR

  • 11

    Exterior characteristic

    Evolution of the voltage U on a given stator phase as a function of the current Iin thisphase, when the alternator drives a load characterized by a constant power factor, atconstant speed and excitation

    =

    =

    =

    =

    constantecosconstanteI

    constantevitesseavec)I(fU e

    !

    Alternator exterior characteristic

    Synchronous machines

    with constant

    constant constant

    speed

  • 12

    Economical organization of power production + Stability of thenetwork despite local defects

    Network connectionNeed for interconnection of electric power plants

    Synchronization of an alternaltor on an ideal (infinitely powerful) AC network

    Large number of production units in parallel constant voltage and frequency

    s

    vXjRUEI

    +

    =

    The current should be zero when the connection is made 4 conditions

    1. same pulsation (correct rotation speed)2. same amplitudes for Ev and U (adjusting Ie)3. no phase shift between Ev and U4. identical phase ordering (in a 3-phase system)

    Daily peak

    Daily load

    Synchronous machines

  • 13

    Behaviour with load

    = cosIU3PPelm

    =

    = cosIUp3

    p/PC

    intv

    ssinEcosIX

    =

    intvs

    sinEUXp3C

    =

    Internal angle

    Electromagnetic power

    Torque

    The variations of the rotormechanical angle mec areproportional to the variations of theinternal (electric) angle int

    After network synchronization, there is no exchanged current.Then :

    If mechanical power is provided to the alternator,Ev gets ahead of U int increases (until the equilibrium ofthe electromagnetic and mechanical torques)

    If a braking torque is applied to the alternator, Ev gets behind U int decreases (negative torque)

    pint

    mec

    =

    Active electric power

    Internal angle

    Synchronous machines

    Stat

    ic in

    stabi

    lity

    St

    atic

    stab

    ility

  • 14

    Behaviour with loadStatic stability

    0int >0int

  • 15

    Behaviour with loadPower diagram

    elmsss

    s PU3XP

    U3XcosIU3

    U3XcosIXMB ====

    QU3XsinIU3

    U3XsinIXB'O sss ===

    Active power P

    Reactive power Q

    Alternator

    Motor

    Synchronous machines

  • 16

    V-curves (Mordey curves)Evolution of the stator current I as afunction of the excitation current Ieof a synchronous machine connectedto an ideal network, at constantactive power

    Constant active power

    Over-excitedmachine

    under-excited machine

    "V"

    Network= inductive loadMachine = capacitif system

    > 0

    > 0 ...

    Synchronous machines

    static stability limit