Synchronous machines - geuzaine/ELEC0431/3_Synchronous.pdfSynchronous machines 1 Synchronous...
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Synchronous machines 1
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)
Evolution of the voltage Ev in a stator phasevs. intensity of the excitation current Ie, for agiven rotation speed and with no generatedstator current
)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.
average characteristicaverage characteristic
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.
ee IF = IFI =and
Vector diagram with loadStator leakage flux
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
Stator leakage reactance
Resistance of stator winding
ee IF = IFI =andIIF er +=
Equivalent excitation current
Er no-load e.m.f. produced by IrSynchronous machines
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?
IXjIRUE fr ++=
Er no-load e.m.f produced by theequivalent current Ir
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)
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
Example: = /2
speed constant constant
Evolution of the stator current as a function of the excitationcurrent Ie, for a given rotation speed and with the statorwindings in short-circuit
IXjIRE fr +=
IXjIRUE fr ++=
rr IE =
with speed constant
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
IXjIRUE sv ++=
Equal angles OAB and AOB
Similar triangles OAB and OAB
A, B and C colinear
Experimental determination of XsBehn-Eschenburgs method Synchronous reactance Xs
( ) ccsv IXjRE +=
vs IEXjR =+ sXR
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
Alternator exterior characteristic
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
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)
Behaviour with load
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)
Active electric power
Behaviour with loadStatic stability
Behaviour with loadPower diagram
U3XsinIXB'O sss ===
Active power P
Reactive power Q
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
Network= inductive loadMachine = capacitif system
> 0 ...
static stability limit