Synchronous Machines

Synchronous machine with uniform air-gap and an excitation winding on rotor: Rotor is of cylindrical construction, with an excitation winding placed on rotor.. It is important to stress

SYNCHRONOUS MACHINES

Synchronous machines come in a variety of different constructions and designs Thedifferences occur in the physical outlay of the rotor and in the way in which excitation flux isprovided (if it is provided at all) in the machine Regardless of the type however, all thesynchronous machines have the same construction of the stator Stator is of cylindrical cross-section, manufactured from laminated sheets of steel, and it carries a three-phase winding that

is supplied with (in the motor case) or that produces (in the generator case) a system of phase voltages The three windings that constitute the stator three-phase winding are displaced

three-in space by 120 degrees around the circumference of the machthree-ine Three-phase voltages havethe phase displacement of 120 degrees

Synchronous machines are the main work-horse of the electricity generation industry.They are used as generators in all the hydro, nuclear, coal-fired, gas-fired and oil-fired powerplants This means that a synchronous generator is a standard machine used for conversion ofmechanical energy into electric energy in all the power plants that rely on conventional energysources Rated powers of synchronous generators are typically from a few megawatts up to afew tens of megawatts, or even a several hundreds of megawatts Synchronous machines areused as motors as well In this case rated power of a synchronous motor is either relativelyvery low (up to few kilowatts) or is in the high power region, from around 150 kW to 15 MW

In between, induction motors are used as a rule, due to their numerous advantages in thispower region

The two types of synchronous machines that are relevant for the discussion that followsare:

1 Machines with uniform air-gap and excitation winding on rotor

2 Machines with non-uniform air-gap and excitation winding on rotor.Rotor cross-section in these two types differs and leads to different mechanisms oftorque production Both machine types are used for both generating and motoring application

In the machine with uniform air-gap torque is produced solely due to interaction between therotor and stator windings (fundamental torque component) In the machine with non-uniformair-gap, there are two torque components: fundamental torque, produced by the interactionbetween the stator and rotor windings, and reluctance torque component that is theconsequence of the non-cylindrical rotor cross-section Since the rotor is not cylindrical, statorwindings see an air-gap of variable length as rotor rotates Consequently, magnetic reluctance

is variable and all the inductances of the stator windings are functions of the rotor position.Reluctance torque component is therefore produced, in addition to the fundamental torquecomponent

Synchronous machine with uniform air-gap and an excitation winding on rotor:

Rotor is of cylindrical construction, with an excitation winding placed on rotor Theexcitation winding is supplied with a controllable DC current Since the rotor rotates, this DC

current has to be supplied somehow from the stationary outside world In the past, slip ringsand brushes were used to connect a stationary DC source to the rotating rotor winding.Nowadays, so-called brushless excitation systems (or just brushless exciters) are used (theseare beyond the scope of interest here) Synchronous machines with uniform air-gap andexcitation winding on rotor are often termed turbo-machines They are used both for motoringapplication and for generation in coal-, oil-, and gas-fired plants and nuclear plants Typicalnumber of magnetic pole pairs is one or two, so that the so-called synchronous speed ofrotation is 3000 rpm or 1500 rpm for 50 Hz stator frequency Synchronous speed is defined as

and this is the so-called mechanical synchronous speed of rotation (that is, actual speed of

rotation) Symbol P stands for the number of magnetic pole pairs (each pole pair consists of

two magnetic poles, one north and one south)

Rotor of a turbo-machine carries, apart from the excitation winding, a short-circuitedmulti-phase winding similar to the squirrel-cage winding of an induction motor The existence

of this winding is crucial for motoring applications since, without it, the machine would not becapable of starting when connected to a three-phase supply on stator side It is importanthowever to emphasise that this winding has no impact on steady-state operation, since nocurrents exist in the short-circuited rotor winding (often called damper winding) in steady-state The damper winding is important in generation as well, since it has an important roleduring transients Once again, however, it has no impact on steady-state operation and istherefore omitted from the schematic representation of a synchronous turbo-machine in Fig 1,where only excitation winding is shown on rotor Stator three phase winding is shown in Fig 1with three concentric turns

It is important to stress once more that an electromagnetic torque in a synchronousmachine with uniform air-gap is produced purely due to the interaction between the statorcurrents and the rotor flux (that stems from the DC current in the rotor winding) The torqueconsist therefore entirely of the fundamental torque component, very much the same as thecase is with other uniform air-gap machines (DC machines, induction machines) According tothe condition of average torque existence, zero frequency in rotor means that the statorfrequency must equal the frequency of rotation Rotor flux, produced by rotor DC current, isstationary with respect to rotor However, as rotor rotates at the frequency of stator supply,rotor flux seen from the stator rotates at the same, synchronous, speed as does the statorrotating field created by the system of stator three-phase currents Hence all the fields in asynchronous machine rotate at the same, synchronous speed Moreover, rotor rotates at thesynchronous speed as well Note that for the constant frequency of stator voltages there is asingle speed at which the machine can rotate This means that, regardless of the loading, asynchronous machine rotates at a constant speed This is in huge contrast to some other types

of electric machines (DC machines, induction machines) where the speed of rotation isdependent on the loading of the machine

Synchronous machine with non-uniform air-gap and excitation winding on rotor:

As already noted, if the air-gap is not uniform, magnetic reluctance (resistance) seen bywindings will vary In synchronous machines with non-uniform air-gap stator remains to becylindrical, but the rotor is not Consequently, magnetic reluctance seen by stator windings willvary as the rotor rotates This gives rise to dependence of stator inductances on instantaneousrotor position and leads to creation of the second torque component, not present in uniform

air-gap machines (reluctance torque component) Since the machine contains an excitationwinding, then a fundamental torque component exists as well, so that the total torque is a sum

of the fundamental torque component and the reluctance torque component

Fig 1 - Synchronous machine with uniform air-gap and excitation winding on rotor.

The structure of the machine is shown in Fig 2 The rotor is of so-called salient-polestructure and the machine is usually used for very low speed of rotation, so that the number ofpoles is very high (say, 84 poles - that is, 42 pole pairs, is a rather common structure) Themachine of Fig 2 is shown as being of 2-pole structure for simplicity This type of synchronousmachines is often called hydro-machine or salient-pole synchronous machine, since thesemachines are used in hydro-powered electric generation plants The machine is used inmotoring application as well, for those cases where a low speed of rotation is required

Rotor of a hydro-machine carries, apart from the excitation winding, a short-circuitedmulti-phase winding similar to the squirrel-cage winding of an induction motor (this winding isnot shown in Fig 2) This is very much the same as for a turbo-machine This winding oncemore has no impact on steady-state operation, since no currents exist in the short-circuitedrotor winding in steady-state (there is not any induced emf, since the rotor rotates at the samespeed as does the stator rotating field)

As already noted, synchronous machines are used as motors either for low powerapplications or for very high power applications In the low power range the advantage ofsynchronous motors is their fixed synchronous speed of rotation that is always governed by theapplied frequency in stator winding In other words, speed of rotation depends only on statorfrequency and it is load independent, in contrast to DC motors and induction motors As far asthe high power region is concerned, the advantage of synchronous motors over the inductionmotors is that they are capable of producing reactive power (while induction motors alwayshave to consume reactive power) The higher capital cost of a synchronous motor, whencompared to an induction motor of the same size, is thus offset by the capability of the machine

to satisfy its own reactive power needs and, if necessary, to delivery reactive power to the grid(it is important to realise that reactive power is not for free; industrial customers are chargedfor the consumed reactive power)

In what follows, only the synchronous machines with uniform air-gap will beelaborated The reason is that an analysis of synchronous machines with non-uniform air-gap ismore involved, due to the existence of the reluctance torque component

The concept of the rotating fields is reviewed next This is followed by an explanation

of the mechanism of the reactive power production in a synchronous machine Motoring mode

of operation and the generating mode of operation are then discussed in two separate sections

b c a

Fig 3 - Individual phase m.m.f.’s of a three-phase winding.

One observes that in terms of spatial dependence, all the three individual phase motive forces are stationary and they act along the defined magnetic axis of the winding From(3) one notices that each of the three m.m.f.’s is varying in time The values of the three phasem.m.f.’s in the given instant of time correspond to those met in any three phase system.

magneto-The resultant magneto-motive force that stems from the three phase system of currentsflowing through spatially displaced windings is the sum of the individual contributions of thethree phases The summation is done in the cross-section of the machine, and it is necessary toobserve the spatial displacement between the three m.m.f.’s One may regard the cross-section

of the machine as a Cartesian co-ordinate system in which phase a magnetic axis corresponds

to x-axis, while y-axis is perpendicular to it For the purposes of calculation this co-ordinatesystem may be treated as a complex plane, with x-axis corresponding to the real axis, and y-axis corresponding to the imaginary axis In terms of the complex plane, spatial displacement

of the m.m.f by 120 degrees corresponds to the so-called ‘vector rotator’, a= exp(j2 π / 3).Hence the resultant magneto-motive force can be written as

1 1

magneto-Im ωt=90°

ωt=135° F res ωt=45°

ωt=0°

Re (a) 1.5NI m

Fig 4 - Resultant field in the three-phase machine for sinusoidal supply conditions.

Since the rotor winding carries excitation current, a field is produced by this current.This field is stationary with respect to rotor Since the rotor rotates at synchronous speed,then, looking in from stationary stator, this rotor field rotates at synchronous speed This isalways the case in any multi-phase AC machine: regardless of whether the rotor rotatessynchronously or asynchronously, all the fields in the machine rotate at synchronous speed

Since the resulting m.m.f is responsible for the resulting flux density and ultimatelyresulting flux, this means that apart from the rotating m.m.f., there is a rotating flux densitywave and a rotating flux in the machine as well The term rotating field in general denotes any

of the three

In other to show how a synchronous machine can produce reactive power, consider theoperation of a synchronous motor The motor will always consume real power; however, it caneither generate or absorb reactive power Let us further consider a couple of characteristicsituations Let us assume at first that a synchronous motor operates under ideal no-loadconditions, so that all the losses in the motor can be neglected This means that the input realpower and the output mechanical power are both zero Such an ideal situation is useful inexplaining the reactive power production and consumption

Suppose at first that the rotor current is zero Therefore the rotor does not produce anyrotating field Rotating field of the stator is generated due to current flow in stator and thestator rotating field equals the total rotating field of the machine (total field is a vectorial sum

of the field generated by the stator currents and the rotor field; it is fixed since the supplyvoltage is fixed, and does not depend on individual values of the rotor and stator fields) Sincerotor current is zero, there is not an induced emf in the stator winding due to rotor flux Underthese conditions the machine behaves like a pure reactance and consumes reactive power Thesituation is illustrated in Fig 5a, where total field and stator rotating field are shown for oneinstant in time If the reactance of a stator phase winding is Xs, then the current in one phase is

I = V/Xs, where V is the rms of the phase to neutral voltage Hence the reactive powerconsumed by the machine is Q = 3 V I = 3V2/Xs

Suppose next that rotor current is now increased to a certain value, say, such that theemf in the stator winding equals one half of the applied phase to neutral voltage The situation

is illustrated in Fig 5b The stator field is now just one half of the value for zero rotor current,since one half of the total field is provided by rotor The current in stator is I = (V - E) /Xs, and

since E is 0.5V, then I = 0.5V/Xs Consequently, reactive power consumed by the machinebecomes Q = 3 V I = 1.5V2/Xs The consumed reactive power is just one half of what it wasoriginally.

Let the rotor current be now exactly such that the induced emf in stator due to rotorflux equals applied voltage This means that the total field exactly equals rotor field and, sincethere is not any current in stator, stator field is zero (Fig 5c) As the stator current is zero, themachine now neither consumes nor delivers the reactive power

Finally, let the rotor current be further increased, so that the induced emf becomes1.5V The corresponding rotor filed is now larger than the total field and consequently statorfield has to change the direction (Fig 5d) This means that the stator current now flows fromthe machine towards the grid, i.e I = (V - E) /Xs= -0.5V/Xs Hence the reactive power is nowequal to Q = - 1.5V2/Xs, where negative sign indicates that the reactive power is delivered tothe grid rather than being absorbed

In all the cases discussed so far stator current was purely reactive and the reactivepower was either taken from or delivered to the grid If a synchronous machine absorbsreactive power it is said that it operates in under-excited mode If a synchronous machinedelivers reactive power to the grid, it is said that it operates in over-excited mode These twoterms are exclusively related to the reactive power balance of the machine One notes that forall these cases the angle between the total rotating field and the rotor rotating field in themachine is zero

Suppose now that the synchronous motor drives a load torque Hence it deliversmechanical power at the shaft and consequently consumes real (active) power at stator windingterminals Let the rotor current be such that the machine is in over-excited mode (Fig 5d).What now happens is that an angular displacement occurs between the rotor field and totalfield This angle is called load angle and it is illustrated in Fig 6, where motoring operation inover-excited mode is depicted This load angle will appear in the phasor diagram later on Aswill be shown, power delivered by a synchronous motor directly depends on the value of thisangle

On the basis of considerations in the previous section, it is easy to derive an equivalentper-phase representation of the synchronous motor The applied stator phase to neutral voltage(note that the value given is always line to line voltage and that stator winding of asynchronous motor is always connected in star) can be represented with a correspondingphasor This voltage phasor corresponds to the total field in Fig 6 Rotor current causes rotorflux, that rotates at synchronous speed and therefore induces an emf in the stationary statorwinding This emf corresponds to the rotor field in the Fig 6 Hence, in phasor diagram, theangle between the grid voltage and the induced emf will be equal to the load angle of Fig 6.Thus equivalent circuit contains an internal voltage source (induced emf) and the externalapplied voltage In between is the stator reactance of the machine, called synchronousreactance Stator winding resistance can usually be neglected and it is omitted from all thefurther considerations Furthermore, iron loss (that takes place in stator core) and mechanicalloss will be neglected as well, so that under these idealised conditions input active powerequals output mechanical power Equivalent circuit of a synchronous motor with excitationwinding on rotor and uniform air-gap is shown in Fig 7

Fig 5 - Illustration of rotating fields in a synchronous motor (for ideal no-load conditions)

for four different values of the rotor current.

Fs

δ ω

The following phasor equation follows directly from Fig 7:

E jX I s

The phasor diagram, that this equation describes, is drawn in Fig 8 for two cases: operation inthe under-excited mode when the power factor is lagging (since the machine consumes reactivepower) and operation in the overexcited mode when the power factor is leading (since themachine consumes active power but simultaneously delivers reactive power to the grid)

Fig 8 - Phasor diagram for motoring operation in under-excited and overexcited modes.

Phasor diagrams of Fig 8 are used most frequently to determine the unknown loadangle and the induced emf on the basis of the known motor loading and stator terminalconditions They simultaneously represent the starting point in deriving the so-called load anglecharacteristic of a synchronous motor Consider the phasor diagram of Fig 8 for overexcitedmode, that is for convenience re-drawn in Fig 9 Due to the correlation that exists, oneimmediately recognises that the angle BCA is equal to the power factor angle (angle betweencurrent and voltage phasors) On the other hand, angles ODA and ABC are right angles Whensolving the phasor diagram of Fig 9, it is much easier to use one of the two triangles (triangleODC or triangle OBC) and project the phasors on the sides of these two triangles, than todirectly solve the complex phasor equation (7)

In order to obtain the load angle characteristic of a synchronous motor one considersthe triangle OBC in Fig 9 By projecting the phasors on sides OB and CB one has

Fig 9 - Phasor diagram for derivation of load angle characteristic.

When terminal voltage, stator current and the power factor are known, these two equationsenable simple calculation of the load angle and the induced emf However, for the purpose ofderiving the load angle characteristic one expresses the active stator current component fromthe second equation of (8) as

The correlation between real (or output) power and load angle is called load anglecharacteristic of a synchronous motor One observes from (11) that, for the given statorvoltage and rotor current (that is, emf) power depends only on the sine of the load angle Thismeans that, higher the load is, higher the value of the load angle will be, and vice versa Inother words, rotor field in Fig 6 will lag the total field more and more as the loading of themachine increases

The maximum power that a synchronous motor can deliver is met when load angleequals 90 degrees Hence, for each rotor current setting (that is, for each value of the emf)there is a maximum power that the motor can deliver The maximum power is

Torque of the motor can be directly obtained from the load angle characteristic bydividing the power with the mechanical synchronous angular speed of rotation:

VE X

f

VE X

Hence the motor torque dependence on load angle is the same as for the power The scalingfactor is the constant, synchronous mechanical angular speed of rotation.

Load angle characteristics of a synchronous motor are illustrated in Fig 10, for acouple of values of the rotor current (i.e emf) An increase in the rotor current causes anincrease in the induced emf Consequently, for the given load, the load angle decreases Anincrease of the rotor current leads to an increase in the maximum power (maximum torque)that the motor can develop

Fig 10 - Load angle characteristic of a synchronous motor.

Reactive power characteristic of the motor can be derived in exactly the same way asthe active power characteristic Consider the phasor diagram for under-excited operation, that

is for convenience re-drawn in Fig 11 The following two equations now correspond to (8):

X

VE X

from (15) that reactive power is positive (i.e absorbed) as long as V > Ecosδ The reactive

power is zero when V = Ecosδ and it becomes negative (i.e the motor delivers reactive power

to the grid) when V < Ecosδ Reactive power characteristic is illustrated in Fig 12

Fig 11 - Phasor diagram of a synchronous motor for under-excited operation.

It is easy to observe in Fig 12 that the reactive power may be both positive andnegative for the given value of the induced electro-motive force (i.e rotor current) Whetherthe reactive power is delivered or absorbed will depend on the loading of the motor, since theload at the shaft determines how much the load angle is The internal reactive powerproduction of a synchronous motor is at maximum value when load angle is zero Thissituation corresponds to the no-load operation, that is not normally met when the machine isused as a motor However, this fact is made use of in so-called synchronous condensers thatare exclusively used for reactive power production and delivery to the grid A synchronouscondenser is in essence a synchronous motor that operates at all times under no loadconditions The load angle, although not exactly zero since there are losses in the machine (thatwere neglected throughout here) is very small, so that the machine produces maximum possibleamount of reactive power Synchronous condensers are essentially reactive power generatorsand they are installed at various points in a power system to provide the necessary reactivepower support

Generating mode of operation is discussed in the subsequent section In principle, allthe characteristics remain valid, but one has to take into account that the active power will now

be produced and delivered to the grid, rather than absorbed This fact does cause someinevitable differences,, especially in terms of the phasor diagrams