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**Introduction**

• Rotating machines that rotate at a speed fixed by the supply frequency and the number of poles are called synchronous machines.

• Three phase synchronous machine is a doubly excited ac machine its field-winding is energized from a dc source i.d. DC exciters, static excitation etc. and Armature winding is connected to an ac source.

• Under steady state conditions, operating speed of synchronous machine depends on the frequency of armature current and number of field poles.

• Synchronous speed

Where P = No. of fields poles

n_{s} = rotor speed in rps (called synchronous speed)

f = frequency of armature current

**Remember:**

• In synchronous machine 3 - ø armature winding is on stator and field winding on rotor.

**Constructional Features**

- In synchronous machines, the armature winding either exports ac power (synchronous generator) or imports ac power (synchronous motor), whereas the field winding is always from a dc source.
- An ac generator, alternator or synchronous generator may have either rotating field poles and stationary armature, or rotating armature and stationary field poles.
- Advantage of providing the field winding on rotor and armature winding on the stator:
**More Efficient:**With armature winding on the stator and field winding on the rotor only two slip rings are required in a synchronous machine.**Better Insulation:**Stationary armature windings can be insulated satisfactorily for higher voltages.**Efficient Cooling:**Stationary armature winding can be cooled more efficiently.**More Output :**Low-power field winding on the rotor gives a lighter rotor and therefore, low centrifugal forces. In view of this, higher rotor speeds are permissible, thus increasing the synchronous machine output for given dimensions.**Lesser Rotor Weight Inertia:**Field winding on the rotor requires less amount of copper and insulation. This reduces overall weight of rotor and its inertia.**Rigid and Convenient Construction:**3 - ø armature winding, capable of handling high voltage and high current, can be more easily braced again electromagnetic forces when it is placed in stator slots.

- Synchronous machines are of two types depending upon the geometrical structure of the rotor:
- salient-pole type.
- cylindrical-rotor, round-rotor or non-salient pole type.

**Remember:**

• The field winding on the salient poles is a concentrated winding.

• In case of cylindrical rotor, the field winding is a distributed winding housed in the rotor slots.

• The salient pole synchronous machines have non-uniform air gap.

- Under the pole centres it is minimum
- In between the poles, the air-gap it is minimum

• In cylindrical rotor synchronous machine, the air-gap is uniform throughout, neglecting the slot-openings.

• Synchronous generators are usually of 3 - ø type because of the several advantage associated with 3 - ø generation, transmission and high-power utilization.

• For the generation of 3 - ø voltage, at least three coils (one coil per phase), phase displaced by 120 electrical degrees in space, are required.

• Oil engines to fewer number of poles, say 2 or 4.

**Generated EMF**

In this type of machines, air-gap flux is constant in amplitude.

**Armature winding**

• The generated emf in any one phase of a synchronous machine

- In a rotating machine, the relative motion between armature coil and flux-density wave, causes flux linking the coil to vary with time and as a result, an emf is induced in the armature coil.
- Flux ø is the total flux per pole.
- The armature winding is distributed and the reduction factor kw must appear in the emf expression.

**The Field Winding**

- The field winding of a synchronous machine is always energized with direct current. Under steady state conditions, the field or exciting current.

I_{f} = V_{f }/r_{f}

Where

V_{f }= Direct voltage applied to the field winding

and r_{f} = Field winding resistance

**FLUX AND MMF PHASORS**

**Cylindrical Rotor Synchronous Machines**

• The alternator terminal voltage at no load is made equal to its rated value by adjusting its field current.

• Generated emf lags by 90º the flux that generates it. This is indicated in Figure, where E_{f} is shown lagging ø_{f} by 90º.

• Field mmf per pole F_{f} is equal to If N_{f} . As saturation is ignored, field flux phasor ø_{f} is also indicated in phase with field mmf F_{f}.

**Case-2:** Unity pf Load

• The emf generated by ø_{f} alone is called the excitation voltage.

- When alternator is connected to 3-phase load, 3-phase generated emf in armature will give rise to 3-phase balanced currents.
- Unity pf means that armature current I
_{a}and excitation voltage are maximum at the same instant of time. - The mmf set up by armature current is called the armature-reaction mmf.
- For balanced poly-phase currents flowing in poly-phase winding, the peak value of the resultant mmf wave is along that phase-axis which carries the maximum current.
- The phasor sum F
_{f }and F_{a}gives the resultant air gap mmf F_{r}. - For generator operation, the prim mover torque must be opposite to this electromagnetic torque.
- Armature rotating mmf F
_{a}, given by equation, is proportional to armature current Ia and is therefore in phase with I_{a}. - Armature mmf F
_{a}is perpendicular to field flux ø_{f}therefore armature reaction mmf at unity pf is cross-magnetizing in nature.

**Case - 3: Zero pf Lagging Load**

• Flux created by armature mmf Fa directly opposes the field mmf F_{f}.

• E_{f} lags ø_{f }by 90º, Ia lags Ef by 90º. Therefore F_{a }lags ø_{f }or F_{f} by 180º, i.e. Fa oppose field mmf F_{f}.

• For zero pf lagging load on the 3-phase alternator, the nature of armature mmf is entirely demagnetizing in nature.

• E_{f} is shown lagging ø_{f} by 90º, Ia leads E_{f} by 90º and F_{a} is in phase with Ff so that resultant mmf F_{r }= algebraic sum of F_{f} and F_{a}.

• Flux created by armature mmf F_{a} directly aids the field mmf F_{f }or the field flux ø_{f} .

**Case 4: Zero pf Leading Load**

• For zero pf leading load on a 3-phase alternator, the armature mmf is entirely magnetizing in nature.

**Case 5 : Lagging pf Load**

• Let us consider a general case of armature current I_{a }lagging the excitation voltage by a time-phase angle ψº electrical. This means that load pf with respect to E_{f} is cos ψº lagging.

• Armature reaction mmf Fa lags behind the field mmf F_{f} by a space angle of (90+ ψº). Resultant of mmfs F_{f} and Fa gives mmf F_{r}.

• I_{a }lags E_{f} by ψº because load pf is cose ψ lagging.

**Cylindrical-rotor Synchronous Motor**

• Rotating armature mmf phasor Fa is in phase with I_{a}. Armature-reaction flux ø_{a} is also in phase with F_{a}.

• The resultant mmf F_{r} is obtained by the phasor sum of F_{a }and F_{f}, i.e.

• For motor operation, the field poles must be dragged behind the resultant air-gap flux by the retarding shaft-load torque.

Combined space and time phasor diagram with I_{a} lagging E_{f}

• When I_{a} lags E_{f} by 90º, armature current I_{a} lags the excitation emf E_{f} by 90º, the nature of armature mmf, or armature reaction mmf Fa is

- Magnetizing in case of alternator and
- Demagnetizing in a synchronous motor.

**Cylindrical Rotor Alternator**

- The flux actually existing in the air-gap of a machine is due to the resultant mmf of all the windings. The field mmf F
_{f }and armature reaction mmf F_{a}have been combined together to give the resultant mmf F_{r}, in a cylindrical-rotor synchronous machine. - The phasor addition of the two mmfs F
_{f }and F_{a}is possible because of the fact that:- These two mmfs are distributed sinusoidally along the air gap periphery and
- the relative velocity between the two mmfs is zero at synchronous speed, i.e. the stator and rotor mmfs are stationary with respect to each other.

**Note:**

• These are useful for finding out the parameters of the synchronous machines and determine their performance.

• For obtaining the open-circuit characteristic (OCC), the alternator is driven at constant rated speed and the open circuit terminal voltage is

noted as the field current is gradually increased from zero.

• The OCC is a graph between the field current If or field mmf F_{f} and the generated emf E_{f}.

• At small value of field current or F_{f}, the air gap requires almost the whole of F_{f} and mmf required by the iron is almost negligible. But when the mmf has exceeded a certain value, the iron parts require a good amount of mmf and the saturation sets in.

**Short Circuit Characteristics**

• For obtaining the short-circuit characteristics, the machine is driven at rated synchronous speed and the armature terminals are shot-circuited through an ammeter.

• Alternator during SC test operates under unsaturated conditions and as a result SCC is a straight line.

**Zero Power-Factor Characteristic and Potier Triangle**

• z.p.f.c. of an alternator is a plot between armature terminal voltage and its field current for constant values of armature current and speed.

• z.p.f.c. in conjugation with OCC, is useful in obtaining the armature leakage reactance x_{al} and armature reaction mmf F_{a}.

• For an alternator, zero-power-facto characteristic is obtained as follow:

- The synchronous machine is run at rated synchronous speed by the prime-mover
- A purely inductive load is connected across the armature terminals and field current is increased till full load armature current is flowing.
- The load is varied in steps and the field current at each step is adjusted to maintain full-load armature current. The plot of armature terminal voltage and field current recorded at each step, gives the zero-power factor characteristic at full load armature current.

• From this figure the terminal voltage V_{1} and the air gap voltage E_{r,} are very nearly in phase

V_{t} = E_{r} – I_{a}x_{aI}

• The resultant m.m.f. F_{r} and the field m.m.f. F_{1} are also related by the simple algebraic equation

**Voltage Regulation of an Alternator**

• Here E_{1} is the no-load excitation voltage and V_{t }is full-load terminal voltage at the same speed and field excitation.

• In large machines, it may not be possible to obtain the voltage regulation by actual loading, because of the cost of dissipating the huge output and also providing the large input. Certain simple tests, involving only small amounts of power, are conducted and from these, the machine constants are determined to compute the voltage regulation

**Methods for Computing Voltage Regulation****Electromotive Force (emf) Method**

• Also known as synchronous impedance method

• This method can be applied to cylindrical rotor synchronous machines only, because the resultant air-gap flux ø_{r} is not affected by the angular position of the rotor.

**Assumptions:**

• The iron par of the magnetic circuit is have constant permeability.

• As the saturation is neglected the mmf can be replaced by their corresponding fluxes and therefore, the corresponding emfs.

• Field mmf F_{f} generates E_{f }lagging it by 90º, resultant mmf Fr generates air-gap voltage E_{r }lagging it by 90º, similarly armature reaction mmf F_{a} must generate armature reactor emf E_{ar }lagging F_{a} by 90º.

• From above figure

• From above figure

Here K is the slope of the air-gap line

• The armature -reaction mmf F_{a}^{-} is in phase with, and proportional to, armature current l_{a}.

where C is a constant.

• Phasor sum of V_{t}, l_{a} r_{a} and l_{a} ×_{a}l gives air gap emf E_{r}.

• As CK has the dimension of a reactance we can assume.

• Reactance X_{ar} is due to the presence of armature reactions mmf F_{a}.

• The total equivalent reactance

X_{al} + X_{ar} = X_{s}

Where Xs is called Synchronous reactance of the cylindrical- rotor synchronous machine.

• The reactance X_{ar,} due to armature reaction mmf is called armature reaction reactance or magnetizing reactance.

**NOTE:-**

• X_{ai} is a fictitious reactance and it accounts for the voltage E_{ar} generated by armature reaction mmf F_{a}.

• The term (r_{a} + jX_{s}) = Z_{s}, is called the synchronous impedance of the cylindrical- rotor synchronous machine.

Equivalent circuit for a cylindrical rotor synchronous generator**Remember :-**

• for an alternator, the power and la flows out of the machine. For a Synchronous motor, the power and l_{a} flows into the machine.

• The synchronous motor voltage equation

**Measurement of Z _{s} and X_{s}**

• Open-circuit and short circuit characteristics are required for the determination of Z

• In open-circuit test, the armature current l_{a} is zero and V_{t }= E_{f.}

• In the short-circuit test, entire emf E_{f} is consumed in circulating the short-circuit current l_{sc}, through the synchronous impedance Z .

Equivalent circuit under short circuit test

Phasor diagram under short circuit test

**NOTE:**

• If there were no saturation, Z_{s} would be constant. Actually Z_{s} is variable and it decreases with the onset of saturation in the OCC.

Determination of synchronous impedance of an alternator

• For calculating the voltage regulation, only one value of Z_{s} can be used the lowest value of Z_{s}, obtained from the largest possible short-circuit current, is used for determining the voltage regulation

• The dc resistance r_{dc} of one phase is measured, by voltmeter ammeter method.

• If the armature winding is star connected and neutral is not available, then

• In case the armature winding is delta-connected, then

• The effective armature resistance per phase

r_{a} = (1.2 to 1.3)r_{dc}

• After r_{a} is calculated , X_{s} can be determined.

Voltage phasor Diagram

• For laggig power factor load

• For leading power factor load

• For unity power factor load

• Now the voltage regulation in percentage

**NOTE:-**

• As unsaturated value of Z_{s} is more than the saturated value, voltage regulation computed by emf method is much higher than the actual value. It is because of this reason that the emf method is called pessimistic method.

The Magnetomotive Force (mmf) method

**Assumption:**

• Each emf is replaced by an equivalent mmf (uniform air-gap and neglect of saturation.)

• The voltage equation of a synchronous machine, working as an alternator

Division of above equation by -jK converts it into an mmf equation

The field mmf F_{f }induces, in the armature winding, an emf E_{f} lagging it by 90º, similarly the mmf F_{r} must induce an emf E' lagging F_{r1} by 90º.

- armature reaction mmf in phase with l
_{a}. Here armature reaction reactance drop l_{a}X_{ar}, has been transformed into mmf F_{a}.

• From above figure

**NOTE:-**

• The mmf (F_{al}^{-} +F_{a} ) is in phase with the armature current l_{a}.

• α is the angle (i) by which l_{a }lags E' and (ii) between the normal line of F_{r1} and (F_{a} + F_{al}).

• To obtain voltage regulation by mmf method

- Plot OCC and SCC
- find and obtain the corresponding value of F
_{r1}from OCC - Find (F
_{a}+ F_{al}) from SCC - Calculate

• AC gives the required value of field mmf F_{f} which is given by the relation

corresponding to field mm F_{f} , obtain E_{f} from OCC and thus the voltage regulation of the alternator.

**Zero Power factor Method**

• The emfs are handled as voltage and the mmfs as field ampere-turns of field amperes.

• The armature reaction mmf F_{a} and armature leakage reactance X_{al} , can be determined from the potier triangle, as explained before

• is obtained and corresponding to F_{f} . excitation voltage E_{f} is recorded from OCC and the voltage regulation obtained.

**Remember:**

• Zpf method required OCC and zpfc, and gives quite accurate results.**New ASA (American standards association) method**

**NOTE:**

• This method is essentially a modification of the mmf method and gives satisfactory results both for cylindrical rotor and salient pole synchronous machines.

• New ASA method requires OCC and zpfc. Only two points A and F', are sufficient to be known on the zpfc.

• The point A is obtained by loading the overexcited alternator by an underexcited synchronous motor till full load armature current at rated voltage is flowing.

• The point F' is obtained by noting field excitation (f_{a} + f_{al} ), required to circulate full load armature current when the alternator is short-circuited.

• The armature leakage reactance X_{al} is determined from the potier reactance drop BC.

• Now determine and use the magnitude of E_{r }in obtaining the saturation effects.

O_{k} = E_{r }. This line intersects the air gap line at H and the OCC at M. The distance HM, On the field excitation scale, gives the additional excitation that must be added to the unsaturated excitation O'H, to determine the total excitation O'M = F_{f }.

• Corresponding to O'M = F_{f }= OF, excitation voltage FP = EF is read from OCC and the voltage regulation obtained.

**Saturation Synchronous Reactance Method**

• In emf and mmf methods, the saturation was neglected. But under actual operating conditions, the magnetic circuit is always in a saturated state.

• The extent of this saturation under load, can be taken into account by introducing saturation factor k.

• The saturation factor

for the same field mmf or field current.

• the synchronous reactance X_{S} has two components, X_{al} and x_{av} the leakage reactance X_{al }remains constant, because the leakage flux path is mainly is air and is almost unaffected by saturation.

• The armature reaction reactance X_{ar} is affected by the magnetic saturation because the path of the armature reaction flux is mainly through iron.

• The saturation factor k, should be applied to the magnetizing reactance X_{ar} only.

for the same field current.

**Remember:-**

• The unsaturated synchronous impedance Z_{sag }remains constant and may be calculated for any value of field current.

• Unsaturated synchronous reactance

• Armature reaction reactance

X_{ar} =X_{sag} - X_{al}.

• The saturated synchronous reactance

• In order to use the saturated synchronous reactance method:

- First calculate air- gap voltage
- Mark E
_{r}= BA on the OCC and find the corresponding voltage BD, on the air-gap line. - Obtain the saturation factor as K = BD/BA
- Calculate X
_{sag} - Find saturation synchronous reactance X
_{ss} - Draw phasor diagram with Xs replaced by X
_{ss}– now calculate E_{f}and thus the voltage regulation.

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