regulation of synchronous generator_saravanan t y_electrical machines-iii

Electrical Machines-III Regulation of Synchronous Generator

T. Y. Saravanan M. Tech., NEC∷GUDUR 92

UNIT – IIi

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3.1. Voltage Regulation:

The variation in the voltage between no-load and full-load is called the voltage regulation.

As we know that the voltage regulation of dc generator should depends on,

i. the resistance the main or armature circuit

ii. the magnitude of the armature current

iii. the armature reaction (i.e., the effect of the armature flux on main flux) In case of the synchronous generator or alternator, in addition to above 3 factors in dc generator,

the voltage regulation depends upon the power factor and armature leakage reactance also.

Voltage Regulation of an alternator is defined as the ratio of “rise in voltage (E0-V) when full-

load is removed (field excitation and speed remaining the same) to the rated terminal voltage.

Rise in voltage = ‘E0-V’ is the arithmetic difference not the vector difference.

E0 = Maximum no-load induced emf magnitude

V = Terminal voltage of an alternator.

Voltage regulation depends on power factor ‘cos ’

∴ % Regulation 'up' = E0- V

V × 100

If we can change the load of an alternator, there is a change in terminal voltage (V). The

magnitude of terminal voltage change depends on,

i. load can changes, the terminal voltage magnitude changes and the power factor (cos∅)

also. [ since V = E - Ia (Re + j Xs) ]

ii. excitation can changes, the magnitude of terminal voltage changes (V).

In case of leading load power factor, terminal voltage (V) will fall on removing full-load. At

lower leading load power factor ‘v ‘ rises with the increase of load, and hence the regulation is

‘-ve’.

For unity and lagging power factors, there is always a voltage drop with increase of load.

The rise in voltage when full-load is removed is not same when full-load is applied.

Note: 1). V < E0, i.e., the voltage regulation is POSITIVE for LAGGING & UNITY power factor

loads.

2). V > E0, i.e., the voltage regulation is NEGATIVE for LEADING power factor loads.



3). A normal alternator has a regulation of about 8-10% at unity power factor (UPF), but

the voltage rise is considerably increased at lagging power factors. The regulation is about

23-35%, or even more

3.2. Determination of voltage regulation:

The following methods which are used to determine the voltage regulation i.e.,

I. Direct loading method (small rating machines i.e., ≤ 5 KVA)

II. Indirect loading method ( >5 KVA )

3.2.1. Direct loading method:

This method is applicable only for the alternators, which their rating is ≤ 5 KVA. Because for

medium and large rating alternators, it requires more power and more losses were occurred.

In this, the alternator is runs at synchronous speed (Ns) and its terminal voltage is adjusted to its

rated value (V). The load is varied until the ammeter, wattmeter indicates the rated values at

given power factor.

Then the load removed, the speed and excitation at kept at constant. The open circuit or no-load

induced emf recorded ‘E0’.

∴ % Voltage Regulation = E0- V

V × 100

3.2.2. Indirect loading method:

For large and medium rating (> 5 KVA) alternators, the regulation which can be determine by

using indirect loading method. Here the load is not applied directly but rated values are given to

alternator. There are various methods to determine the voltage regulation. Some of them ignore the

effect of saturation and some do consider. The following methods are used to obtain the voltage

regulation.

They are,

1. EMF or Synchronous Impedance or Pessimistic or Unsaturated Synchronous Impedance method

2. MMF or Ampere-Turns or ROTHERT’S Ampere-Turns or Optimistic method

3. Zero Power Factor or ZPF or Potier Triangle method

4. ASA (American Standards Association) method

All the above methods require,

a) Open Circuit or No-Load Characteristic Curve (OCC Curve)

b) Short Circuit Characteristic Curve (SCC Curve)

c) Armature effective resistance or Stator resistance (Re)



3.2.3. Open Circuit or No-Load Test: (To obtain OCC Curve)

The connection for Open Circuit test or No-Load test is shown in above circuit diagram. The

armature winding i.e., load terminals are opened and machine should be run at rated or

synchronous speed. The field winding is connected to dc source in series with a field rheostat

and an ammeter.

By adjusting the field rheostat from maximum to minimum, the field current If is taken through

ammeter in steps minimum to maximum respectively. Then Ego or no-load generated emf is also

reads minimum to maximum taken from voltmeter in steps up to rated value.

Draw the Open Circuit Characteristic Curve (OCC Curve) from the above readings. i.e., ‘If’ on

x-axis and Ego on y-axis. The Ego which we obtained from voltmeter is line value that should be

representing in a graph as phase value. i.e., [For a star connected armature, Ego/ph = Ego/line

√3 ].

3.2.4. Short Circuit Test: (To obtain SCC Curve)



The connection for the short circuit test is shown in the above circuit diagram. In this test also

the machine should be maintained at constant speed by the prime mover.

All the 3- load terminals of 3- alternator as shorted. Rheostat of sufficiently high ohmic value is

inserted in the dc field circuit to keep the current in the circuit very low.

Now the field current ‘If’ is adjusted to Isc or Irated of 3- alternator by varying the field rheostat.

From the If and Isc the SCC Curve (Short Circuit Characteristic) is obtained.

The OCC Curve and SCC Curve can be plotted with the common field current axis as shown

below. From these, the value of Synchronous Impedance (Zs) will be calculated.

The Synchronous Impedance ‘Zs’ can be obtained by above graphical representation of OCC and

SCC Curve.

i.e., Zs = Open circuit induced emf

Short circuit current at constant excitation or same field current axis

Zs = Eoc

Isc



3.2.5. Ammeter – Voltmeter Method: (To obtain the value of Re)

The effective armature resistance (Re) per phase can be measured directly by Ammeter-

Voltmeter method (AV-method) or by using Wheatstone bridge.

The above circuit is used to measure the effective armature resistance per phase. The DC supply

is connected to the any one phase of armature winding through rheostat, ammeter in series and

voltmeter to parallel.

Then the rheostat can be varied from maximum to minimum in steps the Va and Ia values are

noted by voltmeter and ammeter respectively and taken average with gives ‘Ra’. i.e., Ra = Va

Ia.

The ‘Ra’ value which we obtained is DC so by converting it to AC value is multiplied 1.5 due to

skin effect and the other losses.

i.e., RAC = 1.5* RDC

Re = RAC

Finally, we obtained the Synchronous Impedance ‘Zs’ from OC and SC test, ‘Re’ obtained by A-

V method then ‘Xs’ as,

Synchronous Reactance = Xs = Zs2- Re

2



3.3. EMF method or Synchronous impedance method:

This method is also called as “Pessimistic or unsaturated synchronous impedance method.”

Assumptions:

In this method the assumptions are,

The drop due to armature reaction is considered as drop due to additional leakage reactance

means the entire drop assumed as drop due to leakage reactance (XL). IXL which depends on

voltage so that it can be represented as “Voltage Vectors or EMF Vectors”. That’s the reason

why this method is called as ‘EMF’ method.

The flux under test conditions is the same as that under load conditions.

The synchronous impedance (Zs) is constant. The Zs is determined by the OCC & SCC. At all

times, the Zs is the ratio of the open-circuit voltage to the short-circuit current. When the OCC

curve & SCC curve are linear, the synchronous impedance is constant. Above the knee of the

OCC when the saturation starts, the Zs decreases due to fact that both OCC & SCC approaches

to each other. The Zs obtained test condition is below saturation is larger than the normal (when

the magnetic circuit becomes saturated). Thus we do not take the effect of saturation. This is the

greatest source of error in the synchronous impedance method.

The magnetic reluctance to the armature flux is constant regardless of the power factor. For a

cylindrical rotor machine this assumption is true because of the uniform air-gap. In salient-pole

machines, the position of the armature flux relative to the field poles varies with the power

factor.

There is no saturation effect.

Steps to find the regulation:

i. OCC curve is plotted from the OC test. (refer OC test)

ii. SCC curve is drawn from the short-circuit test data (refer SC test). It is a straight line

passing through the origin.

Both these curve are drawn on a common field current (If) axis.

iii. Consider a field current (If) with respective to the short circuit current or full load current

‘Isc’ and draw a dotted line to that If which cuts occ at Eoc, the terminal voltage zero when

it is in short-circuit.

Zs = EocIsc

iv. Armature effective resistance can be obtained by A-V method (refer A-V method).

v. The synchronous reactance can be determined by,

Xs = Zs2- Re

2



This emf method is not accurate, because the value of ‘Zs’ is always more than its actual value

under normal voltage and saturation condition.

From the above, the If is same for both OC and SC test. It is observed from the graph it cannot

cross the saturation of OCC curve. So that the ‘Zs’ is also called as “Unsaturated synchronous

impedance”.

i.e., Zs(unsaturated) = EocIsc

(If is at Isc or Ifl)

Zs(un sat) > Zs(sat) (or) Zs(un sat) > Zs(actual)

So that this method is also called as “Unsaturated synchronous impedance method”. Hence, the

value of regulation obtained is more than its actual value.

i.e., Reg(emf) > Reg(act)

That’s the reason why it is called “Pessimistic method”.



The value of ‘Zs’ is not constant; it can be varied with saturation. At low saturation or un

saturation its value is larger because then the effect of a given ampere-turns is more than that

high saturation.

Under short circuit condition, saturation is very low, because armature mmf is directly

demagnetizing.

In this method, the value of ‘Zs’ is usually obtained from full-load current in the short-circuit

test. Here, armature reactance ‘Xa’ has not been treated separately but taken along with leakage

reactance ‘XL’.

Value of ‘E0’ (for lagging load)

Considering load current (Ia) as a

reference, lagging load current ‘Ia’ is lags behind

the voltage (V) by an angle ‘‘.

From the Phasor diagram of lagging power

factor,

OD2 = OB2 + BD2

E02 = OD2 = (OA + AB)2 + (BC + CD)2

E0 = (V cos + IaRe)2+(V sin + IaXs)2

For leading load:

Consider terminal voltage (V) as a

reference, load current (Ia) leads terminal voltage

‘V’ by an angle ‘‘.

From the Phasor diagram of leading power factor,

OC2 = OD2 + DC2

E02 = OC2 = (OE + ED)2 + (BD - BC)2

E0 = (V cos + IaRe)2+ V sin - IaXs2



For Unity Power factor load:

Consider terminal voltage (V) and load

current (Ia) both are in phase i.e., ‘ = 00‘.

From the Phasor diagram of unity power

factor,

OD2 = OC2 + CD2

E02 = OD2 = (OB + BC)2 + (CD)2

E0 = (V+ IaRe)2+ (IaXs)2

% Voltage regulation = E0- VV

× 100 about 30%

Where, V = terminal voltage obtained by rating of an alternator.

3.4. MMF method or Ampere-Turn method: This method is also called as “ROTHERT’S MMF or Optimistic method”.

Assumptions:

The drop due to leakage reactance is considered as drop due to additional armature reaction

means entire drop is assumed to be drop due to armature reaction (IXa).

Since armature reaction is flux phenomena, so drop due to armature reaction is represented with a

“field current vectors (or) mmf vectors”. That is the reason why it is called as “MMF method”.


i. OCC curve is obtained by conduction of OC test.

ii. SCC curve is obtained by conducting SC test i.e., field excitation is adjusted to full-load

current or short circuit current flows through short circuit path of an alternator load

terminals.

From the below,

Ifm is the main field current required to generate rated induced emf under Open-Circuit condition

Ifr is the main field current required to produce the armature or full load current under Short-

Circuit Condition



Ift is the main field current which gives the maximum open circuit induced EMF

Ift , Ifm and Ifrare also represented in terms of ∅fm , ∅fr and ∅ft respectively.

Ift= Ifm+ Ifr

Ifm is required to compensate the armature reaction under various load conditions.

For Lagging power factor load:

Here Ifm and ‘E’ are taken as reference vectors

Ifr lags behind E by ‘’

Ifr1

and Ift1 are actual values i.e., obtained by

direct load method

For lagging, Iftangle 900 +



For Leading power factor load:

Ifr leads E by ‘’

= Load power factor angle

For leading, Iftangle 900 -

For Unity power factor load:

Ifr and E are reference vectors

Ifr and E both are in phase, because = 0

cos = 1

For unity, Iftangle 900

Ifm which gives the induced EMF at rated value. (i.e., E)

Ift which gives the maximum no-load or open-circuit induced emf (i.e., E0) measure ‘E0’ value

corresponding to Ift from OCC curve.

Ifr is not sufficient to give the required field flux lines, because the field poles are saturated. So

more field current required.

% Voltage regulation = E0-V

V*100

In this method, the field current is to overcome the armature reaction is measured from short

circuit condition where the field poles are active.

But under running condition or actual load condition more field current (Ifr1) required. Since

the field poles are little saturated. Therefore ‘E0’ is more.

So that actual regulation is more than ‘mmf’ regulation. That’s why it is also named as

“Optimistic method”

i.e., Reg(mmf) < Reg(actual) about 15%

This method is also not an accurate method.



3.5. Zero Power Factor (ZPF) or Potier Triangle or Power Triangle method: It makes use of the first two methods to some extent.

Assumptions:

In this method the assumptions taken are as follows i.e.,

Here the drop due to armature reactance (Xa) and leakage reactance (XL) are taken as

separately. Hence it gives the more accurate results.

The effective armature resistance (Re) is neglected.

The leakage reactance drop IaXL is independent of excitation.

The armature reaction mmf is constant.

The OCC taken on no-load accurately represents the relation between mmf and voltage on

load.


1. No-Load or Open Circuit Characteristic curve (OCC curve) obtained by OC test.

2. Full-Load zero power factor curve (not the SCC curve) also called the wattless load

characteristic. It is the curve of terminal voltage against excitation when armature is

delivering full-load current at zero power factor.

In this method, the drop due to armature reactance and leakage reactance combinely gives the

maximum open circuit induced emf (E0). It should be noted that if we vectorially add to ‘V’, the

drop due to leakage reactance (XL) and effective resistance (Re) we get ‘E’. if further added the

drop due to ‘Xa’ gives the ‘E0’.



The zero power factor full-load lagging curve can be obtained from,

a. If a similar machine is available, which may be driven at no-load as a synchronous motor

at practically zero power factor

b. Loading the alternators with pure reactors.

c. Connecting the alternators to a 3- line with ammeters and wattmeter’s connected for

measuring current and power, by so adjusting the field current that we get full-load

armature current with zero wattmeter reading.

‘P’ point was obtained when wattmeter was reading zero.

‘A’ point was obtained from a short-circuit test field current with a full-load armature current.

(i.e., Ifr)

‘OA’ represents field current which is equal and opposite to the demagnetizing armature

reaction and balancing leakage reactance drop at full-load.

By knowing ‘P’ and ‘A’ points, the full-load curve at zero power factor ‘A P’ is drawn.

From ’P’, PQ is drawn equal to and parallel to OA. From point –‘Q’, QR is drawn parallel to

OE i.e., tangential or air-gap line. Hence we get ‘R’ point on No-Load or OCC curve, which

corresponds to point ‘P’ on full-load zero power factor curve. The triangle ‘∆PRS’ called

known as potier triangle. This triangle is constant for a given armature current.

Draw RS perpendicular to PQ. The length RS represents the drop in voltage due to armature

leakage reactance XL.

i.e., RS = IXL & PT = Ia(Xa + X L)

PS = field current necessary to overcome demagnetizing effect of armature reaction at full-load.

SQ = balancing the armature leakage reactance drop RS.

Vector diagram for lagging load:

IaRe

D

B

O

T

R

S

IaXa

IaXL

Ia

E0

E

V

900+

900

900

Ift Ifr

Ifm



The ∆OBD which is obtained from the graphical representation. For that,

OD2 = (OB+BC)2 + CD2

Ift = (Ifm+ Ifr sin )2+ (Ifr cos)2


V*100 about 20%

Similarly the vector or phasor diagrams for leading and unity power factor loads as mentioned in

MMF method. The value of E0 can be obtained with respective to Ift for voltage regulation.

3.6. ASA (American Standards Association) method: It is the combination of MMF and ZPF method and is a most accurate method. The drop

due to saturation also considered. In the EMF, MMF, ZPF methods the saturation is not considered.


1. No-Load or Open Circuit Characteristic curve (OCC curve) obtained by OC test.

2. Full-Load zero power factor curve (not the SCC curve) also called the wattless load

characteristic considering saturation. It is the curve of terminal voltage against excitation

when armature is delivering current at zero power factor (Ia or IL = Constant).

In this method, the drop due to armature reactance and leakage reactance combinely gives the

maximum open circuit induced emf (E0). It should be noted that if we vectorially add to ‘V’,

the drop due to leakage reactance (XL) and effective resistance (Re) we get ‘E’. if further added

the drop due to ‘Xa’ gives the ‘E0’.

‘P’ point was obtained when wattmeter was reading zero.

‘A’ point was obtained from a short-circuit test field current with a full-load armature current.

(i.e., Ifr)

D

C B

900

E

O

Ift

Ifr

Ifm



‘OA’ represents field current which is equal and opposite to the demagnetizing armature

reaction and balancing leakage reactance drop at full-load.

By knowing ‘P’ and ‘A’ points, the full-load curve at zero power factor ‘A P’ is drawn.

From ’P’, PQ is drawn equal to and parallel to OA. From point –‘Q’, QR is drawn parallel to

OE i.e., tangential or air-gap line. Hence we get ‘R’ point on No-Load or OCC curve, which

corresponds to point ‘P’ on full-load zero power factor curve. The triangle ‘∆PRS’ called

known as potier triangle. This triangle is constant for a given armature current.

Draw RS perpendicular to PQ. The length RS represents the drop in voltage due to armature

leakage reactance XL.

i.e., RS = IXL & PT = Ia(Xa + X L)

PS = field current necessary to overcome demagnetizing effect of armature reaction at full-load.

SQ = balancing the armature leakage reactance drop RS.



Vector diagram for lagging load:

Ift

1 = field current to compensate drop due to saturation and is added in phase with Ift

Measure ‘E0’ corresponding to Ift1

.


V*100 about 25% to 28%

Similarly the vector or phasor diagrams for leading and unity power factor loads as

mentioned in MMF method. The value of E0 can be obtained with respective to Ift1 for voltage

regulation.

Note: Finally the Voltage Regulation of an Alternator as,

EMF method > ASA method > ZPF method > MMF method

i.e., we concluded that among the four methods the ASA & ZPF method will gives accurate

regulation compared to EMF & MMF

3.7. Two Reaction or BLONDEL Two Reaction theory:

Already we know that armature reaction is directly proportional to armature reactance

(Xa) and inversely proportional to air gap.

i.e., Air-Gap Length ∝ 1

armature reaction ∝

1Xa

In cylindrical type synchronous machine, the air-gap length is uniform. So the armature reaction

is same in between stator conductors and field poles. So ‘Xa’ is same i.e. single reactance is

sufficient for modeling the armature reaction.



In salient-pole type synchronous machine, air-gap is minimum in d-axis or direct-axis and

maximum in q-axis or quadrature or inter polar axis. So it requires both reactances i.e. Xd and Xq

for modeling the armature reaction.

In cylindrical rotor synchronous machine, the air-gap is uniform around the entire air-gap

periphery. So armature reaction is same along the d-axis and q-axis. So finally we concluded

that a single reactance is sufficient for modeling the armature reactance because Xd = Xq.

But in salient pole synchronous machine, the armature reaction is maximum in d-axis and

↓air-gap α 1

armature reaction↑

the armature reaction is minimum in q-axis.

↑air-gap α 1

armature reaction↓

So single reactance is not sufficient to modeling the armature reaction, it requires Xad and Xaq

i.e., Xd and Xq.

Xad > Xaq

Leakage reactance (XL) is same along d-axis and q-axis because it is independent of air-gap

length and dependent applied voltage and flux leakage. Therefore,

Xd = Xad + XL

Xq = Xaq + XL

Where,

Xd = direct axis synchronous reactance.

Xq = quadrature axis or interpolar axis synchronous reactance.



Xad = direct axis armature reactance.

Xaq = quadrature axis armature reactance.

XL = leakage reactance.

In general, Xd > Xq. i.e., Xd ≅ (1.5 to 2) times of Xq.

Xd - Xq = saliency. So that it is called as Salient pole synchronous machine.

For cylindrical type synchronous machine,

Xd - Xq = Zero saliency or non-saliency.

Because Xd = Xq due to uniform air gap.

That’s the reason why it is also called as Non-Salient pole type alternator.

3.8. Determination of Xd and Xq of a Salient pole synchronous machine:

The direct axis synchronous reactance (Xd) can be determined from OC and SC tests and

quadrature or interpolar axis synchronous reactance can be obtained from following three methods.

i.e., 1. Slip-test

2. Maximum – lagging current test

3. Reluctance motor.

3.8.1. Slip Test:

From the slip-test, the values of Xq and Xd can be determined. The synchronous machine is

driven by a separate prime-mover at a speed slightly different from synchronous speed (Ns).

The field winding is left open and +ve sequence balanced voltages of reduced magnitude

(around 25% of rated value) and if rated frequency are impressed across the armature

terminals.



Under these conditions, the relative velocity between the field poles and the rotating armature

mmf wave is equal to the difference between synchronous speed and the rotor speed, i.e., slip

speed.

A small ac voltage across the open field winding indicates that the field poles and rotating

mmf wave is revolving in the same direction then that should be required for slip test.

If field poles revolve in a direction opposite to the rotating mmf wave –ve sequence reactance

would be measured.

At one instant, the peak of armature mmf wave is in line with the filed pole or direct axis, the

reluctance offered by the small air gap is minimum as shown in above figure. At this instant,

the terminal voltage per phase divided by the corresponding armature current per phase gives

d-axis synchronous reactance. (Xd).

Xd = Vmax

Imin because air-gap is minimum

After one – quarter (1/4) of slip cycle, the peak of armature mmf wave acts on the inter polar

or q-axis of the magnetic circuit, and reluctance offered by long air-gap is maximum. At this

instant,

Xq= Vmin

Imax because reluctance in air-gap is maximum

During this test, the induced emf in open field winding is AC Sinusoidal at Slip-frequency.

Rotating field is driven at less than Ns because when the rotor is driven at Ns, the flux linkages

are maximum, so Ia is minimum always. So we want to get maximum values of Ia i.e., field is in

locking with the stator poles.



Oscillograms of armature current and terminal voltage and the emf induced in open circuit field

winding is shown below.

When performing this test, the slip should by small as possible, otherwise the currents induced

in the magnetic circuits would cause large errors in the measurement of Xd and Xq. The

advantages of oscillographic method over Voltmeter – Ammeter method are,

i. elimination of the inertia effects of voltmeter and ammeter.

ii. the possibility of large slip-speed.



3.9. Phasor diagram of Salient – Pole Synchronous Machine: For a generator, the voltages are generated and the currents are opposite currents. For a

synchronous motor, the voltages are applied and the currents are input currents.

Let us consider ‘Eg’ as a reference vector.

δ = load angle or torque angle between Eg and V

For Lagging Load:

∅ = phase angle between V and Ia. (Ia lags behind V by ∅)

= δ + ∅ (lagging, angle between Eg and Ia)

Id = direct axis armature current = Ia sin

Iq = quadrature or inter polar axis armature current

= Ia cos= Ia cos (δ+∅)

Eg = OB = OE + ED + DB

Eg = Vcos δ + IqRa + IdXd ………… (1) lagging power factor load.



From the above phasor diagram tan can be obtained as, (one part of an above vector diagram).

tan = Base

opposite side =

QAQO

= QD + DAOP + PQ

tan = V sin∅ + IaXq

V cos∅ + IaRa ………… (2) lagging power factor.



For leading power factor load: Let us consider, Eg as reference vector,

= angle between Eg and Ia

The vector diagram as follows:

Leading power factor load means ‘V’ leads ‘Eg’ by load angle of ‘δ ’

Eg = V cos δ -IdXd -IqRa

Eg 1 = V cos δ +IqRa- IdXd ………… (3) considering Ef’

tan = V sin∅ - IaXq V cos∅ + IaRa

………… (4)

For a synchronous generator, finally we concluded from (1), (2), (3) and (4) equations.

Eg = V cos∅ +IqRa ± IdXd



+ve for lagging load

-ve for leading power factor load

tan = V sin∅ ± IaXq V cos∅ + IaRa

= ∅ + δ for lagging load +ve

= ∅ - δ for leading load -ve

Thus, for the synchronous motor ‘-Ia’ is substituted for the above equations instead of ‘Ia’.

Therefore,

For salient pole synchronous motor,

Id = Ia sin

Iq = Ia cos

=∅∓δ -ve for lagging power factor load

+ve for lagging power factor load

E = V cos δ -IqRa ∓ IdXd -ve for lagging power factor load

+ve for leading power factor load

tan = V sin ∅∓ IaXq V cos∅ - IaRa



Problems



2. The no-load & full-load zero power factor characteristics for a 23.5MVA, 13.8KV, 3-, star

connected turbo generators are given below in per unit values:

No-load characteristics:

If (A) 0.1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 2.0 2.5

V (v) 0.13 0.23 0.45 0.69 0.87 1.0 1.09 1.15 1.21 1.28 1.36

ZPF characteristics:

If (A) 1.2 1.3 1.4 1.6 1.8 2.0 2.2 2.4 2.6

V (v) 0.015 0.13 0.25 0.49 0.69 0.83 0.92 0.99 1.04

Determine the regulation at full load 0.8 p.f lagging by the ZPF method. Neglect armature resistance.

Ans:

Given data,

3-, star connected alternator/turbo generator

Power = S = 23.5MVA

Line Voltage = VL = 13.8KV

From the characteristic graph, the Potier triangle PRS,

Full load leakage reactance drop = IaXL = RS

= 1.0 – 0.88

= 0.12 pu.

The field current required to overcome the armature reaction on full load is PS from PRS

PS = 2.1 – 1.0 = 1.1pu.



6. A 10KVA, 380V, 50Hz, 3-, Star connected Salient Pole alternator has direct axis and quadrature

axis reactances of 12Ω and 8Ω respectively. The effective armature resistance is 1Ω/ph, the generator

delivers rated load at 0.8 p.f lagging with terminal voltage being maintained at rated value. If the load

angle is 160.151, Determine,

i. the pole and inter-pole axis currents

ii. emf

iii. regulation at rated condition.

Ans:

Given data,

3- Star connected alternator

Rated power = S = 10KVA

VL = 380V

f = 50Hz

Xd = 12Ω

Xq = 8Ω

Torque angle = Load angle = = 160.151

Power factor = cos = 0.8 lagging

= cos-1(0.8) = 360.871

(i). Vph = VL/3

= 380/1.732

= 219.4V

Ia = IL = S/1.732* VL

= 10K/1.732*380

= 15.19A

Direct axis current = Id = Ia sin = Ia sin (+)

= 15.19 sin (160.151 + 360.871)

= 12.13A

I a si

n

Ia cos Iq

Id Ia

V

E



Formulae’s

1. % age voltage Regulation

% Regulation = E0- V

V × 100

where,

Rise in voltage = ‘E0-V’ is the arithmetic difference not the vector difference.

E0 = Maximum no-load induced emf magnitude

V = Terminal voltage of an alternator.

2. Terminal Voltage of an alternator

V = E - Ia (Re + j Xs)

where,

E = induced emf of an alternator (volts)

Ia = load or armature current (Amps)

Re = effective armature resistance [i.e., Re = RAC = 1.5 * RDC] (Ω)

Xs = Synchronous Reactance [Xs = Xa + XL] (Ω) or

Xs = Zs2- Re

2

Zs = Synchronous impedance (Ω)

i.e., Zs = Open circuit induced emf

Short circuit current at constant excitation or same field current axis

Zs = Eoc

Isc

3. EMF method (30% regulation)

Value of E0 for lagging power factor, from phasor diagram

E0= (V cos + IaRe)2+(V sin + IaXs)2

Value of E0 for leading power factor, from phasor diagram

E0= (V cos + IaRe)2+(V sin - IaXs)2

Value of E0 for unity power factor, from phasor diagram

E0= (V+ IaRe)2+ (IaXs)2



4. MMF method (15% regulation)

Value of Ift for lagging power factor, from phasor diagram (Ift angle 900 + )

Ift= (Ifm+ Ifr sin )2+ (Ifr cos)2

Value of Ift for leading power factor, from phasor diagram (Ift angle 900 - )

Ift= (Ifm- Ifr sin )2+ (Ifr cos)2

Value of Ift for unity power factor, from phasor diagram (Ift angle 900)

Ift= (Ifm)2+ (Ifr)2

Where,

Ifm = field current at rated induced emf (E)

Ifr = field current at rated or Full Load or short circuit current (Irated or IFL or Isc)

Ift = field current at maximum open circuit induced emf (E0)

5. ZPF method (20% regulation)

Value of Ift for lagging power factor, from phasor diagram (Ift angle 900 + )

Ift= (Ifm+ Ifr sin )2+ (Ifr cos)2

Value of Ift for leading power factor, from phasor diagram (Ift angle 900 - )

Ift= (Ifm- Ifr sin )2+ (Ifr cos)2

Value of Ift for unity power factor, from phasor diagram (Ift angle 900)

Ift= (Ifm)2+ (Ifr)2

Where,

Ifm = field current at rated induced emf (E)

Ifr = field current at rated or Full Load or short circuit current (Irated or IFL or Isc)

Ift = field current at maximum open circuit induced emf (E0)

PRS = Potier triangle

RS = IaXL drop

E = V + Ia (Re + j XL) = rated induced emf

E0 = V + Ia [Re + j (XL+ Xa)] = maximum open circuit induced emf

Angle between Ifm and E is 900

Angle between Ift and E0 is 900



6. ASA method (25% regulation)

All calculations same as ZPF method but saturation of current is considered .

Ift

1 = field current at maximum open circuit induced emf (E0) when saturation considered.

7. from two reaction analysis

Xd = Xad + XL

Xq = Xaq + XL

Xd = direct or pole axis reactance (Ω)

Xq = quadrature or interpole axis reactance (Ω)

XL = Leakage reactance (Ω)

Xad = direct or pole axis armature reactance (Ω)

Xaq = quadrature or interpole axis armature reactance (Ω)

8. from slip test

Xd = Vmax

Imin because air-gap is minimum

Xq= Vmin

Imax because reluctance in air-gap is maximum

i.e., Air-Gap Length ∝ 1

armature reaction ∝

1Xa

9. from Salient pole alternator

Eg = V cos∅ +IqRa ± IdXd

+ve for lagging load

-ve for leading power factor load



tan = V sin∅ ± IaXq V cos∅ + IaRa

= ∅ + δ for lagging load +ve

= ∅ - δ for leading load -ve

Where,

Id = direct axis armature current = Ia sin

Iq = quadrature or inter polar axis armature current

= Ia cos= Ia cos (δ+∅)

= power factor angle between V and I

= load or torque angle between E and V

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regulation of synchronous generator_saravanan t y_electrical machines-iii

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