Option 2 : Xs = √99 Ω

**Concept:**

Synchronous impedance method:

- The synchronous impedance method of calculating voltage regulation of an alternator is otherwise called as the EMF method.
- The synchronous impedance method or the EMF method is based on the concept of replacing the effect of armature reaction by an imaginary reactance.
- It gives a result that is higher than the original value. That's why it is called the pessimistic method.
- For calculating the regulation, the synchronous method requires the armature resistance per phase, the open-circuit characteristic, and the short circuit characteristic.

Therefore, Synchronous impedance is basically obtained from occ and SCC characteristics of a three-phase alternator and is given by

\(Z_s=\frac{V_{oc}}{I_{sc}}\) at same field current

Where,

Z_{s} = Per phase Synchronous impedance

V_{oc} = Per phase Open circuit voltage of the alternator

I_{sc} = Per phase Short circuit current of the alternator

**Application:**

Given:

Rating of alternator = 500 KVA

Terminal voltage of alternator V_{t}_{ L-L} = 3.3 KV = 3300 V

Short circuit current I_{sc }= 110√3 A

Winding Resistance = 1 Ω

Per phase Open circuit voltage \(V_{oc}=\frac{3300}{√3}\ V\)

Per phase short circuit current I_{sc} = 110√3 A (by default we assume star connected)

Therefore,

\(per\ phase\ Z_s=\frac{\frac{3300}{√3}}{110√3}\)

= 10 Ω

\(Z_s=\sqrt{{R^2+X_s^2}}\)

\(10=\sqrt{{1^2+X_s^2}}\)

100 = 1 + X_{s}^{2}

\(X_s\ = \sqrt{99}\ \Omega\)

Option 3 : 15%

__Concept:__

The voltage regulation of an alternator is defined as the ratio of the rise in voltage when full-load is removed (field excitation and speed remaining the same) to the rated terminal voltage.

% voltage regulation \( = \frac{{{E_0} - V}}{V} \times 100\)

Where E0 is the no-load voltage

And V is the rated voltage

__Calculation:__

Given: no-load induced emf (E0) = 230 V

Rated terminal voltage (V) = 200 V

Voltage regulation \( = \frac{{230 - 200}}{{200}} \times 100 = 15\% \)

Option 2 : the EMF method

__Concept:__

Normally for voltage regulation calculation, we use the following methods.

1. Synchronous impedance or emf method

2. Armature turn or mmf method

3. Zero PF or Potier method

__Synchronous impedance method (EMF Method):__

- The synchronous impedance method of calculating voltage regulation of an alternator is otherwise called the EMF method.
- The synchronous impedance method or the EMF method is based on the concept of replacing the effect of armature reaction with an imaginary reactance.
- This method is not accurate as it gives a result that is higher than the original value. That's why it is called the pessimistic method.
- For calculating the regulation, the synchronous method requires the armature resistance per phase, the open-circuit characteristic, and the short circuit characteristic.

__Armature turn method:__

It is also known as the MMF method. It gives a value which is lower than the original value. That's why it is called an optimistic method.

To calculate the voltage regulation by MMF Method, the following information is required. They are as follows:

- The resistance of the stator winding per phase
- Open circuit characteristics at synchronous speed
- Field current at rated short circuit current

__Potier triangle method:__

- This method depends on the separation of the leakage reactance of armature and its effects.
- It is used to obtain the leakage reactance and field current equivalent of armature reaction.
- It is the most accurate method of voltage regulation.
- For calculating the regulation, it requires open circuit characteristics and zero power factor characteristics.

If the no-load voltage of a 3-phase, 440 V, 50 Hz alternator is 495 V, then its voltage regulation is:

Option 1 : 12.5%

__Concept:__

The voltage regulation of an AC alternator is,

**Percentage voltage regulation \(= \frac{{{E_{g0}} - {V_t}}}{{{V_t}}} \times 100\)**

Eg0 is the internally generated voltage per phase at no load

Vt is the terminal voltage per phase at full load

**Voltage regulation** indicates the drop in voltage from no load to the full load.

There are three causes of voltage drop in the alternator.

- Armature circuit voltage drop
- Armature reactance
- Armature reaction

The first two factors always tend to reduce the generated voltage, the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

__Calculation:__

Given that

E_{g0} = 495 V, V_{t} = 440 V

Now percentage voltage regulation can be calculated as

Percentage voltage regulation \(= \frac{{{495} - {440}}}{{{440}}} \times 100\)

**Percentage voltage regulation = 12.5%**

In the Potier method of voltage regulation, which of the following characteristics is/are determined by conducting tests on the machines running at synchronous speed?

(i) Open-circuit characteristic

(ii) Zero power factor (lagging) characteristic

(iii) Short-circuit characteristicOption 2 : Only (i) and (ii)

Potier triangle method:

- This method depends on the separation of the leakage reactance of armature and its effects.
- It is used to obtain the leakage reactance and field current equivalent of armature reaction.
- It is the most accurate method of voltage regulation.
- For calculating the regulation, it requires open circuit characteristics and zero power factor characteristics.

ΔDEF is Potier triangle which is a right angle triangle

DE = armature MMF (Fa) or field current which compensates armature reaction

DF = IaXal = armature leakage reactance

The following assumptions are made in this method.

- The armature resistance is neglected.
- The O.C.C taken on no-load accurately represents the relation between MMF and voltage on load.
- The leakage reactance voltage is independent of excitation.
- The armature reaction MMF is constant.

__Additional Information__

Synchronous impedance method:

- The synchronous impedance method of calculating voltage regulation of an alternator is otherwise called as the EMF method.
- The synchronous impedance method or the EMF method is based on the concept of replacing the effect of armature reaction by an imaginary reactance.
- It gives a result that is higher than the original value. That's why it is called the pessimistic method.
- For calculating the regulation, the synchronous method requires the armature resistance per phase, the open-circuit characteristic, and the short circuit characteristic.

Armature turn method:

It is also known as the MMF method. It gives a value that is lower than the original value. That's why it is called an optimistic method.

To calculate the voltage regulation by MMF Method, the following information is required. They are as follows:

- The resistance of the stator winding per phase
- Open circuit characteristics at synchronous speed
- Field current at rated short circuit current

Voltage regulation of an alternator is given by:

V_{NL}: Voltage at no load

V_{FL}: Voltage at full load

Option 3 : ((VNL - VFL) / (VFL)) × 100%

__Voltage Regulation (V.R.):__

- The voltage regulation is defined as “the rise in voltage at the terminals, when the load is reduced from full load rated value to zero, speed and field current remaining constant”.
- With the change in load, there is a change in the terminal voltage of an alternator or synchronous generator. The magnitude of this change not only depends on the load but also on the load power factor.
- It is also defined as “the rise in voltage when full load is removed divided by the rated terminal voltage when speed and field excitation remains the same.” It is given by the formula,

V.R. = ((VNL - VFL) / (VFL)) × 100%

Where,

VNL: Voltage at no load

VFL: Voltage at full load

Case 1:

VNL > VFL: Then V.R will be positive and the power factor will be lagging or unity.

Note: V.R under unity power factor is less than voltage regulation under lagging power factor,

Case 2:

VNL < VFL or VNL = VFL: Then VR will be negative and zero respectively and the power factor will be leading.

__Conclusion:__

From the above concept,

Curve D represents V.R at leading power factor.

Curve C represents V.R at a somewhat unity power factor.

Curve A and Curve B represent V.R at lagging power factor.

__Voltage regulation in Transformer:__

Voltage regulation is the change in secondary terminal voltage from no load to full load at a specific power factor of load and the change is expressed in percentage.

E2 = No-load secondary voltage

V2 = Full load secondary voltage

Voltage regulation for the transformer is given by the ratio of change in secondary terminal voltage from no load to full load to no load secondary voltage.

Voltage regulation

\(= \frac{{{E_2} - {V_2}}}{{{E_2}}}\)

Which among the curves (A, B, C and D) represents the characteristics for leading power factor?

Option 4 : D

__Concept:__

Voltage Regulation:

- The voltage regulation is defined as “the rise in voltage at the terminals, when the load is reduced from full load rated value to zero, speed and field current remaining constant”.
- With the change in load, there is a change in the terminal voltage of an alternator or synchronous generator. The magnitude of this change not only depends on the load but also on the load power factor.
- It is also defined as “the rise in voltage when full load is removed divided by the rated terminal voltage when speed and field excitation remains the same.” It is given by the formula,

\(V.R=\frac{E-V}{V}\)

Where,

E is no load voltage

V is the terminal voltage

Case 1:

E > V: Then V.R will be positive and the power factor will be lagging or unity.

Note: V.R under unity power factor is less than voltage regulation under lagging power factor,

Case 2:

E < V or E = V: Then VR will be negative and zero respectively and the power factor will be leading.

__Conclusion:__

From the above concept,

**Curve D represents V.R at leading power factor.**

Curve C represents V.R at a somewhat unity power factor.

Curve A and Curve B represent V.R at lagging power factor.

Option 1 : synchronous motor

**Zero Power Factor Characteristic (ZPFC):**

- ZPFC of a generator is a curve of the armature terminal voltage and the field current.
- The machine is operated with constantly rated armature current at synchronous speed and zero lagging power factor.
- The Zero Power Factor Characteristic is also called as Potier Characteristic.
**For maintaining very low power factor, the alternator is loaded by means of reactors or by an under excited synchronous motor.**- The shape of ZPFC is very much like that of the O.C.C. The phasor diagram corresponding to zero power factor lagging is shown below.

In the phasor diagram shown above, the terminal voltage V is taken as the reference phasor. At zero power factor lagging, the armature current I_{a} lags behind V by 90 degrees. I_{a}R_{a} is drawn parallel to I_{a} and I_{a}X_{aL} perpendicular to I_{a}.

V + I_{a}R_{a} + I_{a}X_{aL} = E_{g}

E_{g} is the generated voltage per phase.

Option 3 : \(\frac{{{E_0} - V}}{V}\)

__Voltage regulation:__

Voltage regulation is the ratio of the change in terminal voltage to the rated voltage when the load is suddenly removed with the same excitation, same speed.

Voltage regulation = \(\frac{{{E_0} - V}}{V}\)

% Voltage regulation \( = \frac{{{E_0} - V}}{V} \times 100\)

Where E0 is the no-load voltage

And V is the rated terminal voltage

__Important Points__

The range of voltage regulation of an alternator is 30-40%

Option 3 : by OC and ZPF test

**Methods of finding Voltage Regulation in Synchronous Generator:**

**Synchronous impedance method**: In the synchronous impedance method voltage regulation is determined by calculating synchronous impedance Z_{s}.

**MMF method:** It is also used to determining voltage drop through MMF, but the drops in machine IaXL is voltage quantity and IaXa is MMF quantity. Because armature reaction is the reduction of flux which is represented through voltage drop.

**Potier Method (ZPF method**): In potier method voltage quantities are calculated on a voltage basis and MMF quantities are calculated on an MMF basis.

It separated leakage reactance and armature reactance and named it Potier reactance.

It requires an open circuit, short circuit, and zero power factor tests.** But to find only leakage reactance open circuits and zero power factor tests are sufficient.**

In an alternator, when the armature current increases, the terminal voltage drops due to:

Option 2 : Armature effective resistance, armature leakage reactance and armature reaction

Variation in the terminal voltage of alternator occurs due to the following reasons:

1. Voltage drop due to armature resistance R_{a}

2. Voltage drop due to armature leakage reactance X_{L}

3. Voltage drop due to armature reaction

**Armature Resistance:**

The armature resistance/phase 'R_{a}' causes a voltage drop/phase of IR_{a,} which is in phase with the armature current I. However, this voltage drop is practically negligible.

**Armature Leakage Reactance:**

When current flows through the armature conductors, fluxes are set up which do not cross the air-gap but take different paths. Such fluxes are known as leakage fluxes.￼

The leakage flux is practically independent of saturation but is dependent on I and its phase angle with terminal voltage V. This leakage flux sets up an e.m.f. of self-inductance which is known as reactance e.m.f. and which is ahead of I by 90°. Hence, armature winding is assumed to possess leakage reactance X_{L} (also known as Potier reactance X_{P}) such that voltage drop due to this equals IX_{L}. A part of the generated e.m.f. is used up in overcoming this reactance e.m.f.

**Armature Reaction:**

As in d.c. generators, armature reaction is the effect of armature flux on the main field flux. In the case of alternators, the power factor of the load has a considerable effect on the armature reaction. Upon which three cases are possible:

(i) when p.f. is unity

(ii) when p.f. is zero lagging and

(iii) when p.f. is zero leading.

Option 1 : Decreasing in nature

**Voltage regulation of an alternator:**

It is defined as the rise in voltage when a full load is removed divided by the rated terminal voltage when speed and field excitation remains the same.

**Formula:**

Percentage voltage regulation is

% VR= \({\frac{E_o -V}{V}}\times 100\)

% VR = \({\frac{I_a{(R_s\cos\phi\pm X_s\sin \phi)}}{V}}\times100\)

E_{o} = Nol-load voltage

V = Full load voltage

I_{a} = Armature current

R_{s} = Synchronous resistance

X_{s} = Synchronous reactance

Voltage regulation is dependent on load current and power factor.

**Effect of power factor on voltage regulation:**

Nature of power factor |
Element |
Nature of voltage regulation |
Performance |
---|---|---|---|

Lagging power factor |
Inductive reactance |
Increases |
Poor voltage regulation |

Leading power factor |
Capacitive reactance |
Decreases |
Voltage regulation improves |

Unity power factor |
Resistance |
Remains constant |
A constant regulation |

The leading power factor reduces voltage regulation value and improves system performance.

Option 2 : Short-circuit characteristic test

To finding the Voltage regulation of the Alternator we need to know about the value of armature resistance (R_{a}) and synchronous reactance (X_{s}),

**It can be found by the following method:**

1. SCC (Short Circuit Characteristic)

2. OCC (Open Circuit Characteristic)

3. DC Resistance Test Method

**1. SCC (Short Circuit Characteristic):**

In this method, the armature terminal is shorted through three ammeters as shown,

- The alternator is running at synchronous speed.
- At the initial stage, the field current should first be decreased to zero and increased up to 150% of the rated value.
- The field current will be an average of three ammeter reading.
**By using this method we found the armature current at different values of excitation or field current in a short time without overheating.**- According to that reading, we plot the characteristics between field current and armature current as shown,

__Additional Information__

**2. OCC (Open Circuit Characteristic):**

In this method the alter run at synchronous speed and the load terminal is kept open as shown

- The field current is gradually increased in steps and terminal voltage is measured in each step with the help of Voltmeter as shown in the circuit.
- The field current is increased in such a way we can get the rated voltage up to 125%.
- Then a graph is plotted between the armature terminal voltage and field current as shown.

**Finding Synchronous Impedance (Zs) with the help of OCC and SCC:**

Synchronous impedance is the ratio of Open circuit voltage per phase to the score circuit armature current at the same value of field current (Excitation).

- Let the rated field current is IA, and we have to find the Open circuit voltage and short circuit armature current at this value by plotting the graph as shown,

From the above characteristics,

At rated field current (I_{A}),

Open Circuit Voltage (V_{OC}) = OB

Short Circuit Current (I_{SC}) = OC

Synchronous Impedance (Z_{s}) = \(\dfrac{OB}{OC}\) Ω

From using the concept of, **Z ^{2} = R^{2} + X^{2}**, we easily find the Synchronous reactance.

And Armature resistance will find by using the Voltage Test Method or (VA or AV) method.

Option 4 : magnetizing

__MMF wave diagrams of synchronous motor:__

The operation of a synchronous machine may be understood by considering its m.m.f. waves.

There are three m.m.f. waves to be considered that

- Due to the field winding ϕf, which is separately excited with the direct current.
- Due to the 3-phase armature winding flux ϕa.
- Their resultant flux ϕr = ϕf ± ϕa

All the MMFs produced in the motor move at synchronous speed with respect to the stator.

__Zero power factor lagging:__

The armature reaction is entirely De-magnetising in nature.

ϕr = ϕf - ϕa

The net flux reduces the load to reduce the terminal voltage.

Voltage regulation is positive.

__Zero power factor leading:__

The armature reaction is entirely Magnetising in nature.

ϕr = ϕf + ϕa

Net flux in the airgap increased to increase induced voltage and the terminal voltage.

Voltage regulation is negative.

Option 3 : 0.8

__Concept:__

Open Circuit Test:

- This test is used for determining the
**synchronous impedance.** - The alternator is running at the rated synchronous speed, and the load terminals are kept open.
- The excitation current may be increased to get 25% more than the rated voltage i.e. up to 125% of the rated voltage.
- A graph is drawn between the open circuit phase voltage Eg and the field current If. The curve so obtained is called Open Circuit Characteristic (O.C.C).
- The linear portion of the O.C.C is extended to form an air gap line.

The Open Circuit Characteristic (O.C.C) and the air gap line is shown in the figure below

Short circuit test:

- The machine is driven at rated synchronous speed and armature terminals are short-circuited through an ammeter.
- Now, field current gradually increased from zero, until the short-circuit armature current reached its safe maximum value, equal to about 125 to 150% of the rated current.
- Latter readings may be taken in a short time to avoid armature overheating.
- A graph is drawn between short-circuit current Isc and field current if as shown in the figure.

**Per Unit calculation with new base:**

\(Z_{pu(new)}=Z_{pu(old)}\times (\frac{MVA_{new}}{MVA_{old}})(\frac{kV_{bold}}{kV_{bnew}})^2\)

**Explanation:**

Given,

Rated kVA, S = 10 kVA

Rated voltage, V = 200 V

**Old Base**: 10 kVA, 200 V

Rated armature current.

\(I_{rated}=\frac{10\times10^3}{200}=50 A\)

\(Z_{base}=\frac{V_{rated}}{I_{rated}}=\frac{200}{50}=4\ \Omega \)

Field current, I_{f1} = 2 A produces Irated = 50 A

∴ field current, If2 = 5 A will produce armature current,

\(I_a=\frac{5}{2}\times 50=125 A\)

Which is nothing but the short-circuit armature current.

I_{sc} = 125 A, V_{oc} = 200 V

Synchronous Impedance,

\(Z_s=\frac{V_{oc}}{I_{sc}}=\frac{200}{125}=1.6\ \Omega \)

\((Z_s)_{pu}=\frac{Z_s}{Z_{base}}=\frac{1.6}{4}=0.4\ \ pu\)

**New Base**: 20 kVA, 200 V

Using the formula mentioned in the concept part,

\((Z_{pu})_{new}=0.4\times (\frac{20}{10})(\frac{200}{200})^2=0.8\ \ pu\)

Hence, for 20 kVA, 200 V base, synchronous impedance =** 0.8 pu**

Option 3 : 5.64 Ω

**Measurement of Synchronous Impedance:**

The measurement of synchronous impedance is done by the following methods. They are known as

__(1) Open Circuit Test:__

- In the open-circuit test for determining the synchronous impedance, the alternator is running at the rated synchronous speed, and the load terminals are kept open.
- This means that the loads are disconnected, and the field current is set to zero.

**(2) Short Circuit Test:**

- The field current should first be decreased to zero before starting the alternator.
- Each ammeter should have a range greater than the rated full load value.
- The alternator is then run at synchronous speed.
- Same as in an open circuit test that the field current is increased gradually in steps and the armature current is measured at each step.
- The field current is increased to get armature currents up to 150% of the rated value.

**Z _{S} = V_{OC} / I_{SC}**

Where,

Z_{S} is the synchronous impedance

V_{OC} is the open-circuit voltage per phase

I_{SC} is the short circuit current per phase

**Calculation:**

Given,

V_{OC} = 4750 V

Output power P = 3.5 MVA

Terminal voltage V = 4160

Full load current I_{L }= I_{ph} = P / √3 V

= 3.5 × 10^{6} /(√3× 4160)

= 485.751 A

The field current of 200 A produces full load current on short circuit

Hence, I_{SC } = 841.34 A

ZS = VOC / ISC

Z_{SC} = 4750 / (√3 × 485.751)

= 5.64 Ω

**Therefore, the synchronous impedance of the alternator is 5.64 Ω **

Option 1 : capacitive only

Voltage regulation: The voltage regulation of an AC alternator is,

Percentage voltage regulation \(= \frac{{{E_{g0}} - {V_t}}}{{{V_t}}} \times 100\)

Eg0 is the internally generated voltage per phase at no load

Vt is the terminal voltage per phase at full load

Voltage regulation indicates the drop in voltage from no load to the full load.

There are three causes of voltage drop in the alternator.

- Armature circuit voltage drop
- Armature reactance
- Armature reaction

The first two factors always tend to reduce the generated voltage, the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

Important Points:

- At unity and lagging power factor loads, the terminal voltage is always less than the induced EMF and the voltage regulation is positive.
- At higher leading loads, the terminal voltage is greater than the induced EMF and the voltage regulation is negative.
- The lower the leading power factor, the greater the voltage rise from no load (Eg0) to full load (Vt)
- The lower the lagging power factor, the greater the voltage decrease from no load (Eg0) to full load (Vt)

Which among the curves (A, B, C, and D) represents the characteristics for unity power factor?

Option 3 : C

**Concept:**

**Voltage Regulation:**

- The voltage regulation is defined as “the rise in voltage at the terminals, when the load is reduced from full load rated value to zero, speed and field current remaining constant”.
- With the change in load, there is a change in the terminal voltage of an alternator or synchronous generator. The magnitude of this change not only depends on the load but also on the load power factor.
- It is also defined as “the rise in voltage when full load is removed divided by the rated terminal voltage when speed and field excitation remains the same.” It is given by the formula,

\(V.R=\frac{E-V}{V}\)

Where,

E is no load voltage

V is the terminal voltage

**Case 1:**

E > V: Then V.R will be positive and the power factor will be lagging or unity.

**Note: **V.R under unity power factor is less than voltage regulation under lagging power factor,

**Case 2:**

E < V or E = V: Then VR will be negative and zero respectively and the power factor will be leading.

**Conclusion:**

From the above concept,

Curve D represents V.R at leading power factor.

**Curve C represents V.R at a somewhat unity power factor.**

Curve A and Curve B represent V.R at lagging power factor.

Option 1 : greater than that at unity power factor

Voltage regulation: The voltage regulation of an AC alternator is,

Percentage voltage regulation \(= \frac{{{E_{0}} - {V}}}{{{V}}} × 100\)

E0 is the internally generated voltage per phase at no load and it is given by,

E_{0} = V + I_{a}Z_{s}

V is the terminal voltage per phase at full load

Voltage regulation indicates the drop in voltage from no load to the full load.

There are three causes of voltage drop in the alternator.

- Armature circuit voltage drop
- Armature reactance
- Armature reaction

The first two factors always tend to reduce the generated voltage, the third factor may tend to increase or decrease the generated voltage. The nature of the load affects the voltage regulation of the alternator.

**Voltage Regulation Curve at different Power Factor:**

**From The curve:**

**Voltage regulation at the lagging power factor will be more than the voltage regulation at the unity power factor.**- Negative voltage regulation and zero voltage regulation occur at the leading power factor.
- Positive voltage regulation occurs at both unities as well as lagging power factors.

**Illustration:**

**Phasor Diagram at Unity Power Factor:**

At unity power factor the value of phase angle will be zero and hence, phasor can be drawn as,

**∴ E _{0} = V + I_{a}R_{a} .... (1)**

**Phasor Diagram at 0.8 lagging Power Factor:**

Given, cos ϕ = 0

∴ ϕ = 36.86°

Now, R_{a} = Z cos ϕ & X_{s} = sin ϕ

Phasor diagram can be drawn as,

From Phasor, the value of E_{0} given by

(E_{0})2 = OA^{2} + AB^{2} = (OD + DA)^{2} + (AC + CD)^{2}

**(E _{0})^{2} = (V cosϕ + I_{a}R_{a})2 + (V sin ϕ + I_{a}X_{s})^{2} .... (2)**

**Proof:**

Let consider,

V = 200 volts (single phase)

R_{a} = 0.06 Ω

X_{s} = 0.8 Ω

Since. X_{s} >> R_{a}

I_{a} = 50 A

**At unity Power,**

E_{0} = V + I_{a}R_{a} = 200 + (50 × 0.06) = 200 + 3 = 203 volts

**∴ Change in voltage = 203 - 200 = 3 volts**

**At 0.8 Lagging Power factor,**

cos ϕ = 0.8 → sin ϕ = 0.6

Now, V cosϕ = 200 × 0.8 = 160 volts

V sin ϕ = 200 × 0.6 = 120 volts

I_{a}R_{a} = 3 volts

I_{a}X_{s} = 50 × 0.8 = 40 volts

From equation (2),

(E_{0})2 = (V cosϕ + I_{a}R_{a})^{2} + (V sin ϕ + I_{a}X_{s})^{2}

(E_{0})2 = (160 + 3)^{2} + (120 + 40)^{2} = 163^{2} + 160^{2}

∴ E_{0} = 228 volts

**∴ Change in voltage = 228 - 200 = 28 volts**

**Hence, Voltage regulation at 0.8 lagging power factor will be more than the voltage regulation at unity power factor.**

Option 2 : 10.5

**Concept:**

Voltage Regulation of a synchronous Generator is the rise in voltage at the terminal when the load is reduced full load rated value to zero, speed and field current remaining constant.

Percentage voltage \( \buildrel \Delta \over = \frac{{\left| {{E_a}} \right| - \left| V \right|}}{{\left| V \right|}} \times 100\)

|E_{a}| = magnitude of Generated voltage per phase

|V| = magnitude of rated terminal voltage per phase

**Calculation:**

Armature Resistance drop IR = 50 V per phase

Reactance drop IX = 500 V per phase

Power factor = Unity

Rated voltage per phase \({V_p} = \frac{{2300}}{{\sqrt 3 }}\)

V_{p} = 1327.9 V

V_{p} = 1327.9 ∠0 V

Let V_{p} be taken as Reference

E_{p} = V_{p} + I_{ap} Z_{s}

∴ Z_{s} = R_{a} + jX_{s}

E_{p} = V_{p} + I_{ap} (R_{a} + J X_{s})

E_{p} = V_{p} + I_{ap} R_{a} + J I_{ap} X_{s}

E_{p} = 1327.9∠0 + 50 + 500∠90°

E_{p} = 1327.9∠0 + 500∠90°

E_{p} = 1465.81∠19.94

|E_{p}| = 1465.81 V

Percentage voltage \(= \frac{{\left| {{E_p}} \right| - \left| {{V_p}} \right|}}{{\left| {{V_p}} \right|}} \times 100\)

\(= \frac{{1465.81 - 1327.9}}{{1327.9}} \times 100\)

= 10.38%