This method of determining the regulation of an alternator is also called Ampere-turn method or Rothert's M.M.F. method. The method is based on the results of open circuit test and short circuit test on an alternator.

For any synchronous generator i.e. alternator, it requires m.m.f. which is product of field current and turns of field winding for two separate purposes.

1. It must have an m.m.f. necessary to induce the rated terminal voltage on open circuit.

2. It must have an m.m.f. equal and opposite to that of armature reaction m.m.f.

**Note**: In most of the cases as number of turns on the field winding is not known, the m.m.f. is calculate and expressed i terms of the field current itself.

The field m.m.f. required to induce the rated terminal voltage on open circuit can be obtained from open circuit test results and open circuit characteristics. This is denoted as F

_{O}. We know that the synchronous impedance has two components, armature resistance and synchronous reactance. Now synchronous reactance also has two components, armature leakage reactance and armature reaction reactance. In short circuit test, field m.m.f. is necessary to overcome drop across armature resistance and leakage reactance and also to overcome effect of armature reaction. But drop across armature resistance and also to overcome effect of armature reaction. But drop across armature resistance and leakage reactance is very small and can be neglected. Thus in short circuit test, field m.m.f. circulates the full load current balancing the armature reaction effect. The value of ampere-turns required to circulate full load current can be obtained from short circuit characteristics. This is denoted as F

_{AR}. Under short circuit condition as resistance and leakage reactance of armature do not play any significant role, the armature reaction reactance is dominating and hence the power factor of such purely reactive circuit is zero lagging. Hence F

_{AR}gives demagnitising ampere turns. Thus the field m.m.f. is entirely used to overcome the armature reaction which is wholly demagntising in nature. The two components of total field m.m.f. which are F

_{O}and F_{AR }are indicated in O.C.C. (open circuit characteristics) and S.C.C. (short circuit characteristics) as shown in the Fig. 1.Fig. 1 |

If the alternator is supplying full load, then total field m.m.f. is the vector sum of its two components F

_{O}and F_{AR}. This depends on the power factor of the load which alternator is supplying. The resultant field m.m.f. is denoted as F_{R}. Let us consider the various power factors and the resultant F_{R}.**Zero lagging p.f.**: As long as power factor is zero lagging, the armature reaction is completely demagnetising. Hence the resultant F

_{R }is the algebraic sum of the two components F

_{O }and F

_{AR}. Field m.m.f. is not only required to produce rated terminal voltage but also required to overcome completely demagnetising armature reaction effect.

Fig. 2 |

OA = F

_{O}

AB = F

_{AR}demagnetising

OB = F

_{R }= F

_{O}+ F

_{AR}

Total field m.m.f. is greater than F

_{O}.

**Zero leading p.f.**: When the power factor is zero leading then the armature reaction is totally magnetising and helps main flux to induce rated terminal voltage. Hence net field m.m.f. required is less than that required to induce rated voltage normally, as part of its function is done by magnetising armature reaction component. The net field m.m.f. is the algebraic difference between the two components F

_{O}and F

_{AR}. This is shown in the Fig. 3.

Fig. 3 |

_{O}

AB = F

_{AR }magnetising

OB = F

_{O}- F

_{AR}= F

_{R}

Total m.m.f. is less than F

_{O}

**Unity p.f.**: Under unity power factor condition, the armature reaction is cross magnetising and its effect is to distort the main flux. Thus and F are at right angles to each other and hence resultant m.m.f. is the vector sum of F

_{O}and F

_{AR}. This is shown in the Fig.4.

Fig. 4 |

_{O}

AB = F

_{AR}cross magnetising

**General Case**: Now consider that the load power factor is cos Φ. In such case, the resultant m.m.f. is to be determined by vector addition of F

_{O }and F

_{AR}.

**cosΦ**

**, lagging p.f.**: When the load p.f. is cosΦ lagging, the phase current I

_{aph }lags V

_{ph }by angle Φ. The component F

_{O }is at right angles to V

_{ph }while F

_{AR}is in phase with the current I

_{aph}. This is because the armature current I

_{aph }decides the armature reaction. The armature reaction F

_{AR}due to current I

_{aph }is to be overcome by field m.m.f. Hence while Finding resultant field m.m.f.

**,**- F

_{AR }should be added to vectorially. This is because resultant field m.m.f. tries to counterbalance armature reaction to produce rated terminal voltage. The phasor diagram is shown in the Fig. 5.

OA = F

_{O }, AB = F

_{AR }, OB = F

_{R }

Consider triangle OCB which is right angle triangle. The F

_{AR }is split into two parts as,

AC = F

_{AR }sinΦ and BC = F

_{AR }cosΦ

Fig. 5 |

**.**( F

^{.}._{R})

^{2}= (F

_{O }+ F

_{AR }sinΦ )

^{2}+ (F

_{AR }cosΦ)

^{2 }................ (1)

From this relation (1), F

_{R}can be determined.

**cosΦ, leading p.f.**: When the load p.f. is cosΦ leading, the phase current I

_{aph }leads V

_{ph }by Φ. The component F

_{O }is at right angles to V

_{ph }and F

_{AR }is in phase with I

_{aph}. The resultant F

_{R }can be obtained by adding - F

_{AR }to F

_{O}. The phasor diagram is shown in the Fig.6.

Fig. 6 |

AC = F

_{AR }sinΦ and BC = F

_{AR }cosΦ

OA = F

_{O}, AB = F

_{AR }and OB = F

_{R }

Consider triangle OCB which is right angles triangle.

**.**(OB)

^{.}.^{2}= (OC)

^{2}+ (BC)

^{2}

**.**( F

^{.}._{R})

^{2}= (F

_{O }- F

_{AR }sinΦ )

^{2}+ (F

_{AR }cosΦ) .................... (2)

From the relation (2), F

_{R}can be obtained.

Using relations (1) and (2), resultant field m.m.f. F

_{R}for any p.f. load condition can be obtained.

Once F

Once E_{R}is known, obtain corresponding voltage which is induced e.m.f. E_{ph}, required to get rated terminal voltage V_{ph}. This is possible from open circuit characteristics drawn.Fig. 7 |

_{ph}is known then the regulation can be obtained as,

**Note**: To obtain E

_{ph }corresponding to F

_{R}, O.C.C. must be drawn to the scale, from the open circuit test readings.

**Note**: This ampere-turn method gives the regulation of an alternator which is lower than the actually observed. Hence the method is called optimistic method.

**Important note**: When the armature resistance is neglected then F

_{O}is field m.m.f. required to produce rated V

_{ph }at the output terminals. But if the effective armature resistance is given then F

_{O }is to be calculated from O.C.C. such that F

_{O}represents the excitation (field current) required a voltage of V

_{ph }+ I

_{aph }R

_{aph }

_{ }cosΦ where

_{ph }= rated voltage per phase

I

_{aph }= full load current per phase

R

_{a }= armature resistance per phase

cosΦ = power factor of the load

It can also be noted that, F

_{R}can be obtained using the cosine rule to the triangle formed by F_{O}, F_{AR }and F_{O}as shown in the Fig. 8.Fig. 8 |

Students can use equations 1, 2 or 3 to calculate F

_{R}.

The angle between E

_{o }and

_{}V

_{ph }is denoted as δ and is called power angle. Neglecting R

_{a }

_{ }we can write,

I

_{a }X

_{s }cosΦ = E

_{o }sinδ

P

_{d }= V

_{ph }I

_{a }cosΦ = internal power of machine

**Note**: This equation shows that the internal power of the machine is proportional to sin δ.

easy to understand ...

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