**Subject :**Electrical Machines II (AC Machines)

**Unit :**Alternators

## MMF method for voltage regulation determination

**MMF method for voltage regulation determination:**

This method of finding voltage regulation considers the opposite view to the synchronous impedance method. It assumes the armature leakage reactance to be additional armature reaction. Neglecting armature resistance (always small), this method assumes that change in terminal p.d. on load is due entirely to armature reaction. The same two tests (viz open-circuit and short-circuit test) are required as for synchronous reactance determination; the interpretation of the results only is different. Under short-circuit, the current lags by 90° (Ra considered zero) and the power factor is zero. Hence the armature reaction is entirely demagnetizing. Since the terminal p.d. is zero, all the field AT (ampere turns) are neutralized by armature AT produced by the short circuit armature current.

(i) Suppose the alternator is supplying full-load current at normal voltage V (i.e., operating load voltage) and zero p.f. lagging. Then d.c. field AT required will be those needed to produce normal voltage V (or if R_{a} is to be taken into account, then V I_{a}R_{a} cosΦ) on no-load plus those to overcome the armature reaction,

Let

AO = field AT required to produce the normal voltage V (or **V I _{a}R_{a} cosΦ**) at no-load & OB

_{1}= fielder required to neutralize the armature reaction

Then total field AT required are the phasor sum of AO and OB_{1} [See Fig. (i)] i.e.,

Total field AT, **AB _{1} = AO OB_{1}**

The AO can be found from O.C.C. and OB_{1} can be determined from S.C.C. Note that the use of a d.c. quantity (field AT) as a phasor is perfectly valid in this case because the d.c. field is rotating at the same speed as the a.c. phasors i.e., ω = 2 πf.

*Fig: 1*

(ii) For a full-load current of zero p.f. leading, the armature AT are unchanged. Since they aid the main field, less field AT are required to produce the given e.m.f.

Therefore, Total field AT, **AB _{2} =AO - B_{2}O**

where B_{2}O = fielder required to neutralize armature reaction

This is illustrated in Fig. (1 (ii)). Note that again AO are determined from O.C.C. and B_{2}O from S.C.C.

(iii) Between zero lagging and zero leading power factors, the armature m.m.f. rotates through 180°. At unity p.f., armature reaction is cross-magnetizing only. Therefore, OB_{3} is drawn perpendicular to AO [See Fig. (1 (iii))]. Now AB_{3} shows the required AT in magnitude and direction.

**General case:**

We now discuss the case when the p.f. has any value between zero (lagging or leading) and unity. If the power-factor is cos Φ lagging, then f is laid off to the right of the vertical line OB_{3} as shown in Fig. (2 (i)). The total field required are AB_{4} i.e., phasor sum of AO and OB_{4}. If the power factor is cos Φ leading, then Φ is laid off to the left of the vertical line OB_{3} as shown in Fig. (2 (ii)).

The total field AT required are AB_{5} i.e., phase sum of AO and OB_{5}.

*Fig: 2 Fig:3*

Since current α AT, it is more convenient to work in terms of field current. Fig. (3) shows the current diagram for the usual case of lagging power factor. Here AO represents the field current required to produce normal voltage V(or **V I _{a}R_{a} cos Φ**) on no-load. The phasor OB represents the field current required for producing full-load current on short-circuit. The resultant field current is AB and is the phasor sum of AO and OB. Note that phasor AB represents the field current required for demagnetizing and to produce voltage V and I

_{a}R

_{a}cos Φ drop (if R

_{a}is taken into account).