M.M.F. Method of Determining Regulation

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

       This is shown in the 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

       OA = F_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

       OA = F_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.

       From the phasor diagram the various magnitude are,
       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

       From the phasor diagram, various magnitudes are,
       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_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

       Once E_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

                     V_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

       Using cosine rule to triangle OAB,

       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.