Synchronous Impedance Method or E.M.F. Method

       The method is also called E.M.F. method of determining the regulation. The method requires following data to calculate the regulation.

1. The armature resistance per phase (R_a).

2. Open circuit characteristics which is the graph of open circuit voltage against the field current. This is possible by conducting open circuit test on the alternator.

3. Short circuit characteristics which is the graph of short circuit current against field current. This is possible by conducting short circuit test on the alternator.

       Let us see, the circuit diagram to perform open circuit as well as short circuit test on the alternator. The alternator is coupled to a prime mover capable of driving the alternator at its synchronous speed. The armature is connected to the terminals of a switch. The other terminals of the switch are short circuited through an ammeter. The voltmeter is connected across the lines to measure the open circuit voltage of the alternator.

       The field winding is connected to a suitable d.c. supply with rheostat connected in series. The field excitation i.e. field current can be varied with the help of this rheostat. The circuit diagram is shown in the Fig. 1.

Fig. 1  Circuit diagram for open circuit and short circuit test on alternator

1.1 Open Circuit Test

       Procedure to conduct this test is as follows :

i) Start the prime mover and adjust the speed to the synchronous speed of the alternator.

ii) Keeping rheostat in the field circuit maximum, switch on the d.c. supply.

iii) The T.P.S.T switch in the armature circuit is kept open.

iv) With the help of rheostat, field current is varied from its minimum value to the rated value. Due to this, flux increasing the induced e.m.f. Hence voltmeter reading, which is measuring line value of open circuit voltage increases. For various values of field current, voltmeter readings are observed.

       The observation for open circuit test are tabulated as below :

Observation table for open circuit test :

       From the above table, graph of (V_oc)_ph against I_f is plotted.

Note : This is called open circuit characteristics of the alternator, called O.C.C. This is shown in the Fig. 2.

Fig. 2  O.C.C. and S.C.C. of an alternator

1.2 Short Circuit Test

       After completing the open circuit test observation, the field rheostat is brought to maximum position, reducing field current to a minimum value. The T.P.S.T switch is closed. As ammeter has negligible resistance, the armature gets short circuited. Then the field excitation is gradually increased till full load current is obtained through armature winding. This can be observed on the ammeter connected in the armature circuit. The graph of short circuit armature current against field current is plotted from the observation table of short circuit test. This graph is called short circuit characteristics, S.C.C. This is also shown in the Fig. 2.

Observation table for short circuit test :

       The S.C.C. is a straight line graph passing through the origin while O.C.C. resembles B-H curve of a magnetic material.

Note : As S.C.C. is straight line graph, only one reading corresponding to full load armature current along with the origin is sufficient to draw the straight line.

1.3 Determination of From O.C.C. and S.C.C.

       The synchronous impedance of the alternator changes as load condition changes. O.C.C. and S.C.C. can be used to determine Z_s for any load and load p.f. conditions.

       In short circuit test, external load impedance is zero. The short circuit armature current is circulated against the impedance of the armature winding which is Z_s. The voltage responsible for driving this short circuit current is internally induced e.m.f. This can be shown in the equivalent circuit drawn in the Fig. 3.

Fig. 3  Equivalent circuit on short circuit

       From the equivalent circuit we can write,
       Z_s = E_ph/ I_asc

       Now value of I_asc is known, which can observed on the alternator. But internally induced e.m.f. can not be observed under short circuit condition. The voltmeter connected will read zero which is voltage across short circuit. To determine Z_s it is necessary to determine value of E which is driving I_asc against Z_s.

       Now internally induced e.m.f. is proportional to the flux i.e. field current I_f.
       E_ph   α   Φ  α  I_f                                              ...... from e.m.f. equation

       So if the terminal of the alternator are opened without disturbing I_f which was present at the time of short circuited condition, internally induced e.m.f. will remain same as E_ph. But now current will be zero. Under this condition equivalent circuit will become as shown in the Fig. 4.

Fig. 4

       It is clear now from the equivalent circuit that as I_a = 0 the voltmeter reading (V_oc)_ph will be equal to internally induced e.m.f. (E_ph).

       This is what we are interested in obtaining to calculate value of Z_s. So expression for Z_s can be modified as,

       So O.C.C. and S.C.C. can be effectively to calculate Z_s.
       The value of Z_s is different for different values of I_f as the graph of O.C.C. is non linear in nature.
       So suppose Z_s at full load is required then,
       I_asc = full load current.

        From S.C.C. determine I_f required to drive this full load short circuit I_a. This is equal to 'OA', as shown in the Fig.2.

       Now for this value of I_f, (V_oc)_ph can be obtained from O.C.C. Extend kine from point A, till it meets O.C.C. at point C. The corresponding (V_oc)_ph value is available at point D.

       (V_oc)_ph  = OD
       While (I_asc)_ph = OE

at full load
      General steps to determine Z_s at any load condition are :

i) Determine the value of (I_asc)_ph for corresponding load condition. This can be determined from known full load current of the alternator. For half load, it is half of the full load value and so on.

ii) S.C.C. gives relation between (I_asc)_ph and I_f. So for (I_asc)_ph required, determine the corresponding value of I_f from S.C.C.

iii) Now for this same value of I_f, extend the line on O.C.C. to get the value of (V_oc)_ph. This is (V_oc)_ph  for same I_f, required to drive the selected (I_asc)_ph.

iv) The ratio of (V_oc)_ph and (I_asc)_ph, for the same excitation gives the value of Z_s at any load conditions.
       The graph of synchronous impedance against excitation current is also shown in the Fig. 2.

1.4 Regulation Calculations

       From O.C.C. and S.C.C., Z_s can be determined for any load condition.

       The armature resistance per phase (R_a) can be measured by different methods. One of the method is applying d.c. known voltage across the two terminals and measuring current. So value of R_a per phase is known.

       So synchronous reactance per phase can be determined.

       No load induced e.m.f. per phase, E_ph can be determined by the mathematical expression derived earlier.

       where     V_ph = Phase value of rated voltage
                      I_a = Phase value of current depending on the load condition
                      cosΦ = p.f. of load

        Positive sign for lagging power factor while negative sign for leading power factor, R_a and X_s values are known from the various tests performed.

       The regulation then can be determined by using formula,

1.5 Advantages and Limitations of Synchronous Impedance Method

       The main advantages of this method is the value of synchronous impedance Z_s for any load condition can be calculated. Hence regulation of the alternator at any load condition and load power factor can be determined. Actual load need not be connected to the alternator and hence method can be used for very high capacity alternators.

       The main limitation of this method is that the method gives large values of synchronous reactance. This leads to high values of percentage regulation than the actual results. Hence this method is called pessimistic method.

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