## Synchronous Impedance or E.M.F. Method for finding a Voltage Regulation

The Synchronous Impedance Method or Emf Method is based on the concept of replacing the effect of armature reaction by an imaginary reactance. The method requires following data to calculate the regulation.

**The open -circuit characteristic (O.C.C) :Â**

- The O.C.C is a plot of the armature terminal voltage as a function of field current with a symmetrical three phase short-circuit applied across the armature terminals with the machine running at rated speed.
- At any value of field current, if E is the open circuit voltage and Isc is the short circuit current then for this value of excitation
- Zs = E/Sic
- At higher values of field current, saturation increases and the synchronous impedance decreases.
- The value of Zs calculated for the unsaturated region.
- The O.C.C is called the unsaturated value of the synchronous impedance.

2. **The short-circuit characteristic (S.C.C)**

- The S.C.C is a plot of short-circuit armature current versus the field current.
- The current range of the instrument should be about 25-50 % more than the full load current of the alternator.
- Starting with zero field current, increase the field current gradually and cautiously till rated current flows in the armature.
- The speed of the set in this test also is tom be maintained at the rated speed of the alternator.

3. **Resistance of the armature winding.**

- Measure the D.C. resistance of he armature circuit of the alternator.
- The effective a.c resistance may be taken to be 1.2 times the D.C. resistance.

**Regulation Calculation**

- From O.C.C. and S.C.C., Z
_{sÂ }can be determined for any load condition.

- The armature resistance per phase 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
_{aÂ }per phase is known.So synchronous reactance per phase can be determined.

- No load induced e.m.f. per phase, E
_{phÂ }can be determined by the mathematical expression derived earlier.Â Â Â Â Â Â Â Â Â Â Â Â Eph= [ âˆš I(V cosÏ†+IRa)Â² +Â I(V SinÏ† +IXs)Â² ]whereÂ Â Â Â V

_{phÂ }= Phase value of rated voltage

I_{aÂ }= Phase value of current depending on the load condition

cosÎ¦ = p.f. of load - Positive sign for lagging power factor while negative sign for leading power factor, R
_{aÂ }and X_{sÂ }values are known from the various tests performed.The regulation then can be determined by using formula,