How to Draw Potier Triangle/ZPF Characteristics ?


Regulation by Zero Power Factor ( ZPF) method  of Alternator:

During the operation of the alternator, resistance voltage drop IaRand armature leakage reactance drop IaXL are actually emf quantities and the armature reaction reactance is a mmf quantity. To determine the regulation of the alternator by this method OCC, SCC and ZPF test details and characteristics are required.

-As explained earlier OC and SC tests are conducted and OCC and SCC are drawn.

-ZPF test is conducted by connecting the alternator to ZPF load and exciting the alternator in such way that the alternator supplies the rated current at rated voltage running at rated speed.
-To plot ZPF characteristics only two points are required. One point is corresponding to the zero voltage and rated current that can be obtained from scc and the other at rated voltage and rated current under zpf load.
-This zero power factor curve appears like OCC but shifted by a factor IXL vertically and horizontally by armature reaction mmf as shown below in figure. 



Following are the steps to draw ZPF characteristics:

-By suitable tests plot OCC and SCC. Draw air gap line. Conduct ZPF test at full load for rated voltage and fix the point B.

-Draw the line BH with length equal to field current required to produce full load
current on short circuit..
-Draw HD parallel to the air gap line so as to cut the OCC. Draw DE perpendicular to HB or parallel to voltage axis.
-Now, DE represents voltage drop IXL and BE represents the field current required to overcome the effect of armature reaction.
-Triangle BDE is called Potier triangle and XL is the Potier reactance. Find E from V, IRa, IXL and .
-Use the expression E =√ (V cos  Ø+ IRa)² + (V sin ) + IXL)² to compute E. Find field current corresponding to E. Draw FG with magnitude equal to BE at angle (90+ ) from field current axis, where is the phase angle of current from voltage vector E (internal phase angle).
-The resultant field current is given by OG. Mark this length on field current axis. From OCC find the corresponding E0. Find the regulation.