# Zero Power Factor Characteristics and Potier Triangle

**Zero Power Factor Characteristics**

Zero Power Factor Characteristics (zpfc) of synchronous generator is a plot between the armature terminal voltage and field current for a constant value of armature current and speed. A purely inductive load is connected across the generator terminal to achieve zero power factor and zpfc.

Zero power factor characteristics along with Open Circuit Characteristics of generator are used to evaluate the value of armature leakage reactance x_{al} and armature reaction mmf F_{a}. zpfc for a synchronous generator is obtained as follows:

- The synchronous machine is operated at synchronous speed by the prime mover.
- A purely inductive load is connected at the generator terminal and field current is increased till rated current starts flowing in the armature winding.
- The load is varied in steps and field current is also adjusted so that rated current flow in the armature. In each step, the armature terminal voltage and field current is measured and noted. A plot between these two noted quantities is drawn. This plot is the zero power factor characteristics of generator.

A typical zpfc is shown in figure below. The figure below also includes the phasor diagram of synchronous generator under the condition of zero power factor.

From the above phasor diagram, it can be easily seen that terminal voltage V_{t} and air gap voltage E_{r} are almost in phase. Since the armature resistance is negligible as compared to leakage reactance x_{al}, therefore

V_{t} = E_{r} − I_{a}x_{al}

The filed mmf F_{f} and resultant air gap mmf F_{r} is also almost in phase, therefore

F_{f} = F_{r} + F_{a}

**Potier Triangle**

Potier Triangle is a right angled triangle whose perpendicular and base represents the voltage drop in armature leakage reactance (I_{a}x_{al}) and armature mmf F_{a} respectively. This triangle is used to draw the zero power factor characteristics (zpfc) from the open circuit characteristics (OCC) of synchronous generator.

In the above figure OCC and zpfc are shown. For field excitation F_{f}, the armature terminal voltage is ‘PK’ under open circuit condition. Keeping filed current I_{f} and speed constant, when the generator armature is connected with purely inductive load, the air gap mmf F_{r} is reduced. Therefore, the generator open circuit terminal voltage corresponding to F_{r} is FC. When voltage drop in leakage reactance i.e. I_{a}x_{al} is subtracted from this voltage FC, generator terminal voltage FB = PA = V_{t} is obtained. Since zero power factor characteristics is a plot between V_{t} and F_{f} or I_{f}, which has not changed from its no load value of OP, the point A lies on the zpfc. The triangle ABC so obtained is called the ** Potier Triangle** where CB = I

_{a}x

_{al}and BA = F

_{a.}Thus from the Potier Triangle armature leakage reactance (x

_{al}) and armature mmf F

_{a}can be obtained.

For a constant armature current, the size of Potier Triangle ABC remains constant. Therefore it can be moved parallel to itself with its corner ‘C’ on OCC and its corner ‘A’ tracing the zero power factor characteristics (zpfc). Thus the shape of zpfc and OCC are same. The only difference being, zpfc is vertically downward by an amount equal to I_{a}x_{al} from the OCC and shifted horizontally right to the origin by an amount equal to F_{a}.