Potier Triangle

Potier triangle method is helpful in obtaining the voltage regulation of synchronous machines. It gives the value of potier reactance and the armature mmf (reaction) by drawing a series of curves on experimental basis.

Potier reactance is the air gap reactance (leakage reactance) of the synchronous machine at full load (rated voltage and current of armature).

Circuit Diagram For Determination of Portier Reactance

First of all we need to find the open circuit characteristics of the synchronous machine. This is done by connecting a voltmeter on any two phase of the stator and increasing the field current slowly up to 125% - 150% of rated value and plotting the armature voltage vs. field current. Since armature current is 0, Vt = Ef. We assume that it remains same under no load and full load condition which is not true.

Next we need to perform a Short Circuit Test, where the terminals of the stator are short circuited and the field current is adjusted such that rated armature current flows. Since Vt =0, the mmf (If equivalent) developed is completely used up to overcome the air gap and armature impedance. The flux is not saturated because of the opposition developed by Fa. Hence the B-H or V-I equivalent curve would be linear. It is also evident from the plot we have drawn.

 

Lastly we need to find the zero power factor lag curve by loading the synchronous machine with pure inductors. Since the load is purely inductive the current lags the voltage by 90 degrees. Increase the excitation until rated current flows. The armature phase voltage and the field current are noted and the zpflc curve is drawn.

Considering armature resistance to be negligible, Ia is almost in Quadrature to Vt (very small ra) and the terminal voltage, the air gap reactance drop and Er are all in phase given by: 

Er = Vt + jIaXl

As you may remember that the field mmf (OA) developed during SCC is minimum mmf required to overcome the leakage impedance drop (Vt=0). Shifting it to the level of Vt would give along the line of rated armature current (O' A') would help us give the value of Er by drawing a line parallel the air gap line from O' and marking the point of intersection (B') on OCC. Line parallel to air gap line is drawn considering B-H curve to be in unsaturated region.

 

So now we know Vt, Er we can find IaXl by algebraically subtracting them or graphically the line B'C' to represent it. The line OG along the mmf axis is the corresponding air gap flux. The flux corresponding to Vt is found by marking the point of intersection of Vt on zpfc line and drawing a vertical line through it which implies that 'For rated terminal voltage the corresponding mmf required  is OH and the Ef (no load voltage ) produced is HF.

We know Fr and Ff, show we can easily find Fa by subtracting these two.

 

Ff - Fr = Fa

Graphically it corresponds to C'A' portion of the curve.

This method is used to find voltage regulation of Synchronous Machine

 

Knowing the rated terminal voltage, we can find Er. Once Er is found we have Fr. From potier triangle we could get Fa. Using Fr and Fa we have Ff and then Ef.

Voltage regulation can hence be found using the formula:

 

VR% =[ (Ef – Vt)/Vt]*100

Lower the voltage regulation, better the machine.

*all suggestions are welcome!