# Power-Angle Curve

Consider a synchronous machine connected to an infinite bus through a transmission line of reactance X_{l} shown in a figure below. Let us assume that the resistance and capacitance are neglected.

Equivalent diagram of synchronous machine connected to an infinite bus through a transmission line of series reactance X_{l} is shown below:

V = V<0⁰ – voltage of infinite bus

E = E<δ – voltage behind the direct axis synchronous reactance of the machine.

X_{d} = synchronous / transient resistance of the machine

The complex power delivered by the generator to the system is

S = VI

Let, Active power transferred to the system

The reactive power transferred to the system

The maximum steady-state power transfers occur when δ = 0

The graphical representation of P_{e} and the load angle δ is called the power angle curve. It is widely used in power system stability studies. The power angle curve is shown below

Maximum power is transferred when δ = 90⁰. As the value of load angle δ is above 90, P_{e} decrease and becomes zero at δ = 180⁰. Above 180⁰, Pe becomes negative, which show that the direction of power flow is reversed, and the power is supplied from infinite bus to the generator. The value of P_{e} is often called pull out power. It is also called the steady-state limit.

The total reactance between two voltage sources E and X is called the transfer reactance. The maximum power limit is inversely proportion to the transfer reactance.