Power Angle Curve of Synchronous Machine
Table of Contents
The Electrical power output of a Synchronous machine is revealed by the power angle curve when the power angle is changed. This curve demonstrates that the output increases sinusoidally as we increase Power Angle from 0 to 90°. But a further increase in power angle δ beyond 90°, the Generator Electrical output Decreases.
Assume that a Synchronous machine is connected to an Infinite bus by the Transmission line of Reactance Xl Depicted in the figure below. Let’s assume that the capacitance and resistance are ignored.
The following Equivalent Diagram Illustrates a Synchronous machine connected to an Infinite bus by a Transmission line with series reactance Xl:
Let,
V = V<0⁰ – voltage of infinite bus
E = E<δ – voltage behind the direct axis synchronous reactance of the machine.
Xd = 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
Power Angle Curve
The power angle curve is the graphic representation of Pe and the load angle. Studies on the stability of power systems frequently employ it. Below is a display of the power angle curve.
Maximum power is transferred when δ = 90⁰. As the value of load angle δ is above 90, Pe 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 Pe 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.