Synchronous Reactance and Synchronous Impedance
Table of Contents
Synchronous Reactance and Synchronous Impedance
Synchronous Reactance
In order to account for the voltage effects in the Armature circuit caused by the actual Armature leakage Reactance and by the change in the air gap flux caused by the Armature reaction, the Synchronous Reactance (XS) is an imaginary Reactance.
Synchronous Impedance
A Fictitious Impedance called Synchronous Impedance ZS is used to account for the voltage effects on the armature circuit caused by the real armature resistance, the real armature leakage reactance, and the change in the air gap flux caused by the armature reaction.
The Two-component voltages are added to create the actual generated voltage. If there wasn’t an armature reaction, one of these Component voltages would be created. It is the voltage that would be produced if the field were the only source of Excitation. This component of the generated voltage is called the Excitation Voltage (Eexc).
The other Component of the generated voltage is known as the Armature Reaction Voltage (EAR). Thus, the two voltages that are the armature reaction voltage and the excitation voltage are added to keep a check on the effect of armature reaction upon the generated voltage. The equation is shown below.
Armature reaction is the cause of the voltage in a circuit that results from the flux change brought on by the current. This effect has an Inductive reactance nature. As a result, the equation below gives EAR, which is equivalent to a voltage of inductive reactance.
The Inductive Reactance XAR is a Fictitious reactance. As a result a voltage is generated in the Armature circuit. Therefore, Armature reaction voltage can be modeled as an Inductor in series with the Internally generated voltage.
The stator winding also has a self-inductance and resistance in addition to the effects of armature reaction.
Let,
- La is the self-inductance of the stator winding
- Xa is the self-inductive reactance of stator winding
- Ra is the armature stator resistance.
The Terminal voltage V is given by the equation shown below.
Where,
- RaIa is the armature resistance drop
- XaIa is the armature leakage reactance drop
- XARIa is the armature reaction voltage
Inductive Reactance can be used to Simulate both the Armature reaction and the Machine’s response to leakage flux. Thus, all of these come together to create the machine XS’s Synchronous Reactance, which is a single Reactance.
Therefore,
Where,
The Impedance ZS in the above equation (7) is the Synchronous Impedance, and XS is the Synchronous Reactance.