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 (E_exc).

The other Component of the generated voltage is known as the Armature Reaction Voltage (E_AR). 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 X_AR 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,

• L_a is the self-inductance of the stator winding
• X_a is the self-inductive reactance of stator winding
• R_a is the armature stator resistance.

The Terminal voltage V is given by the equation shown below.

Where,

• R_aI_a is the armature resistance drop
• X_aI_a is the armature leakage reactance drop
• X_ARI_a 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 Z_S in the above equation (7) is the Synchronous Impedance, and X_S is the Synchronous Reactance.