What is Synchronous Reactance & Synchronous Impedance ?

When an alternator is loaded, there will be a circulation of load current in the armature winding. Once the load on the alternator is increased, the terminal voltage changes (for constant excitation) due to the following reasons,

• Voltage drop due to armature resistance, IR_a.
• Voltage drop due to synchronous reactance.

Armature Resistance :

The armature resistance per phase R_a causes a voltage drop per phase of IR_a which is in phase with the armature current. The armature resistance per phase can be measured directly by voltmeter and ammeter (ohm's law) method or by using a wheat stone bridge.

For working conditions, this measured value of armature resistance is increased from 50% to 60% or so to allow the skin effect and give an effective value of armature resistance R_a.

The effective value of per-phase resistance,

R_a = 1.5 R_dc

Where R_dc = Resistance per-phase measured with dc supply.

Synchronous Reactance :

The synchronous reactance of an alternator or synchronous generator is a combination of armature leakage reactance and armature reaction reactance.

Armature Leakage Reactance (X_L) :

When the current flows through the armature conductors the flux set up by the conductors do not cross the air-gap, but complete its path in the armature through the air around the conductor itself. Such a flux is known as leakage flux as shown below figure.

The leakage flux sets an emf leading the load current I by 90° and proportional to the load current I. Hence, armature winding is assumed to possess leakage reactance X_L (in addition to R_a) such that the voltage drop due to this is IX_L as shown in the below vector diagram.

Generated emf, E will be,

E = V + IR_a + j IX_L

= V + I (R_a + jX_L)

Where, X_L = Armature leakage reactance = 2π f L Ω/ph.

Armature Reaction Reactance (X_a) :

In an alternator or synchronous generator in addition to the armature winding resistance drop and leakage reactance drop, there is a drop in terminal voltage due to armature reaction. Generally, the load connected to the alternator is of inductive type. We know that the armature reaction is of demagnetizing effect for inductive loads i.e., the armature flux due to armature current tries to demagnetize the main flux.

In order to balance the terminal voltage by quantifying the voltage drop due to the armature reaction. The effect of armature reaction is accounted for by assuming the presence of a fictitious reactance X_a in the armature winding known as armature reaction reactance.

Therefore, the sum of the fictitious armature reaction reactance X_a due to the effect of armature reaction and the leakage reactance X_L of the armature is known as synchronous reactance X_s.

i.e., X_s = X_L + X_a

Synchronous Impedance :

The synchronous impedance may be defined as the vector sum of the armature resistance and synchronous reactance. It is denoted as Z_s.

Where,

• R_a = Armature resistance
• X_s = Synchronous reactance (X_L + X_a)

Therefore, the relationship between induced emf E and the terminal voltage V can be represented as,

Where,

• E = EMF induced on load.
• V = Terminal voltage. It is vectorially less than E_o (no-load emf) by IZ_s.
• I = Armature current per-phase.
• IZ_s = Voltage drop in an alternator.

Generally, the alternator rotates at synchronous speed. Hence, when the alternator has loaded the word 'Synchronous' is used to specify the reactance and impedance of the alternator. Since synchronous reactance varies with variation in load condition and its power factor. This in turn also changes the synchronous impedance.

Effect of Synchronous Impedance :

The following are the various effects of synchronous impedance,

• Voltage drop increases.
• Supply voltage decreases.
• Power loss takes place (since impedance includes resistance).
• Heat is produced.
• Voltage regulation increases.
• Efficiency decreases.
• For large alternators cooling system is required.