Flux Linkage Equation

The Constant Flux Linkage Principle in Alternator Transients

The constant flux linkage concept is fundamental to analyzing alternator transients. It states: In a closed circuit with zero resistance and capacitance, flux linkages remain unchanged following a sudden disturbance, preserving their pre-disturbance values.

In alternators, armature and field windings exhibit negligible capacitance, and their resistances are insignificant compared to inductances. Thus, these windings can be treated as purely inductive. Consequently, any abrupt change in current within one winding must be offset by a corresponding current adjustment in the other winding to maintain constant flux linkages—an essential mechanism for transient stability.

Proof of the Constant Flux Linkage Theorem

Mesh voltage equations for electrical circuits can be generally expressed as:

Using the symbol Ψ for the flux linkage (Nϕ), the equations may be written as follows:

Where e1 denotes the resultant voltage, a function of time t.Integrating equation (2) yields the change in flux linkage from an arbitrary initial time, expressed as:

Where Δt represents a small time interval. As Δt approaches zero, the integral term vanishes, leading to ∑Ψ=0.Thus, the instantaneous change in flux linkage is zero.