Susceptance

Susceptance is the imaginary part of the complex admittance of an electrical network. It measures how readily AC current flows in response to voltage due to reactive elements such as capacitors and inductors. The complex admittance is written as Y = G + jB, where G is conductance (the real part) and B is the susceptance (the imaginary part). Susceptance is measured in siemens (S).

For a pure capacitor with capacitance C at angular frequency ω, the admittance is Y = jωC, so B = ωC, a positive quantity. For a pure inductor with inductance L, the admittance is Y = -j/(ωL), so B = -1/(ωL), a negative quantity. Thus positive B indicates capacitive behavior, while negative B indicates inductive behavior. Susceptance can be frequency dependent, since ω appears in the expressions.

In power systems and AC circuit analysis, susceptance is used to model shunt elements, line charging, and the imaginary part of the network’s admittance matrix. The reactive power associated with a shunt admittance Y = G + jB at bus voltage V (phasor) is S = V I* = |V|^2 (G - jB), so the real and reactive powers satisfy P = |V|^2 G and Q = -|V|^2 B. Using the common convention that positive Q is absorbed by the element, Q = |V|^2 B, which implies that a capacitive susceptance (B > 0) supplies reactive power to the network (Q < 0).

Example: a 100 µF capacitor at 50 Hz has B = ωC = 2π(50)(100×10^-6) ≈ 0.0314 S.