Dielectric Dissipation Factor

Formulas

If an alternating voltage V of frequency f is applied across an insulation system comprising capacitance C and equivalent series loss resistance R_S, then the voltage V_R across R_S and the voltage V_C across C due to the resulting current I are:
V_R = IR_S
V_C = IX_C
V = (V_R² + V_C²)^½

The dielectric dissipation factor of the insulation system is the tangent of the dielectric loss angle d between V_C and V:
tand = V_R / V_C = R_S / X_C = 2pfCR_S
R_S = X_Ctand = tand / 2pfC
Note that an increase in the dielectric losses of a insulation system (from an increase in the series loss resistance R_S) results in an increase in tand. Note also that tand increases with frequency.

The dielectric power loss P is related to the capacitive reactive power Q_C by:
P = I²R_S = I²X_Ctand = Q_Ctand

The power factor of the insulation system is the cosine of the phase angle f between V_R and V:
cosf = V_R / V
so that d and f are related by:
d + f = 90°

tand and cosf are related by:
tand = 1 / tanf = cosf / sinf = cosf / (1 – cos²f)^½
so that when cosf is close to zero, tand » cosf

Note that the series loss resistance R_S is not related to the shunt leakage resistance of the insulation system (which is measured using direct current).