## Dielectric dissipation

**
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_{R}^{2} + V_{C}^{2})^{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_{C}tand
= 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 = I^{2}R_{S} = I^{2}X_{C}tand
= Q_{C}tand
**

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 - cos ^{2}f)^{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).