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# Dielectric Dissipation Factor

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### Formulas

If an alternating voltage V of frequency f is applied across an insulation system comprising capacitance C and equivalent series loss resistance RS, then the voltage VR across RS and the voltage VC across C due to the resulting current I are:
VR = IRS
VC = IXC
V = (VR2 + VC2)½

The dielectric dissipation factor of the insulation system is the tangent of the dielectric loss angle d between VC and V:
tand = VR / VC = RS / XC = 2pfCRS
RS = XCtand = tand / 2pfC
Note that an increase in the dielectric losses of a insulation system (from an increase in the series loss resistance RS) 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 QC by:
P = I2RS = I2XCtand = QCtand

The power factor of the insulation system is the cosine of the phase angle f between VR and V:
cosf = VR / 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 RS is not related to the shunt leakage resistance of the insulation system (which is measured using direct current).

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B E f G I j k m N n P p R susceptance induced voltage frequency conductance current j-operator coefficient number of phases number of turns rotational speed power pole pairs resistance [siemens, S] [volts, V] [hertz, Hz] [siemens, S] [amps, A] [1Ð90°] [number] [number] [number] [revs/min] [watts, W] [number] [ohms, W] S s T V X Y Z d F f h q w voltamperes slip torque terminal voltage reactance admittance impedance loss angle magnetic flux phase angle efficiency temperature angular speed [volt-amps, VA] [per-unit] [newton-metres, Nm] [volts, V] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [webers, Wb] [degrees, °] [per-unit] [centigrade, °C] [radians/sec]