### 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**across

_{R}**R**and the voltage

_{S}**V**across

_{C}**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 / 2pfCNote that an increase in the dielectric losses of a insulation system (from an increase in the series loss resistance

**R**) results in an increase in

_{S}**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}tandThe power factor of the insulation system is the cosine of the phase angle **f** between **V _{R}** and

**V**:

**cosf = V**

_{R}/ Vso 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).

NOTATION |
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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. |
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BE 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] |
SsTVXYZdFfhqw |
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] |