### Formulas

#### Voltage Transformer

For a voltage transformer of voltampere rating **S**, rated primary voltage **V _{P}** and rated secondary voltage

**V**, the maximum secondary current

_{S}**I**, maximum secondary burden conductance

_{Smax}**G**and maximum primary current

_{Bmax}**I**are:

_{Pmax}**I _{Smax} = S / V_{S}**

**G _{Bmax} = I_{Smax} / V_{S} = S / V_{S}^{2}**

**I _{Pmax} = S / V_{P} = I_{Smax}V_{S} / V_{P}**

#### Current Transformer

For a measurement current transformer of voltampere rating **S**, rated primary current **I _{P}** and rated secondary current

**I**, the maximum secondary voltage

_{S}**V**, maximum secondary burden resistance

_{Smax}**R**and maximum primary voltage

_{Bmax}**V**are:

_{Pmax}**V _{Smax} = S / I_{S}**

**R _{Bmax} = V_{Smax} / I_{S} = S / I_{S}^{2}**

**V _{Pmax} = S / I_{P} = V_{Smax}I_{S} / I_{P}**

For a protection current transformer of voltampere rating **S**, rated primary current **I _{P}**, rated secondary current

**I**and rated accuracy limit factor

_{S}**F**, the rated secondary reference voltage

**V**, maximum secondary burden resistance

_{SF}**R**and equivalent primary reference voltage

_{Bmax}**V**are:

_{PF}**V _{SF} = SF / I_{S}**

**R _{Bmax} = V_{SF} / I_{S}F = S / I_{S}^{2}**

**V _{PF} = SF / I_{P} = V_{SF}I_{S} / I_{P}**

#### Impedance Measurement

If the primary voltage **V _{pri}** and the primary current

**I**are measured at a point in a system, then the primary impedance

_{pri}**Z**at that point is:

_{pri}**Z _{pri} = V_{pri} / I_{pri}**

If the measured voltage is the secondary voltage **V _{sec}** of a voltage transformer of primary/secondary ratio

**N**and the measured current is the secondary current

_{V}**I**of a current transformer of primary/secondary ratio

_{sec}**N**, then the primary impedance

_{I}**Z**is related to the secondary impedance

_{pri}**Z**by:

_{sec}**Z _{pri} = V_{pri} / I_{pri} = V_{sec}N_{V} / I_{sec}N_{I} = Z_{sec}N_{V} / N_{I} = Z_{sec}N_{Z}**

where **N _{Z} = N_{V} / N_{I}**

If the no-load (source) voltage **E _{pri}** is also measured at the point, then the source impedance

**Z**to the point is:

_{Tpri}**Z _{Tpri} = (E_{pri} – V_{pri}) / I_{pri} = (E_{sec} – V_{sec})N_{V} / I_{sec}N_{I} = Z_{Tsec}N_{V} / N_{I} = Z_{Tsec}N_{Z}**

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. | ||||||

BCEfGhIjLPQ | susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power | [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] | QRStVWXYZfw | quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency | [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec] |