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# Instrument Transformers

### Formulas

#### Voltage Transformer

For a voltage transformer of voltampere rating S, rated primary voltage VP and rated secondary voltage VS, the maximum secondary current ISmax, maximum secondary burden conductance GBmax and maximum primary current IPmax are:

ISmax = S / VS

GBmax = ISmax / VS = S / VS2

IPmax = S / VP = ISmaxVS / VP

#### Current Transformer

For a measurement current transformer of voltampere rating S, rated primary current IP and rated secondary current IS, the maximum secondary voltage VSmax, maximum secondary burden resistance RBmax and maximum primary voltage VPmax are:

VSmax = S / IS

RBmax = VSmax / IS = S / IS2

VPmax = S / IP = VSmaxIS / IP

For a protection current transformer of voltampere rating S, rated primary current IP, rated secondary current IS and rated accuracy limit factor F, the rated secondary reference voltage VSF, maximum secondary burden resistance RBmax and equivalent primary reference voltage VPF are:

VSF = SF / IS

RBmax = VSF / ISF = S / IS2

VPF = SF / IP = VSFIS / IP

#### Impedance Measurement

If the primary voltage Vpri and the primary current Ipri are measured at a point in a system, then the primary impedance Zpri at that point is:

Zpri = Vpri / Ipri

If the measured voltage is the secondary voltage Vsec of a voltage transformer of primary/secondary ratio NV and the measured current is the secondary current Isec of a current transformer of primary/secondary ratio NI, then the primary impedance Zpri is related to the secondary impedance Zsec by:

Zpri = Vpri / Ipri = VsecNV / IsecNI = ZsecNV / NI = ZsecNZ

where NZ = NV / NI

If the no-load (source) voltage Epri is also measured at the point, then the source impedance ZTpri to the point is:

ZTpri = (Epri – Vpri) / Ipri = (Esec – Vsec)NV / IsecNI = ZTsecNV / NI = ZTsecNZ

 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 C E f G h I j L P Q 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] Q R S t V W X Y Z f w 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]