Instrument Transformers

Formulas

Voltage Transformer

For a voltage transformer of voltampere rating S, rated primary voltage V_P and rated secondary voltage V_S, the maximum secondary current I_Smax, maximum secondary burden conductance G_Bmax and maximum primary current I_Pmax are:

I_Smax = S / V_S

G_Bmax = I_Smax / V_S = S / V_S²

I_Pmax = S / V_P = I_SmaxV_S / V_P

Current Transformer

For a measurement current transformer of voltampere rating S, rated primary current I_P and rated secondary current I_S, the maximum secondary voltage V_Smax, maximum secondary burden resistance R_Bmax and maximum primary voltage V_Pmax are:

V_Smax = S / I_S

R_Bmax = V_Smax / I_S = S / I_S²

V_Pmax = S / I_P = V_SmaxI_S / I_P

For a protection current transformer of voltampere rating S, rated primary current I_P, rated secondary current I_S and rated accuracy limit factor F, the rated secondary reference voltage V_SF, maximum secondary burden resistance R_Bmax and equivalent primary reference voltage V_PF are:

V_SF = SF / I_S

R_Bmax = V_SF / I_SF = S / I_S²

V_PF = SF / I_P = V_SFI_S / I_P

Impedance Measurement

If the primary voltage V_pri and the primary current I_pri are measured at a point in a system, then the primary impedance Z_pri at that point is:

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_V and the measured current is the secondary current I_sec of a current transformer of primary/secondary ratio N_I, then the primary impedance Z_pri is related to the secondary impedance Z_sec by:

Z_pri = V_pri / I_pri = V_secN_V / I_secN_I = Z_secN_V / N_I = Z_secN_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_Tpri to the point is:

Z_Tpri = (E_pri – V_pri) / I_pri = (E_sec – V_sec)N_V / I_secN_I = Z_TsecN_V / N_I = Z_TsecN_Z