Current-transformer excitation current ($I_e$)

A current-transformer excitation current is the part of the secondary-referred input current needed for the magnetic core's response and losses rather than delivered to the external secondary circuit. In an ideal current transformer this contribution is neglected. In a real equivalent circuit it helps explain both current-transformer ratio error and current-transformer phase displacement.

Choose terminal polarities so ideal current reproduction is in phase. Let $K_n$ be the nominal primary-to-secondary ratio, $I_0=I_p/K_n$ the secondary-referred input phasor, and $I_s$ the measured secondary phasor. The current balance isRepresent the excitation branch locally by current-transformer excitation admittance $Y_e$ and induced secondary phasor $E_s$. With total secondary winding-plus-burden impedance $Z_t$,The NIST treatment gives the corresponding magnetizing, leakage and burden equivalent circuit and shows how those impedances enter the complex ratio.^[ref]

For an original local model, write $Y_e=G-iB$ with $G,B>0$, and take $Z_t=R_t>0$. When $|Y_e{R}_t|\ll 1$,The amplitude deficit is approximately $G{R}_t$, while the secondary lead is approximately $B{R}_t$ radians. For stipulated $G=0.001\mathrm{S}$, $B=0.005\mathrm{S}$ and $R_t=1\Omega$, these are about $0.1\%$ and 5 milliradians. At an induced $1\mathrm{V}$, the excitation components are 1 milliampere in phase and 5 milliamperes in quadrature; the real branch power is $G|E_s{|}^2=1\mathrm{mW}$.

An increased current-transformer burden raises the induced potential required for a given secondary current. The actual excitation response need not remain linear: core behavior, frequency, waveform and prior magnetic state can change the local parameters. The NIST equivalent-circuit discussion explicitly notes the nonlinear core and current/burden dependence.^[ref]

A proposed characterization varies a known connected burden and compares measured current ratio and phase, keeping the primary-current and frequency conditions recorded. A model that fits one operating point is not thereby validated through saturation or for arbitrary harmonic components. Separating excitation from load delivery explains why a turns ratio alone cannot specify practical measurement accuracy.

Current-transformer excitation admittance represents the secondary-referred magnetic-core response as a complex ratio between current-transformer excitation current and the induced secondary electric potential difference at a stated frequency:For a passive parallel loss-and-magnetization model, $G\ge 0$ is the in-phase conductance and $B>0$ the inductive susceptance magnitude. NIST's equivalent circuit separates this excitation response from leakage and external current-transformer burden.^[ref]

In an original linear model with parallel core-loss electrical resistance $R_c$ and magnetizing inductance $L_m$,Thus $R_c=1/G$ and $L_m=1/(\omega B)$ when those parameters are positive. For stipulated $G=0.001\mathrm{S}$, $B=0.005\mathrm{S}$ and $f=50\mathrm{Hz}$, the corresponding values are $R_c=1000\Omega$ and $L_m\approx 0.6366\mathrm{H}$.

At $E_s=2\mathrm{V}$ RMS, the excitation phasor is $I_e=0.002-0.010i\mathrm{A}$, with magnitude about $10.20\mathrm{mA}$. Mean power in the modeled loss branch is $G|E_s{|}^2=4\mathrm{mW}$. The quadrature current also has physical significance even though it supplies no mean power in this ideal sinusoidal branch.

The admittance can be inferred from a measured complex transfer if the circuit assumptions are known. Let $H=I_s/(I_p/K_n)$, with consistent secondary polarity, and let $Z_t$ be winding-plus-burden impedance. The current balance givesWith the current-transformer ratio correction factor and secondary-leading phase $\alpha$, $H=e^{i\alpha }/\mathrm{RCF}$, so the same inversion isMagnitude-only ratio data cannot determine both $G$ and $B$ without additional information.

A real core is nonlinear, so the effective fundamental ratio can change with excitation amplitude, frequency, waveform and magnetic history. A parameter inferred from a small perturbation about one operating state need not equal the full-signal ratio at another. NIST explicitly notes nonlinear magnetizing impedance and current/burden dependence.^[ref] A proposed check measures ratio and phase at several known burdens, compares the inferred admittance values, and tests whether one local model describes them before applying it outside that range.