 Current transformer

A current transformer is a transformer used to reproduce a scaled version of an alternating primary electric current in a secondary measurement circuit. Many secondary turns around a primary with few turns make large primary electric currents measurable by an instrument. The DOE handbook describes this instrument arrangement and its magnetic operating conditions.^[ref]

For ideal magnitudes, primary and secondary turns $N_p,N_s$ giveThe polarity depends on the chosen terminal directions. The current-transformer burden is the connected secondary load, including the instrument and connection impedance. With a resistive secondary load $R_b$, $V_s\simeq I_s{R}_b$ and its dissipated power is $I_s^2{R}_b$.

For an original example, take $N_p=1$, $N_s=200$, primary current $100\mathrm{A}$ RMS, and total secondary electrical resistance $R_b=2\Omega$. The ideal secondary delivers $0.5\mathrm{A}$, develops $1\mathrm{V}$ and supplies $0.5\mathrm{VA}$ to this resistive burden. The reflected primary electrical resistance isThe primary is measured through magnetic coupling, while the secondary still needs a suitable connected circuit.

Real behavior includes current-transformer ratio error and current-transformer phase displacement. To see why the second matters, let the inferred current magnitude have fractional error $e$ and an extra lag $\delta$ relative to the true current. For a sinusoidal load with lag $\phi$, the estimated-to-true active power ratio isWith $e=0$, $\phi =\pi /3$ and $\delta =0.01$ radians, the first-order error is about $-1.73\%$. Correct amplitude scaling alone does not establish correct power measurement.

Opening an energized conventional current-transformer secondary removes its normal balancing current and can produce a large induced electric potential difference. The DOE handbook specifically explains this open-secondary behavior and its requirement for a closed secondary circuit when the instrument is absent.^[ref] A proposed measurement check therefore uses the intended connected burden and compares ratio and phase at relevant frequencies and current levels. Core response and saturation limit the ideal scaling model; a conventional inductive current transformer does not measure a steady DC component by the same transformer action.