Current-transformer ratio correction factor ($\mathrm{RCF}$)

The current-transformer ratio correction factor multiplies a nominally scaled secondary-current indication to recover primary-current magnitude under stated calibration conditions. If $K_n$ is the marked primary-to-secondary ratio and $K=I_p/I_s$ is the true magnitude ratio, defineNIST distinguishes this factor from ratio correction, which is $\mathrm{RCF}-1$, and from the separately measured phase displacement.^[ref] Correcting amplitude does not remove current-transformer phase displacement.

With the inferred-primary error convention ${ϵ}_I=(K_n{I}_s-I_p)/I_p$, the exact relationship isFor an original example, $K_n=200$, $I_s=2.49\mathrm{A}$ and $\mathrm{RCF}=500/498\approx 1.004016$ give $I_p=500\mathrm{A}$. Using nominal scaling alone gives 498 A. The approximate correction $1-{ϵ}_I=1.004$ would instead give 499.992 A, leaving a small second-order difference.

A calibration correction has its own measurement uncertainty. Treating $K_n$ as an exact label and retaining correlation, first-order propagation givesFor a correction inferred from uncertain ${ϵ}_I$, its local sensitivity is $d\mathrm{RCF}/d{ϵ}_I=-(1+{ϵ}_I{)}^{-2}$. The GUM supplies the general sensitivity-and-covariance propagation rule used here.^[ref]

Nonlinearity also affects averaging. Suppose a stipulated error takes values $+0.01$ and $-0.01$ with equal probabilities. Its mean is zero, but the mean correction factor isThe correction at the mean error is instead one. Convexity of the reciprocal on $1+{ϵ}_I>0$ explains this Jensen's inequality effect. It is an illustrative probability model, not a claim about random drift of a particular transformer.

A correction factor should therefore travel with its current level, frequency, current-transformer burden and uncertainty information. A proposed check repeats the ratio comparison at selected operating conditions and tests whether one retained correction remains adequate. Applying more displayed digits cannot replace that validation.