Ratio and Phase Angle Errors of Instrument Transformers
For satisfactory and accurate performance, it is necessary that the ratio of transformation of the instrument transformer should be constant within close limits. However, in practice, it is found that neither current transformation ratio I1/I2 (in the case of current transformers) nor voltage transformation ratio V1/V2 (in the case of potential transformers) remains constant. The transformation ratio is found to depend on the exciting current as well as the current and the power factor of the secondary circuit. This fact leads to an error called ratio error of the transformer which depends on the working component of primary (Ratio and Phase angle Errors of Instrument Transformers).
It is seen from Figure (A) that the phase angle between the primary and secondary currents is not exactly 180° but slightly less than this value. This difference angle β may be found by reversing vector I2.
The angular displacement between I1 and I2 reversed is called the phase angle error of the current transformer. This angle is reckoned positive if the reversed secondary current leads the primary current. However, on very low power factors, the phase angle may be negative. Similarly, there is an angle of γ between the primary voltage V1 and secondary voltage reversed-this angle represents the phase angle error of a voltage transformer. In either case, the phase error depends on the magnetizing component Iμ of the primary current. It may be noted that ratio error is primarily due to the reason that the terminal voltage transformation ratio of a transformer is not exactly equal to its turn ratio. The divergence between the two depends on the resistance and reactance of the transformer windings as well as upon the value of the exciting current of the transformer. Accuracy of voltage ratio is of utmost importance in a voltage transformer although phase angle error does not matter if it is to be merely connected to a voltmeter. Phase-angle error becomes important only when voltage transformer supplies the voltage coil of a wattmeter i.e. in power measurement. In that case, phase angle error causes the wattmeter to indicate on a wrong power factor.
In the case of current transformers, constancy of current ratio is of paramount importance. Again, phase angle error is of no significance if the current transformer is merely feeding an ammeter but it assumes importance when feeding the current coil of a wattmeter. While discussing errors, it is worthwhile to define the following terms :
(i) Nominal transformation ratio (kn). It is the ratio of the rated primary to the rated secondary current (or voltage).
In the case of current transformers, it may be stated either as a fraction such as 500/5 or 100/1 or simply as the number representing the numerator of the reduced fraction i.e.100. It is also known as marked ratio.
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(ii) Actual transformation ratio (k). The actual transformation ratio or just ratio under any given condition of loading is
In general, k differs from kn except in the case of an ideal or perfect transformer when k = kn for all conditions of loading.
(iii) Ratio Error (σ). In most measurements it may be assumed that I1 = knI2 but for very accurate work, it is necessary to correct for the difference between k and kn. It can be done with the help of ratio error which is defined as
Also 
Accordingly, ratio error may be defined as the difference between the primary current reading (assuming the nominal ratio) and the true primary current divided by the true primary current.
(iv) Ratio Correction Factor (R.C.F.). It is given by
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