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CT “Excitation Test”, Part III

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As you know, inductor is a linear element but if its voltage exceeds a specific limit, the inductor is saturated and enters the non-linear area.

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What we mean by saturation of the inductor is the saturation of its core.

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In fact, when the voltage exceeds the threshold, the core loses its ability to pass more flux and so it is saturated and the inductor turns non-linear.

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But by drawing the saturation curve of a “CT”, you can see that there is also a non-linear area in the lower voltages.

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Up to now we have said that in higher voltages the inductor becomes excited and turns non-linear.

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To explain non-linear area in a lower voltage, the parallel circuit of a “CT” is drawn.

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In this parallel circuit, the turns ratio of the “CT” which is a transformer is “1:N”. “Rs” indicate the resistance of the “CT”.

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In the parallel branch, “Reddy” and “Rh” stand for Foucault and hysteresis losses of the coil and L stands for the magnetizing inductance of the “CT” secondary.

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To perform the excitation test, secondary of the “CT” is fed by voltage and check to see what non-linear element is causing the “CT” to show a non-linear behavior even in lower voltages.

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As mentioned before, the losses of core include Foucault and hysteresis.

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Therefore, to analyze the non-linear behavior of the transformer, we need to examine the Foucault and hysteresis losses.

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Foucault losses are caused by Eddy Current which occurs in the core segment because of time-varying flux in the core and voltage induction.

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Since the flux is directly dependent on the voltage, we can say that the Foucault losses are the result of a pure resistance.

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The relation of the Foucault losses is achieved through an empirical method and is as you can see:

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In this relation, “B” is the flux density which equals “V/f”. By substituting this relation, Foucault losses can be rewritten as Pf= V2/Re.

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From this relation it can be deduced that the Foucault losses are caused by a fixed resistance that are not dependent on voltage and cannot be the reason for the non-linear behavior of the transformer in lower voltages.

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So, it is only possible that the hysteresis losses are the reason for the non-linear behavior in the “CT”.

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Hysteresis losses occur in the core due to the residual magnetism.

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This means that passing of the magnetic flux through the metal core in a direction causes the core to be magnetized and turn into a weak magnet;

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so in the next half-cycle, a small amount of energy is lost to remove the magnetic effect of the previous half-cycle and this is being constantly repeated.

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The empirical relation of hysteresis is Ph= Kh * f * Bx

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The value of “x” depends on the material of the core and can vary from 1.5 to 2.5.

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Also, in this relation, “B” is the flux density which equals “V/f” and by substituting it, the Hysteresis losses can be rewritten as you can see:

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From the resulted relation, it is obvious that the hysteresis resistance is non-linear and dependent on the voltage of its two ends.

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The effect of this resistance in the total equivalent resistance of the “CT” in the lower voltages is significant.

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But from a specific voltage upwards, the effect of this resistance decreases and causes the “CT” current and voltage relation to approach linearity.

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This causes the relation between voltage and current to be non-linear in a specific range in the lower voltages.