## Introduction to the calculator

The spreadsheet ‘CT Saturation Calculator’ is intended to provide quick indication not only of whether or not a CT will saturate in a particular application, but also an accurate indication of the actual waves-hape of the secondary current so that the degree of saturation as a function of time is apparent. Furthermore, the data is available to the user to use as input to a digital relay model, if such is available.

The user can convert the data into a COMTRADE file, for example. There are many technical papers on the subject of modeling the behavior of iron-cored current transformers used for protective relaying purposes. One of the difficulties in using an elaborate model (in any field of engineering) is in getting the parameters in a particular case in order to implement that model easily, efficiently and accurately.

For example, the excitation current in the region below the knee-point is a complex combination of magnetizing, hysteresis and eddy-current components, the parameters of which are usually not known in a particular case.

**This simplifies the solution greatly, with little effect on accuracy.**

If errors under low current, low burden conditions are of interest, a more elaborate model must be used.

### Testing of the Model

**The proof of the pudding is in the eating.** Because this model is new and quite different from those in the literature, testing against real high-current laboratory results was important. To this end, two laboratory examples published in reference (*) were compared against results from this program. The agreement was very close.

In addition, the program has had widespread circulation, and to date there are two utility-user reports of agreement with previous results and no reports of disagreement.

(*) Tziouvaras, D.A., et al, Mathematical Models for Current, Voltage, and Coupling Capacitor Voltage Transformers

### Instructions

The first step is to determine the saturation voltage (Vs) for the CT in question. This is defined as the rms excitation voltage corresponding to ten-per-cent error current. For example, for a nominal five-amp CT which is expected to handle 100 amps with a ten per cent error, **the error current at the saturation voltage Vs, is ten amps**.

Incidentally, the actual measurements by the manufacturer may not have been made with a “true rms” meter. It has been determined that the error due to use of a “rectified average” type meter, for example, is not significant.

**Second step** is to determine the slope (1/S) of the upper part of the saturation curve, being careful that the curve is plotted on log-log scales with the decade spacing equal on both axes. “S” is defined as the reciprocal of this slope. You should get a slope such that S is in the neighborhood of 15 < S < 25. Note that the result is not very sensitive to the value of S.

**Third and the last step:** Enter other parameters such as the CT winding resistance, the burden, the degree of dc-offset in the primary current waveform (up to 1 per unit), the primary system X/R ratio, the remanence **(*)**, and the primary symmetrical rms current.

Once any change to an INPUT parameter is made, a new plot appears automatically. The scale adjustment is automatic and the plot is believed to be self-explanatory.

**he exciting current is both out of phase and non-sinusoidal**, so simple subtraction does not apply.

So when we specify 10 amps error current at 100 amps secondary current, the error is actually less than 1% typically, but includes a phase error of, say 5 degrees, leading.

**(*)** Note that the per unit remanence is defined relative to Vs. If the knee-point voltage (45 degree slope point) is 80% of Vs, then the maximum remanence value is 0.8. Note that the polarities for this simulation are such that a positive remanence is the “worst-case” condition for premature saturation.

Software: | Current transformer (CT) saturation calculator |

Version: | – |

Developer: | IEEE PSRC (Glenn Swift) |

Size: | 2.30Â MB (.xls) |

Price: | Free |

Theory: | Right here |

Download: | Right here | Get Download Updates | Get More With Premium Membership |

I have seen this spreadsheet 5 years ago. It belongs to GE. But here I have not seen any reference to the original work. Please add the reference.

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Very useful information. Thanks.