Parameter Evaluation Procedure for Gapped Core Current Transformers Considering Accuracy Requirements under Transient Conditions

. Particular features of gapped core current transformers and characteristics of transient phenomena inside them are under consideration; a procedure is proposed that allows for evaluating the excitation limiting e.m.f. and overall dimensions of the CT required for installation, based on known parameters of the transient conditions in CT installation point and the specified CT error.


Introduction
Nowadays, electromagnetic current transformers (CTs) with closed core are used, as a rule, to connect the relay protection circuits in power system of Russia. Modern CTs are manufactured of electrical steel characterized by the hysteresis loop similar to rectangle and, thereby, high values of residual flux of the CT magnetic core (up to 86%) [1]. Combination of the high value of CT residual flux and presence of decaying dc component of the corresponding polarity in short circuit current can result in fast CT saturation under transient condition and incorrect operation of relay protection devices connected to the CT [2]. In order to limit the residual magnetic flux of magnetic core, CTs can be manufactured with air gaps in the core (accuracy classes of CTs: PR, TPY, TPZ). Application of gapped core CTs allows for avoiding the CT saturation due to high values of remanent flux of the CT magnetic core, but requires consideration of the particular features of phenomena in their secondary circuits, change in the approach to select the CT parameters.

Excitation Characteristic of Gapped Core CTs
In any operation conditions of CT, magnetizing current adjusted to one turn, can be calculated using the expression [3]:


-air magnetic permeability. Taking into account (1) the dependence of specific magnetizing current from the induction in magnetic circuit with the gap: -demagnetization factor of magnetic circuit. Figure 1 shows the influence of the air gap relative length G ST ll on the type of the CT excitation characteristic. The CT minimum gap is selected due to the reduction of residual magnetic flux up to considerably low values, and for high quality cold-rolled steels it is about 0.001; but under the terms for ensuring the operation accuracy of CTs under transient conditions, the design gap shall be selected several times higher than the minimum.

Equivalent Circuit for Gapped Core CTs
The expression (1) can be presented as follows: where ST  -absolute magnetic permeability of the magnetic circuit steel, Q -its cross-section area,   . According to the equivalent circuit for gapped core CTs, presence of nonmagnetic gaps in the magnetic core leads to reduction in the secondary loop inductance and, consequently, to reduction of the secondary loop time constant.
Inductance of steel magnetic core without gap adjusted to one turn, can be determined as follows: (3) Inductance of the magnetic core with nonmagnetic gap adjusted to one turn:  (3) and (4): -relative magnetic permeability of steel.

Accuracy Classes of Gapped Core CTs [4]
By the nature of imposed requirements to accuracy of gapped core CTs, the following CT accuracy classes are divided: -PR -characteristics of transient conditions are not rated: the requirements are imposed to CT accuracy at effective value of short circuit current; -TPY -characteristics of transient conditions are rated: the requirements are imposed to instantaneous value of CT error during short circuit transient conditions; -TPZ -characteristics of transient conditions are rated: the requirements are imposed to periodic component of CT error during short circuit transient conditions.

Parameter Evaluation Procedure for Gapped Core CTs
A set of CT parameters, including excitation limiting e.m.f., secondary loop time constant, overall dimensions, can be calculated more precisely by the CT manufacturer only, based on the parameters of the primary network and requirements to CT accuracy class provided to him. Nevertheless, at the stage of design works, it is preferably to have an idea about values of all or several magnitudes specified, in order to select one or another class of CT, to carry out preliminary (comparative) feasibility study of the variants.
The engineering practice given below allows for preliminary evaluation of excitation limiting e.m.f., time constant of the secondary circuit and (if overall dimensions require evaluation) the cross-section and the length of the magnetic path of the CT to be installed.
CT parameters are evaluated in the following sequence: 1) Initial (start) value of design secondary loop time constant is taken equal to eternity: where  -circular frequency of industrial current, p Tprimary time constant.
In the cycle of non-successful reclosing "Close -Open -Close", the transient factor is determined as follows. In the course of the first short circuit ( b.act R actual active resistance of the CT secondary circuit burden. 6) The required cross-section area of CT is evaluated using the expression: 7) The value of the CT secondary winding resistance is clarified. For this purpose, the formula can be used to take into account the expected number of turns of secondary winding and the value of CT cross-section area calculated above: Considering the fact that CT excitation branch excitation is determined predominantly by the nonmagnetic gap parameters, length of the gap can be calculated using the simplified expression: -remanence factor of CT with closed magnetic core.

Examples of CT Parameters Calculation
Initial data for calculation of parameters for gapped core CTs are specified in Table 1 Results of CT parameters calculation, carried out as per the procedure given above, are specified in Table 2. Diagrams for variation of the CT instantaneous error under transient condition, illustrating the particular features of behavior of CT classes under examination, are shown in Figures 3 and 4.
In case of relatively large nonmagnetic gap (CT of TPZ class), a considerable fraction of current d.c. component is absorbed by the CT excitation branch and is not converted to the secondary circuit; therewith, a probability of CT saturation in transient mode reduces, but instantaneous error of CT sufficiently increases (see Figure 3).
Length of nonmagnetic gap according to which the secondary circuit time constant is determined, also has a considerable influence on the CT behavior during the reclosing dead time. In case of small lengths of nonmagnetic gap (CT of TPY class), CT instantaneous error cannot fall to zero during the dead time (CT fails to demagnetize); consequently, during the second cycle of short circuit the error takes sufficiently higher values than during the first cycle (see Figure 4). In case of large air gap, instantaneous error reduces almost to zero during the dead time (CT is practically fully demagnetized), therewith, during the second cycle of short circuit the CT accuracy almost does not increase compared to the first cycle (see Figure 3).
The results obtained confirm the practicability to use CTs of TPZ class at quite high values of time constant of the primary network (80-100 ms and more): under any equal conditions the excitation voltage and overall dimensions of TPZ class CT, for which conversion of short circuit current periodic component is rated only, can be considerably low, than TPY class CT, which requires precise conversion of total short circuit current (requirements are imposed to total error of transient condition).

Conclusion
Particular features of phenomena inside gapped core current transformers are examined. A procedure is proposed that allows for evaluating the excitation limiting e.m.f. and overall dimensions of the CT required for installation, based on known parameters of the transient condition in CT installation point and the specified CT error value. A possibility and a practicability to use the developed procedure for design activity (when selecting a CT) should be considered. On the experience of application, this procedure can be revised.