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Impact on GICs

Authors: B. Kasztenny, D. Taylor, and N. Fischer,Schweitzer Engineering Laboratories, USA

**In the case of power transformers**, GICs can potentially cause thermal damage as a result of elevated excitation currents and stray flux closing outside of the transformer magnetic core. Further, the increased excitation current drawn by the transformers is harmonic-rich, which can cause problems for adjacent generators. In this case, the concern is the extra rotor heating caused by certain harmonic currents in the stator that establish a magnetic field rotating in the opposite direction of the rotor.

This article focuses on the performance of current transformers (CTs) with GICs. In steady states, constant currents (such as GICs) are not transformed across the magnetic circuit of a CT, but they offset the magnetic flux and increase CT errors. Therefore, we are concerned with protection security and dependability for faults and switching events that happen when the primary current contains a GIC component.

**GIC Phenomenon**

Sunspots are regions of intense magnetic activity on the surface of the sun that result from spatiotemporal variations of the sun’s magnetic field. Sunspots can produce a sudden release of energy in the form of solar flares and/or coronal mass ejections, which discharge large amounts of electrons, ions, and atoms. Once these particles reach the earth, they push on the earth’s magnetosphere, and as a result, some of the particles enter the earth’s ionosphere. This influx of charges changes the ionospheric current and the magnetic field it produces. As the time-varying magnetic field links conducting loops on the earth’s surface (*such as electrical transmission circuits, railways, or piping systems*), the magnetic field induces an electromotive force around the loops, as dictated by Faraday’s law. These geoelectric electromotive forces then drive GICs in the conducting circuits that superimpose onto the system currents. GICs are especially noticeable in high-latitude locations (*where the effects of geomagnetic storms are the greatest*) and in long, high-voltage lines with tall transmission towers, both of which result in an increased loop area linked by the magnetic field, and therefore, an increased geoelectric electromotive force.

Because of the slow variation of the induced geoelectric field (*relative to the power system frequency*), a GIC is considered a quasi-*dc* current with frequencies in the millihertz range or lower. Figure 1 is a capture of the GIC measured in a transformer neutral in Finland during a geomagnetic storm on March 24, 1991. The plot shows the erratic, yet very slowly changing, level of the induced current. For all practical purposes, GICs are preexisting *dc* currents when considering power system frequencies.

When considering the magnitude of GICs, Figure1provides an excellent example of severe GIC levels. In order to indicate their severity, geomagnetic storms are given a K-index rating. The storm that occurred on March 24, 1991, was a K-9 level storm, the highest level presently defined. The peak magnitude of –200 A that was captured in Figure 1 represents a worst-case expected value. However, this value was measured in the transformer neutral, and the GIC present in each phase conductor is essentially one-third of this amount, or 67 A. This per-phase value corresponds to hand calculations of the GIC levels in the phase conductors given the magnetic field levels during a large geomagnetic storm and the resistance of a transmission line conductor. Practically, when considering CTs, GICs are preexisting dc currents with magnitudes that are below 10% of a typical transmission-grade CT rating.

**Simplified Current Transformer Model for Protection Considerations**

A CT is a system with the primary current as an independent input, the secondary current as the output of interest, the burden, and the magnetic core all intertwined with the applicable laws of physics. The first approximation of this system, sufficient for protection studies, is as follows. The primary (i1) and secondary (i2) currents follow the ampere-turn balance equation, with the excitation current (iµ) modeling the core excitation and saturation. Typically, we have a single primary turn and N secondary turns, yielding the following:

Introducing the primary ratio current (i'1), which is the ratio of i1 to N, we can write (1) in secondary amperes:

Equation (2) signifies that the secondary current equals the primary ratio current less the excitation current. Therefore, the excitation current represents the CT error.

The secondary or excitation voltage (V2) of the CT is the product of the secondary current and the secondary burden (RB), which is predominately resistive for microprocessor-based relays and also includes the secondary winding resistance, the CT leads’, and the relay input resistance. The secondary voltage of the CT is:

The induced excitation voltage is proportional to the rate-of-change of the magnetic flux; therefore, the magnetic flux linkage (λ) is an integral of the excitation voltage and is as follows:

Finally, we recognize the nonlinear relationship between the flux linkage and the excitation.

where *h* is the nonlinear function representing a relationship between the instantaneous excitation current and the instantaneous magnetic flux linkage (we neglect hysteresis because it is noncritical for our considerations).

Equations (1) through (5) are the first principles of a CT shown graphically in Figure 2.

The CT representation in Figure 2b is helpful for understanding how CT errors are introduced in the first place. For small primary currents, the feedback in the form of the excitation current is small, making the secondary current practically equal to the primary ratio current. The higher the current, the higher the burden, and/or the lower the frequency, the larger the feedback and the resulting CT errors.

We tested the performance of our CT signal model by matching its h function to the 60 Hz excitation characteristic of a C10, 150:5 CT, as shown in Figure3. We selected a low-ratio CT in order to apply high multiples of rated current with our test equipment

From Figure 3, note the difference between the CT root-mean-square (rms) excitation curve, which is the curve used in standard practice, and its peak-valued excitation curve, which is the curve we must match the h function to in (5) for our CT model. The difference clearly illustrates the distortion of the excitation current once the CT operation passes its knee point and moves into the saturated region. It also shows that the h function for our CT model matches reasonably well to our laboratory CT.

To illustrate the accuracy of our simple model, we applied a fully offset fault current with a decaying dc component to both the laboratory CT and our CT model. The *dc* component had a 30 ms time constant and a magnitude of 1,350 A rms primary (9 times rated current and the maximum capacity of our laboratory equipment) at 60 Hz. Figure 4a shows the individual CT responses to the fault. The plot shows that the CT model represents the laboratory CT reasonably well at 60 Hz. However, in order for our model to be useful in the analysis of CT performance when subjected to GICs, it needs to model the behavior for lower-frequency currents as well.

Figure 4b captures the CT responses for a fault current of 30 Hz with a time constant of 60 ms and a current magnitude of 675 A rms primary (4.5 times rated current). As before, the model response reasonably matches that of the laboratory CT even at this lower frequency. How is this possible when the *h* function used in our model was matched with data at 60 Hz (Figure3).

The reason is that the h function is actually independent of frequency. The h function ties the flux linkage of the CT to its excitation current, as shown in (5). Because the CT flux linkage is the integral of the excitation voltage, as shown in (4), the frequency information that is present in the voltage signal is accounted for through the integration process. As the signal frequency decreases, the area under the excitation voltage waveform becomes larger (assuming that the voltage peak is held constant), resulting in a higher peak flux. The higher peak flux in turn requires a larger magnetizing current, as dictated by the frequency-independent *h* function.

This principle is the basis for the frequency derating of a CT. When reducing the signal frequency, we need to reduce the applied current proportionally in order to keep the excitation current (i.e., the CT error), and thus the CT response, the same (Figure4). The frequency was doubled and the current was halved in (b) in order to keep the CT response approximately the same as (a).