Frequency response of stray losses in transformers

Jill Duplessis - Global technical marketing manager

This article is intended to familiarise readers with frequency response of stray losses (FRSL) testing for transformers - an invaluable test technique that is rapidly gaining recognition in the industry because of its ability to reveal problems that would be missed by other electrical test methods.

FRSL as a test tool for transformers was first discussed and investigated by Hydro Quebec in the 1970’s because of its ability to detect winding deformation. Hydro Quebec concurrently examined the use of the sweep frequency response analysis (SFRA) method and leakage reactance testing for the same purpose, and ultimately SFRA, together with leakage reactance testing, became the accepted tools for confirming winding deformation.

For some time, FRSL went largely unused. That is, until its seemingly latent diagnostic strengths were exposed. Of particular note was the discovery that FRSL was very useful for revealing short-circuits between individual strands within a conductor bundle. This is a failure mode that, until the advent of FRSL, had been undetectable with electrical test methods.

A conductor bundle may be comprised of any number of individually insulated conductor strands. When two or more of these strands are shorted together, this is not a turn-to-turn fault or even a partial turn-to-turn short-circuit . The latter is a situation when one or more strands within a conductor bundle become short-circuited to one or more strands within an adjacent turn of the conductor bundle. The exciting current test, for example, can reveal a partial turn-to-turn short circuit but is not sensitive to a strand-to-strand short circuit.

Background
When examining FRSL testing, some basic transformer facts have to be kept in mind. The first is that a current through a conductor will create a magnetic field around the conductor and, if it is an alternating current, the resultant magnetic field will be time-varying. The second is that if a time-varying magnetic flux cuts through a conductor, it will induce a voltage within that conductor.

Transformer action is the use of a time-varying magnetic field created by passing AC current through one winding of a transformer to induce a voltage in a second winding. It is observed that more of the magnetic field created by the first winding will link with the second winding when both windings are wound around a steel transformer core, since the silicon-iron used in such cores is an excellent conduit for carrying magnetic flux.

When a transformer is energised but not carrying load, current is present only in the primary winding. This is the exciting current and it is a reflection of the amount of energy required to force transformer action, which is an energy consuming and storing process. It is further noted that, under these conditions, the core steel carries all the flux.

Conversely, when a transformer is connected to a load and is energised, current flows in both the secondary and primary windings. The combined action of current flow in both windings causes some flux to be pushed out of the core for most or part of its path. This is referred to as leakage flux.

Figure 1: Plot of flux lines when transformer is energised and LV windings are short-circuited

The problem with leakage flux is that it discriminates; it does not consistently and uniformly cut all turns of all windings. In Figure 1, counting lines of leakage flux that cut through the low voltage (LV) winding and separately counting those that cut through the high voltage (HV) winding, for example, will reveal that considerably more lines of leakage flux cut through the HV winding. The leakage flux will therefore induce a different voltage in the primary winding than in the secondary winding. But what does this mean in practice?

When you de-energize a transformer and perform a transformer turns ratio test, the ratio of the measured primary voltage to measured secondary voltage should practically represent the ratio of the number of primary to the number of secondary turns. The test confirms that the numbers of turns intended by the transformer designer and manufacturer are present, and are not “missing” by way of open or short circuits. If all is well, the measured turns ratio will match the ratio of the primary to secondary voltage stamped on the nameplate.

However, when the transformer is energised and connected to the load, because of leakage flux, the ratio of primary voltage to secondary voltage is no longer the same as when the transformer was not carrying load. This phenomenon is reflected in the equivalent circuit of a transformer by separate primary and secondary side inductive components.

When leakage flux cuts through the primary or secondary windings and induces voltage, it gives rise to eddy currents within the windings, which contribute to the total losses in the transformer. Eddy losses can be attributed to two different effects: the skin effect and the proximity effect. These differ in principle but both result in a non-uniform current distribution within the conductors that make up the transformer windings. As a consequence, the effective current-carrying cross-sectional area of these conductors is reduced, so their effective resistance increases.

The skin effect is due to opposing eddy currents induced within the conductor that cancel the current flow in the centre of the conductor and reinforce it at the periphery. This means that the majority of current flows in the outer periphery, or skin, of the conductor. The skin depth, or penetration, is a measure of the depth at which the current density falls to 1/e of its value at the surface, where e equals 2.718, the base of natural logarithms.

The smaller the skin depth, the more the current flow is restricted and the higher the effective AC resistance of the conductor. Skin depth relative to the diameter of a conductor is important too; the more current penetration through the conductor, the lower eddy losses. It may very well be that a small skin depth relative to a small diameter conductor – that is, a strand – will represent more current penetration in the strand than will a slightly larger skin depth relative to a much larger diameter conductor.

Dividing a conductor into individually insulated strands and ensuring that each strand encompasses the identical flux will limit the circulation of eddy currents from one strand to another through their terminating interconnections. This is accomplished through transposition and also reduces losses.

When two or more strands within a conductor bundle short circuit together, eddy losses increase. The amalgamated strand has effectively increased in diameter and, depending on the location of the short, the new composition of strands may no longer encompass identical flux so additional eddy currents will circulate. These additional losses will culminate in an increase in measured AC resistance under simulated load conditions of the transformer.

FRSL is essentially the same measurement as the leakage reactance test (LRT); however, entire attention is paid to the resistive portion of the measurement whereas with LRT, the short circuit impedance, made up of both the resistive and reactive components, is assessed. Additionally, FRSL is performed at several discrete frequencies between, for example, 1 Hz and 500 Hz.

The high frequency measurement is critical because this is where the influence of skin effect is most pronounced and where resistance attributed to AC influences represents a larger proportion of the resistance measurement. So a developing or mature strand-to-strand failure, which will result in more eddy losses, will be detectable only at higher frequencies, not at operating frequency.

Analysis of FRSL results
The analysis of FRSL results is best carried out by making comparisons with the results of earlier tests made on the same transformer. If this is not possible, the results for each phase can be compared, and they should be very similar. Figure 2 shows the expected curve shape (a smooth exponential) and a phase comparison.

Figure 2a and b: FRSL test results provided in FRAX software at conclusion of SFRA test

If there is a vertical offset of an entire phase curve from the other two-phase curves, the shorting connections on the aberrant phase should be checked, efforts made to improve them, and the test repeated. The winding resistance test results should be scrutinised in case there is a corresponding anomaly associated with the aberrant phase, as a vertical offset is indicative of increased resistance of the current carrying path.

Short-circuited strands reveal themselves in the data as curves that overlay at low frequencies and then start to diverge at higher frequencies. The CIGRE Guide for Transformer Maintenance published by Working Group A2.34, defines the fail criterion for the FRSL diagnostic as a difference in AC resistance between phases of greater than 15%. However, a problem may manifest itself with a far smaller deviation between phases so caution must be exercised when assessing results.

Even if the curve of one phase is only 2 to 3% different from the other phases, this may be  indicative of a short circuit fault between parallel strands. This makes the need for previous test results even more compelling, as comparisons with historical results make it easier to draw conclusions about changes that may have occurred.

Performing FRSL tests
Though some users may not realise it, when they perform SFRA testing with a Megger FRAX test set, they are also performing an FRSL test. The FRAX software automatically provides the FRSL results, as shown in the example that follows.

In menu Configuration, Models, select Impedance, R (Impedance) and L (Impedance)

In menu Configuration, Graph Views, make sure that Impedance is enabled.

Now you can plot Impedance (Ohms), Resistance (Ohms) and/or Inductance (Henries). The formulas are valid only for low frequencies. The plots below, at low frequencies, show, from top to bottom:

„ ♦ Three graphs of Impedance as function of frequency (increases with frequency since inductance dominates)
„ „♦ Three graphs of resistance as function of frequency (FRSL)

„ ♦ Three graphs of Inductance as function of frequency (important for winding deformation)

Using the zoom window, Figure 2, it is easy to see that, in this case, FRSL give a good response with no indication of problems.