What is a knee point ?
Magnetically ‘soft’ materials – materials that are easy to magnetise, demagnetise and remagnetise – are widely used in electrical power systems. They play a crucial role in transformers and devices like motors and generators that convert one form of energy into another, for example, electrical power into mechanical. Most of the magnetic cores used in these applications are made from grain-oriented or non-oriented electrical steels, but sometimes amorphous ribbon is used, especially in the USA.
Various production technologies are employed to maximise specific performance parameters for electrical steels – there is no single material that fits all needs. For example, a higher operating flux density (magnetisation) means that a smaller magnetic core can be used, but this typically comes at the expense of higher losses. Lower losses can be achieved by using thinner sheets to reduce eddy currents, but this increases costs while reducing the mechanical strength and stacking factor.
Magnetic properties of electrical steels are the focus of continuing research and, over the decades, losses have been significantly reduced through several technological steps. These include: separation of the material into isolated sheets to reduce eddy currents, the addition of 3 % silicon to the iron to reduce eddy currents, adoption of the crystallographic Goss structure which improves permeability, tensile stress coating which reduces the effects of assembly, improved grain orientation resulting in loss reduction at higher flux, double orientation, and so on. An overview of the progress of these improvements is shown in Figure 1.
Magnetic saturation and the magnetisation process
All ferromagnetic materials are internally magnetised to saturation in small local regions called magnetic domains that are separated by domain walls (Figure 2). In demagnetised materials, these domains point in opposing or random directions, such that the net magnetisation of the entire volume is zero.
When a magnetic field is applied, the domain walls move, and the domains change in size. Domains that are aligned in parallel with the field grow at the expense of those that are anti-parallel. As the magnetic field increases, more and more volume is occupied by the parallel domains. When all of the domains are aligned with the magnetising field, the material is completely saturated. No further increase of magnetisation can occur, regardless of the strength of the applied magnetic field.
Figure 1: Progress in reduction of power loss in electrical steels over time, Encyclopedia Magnetica, CC-BY-4.0 [1, 2]
Magnetic knee point
A closer look at the domains’ behaviour reveals that there is an intermediate step between the domains changing size and the onset of saturation, as shown in Figure 3. In the general case, the domains are not aligned with the external magnetic field, but some domains are close to that direction, and hence they grow. As the magnetisation progresses, all the anti-parallel domains are consumed (Point 4 in Figure 3), but magnetocrystalline anisotropy still keeps the internal magnetic field aligned with the direction of the local crystalline structure of the magnetic material.
This means a further increase in the external magnetic field is needed to rotate the remaining domains so that they align with the direction of the applied field. This process requires much more energy than the movement of domain walls. Therefore, the slope of the magnetisation curve becomes markedly shallower, although it is still steep enough to be useful (to some extent) for energy conversion. The material is, however, approaching saturation, so care is needed when applying higher excitation.
The region around Point 4 in Figure 3 is the ‘knee’ of the magnetisation curve, and it is caused by the internal magnetic behaviour of the magnetic domains. Just below the knee, where domain wall movements are still taking place, the material’s permeability remains high, reaching a maximum just above Point 3.
Above the knee point, the permeability of the material reduces rapidly. The ability to concentrate the magnetic field diminishes and eventually vanishes at saturation, which produces two important effects. The first is that, in a transformer driven from a generator, grid, or any other powerful voltage source, the inductance of the primary winding collapses and a current similar to a fault current begins to flow because only the resistance of the winding and the leakage inductance remain to oppose it. Phenomena such as inrush current and ferroresonance are linked to magnetic saturation.
The second effect is that electromagnetic energy, and any information it may carry, can no longer be transmitted to the secondary winding. In saturation (since there is no flux change), all of the supplied current is used as magnetising current and none flows into the secondary load. Hence, protection devices such as current transformers (CT) and voltage transformers (VT) can no longer operate within the required parameters, meaning that the protection will be impaired. This is why some protection CTs have a special design where the operating margin is much wider than normal so that even very heavy fault currents do not saturate the core. Generally, protection class CTs are expected to maintain their accuracy even when exposed to a fault current that is twenty times the rated current. With these factors in mind, it is of paramount importance that transformers always operate within their design parameters. This can be ensured by appropriate testing and by carefully following routine maintenance practices.
Figure 2: The magnetisation process involves changes in the configuration of magnetic domains. Light grey: domains pointing ‘up’. Dark grey: domains pointing ‘down’, Encyclopedia Magnetica, CC-BY-4.0 
Figure 3: Behaviour of magnetic domains, Encyclopedia Magnetica, CC-BY-4.0 
Implications for testing
As shown in Figure 1, there is continuing improvement in the efficiencies of electrical steels. This means that transformers designed and manufactured in the past may well have a larger margin before they reach saturation because if this were not the case, the resulting higher losses coupled with an already less efficient magnetic build would likely lead to heat dissipation problems. However, using newer, more efficient electrical steels makes it possible to optimise the design, which brings with it considerable savings in steel, copper, and insulating materials.
Transformers built 30 to 40 years ago, before the advent of computer modelling and simulations, may therefore be less susceptible to the effects of high currents that result from saturation. This should not be confused with resilience to faults: newer transformers can be built with more modern materials using designs supported by computer simulations. Hence, effects such as the complex distribution of internal mechanical forces can be countered in more effective ways.
Older transformers are almost always more likely to fail under fault conditions simply because of insulation degradation (for example, reduced polymerisation of the cellulose). But because the distance between the operating point and saturation is larger in these transformers, the current rises less steeply. This tempers the impact on the operation of other transmission and protection components that happen to lie in the path of the fault current.
So, old transformers are more vulnerable, but components associated with them will experience fault currents that rise less steeply. Therefore, it is important to demagnetise the core after testing because a magnetised core can lead to deeper saturation at startup, resulting in higher inrush currents that are detrimental to the health of the transformer itself. But if such transformers get saturated, for example due to fault current, it might be more difficult to demagnetise them, thus increasing the danger of excessive inrush currents.
Newer transformers are more efficient than their older counterparts, but they operate closer to their saturation point. For example, in the 1970s, a new type of grain-oriented steel was introduced that had a better orientation of texture. This steel was given the commercial name Hi-B . Permeability was increased, losses were reduced, and operation up to 1.9 T was possible, whereas designs with conventional grainoriented steels were mostly limited to 1.7 T. Yet the saturation for both types of steel was the same because the chemical composition was almost identical.
Figure 4: Typical display when testing a multi-tap current transformer (CT)
Saturation for pure iron is 2.15 T and somewhat lower for silicon steel. This is why transformers that use Hi-B steel have a smaller margin between their nominal operating point and saturation. This is not an exact science, however, so no hard and fast guidelines can be given. But again, it is vital that the nominal parameters of a transformer, such as polarity of windings, turns ratio, winding configuration, etc., are properly observed.
Definitions of ‘knee point’
There are several technical definitions of the knee point in a magnetising curve. As mentioned earlier, above the knee point, the permeability of the material decreases, so inductance and the impedance decrease and current increases. This relationship can be used for defining the location of the knee point quantitatively.
One such definition, for instance, is that the knee point is the point on the magnetisation curve where increasing the supply voltage by 10 % causes the current to double.
This definition indicates that something quite drastic happens to the current flowing through the winding. Moreover, with this definition’s aid, the knee point can be determined very precisely because the supply voltage and current can both be accurately measured. A definition of this type is a basis for the IEC 61869  series of standards which contains guidance on measuring the saturation curves of current transformers.
The corresponding ANSI standard – IEEE C57.13  – defines the knee point differently. In fact, this standard defines two knee points, one for air-gapped core CTs (ANSI 30º), the other for non-gapped CTs (ANSI 45º). For CTs with an air gap, the knee point is the point where the tangent line to the excitation curve forms a 30º angle. For CTs without an air gap, the knee point is where the tangent line forms a 45º angle.
Irrespective of whether the IEC or ANSI standards are being followed, the test procedure for determining the knee point is similar. The test is carried out under AC conditions at nominal operating frequency (50 or 60 Hz). The supply voltage is generated by an accurate signal generator and power amplifier, and its amplitude is increased gradually.
At the beginning of the test, the impedance of the winding under test is high and the resulting current is very small (mA level – see Figure 4). Therefore, the test apparatus must be able to measure these small currents accurately and reliably. The supply voltage is then increased and the resulting curve, typically of supply voltage vs current, is plotted over several orders of magnitude, which is why the plots normally use logarithmic rather than linear scales. It should be noted that the curves in Figure 4 are similar in shape to the magnetisation curve in Figure 3.
The points marked on the curves in Figure 4 denote the precise location of the knee points, in this case, according to the ANSI 45º definition. There are several curves because there are several taps on this particular CT. Advanced test instruments support the connection of multiple taps and can perform all tests simultaneously.
The measured knee point voltage of a protection class CT must be greater than the voltage drop across its burden to maintain the CT core in its linear zone. The burden of a protection CT is relatively high compared to that of a metering class CT, which means that the voltage drop across the burden will be high. The voltage drop across the burden equals the voltage across the CT secondary. If the voltage across the CT secondary is high, it may drive the CT to saturate under normal conditions. And, as mentioned above, a saturated CT is no longer able to convey correct information about the fault current and the protection may also fail to operate.
Power requirements for testing
Since XL = 2 f L, the impedance of a winding is directly proportional to the supply frequency. Therefore, the voltage needed to produce a particular current in the winding is also proportional to the supply frequency. This means that for large CTs, it may be necessary to supply a lot of reactive power if the tests are to be carried out at mains frequency. For example, the ANSI standard for testing class C800 CTs suggests that a minimum voltage of 800 V, and more typically 1300 V, will be needed to produce an excitation current of 1 A. DC voltage can, however, be used to produce the same core saturation, and this approach is described in IEC 60044-6 Annex B-3 .
Essentially, magnetic flux can be increased in two ways: either the time can be kept constant as the voltage increases, or the voltage can be kept constant as the time increases. With AC testing, the time is in effect kept constant as the applied frequency is fixed at either 50 or 60 Hz, and the voltage is increased. With DC testing, the applied voltage is held constant, and the voltage continues to be applied until the core becomes saturated. By integrating the constant DC voltage over the time this takes, the core saturation can be determined. This result can then be mathematically converted to an equivalent 50/60 Hz saturation and will produce the same value as a conventional excitation test.
DC testing has the benefit of removing the need for a high voltage, high power source to carry out the test, meaning that smaller, lighter, and less costly test sets can be used. It also allows tests to be carried out on CTs with high knee point voltages, although the test time will be longer. When DC testing is used, however, it is especially important to ensure that the CT is properly demagnetised before it is returned to service. It should also be borne in mind that the international standards cited as references  and  only define tests that are carried out at the power frequency of 50 or 60 Hz.
 Grain-oriented electrical steel, Encyclopedia Magnetica, https://www.e-magnetica.pl/doku.php/grain-oriented_electrical_steel, accessed
 Y.Kan: No.155-156th Nishiyama Memorial Seminar, Iron and Steel Institute of Japan, (1995)
 Magnetic domain, Encyclopedia Magnetica, https://www.e-magnetica.pl/doku.php/magnetic_domain, accessed 2021-03-29
 S. Taguchi, T. Yamamoto, A. Sakakura, New grain-oriented silicon steel with high permeability “ORIENTCORE HI-B,” IEEE Trans. Magnetics,
Vol. 10 (2), 1974, p. 123-127, https://ieeexplore.ieee.org/document/1058316
 IEC 61869 series of standards for instrument transformers
 IEEE C57.13 IEEE Standard Requirements for Instrument Transformers
 IEC 6044-6 Instrument Transformers Part 6: Requirements for Protective Current Transformers for Transient Performance