Abstract
Chapter 4, “Transient Phenomena”, describes several electromagnetic phenomena that may occur in HVAC cables. The chapter starts by explaining the energisation of a single cable for both-ends bonding and cross-bonding, showing the waveforms for different scenarios and demonstrating how the modal theory can be used to explain the transient waveforms; after this, other phenomena such as the energisation of cables in parallel, zero-missing, transient recovery voltages and restrikes are addressed. Hybrid cable-OHLs are also considered in this chapter, and it is demonstrated how an overvoltage may be very high for some configurations as well as the influence of the bonding configuration in the magnitude of the overvoltage. The interaction between a cable which is highly capacitive and a transformer which is highly inductive is also analysed and some possible resonance scenarios are explained, as well as ferroresonance. To finish the chapter, we study short-circuits in cables which can be rather different from short-circuit in OHLs, because of the current returning in the screen. The screen can also be bonded on different configurations, influencing both the magnitude of the short-circuit current and of the transient recovery voltage.
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- 1.
Given by the V = Q/C relation.
- 2.
Given by approximately 50,000 m/150 m/μs.
- 3.
In reality the cable would discharge, but that takes several seconds or even minutes.
- 4.
The voltage is not the same all along the cable at the disconnection instant, being typically lower at the sending end of the cable, when assuming that the other end is already disconnected. After the disconnection, the voltage in the cable tends to equalise resulting in a voltage increase at the sending end of the cable (for more information on the phenomenon see Sect. 4.10.1).
- 5.
In this case, the voltage difference is ~−1 pu at the energisation instant, and the voltage variations have opposite polarity to the ones shown in Fig. 4.2.
- 6.
They are typically 10–15% larger than in reality.
- 7.
This theoretical maximum does not consider the reflections in other adjacent cables, i.e., the switched cable is much shorter than the cable connected to its sending end. The more normal situation of similar lengths is explained in Sect. 5.2.
- 8.
- 9.
Equivalent to a current of approximately 4.3 kA in Phase A and 0 A in the other two phases.
- 10.
For a frequency of 1.5 kHz.
- 11.
The values are slightly different from the ones that would be obtained using the currents quoted previously. The correction is made to avoid confusion as there would be some small discrepancies between the theory and the values obtained, because of the approximations previously made in the calculation of some of the currents.
- 12.
There are some small differences for Table 8, but it is normal when considering the several approximations that were made.
- 13.
There is some voltage from the intersheath mode, but it has a lower velocity and it arrives later.
- 14.
The same conclusion can be achieved, by knowing that the third coaxial mode is 0.
- 15.
An analysis similar to the one done before for the first crossing point would be very complicated because of the large number of superimposed waves. However, the readers can use the files available online to simulate this case if desired.
- 16.
This is an advantageous for many companies that do not have any advance simulation software, but still need to know if there is a risk for their system when energising cables in parallel.
- 17.
Typically the cable is discharged at the energisation instant and the value is 0 V.
- 18.
The authors want strongly to point out that these formulas are for a general cable, and will change depending on the cable characteristics and installation layout.
- 19.
This also serves to re-demonstrate on how important it is to correct the electrical parameters for the right frequency. Many times there are used the 50 Hz values as they are the only ones available in the datasheet. However, for more than one phenomenon this simplification will lead to inaccurate results.
- 20.
This may not seem an issue in some situation as the faulty phase would still be open when using a CB with synchronise switching. Yet, to have one phase open and the other two close may lead to ferroresonance and a long temporary overvoltage that is even more undesired.
- 21.
See Chap. 2 for more information on the energisation of inductive loads.
- 22.
Remember that a CB typically switch-off for 0 A if operating properly.
- 23.
V1(0) and V2(0) should be similar, the existence differences would be a result of Ferranti Effect.
- 24.
The resonance frequency can be also calculated by fr = fN•x, where f N is the system frequency and the x the reactive power compensation ratio.
- 25.
For a 50 Hz system, 2.778 ms for a 60 Hz system.
- 26.
For more information on shunt reactors including mutual coupling see Sect. 1.4.
- 27.
The full mathematical development is available at [3].
- 28.
Assuming a strong network. In a weak network the voltage would change when the cable is disconnected.
- 29.
It is used a capacitor instead of a cable for simplicity. In the cable there would be reflections in the cable because of travelling waves and the voltage would be lower because of the resistance of the cable. This case is also the worst-case scenario where the restrikes occur at the worst instants.
- 30.
The term syphon line is also commonly used.
- 31.
An introduction to the topic was made in Sect. 3.6.
- 32.
The voltage of an OHL increases after the disconnection because of the capacitance coupling between the phases. Consequently, the voltage at the CB terminal at the restrike instant is larger than 2 pu. However, we consider the value 2 pu in the demonstration of the phenomenon.
- 33.
A good example of this type of line is the connection of an offshore wind farm, where part of the line is a submarine cable and the rest a land cable.
- 34.
The bonding of the cable influences the frequency spectrum as demonstrated in Sect. 3.5. For simplicity, in this section the cable is considered as being bonded in both-ends.
- 35.
The inductance of the equivalent network is an artificial representation of the network for effects of representation, but the physical behaviour is similar.
- 36.
From a more formal point of view, the energisation at zero voltage results in maximum flux that corresponds to a near saturation point in the B–H curve.
- 37.
The same happens for the energisation of a transformer, a phenomenon known as inrush currents.
- 38.
The introduction to travelling waves and the explanation on why a wave is divided into two waves propagating in opposite directions is given in Chap. 3.
- 39.
In this case, the wave speed is much lower than the typical coaxial mode velocities because of the larger inductance of the cable when it does not have a screen. However, for practical reasons a HV cable without a screen would never be installed directly on the ground.
- 40.
For simplification, we consider an ideal short-circuit with a fault resistance of 0 Ω.
- 41.
It is important not to confuse neutral with ground. If there is a grounding grid, this grounding grid is the neutral point, however, it will have a voltage slightly different form the ground.
- 42.
There are other factors influencing the current like the configuration of the substation, however, these parameters are typical of less importance.
- 43.
If we think in the ground as being a small resistor in series with a large inductor, the phenomenon is exactly like the energisation of a shunt reactor.
- 44.
This is assuming typical cases. It may be different if there are other conductors installed in the ground.
- 45.
It is theoretical possible to have a phase-to-phase fault in a cable, as example for low voltages cables that are installed in a tunnel or a duct. However, it is very unlikely to have this type of fault for high voltage cables. Thus, we do not analyse them here.
- 46.
Some simplifications are being made here, most notability we are not considering the voltage induced by the current in the screens of the sound phases, which also increases during the fault. We are going to see later that for low grounding resistances and/or existence of grounding grids the voltage changes after the fault point.
- 47.
Download and run the PSCAD files available online in order to observe this difference in detail.
- 48.
One of modes is an interconductor mode, which is not influenced by the transient.
- 49.
These values have already some tolerance and for real cases the interval is even more narrow.
- 50.
Remember that part of the current returns in the ground.
- 51.
It is virtually impossible for the conductors, but it may happen for the screens.
- 52.
Remember that the magnitude of the current in the screens is rather low for large grounding resistances.
- 53.
The voltage variation is larger for the conductor of the faulted phase (1 pu) than for the screen (≤1 pu). As a result, there is a small initial variation in two of the coaxial modes. However, the larger the grounding resistance the larger the voltage variation in the screen and in the limit case the voltages are almost equal (assuming that the cables are not too far apart from each other).
- 54.
For simplicity we do not consider the link boxes and their impedances.
- 55.
Part of the current continues flowing in the ground until the end of the cable. The division of the current depends on the impedance values as given by classic circuits theory. It would be the same for cables with several major sections.
- 56.
As most of the transient phenomenon, a proper simulation of a fault requires an accurate model. A common error made when simulating this phenomenon is the grounding. The connection of the screens should reflect the real system, typically all three phases are connected together and there is a common resistance for all three. Depending on the software, one should also be careful with the grounding when dividing the projects by different working modules.
- 57.
This is the main difference for a normal de-energisation where V 1 and V 2 have similar values.
- 58.
Remember that during the fault the voltages increases along the conductor of the sound phases from the energised end to the open end.
- 59.
Remember that the current in the screens and conductors is low and there is almost no voltage increase because of mutual coupling.
References and Further Reading
IEC 60071-2 (1996) Insulation co-ordination—Part 2: application guide
IEE 60071-4 (2004) Insulation co-ordination—Part 4: computational guide of insulation co-ordination and modelling of electrical networks
Da Silva FMF (2011) Analysis and simulation of electromagnetic transients in HVAC cable transmission grids. PhD Thesis, Aalborg University, Denmark
Ibrahim AL, Dommel HW (2005) A knowledge base for switching surge transients. International Conference on Power Systems Transients (IPST), Canada, Paper No. 50
Alexander RW, Dufournet D (2008) Transient recovery voltage (TRV) for high-voltage circuit breakers. IEEE Tutorial: Design and Application of Power Circuit Breakers. IEEE-PES General Meeting
Liljestrand L, Sannino A, Breder H, Thorburn S (2008) Transients in collection grids of large offshore wind parks. Wind Energy 11(1):45–61
Ferracci P (1998) La Ferroresonance. Cahier technique n° 190, Groupe Schneider
Greenwood Allan (1991) Electrical transients in power systems, 2nd edn. Wiley, New York
Van der Sluis L (2001) Transients in power systems. Wiley, New York
IEC 60056-1987-03 (1987) High-voltage alternating-current circuit-breakers
IEEE guide for the application of sheath-bonding methods for single-conductor cables and calculation of induced voltages and currents in cable sheaths, IEEE Std. 575 (1988)
IEEE application guide for capacitance current switching for AC high-voltage circuit breakers, IEEE Std. C37.012 (2005)
IEEE Guide for the protection of shunt capacitor banks, IEEE Std. C37.99 (2000)
Cigre Joint Working Group 21/33 (2001) Insulation co-ordination for HV AC underground cable system. Cigre, Paris
Cigre Working Group B1.18 (2005) Special bonding of high voltage power cables. Cigre, Paris
Cigre Working Group C4–502 (2013) Power system technical performance issues related to the application of long HVAC cables. Cigre, Paris
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da Silva, F.F., Bak, C.L. (2013). Transient Phenomena. In: Electromagnetic Transients in Power Cables. Power Systems. Springer, London. https://doi.org/10.1007/978-1-4471-5236-1_4
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