Electromagnetic Transients in Power Cables

“Components Description”, describes several layers of a cable as well as their function. It also shows how to calculate the different electric parameters of a cable, resistance, inductance, capacitance, and how to use those values to calculate the positive-sequence and zero-sequence, including how to adapt the datasheet values for more accurate calculations. The chapter introduces the different bonding configurations typically used for the screens of cables (both-ends bonding and cross-boding) and also presents methods that can be used to estimate the maximum current of a cable for different types of soils, i.e. thermal calculations. The end of the chapter introduces the shunt reactor, which is an important element in cable-based network as it consumes locally the reactive power generated by the cables.

“Simple Switching Transients”, reviews the principles of the Laplace transform and uses it to study simple switching transients, RC-RL-RLC loads for both AC and DC sources. In other words, the chapter demonstrates how analytical analysis of simple systems can be made. These principles will be used in later chapters in the study of more complex scenarios.

“Travelling Waves and Modal Domain”, reviews the Telegraph equations and how to calculate the loop and series impedance matrices as well as the shunt admittance matrix of a cable in function of the frequency. The chapter also introduces the different modes of a cable, how to calculate their impedance and velocity as well as their frequency dependence. The knowledge of modal theory is of outmost importance when working in transient in cables. It is true that in many cases, software is used to run simulations, and the reader may be tempted to think that only those designing the software need to know how to use modal theory. However, several phenomena require at least a minimum knowledge of the topic and for that reason; the book provides a thorough explanation of the subject. This chapter also studies the frequency spectrum of a cable for different modelling configurations, introducing the power of lower resonance frequencies.

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.

“System modelling and harmonics”, starts by proposing a method that can be used when deciding how much of the network to model when doing a simulation of an energisation/restrike together with the possible limitations of the method.The chapter continues by analysing the frequency spectrums of cable-based networks which have lower resonance frequencies than usual because of the larger capacitance of the cables. At the same time, a technique that may help save time when plotting the frequency spectrum of a network is proposed.The chapter ends by proposing a systematic method that can be used when doing the insulation co-ordination study for a line, as well as the modelling requirements, both modelling depth and modelling detail of the equipment, for the study of the different types of transients followed by a step-by-step generic example.