четверг, 25 октября 2012 г.

Transients in Power Systems

Transient Analysis


Basic Concepts and Simple Switching Transients

The purpose of a power system is to transport and distribute the elec- trical energy generated in the power plants to the consumers in a safe and reliable way. Aluminium and copper conductors are used to carry the current, transformers are used to bring the electrical energy to the appropriate voltage level, and generators are used to take care of the conversion of mechanical energy into electrical energy. When we speak of electricity, we think of current flowing through the conductors from gener- ator to load. This approach is valid because the physical dimensions of the power system are large compared with the wavelength of the currents and voltages; for 50-Hz signals, the wavelength is 6000 km. This enables us to apply Kirchhoff’s voltage and current laws and use lumped elements in our modelling of the power system. In fact, the transportation of the electrical energy is done by the electromagnetic fields that surround the conductors and the direction of the energy flow is given by the Poynting vector. For steady-state analysis of the power flow, when the power frequency is a constant 50 or 60 Hz, we can successfully make use of complex calculus and phasors to represent voltages and currents. Power system transients involve much higher frequencies up to kiloHertz and mega- Hertz. Frequencies change rapidly, and the complex calculus and the phasor representation cannot be applied any longer. Now the differen- tial equations describing the system phenomena have to be solved. In addition, the lumped-element modelling of the system components has to be done with care if we want to make use of Kirchhoff’s voltage and current laws. In the case of a power transformer, under normal power frequency–operation conditions, the transformer ratio is given by the ratio between the number of the windings of the primary coil and the number of the windings of the secondary coil. However, for a lightning-induced voltage wave, the stray capacitance of the windings and the stray capaci- tance between the primary and secondary coil determine the transformer ratio. In these two situations, the power transformer has to be modelled differently! When we cannot get away with a lumped-element representation, wherein the inductance represents the magnetic field and the capacitance represents the electric field and the resistance losses, we have to do the analysis by using travelling waves. The correct ‘translation’ of the physical power system and its components into suitable models for the analysis and calculation of power system transients requires insight into the basic physical phenomena. Therefore, it requires careful consideration and is not easy. A transient occurs in the power system when the network changes from one steady state into another. This can be, for instance, the case when lightning hits the ground in the vicinity of a high-voltage transmission line or when lightning strikes a substation directly. The majority of power system transients is, however, the result of a switching action.

Load- breakswitchesanddisconnectorsswitchoffandswitchonpartsofthe network under load and no-load conditions. Fuses and circuit breakers interrupt higher currents and clear short-circuit currents flowing in faulted parts of the system. The time period when transient voltage and current oscillations occur is in the range of microseconds to milliseconds. On this timescale, the presence of a short-circuit current during a system fault can be regarded as a steady-state situation, wherein the energy is mainly in the magnetic field, and when the fault current has been interrupted, the system is transferred into another steady-state situation, wherein the energy is predominantly in the electric field. The energy exchange from the magnetic field to the electric field is when the system is visualised by lumped elements, noticed by transient current and voltage oscillations. In this chapter, a few simple switching transients are thoroughly anal- ysed to acquire a good understanding of the physical processes that play a key role in the transient time period of a power system. As switching devices, we make use of the ideal switch. The ideal switch in closed posi- tion is an ideal conductor (zero resistance) and in open position is an ideal isolator (infinite resistance). The ideal switch changes from close to open position instantaneously, and the sinusoidal current is always interrupted at current zero.

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