Modelling of distorted electrical power and its practical compensation in industrial plant

D.Ing.Alternating current systems employing single-frequency sinusoidal waveforms render optimal service when the currents in that system are also sinusoidal and have a fixed phase relationship to the voltages that drive them. Under unity- power factor conditions, the currents are in phase with the voltages and optimal net-energy transfer takes place under minimum loading conditions, i.e. with the lowest effective values of current and voltage in the system. The above conditions were realised in the earlier years, because supply authorities generated 50 Hz sinusoidal voltages and consumers drew 50 Hz sinusoidal currents with fixed phase relationships to these voltages. Static and rotating electrical equipment like transformers, motors, heating and lighting equipment were equally compatible with this requirement and well-behaved AC networks were more the rule than the exception. The fact that three-phase systems conveyed the bulk of the power from one topographical location to the next did not constrain the utilisation of that concept at all, even though poly-phase transmission systems were necessary to increase the economy of transmission and to furnish non-pulsating power transfer. Also, additional theory had to be developed to handle unbalanced conditions in these multi-phase systems and to take care of complex network analysis and fault conditions. Difficulties begin to manifest themselves when equipment not meeting these requirements is connected to the network and when the currents it draws are not sinusoidal. An increasing number of applications demand DC-voltage supplies from which DC-currents are to be drawn. Because power transmission is carried out by means of AC networks, the DC is furnished by converting or rectifying the AC-supply. Power-electronic circuits, of which the R 2P2 power supplies the AEC employs are no exception, employ line-commutated AC/DC converters in their front-ends, and fall into that category. Although these line-commutated, phase-controlled AC/DC converters are capable of handling giga-watt power levels, line-frequency commutation causes the currents they draw on the AC-side to be distorted, even though still to be periodic. These non-sinusoidal currents, drawn from the source, along the transmission lines and through other distribution system immittances, also give rise to non-sinusoidal voltage drops between the source and the load, which results in distorted voltage waveforms at other nodes and at the load. Harmonic penetration studies are essential to evaluate the performance of transmission systems in the presence of current distortion sources. These sources do not only bring about voltage distortion within the confines of their own borders, but extend their influence outside into those of other consumers as well. Supplyutilities are wary of the distortion introduced into their networks by consumers and initial recommendations have now given way to rigid standards for curbing harmonic pollution by consumers Because conventional steady-state alternating current circuit theory fails in the presence of distortion there are only two ways in which harmonic penetration studies can be carried out. Numerical integration methods are mandatory in the study of transient performance of electrical networks during switching and similar occurrences, but become cumbersome when the networks contain more than just a few nodes and are impossible to use when several tens or hundreds of nodes are encountered. Fortunately, harmonic penetration studies can be confined to steady-state operating conditions in a network in which voltages and currents are distorted but remain periodic and are therefore Fourier transformable. When viewed in the frequency-domain, non-sinusoidal but periodic current and voltage waveforms can be represented by discrete frequency spectra. Frequency-domain analysis offers a number of advantages. From the frequency-domain point of view, distortion can be quantified in terms of complex phasor values of voltages and currents at discrete harmonic frequencies that individually lend themselves to conventional circuit theory, permitting calculations to be carried out in extensive networks. Solutions that apply to these individual harmonic frequencies can then be summated across the spectrum to furnish aggregate or joint parameters of currents, voltages and powers and can also be transformed back into the time-domain for the reconstruction of the relevant time-dependent waveforms. Both the frequency and time-domain waveforms, of voltage and current, constructed in the above manner are concise and convey the same numerical information. When attempting, however, to quantify the circuit behaviour in terms of the classical definitions of active, reactive and apparent power, it is soon discovered that different definitions are possible. The different definitions, unfortunately, lead to divergent results and it is impossible to assess the utility of each different theory on a general basis. Only by applying the different theories in dedicated measurements, can their relative worth be established in terms of specific circumstances. That is the main theme of this dissertation