Optimal capacitor placement to minimise harmonics in power systems and software tools - Hitzeroth, Helmuth Victor (Department of Electrical Engineering, 2016)
Harmonics in power systems is a relatively new area of research. In view of this and the growing awareness of the quality of the electricity supply, the theory of harmonics in power systems is reviewed. The sources and the effects of harmonics are investigated. The algorithms that are used for the frequency analysis of power systems are investigated and compared. These algorithms comprise the companion circuit method, the Gauss-Seidel method, the Newton-Raphson method and the current injection method. In addition various freely and commercially available software packages for the harmonic analysis of power systems are studied and compared. For this purpose a questionnaire was sent out to software developers and suppliers. This questionnaire as well as the results of the comparative investigation are presented. A power system has many configurations due to the switching of power capacitors on to and off the power grid. Some of these configurations can result in unacceptable distortion levels. An existing state space method is investigated to analyse these configurations and an example is worked through, to illustrate how this method works. However, this state space model is only applicable to radial power systems and there have to be power capacitors at the end of every feeder amongst others. Because of these significant disadvantages of this method, a new analytical approach or theoretical foundation for the analysis of power capacitors in radial as well as meshed power systems is developed in this thesis. For this purpose the branch current and nodal voltage equations are determined. Redundant nodal voltages are eliminated from the set of branch current equations. The remaining equations and the nodal voltage equations are then combined to form a system realisation. This system realisation is still overspecified and a further reduction is done to obtain a minimal realisation of the power system. This approach is demonstrated analytically and numerically by way of five case studies. This approach is also verified by comparing it with the current injection method. Identical results are obtained with the state space approach and with the current injection method, demonstrating that the state space approach is indeed valid.