Modelling and analysis of electric arc loads using harmonic domain techniques

Abstract It has been reported that as much as 12% of global electricity production goes into producing artificial light using arc discharge lamps and that global annual production of these lamps may be as much as 1.2 billion units. In the liquid steel production industry, one metric tone of steel demands, on average, 400 kW-hr and in the year 2007, the crude steel output reached 1,343.5 million metric tons. In both instances, engineered electric arcs are present and represent major loads in electrical power systems which require the utmost attention. They observe a highly non-linear behaviour with the capacity to export harmonic distortion and flicker into the power system. Electric arc furnace installations, in particular, are well-known to be sources of dynamic disturbances affecting neighbouring loads. Arc discharge lamps, on aggregate, may exhibit the same perturbing effect. Over the years, the non-linear nature of these loads and their ubiquitous nature have caught the interest of researchers in all corners of the world and from different backgrounds, including this author. The research work reported in this thesis advances current knowledge in the modelling and simulation of electric arcs with particular reference to arc discharge lamps with electromagnetic ballasts and electric arc furnaces with particular reference to operational unbalances and the impact in the installation of ancillary power electronics equipment. In these two quite distinct applications, linked by the presence of engineered electric arcs, the fundamental modelling item is a non-linear differential equation which encapsulates the physic of the electric arc by applying power balance principles. The non-linear differential equation uses the arc conductance as state variable and adapts well to model a wide range of characteristics for which a set of experimental coefficients are available. A fact of perhaps equal relevance is that the non-linear differential equation is amenable to algebraic representations using operational matrices and suitable for carrying out periodic steady-state solutions of electric circuits and systems. The modelling and numerical solution takes place in the harmonic space where all harmonics and cross-couplings between harmonics are explicitly represented. Good application examples are the harmonic domain solution of arc discharge lamps with electromagnetic ballasts and the harmonic domain solution of electric arc furnaces with ancillary power electronics equipment. Building on the experience gained with the representation of the arc discharge lamps with electromagnetic ballasts, the research turns to the representation of the electric arc furnace installation with provisions for reactive power compensation using power electronic control and harmonic filters. This is a three-phase application which comprises several nodes, giving rise a large-scale model of a non-linear system which is solved in the direct frequency domain using a blend of the Newton-Raphson method and the Gauss-Seidel method, achieving robust iterative solution to a very tight tolerance. Both algorithms are implemented in MATLAB code and the raw simulation results which are the harmonic complex conjugated vectors of nodal voltages are used to assess in a rather comprehensive manner the harmonic interactions involved in both kinds of applications.