ABSTRACT

In this chapter the theory of the arbitrary rotating reference frame will be introduced using the voltage equations of simple r–L circuits. Because of economies gained in the cost of transmission and distribution, three-phase networks are used almost exclusively in the generation and utilization of electrical power. It is interesting to now solve a simple static network problem involving an electrical transient. Although the emphasis in this chapter has centered primarily on the solution of sinusoidal sources, it is important to realize that the transformation to the arbitrary reference frame is valid regardless of the form of the source voltages. It is apparent that although the three-phase case is potentially a considerably more complex problem, matrix analysis reduces the work to the same degree of difficulty as for a two-phase case. Although only three-phase circuits have been investigated in this chapter, one could now extend this approach to any number of circuits.