HYPER SPACE VECTORS - A NEW 4-QUANTITY EXTENSION OF SPACE-VECTOR THEORY

The space-vector theory, which allows to describe three linearly depen dent quantities (e. g. three voltages or three currents) using only tw o linearly independent quantities represented in an orthonormal coordi nate system, is widely used in the fields of AC machine theory power d efinitions and active filtering. It can be used very effectively in ca se of circuits with only three terminals. Problems occur in case of fo ur terminals, when four linearly dependent quantities (e. g. four curr ents, the sum of which is always zero) exist. In this case a zero-sequ ence quantity can be additionally introduced, which has to be treated separately with special equations. Vector operations like cross produc t or dot product, which are very useful to calculate e. g. power quant ities, can no longer be used in the general case. This paper presents a method transforming any system represented by four linearly dependen t quantities or by three linearly independent quantities into a three- dimensional orthonormal coordinate system. All four members of a set o f linearly dependent quantities are treated equally. We suggest to cal l this representation Hyper Space Vector (HSV). A lot of vector operat ions can be applied without problems to HSV making calculations much e asier and more graphic.