Hyper space vectors: A new four‐quantity extension of space‐vector theory

Abstract

AbstractThe space‐vector theory, which allows to describe three linearly dependent quantities (e. g. three voltages or three currents) using only two linearly independent quantities represented in an orthonormal coordinate system, is widely used in the fields of AC machine theory, power definitions and active filtering. It can be used very effectively in case of circuits with only three terminals. Problems occur in case of four terminals, when four linearly dependent quantities (e. g. four currents, the sum of which is always zero) exist. In this case a zero‐sequence quantity can be additionally introduced, which has to be treated separately with special equations. Vector operations like cross product or dot product, which are very useful to calculate e. g. power quantities, can no longer be used in the general case. This paper presents a method transforming any system represented by four linearly dependent quantities or by three linearly independent quantities into a three‐dimensional orthonormal coordinate system. All four members of a set of linearly dependent quantities are treated equally. We suggest to call this representation Hyper Space Vector (HSV). A lot of vector operations can be applied without problems to HSV, making calculations much easier and more graphic.