A set of independent admittance bases for decoupled analysis of unbalanced three-phase systems

The d-q transformation is widely used in the three-phase system analysis, targeting for symmetrical and balanced systems where the time-varying line-frequency sinusoidal terms of the system state variables can be fully canceled out. With the introduction of the distributed generations, more and more unbalanced infrastructures can be connected to the grid, creating unbalanced systems. It will be desirable to have effective analytical methods and modeling techniques for unbalanced systems. This paper proposes a new approach to analyzing unbalanced systems by demonstrating a decoupled analytical technique for resolving the unbalanced system into the balanced positive-, negative- and zero-sequence system components in the circuit level. The proposed method decomposes the unbalanced admittance of the system into independent admittance bases (IAB) each of which belongs to one of the positive-, negative-or zero-sequence system component to ease subsequent analyses.