Modeling and application of DQ-sequence dynamic phasors under unbalanced AC conditions

Increasing unbalanced AC operating conditions generates the need of developing models for power electronic equipment in such situations. The dq-sequence dynamic phasor method is proposed in this paper to model power electronic devices controlled in dq-rotating coordinates. Firstly, the instantaneous symmetric component decomposition and Park transformation are sequentially performed on a set of three-phase time-domain signals to define the dq-sequence dynamic phasors. Then, the multiplication property is derived. Next, the general steps for forming the state equations are provided, and the specific expressions of the state matrices are derived. Furthermore, a method is provided for quickly separating the real and imaginary parts of the complex-form state equations, as well as obtaining their simplest real-form. Case study on a two-terminal Modular Multilevel Converter − High Voltage Direct Current system verifies the effectiveness of the proposed modeling method. And the developed state space model is compared with existing similar models to show its advantages.