Reduced-Order State Space Model for Dynamic Phasors in Active Distribution Networks

The rapid proliferation of distributed generation (DG) in active distribution networks (ADNs) increases the power system modeling complexity, which requires more efficient numerical methods to analyze dynamic interactions among DGs in ADN. This paper proposes a reduced-order dynamic phasor (DP) modeling method which is applied to large-scale ADNs with DGs for reducing the modeling scale and allowing larger time steps in ADN analyses. First, a unified state-space DP model, referred to as full-order DP model for linear circuits, is developed on the abc-axis to provide a comprehensive technique for interfacing DGs with other electric devices in large ADNs. The model order reduction (MOR) is applied to this full-order model to reduce the computation burden for large-scale ADNs. The paper develops a state-space DP model on positive and negative sequence synchronous rotating reference frames for three-phase DGs, and a stationary frame for single-phase DGs. The accuracy and the efficiency of the proposed models are verified using the modified IEEE 123-node test feeder and IEEE European low voltage test feeder with DGs.