Relationship and Comparative Analysis of Three Complex Power Vectors-Based Model Predictive Control Under Unbalanced Networks

The previous studies examined the relationship between traditional complex power (TCP) and extended complex power (ECP)-based direct power controls (DPCs). A novel complex power (NCP) is modeled, and we then study the relationship between the NCP and existing complex powers. The frameworks of TCP-, ECP-, and NCP-based model predictive DPC (MPDPC) are established and studied using mathematical models and tools. Under slightly unbalanced grid voltages, we perform a comparative analysis of the above three methods. The inherent equivalence or relationship between the three methods is described in terms of power variations. Under extremely unbalanced grids, the existing TCP- and ECP-based MPDPCs cannot work well, resulting in nonsinusoidal grid currents and larger power ripples. However, the NCP-MPDPC achieves the better steady-state performance. To reveal their inherent relationships, we conduct a comparative study from their output reference voltages. Finally, we are stimulated to design an NCP-based MPDPC. The MPDPC method is realized by selecting one extended active vector and a zero vector. The duty cycles of all voltage vectors are redesigned to achieve sinusoidal grid current and minimize total harmonic distortion (THD). Both the simulations and experiments validate the effectiveness of their inherent relationships of three methods.