Second-order cone programming relaxation-based optimal power flow with hybrid VSC-HVDC transmission and active distribution networks

The detailed topology of renewable resource bases may have the impact on the optimal power flow (OPF) of the voltage source converter (VSC)-based high-voltage direct current (HVDC) transmission network. To address this issue, this study develops an OPF with the hybrid VSC-HVDC transmission and active distribution networks to optimally schedule the generation output and voltage regulation of both networks, which leads to a non-convex programming model. Furthermore, the non-convex power flow equations are based on the second-order cone programming (SOCP) relaxation approach. Thus, the proposed model can be relaxed to an SOCP that can be tractably solved. Numerical results on a three-bus VSC-HVDC network and the European system verify the effectiveness of the proposed model and suggest that the proposed model can guarantee the voltage magnitudes of both networks within the allowable ranges.