Second-Order Cone Programming for Optimal Power Flow in VSC-Type AC-DC Grids

This paper presents a second order cone programming (SOCP) formulation of the optimal power flow problem for AC-DC systems with voltage source converter (VSC) technology. Approximation techniques have been used to derive the SOCP formulation of the AC-DC OPF problem. Later, the SOCP formulation can be solved using the interior point method (IPM) by considering the limits on AC-DC grid. The accuracy of SOCP formulation of AC OPF has been proven with numerical examples using IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus example systems. The results of the SOCP formulation are compared with available commercial software. Then a DC system with VSC technology is modeled in the IEEE 30-bus example system. The SOCP formulation of AC-DC OPF is applied to the modified IEEE 30-bus example system and the results are discussed. The limitations of derived SOCP formulation are also discussed.