Optimal power flow of MT‐HVDC system connected large offshore wind farms using mixed‐integer semi‐definite programming approach

Typically offshore wind farms are connected to the onshore AC grid networks using voltage source converter based MT‐HVDC networks. This article aims to formulating optimal power flow (OPF) problem of MT‐HVDC system connected large offshore wind farms using mixed‐integer semi‐definite programming approach. Both constant power and droop control modes of voltage source converter converters are considered in OPF formulation. Main objective of OPF is to minimize DC power losses and simultaneously optimizing droop gains of the converters. OPF problem is solved using SDP relaxation; while its exactness is discussed using graphical properties. It is found that MT‐HVDC system exhibit acyclic graph property which guarantees that SDP relaxation would give either rank‐1 or ‐2 solutions. For rank‐2 solutions, an iterative rank reduction algorithm is introduced to achieve rank‐1 solutions from which global optimal solutions could be recovered easily. The comparative analysis is also performed with previously employed optimization methods used to solve the OPF problem. Furthermore, steady state solutions obtained from the proposed OPF formulation are also cross‐verified using dynamic simulation studies of offshore wind farms connected MT‐HVDC networks.