Application of the nested convex programming to the optimal power flow in MT-HVDC grids
This paper deals with an application of the nested convex programming to the optimal power flow (OPF) in multi-terminal high-voltage direct-current grids (MT-HVDC). The real-world optimization problem under consideration is non-convex. This fact implies some possible inconsistencies of the conventional numerical minimization algorithms (such as interior point method). Moreover, the constructive numerical treatment of this problem is usually based on some approximative approaches, namely, on the suitable linearizations and problem relaxations. The resulting convex programming model constitutes an approximated model and can naturally involve the significant (approximation) errors. In difference to the strongly approximate computational approaches mentioned above, the numerical scheme we propose takes into account the specific bi-linear structure of the problem and operates with the originally given non-convex formulation of the problem. We implement the proposed nested optimization approach and study the numerical consistency of the resulting optimal design. The Python based numerical experiments demonstrate the imlementability of the proposed methodology. Optimization problem of the modified version of the CIGRE MT-HVDC is next used as a benchmark test for the approach we developed.