Optimization Approaches for Optimal Power Flow Problems in Renewable Energy Grids

In recent years, the global energy crisis confronting humanity is attributable to a deficiency in classical energy sources whereas the energy demands are widespread growth. In overcoming this crisis, increasing the efficiency of energy and sustainability are becoming significantly crucial. Therefore, the integration of various renewable energy resources into the traditional electrical grid is quite a challenging issue due to their intermittent nature. In this dissertation, the main focus is on the operational stage optimization problem considering the optimal power flow (OPF) problem to economically meet time-varying consumer demands. This brings a new level of complexity to the OPF problem that needs to be addressed by new and more performant optimization algorithms. One promising area of research that will be followed in this work is the use of heuristic optimization algorithms. These have been used both alone or in hybrid combinations of two optimization algorithms to compensate for the weaknesses of each.Due to nonlinearity introduced by alternating current power flow equations, this research focuses on improving the non-linear of the OPF problem for an electrical power grid that includes different energy sources along with thermal plants as energy generators. This dissertation illustrates how to improve the numerical stability of the proposed optimization approach by considering different variables to avoid ill-conditioned numerical operations. The proposed optimization approach, on the other hand, is able to deal with non-convex problems with multiple local optima, and also it is able to deal with the additional complexity of the hybrid power grid. This dissertation aimed at improving the use of stand-alone and hybrid AC/DC microgrid systems by minimizing some issues, e.g., global warming emissions and the increasing cost of power systems and losses during the entire time horizon. In this work, some assumptions have been made by considering line constraints on the network to theoretically prove that the performance of the polynomial optimization problem relaxation can satisfy the original power flow equations. Finally, the performance of the proposed algorithm has been examined on different electrical power networks with various power system sizes, such as IEEE 5, 14, and 30 bus. The outcomes of the experiments proved the adaptability of the algorithm when considering large-scale electrical power networks. In addition, this proposed algorithm has been compared with some exiting optimization algorithms given in the literature for similar power systems, where it shows the effectiveness of this proposed method. This achievement will strengthen the use of this convexification approach in its applications on large-scale systems to reduce energy expenses and network system losses.