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Optimal power flow (OPF) is the fundamental mathematical model in power system operations. Improving the solution quality of OPF provide huge economic and engineering benefits. The convex reformulation of the original nonconvex alternating current OPF (ACOPF) model gives an efficient way to find the global optimal solution of ACOPF but suffers from the relaxation gaps. The existence of relaxation gaps hinders the practical application of convex OPF due to the AC-infeasibility problem. We evaluate and improve the tightness of the convex ACOPF model in this paper. Various power networks and nodal loads are considered in the evaluation. A unified evaluation framework is implemented in Julia programming language. This evaluation shows the sensitivity of the relaxation gap and helps to benchmark the proposed tightness reinforcement approach (TRA). The proposed TRA is based on the penalty function method which penalizes the power loss relaxation in the objective function of the convex ACOPF model. A heuristic penalty algorithm is proposed to find the proper penalty parameter of the TRA. Numerical results show relaxation gaps exist in test cases especially for large-scale power networks under low nodal power loads. TRA is effective to reduce the relaxation gap of the convex ACOPF model.
We derive the branch ampacity constraint associated to power losses for the convex optimal power flow (OPF) model based on the branch flow formulation. The branch ampacity constraint derivation is motivated by the physical interpretation of the trans
The uncertainty of multiple power loads and re-newable energy generations in power systems increases the complexity of power flow analysis for decision-makers. The chance-constraint method can be applied to model the optimi-zation problems of power f
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not nec
We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set of sensors
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is