Operation Optimization Adapting to Active Distribution Networks Under Three-Phase Unbalanced Conditions: Parametric Linear Relaxation Programming

Asymmetric phase distributed generation, which is widely used in distribution systems, aggravates the severity of the intrinsic three-phase unbalanced condition of distribution systems. To overcome these problems, operation optimization formulas of the three-phase unbalanced active distribution network (ADN) are established considering soft open point (SOP) and belong to a nonconvex quadratic programming (NQP) problem. However, in conventional methods, either approximations that are not valid for an unbalanced distribution system are used or convex relaxation methods are applied to primitive nonlinear optimization models. However, these methods do not guarantee a feasible optimization solution. Therefore, determining the solution to the NQP problem is challenging. In this article, we propose a parametric linear relaxation algorithm to obtain the optimal feasible solution by solving the operation optimization problem of the three-phase unbalanced ADN with the SOP. The parametric linear relaxation technique is constructed based on the properties of quadratic functions and the mean value theorem, and the NQP is converted to a series of parametric linear relaxation programming problems. The results revealed that the proposed algorithm can achieve the optimal and feasible solution and considerably reduce the computation time compared with an equivalent NLP optimization model for the same distribution system.