Coordinated allocation of distributed generation, soft open points and energy storage systems in unbalanced distribution networks considering flexibility deficiency risk

Optimizing the location and capacity of flexible resources is critical. The increase in the permeability of distributed generation (DG) causes the net load to drastically fluctuate, which sharply increases flexibility demand for the distribution network. The asymmetric access of distributed generators, asymmetric line parameters, and unbalanced loads aggravate the three-phase voltage unbalance of distribution systems. Energy storage systems (ESSs) and soft open points (SOPs) can flexibly adjust power flow direction, which can address the problem. This study analyzed the characteristics of flexibility resources based on the flexibility theory. Furthermore, the potential loss of flexibility demand is quantitatively assessed by conditional value-at-risk, and the coordination planning model of DG, SOP, and ESS for the unbalanced distribution network is constructed considering flexibility and economy. Because the resulting mathematical formulation belongs to a nonconvex quadratic programming problem, an adaptive linear relaxation programming method is proposed to improve computational efficiency. The adaptive linear relaxation technique is constructed based on the properties of quadratic functions and the mean value theorem, and the non-convex quadratic programming problem is converted to a series of parametric linear relaxation programming problems by the technique. Finally, the effectiveness of the proposed model is verified on IEEE 33-bus and IEEE 123-bus systems.