Joint optimization of location and topology of multi-terminal soft open point in distribution networks

• Topology and installation location of MTSOP in distribution networks is studied. • A model by minimizing operating losses and voltage deviation is proposed. • The model is transformed into a second-order cone programming model. • Errors due to relaxation and the feasibility of optimal schemes are assessed. • The performance of MTSOP with different topologies is comparatively analyzed. The popularization of renewable energy has led to problems including excessive current and voltage violations in distribution networks. Soft open point (SOP) enables real-time continuous active and reactive power regulation to alleviate these problems. However, how many terminals of a SOP should be set, and which feeders should be interconnected with these terminals is a crucial issue. To address this issue and fully utilize the performance of SOP, this paper conducts a comparative study of SOP with different topologies. First, a nonlinear programming (NLP) model to reveal the effect of multi-terminal SOP (MTSOP) in minimizing system losses and voltage deviation is developed. Second, to facilitate the solution, the NLP model is transformed into a second-order cone programming (SOCP) model based on cone relaxation. Finally, validation on the IEEE 33-, 69- and 141-node systems is conducted. MTSOP can reduce the total losses of IEEE 33-, 69- and 141-node systems by up to 23.54 %, 37.98 %, and 28.90 %, respectively. Although SOPs with a large number of terminals have excellent performance, they are difficult to gain an advantage in feasibility. Therefore, it is not necessarily better to have more terminals in an MTSOP which should be determined based on the characteristics of distribution networks.