Spectral Risk-Averse optimal operation of active distribution networks incorporating multimode switching of hybrid open points

• An HOP power model considering branch power direction is derived. • An ESRM-based risk-averse scheduling model for HOPs is also established. • A convex relaxation strengthening method is integrated to reduce relaxation errors. The increasing integration of distributed photovoltaic (PV) capacity has gradually raised the requirement for flexibility of active distribution networks (ADNs). The diverse operation modes of hybrid open points (HOPs), devices consisting of soft open points (SOPs) and tie switches in parallel, can help address the challenges arising from growing PV capacity. From the perspective of handling uncertainties of loads and sources within ADNs, an exponential spectral risk measure (ESRM)-based risk management approach provides a sensitive and realistic depiction of risk losses, delivering robustness and efficiency. Accordingly, this study proposes an optimal scheduling strategy that incorporates risk management and HOP deployment. Four control modes of HOPs under different application scenarios are first analyzed. Then, an ESRM-based mixed-integer nonlinear optimization model with distribution network reconfiguration is established. Furthermore, to resolve the relaxation error introduced by convex relaxation in the optimization process, this study adopts a strengthening convex relaxation method that iteratively tightens the relaxation gap to ensure accuracy. Results of case studies demonstrate that HOPs can effectively reduce the operational cost of ADNs, and the adopted algorithm achieves favorable convergence.