Chance-constrained optimization for active distribution networks with virtual power lines

Active distribution networks (ADNs) experience uncertainties because of the high integration of distributed renewable energy resources (RESs). Stochastic analysis approaches are attracting increasing attention owing to the uncertain nature of RESs and load demands. This study proposes a chance-constrained optimal operation framework for ADNs considering virtual power lines (VPLs) solved via the second- order cone programming (SOCP) optimal power flow (OPF) problem. VPLs comprise virtual lines connected to each network's energy storage systems (ESSs). If one ESS is charged, another ESS is discharged by the same amount. We reformulate the constraints into tractable forms using a simplified Z-bus sensitivity matrix and first-order Taylor expansion to solve via SOCP OPF because the chance constraints on voltage magnitudes are generally non-convex and intractable. The efficacy of the proposed approach was verified through its application to two modified IEEE 33-bus systems, each featuring different consumer units, including commercial, residential, and industrial units. The effectiveness of the proposed methods was demonstrated by comparing three different types of constraints: conventional hard constraints, soft constraints with penalties, and chance constraints. The results showed that although the chance constraints case had a slightly higher voltage violation rate, the network power loss was reduced by 3.4% compared to the conventional hard constraints case. Furthermore, modified 85-bus and 65-bus systems are carried out to verify the algorithm's scalability. The proposed approach achieves a trade-off between voltage regulation and power loss minimization, with a voltage violation rate of 0.88% and a power loss reduction to 1.02%.