Uncertainty-aware bilevel energy storage planning for active distribution networks: A fixed-topology DistFlow-based MISOCP framework with voltage-security assessment

Historical renewable-load variability, voltage-security risk, and investment-operation coupling can materially change the assessed value of distribution-level energy storage. This study develops an uncertainty-aware bilevel energy storage system (ESS) planning framework in which the upper level selects a discrete siting-sizing-duration plan and the lower level solves a fixed-topology, multi-scenario mixed-integer second-order cone program (MISOCP) in which the network physics are represented by a DistFlow-SOCP formulation. An ESS-aware topology robustness check is further introduced to examine whether ESS-induced topology changes affect the planning conclusions obtained under the common-topology comparison. Complete daily load, photovoltaic, and wind observations from Denmark in 2016 and 2017 are represented as joint 72-dimensional trajectories. Input-risk-stratified historical-day reduction is examined for K = 3, 5, 10, and 20, with K = 10 used for the principal 33-bus study and K = 20 used as a higher-fidelity scenario-set check. Exhaustive evaluation of 211 alternatives identifies a 1.00 MW/ 2.00 MWh ESS at bus 24. Under K10 and the baseline fixed topology, the proposed design reduces daily TOTEX from 73,151.02 to 51,826.24 CNY/day (29.2%) relative to No ESS, raises the minimum voltage from 0.94138 to 0.95405 p.u., and reduces cumulative undervoltage exposure from 0.013528 to 0.001740 p.u.·h. Cross-year and seven-day chronological tests retain the economic and security pattern. On the released 240-bus feeder, the reference design improves voltage exposure, loading, and losses at a small incremental economic cost. These results show that historical tail conditions, common-topology attribution, and physical security metrics are important for auditable ESS planning.