This paper proposes a scalable stochastic optimization model and a Markov chain-based scenario generation method to benefit from an active distribution network's (ADN's) flexibility. The optimization variables are the dispatch plan, such as the active and reactive power of battery energy storage (BES) and photovoltaic (PV) systems, as well as the active and reactive power and flexibilities given to the transmission network at the point of common coupling (PCC). The uncertainty vector, on the other hand, is made up of the PV system's production capability, electricity demands, the flexibility request of the transmission system operator (TSO), and the voltage at the PCC. The resulting stochastic optimization problem is a second-order cone programming (SOCP) problem that is solved using freely available convex solvers. To validate the performance of the proposed stochastic optimization, the tests were carried out in a laboratory, where a flexible structure mimics different distribution network topologies, such as a real low-voltage radial one in Switzerland.(c) 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).