A Novel Tractable Methodology to Stochastic Multi-Period AC OPF in Active Distribution Systems Using Sequential Linearization Algorithm

The ongoing transition of passive distribution networks to active distribution systems (ADSs) calls for the development of sophisticated and tractable tools to address the needs and challenges of future ADSs. In this regard, this work proposes a novel tractable methodology for flexibility procurement via stochastic multi-period AC optimal power flow (S-MP-OPF). The first novelty of the proposed methodology is the formulation of a new mixed-integer linear programming (MILP) model, which develops novel linear approximations for all nonlinear constraints (i.e., active and reactive power flows and branch currents) that ensure tractability. The proposed linearization approach relies on the second-order Taylor series expansion of trigonometric terms, does not hinge on the flat-voltage, near-voltage and small angle assumptions, and formulates the linear approximations using square of voltage magnitude and voltage angle difference variables. The second novelty is a sophisticated heuristic sequential linearization algorithm (SLA) which incorporates and improves the accuracy of the MILP model in an iterative manner. The bench-marking of proposed SLA is done on a 34-bus ADS for a comprehensive set of flexible options, whereas its versatility and scalability is demonstrated on real-world 31-bus weakly-meshed and 191-bus radial ADSs. Extensive numerical analyses show that the proposed SLA leads to a highly accurate and feasible solution with small optimality gap within few iterations, under normal and stressed operating conditions, outperforms alternative methods in terms of solution accuracy and computational efficiency, and is scalable to large S-MP-OPF problems.