Online early-warning dispatch for voltage violation risk in ADNs considering incomplete measurements

This paper proposes an online early-warning dispatching method for voltage violation risks to suppress the impact of uncertain photovoltaic (PV) power fluctuations on voltages of active distribution networks(ADNs). First, a data-driven approach, incorporating an attention mechanism, is used to learn the probability density function (PDF) of the PV output. In distribution networks with limited measurement data, voltage sensitivity analysis is utilized to map the PDF of the PV output to the PDF of the nodal voltages, thereby enabling a probabilistic assessment of voltage violation risk. Subsequently, a novel two-stage optimization problem is formulated to minimize this risk probability. This model integrates robust optimization constraints into a stochastic optimization framework, establishing an early-warning dispatching strategy that ensures voltage risks remain controllable. To solve this optimization problem efficiently under the specific constraints of voltage violation, a dynamic risk acceptance function is designed. By differentiating the expansion of probabilities, the repeated integration of probability density functions is transformed into a simplified piecewise function, which significantly accelerates the solution process. Finally, the proposed method is tested on the IEEE 69-bus system, and validated by comparing the results with those of conventional stochastic and robust optimization methods.