Optimal Scheduling of Active Distribution Networks With Limited Switching Operations Using Mixed-Integer Dynamic Optimization

The optimal scheduling of active distribution networks (ADNs) significantly enhances voltage security and reduces costs, particularly as the numbers of distributed generation sources and energy storage devices increase. Therefore, this paper proposes a mixed-integer dynamic optimization (MIDO) model for the optimal scheduling of ADNs. This model incorporates loads and distributed generation outputs with continuous trajectories and aims to provide optimal continuous-trajectory schemes for ADNs. The optimization is conducted with the objective of minimizing the daily costs of electricity purchased from distribution substations. However, in practice, discrete control devices are required to adopt a limited number of switching operations, which increase the computational complexity of the MIDO model. Hence, a reduced convex relaxation method is utilized to achieve reduced convex transformation and tight relaxation of the MIDO model with respect to integer variables. This converts the MIDO model into a continuous dynamic optimization model, which is then further approximated as a nonlinear programming model using the Radau collocation method. Meanwhile, the absolute-value constraints limiting the number of switching operations are eliminated by an equivalent conversion to a series of linear inequalities. Numerical simulations on IEEE 33-bus, PG&E 69-bus, and real-world 110-bus ADNs demonstrate the effectiveness and efficiency of the proposed methodology.