Co-optimizing location, capacity, and hourly scheduling of switchable capacitors in power distribution systems considering daily load patterns and voltage dependence

• Two-stage approach for capacitors’ optimal location, capacity, and hourly scheduling. • A novel MISOCP model with multiple time periods, ensuring globally optimum results. • Consideration of the impact of daily load profiles and voltage dependence models. • Presentation of new outcomes for the actual Vietnamese 102-node grid. • Optimally switched capacitors, reducing the energy loss cost by up to 18.06%. This paper introduces a two-stage optimization method for the optimal location, capacity, and hourly scheduling of switchable capacitors. Unlike existing approaches, the proposed optimization framework accounts for daily load consumption shapes and the voltage-dependent power model, crucial for realistic distribution grid operation. The first stage selects the optimal site and capacity of the capacitors to minimize the total annual grid cost, including the annualized investment and energy loss costs. The second stage then optimizes their hourly switching states to minimize yearly energy loss expenses. Both stages are formulated as second-order conic programming with integer variables (MISOCP). The novel MISOCP formulation effectively tackles the complexity of nonlinear mixed-integer programming (MINLP) problems by employing the conic quadratic formulation of power balance equations, linearizing products of binary and continuous variables, and approximating the ZIP (constant impedance, constant current, constant power) load model via Newton’s binomial expansion. Evaluated on the IEEE 33- and 69-node radial test grids, the actual Vietnamese 102-bus radial grid, and the IEEE 33-node mesh grid with distinct scenarios using the GUROBI optimizer in the GAMS programming environment, the proposed approach provides globally optimal solutions. Furthermore, this study is the first to present results for a real-world 102-bus grid in Vietnam, providing a valuable new benchmark. Results demonstrate a significant influence of both dynamic load patterns and voltage-dependent modeling on the optimal location and capacity of switched capacitors. In addition, the analysis quantifies the substantial benefits of the optimal hourly switching of capacitors in reducing the energy loss cost of the distribution grid. The proposed optimization framework is effective and scalable, making it a practical tool for power distribution system performance optimization.