Distribution network planning has traditionally relied on deterministic models that assume fixed load profiles, an assumption increasingly untenable as demand variability and renewable penetration grow. This peer-reviewed study introduces a practical stochastic optimization framework designed to address real-world load uncertainty in capacitor bank planning—a critical component of reactive power management and voltage support in medium-voltage grids.
The proposed methodology employs a two-stage approach: a master optimization stage using a Chu-Beasley genetic algorithm handles discrete decisions about where and how many capacitor units to install, while a slave stage executes successive-approximation power flow calculations to assess each candidate solution across multiple load scenarios. To manage computational complexity, the researchers generated 365 daily load realizations from historical demand data perturbed with 10% Gaussian noise, then reduced them to 10 representative scenarios using k-means clustering—achieving a 36.5-fold reduction in power flow evaluations with less than 2% mean absolute error.
Testing on a 33-bus distribution feeder under three energy cost escalation scenarios (0%, 10%, and 20%) over 20 years, both deterministic and stochastic approaches delivered net present cost reductions of 16.5–17.3% versus the uncompensated baseline. The stochastic framework consistently matched or slightly outperformed deterministic planning (up to 0.16% additional savings) while providing robustness across varying operating conditions.
Critically, the stochastic approach excels when load variability is high and energy costs are low—conditions increasingly common in distribution systems serving renewable-heavy microgrids and dynamic industrial loads. The methodology provides utility planners a computationally tractable tool to quantify investment uncertainty and optimize reactive power resources without oversizing equipment for worst-case scenarios or undersizing for average conditions.
This work validates probabilistic modeling as essential for modern distribution planning, bridging the gap between academic optimization and practical utility deployment.
