Efficient decentralized supply deployment in agricultural steady current flow systems using discrete decisions and probabilistic linear programming

This study fills in the gap in research between oversimplified DC-OPF (10–15% loss error) and non-convex stochastic AC-OPF, which is too hard to compute for agricultural microgrids. Its goal is to create the first globally optimal, scenario-based tool for sizing and siting solar and wind distributed generation under real-world uncertainty. We create a calibrated piecewise-linear envelope that turns the bilinear steady-current-flow (SCF) equations into mixed-integer linear constraints. We then put these constraints into a two-stage stochastic program that uses 8760 h of tropical irrigation, wind, and solar data. We solved 192 seasonal scenarios with no optimality gap in 0.28 s—99% faster than the 38 s needed by the non-linear KNITRO counterpart—while only introducing a 0.45% annual energy-loss error. The method was tested on 21- and 69-bus rural feeders and found to choose the same DG locations as the stochastic AC model. It also cut annual losses by 46–54% compared to running on diesel only, kept the minimum voltage within 0.022% of the full AC solution, and for each 100 kW of installed PV/wind, it displaced 2800 L of diesel per year and stopped 0.2–0.8 g ha⁻¹ of Cd, Pb, and Hg from settling on farmland. The open-source GAMS/CPLEX package gives planners a route to low-cost, low-toxic-emission agricultural energy that is ready to use right away and has been certified as the best one. The proposed framework halves the optimality gap compared to published DC-OPF rural studies. It also scales linearly beyond 500 buses, and a life-cycle assessment shows that it avoids 11 tons of CO₂-eq per installed MW over 25 years. The measured decrease in metal emissions alone can keep 1.8 million hectares of cropland below WHO critical levels for an extra decade. This shows how important the climate-food-health nexus is around the world. • First globally-optimal linearized SCF tool for rural micro-grids. • Solves 192 scenarios in 0.28 s, 99% faster than KNITRO, 0.45% loss error. • Cuts annual losses 46–54% vs diesel, keeps voltage within 0.022% of AC-OPF. • Each 100 kW PV/wind saves 2 800 L diesel and 0.8 g ha⁻¹ toxic metals yearly. • Open-source GAMS/CPLEX package scales to 500 buses for instant farm planning.