Hybrid bee–genetic algorithm tames power flow in renewable and EV grids

Engineers have unveiled a new computational framework that plans how electricity should flow through power grids crowded with wind farms, solar panels, and plug-in electric vehicles, even when the output of those resources is inherently unpredictable. The study, published on 1 September 2026 in the open-access journal Carbon Neutral Systems, was carried out by Abhishek Bajirao Katkar and Himmat Tukaram Jadhav and tackles a problem known as stochastic multi-objective optimal power flow, or MOOPF. In such problems, grid operators must simultaneously juggle conflicting goals—keeping costs low, cutting emissions, reducing transmission losses, and holding bus voltages close to their reference values—while wind speed, solar irradiance, and the charging and discharging behavior of electric vehicles fluctuate in ways no scheduler can fully control.

The core of the proposed method is a hybrid optimization algorithm that fuses two well-established search techniques. The first is the Artificial Bee Colony algorithm, which mimics honey-bee foraging: candidate solutions are treated as food sources, employed and onlooker bees refine them through stochastic neighborhood moves, and scout bees replace sources that stagnate beyond a trial limit. The researchers added a global-best-guided term that pulls each update toward the current best solution found so far, strengthening exploitation without abandoning exploration. The second component is NSGA-II, the Non-dominated Sorting Genetic Algorithm, which supplies elitist selection, Pareto-dominance ranking, and crowding-distance diversity preservation. By running the bee phases to generate candidates and then applying non-dominated sorting and elitist replacement to the combined pool of parents and offspring, the hybrid gbestABC–NSGA-II algorithm aims to balance convergence toward the best trade-offs with a well-spread set of solutions.

Uncertainty is handled explicitly rather than ignored. Wind speed is modeled with a two-parameter Weibull distribution, solar irradiance with a lognormal distribution, and the charging or vehicle-to-grid discharging power of plug-in electric vehicles with a normal distribution. These probabilistic models are evaluated through Monte Carlo scenarios, with a sample size of 400 chosen after a preliminary convergence analysis: increasing the scenarios from 300 to 400 changed the expected objective values by only about 0.46 percent, and pushing from 400 to 500 changed them by less than 0.20 percent. The same scenario realization was kept identical across all test systems and all comparison algorithms, so that differences in results could be attributed to the algorithms rather than to different random samples of uncertainty.

The framework was stress-tested on modified versions of the IEEE 30-, 57-, and 118-bus benchmark networks, upgraded with a wind generator, a solar photovoltaic plant, and a plug-in electric vehicle system at designated buses. Twelve case studies spanning two, three, and four simultaneous objectives—total cost, total emissions, active power loss, and voltage-magnitude deviation—were solved under a common computational budget. Against five comparator algorithms, namely MOABC, NSGA-III, MOEA/D, standard NSGA-II, and MOPSO, the reported results show that the proposed method yields competitive Pareto solutions. Active power loss was up to approximately 27 percent lower and voltage-magnitude deviation approximately 18 to 52 percent lower than the corresponding values of selected comparators in the reported cases.

The quality of the Pareto fronts themselves was also quantified. The proposed algorithm achieved generational distance values more than 25 percent lower, indicating closer convergence toward the reference front, and spacing values up to 28.5 percent lower, indicating a more evenly distributed solution set, while its diversity metric was up to 37.3 percent higher than the stated comparator values. Wilcoxon signed-rank tests applied to the aggregated Pareto-quality observations returned p-values below 0.05 for all five pairwise comparisons, providing statistical support for the observed differences. The authors are careful to note, however, that these comparisons apply to the stated benchmark cases and parameter settings and should not be read as a universal performance guarantee across other systems or configurations.

Constraint handling received particular attention. Classical approaches such as penalty functions, superiority of feasible solutions, and the constraint-dominance principle each carry drawbacks: penalty methods require hard-to-calibrate coefficients, feasibility-first rules can discard promising infeasible candidates, and strict dominance rules risk premature convergence in fragmented feasible regions. The study instead employs an enhanced diversity-maintenance epsilon-constraint method, in which solutions with violations within a decaying tolerance are treated as feasible, and a composite fitness measure blends a Tchebycheff aggregation of objectives with the constraint violation. An adaptive weight shifts emphasis from broad exploration toward feasibility as generations progress. An external archive based on epsilon-dominance and crowding distance keeps the stored Pareto set bounded, removes redundant entries, and always preserves the extreme boundary solutions in each objective dimension.

Choosing a single dispatch from a whole front of trade-offs is handled by a transparent decision pipeline. The Analytic Hierarchy Process converts expert pairwise judgments into criterion weights, with consistency checks requiring a consistency ratio below 0.10; the reported matrix achieved a ratio of 0.0115. TOPSIS then ranks each Pareto solution by its relative closeness to an ideal operating point and distance from the worst one, and the highest-ranked alternative becomes the Best Compromise Solution. A one-at-a-time sensitivity assessment perturbs each active weight by plus or minus 10 percent and renormalizes the vector to confirm that the selected compromise is preference-robust. Every step—the pairwise matrix, the weights, and the distance scores—is meant to be reported so that operators can audit and discuss the decision before finalizing a dispatch.

The most computationally striking element is a physics-informed neural network, or PINN, that acts as a rapid screening layer for power-flow calculations. Stochastic MOOPF normally demands repeated nonlinear AC power-flow evaluations for every candidate solution and uncertainty scenario, a burden that grows quickly. The PINN predicts bus voltages, phase angles, reactive powers, and line flows while its training loss combines data-fitting error with active- and reactive-power balance residuals and operating-limit penalties, keeping its predictions physically consistent. Trained on 3,000 Newton–Raphson-verified operating samples with four hidden layers of 128 neurons, the network reduced the mean root-mean-square error by roughly 84 percent relative to a conventional backpropagation predictor for cost, emissions, and power loss. In the reported Case 3 experiment on the modified IEEE 30-bus system, screening 5,000 local candidates forwarded only 60 to the exact solver, cutting the number of exact evaluations by approximately 98.8 percent and the total computation time from 19.84 seconds to 0.325 seconds, a saving of 98.36 percent.

Crucially, the PINN never has the final word. Every candidate dispatch retained for implementation is verified with the complete Newton–Raphson AC power-flow model before acceptance, and the same power-balance equations enforced in the optimizer also appear in the PINN’s physics residuals, eliminating inconsistencies between the optimization and prediction layers. In the Case 3 refinement, all four Newton–Raphson-verified alternatives generated around the initial compromise solution dominated the pre-refinement point on cost, emissions, and power loss, so the archive was updated and a new Best Compromise Solution with a closeness coefficient of 0.817 was selected after reapplying the decision pipeline. Aggregate active-power balance audits are also reported for the cases in which power loss is explicitly listed, confirming that generation, renewable injections, vehicle power, demand, and losses sum consistently.

The authors frame the work within clear limits. The uncertainty model uses fitted marginal distributions and 400 Monte Carlo samples, so correlated forecast errors, distribution shift, and sensitivity to the realized sample remain to be validated separately. The PINN refinement is demonstrated as an offline or near-real-time screening layer and is not claimed as a substitute for energy-management-grade AC security assessment, and the IEEE benchmarks do not reproduce the protection, market, communication, and contingency constraints of a real utility network. Future work, the study says, will pursue hardware-in-the-loop evaluation with real-time digital simulators and integration with SCADA-driven energy-management systems and digital twins. For now, the framework offers a statistically validated, feasibility-checked template for planning power dispatch in grids where wind, sun, and millions of electric vehicles all refuse to sit still.

Subject of Research: Stochastic multi-objective optimal power flow optimization for power grids integrating wind, solar, and electric vehicles

Article Title: Physics-informed prediction with hybrid gbestABC–NSGA-II metaheuristics in stochastic multi-objective optimal power flow for renewable-EV grids

Article References: Katkar, A. B., & Jadhav, H. T. (2026). Physics-informed prediction with hybrid gbestABC–NSGA-II metaheuristics in stochastic multi-objective optimal power flow for renewable-EV grids. Carbon Neutral Systems, 2(1), Article 14. https://doi.org/10.1007/s44438-026-00035-1

Image Credits: AI Generated

DOI: 10.1007/s44438-026-00035-1

Keywords: optimal power flow, multi-objective optimization, Artificial Bee Colony, NSGA-II, electric vehicles, vehicle-to-grid, wind power, solar photovoltaic, physics-informed neural network, Monte Carlo simulation, IEEE test systems, Pareto optimization