A variational Minimax Optimization Framework for Robust Energy Management in Renewable Integrated Smart Grid Systems

Abstract

The rising penetration of solar and wind generation has introduced substantial variability into distribution-level power balancing, making deterministic dispatch schemes increasingly unreliable under real operating conditions. This paper addresses the problem of sustaining economically efficient and technically secure energy management in renewable-integrated smart grids subject to simultaneous uncertainty in generation and load. A variational minimax optimization framework, referred to as VM-EMS, is proposed, in which the dispatch problem is formulated as a convex-concave saddle-point problem: an outer minimization over dispatch and storage decisions is coupled with an inner maximization over an adversarial, budget-constrained uncertainty set that captures renewable and demand deviations. The resulting saddle-point problem is reformulated through Lagrangian duality and solved with a projected extragradient (mirror-prox) scheme that admits a provable sublinear convergence rate to an epsilon-saddle point. The framework was implemented on a 33-bus radial distribution feeder augmented with photovoltaic, wind, and battery storage resources and evaluated over a 24-hour horizon at 15-minute resolution against deterministic, stochastic-programming, classical box-robust, and reinforcement-learning baselines. Simulation results show that the proposed method lowers worst-case operating cost by approximately 8.9% relative to classical box-constrained robust optimization, reduces the bus voltage deviation index by close to 46 %, and reaches a 0.05 saddle-point gap within 118 iterations, roughly 2.3 times faster than plain gradient descent-ascent. Average computation time was 9.7 seconds per horizon, an order of magnitude below the reinforcement-learning baseline, while remaining within 5.2% of the deterministic lower bound on expected cost. An ablation study further indicates that the extragradient correction and the variational regularization term jointly account for over 60% of the observed convergence-speed improvement. These findings suggest that the proposed formulation offers a computationally tractable and quantifiably more robust alternative to existing energy management strategies for renewable-rich distribution networks.