LAUSR

This paper studies the impact of stochastic load variations on distributed optimal load tracking and allocation (OLTA) problems in cyber-physical DC microgrids (MGs) for transportation electrification. Without load variations, the distributed optimization strategies developed in our earlier work can achieve convergence to global optimal solutions in a multi-objective optimization that balances fair load allocation and power loss reduction. Under persistent stochastic load variations, this paper develops distributed optimal strategies to track time-varying loads under noisy observations and establishes their convergence properties and error bounds. The limiting behavior of the errors characterizes the fundamental impact of the step size on irreducible errors due to conflict between attenuating observation noises and tracking load changes. Optimality conditions and algorithms for selecting the optimal step size are introduced to guide step size selection in practical applications. Simulation studies on real-world systems demonstrate the effectiveness of the proposed algorithms and validate the theoretical results.