Abstract
This paper studies the impact of stochastic load variations on distributed optimal power management 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, loss reduction, and quality enhancement of voltage. Under persistent stochastic load variations, this paper develops distributed optimal strategies to track time-varying loads under noisy observations. Convergence properties and optimality errors are established under persistent load variations and measurement noises. The limiting behavior of the optimality errors reflects fundamental impact of the selection of the step size that must be balanced between attenuation of observation noises and tracking of the load changes. Optimality condition and algorithms for an optimal step size are derived to guide step size selection in practical applications. Illustrative examples are presented to demonstrate the effectiveness of the proposed algorithms and validate the theoretical results.
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