Entropy-regularized optimization models for efficient energy distribution and load management systems

Abstract

Energy distribution and loading control represent important challenges in contemporary smart energy systems due to growing share of renewable energy sources and demand fluctuations. In this paper, entropy-regularized optimization approach is proposed for intelligent energy allocation problem through converting traditional dispatch models into a convex optimization problem. In particular, entropy-based regularization is used in order to stabilize allocation process, speed up computation and improve robustness of energy distribution under varying conditions. Mathematical model takes into account such variables as generation capacity, load requests, constraints and costs of optimization for the sake of finding optimal energy dispatch strategies. New dual mirror-descent optimization method is proposed for solving the problem with the help of improved scalability and convergence properties. Evaluation of the suggested framework is conducted in terms of synthetic energy distribution system that includes 50 controllable loads with a total capacity of 1000 energy units; results are averaged over 100 random cost realizations. Entropy-regularized optimization allows one to perform effective smoothing of the problem, where the number of allocated nodes changes from 1.9 to 42.1 in case of regularize values between 0.1 and 10, but still keeps efficiency loss in the range of 0.05 to 5.84. Optimization algorithm reaches convergence at the optimality gap of 0.253 in 500 iterations. Robustness evaluation under capacity perturbation ±5% and ±10% confirms that allocation deviation stays within stability boundaries. Besides, scalability analysis on the networks of various sizes from 10 to 1000 loads reveals logarithmic growth of the needed iterations amount between 612 and 1145.