Optimal Power Procurement for Green Cellular Wireless Networks Under Uncertainty and Chance Constraints

Entropy, vol. 27, pp. 308

Abstract

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, and hybrid energy systems comprising uncertain renewable energy sources. Despite the stochastic nature of wireless fading channels, the network operator must ensure a certain quality-of-service (QoS) constraint with high probability. This probabilistic constraint prevents using the dynamic programming principle to solve the stochastic optimal control problem. This work introduces a novel time-continuous Lagrangian relaxation approach tailored for real-time, near-optimal energy procurement in cellular networks, overcoming tractability problems associated with the probabilistic QoS constraint. The numerical solution procedure includes an efficient upwind finite-difference solver for the Hamilton-Jacobi-Bellman equation corresponding to the relaxed problem, and an effective combination of the limited memory bundle method (LMBM) for handling nonsmooth optimization and the stochastic subgradient method (SSM) to navigate the stochasticity of the dual problem. Numerical results, based on the German power system and daily cellular traffic data, demonstrate the computational efficiency of the proposed numerical approach, providing a near-optimal policy in a practical timeframe.

Authors 3

1. Nadhir Ben Rached

   University of Leeds

   Affiliation as printed

   Department of Statistics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

2. Shyam Mohan Subbiah Pillai corresponding Aachen Chair of Mathematics for Uncertainty Quantification Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, 52062 Aachen, Germany

3. Raul F. Tempone Aachen Chair of Mathematics for Uncertainty Quantification Department of Mathematics

   RWTH Aachen University · King Abdullah University of Science and Technology

   Affiliation as printed

   Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH Aachen University, 52062 Aachen, Germany

   Computer, Electrical and Mathematical Sciences & Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia