An Energy Sharing Game with Generalized Demand Bidding: Model and Properties

This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several desirable properties of the proposed mechanism are proved based on a generalized game-theoretic model. We show that the Nash equilibrium exists and is the unique solution of an equivalent convex optimization problem. The sharing price at the Nash equilibrium equals to the average marginal disutility of all prosumers. We also prove that every prosumer has the incentive to participate in the sharing market, and prosumers' total cost decreases with increasing absolute value of price sensitivity. Furthermore, the Nash equilibrium approaches the social optimal as the number of prosumers grows, and competition can improve social welfare.Comment: 16 pages, 7 figure

A Conjugate Gradient Method with Global Convergence for Large-Scale Unconstrained Optimization Problems

The conjugate gradient (CG) method has played a special role in solving large-scale nonlinear optimization problems due to the simplicity of their very low memory requirements. This paper proposes a conjugate gradient method which is similar to Dai-Liao conjugate gradient method (Dai and Liao, 2001) but has stronger convergence properties. The given method possesses the sufficient descent condition, and is globally convergent under strong Wolfe-Powell (SWP) line search for general function. Our numerical results show that the proposed method is very efficient for the test problems

Analyzing and Quantifying the Intrinsic Distributional Robustness of CVaR Reformulation for Chance Constrained Stochastic Programs

Chance constrained program (CCP) is a popular stochastic optimization method in power system planning and operation problems. Conditional Value-at-Risk (CVaR) provides a convex approximation for chance constraints which are nonconvex. Although CCP assumes an exact empirical distribution, and the optimum of a stochastic programming model is thought to be sensitive in the designated probability distribution, this letter discloses that CVaR reformulation of chance constraint is intrinsically robust. A pair of indices are proposed to quantify the maximum tolerable perturbation of the probability distribution, and can be computed from a computationally-cheap dichotomy search. An example on the coordinated capacity optimization of energy storage and transmission line for a remote wind farm validates the main claims. The above results demonstrate that stochastic optimization methods are not necessarily vulnerable to distributional uncertainty, and justify the positive effect of the conservatism brought by the CVaR reformulation.©2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.fi=vertaisarvioitu|en=peerReviewed