Multi-Layered Optimization Of Demand Resources Using Lagrange Dual Decomposition

This paper concerns mathematical conditions under which a system-level optimization of supply and demand scheduling can be implemented as a distributed optimization in which users and suppliers, as well as the load serving entities, are decision makers with well-defined sub-objectives. We start by defining the optimization problem of the system that includes the sub-objectives of many different players, both supply and demand entities in the system, and decompose the problem into each player's optimization problem, using Lagrange dual decomposition. A demand entity or a load serving entity's problem is further decomposed into problems of the many different end-users that the load serving entity serves. By examining the relationships between the global objectives and the local/individual objectives in these multiple layers and the optimality conditions of these decomposable problems, we define the requirements of these different objectives to converge. We propose a novel set of methods for coordinating supply and demand over different time horizons, namely day-ahead scheduling and real-time adjustment. We illustrate the ideas by simulating simple examples with different conditions and objectives of each entity in the system.