Market-based coordination of price-responsive demand using Dantzig-Wolfe decomposition method

Abstract

The increasing penetration of Distributed Generation (DG) and Demand Responsive (DR) loads in power systems has necessitated the development of novel approaches to address the coordination problem of Price Responsive Devices (PRD). These PRDs are treated as self-interested players aiming to optimize their consumption patterns based on prevailing prices. In this paper, we propose a new algorithm based on the Dantzig-Wolfe (DW) Decomposition method, which tackles the coordination problem of self-interested PRDs in a distributed manner. Leveraging the distributed nature of the DW approach, we model the self-interested algorithms of PRDs as sub-problems within the DW framework. The coordinator, or grid operator, responsible for collecting the energy consumption information (energy bids) of PRDs, solves the master problem of the DW and determines the price signal accordingly.The proposed algorithm exhibits fast convergence as the sub-problems within DW, which could involve a large number of PRDs (potentially millions), can be solved simultaneously. Additionally, based on the DW theory, if the PRDs' subproblems are convex, reaching the optimal point (equivalent to Nash Equilibrium) is guaranteed within a limited number of iterations. To evaluate the proposed model, we conducted a simulation involving 200 participant households, each equipped with two types of loads: Electric Vehicles (EVs) as examples of interruptible loads, and Electric Water Heaters (EWHs) as examples of Thermostatically Controlled Loads (TCLs). The results demonstrate that when the algorithm converges to the optimal point, both the generation cost and user payment (based on the marginal cost of generation) decrease. Furthermore, there is a significant reduction in the Peak to Average Ratio (PAR) of the aggregate load