Session: 20-17-01: Rising Stars of Mechanical Engineering

Paper Number: 173352

A Game-Theoretic Approach for Building Cluster Demand Response 

The advances in information and communication technologies have made buildings more connected than ever before and catalyzed a new building design and operation paradigm - connected communities (CC). Leveraging the economies of scale, CC allows more cost-effective utilization of renewable energy and aggregated participation in wholesale energy and ancillary service markets, which are not friendly to individual buildings with limited bidding power. In CC operations, there are often coupled costs and/or constraints that are not directly separable among participating buildings. The centralized (dictatorial) control approach has low acceptance since participants are often self-interested and prefer control over their own assets.

This poster presents a new game theoretic control framework where individual entities determine their control actions in their interests while coordination is achieved indirectly through a market mechanism. The internal market may incorporate a cost allocation mechanism designed to incentivize cooperation. The CC operation can be addressed as a Nash equilibrium (NE) seeking problem that can be solved with tailored numerical routines. The game theoretic control framework has been applied in two building cluster demand response scenarios – collective peak demand limiting control and optimal load dispatch.

In the demand limiting scenario, a demand charge or capacity penalty, proportional to the monthly peak demand of the whole aggregation, is considered which is a common coupled cost for CC operations. We have designed a Shapley value-based cost allocation mechanism, along with a log-sum-exponential approximate of the non-differentiable max operator, to formulate an NE game for the aggregate demand reduction problem. The existence and uniqueness of the NE solution were proved. Numerical tests with a commercial community showed that the control performance attained was close to the social optimum with less than 1% performance degradation.

In the optimal load dispatch scenario, we consider a dispatch curve of a hypothetical collection of generators published by the U.S. Energy Information Administration (EIA), which shows the system-wide marginal electricity cost increases close to linearly with the generation capacity over a wide range and the trend becomes exponential at very high demand levels. A linear-plus-exponential marginal cost model, derived from the EIA dispatch curve, was used in formulating the optimal load dispatch problem as a non-cooperative NE problem. The existence and uniqueness of the Nash equilibrium solution were proved aided by the variational inequality theory. A game solution algorithm was developed to solve the control problem with guaranteed convergence. Simulation tests show that the proposed game-theoretical strategy could achieve performance very close to the social optimum with a Price of Anarchy of 1.0041 and a 24% cost reduction compared to a baseline energy-priority strategy.

Presenting Author: Jie Cai Purdue University

Presenting Author Biography: Jie Cai is an Associate Professor of Mechanical Engineering at Purdue University. His research interests span data-driven modeling and advanced control of building energy systems. He is a recipient of the NSF CAREER Award in 2023.

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