Impact of Irrational Consumers on Rational Consumers in a Smart Grid

Leveraging of flexibility in certain types of electric loads such as water heaters, washers, dryers, heating and air conditioning, and electric vehicles, offers an attractive and promising approach for large scale penetration of renewable generation and peak demand reduction. In price/market based approaches, consumers of flexible loads optimize their consumption schedules to meet their energy/power demands while minimizing their total costs. However, it may be that not all consumers will optimize their consumption schedules. We call such consumers "irrational consumers" and use the phrase "rational consumers" for those who optimize their consumption schedules. In this paper, we analyze the impact of irrational consumers on rational consumers in a stylized supply-demand balancing problem. We derive a condition which characterizes when the optimal utility derived by a rational consumer is lower than the case when all consumers act rationally. This condition uses parameters of the utility functions of consumers and the total consumption of the irrational consumers. The result offers some interesting insights into this phenomenon.