  A rational behavior of a consumer is analyzed when the user participates in a
Peak Time Rebate (PTR) mechanism, which is a demand response (DR) incentive
program based on a baseline. A multi-stage stochastic programming is proposed
from the demand side in order to understand the rational decisions. The
consumer preferences are modeled as a risk-averse function under additive
uncertainty. The user chooses the optimal consumption profile to maximize his
economic benefits for each period. The stochastic optimization problem is
solved backward in time. A particular situation is developed when the System
Operator (SO) uses consumption of the previous interval as the
household-specific baseline for the DR program. It is found that a rational
consumer alters the baseline in order to increase the well-being when there is
an economic incentive. As results, whether the incentive is lower than the
retail price, the user shifts his load requirement to the baseline setting
period. On the other hand, if the incentive is greater than the regular energy
price, the optimal decision is that the user spends the maximum possible energy
in the baseline setting period and reduces the consumption at the PTR time.
This consumer behavior produces more energy consumption in total considering
all periods. In addition, the user with high uncertainty level in his energy
pattern should spend less energy than a predictable consumer when the incentive
is lower than the retail price.

Systems and Control