  This paper presents an analysis of competition between generators when
incentive-based demand response is employed in an electricity market. Thermal
and hydropower generation are considered in the model. A smooth inverse demand
function is designed using a sigmoid and two linear functions for modeling the
consumer preferences under incentive-based demand response program. Generators
compete to sell energy bilaterally to consumers and system operator provides
transmission and arbitrage services. The profit of each agent is posed as an
optimization problem, then the competition result is found by solving
simultaneously Karush-Kuhn-Tucker conditions for all generators. A Nash-Cournot
equilibrium is found when the system operates normally and at peak demand times
when DR is required. Under this model, results show that DR diminishes the
energy consumption at peak periods, shifts the power requirement to off-peak
times and improves the net consumer surplus due to incentives received for
participating in DR program. However, the generators decrease their profit due
to the reduction of traded energy and market prices.
