There are plenty of papers that talk about demand response, but what are some methods used to actually model demand response in different kinds studies?
in my opinion this question is quite vague. as such models are valid for a specific region and based on its load consumption history . Moreover, a commercial and industrial demands will vary from the residential load demand.
so, my suggestion is.. you have to first decide which kind of loads you are targeting, for example the base load of your demand may be an industrial load as it may be seen as a constant load from the grid point of view...etc.
I'd like to add one more thing to the answer of Mohamed A. Elgenedy. Besides deciding on which kind loads you are targeting, it is important to decide on what's the main purpose of your demand response: Market balancing, balancing of transmission lines, voltage instability in distribution systems, ... which all have a different time scale between 1 hour to 1 minute, requiring different approaches.
As already indicated it has to be what study you really want to conduct. Furthe you are talking about real time application or off line appiation . That also plays a role.
I prefer the concept of combining the production price and control signal, such that the consumer price and demand response signals are the same, as I discuss in "Creating a MicroGrid Market: Using a Frequency Driven Pricing Curve To Dispatch Load and Embedded Distributed Generation And To Charge and Pay for Participation," Energy Pulse, 2013 July 3 http://www.energycentral.com/generationstorage/distributedandcogeneration/articles/2673
One of the best papers in this field of study is the paper titled "Quantifying the Effect of Demand Response on Electricity Markets" of Professor Daniel Kirschen. I do recommend you read it.
Good luck,
Morteza Shabanzadeh
http://mortezash.blogfa.com/
Article Quantifying the Effect of Demand Response on Electricity Markets
F. Magnago, J. Alemany, and J. Lin, “Impact of Demand Response Resources on Unit Commitment and Dispatch in a Day-Ahead Electricity Market,” International Journal of Electrical Power and Energy Systems, vol. 68, pp 142-149, 2015.
Really happy to see the interesting discussions here. Just for your information that we have done work on modeling the demand response for industrial load - an important player in demand response, as follows: