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Hi Yue,
That's a good question - the short answer is that LEAP is flexible enough to allow the modeler to add a carbon price, but it does not have any such demand reduction capability built into it.
First, a philosophical point - when you add a carbon price as an externality under LEAP's Effects branches, then by definition you are placing it *outside* of the economy. It would appear in your cost-benefit analysis, but once you involve the carbon price in your calculation of energy demand or plant dispatch, it can no longer be thought of as an externality. Therefore the Effects branch is not the appropriate place to add it to your model.
One of your first steps will be to determine the additional price on each fuel, as a result of it's carbon content. A convenient place to do this in LEAP is in the Resources branch of your tree, where you can enter an expression in the Indigenous Cost variable that captures the added price of carbon in the fuel. For example, the additional fuel price (in dollars per unit of energy) due to its carbon content might look something like this:
(CarbonContent / EnergyContent) * (reference to your carbon price variable, in dollars per mass of carbon)
*note that I've used two different fuel properties here, which you can read about here:
http://www.energycommunity.org/WebHelpPro/Expressions/Fuel_Properties.htm
Determining a method for allowing energy demand to respond to the increased price of energy is left up to the modeler - there is no built-in facility in LEAP. You will need to decide how price drives consumption in each of the different sectors (or subsectors) that are being modeled. You may want to use published price elasticities of energy demand, or determine an alternative method, but either way there is plenty of literature to guide you.
Power plants can be dispatched by cost using two different ways. You can either use OSeMOSYS, the built-in algorithm that selects capacity additions and dispatch to minimize total cost (http://www.energycommunity.org/WebHelpPro/Optimization/OptimizationIntroduction.htm), or instead you may also dispatch your plants using LEAP's 'RunningCost' dispatch rule (http://www.energycommunity.org/WebHelpPro/Transformation/Process_Dispatch_Rules.htm). Either of these methods will allow the fuel cost (which you have already modified to include the carbon price) to affect process dispatch.
Note that this approach is data-intensive. You will need to know the costs of all of your power plants, in order to decide how the carbon price will affect their dispatch.
Good luck,
Taylor