09-09-2010, 11:59 AM
Looking for some clever modeling ideas to tackle a fairly simple issue...
In my model, there are a few transport sector technologies which use diesel fuel - e.g., heavy-duty diesel trucks, diesel buses, diesel ships, etc. For simplicity, I have said that bio-diesel is a direct replacement (i.e., perfect substitute) for conventional (fossil) diesel, and so these technologies can choose to use either diesel or bio-diesel, the model will decide. While there are, of course, certain blend shares (e.g., B5, B20, B100), which in reality might make more sense than others, in the aggregate any share is theoretically possible. And in TIMES, I'm basically modeling in the aggregate.
Elsewhere in the model, I have a lower limit constraint that forces the model to use an increasing quantity of bio-diesel over time. This is to represent some biofuel mandates in the US.
The problem is that, from the end-use technology perspective, diesel and bio-diesel are perfect substitutes for each other. Therefore, for a single technology in a particular transport sector the model switches between the two fuels quite erratically. Though, across the entire transport sector, the growth in bio-diesel is quite smooth. For example, in one period bio-diesel consumption for diesel trucks might be zero, fossil diesel supplies all fuel to the diesel engine technologies. In the same period, bio-diesel might be fairly high in the other transport sectors that use it (e.g., buses and ships), and fossil diesel use is fairly low. Then, in the next period the situation is opposite - the model decides to "dump" all bio-diesel into the truck sector, while leaving none for buses and ships. This up-and-down pattern then continues throughout the modeling horizon.
As you can see, this is really not a major problem, since the objective function probably wouldn't change if the model were to apportion bio-diesel more evenly between the various transport sectors. However, from a post-processing and presentation point of view, the results for each transport sector obviously look strange. Bio-diesel consumption in a given sector is up and down, up and down. Therefore, I wonder if there are any simple things I can do to force the model to divide up bio-diesel more evenly. I can imagine adding some very small flow costs for bio-diesel on some of the end-use technologies. But then, I'm afraid the model will simply dump all bio-diesel into the technologies where flow costs are not assigned. Alternately, it could be possible to write a simple user constraint to divide up bio-diesel consumption evenly. But in this case, the coefficients of the constraint would decide what the breakdown is between sectors. And because these coefficients are fixed, it could restrict some of the model's freedom to switch to other technologies/fuels (e.g., natural gas, hydrogen, electricity), which becomes important in deep reduction scenarios.
In my model, there are a few transport sector technologies which use diesel fuel - e.g., heavy-duty diesel trucks, diesel buses, diesel ships, etc. For simplicity, I have said that bio-diesel is a direct replacement (i.e., perfect substitute) for conventional (fossil) diesel, and so these technologies can choose to use either diesel or bio-diesel, the model will decide. While there are, of course, certain blend shares (e.g., B5, B20, B100), which in reality might make more sense than others, in the aggregate any share is theoretically possible. And in TIMES, I'm basically modeling in the aggregate.
Elsewhere in the model, I have a lower limit constraint that forces the model to use an increasing quantity of bio-diesel over time. This is to represent some biofuel mandates in the US.
The problem is that, from the end-use technology perspective, diesel and bio-diesel are perfect substitutes for each other. Therefore, for a single technology in a particular transport sector the model switches between the two fuels quite erratically. Though, across the entire transport sector, the growth in bio-diesel is quite smooth. For example, in one period bio-diesel consumption for diesel trucks might be zero, fossil diesel supplies all fuel to the diesel engine technologies. In the same period, bio-diesel might be fairly high in the other transport sectors that use it (e.g., buses and ships), and fossil diesel use is fairly low. Then, in the next period the situation is opposite - the model decides to "dump" all bio-diesel into the truck sector, while leaving none for buses and ships. This up-and-down pattern then continues throughout the modeling horizon.
As you can see, this is really not a major problem, since the objective function probably wouldn't change if the model were to apportion bio-diesel more evenly between the various transport sectors. However, from a post-processing and presentation point of view, the results for each transport sector obviously look strange. Bio-diesel consumption in a given sector is up and down, up and down. Therefore, I wonder if there are any simple things I can do to force the model to divide up bio-diesel more evenly. I can imagine adding some very small flow costs for bio-diesel on some of the end-use technologies. But then, I'm afraid the model will simply dump all bio-diesel into the technologies where flow costs are not assigned. Alternately, it could be possible to write a simple user constraint to divide up bio-diesel consumption evenly. But in this case, the coefficients of the constraint would decide what the breakdown is between sectors. And because these coefficients are fixed, it could restrict some of the model's freedom to switch to other technologies/fuels (e.g., natural gas, hydrogen, electricity), which becomes important in deep reduction scenarios.
