Constrain a variable capacity factor to be the same for several processes

[pauldodds]

Is there any method to constrain several processes so that the proportion of the total output from each technology is proportional to the relative capacity of each technology?

For example, suppose I have 1000 houses.  I want each to have either a gas boiler or a heat pump (let's say 800 boilers and 200 heat pumps for this example, though in reality the numbers would be flexible).  The use of each boiler or heat pump could vary each year - for example, use might reduce due to elastic demands from price increases, but it is still necessary for each house to have a heating device.  Since I have 800 boilers in a particular year, I want boilers to provide 80% of the total heat output.  But I don't know how many boilers there will be, so I need a constraint that will link relative capacity to relative market share, where both the number of devices and output per device can vary.

All of the equations I've formed have been non-linear, and this might well not be possible.  Any advice anyone has would be appreciated.

[AKanudia]

would it work if you constrain the share of capacities via a UC, in addition to the heat output share?

by the way, you might find this discussion interesting: https://forum.kanors-emr.org/showthread.php?tid=324

[Antti-L]

@Paul: Convex nonlinear constraints can be linearized, and may thus be feasible to model in TIMES using e.g. dummy variables and user constraints. In special cases of general interest, automatic linearization can also be implemented in TIMES, as has been done for example for elastic demand functions.

If I understood you correctly, your constraints are non-convex non-linear, which can only be modelled with global non-linear solvers or with MIP, correct? The MIP option is indeed available in TIMES for basically any user-defined purpose, by using dummy discrete capacity processes and user constraints, but using that option might easily get rather clumsy. So, albeit I think in principle the MIP method would be available, I am not able to offer any efficient formulation to your problem.

But if anyone can show your problem does indeed have a convex formulation, I'd be very happy to turn out proven wrong.