Possibly something like a user defined power forecast for individual loads that could be injected into the optimisation model could be useful.
I know what the forecast external temperature profile is for tomorrow.
A simple power model would be 1kW per degree over say 24°C to a maximum of 4kW and maybe an additional 1kW at 3pm, as my buy price increases at 4pm. So with a one hour time slot the desired power profile for tomorrow would be:
Temp: [22,24,25,26,27,26,26,26,25,24,22,21,20,20]
Power:[ 0, 0, 1, 2, 3, 2, 2, 3, 2, 1, 0, 0, 0, 0]
EMHASS could then use this as another fixed constraint to optimise against.